Free Access
Issue
A&A
Volume 562, February 2014
Article Number A121
Number of page(s) 160
Section Catalogs and data
DOI https://doi.org/10.1051/0004-6361/201321633
Published online 19 February 2014

© ESO, 2014

1. Introduction

Galaxies are constantly evolving. Their properties change because of fast interactions and mergers (Toomre 1977) and also because of slow secular evolution (e.g., Kormendy & Kennicutt 2004; Athanassoula 2012a). Part of the secular evolution in disc galaxies is driven by non-axisymmetries such as bars and oval distortions. Long-lived non-axisymmetries efficiently redistribute material and angular momentum across the discs in a Hubble-Lemaître time, which makes understanding them crucial to describe present-day galaxies. This slow process is, among many other consequences, responsible for the creation of pseudobulges (Kormendy & Kennicutt 2004), for the radial spread of outer parts of discs (Schwarz 1984; Athanassoula 2012b), and also for building spectacular rings and pseudorings. In this paper we study rings and pseudorings in a representative sample of nearby galaxies.

Rings are beautiful closed structures made of stars and/or gas. Pseudorings are their open counterparts, sometimes incomplete versions of rings and sometimes formed by spiral arms that almost connect. Here we use the word rings to refer to the set that includes both rings and pseudorings. The set of closed features is referred to as closed rings.

Rings often host intense star formation and/or are made of young blue stars (see, e.g., Buta & Crocker 1993; Knapen et al. 1995; Crocker et al. 1996; Buta 2002; Knapen 2005; Buta et al. 2007; Comerón et al. 2010; Grouchy et al. 2010). However, “dead” purely stellar rings exist as well (Buta 1991; Erwin & Sparke 1999, 2002; Comerón 2013).

The majority of rings seen in normal disc galaxies are likely caused by the influence of dynamical orbital resonances on the motions of gas clouds in the plane of the disc. The presence of a rotating bar or oval sets up a pattern speed and probably drives spiral patterns that can, via action of gravity torques, secularly evolve into more closed, ring-like features (Schwarz 1981, 1984). The main evidence in support of this idea has come from observations of ring morphologies, intrinsic ring shapes, and intrinsic bar and ring major axis orientations as well as test-particle and n-body simulations (see review by Buta & Combes 1996 and Rautiainen & Salo 2000).

There are four major and two secondary dynamical resonances that are believed to be important for ring formation (for detailed reviews of barred galaxy dynamics, see Sellwood & Wilkinson 1993; Athanassoula 2012a). These are defined (in the epicyclic approximation) by the relation between the bar pattern speed, Ωp, the circular angular speed Ω, and the radial epicyclic frequency κ. The major resonances are the outer Lindblad resonance (OLR, where Ωp = Ω + κ/2), the corotation resonance (CR, where Ωp = Ω), and the two inner Lindblad resonances (ILRs, where Ωp = Ω − κ/2). The secondary resonances are the inner 4:1 resonance (often called the UHR for ultraharmonic resonance, but which is here referred to as I4R, where Ωp = Ω − κ/4) and the outer 4:1 resonance (O4R, where Ωp = Ω + κ/4). Because Ω and κ depend on the rotation curve of a galaxy, resonance locations will be tied to the gravitational potential of the system. For example, depending on the bar pattern speed and the central mass concentration, one or both ILRs may be absent. Typically, the OLR is located at a radius of roughly twice the bar length, the CR is located slightly outside the end of the bar, and the ILRs are well inside the bar.

Between the outermost ILR and the CR, the main family of orbits, called x1 orbits, is parallel to the bar. In the framework of the epicyclic approximation, each time a main resonance is crossed, the orbits change their orientation by 90°. Because of this, orbits that are slightly inside a resonance will intersect with those slightly outside it. Graphic depictions of this can be found, for instance, in Fig. 11 in Knapen et al. (1995) and Fig. 2 in Englmaier & Gerhard (1997). Growing bars redistribute the angular momentum in a galaxy. Gas outside CR tends to be moved to the OLR radius (Lynden-Bell & Kalnajs 1972; Sellwood 1981; Schwarz 1981). Gas inside CR tends to move inwards and is collected either close to the I4R and/or close to the ILRs (Schwarz 1984). Thus, orbits near resonances are fed with gas by the bar angular momentum redistribution. Because of the high gas densities reached there and because of the collisions of gas clumps moving in intersecting orbits, star formation starts and resonance rings are created. Although strictly speaking the epicyclic approximation is no longer valid for strongly perturbed potentials such as those affected by a strong bar (for a good example of that see Salo et al. 1999), the picture described here remains qualitatively valid.

Rings in barred galaxies are classified according to their size compared to that of the bar. The precise location of a resonance cannot be determined unless the rotation curve of the galaxy and the pattern speed of the bar are known. Thus the resonance interpretations come from a confrontation between theory and observation:

  • Outer rings are found at a radius roughly twice as large as that of thebar and are thought to be typically related to the OLR.Occasionally, some outer rings may be linked to the O4R as in thecase of the dimpled ones in Byrdet al. (1998), those in simulationsby Rautiainen & Salo (2000), and in the modellingof NGC 1433 by Treuthardtet al. (2008). The first outer featurethat has been described is that in NGC 1291(Perrine 1922).

  • Inner rings are found slightly outside the bar and are thought to be related to the I4R. They have been observed since R. J. Mitchell’s observations of NGC 4725 in 1858 (Parsons 1880). They were first described by Curtis (1918).

  • Nuclear rings are found well inside the bar and are generally thought to be related to the ILRs (but see Kim et al. 2012, where nuclear rings are suggested to be caused by the centrifugal barrier encountered by gas migrating to the inner regions of the galaxy). They were first seen in NGC 4321 by Keeler (1908) and described in NGC 3351 by Curtis (1918). Nuclear rings are especially bright and correlate with the presence of sigma-drops (sigma-drops are nuclear regions in the centre of galaxies where the stellar velocity dispersion is measured to be lower than in the surroundings; Comerón et al. 2008b).

We caution about the naming conventions and note that inner rings in barred galaxies are not thought to be related to the inner Lindblad resonances, but to the I4R.

Based on data from the Third Reference Catalogue of Bright Galaxies (RC3; de Vaucouleurs et al. 1991), Buta & Combes (1996) found that roughly 10% of disc galaxies host outer rings and that 45% of disc galaxies host inner rings. Comerón et al. (2010) found that the fraction of nuclear rings is roughly 20% for galaxies with Hubble stages between T = −3 and T = 7.

Rings have been associated to resonances since the pioneering works by Marochnik et al. (1972) and Schommer & Sullivan (1976). Subsequently, this connection has been made in simulations by, among others, Schwarz (1981, 1984), Byrd et al. (1994), and Knapen et al. (1995). Because of that, outer, inner, and nuclear rings have historically been called resonance rings.

A complementary theory explains the formation of at least some rings. This theory, called manifold theory, shows in a single framework the creation of outer spirals and outer and inner rings. It proposes that they are made of particles trapped in invariant manifolds (tubes of orbits) that start and end in one of the two unstable Lagrangian points at the end of the bar, L1 and L2 (Romero-Gómez et al. 2006, 2007; Athanassoula et al. 2009b,a, 2010; Athanassoula 2012b). This theory predicts the existence of inner rings and that they are mainly oriented along the bar. It also predicts the existence of the outer R1, R2, and R1R2 rings and their orientation with respect to the bar (for a description of outer ring morphologies see Sect. 3.1). It also predicts the locations and axial ratios of rings. In fact, there is no prediction of the resonance ring simulations that the flux tube manifold theory does not predict as well, while the manifold shapes reproduce well that of rings in the response simulations mentioned above. The latter is possible because the values of the radii of the L1, L2, L3, and L4 Lagrangian points in barred galaxies are so close to that of the corotation radius that for observed galaxies they can be considered as equal. In this way it is possible to overcome the approximation of a resonant radius that is only valid in the linear and epicyclic approximations, that is, not in realistic barred galaxies. In the following we write manifold theory instead of flux tube manifold theory, and we use the generic name resonant rings for resonant and flux tube manifold rings.

Rings are also observed in galaxies that do not host a bar (see, e.g., Figs. 3e and 3f in Buta 1995). Comerón et al. (2010) claimed that the frequency of rings with sizes comparable with those of nuclear rings in unbarred galaxies (19 ± 4%) is similar to the frequency of unbarred disc galaxies. One possibility to explain the existence of such rings is that they are remnants left after the bar dissolved (for possible bar dissolution mechanisms, see e.g., Raha et al. 1991; Friedli & Benz 1993; Bournaud & Combes 2002; Bournaud et al. 2005) or was destroyed in interactions with other galaxies (Athanassoula 1996; Berentzen et al. 2003). However, the possibility of bar dissolution has to be taken with caution because many simulations showed that bars cannot be easily erased without interactions (see, e.g., Martinez-Valpuesta & Shlosman 2004; Debattista et al. 2004, 2006; Berentzen et al. 2007; Athanassoula et al. 2013). Alternatively, these rings that apparently do not fit in the resonance theory might be explained by resonances caused by weak oval distortions, strong spiral patterns (Jungwiert & Palous 1996; Rautiainen & Salo 2000), or by the gravitational potential distortions induced during minor mergers and/or interactions. This last possibility has been suggested by Knapen et al. (2004) for the pseudoring in NGC 278 and by some numerical experiments (Tutukov & Fedorova 2006). Moreover, rings can form out of satellite material during minor mergers (Eliche-Moral et al. 2011).

Another kind of interesting morphological feature in disc galaxies are the lenses. Lenses are typically found in early-type disc galaxies, they have flat luminosity profiles and fairly sharp edges. Lenses, like rings, can be classified as outer, inner, or nuclear, based on their sizes. They have been studied in detail in the Near-Infrared atlas of S0-Sa galaxies (NIRS0S; Laurikainen et al. 2011). Some features, called ring-lenses and first reported by Kormendy (1979), have properties between those of rings and lenses; they are lens-like features with a significant enhancement of luminosity close to their edges. In this paper we included ring-lenses together with classical rings.

Rings can be responsible for a significant fraction of the light emitted by a galaxy. For example, the exceptionally bright nuclear ring in NGC 1097 emits ~10% of the light of the galaxy at 3.6  μm (Sheth et al. 2010). This can be considered as an estimate of the upper limit of the fraction of light coming from rings in present-day galaxies. However, since rings are often regions of intense star formation with a low mass-to-light ratio even in the mid-infrared, the fraction of the galaxy baryonic mass found in them is smaller than that.

Non-resonant mechanisms also produce rings, but they often have an appearance fairly different from that of resonance rings. A ring can be formed at the largest non-looping orbit whose major axis is parallel to the major axis of the bar. Such a ring is called an x1-ring (Regan & Teuben 2004). Collisional rings occur when a disc galaxy collides head-on with a satellite (Lynds & Toomre 1976; Theys & Spiegel 1977). Polar rings occur when part of the mass of a satellite is accreted in an orbit perpendicular to the disc plane of the main galaxy (Schweizer et al. 1983). These three types of rings are rarer than resonance rings.

Moreover, some of the smallest nuclear rings (also called ultra-compact nuclear rings; Comerón et al. 2008a,c) might be related to the interaction of an AGN with the surrounding interstellar medium (Comerón et al. 2010).

Some rings that are coplanar with the galaxy disc may be related to polar rings. In a few galaxies, in-plane rings are found to be made of counterrotating material postulated to come from a recent minor merger. This could be the case, for instance, for the outer ring in IC 2006 (Schweizer et al. 1989; Bettoni et al. 2001), the inner ring in NGC 3593 (Corsini et al. 1998), the inner ring in NGC 4138 (Jore et al. 1996; Thakar et al. 1997), and the innermost ring in NGC 7742 (Sil’chenko & Moiseev 2006; Mazzuca et al. 2006).

In this paper we present a catalogue (Appendix A) and an atlas (Appendix B) of the rings identified in the Spitzer Survey of Stellar Structure in Galaxies (S4G; Sheth et al. 2010). The focus is on resonance rings, hence the title ARRAKIS: atlas of resonance rings as known in the S4G. In the catalogue section, we present data on the projected and intrinsic ring major and minor axes and orientations. We also present the projected and intrinsic highest bar ellipticities, which can be used as a rough estimate of the bar strength, and the bar orientations. The atlas presents images of all the galaxies with rings. We overlay the measured contour of the rings on these images.

The paper is structured as follows: in Sect. 2 we briefly describe the S4G and the ring identification process, in Sect. 3 we describe the types of rings detected in the S4G, and in Sect. 4 we describe the production process of the catalogue. We compare our measured ring properties with those in previous studies in Sect. 5, we present some statistical results on the ring fraction, their intrinsic axis ratio, their position angle (PA) offset with bars, and sizes in Sect. 6, and we discuss some of these points in Sect. 7. We summarise our results and conclusions in Sect. 8. The catalogue is presented in Appendix A and the atlas of rings is presented in Appendix B. Appendix C contains a list of galaxies in the catalogue with a duplicated NGC/IC identification.

2. Identification of rings and pseudorings in the S4G

2.1. The S4G

The rings in this paper are identified and described using S4G images. The S4G is a mid-infrared survey that has observed a sample of galaxies representative of the local Universe using the InfraRed Array Camera (IRAC; Fazio et al. 2004) of the Spitzer Space Telescope (Werner et al. 2004). The goal of the S4G is to describe the stellar mass distribution in the local Universe. The mid-infrared is the ideal band to do so because it has little dust absorption. The selection criteria of the sample are the following:

  • Radio radial heliocentric velocity vradio < 3000   km   s-1, which is equivalent to adistance of D < 41 Mpc when using aHubble-Lemaître constant of H0 = 73   km   s-1   Mpc-1.

  • Integrated blue magnitude mB,corr < 15.5 mag. The magnitude considered here is that corrected for Galactic extinction, inclination, and K-correction.

  • Angular diameter D25 > 1′.

  • Galactic latitude b |  > 30° to avoid the observations to be overly affected by foreground stars and other Galactic emission.

All these parameters were taken from HyperLeda (Paturel et al. 2003). One of the reasons why the sample is representative and not volume-limited is that the galaxies in the sample are limited in diameter and in brightness. Another source of incompleteness is that one of the main inputs of HyperLeda is the RC3, which is only reasonably complete at mB < 15.5 mag (this time the blue magnitude is uncorrected). An additional reason is that some galaxies, especially those of earlier types, did not have a radial velocity in radio in HyperLeda at the time when the sample was defined. The final S4G sample size is 2352 galaxies.

The images were taken to map the galaxies at least up to 1.5 × D25 and mosaics were produced when needed. The galaxies were observed in the 3.6 and 4.5  μm filters of IRAC with a total integration time of four minutes, obtaining images with a surface brightness sensitivity of μ(AB)3.6  μm ~ 27   mag   arcsec-2. Such deep images are unprecedented for a large survey of galaxies in the mid-infrared.

Because the distances used here are redshift-independent or Hubble-Lemaître flow-corrected, some of the galaxy distances listed in the table in Appendix A exceed 41 Mpc, as explained in Sect. 6.5.

The S4G data is now public and can be downloaded from the NASA/IPAC Infrared Science Archive (IRSA) website1.

Some galaxies in the S4G have two identifications in the NGC and IC catalogues (Dreyer 1888, 1895). To facilitate the comparison of the data presented here with other samples, Appendix C presents a list of the galaxies with a double identification that have been included in ARRAKIS. This list has been made by using mostly data from The Historically Corrected New General Catalogue 2, but also from NED and HyperLeda.

2.2. Morphological classification of S4G galaxies

Buta et al. (in prep.) classified most of the galaxies in the S4G using the criteria described in Buta et al. (2010) and Laurikainen et al. (2011). In brief, the galaxies were classified using the de Vaucouleurs revised Hubble-Sandage system (de Vaucouleurs 1959) and its revision (de Vaucouleurs 1963), which has three dimensions, namely the stage (E, E+, S0, S0°, S0+, S0/a, Sa, Sab, Sb, Sbc, Sc, Scd, Sd, Sdm, Sm, Im), the family (SA, SAMathematical equation: \hbox{${\underline{\rm A}}$}B, SAB, SABMathematical equation: \hbox{${\underline{\rm B}}$}, SB), and the variety (r, rMathematical equation: \hbox{${\underline{\rm r}}$}s, rs, rsMathematical equation: \hbox{${\underline{\rm s}}$}, s). Additional dimensions were added to the classification by indicating which galaxies are highly inclined (spindle or sp), which galaxies are double-staged, which galaxies have shells, lenses, nuclear bars, nuclear discs, triaxial bulges, ansæ, X-shaped bars, tidal debris, pseudobulges, and other peculiarities. Most important for this work, they also classified which galaxies host outer and nuclear rings. For an extensive review of this matter see Buta (2013).

The galaxies were classified using the S4G 3.6  μm band and interpreting the images as if they were blue light. The classifications in both bands are in general very similar and only differ in galaxies with stages between S0/a and Sc, for which the classification in 3.6  μm is on average one stage earlier than in the B band (Buta et al. 2010). This one-stage shift should be taken into account when comparing ARRAKIS results with those in previous studies based on B-band imaging.

Thumbnail: Fig. 1 Refer to the following caption and surrounding text. Fig. 1

Schematic classification of the ring types found in ARRAKIS. Multiple ring combinations are also included.

A problem may appear when, assuming that rings are related to resonances, those in unbarred galaxies are classified as outer, inner, and nuclear rings. In that case, they were classified comparing the ring size with the galaxy radius and/or the location where they appear in relation to spiral arms. This approach may cause some rings to be misclassified, as discussed in Buta (1995) and Comerón et al. (2010).

A few of the classified galaxies have two or even three features that fit in the outer, inner, or nuclear categories. For example, NGC 5055 is an SA(rs,rl)bc galaxy and has two inner features. In this case, the feature that appears first in the classification (rs) is the outermost feature. The only exceptions for this rule are R1R2Mathematical equation: \hbox{$_2^{\prime}$} and R1Mathematical equation: \hbox{$_1^{\prime}$}R2Mathematical equation: \hbox{$_2^{\prime}$} combinations, for which the order is reversed because of historical reasons.

Because of the limited amount of dust obscuration it suffers, the 3.6  μm band presents an advantage over optical wavelengths at detecting and describing rings that otherwise could remain hidden. This, combined with the angular resolution of the images in the S4G (0.′′Mathematical equation: \hbox{$.\!\!^{\prime\prime}$}75 pixel size and a full width at half maximum of ~ 2″), allowed us to identify rings with diameters down to ~ 10″ in low-inclination galaxies. We here considered low-inclination galaxies to be those with i ≤ 60°. This value is based on our ability to measure bar properties as explained in Sects. 4.5 and 4.6. The ring identification becomes increasingly difficult for higher disc inclinations due to higher optical depth and ring foreshortening (see, e.g., Tables IV and V in Buta & Combes 1996). A diameter of 10″ corresponds to 1.0 kpc at a distance 20 Mpc, and to 2.4 kpc at a distance of 50 Mpc, below which 98% of ARRAKIS galaxies are found.

The completeness regarding outer rings is hard to assess; some outer rings are known to be exceedingly faint and some may have surface brightnesses below the sensitivity level of the S4G. Additionally, in some cases, outer features are better seen in blue light: for example, the outer ring in NGC 7743, which is distinguishable in the B-band image in Buta et al. (2007), is not seen in the mid-infrared. Moreover, in at least one case (NGC 4151) an outer ring has not been detected here because it is larger than the region covered by the S4G frame.

The completeness in the detection of inner rings is very high. When looking at galaxies with D < 20 Mpc, we find that only 5% of inner rings have a diameter smaller than 2.4 kpc and therefore could not be detected for galaxies at D = 50 Mpc. We therefore expect to be missing less than 5% of the inner rings due to spacial resolution problems.

Regarding nuclear features, we cannot expect to be as complete as we are at finding inner rings: at a distance D = 20 Mpc, 5″ correspond to a ring radius of r = 500 pc, which is similar to the average size of the nuclear rings detected in Comerón et al. (2010). Therefore, any statistics based on the nuclear rings in ARRAKIS must be considered uncertain and only representative of the behaviour of the largest nuclear rings.

A total of 2347 S4G galaxies have been classified in Buta et al. (in prep.). One of these galaxies, NGC 7204 (also named PGC 68061), is a pair composed of NGC 7204A and NGC 7204B, leading the count of S4G classified galaxies to 2348. Four S4G galaxies could not be classified because they appear close to very bright saturated stars which makes the galaxy morphology hard to describe. In addition, 70 galaxies were classified that not belong to the S4G sample, but appear in the S4G frames. Most of these galaxies are satellites of galaxies in the S4G sample or background galaxies. Thus, we have data of a total of 2418 galaxies for which there is a classification that considers the presence of rings.

The total number of galaxies that appear in S4G frames and have been classified to host rings is 735. Of these, 724 galaxies are included in the original S4G sample. These 724 galaxies have 295 outer rings, 609 inner rings, 47 nuclear rings, 4 x1-rings, 4 collisional rings, and 7 polar rings.

To ensure the reliability of the ring statistics we considered only the galaxies in the S4G sample, which, as said before, is representative of the local Universe. However, for the sake of completeness, in the appendices we also included the data and the images corresponding to rings in galaxies not included in the original S4G sample.

3. Ring morphologies

Table 1

Glossary with some notation used in galaxy classification.

The types of rings studied here are described below. A schematic description of the different ring categories can be found in Fig. 1. A glossary of some common morphological features is presented in Table 1. For more information on ring classification and morphology see, for example, Buta et al. (2007) and Buta (2013).

3.1. Outer rings

Thumbnail: Fig. 2 Refer to the following caption and surrounding text. Fig. 2

Selection of S4G galaxies hosting a variety of outer rings. The images are in the 3.6  μm band, have a size twice that of the μ3.6  μm = 25.5   mag   arcsec-2 diameter isophote and are oriented with north up and east left. The top row shows galaxies with outer features compatible with the R1 and R2 ring morphologies seen in simulations by Schwarz (1981, 1984) and defined by Buta (1986a). The second row shows outer rings that cannot be easily recognised to belong to these categories in either barred or unbarred galaxies. The third row has three example of ring-lenses and a rare example of a galaxy with two outer rings. The names of the galaxies and their morphological classification (from Buta et al., in prep.) can be found below each image.

In barred galaxies, outer rings are those with roughly twice the size of the bar. They are thought to be related to the OLR or, occasionally, to the O4R. Since the work from de Vaucouleurs (1959), outer features have been divided into closed rings (R) and pseudorings (R), depending on whether the feature is closed/complete or not.

Additional subdivisions have been made later based on the morphology of the outer features in the simulations of Schwarz (1981, 1984) (see Fig. 2 in Buta 1986a). R1 closed rings and R1Mathematical equation: \hbox{$_1^{\prime}$} pseudorings consist of arms that start at one end of the bar and end after a 180° bend in the other end of the bar. These rings typically have a dimpling in the region of the end of the bar and thus are 8-shaped. R2 closed rings and R2Mathematical equation: \hbox{$_2^{\prime}$} pseudorings consist of two spiral arms, each starting at one of the ends of the bar and intersecting with each other at a position roughly perpendicular to the main axis of the bar after a 270° bend. ARRAKIS includes some R2Mathematical equation: \hbox{$_2^{\prime}$} pseudorings, but no R2 rings. According to the simulations from Schwarz (1981, 1984), R1 features are expected to be elongated and perpendicular to the major axis of the bar, and R2 features are expected to be elongated and parallel to the major axis of the bar. Sometimes galaxies host an R1Mathematical equation: \hbox{$_1^{\prime}$}R2Mathematical equation: \hbox{$_2^{\prime}$} or an R1R2Mathematical equation: \hbox{$_2^{\prime}$} combination.

When an outer feature could not be unambiguously classified in the R1 and R2 categories (for example in unbarred galaxies), it was classified as R in the case of closed rings and as R in the case of pseudorings.

Some outer features have properties intermediate between rings and lenses and were classified as outer ring-lenses. They are indicated by adding an L to the morphological classifications, for instance, RL and R1Mathematical equation: \hbox{$_1^{\prime}$}L. Subtler degrees of ringness of outer ring-lenses are sometimes described by underlines, forming the sequence R, RMathematical equation: \hbox{${\underline{\rm R}}$}L, RL, RLMathematical equation: \hbox{${\underline{\rm L}}$}, L.

A selection of galaxies showing a variety of outer rings observed in the S4G is presented in Fig. 2.

3.2. Inner rings

Thumbnail: Fig. 3 Refer to the following caption and surrounding text. Fig. 3

Selection of S4G galaxies hosting a variety of inner rings presented in the same way as those in Fig. 2. The top row presents a succession of increasingly more spiral-like inner features in a series of SAB or moderately barred galaxies. The second line shows example of inner rings in unbarred galaxies and two examples of ring-lenses in early-type disc galaxies.

In barred galaxies, inner rings are those that are roughly the size of the bar or slightly larger than the bar. They are thought to be related to the I4R. They are classified in a sequence of openness of the spiral arms that curve to form the ring. This sequence ranges from completely closed inner rings to spirals in the following order, r, rMathematical equation: \hbox{${\underline{\rm r}}$}s, rs, rsMathematical equation: \hbox{${\underline{\rm s}}$}, s (de Vaucouleurs 1963). Underlines indicate transitions between the r, rs, and s varieties. Intermediate varieties between r and s may also indicate rings that are not complete. Features classified as inner pseudorings (rMathematical equation: \hbox{${\underline{\rm r}}$}s, rs, rsMathematical equation: \hbox{${\underline{\rm s}}$}) are sometime denoted as r in the literature.

Inner features can also be ring-lenses. Closed inner ring-lenses are indicated as rl and inner pseudoring-lenses are indicated as rl. Subtler degrees of ringness of inner ring-lenses are sometimes described by underlines, forming the sequence r, rMathematical equation: \hbox{${\underline{\rm r}}$}l, rl, rlMathematical equation: \hbox{${\underline{\rm l}}$}, l.

A selection of galaxies showing a variety of inner rings observed in the S4G is presented in Fig. 3.

3.3. Nuclear rings

Thumbnail: Fig. 4 Refer to the following caption and surrounding text. Fig. 4

Selection of S4G galaxies hosting a variety of nuclear features. The images in the top row are presented in the same way as those in Fig. 2. The bottom panels are zoomed by a factor of five compared with those in the top row. The frames show galaxies hosting a ring, a pseudoring, a ring-lens, and a pseudoring-lens, respectively.

Although generally small, several nuclear features are visible in the S4G images. In barred galaxies, nuclear rings are found inside bars. They are thought to be related to the ILRs (but see Kim et al. 2012). They are expected to be located between the outer and the inner ILR when both are present and inside the ILR when the galaxy has only one of them (see, e.g., Shlosman 1999; Sheth et al. 2000). Nuclear rings have been studied in detail in the atlas of images of nuclear rings (AINUR; Comerón et al. 2010).

Nuclear features are classified into the closed nuclear ring (nr) and nuclear pseudoring (nr) subtypes depending on whether the feature appears completely closed or not. Closed nuclear ring-lenses and pseudoring-lenses are denoted as nrl and nrl, respectively.

A selection of galaxies showing a variety of nuclear rings observed in the S4G is presented in Fig. 4.

3.4. x1, collisional, polar, and accretion rings

Thumbnail: Fig. 5 Refer to the following caption and surrounding text. Fig. 5

Selection of S4G galaxies hosting a variety of non-resonance rings presented in the same way as those in Fig. 2. The first frame shows a galaxy with an x1-ring, the second one a galaxy with a collisional one, and the last two show galaxies with polar rings.

Although the rings discussed in this subsection have a non-resonant origin, they have been included in ARRAKIS for the sake of completeness.

x1-rings, indicated as x1r in the morphological classification, are very elongated and parallel to bars. Collisional rings, indicated as RG, are in general as large as outer rings, but their centres are typically significantly offset from the galaxy nucleus. They often appear to be intrinsically elliptical (see, e.g., Appleton & Struck-Marcell 1996). Finally, polar rings, indicated as PRG, are typically seen as needle-like features roughly perpendicular to the major axis of the galaxy, although they can be at other angles, like in the case of NGC 660, which is shown in Fig. 5 (Whitmore et al. 1990; van Driel et al. 1995).

Accretion rings are thought to be similar to polar rings, but in their case the material has been accreted at a small angle compared to the galaxy main plane. Since accretion rings are indistinguishable from resonance rings unless kinematic data are available, we included them in the statistics together with resonance rings. To our knowledge, the only rings in this paper that belong to this category are the inner ring in NGC 3593 (Corsini et al. 1998), the inner ring in NGC 4138 (Jore et al. 1996; Thakar et al. 1997), and the innermost ring in NGC 7742 (Sil’chenko & Moiseev 2006; Mazzuca et al. 2006).

A selection of images showing galaxies with x1, collisional, and polar rings observed in the S4G is presented in Fig. 5.

4. Preparation of the catalogue

4.1. Description of the projected shapes of rings

To describe the shapes of rings, we assumed that they are intrinsically circular or elliptical, as was done in other statistical ring studies (de Vaucouleurs & Buta 1980; Buta 1986a, 1995; Buta & Crocker 1993; Knapen et al. 2002; Comerón et al. 2010; Grouchy et al. 2010; Laurikainen et al. 2011). Because an ellipse in projection is also an ellipse, the geometrical description of a projected ring in these studies was done by giving the sizes of its major and minor axes (Dr and dr) or by giving its major axis and its axial ratio (qr = dr/Dr). To fully characterize the ring geometrical properties, its projected major axis position angle, PAr, is sometimes given as well.

Although the original S4G frames have been used for the identification of the rings in Buta et al. (in prep.), working with these images is not always optimal when describing their shape because the contrast between rings and the rest of the galaxy is sometimes very low. A way to overcome this problem is to model the emission of the main components of the galaxy (bulge, bar, disc, etc.) and subtract this model from the original image. This results in the so-called residual image where the disc substructure, such as rings and spiral arms, appears contrast-enhanced. This procedure was preferred to other methods to enhance rings such as unsharp masking because the galaxies were modelled by the S4G pipeline 4 (P4; Salo et al., in prep.). In short, P4 models were made by fitting the S4G images with up to four components (nucleus, bulges, discs, and/or bars) using version 3.0 of Galfit (Peng et al. 2002, 2010). When fitting the model, the disc ellipticity (ϵd = 1 − qd) and position angle (PAd) were fixed to the values corresponding to deep outer-disc isophotes obtained with an ellipse-fitting routine. A model galaxy image and a residual image were obtained as an output of P4. For the few ARRAKIS galaxies not included in the S4G sample, additional ellipse fits and decompositions were made using the P4 software.

Thumbnail: Fig. 6 Refer to the following caption and surrounding text. Fig. 6

Original image, P4 model, and model-subtracted image of NGC 4579. The model has three components, namely a bulge, a bar, and a disc. NGC 4579 is a galaxy classified as (RL,R)SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})a by Buta et al. (in prep.). NGC 4579 has an exceedingly diffuse outer ring as seen in the first frame. The ring becomes more obvious in the model-subtracted image. The axis units are arcseconds.

Thumbnail: Fig. 7 Refer to the following caption and surrounding text. Fig. 7

Original image, P4 model, and model-subtracted image of NGC 1097, which is classified as an (R)SB(rs,nr)abMathematical equation: \hbox{${\underline{\rm b}}$} pec galaxy in Buta et al. (in prep.). The red ellipses indicate in an outside-in order the average of the two ellipse fits made to the outer, the inner, and the nuclear rings. The green ellipses are the result of an ellipse fit at the radius of the highest bar ellipticity. The red crosses indicate the centre of the galaxy. The axis units are arcseconds.

We examined the original and residual images of the galaxies and decided for each ring in which image, original or residual, it was better defined, and thus in which image its shape was easier to measure. Although a priori this should always be the residual image (see, e.g., the example in Fig. 6), because of the galaxies with complicated morphologies and/or because P4 models were intentionally kept simple, some residual images have artefacts that hinder defining the outline of a ring. This occurs more often when looking at the inner features in galaxies with strong bars.

After selecting the image in which the rings were better defined, we used IRAF’s3 (Tody 1986, 1993) TVMARK task to describe them. When used in interactive mode, TVMARK allows marking points in an image displayed in DS9 (Joye & Mandel 2003). This was used to characterise the shape of rings by marking by hand bright star-forming patches belonging to the feature or stellar emission that probably belonged to the ring, as was done in Grouchy et al. (2010). All the ring features were measured by the same person (S. Comerón). This procedure was repeated twice for each ring, typically with several days to a few months between the two measurements.

The points marking the outline of the rings for each of the two sets of measurements were fitted with an ellipse using a least-squares fitting algorithm. The output of the fits was the ring diameter in the major axis direction Dr, the diameter along the minor axis direction dr, and the major axis PA (PAr). The data used for the statistics in this paper are presented in Appendix A and were obtained by averaging the Dr, dr, and PAr values obtained from the fits to the two sets of measurements for each ring. Ellipses made from these averaged values are overlayed on the atlas images and in the example shown in Fig. 7.

4.2. Accuracy of the measured projected ring properties

Thumbnail: Fig. 8 Refer to the following caption and surrounding text. Fig. 8

Top-left panel: residuals of the ring diameters along the major and minor axes as a function of the averaged diameters, ⟨ dr,Dr ⟩. Top-right panel: residuals of the ring axis ratios, qr = dr/Dr, as a function of the mean axis ratios ⟨ qr ⟩  =  ⟨ dr ⟩ / ⟨ Dr ⟩. Bottom-left panel: residuals of the ring position angles as a function of the averaged ring major axis ⟨ Dr ⟩. Bottom-right panel: residuals of the ring position angles as a function of the mean ring axis ratios. N refers to the number of points in each plot.

To study the accuracy of the Dr, dr, and PAr measurements, we examined the residuals between the values of these parameters obtained for each of the two fits and the averaged values, that is, dr,Dr −  ⟨ dr,Dr ⟩ and PAr −  ⟨ PAr ⟩. These residuals can be considered as a rough estimate of internal errors caused by the observer’s judgement (Fig. 8). However, we warn that these error estimates do not include those associated with the use of a given method when measuring ring properties. A different ring measurement method may yield values differing from those presented here by many times the error estimate that we discuss.

The top-left panel in Fig. 8 shows how the error in the major and minor diameters tends to grow with ring radii: for small diameters, the dr,Dr −  ⟨ dr,Dr ⟩ never exceeds 0.Mathematical equation: \hbox{$.\mkern-4mu^\prime$}2, but for larger diameters, it can increase up to 0.Mathematical equation: \hbox{$.\mkern-4mu^\prime$}6. The four points with larger dr,Dr −  ⟨ dr,Dr ⟩ correspond, from left to right, to the major axis diameters of the outer features of NGC 4736 and NGC 4258. The outer ring of NGC 4736 appears to be double in its south-eastern side. Our choice in selecting the outline of the ring changed between the two measurements, which explains the large error. NGC 4258 is a galaxy for which the S4G frame does not fully cover the disc, thus a significant fraction of the outer ring lies outside the frame and cannot be studied, causing a large uncertainty in the Dr measurement. The range of dr,Dr −  ⟨ dr,Dr ⟩ values is similar to that found in the catalog of southern ringed galaxies (CSRG; Fig. 5a in Buta 1995).

The errors in the measured ring axis ratios are presented in the top-right panel of Fig. 8. We found that the average error is | Δqr |  = 0.02.

Thumbnail: Fig. 9 Refer to the following caption and surrounding text. Fig. 9

Top panel: internal errors of dr,Dr as a function of ⟨ dr,Dr ⟩. Bottom panel: internal errors of PAr as a function of ⟨ qr ⟩. The solid lines represent the fits described in Eqs. (1) and (2) and the dashed lines correspond to the same expressions as presented in the CSRG. Darker grey areas indicate the 95% confidence interval of the fit for ARRAKIS and lighter grey indicates the same for the CSRG.

The PAr uncertainty is larger for smaller and/or rounder rings, as seen in the bottom panels of Fig. 8; this is natural since for a round ring PAr is undefined. The range of PAr −  ⟨ PAr ⟩ in our study and its behaviour as a function of ⟨ Dr ⟩ and ⟨ qr ⟩  = 1 − ϵr =  ⟨ dr ⟩ / ⟨ Dr ⟩ is qualitatively similar to that in Figs. 5c,d of the CSRG.

Because the CSRG is the largest ring catalogue with an internal error estimate, it can be compared with our results. The CSRG data come from analogically measuring diameters and PAs in photographic plates, but here we present data measured by digital means, which may yield significantly different accuracies.

The CSRG presents two internal error functions that we reproduce here with S4G data. The internal error function for the diameter residuals was obtained by sorting the residuals according to their mean diameter and then calculating the standard deviation for groups of 200 residuals, σ(dr,Dr) (top panel in Fig. 9). As in the CSRG, we linearly fitted the points and obtained σ(dr,Dr)=0.009+0.023dr,Dr.Mathematical equation: \begin{equation} \sigma(d_{\rm r},D_{\rm r})=0.\mkern-4mu^{\prime}009+0.023\protect\langle d_{\rm r},D_{\rm r}\protect\rangle. \label{e1} \end{equation}(1)Since in ARRAKIS the error grows slower with increasing dr,Dr, our accuracy is slightly better than that obtained in the CSRG (σ(dr,Dr) = 0.Mathematical equation: \hbox{$.\mkern-4mu^\prime$}009 + 0.029 ⟨ dr,Dr ⟩). The 95% confidence bands in Fig. 9 were calculated with the assumption that the errors are normally distributed. The statistics for the confidence bands corresponding to the CSRG were obtained by measuring the position of the data points in a magnified version of Fig. 5e in the CSRG.

The internal errors for the ring orientations were calculated by sorting the PAr residuals according to their qr and then calculating the standard deviation for groups of 100 residuals (bottom panel in Fig. 9). As in the CSRG, we produced a fit that scales inversely with the fitted ellipticity σ(PAr)=0.87+1.35/(1qr),Mathematical equation: \begin{equation} \sigma({\rm PA}_{\rm r})=-0.\mkern-5mu^{\circ}87+1.\mkern-5mu^{\circ}35/(1-\langle q_{\rm r}\rangle), \label{e2} \end{equation}(2)and thus our PAr determinations are better than those in the CSRG for qr < 0.83 (in the CSRG σ(PAr) = 2.Mathematical equation: \hbox{$.\!\!^\circ$}29 + 0.Mathematical equation: \hbox{$.\!\!^\circ$}81/(1 −  ⟨ qr ⟩)). Our PAr measurements are at least twice as precise than those in the CSRG for qr < 0.53. However, perhaps surprisingly, the manual PAr determination in the CSRG seems to have fewer internal errors than ARRAKIS for rings that are nearly round (qr > 0.83). This is no problem because PAr becomes meaningless for almost round rings. We calculated the confidence bands for this fit in the same way as for the top panel. For the CSRG fit, we made the statistics based on the information on CSRG’s Fig. 5f.

We can thus conclude that the internal errors in ARRAKIS are the smallest for such a large dataset of rings so far and that this can be attributed to the use of digital deep images.

4.3. Obtaining the projected bar parameters

Simulations by Schwarz (1981, 1984) and the flux tube manifold orbital calculations (Athanassoula et al. 2009b,a) predict R1 rings to be elongated and perpendicular to bars, R2 rings to be elongated and parallel to bars, and inner rings to be elongated and parallel to bars. It is thus interesting to know the bar PA in galaxies with rings. We also measured the highest bar ellipticity ϵb = 1 − qb = 1 − db/Db (Db and db are the bar major and minor diameters and qb is the bar axis ratio). ϵd roughly scales with more sophisticated bar strength indicators such as the bar torque (Block et al. 2001; Laurikainen et al. 2002).

The bar data were obtained by studying the ellipticity fits from S4G’s P4. We searched for the peak ellipticity within the radius of the bar, regardless of how big the drop in the ellipticity after the maximum was or how the PA varied with radius. We considered the PA at that radius to be representative of the bar orientation. Moreover, the maximum ellipticity radius is typically a lower estimate of the bar length (Erwin 2005), except in galaxies in which the bar merges with rings and/or spiral arms. In the catalogue of Appendix A, we present the diameters along the major and minor axes of the ellipse fits at the position of the bar maximum ellipticity (Db and db) and the bar PA at the same position, (PAb). We checked that each individual PAb roughly corresponds to what would be expected from visual inspection. If it did not, we labelled it as unsuitable for bar analysis, as discussed at the end of Sect. 4.5.

4.4. Obtaining the intrinsic ring and bar shape and orientation

ARRAKIS is the first large ring catalogue that provides intrinsic ring shapes and orientations. The reason is that deprojecting rings requires knowing, within a few percent, the disc orientation parameters, that is, the ellipticity, ϵd = 1 − qd, and the position angle, PAd. Under the assumption of discs being intrinsically circular, one needs very deep images to measure ϵd and PAd in the outer disc, a region where the effect of perturbing non-axisymmetries such as bars is most likely weak. This was not possible for the CSRG because it was produced using photographic plates, but was performed in Knapen et al. (2002), Comerón et al. (2010), and Grouchy et al. (2010).

The S4G P4 makes use of deprojection parameters obtained from isophote fits at low surface brightness (for more details see Salo et al., in prep.). These are the deprojection parameters that we used here for obtaining intrinsic ring and bar shapes (qr,0 and qb,0) except for the few ARRAKIS galaxies not in the S4G sample (but appearing in S4G frames) and NGC 4698. For this last galaxy our interpretation of the deprojection parameters is very different from that in P4. P4 deprojection parameters were also used to calculate the counter-clockwise angular distance between the line of nodes and the ring and bar major axis (θr and θb), under the assumptions that the outer parts of discs are circular and that rings and bars are roughly elliptical. The equations that we used for deprojection can be found in Appendix A of Gadotti et al. (2007). The deprojected D and d values for both rings and bars are presented in the catalogue of Appendix A. The angle difference between the deprojected major axis and the line of nodes of the deprojection is also indicated. The only rings for which we have not included deprojected parameters are the polar rings, because they are known not to lie in the galaxy disc plane.

4.5. Reliability of the deprojected bar parameters

Thumbnail: Fig. 10 Refer to the following caption and surrounding text. Fig. 10

Measured orientation of the bar with respect to the line of nodes of the galaxy (θb) as a function of the galaxy inclination (i) for each of our four galaxy models described in the text and Table 2. Each coloured line represents a single real θb value, which is the one corresponding to the position at which the line crosses the i = 0° axis, that is, from purple to red (bottom to top), θb = 0°, θb = 10°, θb = 20°, θb = 30°, θb = 40°, θb = 50°, θb = 60°, θb = 70°, θb = 80°, and θb = 90°. The images at the bottom-right corner of each panel represent the corresponding galaxy when θb = 0° and i = 0°.

The presence of a bar can be recognised in very inclined galaxies and sometimes also in edge-on galaxies (see, e.g., how box/peanut bulges are related to bars in Kuijken & Merrifield 1995). However, obtaining their orientation and ellipticity from ellipse fits can be very difficult. Indeed, the ellipse deprojection would give precise bar parameters for isolated infinitely thin bars. But real bars have some amount of vertical thickening and are embedded in galaxies with discs and bulges. As a natural consequence of that, the more inclined a galaxy, the harder it is to obtain accurate bar intrinsic parameters.

To estimate how precise our bar measurements are, we prepared a set of four toy model galaxies with an exponential disc, a classical spherical bulge, and a Ferrers bar (Ferrers 1877). Assuming that the centre of the galaxy is located at x = 0, y = 0, and z = 0 and that the disc lies in the x − y plane, this simplified disc can be described as ρd(R,z)=ρd,0eR/hRe|z|/hz,Mathematical equation: \begin{equation} \rho_{\rm d}(R,z)=\rho_{\rm d,0}\,{\rm e}^{-R/h_{R}}\,{\rm e}^{-|z|/h_{z}}, \end{equation}(3)where R is the radius in the plane of the galaxy (R=x2+y2Mathematical equation: \hbox{$R=\sqrt{x^2+y^2}$}), ρd,0 stands for the disc central mass density, hR for the disc scale-length, and hz for the disc scale-height.

To describe the bulge we used a Jaffe profile (Jaffe 1983) which, when projected onto a plane, results approximately in a de Vaucouleurs profile (de Vaucouleurs 1948): ρbulge(r)=ρbulge,0(rr0)-2(1+rr0)-2,Mathematical equation: \begin{equation} \rho_{\rm bulge}(r)=\rho_{\rm bulge,0}\,\left(\frac{r}{r_{0}}\right)^{-2}\left(1+\frac{r}{r_{0}}\right)^{-2}, \end{equation}(4)where r is the 3D radius (r=x2+y2+z2Mathematical equation: \hbox{$r=\sqrt{x^2+y^2+z^2}$}), ρbulge,0 controls the bulge mass, and r0 controls its size.

Finally, the bar was described as ρbar(m)=ρb,0(1m2)form1,ρb=0form>1,Mathematical equation: \begin{equation} \rho_{\rm bar}(m)=\rho_{\rm b,0}\left(1-m^2\right)\,\,\,{\rm for}\,\,\,m\leq1,\,\rho_{\rm b}=0\,\,\,{\rm for}\,\,\,m>1, \end{equation}(5)where ρbar,0 is the central bar mass density and m2(x,y,z)=x2a2+y2b2+z2c2·Mathematical equation: \begin{equation} m^2(x,y,z)=\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}\cdot \end{equation}(6)Here, a is the major axis, b is the minor axis, and c is the vertical axis of the bar.

The four model galaxies had (in arbitrary units) ρd,0 = 1, ρbar,0 = 1, hR = 30, hz = 5, and r0 = 5. The other parameters were model-dependent and are listed in Table 2. Table 2 also presents the fraction of mass in the bulge and in the bar for each model. As seen there, the fraction of mass in bars is rather low and thus our fit to models is a worst-case study.

We decided that the x axis would be the line of nodes of our rotation. We first rotated the bar by a given angle θb with respect to the line of nodes and then inclined the galaxy by an angle i. We defined θb to vary from θb = 0° to θb = 90° in steps of 10°. We explored the space of galaxy inclinations from i = 0° to i = 80° in steps of 10°. The rotated and inclined galaxies were then projected onto 2D fits images. We used these images to measure the bar properties by fitting ellipticity profiles. We considered that a bar ellipticity and PA could be measured when a peak in ellipticity with prominence larger than 0.01 occurred within the bar radius. We used the ellipticity fit at the maximum ellipticity peak to obtain the deprojected bar parameters, as was done for observed bars in Sect. 4.4. The results on the recovery of the original bar PA with respect to the line of nodes, θb, and the original bar ellipticity, ϵb,0 = 1 − qb,0, are presented in Figs. 10 and 11. In several cases in highly inclined galaxies, no clear maximum in ellipticity was found, therefore no deprojection of the bar properties was obtained.

Table 2

Parameters of the model galaxies used to study the reliability of the bar deprojected parameters.

Thumbnail: Fig. 11 Refer to the following caption and surrounding text. Fig. 11

Measured bar ellipticity (measured 1 − qb,0) as a function the galaxy inclination (i) for each of our four galaxy models. Each coloured line represents a single θb value colour-coded in the same way as in Fig. 10 (also ordered here from bottom to top). The intrinsic 1 − qb,0 value is that corresponding to i = 0°. The images at the top-right corner of each panel represent the corresponding galaxy when θb = 0° and i = 0°.

The angle θb is typically well recovered for galaxies with i ≤ 40° when the bar is small compared to the bulge size (models 1 and 2 in Fig. 10). For galaxies with longer bars (models 3 and 4), θb is well recovered for i ≤ 60°. The reason for this is that the bulge, which is intrinsically spherical, and to some extent also the disc, soften the isophotes, which makes them less elliptical. In some cases, for low real θb values and high disc inclinations, this effect is so strong that the measured projected ellipticity becomes lower than the ellipticity of the projected disc, causing the measured θb to shift by some 90° from the real value.

The measured intrinsic bar ellipticity ϵb,0 = 1 − qb,0 is highly dependent on the real θb. When the bar is parallel to the line of nodes (real θb ~ 0°), 1 − qb,0 becomes increasingly underestimated for increasing i. For bars oriented perpendicular to the line of nodes (real θb ~ 90°), the effect is reversed.

Because the S4G sample is under-abundant in early-type galaxies, bulges are in general not expected to play a significant role when producing ellipticity profiles. Therefore, we considered the parameters of the bars in galaxies with i ≤ 60° (corresponding to a disc ellipticity ϵd = 1 − qd ≤ 0.5) to be reliably measured. The properties of bars in such discs almost always appear in the catalogue in Appendix A and the ellipse fit to the highest bar ellipticity is overlayed on the images of the atlas in Appendix B.

However, even for galaxies with i ≤ 60° six bar fits were found to be unreliable and were excluded from the appendices. The reason for this is that the bar fit is obviously wrong in galaxies with bars with a low contrast (NGC 2552) or that are influenced by surrounding bright regions such as a ring (NGC 2967, NGC 4351, NGC 5595, NGC 5744, and NGC 6923). For five additional galaxies with ϵd ≤ 0.5 classified as barred by Buta et al. (in prep.), ESO 443-80, NGC 2460, NGC 5633, NGC 6278, and UGC 5814, we were unable to distinguish a peak corresponding to a bar in the ellipticity profiles. Finally, the centre of NGC 4108B is affected by an image artefact that made impossible to measure the bar properties. For galaxies with i > 60°, we did not include the bar properties in the appendices even for those that are obviously barred.

Moreover, even though inner rings are defined to be surrounding the bar, for 73 galaxies the maximum in ellipticity that we fitted as an estimate for the bar radius is slightly larger than the inner ring radius in projection and/or in deprojection. This is caused by our very simple approach at describing bars. In most of these cases the bar merges with the ring and the junction points have strong star-forming regions, ansæ, and/or the beginning of spiral arms, which affect the ellipticity fits in such a way as to move the ellipticity maximum outwards. In other cases, the reason that the bar is larger than the fitted ring diameter may be that some rings slightly deviate from an elliptical shape in such a way that the bar fits within them. These deviations are not captured by our simple ring-fitting approach. In none of the cases considered for the statistics in this paper would this change the bar orientation by more than a few degrees from what would be measured visually.

4.6. Reliability of the deprojected ellipse parameters in discs with a finite thickness

Thumbnail: Fig. 12 Refer to the following caption and surrounding text. Fig. 12

Top panel: difference between the measured intrinsic axis ratio of a ring, qr0, and the real one, qr,0Mathematical equation: \hbox{$q^{\prime}_{\rm r,0}$}, as a function of the real galaxy inclination, i, for four disc scale-height to scale-length ratios. The colour code corresponds in an outside-in order to hz/hR = 1/3 (red), hz/hR = 1/5 (green), hz/hR = 1/7 (blue), and hz/hR = 1/10 (purple). Bottom panel: difference of the measured angle difference between the orientation of the major axis of a ring with respect to the line of nodes, θr, with respect to the real one, θrMathematical equation: \hbox{$\theta^{\prime}_{\rm r}$}, as a function of the real galaxy inclination. In both panels, the solid lines indicate the maximum and the minimum qr,0qr,0Mathematical equation: \hbox{$q_{\rm r,0}-q^{\prime}_{\rm r,0}$} (|θrθr|Mathematical equation: \hbox{$|\theta_{\rm r}-\theta^{\prime}_{\rm r}|$}) for a given i colour-coded as in the top panel. The dashed lines indicate the limits of the region enclosing 68.2% of qr,0qr,0Mathematical equation: \hbox{$q_{\rm r,0}-q^{\prime}_{\rm r,0}$} (|θrθr|Mathematical equation: \hbox{$|\theta_{\rm r}-\theta^{\prime}_{\rm r}|$}) values at a given i.

The reliability of the deprojected ring parameters depends on the quality of the P4 measured disc deprojection parameters. One source of error when deprojecting is the assumption that discs are infinitely thin. Indeed, the thicker a galaxy disc, the more the measured galaxy inclination, i, will differ from the real inclination, i.

The thickness of discs has been studied by de Grijs (1998). He found that the ratio between the disc scale-height and the disc scale-length (hz and hR, respectively) decrease monotonically with Hubble stage. The average hz/hR is around 1/3 for S0 galaxies and decreases to 1/9 for Sd galaxies. However, for a given stage the scatter in hz/hR is large, so the relationship described by de Grijs (1998) cannot be used for correcting the finite thickness effects in deprojected parameters without adding a substantial error. Instead, in this section we adopt the approach of quantifying possible biases in the deprojected parameters.

Hubble (1926) described the formalism for finding inclination of an oblate ellipsoid, cos2i=qd2qz21qz2,Mathematical equation: \begin{equation} {\rm cos}^2i^{\prime}=\frac{q^2_{\rm d}-q^2_z}{1-q^2_z}, \end{equation}(7)where qd is the observed galaxy disc axis ratio and qz is the galaxy flattening, that is, hz/hR. From this, and knowing that cos   i = qd, we can derive the formula for calculating the i corresponding to a given i: i=arccos(qz2+(1+qz2)cos2i).Mathematical equation: \begin{equation} \label{eqdeproj} i={\rm arccos}\,\Bigg(\!\!\sqrt{q_{z}^2+(1+q_{z}^2)\,{\rm cos}^2i^{\prime}}\Bigg). \end{equation}(8)From this expression we can deduce that the maximum bias at finding a disc inclination comes from the galaxies with thicker discs, namely S0s with hz/hR ~ 1/3. Most of our results in Sect. 6 are based on galaxies with i ≤ 60°. For an S0 galaxy with i′ = 60°Δi = i′ − i ~ 5°. Accordingly, for most of the galaxies with i ≤ 60°, i ~ i.

To examine how the biased i values calculated from Eq. (8) would affect our ring deprojection values, we created four model galaxies with hz/hR = 1/3, hz/hR = 1/5, hz/hR = 1/7, and hz/hR = 1/10. We then inclined each of them with angles in the range i′ = 0° to i′ = 80° with 10° intervals.

We checked how the underestimated inclination measurements would affect the measured intrinsic ring ellipticities, qr,0, and the angle between their major axes and the lines of nodes of the deprojection, θr. To do this, we considered a population of rings with a Gaussian distribution of intrinsic axis ratios, qr,0Mathematical equation: \hbox{$q^{\prime}_{\rm r,0}$}, with the centre of the Gaussian at qr,0=0.8Mathematical equation: \hbox{$q^{\prime}_{\rm r,0}=0.8$} and a dispersion of σ′ = 0.13. These values are representative of the measured axis ratio distribution of inner rings as seen in Sect. 6.3. For each galaxy model with a given hz/hR and for each of the studied inclinations, we obtained 1000 random ring axis ratios. The intrinsic axis ratio of each of these rings was recovered after projecting it using the real galaxy inclination, i, and deprojecting it using the measured galaxy inclination, i. This was repeated for 19 angle differences between the ring major axis and the line of nodes used for inclining the model galaxy. These angles ranged from θr=0Mathematical equation: \hbox{$\theta^\prime_{\rm r}=0^\circ$} to θr=90Mathematical equation: \hbox{$\theta^\prime_{\rm r}=90^\circ$} in steps of .

In the top panel in Fig. 12 we study the accuracy of the measured ring axis ratios. If, as in our results section, we focus on galaxies with i′ ≤ 60°, the errors at measuring qr,0 are always below | Δqr,0 |  = 0.05 except for galaxies with hz/hR = 1/3 and a few cases with hz/hR = 1/5. Except in exceptional cases for hz/hR = 1/3, | Δqr,0 |  ≤ 0.10. For i′ ≤ 40°, the uncertainties in q0 due to the finite thickness of discs are always rather small and in the order of the uncertainty in the measurement of qr (| Δqr |  = 0.02) as measured in Sect. 4.2.

In the bottom panel in Fig. 12 we study the accuracy of the measured ring intrinsic orientation. We find that for galaxies with i′ ≤ 60°, the maximum |θrθr|Mathematical equation: \hbox{$|\theta_{\rm r}-\theta^\prime_{\rm r}|$} is always below 10° except, again, for galaxies with hz/hR = 1/3 and in a few cases in those with hz/hR = 1/5.

We conclude this section by saying that as found for bars in Sect. 4.5, results from deprojected parameters seem in general reliable for galaxies with i ≤ 60°. The exception are the moderately inclined galaxies (i = 40 − 60°) with a larger disc thickness relative to the scale-length (S0 galaxies), whose deprojected ring parameters are in some cases not very accurate.

5. Comparison of ring properties in ARRAKIS with the data in the literature

In this section we compare the measured properties of rings with those reported in a set of significant papers in the literature that have samples in common with ours.

In several cases, significant discrepancies have been found between the ring diameters in ARRAKIS and those in the literature. In most of them, we found that this is because the features are classified in a different way in ARRAKIS and in the literature. For example, the feature with an ARRAKIS major diameter of 1.Mathematical equation: \hbox{$.\mkern-4mu^\prime$}48 in NGC 4736 was classified as an inner ring by de Vaucouleurs & Buta (1980). Here, this feature is considered as a nuclear ring because it is found inside a very broad bar/oval that was unnoticed by de Vaucouleurs & Buta (1980). The broad bar in NGC 4736 is here recognized as being surrounded by a subtle ring-lens 4.Mathematical equation: \hbox{$.\mkern-4mu^\prime$}48 in major diameter that was considered to be an outer lens in de Vaucouleurs & Buta (1980). Therefore, when comparing the inner ring in de Vaucouleurs & Buta (1980) with that in ARRAKIS, we are actually comparing two different features. Such features with a wrong classification appear as outliers in Figs. 1317 and have not been considered for the statistics in this section.

5.1. ARRAKIS and de Vaucouleurs & Buta (1980)

Thumbnail: Fig. 13 Refer to the following caption and surrounding text. Fig. 13

Comparison of the angular diameters of ARRAKIS rings with those in VB80. The line corresponds to a linear fit to the data points in the plot. The outliers due to the wrong identification of the resonance to which a ring is linked in VB80 are marked with asterisks and are excluded from the fit. The numbers in the top-left corner indicate the number of points considered in the fit and their correlation coefficient.

De Vaucouleurs & Buta (1980, hereafter VB80) compiled a catalogue that includes the diameter of outer and inner rings in 532 bright galaxies. The S4G and the VB80 samples have 303 galaxies in common.

We compared the sizes of the rings listed both in ARRAKIS and VB80. For this, we performed a linear least-squares fit of the major and minor axis diameter measurements in the two surveys. The fit takes into account the errors both in the ARRAKIS and the VB80 measurements. The ARRAKIS diameter errors were considered to follow the internal error function in Eq. (1). VB80 did not quantify their errors. Since their data are collected from photographic plates, we considered that their errors are probably similar to those in the CSRG, and therefore we used the CSRG internal error function for their diameters.

The fit we obtained is dr,Dr(ARRAKIS)=0.013±0.006+(1.021±0.003)(dr,Dr)(VB80)Mathematical equation: \begin{eqnarray} d_{\rm r},D_{\rm r}({\rm ARRAKIS})&= &0.\mkern-4mu^{\prime}013\pm0.\mkern-4mu^{\prime}006 \nonumber\\ &&\quad+(1.021\pm0.003)(d_{\rm r},D_{\rm r}) (\rm VB80) \end{eqnarray}(9)with a correlation factor r = 0.989. This means that the agreement between the measurements in ARRAKIS and in VB80 is very good.

5.2. ARRAKIS and Buta & Crocker (1993)

Thumbnail: Fig. 14 Refer to the following caption and surrounding text. Fig. 14

As in Fig. 13, but with data from BC93.

Buta & Crocker (1993, hereafter BC93) studied galaxies with nuclear components, mostly nuclear rings, but also lenses and spirals. In BC93, galaxies with nuclear features also had their inner and outer features classified. The BC3 catalogue lists 64 galaxies, 37 of which are included in the S4G. Figure 14 compares the sizes of the features measured in ARRAKIS with those in BC93.

As with the VB80 data, we performed a least-squares fit to compare the BC93 data with ours. Again, the CSRG internal error function was used to describe the errors in the diameters in BC3. The fit gives dr,Dr(ARRAKIS)=0.008±0.016+(1.016±0.006)(dr,Dr)(BC93)Mathematical equation: \begin{eqnarray} d_{\rm r},D_{\rm r}({\rm ARRAKIS})&=&-0.\mkern-4mu^{\prime}008\pm0.\mkern-4mu^{\prime}016 \nonumber\\ &&\quad+(1.016\pm0.006)(d_{\rm r},D_{\rm r}) (\rm BC93) \end{eqnarray}(10)with a correlation factor r = 0.992.

5.3. ARRAKIS and the CSRG

Thumbnail: Fig. 15 Refer to the following caption and surrounding text. Fig. 15

Top-left panel: as in Fig. 13, but with data from the CSRG. Top-right panel: comparison of the PA offset between the major axis of bars and that of rings in the CSRG and ARRAKIS. Bottom panels: difference in the PA offsets between the bar and the ring major axis as a function of the ring size and of the ring axis ratio. In the three last panels, only points for barred galaxies with ϵd ≤ 0.5 are presented.

The CSRG includes 3692 galaxies that host outer and inner rings and lenses south of declination δ = −17°. The CSRG has 120 galaxies in common with the S4G.

In the top-left panel of Fig. 15 we compare the size of a feature when it is identified in both the CSRG and ARRAKIS. A linear fit to the data accounting for the ARRAKIS and CSRG interal error functions at measuring diameters yields dr,Dr(ARRAKIS)=0.018±0.011+(0.994±0.005)(dr,Dr)(CSRG),Mathematical equation: \begin{eqnarray} d_{\rm r},D_{\rm r}({\rm ARRAKIS})&=&-0.\mkern-4mu^{\prime}018\pm0.\mkern-4mu^{\prime}011 \nonumber\\ &&\quad+(0.994\pm0.005)(d_{\rm r},D_{\rm r}) (\rm CSRG) , \end{eqnarray}(11)and a correlation factor r = 0.992, again indicating excellent agreement.

The CSRG describes the projected ring orientation as the PA offset between the bar and the ring major axis. ARRAKIS has such data only for galaxies with qd > 0.5 because we considered more inclined galaxies to have unreliable bar axis ratio determinations (Sect. 4.5). The correlation between the ring orientation values for the CSRG and ARRAKIS is not as tight as it is for the angular sizes (top-right panel in Fig. 15). This is probably due to the analogue procedure used for building the CSRG. Indeed, it is conceivable to obtain accurate results on ring diameters using a magnifying device, but the determination of the major axis of bars and especially rings is doomed to be much more subjective.

The difference between the CSRG PAr − PAb values and ours is plotted in the bottom-left and bottom-right panels of Fig. 15 as a function of the ring size and the ring axis ratio. The differences in PAr − PAb are larger than our internal error for PAr, which is generally below 10° for rings with Dr > 3′ and/or qr < 0.7 (Fig. 8).

5.4. ARRAKIS and AINUR

AINUR contains the most complete catalogue of nuclear rings to date, mostly relying on Hubble Space Telescope images that in some cases have an angular resolution as high as ~0.′′Mathematical equation: \hbox{$.\!\!^{\prime\prime}$}1. Because of that, it contains detailed information of angularly small rings that cannot be expected to be described this thoroughly in ARRAKIS. Sixty out of 107 galaxies in AINUR are in the S4G sample. Of these 60 galaxies 26 are reported here to have a nuclear ring.

When comparing the major axis diameter of features classified as nuclear rings both in AINUR and ARRAKIS, we obtain dr,Dr(ARRAKIS)=0.022±0.010+(0.858±0.029)(dr,Dr)(AINUR),Mathematical equation: \begin{eqnarray} d_{\rm r},D_{\rm r}({\rm ARRAKIS})&=&0.\mkern-4mu^{\prime}022\pm0.\mkern-4mu^{\prime}010 \nonumber\\ &&\quad+(0.858\pm0.029)(d_{\rm r},D_{\rm r}) (\rm AINUR) , \end{eqnarray}(12)with a correlation factor r = 0.983. Here, the internal error functions for the diameters are those in Eq. (1) both for AINUR and ARRAKIS. We chose this error function for AINUR because, as for ARRAKIS, the ring measurements were made on digital images. This fit is much poorer than those found for VAU80, BU93, CSRG, and NIRS0S. This is probably because of the difficulty found in measuring the properties of features that are often barely resolved in the S4G. The difference may also reflect that the procedures used to measure the ring properties in the two works are different.

5.5. ARRAKIS and NIRS0S

Thumbnail: Fig. 16 Refer to the following caption and surrounding text. Fig. 16

As in Fig. 13, but with data from AINUR.

NIRS0S is a ground-based survey of 206 nearby early-type disc galaxies with a sample dominated by S0s. The survey was produced using the Ks band. NIRS0S does not reach as deep as the S4G but has a better angular resolution (typical pixel resolution of 0.′′Mathematical equation: \hbox{$.\!\!^{\prime\prime}$}3 and typical seeing around 1″). NIRS0S and the S4G have 93 galaxies in common.

The ring sizes measured in NIRS0S agree very well with ours (Fig. 17). When comparing the ring diameters from ARRAKIS and NIRS0S (in both cases we use the internal error function from Eq. (1) because in both cases the rings are measured on digital images), we obtain the following excellent linear fit dr,Dr(ARRAKIS)=0.006±0.009+(0.993±0.005)(dr,Dr)(NIRS0S),Mathematical equation: \begin{eqnarray} d_{\rm r},D_{\rm r}({\rm ARRAKIS})&=&0.\mkern-4mu^{\prime}006\pm0.\mkern-4mu^{\prime}009 \nonumber\\ &&\quad+(0.993\pm0.005)(d_{\rm r},D_{\rm r}) (\rm NIRS0S), \end{eqnarray}(13)and the correlation factor is r = 0.988.

Figure 17 also shows that the agreement in the measured position angle of the ring major axis is very good and much better than when comparing this paper with the CSRG. One possible reason is that NIRS0S is a digital survey where PAr can be measured more easily. The second reason is that in the CSRG the position angle difference between the ring and the bar major axis was measured. This measurement includes two errors: that related to the orientation of the ring, and that related to the orientation of the bar, and thus causes larger discrepancies than those found when comparing NIRS0S with this paper. As we found when we compared ARRAKIS with the CSRG and from our internal errors, the uncertainty in the orientation measurement increases for smaller and/or rounder rings.

6. Results

We recall that in this paper rings refers to the set including both open pseudorings and closed features. Here, the set including only closed features is referred to as closed rings.

6.1. Fraction of rings as a function of the Hubble stage

Thumbnail: Fig. 17 Refer to the following caption and surrounding text. Fig. 17

As in Fig. 15, but with data from NIRS0S.

Thumbnail: Fig. 18 Refer to the following caption and surrounding text. Fig. 18

Top panels: stage distribution of the S4G sample (black line), of galaxies hosting outer rings (continuous darker blue line), inner rings (dashed darker green line), and nuclear rings (dash-point red line). Lighter blue and green lines indicate histograms considering only galaxies hosting closed outer and closed inner rings, respectively. Bottom panels: fraction of galaxies with resonant features for a given stage colour-coded as in the two top panels. Left panels are for the whole sample and right panels for galaxies with a disc ellipticity ϵd ≤ 0.5. The numbers in the top panels indicate the number of galaxies included in the histograms that corresponds to the colour and line pattern of the adjacent box.

Stage classification is commonly described by a numerical code ranging from –5 to 10 corresponding to the sequence going from E to I galaxies. However, in some cases, a more detailed classification can be made and is then denoted with intermediate stages such as SbcMathematical equation: \hbox{${\underline{\rm c}}$} or ScMathematical equation: \hbox{${\underline{\rm c}}$}d, which in turn are codified as T = 4.5 and T = 5.5. In the few particular cases for which such a classification is provided, we rounded up the stage so that, for example, SbcMathematical equation: \hbox{${\underline{\rm c}}$} becomes Sc (T = 5) and ScMathematical equation: \hbox{${\underline{\rm c}}$}d becomes Scd (T = 6).

Some galaxies in Buta et al. (in prep.) have not been classified into categories that fit in the traditional Hubble fork. Indeed, based on the van den Bergh (1976) hypothesis that S0 galaxies form a sequence from early to late galaxies just like normal disc galaxies do, some galaxies have been classified as S0b, S0bc, S0c, S0cd, S0d, and S0m. This is true for 36 S4G galaxies, three of which host rings. These galaxies were included in the bin corresponding to their counterpart in the traditional sequence (e.g., S0b galaxies were grouped together with Sb galaxies).

A few galaxies (12) have a double stage (for details on double-stage galaxies see Buta et al. 2010), five of which are ringed. These galaxies were not included in the stage statistics. We also excluded the dwarf elliptical galaxies from the results in this subsection (34 galaxies, none of which is ringed). Finally, we also excluded 12 S4G galaxies that are so difficult to classify that there were assigned no stage. None of these galaxies is ringed.

The distribution of resonant features varies greatly with the stage of the galaxies, as seen in Fig. 18. The bottom-row panels in that figure have 1 − σ (68%) confidence levels calculated using binomial distribution statistics, Δ(p)=p(1p)n,Mathematical equation: \begin{equation} \label{epoisson} \Delta(p)=\sqrt{\frac{p\left(1-p\right)}{n}}, \end{equation}(14)where p is the probability of a galaxy in a given stage bin to have a specific type of ring and n the total number of galaxies in that stage bin. All the uncertainties given in this section were calculated using this expression. When the data in this section are quantitatively compared with the data in other papers, we verified that the uncertainties in those papers were computed in the same way as we did.

Inclination has to be taken into account before discussing in detail the stage distributions statistics. Indeed, it is more likely for inclined galaxies to have unidentified or misinterpreted rings. We found that of the whole sample of galaxies, 31% have some resonant feature, but that this fraction is increased to 41% for the subsample with ϵd ≤ 0.5. These numbers indicate that as much as ~ 50% of the resonant features are missed in inclined galaxies. This effect is especially pronounced for inner features, most likely because they are found in regions of galaxies that are hard to interpret because of bars, spiral arms, and/or intense star formation regions.

6.1.1. Outer rings

The stage distribution of outer rings based on the S4G subsample with ϵd ≤ 0.5 indicates the following (see also continuous blue lines in Fig. 18):

  • They are found in 16 ± 1% of S4G galaxies.

  • They are mostly found at − 1 ≤ T ≤ 2 where they appear in over 40% of galaxies. This number is similar to the 53 ± 5% fraction of outer features found in NIRS0S for stages − 1 ≤ T ≤ 1 (Laurikainen et al. 2011).

  • For T ≥ 4 they are quite rare, and their frequency drops below 10%.

  • Outer closed rings (continuous light blue lines) are most frequent for T ≤ 0, with a peak frequency of ~ 50% at T = −1. Above T = 0 their frequency drops fast with increasing stage. This behaviour is also seen in NIRS0S.

  • Outer closed rings and closed ring-lenses account for 100% of the outer features for T ≤  − 1. This is a difference with NIRS0S: the fraction of pseudorings for T ≤ 1 NIRS0S galaxies is non-zero, though still rather small, 19 ± 7%. Of the five NIRS0S galaxies with T ≤  − 1 and with an outer pseudoring, two are included in the S4G sample. These two galaxies have been classified with the same stage in NIRS0S and Buta et al. (in prep.), which means that the difference between NIRS0S and ARRAKIS probably caused by the different appearance of outer features at different wavelengths and not by problems in the stage classification.

Buta & Combes (1996) found qualitatively similar results using RC3 data. Using data from VB80, Elmegreen et al. (1992) also found that earlier-type galaxies are more likely to have outer rings.

Thumbnail: Fig. 19 Refer to the following caption and surrounding text. Fig. 19

Top panels: family distribution of the S4G sample and ringed galaxies colour- and line-coded as in Fig. 18. Bottom panels: fraction of galaxies with rings for a given family colour- and line-coded as in the two top panels. Left panels are for the whole sample and right panels for galaxies with a disc ellipticity ϵd ≤ 0.5. The numbers in the top panels indicate the number of galaxies included in the histogram that corresponds to the colour- and line-pattern of the adjacent box.

6.1.2. Inner rings

The stage distribution of inner rings based on the S4G subsample with ϵd ≤ 0.5 indicates the following (see also dashed green lines in Fig. 18):

  • They are found in 35 ± 1% of S4G galaxies.

  • They have a frequency of over 40% for stages − 1 ≤ T ≤ 6. The distribution is not very peaked and has its maximum for − 1 ≤ T ≤ 3 (more than 60% of these galaxies have inner features).

  • Their frequency drops below 20% for galaxies with T ≤  − 3 and T ≥ 8. They are therefore very frequent in most disc galaxy stages.

  • The peak in the inner closed ring frequency is found at T = −1 (light green lines) as also found in NIRS0S. The inner closed ring frequency distribution is shifted towards earlier types than that of the inner ring distribution.

  • Inner closed rings are more frequent than inner pseudorings for T ≤ 1. This agrees very well with the results in NIRS0S. There the fraction of inner features that are inner closed rings in galaxies with − 3 ≤ T ≤  − 1 is 75 ± 7%, we found 81 ± 6%. For galaxies with types 0 ≤ T ≤ 1 NIRS0S reports a fraction of inner closed rings among inner features of 38 ± 8%, we found 40 ± 5%.

These results differ from those presented in Buta & Combes (1996), which were based on RC3 data. These authors found the inner closed ring fraction to be roughly constant for all types of disc galaxies with T ≤ 5 (here the distribution is peaked at T = −1) and also that they are more frequent than pseudorings for T ≤ 3 (here, this only occurs for T ≤  − 1). These differences are too large to be a consequence of the one stage shift caused by classifying galaxies in 3.6  μm instead of the B band.

The stage distribution of outer and inner rings is quite different. While the outer ring distribution drops between types T = 3 and T = 4, the inner rings distribution does so between types T = 7 and T = 8.

6.1.3. Nuclear rings

Nuclear rings (dash-point red lines in Fig. 18) are found in galaxies with − 1 ≤ T ≤ 6, which is similar to that obtained in AINUR (− 3 ≤ T ≤ 7). However, the peak in the distribution (T = 2) does not coincide with those in AINUR (T = −1 and T = 4). These differences are probably not significant, because the number of nuclear rings here is a factor of three smaller than in AINUR.

In AINUR nuclear rings were found in ~ 20% of galaxies with stages − 3 ≤ T ≤ 7. A similar fraction was given by Knapen (2005). However, the fraction of low inclination (ϵd ≤ 0.5) S4G galaxies that host nuclear rings is 5 ± 1% in the same range of stages. The reason for the discrepancy is that, because of angular resolution problems, many of the smaller rings are undetected or are classified as nuclear lenses in the S4G.

6.2. Fraction of rings as a function of the galaxy family

Of the 2348 S4G galaxies that have been classified in Buta et al. (in prep.), 1725 are disc galaxies (− 3 ≤ T ≤ 9) to which a family has been assigned (SA, SAMathematical equation: \hbox{${\underline{\rm A}}$}B, SAB, SABMathematical equation: \hbox{${\underline{\rm B}}$}, SB). Some disc galaxies (233) have no assigned family and are mostly close to edge-on galaxies without obvious signatures of edge-on bars such as boxy inner isophotes. The ring distribution with family is shown in Fig. 19.

6.2.1. Outer rings

The fraction of galaxies with ϵd ≤ 0.5 that host outer rings (blue continuous lines in Fig. 19) increases steadily from SA (15 ± 2%) to SABMathematical equation: \hbox{${\underline{\rm B}}$} (32 ± 7%). For stronger bars (SB), it drops to 20 ± 2%.

The distribution of outer closed rings (light blue continuous lines) is qualitatively similar: the fraction of galaxies that host closed rings rises from 7 ± 2% to 20 ± 6% between SA and SABMathematical equation: \hbox{${\underline{\rm B}}$} and then drops down to 5 ± 1% for the SB family.

6.2.2. Inner rings

The inner ring family distribution is quite different from that for the outer rings (green dashed lines in Fig. 19). The fraction of galaxies that host inner rings remains roughly constant from SA to SAB at a level of ~ 40% and then suddenly increases to 64 ± 7% for SABMathematical equation: \hbox{${\underline{\rm B}}$} galaxies. The fraction of SB galaxies that host inner rings is similar to that in SA to SAB galaxies.

We also find that galaxies with no bars or weak bars (SA and SAMathematical equation: \hbox{${\rm{\underline A}}$}B) have a higher fraction of inner closed rings (light green dashed lines) than galaxies with stronger bars.

6.2.3. Nuclear rings

The number of nuclear rings in ARRAKIS is small and thus the validity of the statistics is uncertain. However, we can see that the nuclear feature fraction increases from families SA to SAB and then remains roughly constant (dash-point red lines in Fig. 19).

6.3. Ring shapes

6.3.1. Projected ring shapes

The top-left panel in Fig. 20 shows the projected axis ratio of resonance rings, under the assumption that they can be described by an ellipse coplanar with the disc of the galaxy. It is qualitatively similar to that found in the CSRG (top panels of its Fig. 7): the distribution grows gently from zero and has a maximum for quite round rings (0.8 < qr ≤ 0.9 for inner and outer rings here and 0.7 < qr ≤ 0.8 in the CSRG). It then drops abruptly for even rounder rings.

The statistical expectation is that if rings were intrinsically circular and sitting in perfectly circular discs, with their rotation axis with random orientations, the projected ring axis ratio probability density function would be uniform. As explained in the CSRG, the reason to justify the lack of rings with a low apparent axis ratio is that they become increasingly harder to identify in inclined galaxies. It is interesting to see that just like in the CSRG, for the axis ratios close to qr = 0, outer rings show a behaviour closer to the statistical expectation than inner rings. This is because they are found in outer parts of the galaxy that are less messy and easier to interpret than inner regions when seen close to edge-on. We do not observe the distribution to be uniform near qr = 1 because there is a dip in the observed distribution of rings. The reason why we do not see more rings that appear nearly round in projection is that they are not intrinsically circular, as described in the next subsubsection.

6.3.2. Deprojected ring shapes

One of the improvements of this study over the largest systematic study of rings conducted so far, the CSRG, is that the S4G P4 provides us with reliable orientations of the galaxies. This allows us to obtained intrinsic ring shapes and orientations, as explained in Sect. 4.4.

In the CSRG, the deprojected ring axis ratio distribution was studied under several assumptions and using a statistical treatment. One of the assumptions was that the actual shape of the deprojected axis ratio distribution is Gaussian, with a peak at ⟨ qr,0 ⟩ and a dispersion σ. With our deprojected data we do not need this assumption.

Table 3

Number of galaxies in the histograms in Figs. 2022 and parameters of the Gaussian fits to the qr,0 distributions.

The deprojected ring distribution is shown in the bottom panels of Fig. 20. We overlay Gaussian fits to show how well the Gaussian distribution hypothesis works. The parameters of the Gaussian fits in this section can be found in Table 3. Although the fitted Gaussians are nearly the same when fitting rings in all galaxies and when fitting them only for galaxies with ϵd ≤ 0.5, the distributions are slightly different in the low-qr wing; indeed, when considering all galaxies, the left wing for outer and inner rings extends farther than when considering only galaxies with ϵd ≤ 0.5. This is because for close to edge-on galaxies deprojections based on the shape of outer isophotes of discs become unreliable due to the non-zero thickness of discs (see Sect. 4.6) and/or the presence of extended bulges and haloes. Thus, for some galaxies, the obtained deprojection parameters can be considered to be tentative at best and may cause the calculated deprojected ring shapes to be unrealistically stretched. A notorious case is NGC 4594 (the Sombrero galaxy), where outer isophotes have an ellipticity of about ϵd = 0.58 even though the real figure is probably closer to ϵd = 0.83 (see, e.g., Jardel et al. 2011). All but one ring with deprojected axis ratio qr,0 ≤ 0.4 are found in galaxies with fitted disc ellipticity ϵd > 0.5 (IC 5264, NGC 4594, NGC 5078, NGC 5746, NGC 5777, and NGC 5900). The exception is NGC 986, a galaxy with ϵd = 0.1 and a peculiar elongated nuclear ring. Because this effect may also occur (although in a less obvious way) in other inclined galaxies, we continue our analysis of intrinsic ring shapes based only on galaxies with ϵd ≤ 0.5.

Thumbnail: Fig. 20 Refer to the following caption and surrounding text. Fig. 20

Distribution of the resonance ring axis ratios colour- and line-coded as in Fig. 18. The left-hand plots are for the whole ARRAKIS sample and the right-hand plots correspond to rings in host galaxies with ϵd ≤ 0.5. The top-row plots show the distribution of projected axis ratios, the bottom row shows the distribution of deprojected ones.

Thumbnail: Fig. 21 Refer to the following caption and surrounding text. Fig. 21

Distribution of the resonance ring deprojected axis ratios colour- and line-coded as in Fig. 18 for different galaxy families and for ϵd ≤ 0.5. The left panel shows SA galaxies, the middle one SAMathematical equation: \hbox{${\underline{\rm A}}$}B to SABMathematical equation: \hbox{${\underline{\rm B}}$} galaxies, the right panel SB galaxies.

Thumbnail: Fig. 22 Refer to the following caption and surrounding text. Fig. 22

Distribution of the resonance ring deprojected axis ratios colour- and line-coded as in Fig. 18 for different galaxy stage ranges and for ϵd ≤ 0.5. The left panel represents galaxies with − 5 ≤ T ≤ 0, the middle panel galaxies with 1 ≤ T ≤ 3, the right panel galaxies with 4 ≤ T ≤ 10.

Based on the fitted ⟨ qr,0 ⟩, we find that outer rings are generally rounder than the inner ones. More specifically, for the ARRAKIS sample we find ⟨ qr,0(O) ⟩  = 0.88 and ⟨ qr,0(I) ⟩  = 0.80, respectively. Outer closed rings have the same average ⟨ qr,0(O) ⟩ as outer features in general, but inner closed rings are on average slightly rounder than the average for inner features.

Rings become systematically more elliptical when moving along the family sequence from SA to SB (Fig. 21). However, the dispersion in each of the Gaussian distributions is always wide enough to allow very round rings to exist, even for SB galaxies. Fits for outer rings in SA galaxies are not shown because they yield that the centre of the Gaussian would be located at ⟨ qr,0(O) ⟩  > 1.

Inner rings tend to become more elliptical with increasing galaxy stage. This trend is not found for the outer features, although this might be explained by the low number of them found at stages T ≥ 4.

6.4. Ring orientations

In this subsection we describe the orientations of the rings with respect to bars. We focus only on barred galaxies for which we are able to accurately measure their orientation (that is, most of those in galaxies with ϵd ≤ 0.5). We compared the PA of the major axis of the ring, PAr, and the bar, PAb. We denote the difference between those major axis as PAr − PAb. However, because we define it to be in the first quadrant, it should be formally written as minimum(|PAr − PAb|,|PAb − PAr|). Since PAr is ill-defined for rings that are almost round in projection, we only studied features with a projected axis ratio qr ≤ 0.85.

Because for deprojected rings and bars the concept of PA is no longer applicable, we defined the deprojected orientation of a ring or a bar to be the counter-clockwise difference in angle between the orientation of its major axis and the line of nodes, θr and θb. Thus, for deprojected galaxies we denote the orientation difference between a ring and the bar as θr − θb [although it is defined as minimum(|θr − θb|,|θb − θr|)]. Because θr is ill-defined for rings that are almost round in deprojection, we only studied features with a deprojected axis ratio qr,0 ≤ 0.85. In Fig. 23 we present the distributions of PAr − PAb and θr − θb.

For the outer rings PAr(O) − PAb there is some hint that the distribution has two mild peaks at PAr(O) − PAb = 0° and PAr(O) − PAb = 90° divided by a shallow valley. This behaviour is similar to that found in the CSRG, although there the peak at PAr(O) − PAb = 0° has more contrast; this may be due to our relatively low number of outer features (our plot has five times fewer objects than Fig. 7g in the CSRG).

The distribution for inner rings has a large peak at PAr(I) − PAb = 0° and the distribution drops until it stabilises between PAr(I) − PAb = 50° and PAr(I) − PAb = 90°.

In deprojected galaxies, the outer rings have two preferred orientations, namely parallel and perpendicular to bars [θr(O) − θb = 0° and θr(O) − θb = 90°], which can be associated with the R2 and R1 ring types in the simulations of Schwarz (1981, 1984) as well as with the predictions from non-deprojected data in the CSRG.

Table 4

Number of galaxies in the histograms in Figs. 2325 and parameters of the Gaussian fits to the qr,0 distributions.

The intrinsic inner ring orientation distribution has a clear peak parallel to the bar [θr(I) − θb = 0°], as was previously hinted at in other works (e.g., the CSRG, de Vaucouleurs et al. 1964; Schwarz 1981, 1984; Buta 1986b; Athanassoula et al. 2009b). However, we also found that a significant fraction of rings have random orientations with respect to the bar, as indicated by the flat distribution for θr(I) − θb > 30°. Such a randomly oriented inner ring fraction, although sometimes suspected on the basis of a few individual cases of obvious bar/ring misalignment [ESO 565-11 (Buta et al. 1995), NGC 309 (Buta et al. 2007), NGC 4319 (Sulentic & Arp 1987), and NGC 6300 (Buta 1987)] has never been described before.

We fitted the outer ring θr(O) − θb distribution with the superposition of two Gaussian curves centred at θr(O) − θb = 0° and θr(O) − θb = 90°, as assumed in the CSRG. For the inner rings, we fitted the superposition of a Gaussian centred at θr(I) − θb = 0°, describing the population of inner features parallel to the bar and a constant distribution representing the population of rings oriented at random with respect to the bar. The fitted parameters and the number of galaxies in each histogram are tabulated in Table 4. The fit also provides the fraction of rings that belong to the components parallel and anti-parallel to the bar for outer rings (w and w90°) and parallel and oriented at random with respect to the bar for inner rings (w and wc). We found that the fraction of outer rings aligned parallel to the bar is 35 ± 18% and that of features oriented perpendicular to the bar is 65 ± 39%. For inner rings, we found that some 48 ± 12% are aligned parallel to the bar and the other 52 ± 10% have random orientations.

The distribution of the intrinsic orientations of outer features does not change much when looking separately at weakly and strongly barred galaxies (Fig. 24). The inner ring distribution changes more, since the width of the distribution of galaxies parallel to the bar decreases from 17 ± 1° for galaxies with families SAMathematical equation: \hbox{${\underline{\rm A}}$}B to SABMathematical equation: \hbox{${\underline{\rm B}}$} to only 9 ± 1° for SB galaxies.

The outer ring orientation distribution is also independent of the galaxy stage (Fig. 25). But again, this is not the case for the inner ring distribution. Indeed, the later the stage, the larger the fraction of inner rings oriented at random with respect to the bar. This fraction increases from 28 ± 28% (− 5 ≤ T ≤ 0) and 31 ± 20% (1 ≤ T ≤ 3) to 75 ± 10% for galaxies with 4 ≤ T ≤ 10. For inner rings in late-type stages there is even some hint of a preferred orientation perpendicular to the bar (right panel in Fig. 25).

Thumbnail: Fig. 23 Refer to the following caption and surrounding text. Fig. 23

Distribution of the projected resonance ring PA differences with respect to the bar (left panel) and ring orientation with respect to the bar in the deprojected galaxies (right panel). The histograms are colour- and line-coded as in Fig. 18. The plots only include rings with qr ≤ 0.85 (left panel) and qr,0 ≤ 0.85 (right panel) and in host galaxies with ϵd ≤ 0.5. The numbers in the left panel indicate the number of galaxies included in the histogram corresponding to the colour of the adjacent box.

Thumbnail: Fig. 24 Refer to the following caption and surrounding text. Fig. 24

Distribution of the resonance ring deprojected major axis angle difference with the bar colour- and line-coded as in Fig. 18 for different galaxy families and for ϵd ≤ 0.5. The left panel is for SAMathematical equation: \hbox{${\underline{\rm A}}$}B to SABMathematical equation: \hbox{${\underline{\rm B}}$} galaxies, the right panel for SB galaxies. The plots only include rings with qr,0 ≤ 0.85.

Thumbnail: Fig. 25 Refer to the following caption and surrounding text. Fig. 25

Distribution of the resonance ring deprojected major axis angle difference with the bar colour- and line-coded as in Fig. 18 for different galaxy stage ranges and for ϵd ≤ 0.5. The left panel represents galaxies with − 5 ≤ T ≤ 0, the middle panel galaxies with 1 ≤ T ≤ 3, the right panel galaxies with 4 ≤ T ≤ 10. The plots only include rings with qr,0 ≤ 0.85.

Table 5

Number of galaxies in the histograms in Figs. 2628 and average and standard deviation of the absolute ring deprojected diameters for several ARRAKIS subsamples.

6.5. Absolute ring sizes

Absolute ring diameters were obtained using the average of the redshift-independent distances provided by NED as the host galaxy distance. If such a distance measurement was not available, we used the NED Hubble-Lemaître flow distance corrected for the effects of the Virgo cluster, the Great Attractor, and the Shapley cluster (Hubble-Lemaître constant H0 = 73   km   s-1   Mpc-1). Because the S4G sample selection was based on uncorrected flow distances, this means that some of the galaxy distances listed in Appendix A exceed 41 Mpc. Of these galaxies with rings, only six are farther away than 60 Mpc (ESO 576-1, NGC 4722, NGC 5600, PGC 47721, and UGC 5814). Such high distances might indicate either inaccurate redshift-based or redshift-independent distance determinations. However, since these galaxies are only a few, we did not exclude them from the study of absolute ring sizes.

Here, we define the size of a ring to be its major axis diameter. That is, Dr in the projected case and Dr,0 in the deprojected case. Because rings are in general almost circular, their absolute size distribution does not vary much when comparing the projected and the deprojected sizes (Fig. 26). Moreover, because the ring size is easier to measure than its orientation, the size distribution does not vary much when studying our whole sample or a subsample restricted by disc ellipticity. The averages and the standard deviations of each deprojected distribution in the plots are listed in Table 5.

The average absolute size for each of the three ring flavours is nearly independent of galaxy family (Fig. 27 and Table 5). It is noteworthy that the dispersion in the size of inner rings in SA galaxies is higher than that in barred galaxies. This high dispersion can also be seen by examining the smallest and largest rings in the top panel in Fig. 27; the smallest resonance feature in SA galaxies is an inner pseudoring. This is also the case for the third-largest feature in this panel. Such a behaviour is not seen in barred galaxies, where the small- and large-size tails are dominated by nuclear and outer rings, respectively. A possible explanation of this high dispersion in the size of inner features found in SA galaxies is that a fraction of outer and nuclear resonant features have been misclassified as inner rings.

Outer and inner rings in galaxies with stages 4 ≤ T ≤ 10 are on average much smaller than those found in earlier stages (Fig. 28). This effect is not seen for nuclear features, but this may well be because some of them are too small to be resolved in the S4G.

6.6. Ring sizes relative to the size of the galaxy

One of the outputs of the S4G pipeline 3 (Muñoz-Mateos et al., in prep.) is the diameter at the μ3.6  μm = 25.5   mag   arcsec-2 level, D25.5. This diameter can be used as an indicator of the size of the disc, although in a few cases it may be overestimating its true size because of the effect of bright extended spheroidal components (an obvious case probably is the Sombrero galaxy). Since D25.5 is located in the outskirts of the galaxy, in the region where its orientation is typically measured, it does not need to be deprojected. D25.5 is available for all sample galaxies but two, NGC 253 and NGC 4647. For NGC 253 this is because the galaxy is tightly fitted in the S4G frame and the D25.5 diameter is close to the limits of the frame or even beyond. For NGC 4647 this is because the galaxy isophotes are distorted because of a close galaxy in the same frame.

Thumbnail: Fig. 26 Refer to the following caption and surrounding text. Fig. 26

Distribution of the resonance ring absolute diameters. The top row shows the projected diameters and the bottom row the deprojected ones. The left column shows all galaxies, the right column galaxies with ϵd ≤ 0.5. The histograms are colour- and line-coded as in Fig. 18.

Thumbnail: Fig. 27 Refer to the following caption and surrounding text. Fig. 27

Distribution of the resonance ring deprojected major axis absolute diameter colour- and line-coded as in Fig. 18 for different galaxy families and for ϵd ≤ 0.5. The left panel shows SA galaxies, the middle one SAMathematical equation: \hbox{${\underline{\rm A}}$}B to SABMathematical equation: \hbox{${\underline{\rm B}}$} galaxies, the right panel SB galaxies.

Thumbnail: Fig. 28 Refer to the following caption and surrounding text. Fig. 28

Distribution of the resonance ring deprojected major axis absolute diameter colour- and line-coded as in Fig. 18 for different galaxy stage ranges and for ϵd ≤ 0.5. The left panel represents galaxies with −5 ≤ T ≤ 0 galaxies, the middle panel galaxies with 1 ≤ T ≤ 3, the right panel galaxies with 4 ≤ T ≤ 10.

The distribution of projected and deprojected relative radii of the rings, Dr/D25.5 and Dr,0/D25.5, (Fig. 29) shows that these magnitudes are much more useful than Dr and Dr,0 for separating the three flavours of resonance features. The overlap in radius of the different types of features is much smaller than that found when looking at absolute radii because distributions are much more peaked. Indeed, comparing Tables 5 and 6 shows that for outer rings in galaxies with ϵd ≤ 0.5 the ratio between the peak value of the distribution and its dispersion is [Dr,0(O)/D25.5]/σ[Dr,0(O)/D25.5] = 3.2, which is almost twice higher than Dr,0(O)/σ[Dr,0(O)] = 1.6. For inner rings the values are [Dr,0(I)/D25.5]/σ[Dr,0(I)/D25.5] = 2.2 and Dr,0(I)/σ[Dr,0(I)] = 1.5.

This effect is not seen for nuclear rings; a reason may be that outer and inner rings are associated to a single resonance or manifold structure that is found at a given radius relative to the bar (with small variations due to the bar pattern speed and the galaxy rotation curve). Instead, nuclear rings are associated to the range of radii between the two ILRs, or to the range of radii between the centre and the ILR, in case of galaxies with only one such resonance. A complementary explanation is that we are missing all nuclear features below a given angular size. If enough galaxies of a possible Dr,0(N)/D25.5 peak were smaller than that threshold, the scatter of the nuclear ring absolute size distribution would not be reduced by much when using the ring diameters normalised with D25.5.

When segregating galaxies according to their family (Fig. 30), we found a large overlap between the range of relative radii occupied by the inner and nuclear rings in SA galaxies. Such a large overlap is not seen in barred galaxies and may indicate, as commented before when looking at the absolute radii of rings, that some nuclear rings may have been classified as inner features in unbarred galaxies. We also found that the peak in the inner ring relative size distribution increases systematically with increasing bar strength. This is probably because of a slight tendency of stronger bars (SB) to be longer on average relative to galaxy size than weaker bars (SAMathematical equation: \hbox{${\underline{\rm A}}$}B, SAB, SABMathematical equation: \hbox{${\underline{\rm B}}$}), at least for late-type galaxies. This was originally shown by Erwin (2005), based on the data of Martin (1995). Erwin (2005) used the RC3 R25 measurement as the galaxy size.

Finally, we find that the relative ring size distributions are not sensitive to galaxy stage (Fig. 31).

Thumbnail: Fig. 29 Refer to the following caption and surrounding text. Fig. 29

Distribution of the resonance ring deprojected major axis diameters relative to D25.5. The left column shows all galaxies, the right column galaxies with ϵd ≤ 0.5. The histograms are colour and line-coded as in Fig. 18.

6.7. Outer ring sizes relative to those of inner rings

Our sample contains 163 galaxies with both outer and inner features. We calculated the ratio of the major axis of these features, Dr,0(O)/Dr,0(I). Our sample has 19 galaxies with outer and inner features that also have more than one outer ring and/or more than one inner ring. When that was the case, the average of the major axis diameters of the outer (inner) features was used as the diameter of the outer (inner) feature.

The resulting diameter ratio distribution is represented in Fig. 32, colour- and line-coded according to different host galaxy families and stages. One galaxy, NGC 5033, has Dr,0(O)/Dr,0(I) = 17.5 and is beyond the horizontal limits of the plots. This high ratio may indicate that the innermost resonance feature in this unbarred galaxy is a nuclear and not an inner ring. In fact, this innermost feature in NGC 5033 is classified as a nuclear ring in AINUR.

In Fig. 32, the histograms for barred galaxies and those for stages − 5 ≤ T ≤ 3 have a shape that can be roughly approximated by a Gaussian, therefore we fitted them with that function. Other histograms (SA galaxies and galaxies with stages 4 ≤ T ≤ 10) have too few galaxies to be fitted. The histograms for SA galaxies are very flat and have no distinct peak. The results of the fits and the number of galaxies included in each histogram, are listed in Table 7.

We found that Dr,0(O)/Dr,0(I) is larger for weaker bars and also for earlier-type galaxies.

The peaks of the fitted distributions in Fig. 32 are always about Dr,0(O)/Dr,0(I) = 2, which is consistent with the CSRG, Kormendy (1979), (Athanassoula et al. 1982), and (Buta 1986a).

7. Discussion

7.1. Why is the stage distribution of inner and outer resonance features different?

Table 6

Number of galaxies in the histograms in Figs. 2931 and average and standard deviation of the ring deprojected diameters relative to D25.5 for several ARRAKIS subsamples.

In Sect. 6.1 we found that the distribution of stages (morphological type) for inner and outer rings is significantly different. Indeed, the outer ring fraction is high (above 20%) for − 1 ≤ T ≤ 3 before dropping at later stages, but the inner ring distribution only drops at T = 6 or T = 7 (see a schematic view of this in Table 8 where the stages with a frequency of rings one fourth that of the peak for that ring flavour are considered to rarely host rings). For stages below T = 3 outer rings are at least 40% as abundant as inner rings, but this ratio decreases for later stages. Thus, there is a significant under-abundance of outer rings for late-type galaxies (Fig. 33).

A possible justification for this effect can be found in the simulations by Combes & Elmegreen (1993), who compared models designed to mimic both early- and late-type spirals distinguished by steeply and slowly rising inner rotation curves, respectively. However, to what extent their galaxy models are realistic is a matter of debate, since their t = 0 models were sharply truncated at a radius of only a few disc scale-lengths (as little as 1.5 scale-lengths in some cases). Therefore, any explanation based on these simulations has to be taken with some caution. Combes & Elmegreen (1993) found that for early-type galaxies the CR radius is well inside the optical disc of the galaxy, but for later-type galaxies the CR is moved farther out. As a consequence, for a late-type galaxy, the OLR radius is typically found in a low-density region, and very little material is rearranged into a ring shape. Eventually, an outer feature forms when particles near the CR obtain angular momentum and are moved outwards, but this is a secular process that is even slower in late-type galaxies because regions near the CR have a lower particle density than that in earlier-type galaxies. Our results show that for this particular problem, the transition between an early- and a late-type disc galaxy is at T = 3. The connection discussed here between simulations and observational data was previously made by Combes & Elmegreen (1993).

Thumbnail: Fig. 30 Refer to the following caption and surrounding text. Fig. 30

Distribution of the resonance ring deprojected major axis relative to D25.5 colour- and line-coded as in Fig. 18 for different galaxy families and for ϵd ≤ 0.5. The left panel shows SA galaxies, the middle one SAMathematical equation: \hbox{${\underline{\rm A}}$}B to SABMathematical equation: \hbox{${\underline{\rm B}}$} galaxies, the right panel SB galaxies.

Thumbnail: Fig. 31 Refer to the following caption and surrounding text. Fig. 31

Distribution of the resonance ring deprojected major axis diameter relative to D25.5 colour and line-coded as in Fig. 18 for different galaxy stage ranges and for ϵd ≤ 0.5. The left panel is for − 5 ≤ T ≤ 0 galaxies, the middle panel is for 1 ≤ T ≤ 3 galaxies, and the right panel is for 4 ≤ T ≤ 10 galaxies.

Thumbnail: Fig. 32 Refer to the following caption and surrounding text. Fig. 32

Distribution of the ratios of the diameters of outer and inner rings. The left column shows all galaxies, the right column galaxies with ϵd ≤ 0.5. The of histograms are colour- and line-coded according to the host galaxy family (top panels) and stage (bottom panels). One galaxy, NGC 5033, has Dr,0(O)/Dr,0(I) = 17.5 and is beyond the horizontal limits of the plots.

7.2. Why is the family distribution of inner and outer resonance features different?

Table 7

Number of galaxies in the histograms in Fig. 32 and parameters of the Gaussian fits to the Dr,0(O)/Dr,0(I) distributions.

Table 8

Simplified behaviour of the probability of finding outer and inner rings for different galaxy stage ranges.

In Sect. 6.2 we showed that the outer and inner ring distributions differ in the range of families from SA to SAB. In that range, the fraction of galaxies that host inner rings is constant within the error bars, but that of galaxies that host outer features increases steadily (15 ± 2% for SA galaxies, 15 ± 4% for SAMathematical equation: \hbox{${\underline{\rm A}}$}B galaxies, and 22 ± 3% for SAB galaxies). A straightforward explanation for this effect is that outer rings do not form easily in unbarred galaxies. Indeed, weaker bars are likely to be less effective at redistributing material and angular momentum. It is therefore reasonable to assume that some have not yet had time to bring enough material from the CR region to the OR and, as a consequence, there is not enough material there to build an outer ring.

7.3. Rings in unbarred galaxies

Based on the information in Fig. 19 we found that 15 ± 2% of SA galaxies have an outer ring. This fraction increases to 21 ± 2% for galaxies with bars (SAMathematical equation: \hbox{${\underline{\rm A}}$}B, SAB, SABMathematical equation: \hbox{${\underline{\rm B}}$}, SB). For inner rings the values are 40 ± 3% and 44 ± 2%, respectively.

In the range − 1 ≤ T ≤ 3, which is where outer features are frequently found according to Table 8, outer rings are found in 29 ± 5% of the SA galaxies and in 49 ± 3% of the barred galaxies. In the range − 1 ≤ T ≤ 7, where most inner features are found, the fraction of SA galaxies with inner rings is 46 ± 4% and that of barred ones hosting them is 59 ± 2%.

These numbers indicate that outer rings are 1.7 times more frequent in the SAMathematical equation: \hbox{${\underline{\rm A}}$}B to SB families than in the SA family. For inner rings the fraction in barred galaxies is only larger by a factor of about 1.3 than that in SA galaxies.

Our results are again mostly similar to those that can be obtained from the NIRS0S galaxy classifications (Laurikainen et al. 2011), which include disc galaxies in the range of stages − 3 ≤ T ≤ 1. For outer features, we (they) found that the fraction of SA galaxies hosting them is 27 ± 5% (15 ± 5%) and that the fraction of barred galaxies hosting them is 49 ± 4% (47 ± 5%). For inner features in that range of stages, we (they) found that the fraction of SA galaxies hosting them is 51 ± 5% (24 ± 6%) and that the fraction of barred galaxies hosting them is 60 ± 4% (56 ± 5%). The NIRS0S statistics were calculated here excluding the galaxies labelled as spindle in Laurikainen et al. (2011) and ours were calculated with galaxies with ϵd ≤ 0.5.

The fact that outer features are more sensitive to the presence of a bar than inner features fits naturally with a scenario in which the rings in SA galaxies have formed due to broad oval distortions or long-lasting spiral modes (Rautiainen & Salo 2000) or with a model in which bars have been destroyed or dissolved after forming the rings. In the first case, simulations show that outer resonance features take longer to form than their inner counterparts. In the second case, the deficit of outer rings in unbarred galaxies can be explained because they can be destroyed easily by the interaction with companion galaxies (Elmegreen et al. 1992). Alternatively, this effect can be attributed to the fact that a significant fraction of outer rings may have been misclassified as inner rings in unbarred galaxies (Sect. 6.5).

Thumbnail: Fig. 33 Refer to the following caption and surrounding text. Fig. 33

Fraction of galaxies with ϵd ≤ 0.5 with outer rings divided by that with inner rings, as a function of the galaxy stage.

Quantifying the link between resonance features and ovals or spiral patterns requires studying parameters such as the non-axisymmetric torque, Q. This was defined by Combes & Sanders (1981) and indicates the strength of the non-axisymmetries of the galactic potential. This parameter can be local (Qr, the local non-axisymmetric torque) or global (Qg, the maximum of all Qr). In a study that contained 16 unbarred and 31 barred galaxies, Grouchy et al. (2010) pointed out a correlation between the ring axis ratio and the Qr at its radius independently of whether the host galaxy is barred or not. This shows that, indeed, not only bars are responsible for shaping the rings, but also other non-axisymmetries in the galactic potential such as those caused by ovals and spiral arms. Further investigation will require analysing larger samples, which may be drawn from the S4G.

7.4. Why is the inner ring orientation dependent on the host galaxy stage?

Thumbnail: Fig. 34 Refer to the following caption and surrounding text. Fig. 34

Fraction of galaxies with inner rings aligned with the bar (θr − θb ≤ 30°; in black) and inner rings misaligned with the bar (θr − θb > 30°; in grey) that have a given disc axis ratio. The top panel shows galaxies with stages 1 ≤ T ≤ 3, the bottom panel galaxies with stages 4 ≤ T ≤ 10. Only galaxies with deprojected ring axis ratios qr,0(I) < 0.85 and disc axis ratios qd ≤ 0.5 are included. The error bars are calculated using binomial statistics.

Thumbnail: Fig. 35 Refer to the following caption and surrounding text. Fig. 35

Ring deprojected major axis angle difference with the bar as a function of the galaxy disc ellipticity for 1 ≤ T ≤ 3 and ϵ ≤ 0.5.

Thumbnail: Fig. 36 Refer to the following caption and surrounding text. Fig. 36

Selection of close to face-on S4G galaxies with stages 4 ≤ T ≤ 10 that host inner pseudorings misaligned with the bar. The images have the same properties as those in Fig. 2. The name of the galaxies, their morphological classification, and the bar-pseudoring intrinsic misalignment can be found below each image.

In Sect. 6.4 we found that inner rings prefer to be aligned in parallel with the bar major axis. However, we also found that a significant fraction of inner rings (~ 50%) is oriented at random with respect to the bar. The fraction of rings with random orientations is low (20–30%) for early-type galaxies, but increases to ~ 70% for galaxies with T ≥ 4.

We investigated whether this effect might be related to a high galaxy inclination, which would prevent the accurate measurement of bar and ring orientations. To do this, we divided the galaxies that host inner rings into two groups: those whose inner rings are roughly aligned with the bar (θr − θb ≤ 30°), and those that are misaligned with it (θr − θb > 30°). For each of these groups we plotted the fraction of galaxies that can be found at a given disc axis ratio, restricting ourselves to ϵ ≤ 0.5. The expectation for circular discs with their rotation axis pointing at random is that the distribution is uniform. We calculated this for galaxies with 1 ≤ T ≤ 3 and 4 ≤ T ≤ 10 (top and bottom panels in Fig. 34 respectively). Earlier-type galaxies have nearly no misaligned inner rings.

The top panel in Fig. 34 suggests that misaligned rings tend to be found more frequently in the bins with more highly inclined galaxies, and the reversed trend is seen for galaxies oriented parallel with the ring (if we except the bin centred at qd = 0.95). To verify whether this trend is statistically significant, we plotted in Fig. 35 the intrinsic ring/bar misalignments as a function of the disc ellipticity for all galaxies in the top panel of Fig. 34. We can see that misaligned rings have a preference for inclined galaxies. We calculated the Spearman coefficient of the data in Fig. 35 and found that ρ = 0.37 and that the probability of the variables in the two axes to be uncorrelated is p = 0.002. It is therefore very likely that at least some of the misalignments are caused by incorrect deprojections. We see no such effect for galaxies with 4 ≤ T ≤ 10 (bottom panel in Fig. 34), which suggests that these deprojection problems might be related to the thickness of the discs. Indeed, as discussed in Sect. 4.6, earlier-type galaxies have thicker discs.

For late-type discs, the distributions in Fig. 34 differ from the uniform expectation in the sense that the bin for rounder discs is less populated than the others. This effect is well known for disc galaxies in general and has been attributed to genuine disc deviations from circularity of the order of b/a = 0.9 or to the presence of substructure in the discs (Lambas et al. 1992). We examined whether these deviations from perfectly circular discs might be responsible for rings misaligned with their bars if we were wrongly assuming purely circular discs. We did this by projecting several thousand elliptical discs with random orientations. These discs had a bar also oriented at random and rings with an orientation differing from that of the bar following a normal distribution with a dispersion of the order of 10°. Then, we deprojected the galaxies, but this time we assumed that they were circular. We found that for moderate disc intrinsic ellipticities (b/a ≳ 0.8), this did not cause a fraction of ~70% rings apparently oriented at random with respect to the bar, as we observe for the late spirals. However, the fraction of rings oriented at random with respect to the bar for galaxies with 1 ≤ T ≤ 3 can be explained in this way. This is natural since, as we already argued, at least some ring/bar misalignments in early spirals might be caused by errors in the deprojections.

Therefore our results indicate that at least for late-type galaxies misalignments are not caused by uncertainties in bar and ring properties measured in highly inclined discs or because discs might not exactly be circular, as assumed when calculating the deprojections. Therefore, a significant fraction of inner rings are intrinsically misaligned, especially those in late-type galaxies. A selection of very low-inclination galaxies with such misaligned inner rings is shown in Fig. 36.

The existence of misaligned inner features was also shown in simulations by Rautiainen & Salo (2000). In their study, this misalignment appears because a spiral mode with a pattern speed lower than that of the bar dominates the Fourier amplitude spectrum at the radius of the inner ring. This means that our results would be consistent with spiral modes rotating with a pattern speed different from that of the bar and with a significant contribution at the I4R radius for late-type galaxies. Alternatively, this is caused by a rotation of the Lagrangian points from their usual position, in the direction of the bar major axis, by an angle that increases with increasing spiral amplitude (e.g., Athanassoula et al. 2010). A way to explore these possibilities would be to compare the amplitude of the bar and spiral arm torque at the ring radius in our sample galaxies as reported, for instance, by Block et al. (2004) and Salo et al. (2010). The latter authors described that the spiral density amplitude correlates well with the local bar torque as long as it is measured within 1.5 times the bar length. Since bars in late-type galaxies can significantly shorter than their CR radius (see, e.g., Combes & Elmegreen 1993), a correlation between the bar and the spiral torque at the inner ring radius may not be found.

An alternative possibility is that the apparent random orientation between bars and rings is caused by errors in measuring the inner feature position angle. This is because the later a galaxy is, the more ill-defined its rings become. Also, inner pseudorings in late-type galaxies tend to be more spiral-like than those in early-type galaxies, which partly invalidates the approximation made when fitting them with ellipses.

8. Summary and conclusions

Thumbnail: Fig. 37 Refer to the following caption and surrounding text. Fig. 37

Fraction of galaxies with outer rings (top panel) and inner rings (bottom panel) for a given stage. The plots only include galaxies with a disc ellipticity ϵd ≤ 0.5. In each of the panels, both rings as a whole and closed rings are indicated.

Thumbnail: Fig. 38 Refer to the following caption and surrounding text. Fig. 38

As in Fig. 37, but now with the bar family instead of stage.

We presented ARRAKIS, the atlas of resonant rings as known in the S4G, and a catalogue of the ring and pseudoring properties. The preliminary analysis of the data contained in the catalogue (Appendix A) and the atlas (Appendix B) was also presented. In this paper rings and pseudorings have been collectively termed rings.

The most common rings are resonance rings. These rings are thought to be due to gathering of gas, which can later be transformed into stars, at or close to the radii of the resonances caused by non-axisymmetries such as bars, ovals, and strong spiral patterns (e.g., Schwarz 1981, 1984; Sellwood & Wilkinson 1993; Byrd et al. 1994; Rautiainen & Salo 2000). They come in three flavours (outer, inner, and nuclear), depending on their radius relative to that of the bar. Outer features are thought to be related to the OLR or occasionally to the O4R, inner features to the I4R, and nuclear features to the ILRs. Inner and outer rings might also be based on flux tube manifolds triggered by the bar or oval distortion (Romero-Gómez et al. 2006, 2007; Athanassoula et al. 2009b,a, 2010; Athanassoula 2012b). Either way, rings are tracers of the underlying galactic potential, which makes them important clues for the understanding of the secular evolution of disc galaxies.

The S4G is a survey of 2352 galaxies representative of the local Universe observed at 3.6 and 4.5  μm wavelengths. The galaxies in the S4G were classified by R. J. Buta, who also identified the rings (Buta et al., in prep.). We studied all the rings in the S4G frames, but our focus was on resonance rings in the S4G galaxy sample. Because dust obscuration is weak in the mid-infrared, the chances that rings are hidden by dust are much lower than at optical wavelengths. This makes the S4G a very good tool for studying rings.

We described the ring shape and orientation by marking their contours and fitting ellipses to them. To do this, we used model-subtracted images of the galaxies produced by the P4 of the S4G (Salo et al., in prep.). We obtained intrinsic ring shapes and orientations by deprojecting the fitted ellipses. The deprojection parameters were obtained from the P4 ellipse fits to the outer parts of S4G galaxies. Bar orientations and ellipticities (a rough indicator of bar strength) were measured by looking at the ellipse fit corresponding to the radius where the highest ellipticity was found within the bar. They were deprojected in the same way as for rings.

We summarise our findings as follows:

  • Section 6.1 and Figs. 18 and 37:outer rings are found in 16 ± 1% of the S4G galaxies and are more frequentfor stages − 1 ≤ T ≤ 2 (over 40% frequency). Outer closed rings account for100% of outer features with T ≤  − 1. Inner rings are the most frequentresonance feature in the local Universe (35 ± 1% frequency in the S4Gsample). They are typically found in the range − 1 ≤ T ≤ 6 (over 40% frequency)and their frequency peaks at stages − 1 ≤ T ≤ 3 (over 60% frequency). The innerclosed ring distribution is shifted to earlier stages than that of innerfeatures.

  • Sections 6.2 and 7.2 and Figs. 19 and 38: the outer ring frequency increases from 15 ± 2% to 32 ± 7% along the family sequence from SA to SABMathematical equation: \hbox{${\underline{\rm B}}$}, and decreases again to 20 ± 2% for SB galaxies. The inner ring frequency is qualitatively different, since it is roughly constant at ~ 40% for all families except for a peak at 64 ± 7% frequency for SABMathematical equation: \hbox{${\underline{\rm B}}$} galaxies. The reason might be that outer rings take a longer time than inner rings to be built in galaxies with weaker non-axisymmetries. We also found that inner closed rings have a preference for unbarred and weakly barred galaxies.

  • Section 7.3: barred galaxies have outer rings 1.7 times more often than unbarred ones. Barred galaxies have 1.3 more inner rings than their unbarred counterparts. This indicates that although they are stimulated by bars, rings do not need them to exist. Simulations suggest (e.g., Salo et al. 1999; Rautiainen & Salo 2000) that rings in unbarred galaxies may be related to weak ovals and/or long-lived spiral modes. Alternatively, they may have formed because of bars that have since been destroyed or have dissolved.

  • Sections 6.1 and 7.3: we confirmed the results of the NIRS0S survey regarding the frequencies of outer and inner rings as a function of the stage and the family for galaxies with stages − 3 ≤ T ≤ 1.

  • Section 6.3 and Figs. 20, 21, and 22: the axis ratio distribution of each of the three ring flavours – outer, inner, and nuclear – can be fitted with a Gaussian curve. Their intrinsic axis ratios typically range from qr,0 = 0.6 to qr,0 = 1.0. Inner rings are in general more elliptical than their outer counterparts. We found that outer and inner rings become on average more elliptical when the bar strength increases (when the galaxy family changes from SA to SB) and that inner rings are more elliptical in late-stage galaxies than in earlier-stage galaxies.

  • Section 6.4 and Fig. 23: we confirmed that outer rings have two preferred orientations, namely parallel and perpendicular to the bar. Of the outer rings in barred galaxies 35 ± 18% are parallel to the bar and 65 ± 39% are oriented perpendicular to it.

  • Sections 6.4 and 7.4 and Figs. 23 and 25: we found that many inner rings have their major axes oriented parallel to the bar, as predicted in simulations and as previously reported from observations. However, we also found that maybe as much as 50% of inner rings have random orientations with respect to the bar. These misaligned inner rings are mostly found in late-type spirals (T ≥ 4). We speculate that this may be because the Fourier amplitude spectrum at the radius of the I4R is dominated by spiral modes with a pattern speed different from that of the bar late-type galaxies. Alternatively, this can be due to the increased difficulty of measuring inner ring properties when they become ill-defined at late stages.

  • Sections 6.5 and 6.6 and Figs. 26, 27, 29, and 30: the size of a ring relative to that of the galaxy is a much better indicator of its flavour (outer, inner, or nuclear) than its absolute size. The wings of both the absolute and relative size distributions of inner rings are more extended in unbarred galaxies than for those with bars. This may indicate that several outer and nuclear rings have been misclassified as inner features in unbarred galaxies.

  • Section 6.7: several of our sample galaxies have both an outer and an inner ring. The distribution of their diameter ratio peaks at Dr,0(O)/Dr,0(I) ~ 2, which agrees with the literature.

8.1. Open questions

We discussed two very interesting questions on rings which still have no clear solution. Why are some rings found in apparently unbarred galaxies? And why do inner rings in late-type galaxies have a higher tendency to be oriented at random with respect to the bar than those in earlier-type galaxies?

As developed in the discussion in Sect. 7, galaxies with these properties have occasionally been found in simulations. However, to test whether the mechanism creating rings in unbarred galaxies and the one shaping inner rings that are misaligned with the bar is the same in nature and in simulations, one has to study each galaxy at a deeper level of detail than we did here. Indeed, visual identification of the bar and a rough estimate of its orientation may be insufficient and one may need to perform a Fourier analysis to unveil the effects of non-axisymmetries induced by spiral arms or broad weak ovals. Again, the S4G is the right tool for this type of research because the mid-infrared is an excellent tracer of the stellar mass and thus of the baryonic matter contribution to the galactic potential.


3

IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.

Acknowledgments

We thank our anonymous referee, who very carefully read this paper. The authors wish to thank the entire S4G team for their efforts in this project. We thank Pertti Rautiainen for useful discussions on the ring formation in his simulations, Simón Díaz-García for helping with fundamental statistical concepts, and Glenn van de Ven for his useful comments. We acknowledge financial support to the DAGAL network from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007-2013/ under REA grant agreement number PITN-GA-2011-289313. E.A. and A.B. acknowledge financial support from the CNES (Centre National d’Études Spatiales – France). K.S., J.-C.M.-M., T.K., and T.M. acknowledge support from the National Radio Observatory, which is a facility of the National Radio Astronomy Observatory operated under cooperative agreement by Associated Universities, Inc. S.C., H.S., E.L., M.H.-H., and J.L. acknowledge support from the Academy of Finland. This work is based on observations and archival data made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. We are grateful to the dedicated staff at the Spitzer Science Center for their help and support in planning and execution of this Exploration Science program. We also gratefully acknowledge support from NASA JPL/Spitzer grant RSA 1374189 provided for the S4G project. This research has made use of SAOImage DS9, developed by Smithsonian Astrophysical Observatory. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

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Appendix A: Catalogue

The catalogue contains two tables. One for galaxies included in the S4G sample and a second one for galaxies that appear in S4G frames, but are not included in the original sample. The information in the tables in the catalogue is organized as follows:

Column 1 Galaxy ID
Column 2 NED redshift-independent distance if available, NED redshift distance corrected for Virgo Cluster, Great Attractor,
and Shapley Cluster effects with H0 = 73   km   s-1   Mpc-1 otherwise
Column 3 Type of feature (ring, pseudoring, or bar) described in that row
Column 4 Feature major projected diameter (maximum ellipticity major diameter for bars)
Column 5 Feature minor projected diameter (maximum ellipticity minor diameter for bars)
Column 6 Feature major axis PA
Column 7 Feature major intrinsic diameter (maximum ellipticity major diameter for bars)
Column 8 Feature minor intrinsic diameter (maximum ellipticity minor diameter for bars)
Column 9 Counter-clockwise angular distance between the line of nodes of the galaxy deprojection and the major axis of the feature

Deprojected ring parameters are not given for polar rings.

Appendix B: Atlas

The atlas contains two sets of galaxies. One for galaxies included in the S4G sample and a second one for galaxies that appear in S4G frames, but are not included in the original sample. The information in the atlas is organized as follows:

  • Line 1: Galaxy ID

  • Line 2: Galaxy classification according to Buta et al. (in prep.).

  • S4G original galaxy image and P4 model-subtracted image (Salo et al. in prep.). The red ellipses indicate the rings in the galaxy. The green ellipses are the result of an ellipse fit at the radius of the maximum bar ellipticity. The red crosses indicate the centre of the galaxy. The axis units are arcseconds. North is up and east is left.

  • Below this information we present a table showing the information on the projected and deprojected information on the rings, pseudorings, and bars of that galaxy as shown in the catalogue in Appendix A.

Appendix B.1: Atlas of galaxies in the S4G sample that host rings

ESO 13-16 ESO 26-1
SB(rs)cd (R2Mathematical equation: \hbox{$_{2}^{\prime}$})SAB(s)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.78 0.66 161.7 1.01 0.78 92.5 R2Mathematical equation: \hbox{$_{2}^{\prime}$} 1.25 0.92 37.4 1.26 0.97 22.3
bar 0.30 0.08 166.0 0.30 0.12 0.5 bar 0.23 0.07 66.9 0.24 0.08 49.8

ESO 54-21 ESO 119-16
(R)SAB(s)d pec (R)SAB(s)dm:
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 3.15 1.55 101.6 3.78 2.65 53.9 R 2.24 0.56 30.3 2.33 1.50 22.4

ESO 202-41 ESO 234-49
SB(rs)m SA(r)cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.85 0.75 174.4 1.13 0.83 82.9 r 0.24 0.12 170.7 0.25 0.12 92.2
bar 0.73 0.22 166.9 0.75 0.32 19.9

ESO 240-11 ESO 285-48
SA(rs:)b sp SB(rs)d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 1.05 0.11 127.8 1.06 0.70 5.0 rs 0.64 0.30 80.7 0.70 0.64 99.8

ESO 355-26 ESO 358-25
SA(r)bc SA(l,nr)0+/SA0d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.23 0.17 154.7 0.32 0.23 91.0 nr 0.14 0.09 57.4 0.15 0.14 75.4

ESO 362-19 ESO 399-25
(R)SB(s)d (RL)E(d)2
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.82 0.39 3.9 1.87 1.23 19.0 RL 3.08 1.16 153.0 3.09 1.62 171.3

ESO 402-26 ESO 402-30
(R)SAMathematical equation: \hbox{${\underline{\rm A}}$}B(r,nl)ab SA(rs)0o
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.80 0.61 113.0 1.91 1.59 38.9 rs 0.18 0.07 134.4 0.18 0.12 171.4
r 0.61 0.27 100.4 0.83 0.56 111.4

ESO 404-12 ESO 407-7
SAB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)b SA(rl)a: sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

bar 0.49 0.17 131.1 0.50 0.19 15.1 rl 0.49 0.07 168.7 0.49 0.34 4.8
rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.41 0.40 145.6 0.47 0.41 86.3

ESO 407-14 ESO 418-8
SA(r)ab (R)SB(s)dm:
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.41 0.16 40.3 0.41 0.30 0.6 R 0.80 0.50 151.7 0.86 0.68 42.7
bar 0.13 0.04 9.0 0.17 0.04 63.8

ESO 420-9 ESO 422-5
SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rs)c SB(rsMathematical equation: \hbox{${\underline{\rm s}}$}:)dm:
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.40 0.36 76.9 0.50 0.38 81.2 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.47 0.40 51.0 0.58 0.44 74.9
bar 0.12 0.06 39.8 0.12 0.08 13.0 bar 0.25 0.13 79.5 0.32 0.14 69.2

ESO 422-41 ESO 440-4
(R)SA(l)c: SAB(rl)d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.26 1.87 91.1 2.39 2.15 55.8 rl 0.98 0.75 82.4 1.80 0.98 87.7

ESO 440-11 ESO 443-69
SB(rs)cd SB(rs)dm
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.58 0.44 15.9 0.59 0.48 154.5 rs 0.67 0.59 172.9 0.73 0.61 67.1
bar 0.29 0.08 176.5 0.30 0.09 140.3 bar 0.52 0.18 174.0 0.56 0.19 53.2

ESO 443-80 ESO 479-4
Pec/RG? or SAB(s)m? SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RG 1.34 0.57 142.5 1.37 0.79 162.1 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.84 0.49 59.3 0.92 0.83 72.1
bar 0.20 0.06 37.4 0.23 0.09 143.8

ESO 482-35 ESO 507-65
SB(rs)b (R)Sm?
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.70 0.45 8.3 0.75 0.66 50.4 R 0.77 0.24 16.8 0.77 0.56 3.4
bar 0.69 0.19 28.5 0.80 0.25 42.3

ESO 508-7 ESO 508-24
SABMathematical equation: \hbox{${\underline{\rm B}}$}(rs)d SAB(rs)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.59 0.39 111.8 0.91 0.48 72.9 rs 0.60 0.35 72.9 0.60 0.41 167.3
bar 0.37 0.18 91.2 0.42 0.30 46.4 bar 0.21 0.11 57.6 0.22 0.12 149.0

ESO 509-74 ESO 510-58
S(nd or nr)bc sp (R)SAB(s,nb)m or RG?
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

nr 0.14 0.03 136.2 0.14 0.12 151.3 R 0.79 0.48 5.9 0.82 0.69 36.4
bar 0.35 0.23 161.1 0.38 0.31 128.9

ESO 510-59 ESO 532-22
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})c SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.59 0.51 127.8 0.89 0.54 82.3 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.51 0.42 0.5 0.71 0.46 77.6
bar 0.33 0.07 116.2 0.41 0.09 49.8 bar 0.45 0.13 17.3 0.63 0.13 70.6

ESO 545-16 ESO 547-5
(R)SAm SAB(rs)m
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.54 1.39 36.9 1.79 1.54 89.5 rs 0.66 0.42 52.1 0.66 0.57 7.1
bar 0.29 0.11 31.8 0.30 0.14 153.4

ESO 548-5 ESO 548-23
SAB(rs)dm (RL:)SA0
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.73 0.56 53.7 0.73 0.65 19.9 RL 0.66 0.35 24.3 0.68 0.66 70.0
bar 0.59 0.29 29.4 0.60 0.34 159.1

ESO 548-25 ESO 549-18
(RL)SB(s)a/d (L,R2Mathematical equation: \hbox{$_{2}^{\prime}$})SAB(s)a/c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 0.90 0.41 81.5 0.92 0.77 154.2 R2Mathematical equation: \hbox{$_{2}^{\prime}$} 1.34 0.89 11.2 1.51 1.29 112.9
bar 0.25 0.13 172.2 0.47 0.13 88.2 bar 0.66 0.22 16.8 0.66 0.36 175.2

ESO 572-18 ESO 576-1
SABMathematical equation: \hbox{${\underline{\rm B}}$}(rs)b: SAMathematical equation: \hbox{${\underline{\rm A}}$}B(r)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.67 0.27 45.4 0.70 0.52 27.4 r 0.33 0.19 164.1 0.39 0.31 68.2
bar 0.27 0.15 178.7 0.43 0.19 109.4 bar 0.21 0.14 32.7 0.38 0.15 79.2

ESO 576-3 ESO 576-32
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})dm SB(rs)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.04 0.24 93.4 1.05 0.61 169.0 bar 0.69 0.17 153.2 0.73 0.23 26.7
rs 0.67 0.46 131.6 0.68 0.65 149.0

ESO 576-50 ESO 580-29
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})cd S(rs)b sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.75 0.39 166.4 0.84 0.56 137.4 rs 0.76 0.09 71.6 0.77 0.49 168.2
bar 0.19 0.08 70.0 0.29 0.09 75.6

ESO 580-41 ESO 581-25
SB:(rsMathematical equation: \hbox{${\underline{\rm s}}$})dm sp SB(rsMathematical equation: \hbox{${\underline{\rm s}}$},nr?)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.48 0.12 78.6 0.63 0.47 77.1 rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.03 0.12 59.2 1.03 0.62 176.8
nr 0.21 0.05 57.6 0.26 0.20 108.0

ESO 602-30 IC 51
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})d PRG
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.39 0.29 65.6 0.40 0.38 140.9 PRG 0.50 0.10 113.9
bar 0.11 0.05 49.1 0.11 0.07 145.4

IC 719 IC 749
SA(rl)0o SB(rs)cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rl 0.28 0.06 51.8 0.28 0.14 4.5 rs 0.70 0.60 53.1 0.78 0.61 106.4
bar 0.35 0.15 42.1 0.39 0.15 104.7

IC 863 IC 1014
(R)SB(rs)b SB(r)m
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 0.51 0.30 44.1 0.51 0.40 167.6 r 0.75 0.54 78.2 0.83 0.73 116.6
rs 0.24 0.22 76.6 0.30 0.24 78.7 bar 0.37 0.16 54.2 0.43 0.20 130.3
bar 0.24 0.13 102.8 0.30 0.14 65.8

IC 1029 IC 1048
(R)SBa(s,nd)a (R)SB(s)d sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.30 0.33 147.6 2.34 1.41 167.1 R 1.08 0.14 164.6 1.11 0.62 15.7

IC 1055 IC 1067
(R)SA(rs,r)ab SB(r)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.53 0.54 5.7 1.54 1.33 6.3 r 0.63 0.51 114.0 0.65 0.63 106.0
rs 0.90 0.28 3.2 0.91 0.69 170.7 bar 0.61 0.22 150.0 0.67 0.25 41.4
r 0.33 0.13 7.6 0.34 0.31 42.4

IC 1158 IC 1210
SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rMathematical equation: \hbox{${\underline{\rm r}}$}s)cd SAB(r)a: pec
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.31 0.17 141.2 0.33 0.29 39.9 r 0.47 0.24 172.9 0.54 0.45 64.6
bar 0.17 0.10 81.8 0.26 0.11 105.7

IC 1265 IC 1438
SA(r)0/a: (R1)SABa(rl,nl)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.39 0.18 73.1 0.40 0.33 155.2 R1 1.77 1.32 23.4 1.86 1.40 48.6
rl 0.73 0.49 127.5 0.77 0.52 133.1
bar 0.70 0.34 123.4 0.74 0.36 132.3

IC 1596 IC 1953
SA(rs)bc: SB(rs)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.27 0.17 111.6 0.45 0.27 90.7 bar 0.87 0.22 157.8 1.04 0.27 48.6
rs 0.77 0.70 100.8 1.07 0.76 95.4

IC 1954 IC 1993
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})cd (R)SAMathematical equation: \hbox{${\underline{\rm A}}$}B(s)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.48 0.25 77.3 0.56 0.39 50.6 R 1.47 1.44 78.5 1.58 1.44 88.8
bar 0.13 0.05 91.6 0.17 0.07 52.3 bar 0.54 0.39 43.8 0.56 0.40 56.2

IC 2051 IC 2056
SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)b SA(rsMathematical equation: \hbox{${\underline{\rm s}}$})bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.87 0.54 74.0 0.91 0.86 71.7 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.27 0.23 114.5 0.31 0.24 94.5
bar 0.75 0.40 12.8 1.16 0.43 105.2

IC 2361 IC 2764
SA(rsMathematical equation: \hbox{${\underline{\rm s}}$})bc (R)SA(l)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.39 0.14 80.4 0.43 0.36 46.0 R 0.84 0.70 3.3 0.84 0.82 9.6

IC 2969 IC 3102
SA(r)d (RL)SAB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.37 0.30 101.5 0.45 0.37 80.4 RL 2.76 1.45 119.9 2.77 2.33 8.0
rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.55 0.81 117.6 1.55 1.30 178.8
bar 0.78 0.38 128.0 0.81 0.59 27.7

IC 3267 IC 3391
SA(rs)a SA(r?)c pec
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.61 0.48 120.8 0.61 0.52 174.0 r 0.23 0.13 50.6 0.24 0.17 150.3

IC 3392 IC 3806
SA(rs)ab SA(r)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.58 0.25 39.3 0.60 0.56 47.4 r 0.40 0.12 179.6 0.41 0.28 12.0

IC 4214 IC 4216
(R1)SAMathematical equation: \hbox{${\underline{\rm A}}$}Ba(rl,nr,nb)0/a SB(rl=R2Mathematical equation: \hbox{$_{2}^{\prime}$})d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R1 2.03 1.25 2.2 2.13 1.76 36.1 rl 0.73 0.43 51.4 1.02 0.73 94.3
bar 0.90 0.42 150.0 1.00 0.57 141.4
rl 0.89 0.48 160.9 0.92 0.68 153.7
nr 0.21 0.13 165.2 0.21 0.19 141.4

IC 4221 IC 4237
SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)dm SBx(r)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.31 0.24 177.9 0.45 0.31 86.2 r 0.57 0.39 152.3 0.60 0.53 49.8
bar 0.24 0.09 148.9 0.30 0.14 132.8 bar 0.49 0.15 118.0 0.54 0.19 144.5

IC 4536 IC 4901
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})cd SB(r)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.66 0.64 68.5 0.76 0.65 84.2 r 0.45 0.36 163.0 0.59 0.39 72.5
bar 0.45 0.12 169.1 0.46 0.14 154.8 bar 0.41 0.18 119.0 0.42 0.25 172.7

IC 5039 IC 5156
SABMathematical equation: \hbox{${\underline{\rm B}}$}(rsMathematical equation: \hbox{${\underline{\rm s}}$})cd SBa(rsMathematical equation: \hbox{${\underline{\rm s}}$})a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.31 0.17 158.6 0.51 0.31 85.3 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.61 0.29 179.4 0.72 0.58 66.9

IC 5240 IC 5264
SBx(r)0/a (R)SA0+ sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

bar 1.33 0.36 89.7 1.34 0.51 166.6 R 1.58 0.13 81.0 1.58 0.57 177.5
r 1.26 0.82 108.7 1.31 1.11 34.7

IC 5267 IC 5271
(RL)SA(r,l,nl)0/a SAB(rs)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 4.65 3.31 148.4 4.80 4.33 38.4 rs 1.07 0.39 138.8 1.07 1.02 22.3
r 2.71 1.95 136.3 2.74 2.61 151.0

IC 5334 NGC 24
(R)SA(l)0/a sp S(rs)d: sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.09 0.22 126.1 1.09 0.60 1.9 rs 0.85 0.22 45.9 0.88 0.81 40.9

NGC 131 NGC 134
SAB(rsMathematical equation: \hbox{${\underline{\rm s}}$})b: SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rs)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.83 0.23 64.8 0.83 0.64 10.8 rs 1.26 0.34 45.5 1.30 1.18 146.8

NGC 148 NGC 150
(L)SAMathematical equation: \hbox{${\underline{\rm A}}$}B(r,nl)0+ SAB(rsMathematical equation: \hbox{${\underline{\rm s}}$})ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.70 0.19 88.9 0.71 0.49 4.3 rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.64 0.64 109.1 1.64 1.25 0.8
bar 0.62 0.23 51.3 1.08 0.26 105.7

NGC 210 NGC 244
(R1Mathematical equation: \hbox{$_{1}^{\prime}$},R2L)SAB(rl,nr)ab (L)SA(rs:)m
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R2Mathematical equation: \hbox{$_{2}^{\prime}$}L 4.08 2.90 170.4 4.56 4.00 70.1 rs 0.18 0.14 26.1 0.18 0.15 138.2
R1Mathematical equation: \hbox{$_{1}^{\prime}$} 2.94 2.06 144.8 3.49 2.67 116.9
rl 1.47 0.88 169.9 1.51 1.32 30.8
bar 1.05 0.52 172.0 1.08 0.78 21.4
nr 0.20 0.14 155.5 0.22 0.19 112.7

NGC 253 NGC 254
SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)bc sp (R)SAB(l)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rMathematical equation: \hbox{${\underline{\rm r}}$}s 5.80 1.38 52.4 7.22 5.76 80.7 R 1.59 1.25 139.5 1.91 1.57 79.9
bar 0.89 0.44 132.4 0.89 0.66 2.5

NGC 255 NGC 274
SB(rs)cd (R)SA(l)0
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.74 0.53 62.0 0.81 0.53 71.7 R 0.57 0.51 167.4 0.59 0.52 56.4
bar 0.20 0.07 57.4 0.22 0.07 64.9

NGC 289 NGC 470
(R:,RL)SABMathematical equation: \hbox{${\underline{\rm B}}$}(rs1,rMathematical equation: \hbox{${\underline{\rm r}}$}s2)ab SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rsMathematical equation: \hbox{${\underline{\rm s}}$})ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 6.07 4.68 139.9 7.19 5.79 69.9 rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.23 0.69 145.3 1.43 1.13 121.6
RL 3.00 2.18 117.6 3.26 2.95 111.6 bar 0.76 0.34 12.0 1.10 0.45 62.5
rs 1.35 1.11 120.4 1.63 1.35 93.4
bar 0.69 0.26 125.4 0.69 0.38 3.1
rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.66 0.63 43.2 0.97 0.63 91.1

NGC 473 NGC 474
(L)SA(r)0+ (R)SAB(l)0/a (shells/ripples)
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.36 0.23 156.4 0.36 0.34 29.0 R 2.23 2.07 67.2 2.28 2.21 62.5
bar 0.81 0.63 16.8 0.84 0.66 130.3

NGC 485 NGC 488
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})c SA(rl)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.76 0.17 2.1 0.77 0.44 172.7 rl 0.92 0.76 178.1 0.95 0.88 135.4

NGC 489 NGC 493
(R)S0+ sp SA(rs)d sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 0.67 0.08 121.3 0.67 0.30 2.3 rs 0.96 0.24 53.7 1.01 0.77 150.4

NGC 532 NGC 600
SABxa(r)0+ SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 1.72 0.35 29.4 1.72 1.24 1.4 rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.07 0.76 76.0 1.09 0.81 35.4
bar 0.23 0.04 16.9 0.24 0.04 147.7

NGC 613 NGC 615
SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s,nr)b (R2Mathematical equation: \hbox{$_{2}^{\prime}$})SAMathematical equation: \hbox{${\underline{\rm A}}$}Bx(rMathematical equation: \hbox{${\underline{\rm r}}$}l)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

bar 2.90 0.70 123.3 2.90 0.90 176.6 R2Mathematical equation: \hbox{$_{2}^{\prime}$} 2.26 0.70 157.8 2.26 1.72 177.3
rMathematical equation: \hbox{${\underline{\rm r}}$}s 2.36 1.18 124.3 2.36 1.52 177.4 rMathematical equation: \hbox{${\underline{\rm r}}$}l 0.69 0.21 159.0 0.69 0.51 3.2
nr 0.15 0.08 114.9 0.15 0.11 160.9

NGC 658 NGC 660
SA(rsMathematical equation: \hbox{${\underline{\rm s}}$})bc PRG
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.60 0.24 18.4 0.62 0.39 157.6 PRG 5.98 1.33 175.5

NGC 672 NGC 676
(R)SB(s)d SA(r)0+ sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 3.51 1.34 69.1 3.51 2.93 1.4 r 1.53 0.29 174.7 1.56 0.87 15.5

NGC 691 NGC 701
(R)SA(rs,r)ab SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.74 1.93 98.8 2.79 2.55 29.0 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.59 0.30 51.9 0.64 0.53 47.5
rs 1.67 1.06 98.6 1.68 1.41 17.0 bar 0.21 0.06 63.0 0.24 0.10 37.4
r 1.03 0.75 89.5 1.04 1.00 151.7

NGC 718 NGC 723
(R)SAB(rs,nl)a (R)SA(s)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.42 1.09 24.7 1.43 1.27 24.6 R 0.45 0.40 151.2 0.45 0.41 179.0
rs 0.66 0.56 148.5 0.75 0.58 112.3
bar 0.66 0.39 154.4 0.72 0.42 129.7

NGC 755 NGC 779
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})d (L)SAMathematical equation: \hbox{${\underline{\rm A}}$}Bx(rs)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.89 0.44 50.0 1.18 0.89 89.5 rs 0.94 0.30 163.4 0.98 0.85 33.8

NGC 864 NGC 895
SABMathematical equation: \hbox{${\underline{\rm B}}$}(rsMathematical equation: \hbox{${\underline{\rm s}}$})bc SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rMathematical equation: \hbox{${\underline{\rm r}}$}s)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.17 0.83 59.2 1.46 0.97 64.8 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.29 0.19 94.6 0.32 0.24 138.9
bar 0.87 0.37 104.8 1.27 0.37 83.1 bar 0.14 0.08 158.9 0.17 0.09 64.4

NGC 908 NGC 936
SA(rs)b (L)SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s,bl)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.99 0.46 66.8 1.08 0.80 140.6 rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.55 1.22 139.8 1.71 1.49 64.1
bar 1.33 0.69 81.2 1.61 0.77 120.6

NGC 941 NGC 986
(R:)SAMathematical equation: \hbox{${\underline{\rm A}}$}B(r:)c (R)SB(rs,nr:,nb)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.11 1.52 169.4 2.15 2.08 54.4 R 3.52 2.59 130.1 3.60 2.81 31.7
r 0.86 0.79 113.2 1.17 0.81 95.9 bar 1.62 0.52 57.6 1.73 0.54 126.4
bar 0.33 0.17 13.7 0.37 0.21 43.4 rs 1.56 1.05 51.5 1.69 1.08 117.2
nr 0.33 0.10 89.9 0.33 0.11 160.0

NGC 1015 NGC 1022
SB(r)0/a (RL)SAB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.81 0.67 17.7 0.81 0.77 22.7 RL 2.08 1.66 143.7 2.13 1.74 138.1
bar 0.73 0.35 102.3 0.85 0.35 89.9 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.94 0.87 59.0 1.00 0.88 76.3
bar 0.59 0.35 107.7 0.63 0.36 109.1

NGC 1068 NGC 1073
(R)SA(s,nr)a SB(rs)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 5.81 4.89 63.5 5.81 5.09 2.5 rs 1.64 1.46 138.6 1.90 1.50 103.9
nr 0.56 0.48 51.9 0.56 0.50 166.9 bar 1.59 0.43 61.1 1.77 0.46 55.0

NGC 1079 NGC 1087
(L)SAMathematical equation: \hbox{${\underline{\rm A}}$}Ba(rMathematical equation: \hbox{${\underline{\rm r}}$}s,bl)0+ SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.36 0.75 86.8 1.42 1.18 32.8 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.62 0.49 14.1 0.79 0.61 78.2
bar 1.01 0.51 119.5 1.37 0.62 62.7 bar 0.50 0.22 128.5 0.71 0.25 111.9

NGC 1090 NGC 1097
SAB(s,nrl)bc (R)SB(rs,nr)abMathematical equation: \hbox{${\underline{\rm b}}$} pec
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

nrl 0.26 0.10 93.7 0.27 0.21 155.4 R 7.18 4.92 105.7 8.38 6.31 121.4
rs 3.44 2.03 136.9 3.60 2.91 33.2
bar 3.17 1.12 147.0 3.44 1.55 33.3
nr 0.34 0.29 167.3 0.47 0.31 80.1

NGC 1163 NGC 1179
SA(r:)0+ sp SABMathematical equation: \hbox{${\underline{\rm B}}$}(rsMathematical equation: \hbox{${\underline{\rm s}}$})cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.55 0.07 142.7 0.55 0.30 178.3 rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.18 1.10 46.0 1.33 1.18 92.0
bar 0.44 0.21 154.4 0.53 0.21 101.7

NGC 1187 NGC 1232
SABMathematical equation: \hbox{${\underline{\rm B}}$}(rs)bc SAB(rs)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 1.59 0.76 115.5 1.60 1.02 167.4 rs 0.78 0.51 92.2 0.78 0.59 177.0
bar 1.31 0.38 131.5 1.32 0.51 12.9 bar 0.78 0.35 88.9 0.78 0.41 173.2

NGC 1249 NGC 1258
SB(rs:)m (R)SAB(s)a:
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 1.80 0.65 75.0 1.96 1.42 142.7 R 0.78 0.35 4.5 0.80 0.47 160.0
bar 0.31 0.21 83.3 0.42 0.21 77.3

NGC 1291 NGC 1297
(R)SAB(l,nb)0+ SA(rl,nl)0o
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 8.47 7.08 69.6 8.51 7.10 53.1 rl 0.76 0.72 174.1 0.78 0.75 121.4
bar 3.17 1.88 166.3 3.18 1.90 148.2

NGC 1300 NGC 1302
(R)SB(s,nrl)b (RoRi)SAB(r)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 5.63 4.90 109.5 5.88 5.62 79.1 R 3.19 2.98 17.8 3.20 3.09 13.0
bar 2.82 0.63 102.3 2.82 0.75 175.3 R 2.19 1.95 60.7 2.24 1.98 57.7
nrl 0.15 0.14 114.0 0.17 0.15 84.0 r 1.02 0.94 4.6 1.02 0.97 167.1
bar 0.93 0.62 169.4 0.93 0.64 155.7

NGC 1310 NGC 1326
SB(rs)cd (R1)SABa(r,bl,nr)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.34 0.27 93.1 0.36 0.32 42.8 R1 2.83 1.87 85.9 2.84 2.34 12.2
bar 0.25 0.09 89.0 0.25 0.11 12.6 r 1.09 0.89 63.2 1.18 1.04 120.9
bar 1.07 0.62 18.6 1.29 0.65 109.5
nr 0.18 0.16 61.9 0.20 0.18 112.1

NGC 1341 NGC 1350
(R)SB(s)d pec (R)SABa(r,bl)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 0.70 0.57 96.8 0.73 0.57 80.2 R 5.35 2.60 179.5 5.56 4.75 147.5
bar 0.30 0.10 161.9 0.30 0.10 141.9 r 2.25 1.15 14.1 2.49 1.97 47.4
bar 1.86 0.78 36.7 2.56 1.08 58.3

NGC 1353 NGC 1357
SAB(rs,nl)a (RL)SA(rMathematical equation: \hbox{${\underline{\rm r}}$}s)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 1.32 0.38 135.9 1.32 0.91 174.4 RL 2.74 2.20 69.5 2.89 2.64 124.6
rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.05 0.86 69.4 1.12 1.02 119.3

NGC 1365 NGC 1366
(R)SB(rsMathematical equation: \hbox{${\underline{\rm s}}$},nr)bc SA(rl)0 sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 10.56 5.03 41.4 11.08 8.15 29.6 rl 0.38 0.15 1.9 0.38 0.34 177.5
bar 3.04 1.11 84.7 4.58 1.26 68.7
rsMathematical equation: \hbox{${\underline{\rm s}}$} 3.03 2.54 90.4 4.97 2.63 83.2
nr 0.30 0.18 15.6 0.35 0.26 124.6

NGC 1367 NGC 1385
(RL,RL)SAB(rs)0/a SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})dm pec /Sph
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 3.91 2.91 137.7 4.26 3.88 75.9 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.68 0.60 39.5 0.99 0.63 82.6
RL 2.63 1.74 119.5 2.85 2.34 133.0 bar 0.20 0.06 78.5 0.31 0.06 87.6
rs 1.32 0.94 131.9 1.36 1.32 107.7
bar 0.75 0.42 107.3 0.85 0.53 132.5

NGC 1386 NGC 1398
(R)SA(r)0/a (R)SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s,bl)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.67 0.58 25.8 1.67 1.42 1.6 R 4.64 3.17 87.7 4.70 4.22 156.8
r 0.50 0.20 24.8 0.51 0.49 157.2 rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.63 1.36 107.3 1.88 1.60 73.9
bar 1.33 0.83 13.4 1.78 0.84 95.7

NGC 1415 NGC 1425
(RL)SABa(rl,nr)0+ (RR)SA(rl)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 4.10 1.35 157.4 4.29 3.21 27.0 R 4.34 1.56 132.6 4.35 3.51 6.0
rl 1.60 0.51 145.1 1.72 1.18 147.8 R 2.17 0.91 134.6 2.24 2.00 33.1
nr 0.24 0.11 164.0 0.32 0.22 63.4 rl 0.65 0.30 137.1 0.73 0.61 57.5

NGC 1433 NGC 1436
(R1Mathematical equation: \hbox{$_{1}^{\prime}$})SB(r,nr,nb)a (R)SAB(s)ab /Sph
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R1Mathematical equation: \hbox{$_{1}^{\prime}$} 6.26 4.48 14.3 6.31 5.17 162.3 R 1.59 0.99 151.8 1.60 1.40 13.7
r 2.96 2.20 96.4 3.40 2.22 78.3 bar 0.66 0.29 125.7 0.72 0.39 143.6
bar 2.87 1.00 95.2 3.29 1.01 74.0
nr 0.26 0.25 151.7 0.30 0.25 97.3

NGC 1438 NGC 1448
SABMathematical equation: \hbox{${\underline{\rm B}}$}(r)0/a SA(rs)c sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 1.05 0.48 70.7 1.06 1.00 21.1 rs 1.36 0.19 42.5 1.36 0.97 177.6

NGC 1452 NGC 1483
(RL)SB(r,bl)0/a (R)SB(s)d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 2.54 1.43 115.1 2.55 2.38 13.0 R 0.83 0.55 141.0 0.85 0.66 28.3
r 1.63 0.91 113.7 1.63 1.53 179.8 bar 0.60 0.20 2.9 0.70 0.21 63.5
bar 0.91 0.48 31.6 1.52 0.48 93.8

NGC 1493 NGC 1512
SB(rs)c (RL)SB(r,nr)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 1.23 0.99 41.5 1.23 1.01 171.4 RL 5.26 4.21 64.8 5.83 5.16 108.6
bar 0.89 0.34 78.0 0.90 0.34 29.0 r 2.54 2.01 52.0 2.94 2.36 114.5
bar 2.45 0.84 44.4 2.72 1.03 139.1
nr 0.27 0.21 85.8 0.30 0.26 69.3

NGC 1515 NGC 1532
(L)SABMathematical equation: \hbox{${\underline{\rm B}}$}(rMathematical equation: \hbox{${\underline{\rm r}}$}s,nba)0/a sp SAB(rs,nd)ab sp pec
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rMathematical equation: \hbox{${\underline{\rm r}}$}s 2.25 0.44 17.0 2.26 1.68 174.3 rs 2.34 0.46 34.4 2.34 1.45 0.4

NGC 1533 NGC 1546
(RL)SB0o E(b)3/(R)SA(r)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 1.66 1.43 135.7 1.66 1.48 11.5 R 0.96 0.40 150.8 0.99 0.87 33.8
bar 0.89 0.56 166.4 0.91 0.58 41.9 r 0.53 0.17 148.0 0.53 0.39 2.9

NGC 1553 NGC 1566
SA(rl,nrl)0+ (R1Mathematical equation: \hbox{$_{1}^{\prime}$})SAB(rl,s,nb)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rl 1.18 0.67 150.6 1.18 0.93 174.3 R1Mathematical equation: \hbox{$_{1}^{\prime}$} 7.55 6.34 85.3 7.55 7.49 167.7
nrl 0.30 0.16 153.7 0.30 0.23 1.8 rl 4.07 3.00 14.1 4.76 3.04 101.6
bar 3.94 2.35 12.6 4.61 2.38 102.3

NGC 1640 NGC 1672
(R)SBa(r,bl)a (R)SABMathematical equation: \hbox{${\underline{\rm B}}$}(rs,nr)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.74 1.55 150.9 1.89 1.56 99.9 R 4.89 3.84 163.7 4.95 4.24 26.0
bar 1.01 0.38 46.5 1.01 0.41 4.2 bar 2.82 0.89 94.5 3.04 0.92 122.4
r 0.97 0.74 44.5 0.97 0.81 2.5 rs 2.43 1.54 91.5 2.65 1.58 116.8
nr 0.22 0.17 124.3 0.23 0.19 143.2

NGC 1808 NGC 2460
(R1)SAB(s,nr)a SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rs)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R1 6.38 4.62 130.5 6.52 6.18 42.2 rs 0.37 0.29 21.3 0.45 0.34 110.1
bar 2.55 0.84 144.3 2.67 1.10 26.8
nr 0.24 0.14 138.8 0.25 0.18 26.1

NGC 2550 NGC 2552
(R)SAB(s)b pec (R)SAB(s)m
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 0.82 0.23 102.0 0.82 0.54 177.6 R 1.88 1.22 53.6 1.96 1.67 35.9

NGC 2591 NGC 2604
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})d sp (R1Mathematical equation: \hbox{$_{1}^{\prime}$})SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.18 0.16 34.7 1.21 0.86 16.8 R1Mathematical equation: \hbox{$_{1}^{\prime}$} 0.88 0.57 146.2 1.01 0.57 97.1
bar 0.61 0.12 52.9 0.61 0.14 7.3
rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.55 0.43 123.0 0.63 0.43 81.2

NGC 2608 NGC 2633
SABMathematical equation: \hbox{${\underline{\rm B}}$}(rsMathematical equation: \hbox{${\underline{\rm s}}$})b SAB(rs)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.33 0.60 70.1 1.53 0.74 46.9 rs 0.66 0.32 173.9 0.69 0.49 155.5
bar 1.04 0.34 83.8 1.27 0.39 57.3 bar 0.60 0.25 171.2 0.63 0.38 154.5

NGC 2648 NGC 2654
SA(r)a SBx(r,nd)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.55 0.25 150.1 0.87 0.54 81.7 r 1.17 0.17 64.6 1.17 0.63 178.5

NGC 2681 NGC 2683
(R)SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rMathematical equation: \hbox{${\underline{\rm r}}$}s)0/a (RL)SBx(rMathematical equation: \hbox{${\underline{\rm r}}$}s)0/a sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.35 2.13 105.0 2.35 2.16 165.7 RL 6.82 0.91 43.8 6.83 3.50 3.8
rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.62 0.59 172.5 0.62 0.59 66.1 rMathematical equation: \hbox{${\underline{\rm r}}$}s 3.34 0.39 43.3 3.34 1.48 0.8
bar 0.58 0.42 76.8 0.58 0.42 138.4

NGC 2684 NGC 2685
SA(rs)b (R)S0o PRG pec
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.38 0.34 35.7 0.42 0.38 105.4 R 4.08 1.80 33.9 4.39 2.65 147.0
PRG 1.36 0.70 114.0

NGC 2712 NGC 2715
(R)SAB(rs,nl)ab SA(rs)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.73 1.16 178.0 2.74 2.36 170.2 rs 1.09 0.42 23.2 1.16 1.05 53.0
rs 0.85 0.52 175.3 1.07 0.84 98.5

NGC 2726 NGC 2735
SB?(rs)0/a SA:(r)0/a sp pec
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.47 0.13 87.3 0.47 0.34 175.3 r 0.45 0.13 102.9 0.51 0.33 37.7

NGC 2743 NGC 2748
SB(rs)m (R)SAB(r)bc + PR?
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.33 0.25 96.9 0.39 0.32 106.6 PRG 1.32 0.51 134.5
bar 0.25 0.10 123.8 0.26 0.15 31.0 R 1.08 0.21 38.2 1.11 0.70 163.5
r 0.39 0.16 35.3 0.57 0.38 104.5

NGC 2764 NGC 2770
E(b)3/S(rs)a sp SABMathematical equation: \hbox{${\underline{\rm B}}$}(rs)c sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.50 0.10 20.3 0.51 0.29 172.8 rs 1.03 0.33 141.3 1.22 0.96 119.0

NGC 2775 NGC 2780
SA(r,l)0+ (R)SB(rs)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 1.42 1.06 157.2 1.44 1.30 160.4 R 0.67 0.49 146.6 0.73 0.65 114.3
bar 0.41 0.10 115.5 0.49 0.12 129.8
rs 0.35 0.30 165.4 0.44 0.34 83.8

NGC 2782 NGC 2787
SA(rs,nr)a pec (shells/ripples) (L)SBa(r,bl)0o
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 1.01 0.87 81.8 1.10 0.95 117.7 r 1.67 0.82 101.9 1.74 1.42 149.5
nr 0.15 0.11 80.8 0.17 0.13 133.6 bar 0.93 0.60 147.6 1.41 0.72 71.2

NGC 2793 NGC 2805
RG pec (R)SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rsMathematical equation: \hbox{${\underline{\rm s}}$})c pec
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RG 0.74 0.64 48.3 0.82 0.67 111.5 R 1.60 1.26 152.1 1.69 1.52 51.4
rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.53 0.36 90.5 0.63 0.39 115.5
bar 0.37 0.25 114.7 0.40 0.30 134.5

NGC 2841 NGC 2844
SAMathematical equation: \hbox{${\underline{\rm A}}$}B(r)a SA(r)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 2.01 0.86 149.9 2.01 1.88 4.9 r 0.28 0.12 10.3 0.28 0.21 169.3

NGC 2854 NGC 2859
SAB(r)a (R)SABa(rl,bl,nl,nb?)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.33 0.15 51.7 0.33 0.29 172.1 R 3.42 2.73 85.5 3.48 3.38 47.9
bar 0.32 0.10 58.1 0.33 0.19 14.3 rl 1.33 1.16 92.7 1.47 1.31 76.5
bar 1.13 0.71 161.6 1.41 0.71 83.4

NGC 2882 NGC 2893
SA(rs)b (RL)SAB(l)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.62 0.30 77.4 0.64 0.60 143.0 RL 0.87 0.69 58.4 0.88 0.73 11.6
bar 0.37 0.22 168.0 0.38 0.22 116.6

NGC 2894 NGC 2903
(R:)SAB:0 (R)SB(rs,nr)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.52 0.65 26.2 1.52 1.43 164.5 R 10.12 3.62 19.5 10.12 7.44 179.5
rs 2.55 1.28 7.7 3.03 2.21 124.8
nr 0.16 0.09 24.2 0.19 0.16 70.2

NGC 2906 NGC 2962
SA(rs)ab or SA(rs)b /Sph (R)SAMathematical equation: \hbox{${\underline{\rm A}}$}Ba(rl)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.61 0.33 85.3 0.61 0.55 23.0 R 2.13 1.42 7.5 2.18 2.12 108.1
bar 0.94 0.43 174.5 0.99 0.62 151.3
rl 0.93 0.55 2.7 0.95 0.82 155.6

NGC 2964 NGC 2966
SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rsMathematical equation: \hbox{${\underline{\rm s}}$})b (R?)SABMathematical equation: \hbox{${\underline{\rm B}}$}(rl,nl)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.18 0.58 87.3 1.25 0.92 147.9 R 2.34 1.69 46.0 2.34 2.09 8.2
bar 0.63 0.29 164.6 1.00 0.31 77.9 rl 1.48 0.62 71.5 1.57 0.73 36.6
bar 1.45 0.42 76.4 1.56 0.48 40.1

NGC 2967 NGC 2968
(R)SAB(rs)c SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.55 1.43 126.4 1.61 1.44 71.6 bar 1.18 0.65 39.9 1.31 0.80 134.9
rs 0.61 0.47 88.2 0.61 0.49 28.4 rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.14 0.75 43.1 1.28 0.93 130.4

NGC 2974 NGC 2985
SA(r)0/a (R)SA(rl)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 1.55 0.92 38.2 1.60 1.29 154.3 R 3.34 2.13 1.3 3.36 2.69 13.6
rl 1.48 1.00 175.3 1.48 1.27 0.7

NGC 3003 NGC 3020
SB(rs)d SB(rs)dm
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 1.44 0.28 72.1 1.68 0.99 139.6 rs 0.46 0.24 104.9 0.51 0.44 58.1

NGC 3031 NGC 3032
SA(rs,r,nb)a SA(rl,l)0o
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 6.45 3.29 148.7 6.88 5.68 139.9 rl 0.61 0.54 90.2 0.68 0.61 98.3
r 4.30 2.07 157.4 4.30 3.80 6.8

NGC 3041 NGC 3061
SA(rs)b SAB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)b pec
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 1.15 0.81 84.8 1.30 1.14 104.6 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.59 0.41 2.2 0.61 0.48 34.8
bar 0.35 0.15 158.7 0.35 0.18 174.6

NGC 3066 NGC 3147
SAB(rs)ab pec SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rsMathematical equation: \hbox{${\underline{\rm s}}$})b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

bar 0.44 0.20 91.6 0.46 0.21 135.1 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.67 0.65 75.3 0.81 0.65 92.0
rs 0.41 0.37 39.5 0.45 0.37 88.8 bar 0.64 0.51 136.3 0.66 0.59 134.7

NGC 3153 NGC 3166
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})cd (RL)SBa(rl)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.65 0.47 172.0 1.03 0.64 84.9 RL 4.11 1.73 84.4 4.17 3.03 15.2
rl 0.92 0.66 89.8 1.21 0.90 78.8
bar 0.61 0.51 164.9 1.09 0.51 88.9

NGC 3177 NGC 3182
(R)SA(rsMathematical equation: \hbox{${\underline{\rm s}}$})ab SA(rl)0o
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 0.63 0.43 130.8 0.63 0.49 169.7 rl 0.19 0.16 132.4 0.20 0.19 91.8
rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.24 0.17 27.9 0.27 0.17 75.7

NGC 3184 NGC 3185
SA(rsMathematical equation: \hbox{${\underline{\rm s}}$})bc (RL?)SABax(rMathematical equation: \hbox{${\underline{\rm r}}$}s)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.95 0.81 142.8 0.99 0.82 96.1 RL 2.51 1.65 142.6 2.65 2.41 51.5
rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.27 0.73 130.6 1.29 1.10 156.8
bar 1.13 0.45 114.6 1.25 0.62 142.6

NGC 3198 NGC 3248
SAB(rsMathematical equation: \hbox{${\underline{\rm s}}$})bc (RL)SA(l)0o
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.85 0.40 40.1 1.99 1.12 27.5 RL 1.77 1.10 117.8 1.79 1.77 125.6

NGC 3259 NGC 3266
SA(rl)bc (RL)SB0o
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rl 0.27 0.15 23.9 0.28 0.26 41.2 RL 0.79 0.60 86.2 0.79 0.66 170.9
bar 0.32 0.23 8.3 0.35 0.24 94.7

NGC 3301 NGC 3310
(RL)SABx(r)0+ sp SA(rMathematical equation: \hbox{${\underline{\rm r}}$}s)bc pec (shells/ripples)
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 2.25 0.53 50.5 2.26 1.67 172.6 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.30 0.19 130.7 0.31 0.21 139.9
r 0.99 0.28 53.7 1.01 0.87 26.3

NGC 3319 NGC 3321
(R)SB(s)cd SABMathematical equation: \hbox{${\underline{\rm B}}$}(rMathematical equation: \hbox{${\underline{\rm r}}$}s)cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 5.38 2.94 37.2 5.64 4.96 139.1 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.54 0.34 14.0 0.76 0.50 107.9
bar 0.48 0.06 39.0 0.48 0.11 172.7

NGC 3338 NGC 3344
SA(rs,l)bc SAB(r)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.68 0.42 92.5 0.87 0.67 98.7 r 1.02 0.87 125.2 1.04 0.95 139.8
bar 0.84 0.52 4.5 0.89 0.55 49.2

NGC 3346 NGC 3351
SB(rs)cd (R)SB(r,nr)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.63 0.43 149.6 0.68 0.47 46.9 R 4.61 3.34 8.7 4.72 4.60 85.5
bar 0.50 0.14 93.7 0.52 0.17 152.9 r 2.18 1.75 6.2 2.48 2.18 93.7
bar 2.01 1.08 112.5 2.81 1.10 98.3
nr 0.20 0.15 26.1 0.23 0.19 63.4

NGC 3359 NGC 3361
SB(rs)d SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rs)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 1.44 1.32 127.1 2.31 1.39 94.6 rs 0.30 0.17 171.0 0.47 0.27 72.3
bar 0.62 0.12 15.7 0.77 0.16 47.3

NGC 3368 NGC 3380
(RL)SAB(rMathematical equation: \hbox{${\underline{\rm r}}$}s,nrl,nb)0+ (RL)SABMathematical equation: \hbox{${\underline{\rm B}}$}(rMathematical equation: \hbox{${\underline{\rm r}}$}s)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 5.94 3.57 177.8 6.04 5.31 24.5 RL 1.35 1.29 119.1 1.44 1.29 82.5
rMathematical equation: \hbox{${\underline{\rm r}}$}s 2.42 1.58 156.1 2.73 2.13 127.2 bar 0.66 0.28 19.7 0.67 0.29 149.9
bar 2.09 1.20 125.0 2.82 1.35 113.2 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.57 0.39 16.7 0.58 0.41 144.3
nrl 0.22 0.15 169.0 0.24 0.22 112.6

NGC 3381 NGC 3389
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})dm SAB(rsMathematical equation: \hbox{${\underline{\rm s}}$})c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.61 0.54 61.6 0.65 0.61 81.0 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.49 0.29 103.5 0.68 0.49 95.7
bar 0.59 0.13 75.6 0.60 0.16 22.3

NGC 3403 NGC 3437
SA(rs)bc: SA(rs)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.71 0.28 69.0 0.79 0.63 131.4 rs 0.54 0.21 119.1 0.54 0.51 10.5

NGC 3455 NGC 3471
SA(rs:)c (R)SB(s)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.36 0.22 63.5 0.41 0.36 85.7 R 1.10 0.65 13.5 1.11 0.97 13.0
bar 0.09 0.03 32.9 0.10 0.04 35.0

NGC 3485 NGC 3486
SABMathematical equation: \hbox{${\underline{\rm B}}$}(rMathematical equation: \hbox{${\underline{\rm r}}$}s)b SAB(r)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

bar 0.91 0.25 45.8 0.93 0.26 32.1 bar 0.76 0.33 75.3 0.77 0.44 166.5
rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.70 0.61 58.9 0.72 0.63 57.3 r 0.70 0.62 84.9 0.84 0.70 89.1

NGC 3489 NGC 3495
(R)SB(r:)0o (R)SB(rs)c:
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.53 0.45 73.2 1.54 0.90 6.4 R 3.05 0.58 20.1 3.06 2.18 171.6
r 0.71 0.58 39.7 1.25 0.66 97.3 rs 1.01 0.30 20.6 1.12 1.01 99.0

NGC 3504 NGC 3507
(R1Mathematical equation: \hbox{$_{1}^{\prime}$})SABMathematical equation: \hbox{${\underline{\rm B}}$}(rMathematical equation: \hbox{${\underline{\rm r}}$}s,nl)a (R)SABMathematical equation: \hbox{${\underline{\rm B}}$}(s)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R1Mathematical equation: \hbox{$_{1}^{\prime}$} 2.03 1.89 109.2 2.04 1.93 148.6 R 2.34 2.11 75.8 2.44 2.34 101.3
rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.18 0.65 154.7 1.18 0.67 24.6 bar 0.79 0.34 109.3 0.82 0.38 34.6
bar 1.13 0.40 145.8 1.13 0.41 15.1

NGC 3513 NGC 3521
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})c SA(rl,r)bc/E(b?)3 pec
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.82 0.67 64.0 0.83 0.81 135.1 rl 1.97 0.89 156.1 2.16 1.79 131.3
bar 0.72 0.19 118.3 0.82 0.20 57.0 r 0.83 0.27 160.0 0.83 0.59 170.6

NGC 3547 NGC 3556
SB(rs)cd SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.41 0.17 13.0 0.44 0.32 29.0 rsMathematical equation: \hbox{${\underline{\rm s}}$} 3.87 0.86 80.6 3.87 2.94 179.3
bar 0.25 0.07 174.7 0.26 0.13 154.4

NGC 3583 NGC 3593
(R)SAB(rs)abMathematical equation: \hbox{${\underline{\rm b}}$} SA(r)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.96 1.04 118.7 2.00 1.30 159.6 r 0.32 0.11 89.7 0.32 0.24 1.7
bar 0.71 0.29 77.4 0.85 0.31 117.6
rs 0.69 0.53 77.4 0.84 0.56 108.5

NGC 3611 NGC 3614
(R:)SA(r)a SA(r)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.96 1.08 27.9 1.96 1.72 172.6 r 0.47 0.24 70.9 0.63 0.32 119.9
r 0.17 0.12 17.8 0.20 0.17 113.5

NGC 3623 NGC 3625
(R)SABx(rs)a SB(rs)cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 5.85 1.32 172.5 5.90 4.65 166.7 rs 0.37 0.15 155.5 0.40 0.35 52.8
rs 3.86 0.88 169.5 4.16 2.91 148.0

NGC 3626 NGC 3633
(RL,R)SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rl,nl?)0/a SA(r)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 2.35 1.55 166.8 2.37 2.22 26.1 r 0.32 0.10 68.8 0.33 0.27 159.8
R 1.47 1.07 152.9 1.62 1.41 118.6
rl 0.69 0.47 160.6 0.70 0.67 139.0
bar 0.66 0.33 169.8 0.66 0.47 14.8

NGC 3637 NGC 3642
(RL)SBa(rl,bl)0+ SA(rl)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 1.44 1.12 133.7 1.44 1.25 171.9 rl 0.42 0.40 105.1 0.44 0.42 85.4
rl 0.55 0.52 159.1 0.59 0.55 73.6
bar 0.49 0.33 35.7 0.55 0.33 80.5

NGC 3664 NGC 3673
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})m SABxMathematical equation: \hbox{${\underline{\rm B}}_{\rm x}$}(rs)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

bar 1.42 0.27 40.1 1.65 0.30 125.5 bar 1.47 0.38 84.3 1.50 0.62 14.1
rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.34 1.26 80.2 1.62 1.34 92.4 rs 1.42 0.74 77.7 1.42 1.22 4.6

NGC 3675 NGC 3681
(R,R)SA(s)b/E(d)4 SAB(r,l)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.42 0.89 177.7 2.45 2.03 161.5 r 0.60 0.51 159.8 0.63 0.53 55.8
R 1.62 0.54 179.4 1.62 1.25 174.3 bar 0.26 0.16 154.8 0.27 0.18 38.6

NGC 3682 NGC 3683A
SA(r)0+ SAB(rs)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.20 0.13 98.0 0.21 0.19 41.5 rs 0.46 0.24 67.8 0.47 0.36 8.5
bar 0.18 0.11 76.7 0.19 0.15 33.5

NGC 3684 NGC 3687
(R)SAB(s)c (RL)SABMathematical equation: \hbox{${\underline{\rm B}}$}(rs)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.52 0.98 114.6 1.56 1.42 147.8 RL 1.43 1.34 164.6 1.49 1.35 108.7
bar 0.36 0.17 128.5 0.37 0.24 17.3 rs 0.44 0.41 123.7 0.46 0.41 85.5
bar 0.43 0.21 174.8 0.44 0.22 130.4

NGC 3689 NGC 3691
SA(r)b SB(r)m
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.24 0.13 94.3 0.24 0.21 15.6 r 0.75 0.51 11.4 0.77 0.65 150.9
bar 0.70 0.17 31.2 0.71 0.22 13.1

NGC 3692 NGC 3701
(RL)SA(r)0/a sp SA(rs)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 1.81 0.40 92.9 1.83 1.59 163.4 rs 0.26 0.15 155.7 0.33 0.24 67.8
r 0.68 0.15 94.0 0.68 0.61 2.7

NGC 3705 NGC 3715
(R)SAB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)b SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rs)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.53 1.06 119.6 2.54 2.00 4.8 rs 0.32 0.27 112.0 0.35 0.30 119.6
rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.17 0.49 121.8 1.18 0.92 13.3 bar 0.25 0.18 75.8 0.30 0.18 108.1
bar 0.42 0.37 65.5 0.77 0.38 94.9

NGC 3718 NGC 3726
SAB(r,l,nl)a pec SABMathematical equation: \hbox{${\underline{\rm B}}$}(r)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 2.91 2.14 154.3 6.29 2.57 98.2 r 1.50 0.84 12.1 1.54 1.31 154.0
bar 1.38 0.30 30.2 1.43 0.47 20.2

NGC 3729 NGC 3730
(L)SB(r)0/a + dwarf comp. SA(rs)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 1.25 0.59 160.4 1.28 0.80 158.1 rs 0.21 0.18 94.9 0.21 0.19 32.6
bar 0.70 0.24 25.3 0.80 0.30 45.5

NGC 3735 NGC 3755
SAB(rs)c: sp (R)SABMathematical equation: \hbox{${\underline{\rm B}}$}(s)c pec
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.79 0.15 130.7 0.80 0.64 18.8 R 2.64 0.97 130.3 2.71 2.59 52.2

NGC 3769 NGC 3780
(R)SB(s)cd SA(rs)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 0.98 0.30 145.5 1.07 0.87 136.8 rs 0.48 0.27 77.5 0.48 0.35 171.7

NGC 3782 NGC 3786
SB(rs)dm (R)SA(r)0/a pec
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.93 0.47 175.2 0.94 0.57 170.3 R 1.77 0.79 75.1 1.79 1.43 17.4
bar 0.45 0.12 172.6 0.45 0.14 168.3 r 0.85 0.40 69.4 0.85 0.73 171.9

NGC 3788 NGC 3835
SA(r)a (L)SA(rMathematical equation: \hbox{${\underline{\rm r}}$}s)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.44 0.14 0.3 0.61 0.42 72.2 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.51 0.16 58.8 0.51 0.48 9.3

NGC 3870 NGC 3876
SB(rs)0o? Ring pec
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.66 0.55 28.9 0.76 0.66 82.8 RG 0.56 0.39 110.0 0.68 0.55 74.0
bar 0.32 0.14 29.8 0.32 0.19 12.1

NGC 3885 NGC 3887
(L)SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rlMathematical equation: \hbox{${\underline{\rm l}}$},nl)0+ (RL)SABxMathematical equation: \hbox{${\underline{\rm B}}_{\rm x}$}(rs)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rlMathematical equation: \hbox{${\underline{\rm l}}$} 0.66 0.32 126.6 0.78 0.63 65.7 RL 3.38 2.33 9.9 3.42 2.74 158.3
bar 1.13 0.33 1.9 1.16 0.39 155.7
rs 1.13 0.82 174.0 1.20 0.92 134.8

NGC 3888 NGC 3892
SA(rs)b (RL)SABMathematical equation: \hbox{${\underline{\rm B}}$}(rl)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.42 0.30 129.6 0.43 0.39 41.2 RL 2.55 2.20 4.0 2.66 2.20 85.5
rl 1.16 0.91 92.6 1.16 0.94 171.5
bar 1.13 0.60 100.5 1.13 0.63 0.9

NGC 3898 NGC 3900
(RR)SA0+ SA(r)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.38 0.84 104.0 2.40 1.48 170.1 r 1.10 0.43 179.7 1.10 0.79 171.7
R 1.80 0.65 106.2 1.81 1.14 175.3

NGC 3936 NGC 3941
SA(rs)c sp (R)SBa0o
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.42 0.12 64.5 0.77 0.42 89.2 R 1.78 0.94 3.9 1.80 1.47 164.0
bar 0.70 0.39 174.9 0.76 0.57 141.3

NGC 3949 NGC 3953
SAB(rsMathematical equation: \hbox{${\underline{\rm s}}$})c SB(r)bMathematical equation: \hbox{${\underline{\rm b}}$}c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.67 0.33 117.3 0.68 0.53 164.6 r 1.60 0.73 6.6 1.68 1.33 147.0
bar 0.19 0.10 113.5 0.20 0.17 143.2 bar 0.91 0.42 47.3 1.29 0.57 61.4

NGC 3955 NGC 3956
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})bc/S0 /Sph SAB(rs)cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.66 0.16 173.3 0.71 0.42 30.0 rs 0.78 0.21 54.7 0.93 0.57 134.5

NGC 3976 NGC 3982
SAB(rs)bMathematical equation: \hbox{${\underline{\rm b}}$}c SA(rs)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.85 0.22 58.6 0.85 0.67 7.8 rs 0.47 0.42 64.8 0.51 0.44 69.9

NGC 3985 NGC 3992
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})m SB(rs,nb)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.24 0.20 91.9 0.27 0.23 74.0 rs 2.73 1.69 73.4 2.99 2.70 72.7
bar 0.15 0.09 139.5 0.19 0.09 73.0 bar 1.80 0.69 38.5 2.32 0.94 126.7

NGC 3998 NGC 4027
SA(r)0o SB(rs)dm
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 1.21 1.01 139.1 1.26 1.20 73.9 rs 0.65 0.56 102.3 0.79 0.57 98.6
bar 0.22 0.06 87.0 0.28 0.06 94.9

NGC 4030 NGC 4037
SA(rs)bc SAB(rs)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.43 0.31 34.7 0.44 0.40 21.7 bar 1.08 0.40 13.3 1.13 0.44 37.1
rs 0.91 0.85 105.0 1.05 0.86 100.1

NGC 4041 NGC 4045
SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rs)c (R1Mathematical equation: \hbox{$_{1}^{\prime}$}L)SAB(rMathematical equation: \hbox{${\underline{\rm r}}$}s,nl)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.35 0.30 83.6 0.37 0.31 55.9 R1Mathematical equation: \hbox{$_1^{\prime}$}L 1.91 0.95 89.1 1.91 1.43 3.2
bar 0.20 0.10 74.5 0.21 0.10 37.0 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.65 0.48 85.2 0.73 0.65 96.8
bar 0.54 0.33 17.9 0.80 0.34 100.1

NGC 4050 NGC 4051
(RL)SABMathematical equation: \hbox{${\underline{\rm B}}$}(rMathematical equation: \hbox{${\underline{\rm r}}$}s)a SAB(rs)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 3.36 2.01 88.8 3.38 3.03 165.9 bar 2.22 0.59 132.1 2.23 0.68 11.6
rMathematical equation: \hbox{${\underline{\rm r}}$}s 2.02 1.33 90.1 2.04 1.99 142.6 rs 2.07 1.32 115.9 2.07 1.53 170.3
bar 1.81 0.54 77.8 1.89 0.78 157.3

NGC 4062 NGC 4064
SA(rs)b (RL)SB(ls)0o/d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.72 0.37 107.6 0.98 0.69 72.4 RL 3.27 1.16 148.2 3.27 2.46 176.9

NGC 4067 NGC 4094
SB(rs)ab (R)SB(s)cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.38 0.33 45.3 0.44 0.38 89.0 R 1.74 0.64 55.8 2.03 1.47 130.4
bar 0.37 0.17 61.7 0.38 0.21 27.4

NGC 4100 NGC 4102
(RL)SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rs,nr?)ab sp (R)SAMathematical equation: \hbox{${\underline{\rm A}}$}Ba(l)ab /Sph
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 4.65 1.48 166.1 4.80 4.36 36.1 R 1.24 0.67 42.8 1.27 1.19 42.1
rs 0.94 0.29 155.0 1.14 0.72 131.7 bar 0.44 0.27 57.9 0.55 0.38 62.7
nr 0.12 0.05 151.7 0.18 0.10 110.2

NGC 4108 NGC 4108B
SAB(rs)c SABMathematical equation: \hbox{${\underline{\rm B}}$}(rs)cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.26 0.17 97.0 0.26 0.21 4.2 rs 0.29 0.22 114.8 0.32 0.24 125.0
bar 0.13 0.08 101.4 0.13 0.09 11.0

NGC 4116 NGC 4120
SB(rs)d SB(rs:)d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 1.58 1.00 135.4 1.88 1.51 111.8 rs 0.42 0.20 168.9 0.68 0.42 88.6
bar 1.52 0.43 142.7 1.53 0.76 175.2

NGC 4123 NGC 4136
SBx(rs)b SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rs)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

bar 1.75 0.42 106.1 1.84 0.59 155.0 rs 0.68 0.50 92.4 0.74 0.52 57.9
rs 1.61 1.05 114.4 1.68 1.47 141.1 bar 0.49 0.23 22.9 0.50 0.25 154.3

NGC 4138 NGC 4141
SA(r)0+ SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.74 0.40 154.3 0.76 0.68 35.8 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.38 0.28 57.2 0.41 0.34 125.9
bar 0.24 0.11 86.2 0.25 0.15 17.9

NGC 4145 NGC 4152
SAB(rs)d SAB(rsMathematical equation: \hbox{${\underline{\rm s}}$})c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.79 0.35 81.1 0.88 0.55 141.6 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.32 0.27 93.5 0.38 0.30 107.1
bar 0.36 0.16 135.6 0.49 0.20 60.9 bar 0.17 0.11 40.9 0.22 0.11 94.3

NGC 4158 NGC 4162
(RL)SABa(r)a SA(r)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 0.62 0.44 68.5 0.62 0.57 5.0 r 0.37 0.22 166.8 0.37 0.34 161.7
r 0.30 0.21 77.4 0.31 0.27 32.4
bar 0.23 0.13 52.0 0.24 0.17 151.3

NGC 4178 NGC 4189
(R2Mathematical equation: \hbox{$_{2}^{\prime}$})SB(s)d SABMathematical equation: \hbox{${\underline{\rm B}}$}(rsMathematical equation: \hbox{${\underline{\rm s}}$})bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R2Mathematical equation: \hbox{$_{2}^{\prime}$} 3.53 1.07 31.3 3.81 3.51 101.7 bar 0.84 0.24 102.5 0.91 0.28 38.7
rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.73 0.58 109.5 0.86 0.64 66.1

NGC 4192 NGC 4193
(R)SABx(rs,nd)a (RL)SAB(rsMathematical equation: \hbox{${\underline{\rm s}}$})a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 7.96 1.67 155.5 7.97 5.39 175.6 RL 1.75 0.79 88.3 1.75 1.71 159.0
rs 4.10 0.81 151.2 4.32 2.47 156.4 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.44 0.28 95.5 0.63 0.43 82.0

NGC 4210 NGC 4212
SB(rs)bc SA(rs)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.47 0.33 123.0 0.54 0.39 55.8 rs 0.72 0.40 76.5 0.72 0.61 6.2
bar 0.38 0.16 45.4 0.46 0.17 121.3

NGC 4216 NGC 4220
(R)SABbox,a(r,nd)a (L)SAB(r)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 5.84 0.55 20.9 5.85 3.02 3.9 r 1.17 0.21 137.8 1.17 0.70 172.7
r 1.86 0.26 19.2 1.89 1.42 165.5

NGC 4224 NGC 4234
(R)SA0+ (L)SB(rs)m
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.44 0.28 57.8 1.45 0.70 9.4 bar 0.64 0.11 78.3 0.67 0.13 33.5
rs 0.54 0.37 71.3 0.56 0.43 37.9

NGC 4237 NGC 4245
(R)SA(s)b (RL)SB(r,nr)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.14 0.71 105.8 1.15 1.14 37.5 RL 2.65 1.89 16.6 2.72 2.20 30.5
bar 1.25 0.61 136.5 1.38 0.66 128.1
r 1.21 0.90 151.8 1.30 1.01 132.4
nr 0.16 0.13 176.3 0.16 0.15 168.2

NGC 4250 NGC 4256
(R)SAB(rl,nl!)0+ (R)S0+ sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 3.10 2.68 83.8 3.19 2.96 133.1 R 2.37 0.20 41.6 2.37 1.10 0.3
rl 1.43 1.01 166.5 1.60 1.02 73.7
bar 1.43 0.60 165.1 1.60 0.61 69.8

NGC 4258 NGC 4260
(R)SAB(rs,nb or ndsp)a SABMathematical equation: \hbox{${\underline{\rm B}}$}(rsMathematical equation: \hbox{${\underline{\rm s}}$})a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 16.51 5.47 146.6 23.39 15.26 69.9 rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.12 0.62 57.9 1.61 1.12 89.4
rs 6.33 2.03 155.7 10.90 4.66 66.2

NGC 4268 NGC 4274
SA:(rMathematical equation: \hbox{${\underline{\rm r}}$}s)0+ sp (R)SB(r,nr)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.66 0.21 48.6 0.67 0.42 13.6 R 5.92 1.50 100.8 5.93 4.41 177.3
r 2.79 0.91 100.3 2.81 2.66 155.6
nr 0.26 0.08 102.7 0.26 0.24 29.5

NGC 4286 NGC 4293
d(RLMathematical equation: \hbox{${\underline{\rm L}}$})SA(l)0o,N /Sph (R)SBx(rs)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 0.78 0.55 160.2 0.91 0.77 74.3 R 4.20 2.11 64.4 4.51 4.19 86.2
rs 2.49 0.99 72.8 2.71 1.96 36.5

NGC 4298 NGC 4303
(R)SA(rs)bc SAB(rs,nl)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.13 0.96 138.3 2.20 1.62 22.8 bar 1.86 0.56 2.1 1.95 0.60 42.4
rs 0.71 0.25 132.5 0.71 0.43 3.4 rs 1.59 1.33 81.0 1.76 1.35 106.8

NGC 4309 NGC 4310
SAB(rl)0o SA(rMathematical equation: \hbox{${\underline{\rm r}}$}s)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rl 0.99 0.37 90.5 1.00 0.68 172.5 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.43 0.14 157.2 0.43 0.30 177.0
bar 0.66 0.34 73.9 0.80 0.52 126.3

NGC 4313 NGC 4314
(R)SB(s)0/a sp (R1Mathematical equation: \hbox{$_{1}^{\prime}$})SB(rl,nr)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.40 0.20 142.0 1.41 0.87 4.5 R1Mathematical equation: \hbox{$_{1}^{\prime}$} 3.72 3.03 51.2 3.72 3.23 179.4
bar 2.22 0.80 146.9 2.37 0.80 94.9
rl 2.07 1.74 155.1 2.20 1.74 99.8
nr 0.23 0.18 140.0 0.25 0.18 88.7

NGC 4316 NGC 4319
SB(rs?)c sp (R)SABMathematical equation: \hbox{${\underline{\rm B}}$}(rMathematical equation: \hbox{${\underline{\rm r}}$}s)a pec
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.95 0.06 111.9 0.95 0.39 2.1 R 2.16 1.69 168.0 2.32 2.00 53.9
rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.12 0.61 134.4 1.16 0.76 154.5
bar 0.60 0.30 162.8 0.61 0.37 19.2

NGC 4321 NGC 4324
SAB(rsMathematical equation: \hbox{${\underline{\rm s}}$},nr)bc (L)SA(r)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

bar 2.22 0.90 107.9 2.52 0.96 122.5 r 0.72 0.32 54.0 0.75 0.71 119.1
rsMathematical equation: \hbox{${\underline{\rm s}}$} 2.03 1.70 103.0 2.38 1.75 106.3
nr 0.30 0.24 158.6 0.30 0.29 1.6

NGC 4336 NGC 4343
SAB(r)0/a (R)SBx(r)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.59 0.32 167.0 0.60 0.53 26.8 R 0.92 0.14 127.5 0.93 0.41 171.3
bar 0.28 0.18 101.7 0.45 0.19 102.2 r 0.45 0.10 132.9 0.46 0.28 12.6

NGC 4344 NGC 4348
dSA(r)0+, N SB(rs)bc sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.31 0.27 155.8 0.35 0.27 94.8 rs 0.68 0.14 33.8 0.71 0.58 151.3

NGC 4351 NGC 4355
(R)SAMathematical equation: \hbox{${\underline{\rm A}}$}B(s)dm imbedded (RL)SAMathematical equation: \hbox{${\underline{\rm A}}$}B(l)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.25 0.83 76.9 1.38 1.11 51.4 RL 0.97 0.49 60.1 1.01 0.95 129.5
bar 0.63 0.32 61.6 0.63 0.62 127.3

NGC 4369 NGC 4371
(R)SB(rs)0/a: pec (L)SBa(r,nr)0o
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.42 1.30 156.8 1.45 1.31 62.2 r 2.09 1.04 91.1 2.14 1.97 35.1
rs 0.28 0.25 105.6 0.28 0.26 5.9 bar 1.13 0.84 158.0 2.13 0.86 84.7
bar 0.27 0.10 150.5 0.27 0.10 50.2 nr 0.35 0.14 87.3 0.35 0.27 177.0

NGC 4378 NGC 4380
(R)SA(l)a (R)SA(r,l)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.93 2.45 178.5 2.99 2.85 43.2 R 2.02 1.07 156.5 2.03 1.93 169.8
r 0.98 0.54 151.8 1.04 0.92 132.5

NGC 4384 NGC 4385
(L)SB(rs)dm SABMathematical equation: \hbox{${\underline{\rm B}}$}(rs)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.30 0.15 75.5 0.30 0.20 168.3 rs 1.03 0.60 84.7 1.10 0.96 46.6
bar 0.07 0.04 157.9 0.09 0.04 80.3 bar 0.97 0.37 99.4 1.12 0.55 41.7

NGC 4388 NGC 4389
SA:(rs)a sp SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)0/a/d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 1.39 0.17 89.3 1.40 0.62 172.4 rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.50 0.75 101.9 1.52 1.16 15.7
bar 1.38 0.25 104.6 1.40 0.38 13.4

NGC 4394 NGC 4402
(R)SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s,nl)0/a (R)SAMathematical equation: \hbox{${\underline{\rm A}}$}B(s)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.74 2.45 77.5 2.99 2.60 113.0 R 1.86 0.20 89.8 1.95 1.28 23.2
bar 1.52 0.65 142.2 1.60 0.72 38.3
rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.50 1.31 129.2 1.58 1.44 58.5

NGC 4405 NGC 4411A
(R)SABMathematical equation: \hbox{${\underline{\rm B}}$}(rMathematical equation: \hbox{${\underline{\rm r}}$}s)a SB(rs)cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.05 0.66 24.2 1.05 0.87 13.3 rs 0.57 0.43 32.6 0.68 0.43 94.5
rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.37 0.32 13.8 0.42 0.37 96.4 bar 0.16 0.03 109.7 0.16 0.03 173.4
bar 0.34 0.14 7.9 0.34 0.18 163.6

NGC 4412 NGC 4413
SABMathematical equation: \hbox{${\underline{\rm B}}$}(rsMathematical equation: \hbox{${\underline{\rm s}}$})bc (RL)SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.73 0.56 77.9 0.73 0.58 24.3 RL 2.81 1.52 68.5 2.81 2.14 178.2
bar 0.54 0.16 119.7 0.56 0.16 63.5 rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.28 0.64 58.6 1.31 0.88 159.1
bar 0.49 0.24 14.2 0.64 0.26 112.6

NGC 4414 NGC 4416
SA(rl)bc (RL)SB(rs)dm
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rl 0.68 0.39 145.2 0.82 0.60 122.0 RL 1.08 1.01 98.4 1.17 1.07 82.4
rs 0.41 0.32 66.6 0.43 0.36 139.6
bar 0.19 0.06 7.5 0.22 0.06 97.7

NGC 4424 NGC 4430
(R2Mathematical equation: \hbox{$_{2}^{\prime}$}L)SB(s)0/a pec SAB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)dm
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R2Mathematical equation: \hbox{$_{2}^{\prime}$}L 3.18 1.53 89.9 3.25 2.70 22.5 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.56 0.51 102.8 0.62 0.54 72.6
bar 1.62 0.58 97.6 1.73 0.98 29.1 bar 0.50 0.21 118.1 0.55 0.22 50.5

NGC 4448 NGC 4450
(R)SB(r)a (R)SAB(rs)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.50 0.74 92.6 2.50 2.28 10.9 R 3.43 2.20 164.1 3.56 3.04 145.7
r 1.47 0.49 92.2 1.51 1.47 82.6 rs 1.51 0.96 10.0 1.64 1.28 44.2
bar 1.46 0.68 7.0 1.52 0.94 25.0

NGC 4451 NGC 4454
SA(r)0+c (RL)SAB(r)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.43 0.23 157.4 0.43 0.32 172.6 RL 2.00 1.83 105.1 2.09 1.83 83.0
r 1.09 0.80 34.4 1.10 0.83 10.0
bar 1.02 0.49 22.0 1.02 0.51 175.8

NGC 4457 NGC 4460
(RR)SAB(l)0+ SA(r:)0c sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 4.04 3.76 78.8 4.11 3.98 52.8 r 0.42 0.13 38.9 0.49 0.42 95.4
R 2.42 2.24 162.7 2.61 2.24 93.3
bar 0.97 0.61 65.8 0.97 0.65 179.3

NGC 4461 NGC 4462
SA(r,l)0+ SABx(rs)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 1.47 0.54 5.1 1.58 1.34 134.2 rs 1.33 0.41 118.6 1.33 0.90 174.8

NGC 4491 NGC 4492
SB(rs)0/a SA(rMathematical equation: \hbox{${\underline{\rm r}}$}s)0
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.89 0.43 151.7 0.94 0.80 38.4 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.48 0.42 55.9 0.50 0.45 55.0
bar 0.40 0.18 130.3 0.46 0.29 134.4

NGC 4496A NGC 4498
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})d SB(rs)d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.99 0.89 70.0 1.02 0.98 70.5 rs 1.24 0.62 129.4 1.29 0.97 153.2
bar 0.53 0.11 52.6 0.53 0.12 168.7 bar 1.05 0.19 123.5 1.10 0.30 155.6

NGC 4501 NGC 4504
SA(rsMathematical equation: \hbox{${\underline{\rm s}}$})abMathematical equation: \hbox{${\underline{\rm b}}$} SAB(rs)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.55 0.61 137.4 1.59 1.18 159.9 rs 0.93 0.71 134.1 1.18 0.92 98.6
bar 0.36 0.18 149.4 0.37 0.29 25.2

NGC 4519 NGC 4522
SAB(rsMathematical equation: \hbox{${\underline{\rm s}}$})cd (R)SABa?(r,rs)a: pec
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.67 0.54 69.2 0.85 0.54 95.5 R 2.38 0.56 32.9 2.41 2.12 158.6
bar 0.49 0.24 69.9 0.62 0.24 99.1 r 1.32 0.36 35.4 1.39 1.28 57.7
rs 0.74 0.17 35.1 0.75 0.65 14.5

NGC 4525 NGC 4527
(R)SB(s)cd (R2Mathematical equation: \hbox{$_{2}^{\prime}$})SAB(rs,nr)bcMathematical equation: \hbox{${\underline{\rm c}}$}
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.28 0.56 34.9 1.49 0.87 136.0 R2Mathematical equation: \hbox{$_{2}^{\prime}$} 4.75 0.95 65.4 4.79 3.41 169.1
bar 0.46 0.20 80.2 0.58 0.28 53.2 rs 1.56 0.33 68.4 1.58 1.20 12.4
nr 0.23 0.07 61.7 0.28 0.20 120.4

NGC 4528 NGC 4531
SB(r)0o (L)SA(rMathematical equation: \hbox{${\underline{\rm r}}$}s)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.37 0.19 5.4 0.37 0.32 176.7 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.69 0.46 164.8 0.74 0.64 51.1
bar 0.17 0.15 63.9 0.28 0.15 85.0

NGC 4536 NGC 4540
SAB(rs)bMathematical equation: \hbox{${\underline{\rm b}}$}c SAB(rs)b: or SAB(rs)m /Sph, N
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 3.05 0.85 121.1 3.11 1.92 164.8 rs 0.69 0.66 111.6 0.72 0.66 72.5
bar 0.30 0.12 53.6 0.30 0.13 177.4

NGC 4548 NGC 4565
SB(rs)a SBx(r)aMathematical equation: \hbox{${\underline{\rm a}}$}b sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 2.04 1.52 85.2 2.56 1.56 103.7 r 3.12 0.22 135.6 3.13 1.33 3.3
bar 1.93 0.90 61.3 2.49 0.90 91.5

NGC 4567 NGC 4568
SA(rs)bc SA(rsMathematical equation: \hbox{${\underline{\rm s}}$})bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.51 0.37 36.6 0.71 0.41 106.7 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.41 0.22 22.4 0.50 0.40 108.9
bar 0.28 0.21 56.0 0.36 0.25 109.9

NGC 4569 NGC 4579
(L)SBx(rs,x1r)a (RL,R)SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 4.01 1.76 17.5 4.73 3.66 121.4 RL 4.33 3.10 96.7 4.39 4.10 27.5
x1r 2.20 0.38 16.0 2.34 0.87 156.3 R 3.13 2.20 98.7 3.18 2.90 29.6
rsMathematical equation: \hbox{${\underline{\rm s}}$} 2.22 1.34 66.1 2.44 1.62 135.4
bar 1.41 0.73 59.2 1.59 0.87 132.3

NGC 4580 NGC 4591
(R)SA(rMathematical equation: \hbox{${\underline{\rm r}}$}s1,rs2)a SAB(rs)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.86 1.26 161.6 1.88 1.64 20.8 bar 0.28 0.10 38.7 0.28 0.19 6.2
rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.12 0.81 158.3 1.12 1.06 19.4 rs 0.26 0.15 31.1 0.30 0.26 115.2
rs 0.67 0.40 156.2 0.68 0.52 2.4

NGC 4593 NGC 4594
(R)SB(rs)a (R)SA(l)0+ sp/E1
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 3.54 2.51 108.2 3.55 3.00 8.0 R 4.59 0.44 89.0 4.59 1.06 0.4
rs 2.03 1.30 81.4 2.11 1.50 145.3
bar 1.75 0.70 57.5 1.95 0.75 126.2

NGC 4596 NGC 4597
(RLMathematical equation: \hbox{${\underline{\rm L}}$})SB(rs)0/a (R)SB(s)dm
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 3.40 2.66 140.1 3.63 3.07 49.1 R 2.52 1.09 39.6 2.65 2.40 131.3
rs 2.11 1.44 82.3 2.34 1.60 126.7
bar 1.79 0.85 74.1 2.01 0.92 125.8

NGC 4618 NGC 4625
(R)SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})m (R)SAB(rs)m
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.26 2.03 33.2 2.78 2.22 81.0 R 0.95 0.85 151.3 0.96 0.90 159.8
rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.17 0.94 82.2 1.55 0.95 81.4 rs 0.33 0.28 80.8 0.35 0.28 96.9
bar 0.68 0.25 65.3 0.83 0.27 61.8 bar 0.27 0.17 23.2 0.28 0.18 46.1

NGC 4628 NGC 4639
(R)SBa(s)a beams from ce (R)SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.12 0.19 44.4 1.13 0.66 176.9 R 2.36 1.38 116.4 2.63 1.90 134.2
rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.89 0.79 127.6 1.22 0.89 92.5
bar 0.84 0.37 169.5 1.03 0.47 53.3

NGC 4641 NGC 4643
SA(rl)0o (L)SB(r,nl)0o
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rl 0.19 0.17 35.4 0.20 0.18 119.4 r 1.82 1.55 54.8 1.95 1.82 95.6
bar 1.59 0.84 132.3 1.96 0.85 79.5

NGC 4647 NGC 4651
SAB(rs)cd SA(rMathematical equation: \hbox{${\underline{\rm r}}$}s)bMathematical equation: \hbox{${\underline{\rm b}}$}c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.27 0.17 12.2 0.35 0.18 74.3 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.80 0.49 79.5 0.85 0.80 74.5
bar 0.14 0.09 114.1 0.14 0.11 147.0

NGC 4654 NGC 4658
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})cd SB(rs)d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.17 0.73 126.8 1.36 1.14 71.3 bar 0.31 0.08 36.0 0.41 0.11 52.8
bar 0.84 0.27 120.1 0.84 0.49 178.6 rs 0.30 0.22 40.3 0.46 0.25 75.0

NGC 4659 NGC 4680
(R)SAB(l)0o SAB(rs)b /Sph
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.04 0.64 2.8 1.06 0.86 25.0 rs 0.53 0.28 58.1 0.55 0.35 31.3
bar 0.26 0.22 72.4 0.36 0.22 86.1 bar 0.31 0.12 168.5 0.37 0.13 121.0

NGC 4682 NGC 4689
SA(r)bc (R)SA(rs)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.22 0.16 82.6 0.32 0.22 90.9 R 1.86 1.51 165.3 1.88 1.85 62.0
rs 0.57 0.44 127.2 0.64 0.48 120.1

NGC 4691 NGC 4698
(RL,R)SBm/S0/a (R)SA(rr)0/a/E2
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 2.79 2.15 25.3 2.81 2.59 161.7 R 7.91 2.73 167.7 7.91 4.85 2.2
R 1.58 1.37 73.0 1.82 1.44 70.9 r 2.15 0.71 169.4 2.15 1.25 6.3
bar 0.46 0.10 98.2 0.55 0.10 71.7 r 1.58 0.50 168.9 1.58 0.89 5.0

NGC 4699 NGC 4710
(R)SB(l)0/a SBx(nr)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.95 1.49 47.9 1.97 1.72 20.3 nr 0.31 0.03 28.6 0.31 0.14 7.1
bar 0.41 0.22 48.5 0.42 0.26 13.2

NGC 4713 NGC 4722
SABMathematical equation: \hbox{${\underline{\rm B}}$}(rs)c SB(rs)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.44 0.38 65.0 0.61 0.42 98.6 rs 0.65 0.18 30.5 0.65 0.48 167.1
bar 0.38 0.14 84.9 0.39 0.22 164.6

NGC 4725 NGC 4736
SAB(r,nb)a (R)SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rl,nr,nl,nb)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

bar 4.35 1.37 48.8 4.53 1.93 23.5 R 10.58 8.68 134.8 10.94 10.13 47.1
r 4.14 2.34 34.2 4.14 3.42 0.7 bar 4.71 3.48 94.4 5.07 3.91 131.4
rl 4.48 3.47 103.9 4.70 3.99 136.6
nr 1.48 1.13 114.0 1.50 1.34 152.9

NGC 4746 NGC 4750
(R)Sc sp (R)SA(rMathematical equation: \hbox{${\underline{\rm r}}$}s)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.45 0.17 119.0 1.45 0.77 176.2 R 1.52 1.33 156.7 1.69 1.51 101.5
rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.55 0.49 146.0 0.63 0.53 103.6

NGC 4771 NGC 4772
SA(r)b sp (R)SA(r)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.62 0.20 139.8 0.93 0.58 72.3 R 3.85 1.93 147.4 3.86 3.68 19.5
r 2.36 0.61 145.3 2.36 1.16 178.0

NGC 4779 NGC 4791
SB(rs)b SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rl)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

bar 0.95 0.29 9.2 1.13 0.31 114.2 rl 0.32 0.18 55.7 0.33 0.25 155.8
rs 0.79 0.62 14.0 0.94 0.65 107.7 bar 0.21 0.14 90.2 0.23 0.17 55.1

NGC 4793 NGC 4795
SA(rs)c (R)SB(l)a pec
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.50 0.31 59.7 0.60 0.47 65.0 R 1.38 1.13 116.5 1.56 1.38 87.1
bar 0.33 0.23 23.8 0.45 0.23 89.5

NGC 4800 NGC 4814
(R)SA(rs)a (R)SA(rsMathematical equation: \hbox{${\underline{\rm s}}$})bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.22 0.97 40.5 1.34 1.16 61.5 R 1.45 0.85 117.8 1.47 1.08 159.3
rs 0.34 0.24 33.8 0.35 0.31 33.9 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.84 0.58 112.0 0.89 0.72 141.2

NGC 4818 NGC 4826
(R)SBx(l)0o (R)SA(rs,r,nl)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.43 0.67 1.0 2.48 1.70 164.2 R 7.17 3.10 117.1 7.18 5.59 4.5
rs 2.73 1.44 117.9 2.75 2.57 22.6
r 1.43 0.70 112.9 1.44 1.26 162.3

NGC 4845 NGC 4856
(R)SABx(rMathematical equation: \hbox{${\underline{\rm r}}$}s,nd)0/a (RL)SB0
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 4.35 0.87 82.0 4.47 3.30 19.9 RL 2.44 0.65 36.2 2.46 1.79 169.3
rMathematical equation: \hbox{${\underline{\rm r}}$}s 2.09 0.34 76.2 2.17 1.29 159.5

NGC 4866 NGC 4880
(L)SA(rl)0+ (RL)SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rl)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rl 2.52 0.31 87.0 2.53 1.29 175.4 RL 2.05 1.48 148.0 2.13 1.80 143.2
rl 0.89 0.63 167.8 0.89 0.79 15.3
bar 0.29 0.18 169.0 0.30 0.22 11.7

NGC 4897 NGC 4900
SABMathematical equation: \hbox{${\underline{\rm B}}$}(rMathematical equation: \hbox{${\underline{\rm r}}$}s)b (R)SB(s)cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.48 0.31 164.9 0.48 0.37 21.2 R 1.18 0.99 118.9 1.19 1.03 150.6
bar 0.40 0.20 5.7 0.43 0.23 42.1 bar 0.72 0.23 140.1 0.72 0.24 179.3

NGC 4902 NGC 4941
SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)b (RL)SA(rMathematical equation: \hbox{${\underline{\rm r}}$}s)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.88 0.79 171.9 0.95 0.79 78.0 RL 3.33 2.36 22.5 3.33 3.09 175.5
bar 0.88 0.36 68.4 0.90 0.38 144.2 rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.96 0.96 20.0 1.97 1.25 174.2

NGC 4951 NGC 4961
(R)SA(rs)b SB(rs)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.67 0.64 90.8 1.89 1.67 95.8 rs 0.40 0.26 105.3 0.41 0.36 25.1
rs 0.61 0.25 88.5 0.76 0.60 104.3 bar 0.21 0.11 133.9 0.25 0.14 53.3

NGC 4980 NGC 4984
(R)SAB(s)d /Sph (RR)SABa(l,nl)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.17 0.53 173.5 1.19 1.01 22.8 R 5.07 2.82 24.7 5.07 4.77 0.5
bar 0.89 0.41 159.1 0.98 0.72 139.2 R 3.26 1.90 20.1 3.39 3.10 136.6
bar 0.93 0.65 92.2 1.53 0.67 81.9

NGC 4995 NGC 5005
SABa(rs)ab (R2Mathematical equation: \hbox{$_{2}^{\prime}$})SABx(rMathematical equation: \hbox{${\underline{\rm r}}$}s)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.72 0.63 118.6 1.01 0.69 82.4 R2Mathematical equation: \hbox{$_{2}^{\prime}$} 3.53 1.23 63.2 3.66 3.01 151.8
bar 0.64 0.31 34.5 0.93 0.33 107.1 rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.24 0.42 71.5 1.29 1.02 28.4

NGC 5016 NGC 5033
SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rMathematical equation: \hbox{${\underline{\rm r}}$}s)c (R)SA(rs)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.24 0.14 77.5 0.25 0.18 27.1 R 8.84 4.26 167.0 9.07 7.75 153.3
bar 0.12 0.09 18.7 0.15 0.10 113.2 rs 0.52 0.19 170.9 0.52 0.35 178.0

NGC 5054 NGC 5055
(R)SA(s,nr)bc SA(rs,rl)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 4.45 2.48 157.6 4.45 4.06 6.7 rs 1.40 0.64 93.8 1.45 1.10 152.6
nr 0.19 0.11 166.9 0.20 0.16 40.5 rl 0.69 0.31 100.0 0.69 0.57 173.5

NGC 5068 NGC 5078
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})d E(d)5/S(r)b sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 2.06 1.79 69.2 2.07 1.82 145.0 r 0.71 0.09 146.0 0.71 0.27 177.5
bar 0.79 0.21 150.5 0.81 0.22 52.2

NGC 5079 NGC 5085
(R)SAB(s)b SA(rs)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 0.68 0.42 25.2 0.82 0.68 100.4 rs 0.28 0.19 45.8 0.28 0.21 171.6
bar 0.36 0.16 157.6 0.61 0.19 108.2

NGC 5088 NGC 5101
(R)SABMathematical equation: \hbox{${\underline{\rm B}}$}d (R1R2Mathematical equation: \hbox{$_{2}^{\prime}$})SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s,nl?)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.43 0.41 177.2 1.44 1.17 164.9 R2Mathematical equation: \hbox{$_{2}^{\prime}$} 5.31 4.61 153.9 5.46 4.84 45.4
R1 4.24 3.37 3.8 4.50 3.42 66.1
rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.70 1.41 122.3 1.70 1.52 175.6
bar 1.62 0.76 122.0 1.62 0.82 176.7

NGC 5105 NGC 5112
SAB(rsMathematical equation: \hbox{${\underline{\rm s}}$})cd SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.54 0.42 134.8 0.57 0.54 93.6 rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.37 0.59 118.5 1.37 0.88 177.5
bar 0.19 0.10 1.4 0.23 0.11 60.4 bar 0.33 0.05 131.5 0.33 0.08 18.1

NGC 5117 NGC 5122
(R)SAB(s)d S0 sp + PR sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.08 0.69 160.6 1.31 1.05 73.1 PRG 1.79 0.16 25.6
bar 0.78 0.24 157.5 0.79 0.44 12.0

NGC 5134 NGC 5145
(R)SABMathematical equation: \hbox{${\underline{\rm B}}$}(rs)0/a SA(r,nl)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 3.53 2.99 71.8 3.53 3.09 171.0 r 0.34 0.18 86.5 0.34 0.23 21.1
bar 1.55 0.60 154.7 1.60 0.60 76.3
rs 1.51 0.74 150.2 1.56 0.74 72.1

NGC 5147 NGC 5170
(R)SB(s)c (R)SABx,box(l)0/a sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.10 0.96 128.3 1.19 1.09 77.2 R 4.85 0.29 126.0 4.85 1.97 177.9
bar 0.35 0.18 12.0 0.42 0.18 76.8

NGC 5194 NGC 5195
SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rs,nr)bc SAB(r)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.84 0.75 87.0 0.97 0.77 73.4 r 1.54 1.41 130.5 1.91 1.51 81.7
bar 0.74 0.50 138.4 0.88 0.50 96.3 bar 1.34 0.84 177.8 1.74 0.85 80.1
nr 0.44 0.41 79.8 0.50 0.42 77.3

NGC 5205 NGC 5218
SB(rs)ab SB(rs)a pec
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.55 0.38 167.0 0.70 0.55 89.5 rs 0.63 0.35 69.3 0.72 0.36 114.2
bar 0.37 0.19 107.5 0.63 0.21 103.9 bar 0.45 0.17 97.9 0.48 0.19 143.6

NGC 5236 NGC 5247
SAB(s,nr)c SA(r)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

bar 4.18 1.29 53.7 4.33 1.32 51.5 r 0.30 0.25 5.3 0.34 0.26 108.8
nr 0.33 0.20 158.5 0.33 0.21 151.5

NGC 5248 NGC 5289
(R)SAB(s,nr)bcMathematical equation: \hbox{${\underline{\rm c}}$} (R)SA(rl)0/a sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 5.97 4.36 100.2 5.99 5.55 163.7 R 1.31 0.24 97.7 1.32 0.90 168.2
bar 2.81 1.17 125.2 2.94 1.44 29.5 rl 0.42 0.09 98.8 0.42 0.36 170.8
nr 0.22 0.19 139.5 0.26 0.20 68.9

NGC 5300 NGC 5313
SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rsMathematical equation: \hbox{${\underline{\rm s}}$})c SA(r)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.55 0.32 133.6 0.61 0.45 135.7 r 0.42 0.24 49.8 0.43 0.40 38.1
bar 0.30 0.18 163.9 0.33 0.26 47.7

NGC 5320 NGC 5334
SA(rl)bc SB(rs,x1r)cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rl 0.23 0.15 20.7 0.31 0.23 85.1 rs 0.84 0.78 118.3 1.10 0.78 92.7
bar 0.44 0.15 47.1 0.48 0.17 41.7
x1r 0.42 0.11 44.7 0.45 0.14 38.1

NGC 5336 NGC 5337
SAB(rs)c SB(rs)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.23 0.17 44.5 0.28 0.18 109.4 rs 0.41 0.22 18.3 0.48 0.40 104.3
bar 0.20 0.12 78.9 0.21 0.14 145.5

NGC 5338 NGC 5339
SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)0o SB(rs)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.48 0.30 90.8 0.62 0.48 95.1 rs 0.92 0.76 22.2 1.05 0.86 113.3
bar 0.79 0.23 81.8 0.87 0.27 42.2

NGC 5347 NGC 5350
SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)a SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)abMathematical equation: \hbox{${\underline{\rm b}}$}
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

bar 1.01 0.42 100.9 1.01 0.45 12.8 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.80 0.53 42.6 0.83 0.80 100.6
rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.00 0.73 105.7 1.01 0.78 21.4 bar 0.73 0.29 122.1 1.13 0.29 83.3

NGC 5364 NGC 5371
SA(r,is)b SAB(rsMathematical equation: \hbox{${\underline{\rm s}}$})b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 1.15 0.66 40.2 1.16 0.98 16.2 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.82 0.62 42.2 0.90 0.71 51.6
bar 0.70 0.42 99.8 0.88 0.42 86.1

NGC 5375 NGC 5376
(R)SBa(rMathematical equation: \hbox{${\underline{\rm r}}$}s,bl)a SA(rMathematical equation: \hbox{${\underline{\rm r}}$}s,l)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.24 1.82 164.7 2.25 2.09 16.0 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.57 0.38 57.8 0.66 0.56 106.2
bar 0.91 0.38 168.0 0.91 0.44 10.7
rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.85 0.75 7.0 0.91 0.81 61.4

NGC 5377 NGC 5383
(R1)SABMathematical equation: \hbox{${\underline{\rm B}}$}(s,nl)0/a SB(rs,nr)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R1 4.05 2.03 21.4 4.19 3.64 146.7 rs 1.98 1.72 102.4 2.11 1.96 106.2
bar 3.17 1.11 44.3 3.62 1.81 39.0 bar 1.67 0.61 123.5 1.69 0.73 16.6
nr 0.29 0.14 79.1 0.31 0.16 139.6

NGC 5426 NGC 5427
SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rs)c SA(r)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.66 0.31 4.2 0.78 0.53 49.8 r 0.22 0.15 29.3 0.24 0.16 130.2
bar 0.17 0.10 177.2 0.20 0.16 69.8

NGC 5430 NGC 5443
(R)SB(s,tb)b (RL)SABx(rMathematical equation: \hbox{${\underline{\rm r}}$}s)a sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.59 0.83 12.1 1.63 1.23 22.0 RL 2.50 0.73 36.9 2.52 1.94 10.8
bar 0.56 0.23 153.6 0.65 0.29 133.2 rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.38 0.36 34.3 1.38 0.96 176.2

NGC 5448 NGC 5457
(R1)SAB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)a SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rsMathematical equation: \hbox{${\underline{\rm s}}$})c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R1 3.34 1.34 115.7 3.62 2.96 43.3 rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.81 1.60 178.7 1.88 1.65 124.1
rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.67 0.54 110.2 1.67 1.28 179.9 bar 0.84 0.58 80.4 0.87 0.60 48.7

NGC 5472 NGC 5492
(R)SABa0/a SA(rs)b: sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 0.59 0.17 35.0 0.59 0.45 172.4 rs 0.40 0.09 150.0 0.40 0.33 18.8

NGC 5523 NGC 5534
SA(rs)cd (RL)SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})a pec
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.81 0.22 89.8 0.89 0.72 135.6 RL 1.21 0.83 170.3 1.30 0.86 58.7
rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.50 0.37 77.6 0.53 0.39 127.2
bar 0.50 0.22 74.9 0.53 0.23 130.3

NGC 5566 NGC 5577
(R)SAB(r,nr)a SA(rs)cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 5.07 1.47 36.0 5.09 3.99 7.4 rs 0.40 0.16 62.3 0.60 0.37 72.2
r 1.35 0.74 24.8 2.10 1.28 102.6
nr 0.20 0.08 34.1 0.22 0.20 100.3

NGC 5584 NGC 5587
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})cd SA(r)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.31 0.27 27.4 0.42 0.29 80.0 r 0.64 0.16 158.2 0.67 0.45 157.0
bar 0.27 0.14 35.9 0.36 0.15 70.1

NGC 5595 NGC 5600
SAB(rsMathematical equation: \hbox{${\underline{\rm s}}$})cd SB(rs)dm
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.36 0.31 53.0 0.51 0.36 87.9 bar 0.44 0.20 155.6 0.45 0.21 166.1
rs 0.44 0.35 144.0 0.45 0.37 147.0

NGC 5602 NGC 5633
(RL)SA(l)0+ SAMathematical equation: \hbox{${\underline{\rm A}}$}B(r)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 1.05 0.54 166.2 1.05 0.97 165.1 r 0.46 0.30 10.3 0.46 0.39 157.7

NGC 5636 NGC 5665
SAB(r)0/a SAB(rs)c pec /Sph
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.84 0.52 35.3 0.85 0.56 152.1 rs 0.95 0.60 139.8 1.09 0.85 123.9
bar 0.68 0.23 76.3 0.68 0.26 20.6 bar 0.20 0.09 128.9 0.24 0.12 133.3

NGC 5668 NGC 5669
SAB(rs)cd SB(rs)d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.41 0.37 146.7 0.43 0.41 79.8 rs 0.38 0.31 89.1 0.45 0.35 70.5
bar 0.38 0.25 106.5 0.41 0.27 134.3 bar 0.17 0.04 40.5 0.17 0.05 152.4

NGC 5678 NGC 5689
(R:)SA(rMathematical equation: \hbox{${\underline{\rm r}}$}s)b /RG (R)SABboxy(rl,nd)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.31 1.17 1.3 2.32 2.14 169.1 R 2.50 0.40 83.9 2.50 1.49 179.1
rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.35 0.57 178.3 1.36 1.03 164.9 rl 1.05 0.25 87.0 1.10 0.88 31.5

NGC 5690 NGC 5701
(R)SB(s)d sp (R1Mathematical equation: \hbox{$_{1}^{\prime}$})SB(rl)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.03 0.39 141.6 2.03 1.60 177.2 R1Mathematical equation: \hbox{$_{1}^{\prime}$} 3.21 2.72 77.2 3.24 2.80 32.7
rl 1.34 1.08 178.3 1.37 1.10 123.6
bar 1.28 0.74 177.2 1.31 0.75 125.1

NGC 5713 NGC 5719
(R)SB(rs)ab: pec (R)SB(nr)0/a sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.67 1.48 87.2 1.89 1.49 82.1 R 1.42 0.35 104.2 1.47 0.97 20.7
rs 0.65 0.49 88.8 0.73 0.49 79.8 nr 0.17 0.05 100.3 0.17 0.15 7.0
bar 0.39 0.14 95.7 0.44 0.14 83.1

NGC 5728 NGC 5740
(R1)SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s,nr,nb)0/a (R)SABMathematical equation: \hbox{${\underline{\rm B}}$}(r)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R1 3.61 2.34 1.3 3.65 3.17 161.9 R 2.16 1.17 156.3 2.34 2.04 127.3
bar 1.89 0.57 33.4 2.06 0.72 36.5 r 0.70 0.41 157.3 0.80 0.68 108.0
rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.81 0.89 33.0 1.99 1.11 40.8 bar 0.53 0.28 127.8 0.78 0.36 115.3
nr 0.20 0.12 7.9 0.20 0.16 3.1

NGC 5744 NGC 5746
SAB(rs)ab: pec (R)SBx(r,nd)0/a sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.27 0.18 132.9 0.29 0.23 43.8 R 5.06 0.39 170.7 5.09 2.02 6.8
r 2.43 0.25 171.4 2.47 1.28 12.4

NGC 5750 NGC 5756
(RL)SAB(rr)0/a (R)SABMathematical equation: \hbox{${\underline{\rm B}}$}(s)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 2.70 1.30 66.6 2.80 2.52 39.3 R 2.80 1.02 63.9 2.90 2.37 26.9
r 1.56 0.80 63.2 1.61 1.56 81.1
r 1.13 0.56 63.4 1.14 1.12 44.0

NGC 5757 NGC 5768
(R2Mathematical equation: \hbox{$_{2}^{\prime}$})SB(rs)aMathematical equation: \hbox{${\underline{\rm a}}$}b SAB(rs)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R2Mathematical equation: \hbox{$_{2}^{\prime}$} 1.35 1.19 50.7 1.46 1.31 67.2 rs 0.55 0.50 113.8 0.55 0.54 152.8
rs 0.77 0.53 161.2 0.87 0.56 118.4 bar 0.36 0.16 149.2 0.37 0.17 31.4
bar 0.66 0.23 164.8 0.73 0.25 127.8

NGC 5770 NGC 5777
SAB(r,bl)0+ (R)SBbox(l,nl)0+ sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.75 0.72 71.4 0.79 0.73 74.8 R 2.08 0.17 142.8 2.08 0.79 177.5
bar 0.73 0.41 111.5 0.79 0.42 75.3

NGC 5781 NGC 5792
(R)SB(rs)a/d (R1Mathematical equation: \hbox{$_{1}^{\prime}$})SAB(r,nd,nr)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.36 0.78 28.5 1.59 1.31 111.4 R1Mathematical equation: \hbox{$_{1}^{\prime}$} 7.09 1.19 81.6 7.55 3.38 156.3
rs 0.72 0.43 28.6 0.86 0.70 107.8 r 2.35 0.69 85.6 2.42 2.02 154.2
bar 0.25 0.05 30.0 0.25 0.09 169.2 nr 0.18 0.06 84.1 0.20 0.16 139.0

NGC 5806 NGC 5809
(R)SAB(rs,nr)ab SA(rs)a /Sph
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.68 1.46 170.1 2.77 2.56 42.5 rs 0.37 0.12 147.2 0.37 0.28 177.6
bar 1.25 0.40 176.3 1.30 0.70 22.2
rs 1.23 0.76 175.7 1.44 1.17 65.5
nr 0.12 0.07 162.5 0.14 0.12 107.7

NGC 5821 NGC 5850
SAMathematical equation: \hbox{${\underline{\rm A}}$}B(r)a (R)SB(r,nr,nb)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.53 0.31 145.6 0.54 0.52 166.7 R 4.00 3.31 3.8 4.26 3.84 58.6
bar 0.17 0.10 144.0 0.18 0.17 114.9 bar 2.09 0.79 116.7 2.42 0.85 120.0
r 2.09 1.83 122.8 2.47 1.91 105.5
nr 0.26 0.22 150.6 0.28 0.25 122.3

NGC 5854 NGC 5878
(R)SBx(r)0+ SABax(rs)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.67 0.39 50.5 1.73 1.15 158.9 rs 1.08 0.39 10.3 1.23 0.93 48.0
r 0.66 0.18 57.4 0.68 0.53 22.4

NGC 5879 NGC 5892
SABa(rs)bc SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.58 0.27 5.0 0.71 0.58 85.6 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.45 0.39 144.1 0.48 0.41 62.0
bar 0.16 0.09 157.1 0.17 0.09 56.2

NGC 5899 NGC 5900
SABMathematical equation: \hbox{${\underline{\rm B}}$}(rsMathematical equation: \hbox{${\underline{\rm s}}$})bc (R)Sb sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.49 0.32 5.4 0.86 0.47 99.4 R 1.15 0.09 127.7 1.15 0.40 179.3

NGC 5913 NGC 5915
(RL)SB(r)0/a SA(r:)c: pec
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 2.29 0.84 159.5 2.30 1.92 170.6 r 0.42 0.30 80.8 0.55 0.31 76.9
r 0.98 0.45 163.6 1.05 0.96 59.9

NGC 5921 NGC 5930
SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)b (L)SABa(rs)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

bar 1.52 0.44 18.6 1.72 0.47 59.6 rs 0.42 0.26 159.4 0.50 0.41 97.1
rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.19 0.82 23.7 1.38 0.85 69.3 bar 0.25 0.18 73.2 0.46 0.18 90.3

NGC 5937 NGC 5953
SA(rs)bc SA(r)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.22 0.17 40.8 0.30 0.20 77.9 r 0.21 0.17 72.9 0.22 0.18 47.3

NGC 5954 NGC 5956
(R)SA(rs)b SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 0.70 0.28 178.8 0.71 0.44 167.2 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.27 0.23 15.4 0.28 0.23 103.9
rs 0.28 0.17 0.2 0.29 0.27 146.5 bar 0.23 0.13 30.7 0.23 0.13 120.4

NGC 5957 NGC 5958
(R)SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s,bl)a SB(rs)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.38 2.08 165.4 2.43 2.25 138.2 rs 0.38 0.34 176.7 0.39 0.37 125.1
bar 0.96 0.41 95.1 1.06 0.41 92.0 bar 0.19 0.09 137.5 0.20 0.10 124.6
rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.94 0.92 118.7 1.04 0.93 93.8

NGC 5962 NGC 5964
SAB(rs,nr)c SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.65 0.31 109.1 0.65 0.43 5.7 rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.17 0.86 121.3 1.37 1.01 119.5
bar 0.39 0.19 147.7 0.47 0.22 57.3 bar 0.60 0.09 147.7 0.60 0.12 176.2
nr 0.13 0.08 81.5 0.15 0.11 130.9

NGC 6012 NGC 6014
(R)SB(r,x1r)ab SABMathematical equation: \hbox{${\underline{\rm B}}$}(rs,bl)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.57 2.32 168.5 2.91 2.44 106.6 bar 0.56 0.36 31.2 0.66 0.37 70.2
r 1.48 0.94 166.7 1.61 1.03 130.0 rs 0.54 0.52 111.9 0.65 0.53 96.8
x1r 0.74 0.15 151.7 0.84 0.16 121.7
bar 0.63 0.17 156.1 0.70 0.19 125.6

NGC 6070 NGC 6155
SA(r)c (RR)SB(rs)cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 1.08 0.44 60.6 1.09 0.95 7.3 R 1.08 0.70 145.0 1.09 0.93 17.6
R 0.52 0.40 147.8 0.55 0.50 57.8
rs 0.23 0.20 14.6 0.29 0.20 79.1
bar 0.19 0.10 120.7 0.20 0.13 147.7

NGC 6207 NGC 6217
SAB(rs)c (R)SB(rs)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.62 0.26 2.6 0.69 0.40 140.8 R 2.72 2.46 91.1 2.73 2.68 164.8
bar 0.27 0.12 36.6 0.30 0.19 42.6 rs 1.34 1.00 158.0 1.44 1.02 70.3
bar 1.23 0.33 149.3 1.30 0.33 58.5

NGC 6267 NGC 6278
SB(rs)b (L)SA(r)0o
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.70 0.53 53.1 0.79 0.68 64.3 r 0.43 0.20 115.9 0.45 0.32 146.5
bar 0.57 0.15 157.6 0.77 0.16 108.5

NGC 6340 NGC 6412
(R)SA(l)0/a SB(rs)cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.80 1.52 98.8 2.02 1.54 103.5 rs 0.42 0.33 69.7 0.44 0.33 72.4
bar 0.25 0.14 160.9 0.25 0.15 157.4

NGC 6434 NGC 6870
(R)SABa(rs)b SAB(rr)a + PR?
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.25 0.50 92.6 1.27 1.11 161.5 PRG 1.89 1.40 102.0
rs 0.50 0.25 88.2 0.60 0.48 114.8 rs 1.17 0.39 87.1 1.19 1.01 20.1
rs 0.78 0.23 85.7 0.78 0.60 6.0

NGC 6887 NGC 6889
SABMathematical equation: \hbox{${\underline{\rm B}}$}(rsMathematical equation: \hbox{${\underline{\rm s}}$})b SB(rs)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.52 0.19 106.5 0.54 0.51 56.1 rs 0.26 0.19 71.7 0.27 0.26 122.7
bar 0.17 0.10 163.5 0.23 0.10 90.5

NGC 6902 NGC 6923
SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rMathematical equation: \hbox{${\underline{\rm r}}$}s,nl)a SABa(rl)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.68 0.58 147.8 0.71 0.68 91.6 rl 0.36 0.17 73.4 0.36 0.25 178.9
bar 0.60 0.34 129.4 0.62 0.41 151.3

NGC 6925 NGC 7051
SB(rs)b (R1Mathematical equation: \hbox{$_{1}^{\prime}$}R2Mathematical equation: \hbox{$_{2}^{\prime}$})SABa(rs)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.97 0.25 6.0 0.97 0.76 172.9 R2Mathematical equation: \hbox{$_{2}^{\prime}$} 1.12 0.97 57.4 1.13 1.04 163.5
R1Mathematical equation: \hbox{$_{1}^{\prime}$} 0.76 0.58 179.4 0.81 0.59 108.4
rs 0.29 0.22 78.4 0.30 0.23 15.7
bar 0.28 0.14 79.4 0.28 0.15 14.7

NGC 7070 NGC 7098
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})c (R)SABa(rl,nl,nb)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.38 0.28 170.4 0.40 0.30 140.8 R 3.63 2.26 80.7 4.13 3.46 62.9
bar 0.23 0.12 77.6 0.26 0.12 64.7 rl 1.87 1.07 67.8 1.95 1.78 134.9
bar 1.38 0.63 50.6 1.63 0.93 133.1

NGC 7107 NGC 7140
(R)SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})dm (R)SABxMathematical equation: \hbox{${\underline{\rm B}}_{\rm x}$}(rs,nl)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.33 1.06 121.4 1.38 1.18 38.2 R 3.72 2.60 176.0 4.13 3.62 113.2
rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.82 0.60 120.2 0.84 0.66 30.3 rs 1.94 1.16 22.0 2.19 1.59 48.6
bar 0.50 0.16 130.4 0.52 0.18 34.1 bar 1.92 0.48 19.1 2.02 0.71 25.3

NGC 7162 NGC 7179
(R)SAB(rs)c SBxa(r)0/a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.19 0.47 11.4 1.20 1.11 159.9 bar 0.91 0.23 44.7 0.93 0.44 166.6
rs 0.38 0.22 13.7 0.52 0.38 88.1 r 0.89 0.41 50.4 0.89 0.80 179.3

NGC 7184 NGC 7188
SB(r,nd)ab (R)SAB(s)b:
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 1.71 0.42 59.1 1.71 1.64 164.6 R 0.79 0.37 48.6 0.80 0.74 28.3

NGC 7191 NGC 7205
(R)SABMathematical equation: \hbox{${\underline{\rm B}}$}(s)b pec SA(rs)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 0.83 0.37 133.5 0.90 0.80 122.4 rs 0.47 0.25 63.1 0.52 0.46 115.7

NGC 7213 NGC 7218
(L)SA(r,l)0o SB(rs)cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.88 0.79 5.2 0.90 0.82 42.9 rs 0.54 0.37 28.2 0.82 0.53 83.3

NGC 7219 NGC 7290
(R2Mathematical equation: \hbox{$_{2}^{\prime}$})SAMathematical equation: \hbox{${\underline{\rm A}}$}B(r)a SA(rs)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R2Mathematical equation: \hbox{$_{2}^{\prime}$} 1.36 0.83 33.0 1.39 1.27 31.6 rs 0.36 0.21 156.7 0.38 0.36 105.4
r 0.33 0.24 50.3 0.41 0.30 67.2
bar 0.29 0.20 86.7 0.42 0.21 76.9

NGC 7314 NGC 7328
SAB(rs)bc SAB(rs)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 1.08 0.32 179.6 1.10 0.80 164.5 rs 0.36 0.23 65.3 0.61 0.32 103.5

NGC 7378 NGC 7416
(L)SA(rMathematical equation: \hbox{${\underline{\rm r}}$}s)0/a (R)SB(r)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.64 0.26 0.8 0.65 0.42 10.9 R 2.74 0.43 108.9 2.74 1.65 0.8
r 1.25 0.29 109.2 1.25 1.10 6.8

NGC 7418 NGC 7421
SAB(rs)c (R)SB(rs,bl)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

bar 1.10 0.25 119.5 1.12 0.33 163.5 R 1.68 1.54 76.7 1.76 1.66 71.8
rs 1.07 0.71 107.1 1.18 0.87 131.1 rs 0.91 0.74 75.1 0.92 0.83 23.5
bar 0.73 0.25 93.0 0.76 0.28 32.3

NGC 7424 NGC 7437
SBa(rsMathematical equation: \hbox{${\underline{\rm s}}$})cd SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rs)c:
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.27 0.90 71.5 1.34 0.94 50.8 rs 0.42 0.32 70.0 0.45 0.34 58.5
bar 0.36 0.11 133.3 0.39 0.11 102.4 bar 0.24 0.16 13.9 0.24 0.18 164.2

NGC 7463 NGC 7465
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})c E(d)1-2?/S0 sp + PR material?
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.38 0.18 75.2 0.54 0.31 116.7 PRG 0.71 0.09 160.1

NGC 7479 NGC 7496
(R)SB(s)b SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 2.77 2.13 27.6 2.92 2.69 57.2 rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.43 1.00 160.2 1.47 1.02 123.7
bar 1.65 0.41 8.1 1.68 0.53 164.3 bar 1.33 0.31 147.9 1.37 0.32 113.7

NGC 7513 NGC 7531
SB(rs)a SABx(r)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 1.31 0.87 90.2 1.46 1.17 127.5 bar 0.99 0.33 11.7 1.03 0.59 156.3
bar 1.27 0.34 71.0 1.51 0.43 131.9 r 0.95 0.39 17.1 0.96 0.72 164.7

NGC 7537 NGC 7552
SA(rMathematical equation: \hbox{${\underline{\rm r}}$}s)c (R1Mathematical equation: \hbox{$_{1}^{\prime}$})SB(rsMathematical equation: \hbox{${\underline{\rm s}}$},nr)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.24 0.11 76.9 0.34 0.24 90.5 R1Mathematical equation: \hbox{$_{1}^{\prime}$} 3.08 2.52 179.1 3.14 2.57 135.0
rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.96 1.23 99.7 2.02 1.24 63.3
bar 1.20 0.43 91.2 1.23 0.44 54.1
nr 0.12 0.10 104.7 0.12 0.10 71.4

NGC 7582 NGC 7590
(R1Mathematical equation: \hbox{$_{1}^{\prime}$})SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})a SAB(rsMathematical equation: \hbox{${\underline{\rm s}}$})bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R1Mathematical equation: \hbox{$_{1}^{\prime}$} 4.03 1.77 148.5 4.12 3.75 148.5 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.85 0.31 33.8 0.88 0.82 41.3
rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.97 0.79 154.2 2.00 1.69 20.7

NGC 7606 NGC 7689
SA(r)b SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rs)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.85 0.38 140.2 1.02 0.81 113.4 bar 0.26 0.10 100.8 0.30 0.13 136.5
rs 0.26 0.22 134.5 0.33 0.26 85.9

NGC 7690 NGC 7716
SA(r)0/a SAMathematical equation: \hbox{${\underline{\rm A}}$}B(r)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.23 0.11 128.1 0.23 0.22 171.0 r 0.47 0.34 30.3 0.47 0.40 178.0
bar 0.13 0.10 54.3 0.14 0.11 39.4

NGC 7723 NGC 7724
SB(rs)ab (R)SAB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.71 0.55 54.0 0.85 0.69 73.6 R 0.88 0.54 33.4 0.88 0.78 14.1
bar 0.64 0.23 68.4 0.73 0.30 42.8 bar 0.36 0.17 62.6 0.42 0.21 49.5
rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.30 0.20 77.1 0.39 0.22 67.8

NGC 7731 NGC 7741
(R1R2Mathematical equation: \hbox{$_{2}^{\prime}$})SAMathematical equation: \hbox{${\underline{\rm A}}$}B(r)a (R2Mathematical equation: \hbox{$_{2}^{\prime}$})SB(s)cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R2Mathematical equation: \hbox{$_{2}^{\prime}$} 1.09 0.85 92.6 1.27 1.03 66.9 R2Mathematical equation: \hbox{$_{2}^{\prime}$} 2.76 2.23 168.8 3.21 2.74 79.2
R1 0.69 0.53 88.9 0.78 0.66 64.4 bar 1.46 0.49 95.9 2.00 0.52 107.0
bar 0.28 0.15 43.3 0.32 0.19 131.1
r 0.27 0.22 50.5 0.33 0.26 107.4

NGC 7742 NGC 7743
SA(rr)0+ SAB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.73 0.68 119.8 0.74 0.70 54.2 rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.38 1.14 119.4 1.80 1.16 79.6
r 0.34 0.32 142.3 0.35 0.32 67.6 bar 1.32 0.63 94.7 1.52 0.73 51.7

NGC 7750 NGC 7755
SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rs)bc SABMathematical equation: \hbox{${\underline{\rm B}}$}(rs,nr)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.54 0.24 173.5 0.54 0.48 20.7 rs 0.94 0.77 32.9 1.29 0.93 85.5
bar 0.84 0.37 123.6 1.39 0.37 94.2
nr 0.12 0.09 28.5 0.14 0.12 83.4

NGC 7817 PGC 2492
SAB(rs,nd)bc SAB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)a/d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.66 0.26 50.8 0.86 0.63 71.7 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.75 0.67 168.7 0.97 0.75 88.4
bar 0.37 0.17 171.5 0.38 0.24 13.4

PGC 3853 PGC 6228
(R)SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)cd SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})dm
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 3.93 3.03 100.8 4.12 3.87 117.8 rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.06 0.31 65.9 1.14 0.75 149.4
rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.55 1.12 78.9 1.76 1.32 123.5
bar 0.39 0.19 38.1 0.51 0.19 104.6

PGC 6626 PGC 11248
(R)SB(rs)cd SB(rs)d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.88 1.67 47.7 2.02 1.72 115.0 rs 1.00 0.39 123.6 1.00 0.87 174.5
rs 0.92 0.75 40.4 0.99 0.77 116.4
bar 0.91 0.46 20.6 1.00 0.47 105.9

PGC 12633 PGC 12664
SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rs)ab SABMathematical equation: \hbox{${\underline{\rm B}}$}(rsMathematical equation: \hbox{${\underline{\rm s}}$})cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.66 0.56 99.0 0.66 0.57 42.3 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.72 0.57 130.3 1.02 0.67 102.2
bar 0.63 0.31 99.4 0.63 0.31 39.7 bar 0.17 0.07 88.1 0.28 0.08 101.6

PGC 12981 PGC 13684
SAB(s,nr?)m pec SAB(rsMathematical equation: \hbox{${\underline{\rm s}}$})c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

bar 0.56 0.28 91.2 0.57 0.36 166.4 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.59 0.26 167.0 0.59 0.48 2.2
nr 0.24 0.13 95.3 0.24 0.17 172.0 bar 0.18 0.12 112.7 0.31 0.13 103.0

PGC 13716 PGC 14037
SA(rsMathematical equation: \hbox{${\underline{\rm s}}$})c sp SB(rs)c:
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.48 0.12 138.7 0.48 0.29 4.9 rs 0.40 0.25 129.1 0.56 0.39 102.8

PGC 32091 PGC 36274
SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rsMathematical equation: \hbox{${\underline{\rm s}}$})c (R)SAB(s)m /RG
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.67 0.54 50.9 0.68 0.59 21.5 R 1.09 0.67 57.4 1.17 0.91 41.1
bar 0.42 0.22 54.3 0.42 0.25 18.6 bar 0.30 0.19 75.2 0.36 0.23 59.4

PGC 36551 PGC 36643
(R)SA(s)d (R)SB(s)d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.29 0.42 73.4 1.31 1.05 19.2 R 1.58 0.52 139.1 1.93 1.44 60.1

PGC 38250 PGC 44735
SAB(rs)m: SAB(rs)dm
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.43 0.38 126.1 0.49 0.42 78.6 rs 0.53 0.32 82.6 0.73 0.45 113.3
bar 0.38 0.19 65.0 0.43 0.21 125.1 bar 0.25 0.17 56.1 0.44 0.19 102.9

PGC 44952 PGC 47721
SA(r)d: SA(rMathematical equation: \hbox{${\underline{\rm r}}$}s,r2,r3)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.52 0.33 0.0 0.62 0.48 61.9 rMathematical equation: \hbox{${\underline{\rm r}}$}s 1.47 0.74 117.5 1.49 1.27 162.7
r 1.12 0.48 117.5 1.12 0.82 169.2
r 0.70 0.34 116.4 0.71 0.58 161.7

PGC 48179 PGC 53093
SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})cd (RR)SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 1.13 1.01 20.6 1.19 1.03 115.7 R 1.03 0.59 100.8 1.05 1.00 135.8
bar 0.88 0.30 0.2 0.94 0.31 109.5 R 0.66 0.42 95.7 0.75 0.64 115.5
rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.31 0.17 98.1 0.32 0.29 140.2
bar 0.17 0.08 58.3 0.25 0.10 113.6

PGC 53415 PGC 54944
(R)Sph/SA(rs)a SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.86 0.63 47.4 1.86 1.19 0.4 bar 0.60 0.15 35.3 0.62 0.21 22.0
rs 0.29 0.08 50.1 0.29 0.16 7.1 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.58 0.30 10.8 0.59 0.42 157.9

PGC 66242 UGC 313
(R)SB(s)d (R1Mathematical equation: \hbox{$_{1}^{\prime}$})SBa(s)b /Sph
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.45 0.66 39.1 1.49 1.40 140.3 R1Mathematical equation: \hbox{$_{1}^{\prime}$} 0.38 0.15 14.9 0.38 0.24 0.1
bar 0.14 0.04 102.6 0.23 0.04 88.6

UGC 1551 UGC 1862
SB(rs)cd (R)SA(s)b:
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.65 0.55 170.7 0.73 0.57 69.0 R 0.79 0.65 2.4 0.85 0.74 121.5
bar 0.57 0.19 81.2 0.62 0.21 132.7

UGC 4151 UGC 4306
SA(rl)c SA(r)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rl 0.12 0.10 36.0 0.13 0.10 73.3 r 0.21 0.06 140.2 0.21 0.10 5.7

UGC 4549 UGC 4551
SA(r)c SB(r)0+ sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.18 0.16 84.2 0.22 0.16 83.4 r 1.00 0.26 113.4 1.01 0.68 6.3

UGC 4559 UGC 4621
SA(r)0/a SB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)ab
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 0.51 0.08 51.1 0.51 0.28 2.1 rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.56 0.33 132.1 0.56 0.55 142.6
bar 0.48 0.19 150.6 0.53 0.28 35.2

UGC 4623 UGC 4714
SA(rs)bc SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rs)m
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.31 0.14 56.6 0.51 0.31 92.9 rs 0.27 0.22 100.3 0.27 0.27 90.0
bar 0.21 0.11 59.4 0.24 0.12 129.5

UGC 4824 UGC 4867
SB(rs)d SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.89 0.28 95.4 1.04 0.84 116.8 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.41 0.25 94.8 0.42 0.40 35.6
bar 0.14 0.07 179.4 0.23 0.07 88.6

UGC 4922 UGC 4982
SAB(rs)cd SA(r)c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.78 0.45 52.6 1.01 0.76 103.4 r 0.25 0.12 176.4 0.31 0.24 113.4

UGC 5228 UGC 5354
(R2Mathematical equation: \hbox{$_{2}^{\prime}$})SB(s)cd (R:)SAB(s)dm
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R2Mathematical equation: \hbox{$_{2}^{\prime}$} 1.81 0.38 123.8 1.81 1.25 0.0 R 0.98 0.63 79.0 1.11 0.97 80.7
bar 0.56 0.23 71.5 0.56 0.41 165.4

UGC 5393 UGC 5446
(R)SB(s)m SAB(rs)dm sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 0.94 0.63 122.0 1.24 0.93 83.9 rs 0.28 0.13 47.8 0.56 0.28 93.6
bar 0.19 0.08 145.7 0.25 0.11 56.0

UGC 5633 UGC 5646
SB(rs)dm SA:(rs:)d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 1.01 0.69 160.3 1.17 0.94 116.1 rs 0.49 0.14 169.3 0.53 0.43 40.0
bar 0.79 0.15 162.9 0.82 0.23 161.6

UGC 5676 UGC 5707
SABMathematical equation: \hbox{${\underline{\rm B}}$}(s)m:/RG? SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RG 1.09 0.50 22.3 1.12 0.89 24.7 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.32 0.21 59.8 0.39 0.22 77.8
bar 0.16 0.10 88.6 0.29 0.10 83.2 bar 0.18 0.07 64.9 0.21 0.07 79.7

UGC 5814 UGC 5841
(RL)SB0/a (shells?) pec (R)SB(rsMathematical equation: \hbox{${\underline{\rm s}}$}:)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 0.52 0.41 105.2 0.74 0.48 104.1 R 0.76 0.45 127.0 0.82 0.74 116.8
bar 0.43 0.14 136.7 0.43 0.25 11.6
rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.38 0.21 136.1 0.40 0.35 33.1

UGC 6023 UGC 6162
SAB(rMathematical equation: \hbox{${\underline{\rm r}}$}s)c (R)SA(s)d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rMathematical equation: \hbox{${\underline{\rm r}}$}s 0.43 0.22 48.0 0.45 0.42 129.8 R 1.67 0.94 90.6 1.74 1.54 38.9
bar 0.38 0.12 47.7 0.38 0.23 173.5

UGC 6169 UGC 6309
(R)SBa(s)b: sp SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 0.59 0.10 178.4 0.61 0.34 162.6 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.69 0.50 104.2 0.72 0.57 144.0
bar 0.61 0.13 139.7 0.61 0.15 16.7

UGC 6335 UGC 6517
SAB(rs)c SA(r)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.20 0.15 160.4 0.24 0.15 91.1 r 0.32 0.18 21.4 0.35 0.28 131.3
bar 0.14 0.09 51.4 0.15 0.11 154.5

UGC 6983 UGC 7184
SB(r)s)dm pec SB(rs)d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

r 1.04 0.99 113.3 1.51 1.03 86.9 rs 0.64 0.28 147.5 0.65 0.54 25.0
bar 0.94 0.28 89.0 0.94 0.42 3.5 bar 0.47 0.12 163.5 0.57 0.21 41.5

UGC 7239 UGC 7848
(R)SB(s)m SABa(s,x1r)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.24 1.10 11.1 1.54 1.11 86.1 x1r 0.30 0.14 75.3 0.40 0.24 59.9
bar 0.36 0.19 21.3 0.45 0.19 89.2

UGC 8155 UGC 8909
SA(rs,l)a SAB(rsMathematical equation: \hbox{${\underline{\rm s}}$})c:
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 1.24 0.90 12.8 1.24 1.13 172.4 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.28 0.19 68.5 0.28 0.23 21.2
bar 0.17 0.11 131.3 0.20 0.11 79.4

UGC 8995 UGC 9215
(R:)SA(s)cd: (R)SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

R 1.44 0.62 6.7 1.51 1.29 38.0 R 1.60 0.70 160.5 1.60 1.56 168.4
rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.94 0.58 157.1 1.31 0.93 95.4

UGC 9245 UGC 9291
SB(rs)dm SAB(rs)bc
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 1.21 0.64 173.2 1.21 0.88 171.7 rs 0.50 0.32 110.9 0.59 0.49 71.3
bar 0.26 0.03 9.3 0.26 0.04 16.6 bar 0.23 0.10 84.7 0.27 0.16 136.4

UGC 9356 UGC 9364
(RL)SAB(rs)bc: (R)SA(s)cd
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 1.07 0.45 107.0 1.08 0.86 13.6 R 0.91 0.40 17.8 0.92 0.81 164.8
rs 0.59 0.27 99.2 0.61 0.51 152.9
bar 0.24 0.10 60.8 0.37 0.12 113.4

UGC 9389 UGC 9569
SB(rs)dm SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})c
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 1.24 0.34 47.1 1.27 1.21 136.5 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.69 0.46 168.1 0.80 0.51 60.3
bar 0.43 0.17 168.8 0.50 0.19 53.3

UGC 9746 UGC 9858
SB(rs)cd sp SA(rs)b
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.97 0.19 137.8 0.97 0.71 179.3 rs 0.46 0.13 67.5 0.62 0.36 123.1

UGC 10054 UGC 10791
SB(rs)d SB(rs)d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 1.13 0.56 145.1 1.15 1.04 27.7 rs 0.70 0.53 111.4 0.86 0.68 75.5
bar 0.60 0.10 154.0 0.64 0.18 23.4 bar 0.29 0.12 155.9 0.42 0.13 70.0

UGC 10854 UGC 12151
SAB(rsMathematical equation: \hbox{${\underline{\rm s}}$})m SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})d
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.44 0.24 79.0 0.60 0.41 110.3 rsMathematical equation: \hbox{${\underline{\rm s}}$} 0.60 0.47 7.5 0.78 0.59 81.3
bar 0.26 0.07 173.8 0.26 0.12 173.3

Appendix B.2: Atlas of galaxies not in the S4G sample that host rings

IC 3062 NGC 2856
SA(rs)bc SAB(r)a:
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.27 0.21 149.9 0.30 0.23 119.1 r 0.37 0.16 144.6 0.43 0.28 47.1

NGC 2950 NGC 4175
(RL)SABaMathematical equation: \hbox{${\underline{\rm B}}_{\rm a}$}(rlMathematical equation: \hbox{${\underline{\rm l}}$},bl)0+ SA(r,PR?)0/a sp
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

RL 1.99 1.50 115.9 2.25 1.96 104.8 r 0.41 0.11 130.4 0.41 0.32 176.0
rlMathematical equation: \hbox{${\underline{\rm l}}$} 0.97 0.68 122.2 1.00 0.97 93.9 PRG 0.29 0.03 38.7
bar 0.80 0.47 155.7 0.98 0.57 56.5

NGC 4277 NGC 4288A
SAB(rs)0+ (L)SAMathematical equation: \hbox{${\underline{\rm A}}$}B(rl)0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.57 0.43 117.5 0.59 0.57 87.9 rl 0.25 0.25 40.7 0.26 0.25 89.7
bar 0.41 0.25 169.7 0.51 0.27 67.0 bar 0.23 0.17 161.2 0.24 0.17 115.5

NGC 4342 PGC 43690
S0 sp + vF PR? (R1Mathematical equation: \hbox{$_{1}^{\prime}$})SABa(ls)a
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

PRG 0.40 0.04 80.7 R1Mathematical equation: \hbox{$_{1}^{\prime}$} 0.80 0.40 108.9 0.81 0.60 169.2
bar 0.16 0.13 18.8 0.25 0.13 88.7

PGC 50803 PGC 52269
SB(rs)a (R)SB0+
Mathematical equationMathematical equationMathematical equation Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o) () () (o) () () (o)

rs 0.31 0.19 94.4 0.32 0.24 145.7 R 0.35 0.33 130.1 0.36 0.35 71.2
bar 0.30 0.10 114.2 0.30 0.14 7.2 bar 0.17 0.12 165.4 0.18 0.13 50.3

PGC 59663
(R)Sa sp
Mathematical equationMathematical equationMathematical equation
Feature D r,b d r,b PAr,b D r,b,0 d r,b,0 θ r,b
() () (o) () () (o)

R 0.37 0.10 87.0 0.41 0.29 141.9

Appendix C: Double NGC and IC identifications

Table C.1

List of ARRAKIS galaxies with a double NGC/IC identification

All Tables

Table 1

Glossary with some notation used in galaxy classification.

Table 2

Parameters of the model galaxies used to study the reliability of the bar deprojected parameters.

Table 3

Number of galaxies in the histograms in Figs. 2022 and parameters of the Gaussian fits to the qr,0 distributions.

Table 4

Number of galaxies in the histograms in Figs. 2325 and parameters of the Gaussian fits to the qr,0 distributions.

Table 5

Number of galaxies in the histograms in Figs. 2628 and average and standard deviation of the absolute ring deprojected diameters for several ARRAKIS subsamples.

Table 6

Number of galaxies in the histograms in Figs. 2931 and average and standard deviation of the ring deprojected diameters relative to D25.5 for several ARRAKIS subsamples.

Table 7

Number of galaxies in the histograms in Fig. 32 and parameters of the Gaussian fits to the Dr,0(O)/Dr,0(I) distributions.

Table 8

Simplified behaviour of the probability of finding outer and inner rings for different galaxy stage ranges.

Table C.1

List of ARRAKIS galaxies with a double NGC/IC identification

All Figures

Thumbnail: Fig. 1 Refer to the following caption and surrounding text. Fig. 1

Schematic classification of the ring types found in ARRAKIS. Multiple ring combinations are also included.

In the text
Thumbnail: Fig. 2 Refer to the following caption and surrounding text. Fig. 2

Selection of S4G galaxies hosting a variety of outer rings. The images are in the 3.6  μm band, have a size twice that of the μ3.6  μm = 25.5   mag   arcsec-2 diameter isophote and are oriented with north up and east left. The top row shows galaxies with outer features compatible with the R1 and R2 ring morphologies seen in simulations by Schwarz (1981, 1984) and defined by Buta (1986a). The second row shows outer rings that cannot be easily recognised to belong to these categories in either barred or unbarred galaxies. The third row has three example of ring-lenses and a rare example of a galaxy with two outer rings. The names of the galaxies and their morphological classification (from Buta et al., in prep.) can be found below each image.

In the text
Thumbnail: Fig. 3 Refer to the following caption and surrounding text. Fig. 3

Selection of S4G galaxies hosting a variety of inner rings presented in the same way as those in Fig. 2. The top row presents a succession of increasingly more spiral-like inner features in a series of SAB or moderately barred galaxies. The second line shows example of inner rings in unbarred galaxies and two examples of ring-lenses in early-type disc galaxies.

In the text
Thumbnail: Fig. 4 Refer to the following caption and surrounding text. Fig. 4

Selection of S4G galaxies hosting a variety of nuclear features. The images in the top row are presented in the same way as those in Fig. 2. The bottom panels are zoomed by a factor of five compared with those in the top row. The frames show galaxies hosting a ring, a pseudoring, a ring-lens, and a pseudoring-lens, respectively.

In the text
Thumbnail: Fig. 5 Refer to the following caption and surrounding text. Fig. 5

Selection of S4G galaxies hosting a variety of non-resonance rings presented in the same way as those in Fig. 2. The first frame shows a galaxy with an x1-ring, the second one a galaxy with a collisional one, and the last two show galaxies with polar rings.

In the text
Thumbnail: Fig. 6 Refer to the following caption and surrounding text. Fig. 6

Original image, P4 model, and model-subtracted image of NGC 4579. The model has three components, namely a bulge, a bar, and a disc. NGC 4579 is a galaxy classified as (RL,R)SB(rsMathematical equation: \hbox{${\underline{\rm s}}$})a by Buta et al. (in prep.). NGC 4579 has an exceedingly diffuse outer ring as seen in the first frame. The ring becomes more obvious in the model-subtracted image. The axis units are arcseconds.

In the text
Thumbnail: Fig. 7 Refer to the following caption and surrounding text. Fig. 7

Original image, P4 model, and model-subtracted image of NGC 1097, which is classified as an (R)SB(rs,nr)abMathematical equation: \hbox{${\underline{\rm b}}$} pec galaxy in Buta et al. (in prep.). The red ellipses indicate in an outside-in order the average of the two ellipse fits made to the outer, the inner, and the nuclear rings. The green ellipses are the result of an ellipse fit at the radius of the highest bar ellipticity. The red crosses indicate the centre of the galaxy. The axis units are arcseconds.

In the text
Thumbnail: Fig. 8 Refer to the following caption and surrounding text. Fig. 8

Top-left panel: residuals of the ring diameters along the major and minor axes as a function of the averaged diameters, ⟨ dr,Dr ⟩. Top-right panel: residuals of the ring axis ratios, qr = dr/Dr, as a function of the mean axis ratios ⟨ qr ⟩  =  ⟨ dr ⟩ / ⟨ Dr ⟩. Bottom-left panel: residuals of the ring position angles as a function of the averaged ring major axis ⟨ Dr ⟩. Bottom-right panel: residuals of the ring position angles as a function of the mean ring axis ratios. N refers to the number of points in each plot.

In the text
Thumbnail: Fig. 9 Refer to the following caption and surrounding text. Fig. 9

Top panel: internal errors of dr,Dr as a function of ⟨ dr,Dr ⟩. Bottom panel: internal errors of PAr as a function of ⟨ qr ⟩. The solid lines represent the fits described in Eqs. (1) and (2) and the dashed lines correspond to the same expressions as presented in the CSRG. Darker grey areas indicate the 95% confidence interval of the fit for ARRAKIS and lighter grey indicates the same for the CSRG.

In the text
Thumbnail: Fig. 10 Refer to the following caption and surrounding text. Fig. 10

Measured orientation of the bar with respect to the line of nodes of the galaxy (θb) as a function of the galaxy inclination (i) for each of our four galaxy models described in the text and Table 2. Each coloured line represents a single real θb value, which is the one corresponding to the position at which the line crosses the i = 0° axis, that is, from purple to red (bottom to top), θb = 0°, θb = 10°, θb = 20°, θb = 30°, θb = 40°, θb = 50°, θb = 60°, θb = 70°, θb = 80°, and θb = 90°. The images at the bottom-right corner of each panel represent the corresponding galaxy when θb = 0° and i = 0°.

In the text
Thumbnail: Fig. 11 Refer to the following caption and surrounding text. Fig. 11

Measured bar ellipticity (measured 1 − qb,0) as a function the galaxy inclination (i) for each of our four galaxy models. Each coloured line represents a single θb value colour-coded in the same way as in Fig. 10 (also ordered here from bottom to top). The intrinsic 1 − qb,0 value is that corresponding to i = 0°. The images at the top-right corner of each panel represent the corresponding galaxy when θb = 0° and i = 0°.

In the text
Thumbnail: Fig. 12 Refer to the following caption and surrounding text. Fig. 12

Top panel: difference between the measured intrinsic axis ratio of a ring, qr0, and the real one, qr,0Mathematical equation: \hbox{$q^{\prime}_{\rm r,0}$}, as a function of the real galaxy inclination, i, for four disc scale-height to scale-length ratios. The colour code corresponds in an outside-in order to hz/hR = 1/3 (red), hz/hR = 1/5 (green), hz/hR = 1/7 (blue), and hz/hR = 1/10 (purple). Bottom panel: difference of the measured angle difference between the orientation of the major axis of a ring with respect to the line of nodes, θr, with respect to the real one, θrMathematical equation: \hbox{$\theta^{\prime}_{\rm r}$}, as a function of the real galaxy inclination. In both panels, the solid lines indicate the maximum and the minimum qr,0qr,0Mathematical equation: \hbox{$q_{\rm r,0}-q^{\prime}_{\rm r,0}$} (|θrθr|Mathematical equation: \hbox{$|\theta_{\rm r}-\theta^{\prime}_{\rm r}|$}) for a given i colour-coded as in the top panel. The dashed lines indicate the limits of the region enclosing 68.2% of qr,0qr,0Mathematical equation: \hbox{$q_{\rm r,0}-q^{\prime}_{\rm r,0}$} (|θrθr|Mathematical equation: \hbox{$|\theta_{\rm r}-\theta^{\prime}_{\rm r}|$}) values at a given i.

In the text
Thumbnail: Fig. 13 Refer to the following caption and surrounding text. Fig. 13

Comparison of the angular diameters of ARRAKIS rings with those in VB80. The line corresponds to a linear fit to the data points in the plot. The outliers due to the wrong identification of the resonance to which a ring is linked in VB80 are marked with asterisks and are excluded from the fit. The numbers in the top-left corner indicate the number of points considered in the fit and their correlation coefficient.

In the text
Thumbnail: Fig. 14 Refer to the following caption and surrounding text. Fig. 14

As in Fig. 13, but with data from BC93.

In the text
Thumbnail: Fig. 15 Refer to the following caption and surrounding text. Fig. 15

Top-left panel: as in Fig. 13, but with data from the CSRG. Top-right panel: comparison of the PA offset between the major axis of bars and that of rings in the CSRG and ARRAKIS. Bottom panels: difference in the PA offsets between the bar and the ring major axis as a function of the ring size and of the ring axis ratio. In the three last panels, only points for barred galaxies with ϵd ≤ 0.5 are presented.

In the text
Thumbnail: Fig. 16 Refer to the following caption and surrounding text. Fig. 16

As in Fig. 13, but with data from AINUR.

In the text
Thumbnail: Fig. 17 Refer to the following caption and surrounding text. Fig. 17

As in Fig. 15, but with data from NIRS0S.

In the text
Thumbnail: Fig. 18 Refer to the following caption and surrounding text. Fig. 18

Top panels: stage distribution of the S4G sample (black line), of galaxies hosting outer rings (continuous darker blue line), inner rings (dashed darker green line), and nuclear rings (dash-point red line). Lighter blue and green lines indicate histograms considering only galaxies hosting closed outer and closed inner rings, respectively. Bottom panels: fraction of galaxies with resonant features for a given stage colour-coded as in the two top panels. Left panels are for the whole sample and right panels for galaxies with a disc ellipticity ϵd ≤ 0.5. The numbers in the top panels indicate the number of galaxies included in the histograms that corresponds to the colour and line pattern of the adjacent box.

In the text
Thumbnail: Fig. 19 Refer to the following caption and surrounding text. Fig. 19

Top panels: family distribution of the S4G sample and ringed galaxies colour- and line-coded as in Fig. 18. Bottom panels: fraction of galaxies with rings for a given family colour- and line-coded as in the two top panels. Left panels are for the whole sample and right panels for galaxies with a disc ellipticity ϵd ≤ 0.5. The numbers in the top panels indicate the number of galaxies included in the histogram that corresponds to the colour- and line-pattern of the adjacent box.

In the text
Thumbnail: Fig. 20 Refer to the following caption and surrounding text. Fig. 20

Distribution of the resonance ring axis ratios colour- and line-coded as in Fig. 18. The left-hand plots are for the whole ARRAKIS sample and the right-hand plots correspond to rings in host galaxies with ϵd ≤ 0.5. The top-row plots show the distribution of projected axis ratios, the bottom row shows the distribution of deprojected ones.

In the text
Thumbnail: Fig. 21 Refer to the following caption and surrounding text. Fig. 21

Distribution of the resonance ring deprojected axis ratios colour- and line-coded as in Fig. 18 for different galaxy families and for ϵd ≤ 0.5. The left panel shows SA galaxies, the middle one SAMathematical equation: \hbox{${\underline{\rm A}}$}B to SABMathematical equation: \hbox{${\underline{\rm B}}$} galaxies, the right panel SB galaxies.

In the text
Thumbnail: Fig. 22 Refer to the following caption and surrounding text. Fig. 22

Distribution of the resonance ring deprojected axis ratios colour- and line-coded as in Fig. 18 for different galaxy stage ranges and for ϵd ≤ 0.5. The left panel represents galaxies with − 5 ≤ T ≤ 0, the middle panel galaxies with 1 ≤ T ≤ 3, the right panel galaxies with 4 ≤ T ≤ 10.

In the text
Thumbnail: Fig. 23 Refer to the following caption and surrounding text. Fig. 23

Distribution of the projected resonance ring PA differences with respect to the bar (left panel) and ring orientation with respect to the bar in the deprojected galaxies (right panel). The histograms are colour- and line-coded as in Fig. 18. The plots only include rings with qr ≤ 0.85 (left panel) and qr,0 ≤ 0.85 (right panel) and in host galaxies with ϵd ≤ 0.5. The numbers in the left panel indicate the number of galaxies included in the histogram corresponding to the colour of the adjacent box.

In the text
Thumbnail: Fig. 24 Refer to the following caption and surrounding text. Fig. 24

Distribution of the resonance ring deprojected major axis angle difference with the bar colour- and line-coded as in Fig. 18 for different galaxy families and for ϵd ≤ 0.5. The left panel is for SAMathematical equation: \hbox{${\underline{\rm A}}$}B to SABMathematical equation: \hbox{${\underline{\rm B}}$} galaxies, the right panel for SB galaxies. The plots only include rings with qr,0 ≤ 0.85.

In the text
Thumbnail: Fig. 25 Refer to the following caption and surrounding text. Fig. 25

Distribution of the resonance ring deprojected major axis angle difference with the bar colour- and line-coded as in Fig. 18 for different galaxy stage ranges and for ϵd ≤ 0.5. The left panel represents galaxies with − 5 ≤ T ≤ 0, the middle panel galaxies with 1 ≤ T ≤ 3, the right panel galaxies with 4 ≤ T ≤ 10. The plots only include rings with qr,0 ≤ 0.85.

In the text
Thumbnail: Fig. 26 Refer to the following caption and surrounding text. Fig. 26

Distribution of the resonance ring absolute diameters. The top row shows the projected diameters and the bottom row the deprojected ones. The left column shows all galaxies, the right column galaxies with ϵd ≤ 0.5. The histograms are colour- and line-coded as in Fig. 18.

In the text
Thumbnail: Fig. 27 Refer to the following caption and surrounding text. Fig. 27

Distribution of the resonance ring deprojected major axis absolute diameter colour- and line-coded as in Fig. 18 for different galaxy families and for ϵd ≤ 0.5. The left panel shows SA galaxies, the middle one SAMathematical equation: \hbox{${\underline{\rm A}}$}B to SABMathematical equation: \hbox{${\underline{\rm B}}$} galaxies, the right panel SB galaxies.

In the text
Thumbnail: Fig. 28 Refer to the following caption and surrounding text. Fig. 28

Distribution of the resonance ring deprojected major axis absolute diameter colour- and line-coded as in Fig. 18 for different galaxy stage ranges and for ϵd ≤ 0.5. The left panel represents galaxies with −5 ≤ T ≤ 0 galaxies, the middle panel galaxies with 1 ≤ T ≤ 3, the right panel galaxies with 4 ≤ T ≤ 10.

In the text
Thumbnail: Fig. 29 Refer to the following caption and surrounding text. Fig. 29

Distribution of the resonance ring deprojected major axis diameters relative to D25.5. The left column shows all galaxies, the right column galaxies with ϵd ≤ 0.5. The histograms are colour and line-coded as in Fig. 18.

In the text
Thumbnail: Fig. 30 Refer to the following caption and surrounding text. Fig. 30

Distribution of the resonance ring deprojected major axis relative to D25.5 colour- and line-coded as in Fig. 18 for different galaxy families and for ϵd ≤ 0.5. The left panel shows SA galaxies, the middle one SAMathematical equation: \hbox{${\underline{\rm A}}$}B to SABMathematical equation: \hbox{${\underline{\rm B}}$} galaxies, the right panel SB galaxies.

In the text
Thumbnail: Fig. 31 Refer to the following caption and surrounding text. Fig. 31

Distribution of the resonance ring deprojected major axis diameter relative to D25.5 colour and line-coded as in Fig. 18 for different galaxy stage ranges and for ϵd ≤ 0.5. The left panel is for − 5 ≤ T ≤ 0 galaxies, the middle panel is for 1 ≤ T ≤ 3 galaxies, and the right panel is for 4 ≤ T ≤ 10 galaxies.

In the text
Thumbnail: Fig. 32 Refer to the following caption and surrounding text. Fig. 32

Distribution of the ratios of the diameters of outer and inner rings. The left column shows all galaxies, the right column galaxies with ϵd ≤ 0.5. The of histograms are colour- and line-coded according to the host galaxy family (top panels) and stage (bottom panels). One galaxy, NGC 5033, has Dr,0(O)/Dr,0(I) = 17.5 and is beyond the horizontal limits of the plots.

In the text
Thumbnail: Fig. 33 Refer to the following caption and surrounding text. Fig. 33

Fraction of galaxies with ϵd ≤ 0.5 with outer rings divided by that with inner rings, as a function of the galaxy stage.

In the text
Thumbnail: Fig. 34 Refer to the following caption and surrounding text. Fig. 34

Fraction of galaxies with inner rings aligned with the bar (θr − θb ≤ 30°; in black) and inner rings misaligned with the bar (θr − θb > 30°; in grey) that have a given disc axis ratio. The top panel shows galaxies with stages 1 ≤ T ≤ 3, the bottom panel galaxies with stages 4 ≤ T ≤ 10. Only galaxies with deprojected ring axis ratios qr,0(I) < 0.85 and disc axis ratios qd ≤ 0.5 are included. The error bars are calculated using binomial statistics.

In the text
Thumbnail: Fig. 35 Refer to the following caption and surrounding text. Fig. 35

Ring deprojected major axis angle difference with the bar as a function of the galaxy disc ellipticity for 1 ≤ T ≤ 3 and ϵ ≤ 0.5.

In the text
Thumbnail: Fig. 36 Refer to the following caption and surrounding text. Fig. 36

Selection of close to face-on S4G galaxies with stages 4 ≤ T ≤ 10 that host inner pseudorings misaligned with the bar. The images have the same properties as those in Fig. 2. The name of the galaxies, their morphological classification, and the bar-pseudoring intrinsic misalignment can be found below each image.

In the text
Thumbnail: Fig. 37 Refer to the following caption and surrounding text. Fig. 37

Fraction of galaxies with outer rings (top panel) and inner rings (bottom panel) for a given stage. The plots only include galaxies with a disc ellipticity ϵd ≤ 0.5. In each of the panels, both rings as a whole and closed rings are indicated.

In the text
Thumbnail: Fig. 38 Refer to the following caption and surrounding text. Fig. 38

As in Fig. 37, but now with the bar family instead of stage.

In the text

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