© J. A. Gómez-López et al. 2019

1. Introduction

One of the main processes regulating galaxy evolution is star formation. The gas located along the disk of spiral galaxies collapses inside molecular clouds to form stars following the Kennicutt–Schmidt law (Schmidt 1959; Kennicutt 1989). Besides enriching the interstellar medium (ISM) with chemical elements, massive evolved stars and supernovae inject a large amount of kinetic energy into the ISM (van den Bosch 2000), driving the formation and evolution of new generations of stars. Finally, the star formation process also affects the intergalactic medium (IGM, Boselli 2011).

We are far from fully understanding the complexity of the star formation process. It is still unclear as to which mechanism triggers the collapse of the gas inside molecular clouds that forms new stars; nowadays, this topic is still under debate. The kinematical properties in late-type galaxies seems to play a crucial role in triggering the star formation process, at large scales via through the instability of the rotating disk (Toomre 1964; Larson 1992; Kennicutt 1998a,b; Tan 2000; Boissier et al. 2003) and the dynamical influence of the spiral arms (Wyse 1986; Tan 2000), and at small scales through turbulence (Wang & Silk 1994; Corbelli 2003; Leroy et al. 2008; Krumholz & McKee 2005; Krumholz et al. 2012; Elmegreen 2015).

The study of the relationship between the star formation rate (SFR), the gas column density (Σ_gas), and the kinematical properties of galaxies based on a strong statistical basis would require a well representative sample, having multifrequency resolved images and 2D-spectroscopic observations. The distribution of the atomic and molecular gas can be derived using H I and CO observations. Whereas, the distribution of the star formation activity that uses direct tracers, such as the Balmer Hα emission line or the UV emission, properly corrects for dust attenuation that uses the far-infrared emission, for instance, or SED fitting codes when multifrequency data are available.

The Herschel Reference Survey (HRS, Boselli et al. 2010) is a complete sample of 323 nearby galaxies that aims to study the relationship between the star formation process and the different components of the ISM. This sample has been observed at all frequencies in order to provide the community with the largest possible set of homogeneous data. This unique dataset includes photometric data in the UV and optical bands (Cortese et al. 2012; Boselli et al. 2011; Ferrarese et al. 2012), in the mid- and far-infrarred (IR) (Ciesla et al. 2012, 2014; Cortese et al. 2014a; Bendo et al. 2012), and in the Hα line (Boselli et al. 2015). Spectroscopic data are also avalibale in the visible (Boselli et al. 2013; Gavazzi et al. 2004, 2018) and in the radio at 21 cm (H I) and at 2.6 mm (CO) (Boselli et al. 2014a).

Two-dimensional kinematical data are however still lacking. As a result, we are undertaking an Hα kinematic survey of the HRS star-forming galaxies using Fabry–Perot interferometry. This technique is perfectly adapted for this sample since it allowed us to gather, using typical integration times of aproximately two hours per galaxy and a 2 m-class telescope, seeing-limited (  ∼  2 arcsec) datacubes of galaxies within a large field-of-view (FoV  ∼  5.8  ×  5.8 arcmin²), that is, surrounding their nearby environment, with a high spectral resolution (R >  10 000). The large FoV allowed us to get high resolution Hα spectra for hundreds or up to thousands of independent spatial elements.

This paper presents new Fabry–Perot data for 152 HRS star-forming galaxies gathered during nine observing runs at the Observatoire de Haute Provence (OHP). These data are used to derive the kinematical properties of the ionized gas at high spatial and spectral resolution. By combining this new set of data with other Fabry–Perot data available in the literature, we study the relationship between the dynamical and the baryonic mass. The latter was directly measured using multifrequency observations. We also derive, for the first time in the literature, the dynamical mass main sequence for a representative sample of the local universe.

The paper is organized as follows. Section 2 describes the HRS sample, and Sect. 3 explains the observations made and data reduction. In Sect. 4 we derive the kinematical parameters. In Sect. 5 we compare several kinematical scaling relations derived for the HRS with those proposed in the literature. The summary and conclusions are given in Sect. 6. All the data products, including comments on individual objects, are given in the different Appendices. Consistent with our previous works, all of the Fabry–Perot data are made available on the HRS dedicated database HeDAM¹ and on the Fabry–Perot database².

2. The sample

The Herschel Reference Survey (HRS) is a K-band-selected (where the K-band is a proxy of stellar mass, Gavazzi et al. 1996), volume-limited (15 <  D <  25 Mpc) complete sample of 323 galaxies spanning a wide range in morphological type (from ellipticals to late-type spirals and irregulars) and stellar mass (10⁸ <  M_star <  10¹¹ M_⊙). The sample, which has been extensively presented in Boselli et al. (2010), includes galaxies belonging to different environments, from the Virgo cluster to isolated systems in the field. Out of the 323 galaxies of the sample, 261 objects are late-type systems, with an ongoing star formation activity, as indicated by their strong Balmer line emission (Boselli et al. 2015). These late-type systems are thus adapted targets for a kinematical survey of the ionised gas using a Fabry–Perot interferometer. Thanks to its statistical completeness, the HRS is becoming the ideal reference for local and high-redshift studies as well as for models and simulations. It is thus a tailored sample for tracing the kinematical scaling relation of a complete sample of nearby galaxies.

In this work we present new Fabry–Perot data for 152 star forming galaxies observed at the OHP (see Table E.1). Fabry–Perot are also available in the literature for other 40 galaxies from the following references: GHASP (Garrido et al. 2005; Epinat et al. 2008b), SINGS (Daigle et al. 2006a), Virgo cluster (Chemin et al. 2006), and Loose Groups (Marino et al. 2013). So far, Fabry–Perot data are thus available for 192 out of the 261 star-forming galaxies of the sample (73.6% complete). Figure 1 compares the distribution in morphology and stellar masses (taken from Cortese et al. 2012) of the HRS galaxies to the Fabry–Perot dataset presented in this paper and available from the literature. This figure shows that the available kinematical data constitue a representative subsample of the HRS, suitable for statistical studies, since they already include a large number of galaxies spanning a wide range in morphological type and stellar mass.

3. Observations and data reduction

Fabry–Perot observations scanning the Hα emission line of 152 late-type galaxies have been obtained along 91 nights at the OHP (9 runs from February 2016 to April 2018). The observations have been carried out in good photometric conditions and with a typical integration time of 2 h per galaxy. The journal of the observations is given in Table E.2.

3.1. GHASP instrumental setup

Fabry–Perot observations provide datacubes with dimensions x (right ascension α), y (declination δ) and z (wavelength λ), containing Hα profiles for each pixel along the field-of-view (FoV). The instrument we use at OHP is GHASP, a focal reducer containing a scanning Fabry–Perot interferometer attached at the Cassegrain focus of the 1.93 m telescope. The principles and characteristics of the GHASP instrument are extensively explained in Garrido et al. (2002, 2003, 2004, 2005) and Epinat et al. (2008b). The focal reducer has an aperture ratio of f/3.9, with a FoV of ≃5.9 × 5.9 arcmin in a 512 × 512 pixels window with a pixel size of ≃0.69 arcsec pix⁻¹. The angular resolution is limited by the seeing, typically ranging between ≃1.5 and ≃3 arcsec. The interference order of the Fabry–Perot interferometer we used is 798 at Hα rest wavelength, giving a free spectral range (FSR) of 376 km s⁻¹, reaching a spectral resolution of R ≃ 10 000 (velocity sampling ≃10 km s⁻¹ for a resolution of ≃30 km s⁻¹). The pattern of interference rings varies along the FoV when the separation of the plates is changed by applying different voltage on the piezoelectric actuators. Because of that, the wavelength varies according to the position on the FoV, so we must calibrate the Hα profiles for each pixel by comparing them with reference profiles given by a monochromatic source such as a neon lamp (6598.95 Å) in order to give the same wavelength origin (or phase) to all the pixels and associate a specific wavelength to each spectral channel. Two calibration cubes are taken, one before and one after each galaxy exposure, to account for flexion conditions and temperature variations.

The detector, an Image Photon Counting System (IPCS), has the significant advantage of zero readout noise and enables to scan the interferometer quickly, taking 10 s per scanning step, typically 32 (for 146 galaxies) or 48 channels (for 6 galaxies) to cover the whole FSR, so that we can repeat the FSR scanning many times (or cycles) and then add up the successive exposures, enabling to greatly reduce the effects of variation in atmospheric transmission and to correct any eventual telescope drift in a very efficient manner.

To cover the Hα line in the range 6565 Å–6635 Å, we use seven different interference filters having a typical FWHM ∼15 Å, allowing to scan the isolated Hα line of ionised hydrogen (6562.78 Å) and rejecting other emission lines (e.g. [N II] contaminating contribution) as well as the sky background emission (mainly OH lines). If necessary, we tilt by a couple of degrees the corresponding filter to blue shift the central wavelength of the transmitivity peak the closest to the systemic velocity (V_sys) of the corresponding galaxy, as indicated in Table E.2.

3.2. Comparison with other Integral Field Spectrographs

The gain in FoV is significant with respect to other seeing-limited IFS instruments, such as CALIFA (Sánchez et al. 2012), MaNGA (Bundy et al. 2015), SAMI (Bryant et al. 2015) and MUSE (Bacon et al. 2017) have a FoV ∼ 1.30 × 1.30, 0.20 × 0.20 or 0.53 × 0.53, 0.25 × 0.25, and 1.0 × 1.0 arcmin² respectively. The large FoV of our instrument enables to cover the galaxies of the HRS up to their optical limit r_opt³, ranging from 0.16 to 2.55 arcmin, with a mean and median value of 1.08 and 0.99 arcmin, respectively. In terms of effective radius r_eff, r_opt spans from 1.47 to 4.26 r_eff, with a mean spatial coverage of 2.56 ± 0.59 r_eff. The mean/median radius reached in HRS sample is nevertheless smaller than the mean/median one in the GHASP sample (Epinat et al. 2008a,b), this is due to the galaxy environment. Galaxies in the GHASP sample are mainly located in an isolated environment while 25.8% galaxies of our HRS sample are situated at a projected distance smaller that 3.4 Mpc from the Virgo center and are furthermore potentially affected by environmental effects (ram pressure stripping, tidal stripping, quenching, etc.).

In order to quantify the spatial coverage of our observations, for each galaxy, we compute the number of independent seeing elements, hereafter refereed as N_beams. N_beams is the total number of pixels covering a galaxy with a signal-to-noise ratio per bin> 7 (see next paragraph) divided by the number of pixels per seeing element, for each observation. N_beams are listed in Table E.3, they range from 66 to 21153 with a mean/median value of 3138/2066. For comparison, the half of the FoV⁴ of CALIFA, MaNGA and SAMI gives N_beams equal to 234, 75 and 33, respectively.

Within a narrow spectral domain around Hα, the gain in spectral resolution R is also significant with respect to other IFS instruments: CALIFA (R ∼ 850 − 1650), MaNGA (R ∼ 2000), SAMI (from R ∼ 1700 to R ∼ 4500), MUSE (R ∼ 3000). This allows to study the kinematics down to the scale of single H II regions (σ ≃ 30 km s⁻¹, Boselli et al. 2010).

3.3. Data reduction

The Fabry–Perot data reduction procedure⁵ basically follows the same used in Daigle et al. (2006b) and in Epinat et al. (2008b). The reduction procedure consists of:

First, obtaining the phase map. Such a map is computed from the rings of calibration cubes. The consistency of both calibrations is checked and the phase is calculated by averaging the two calibration exposures. The phase map gives the reference scanning channel as origin wavelength for the spectrum of each pixel.

Second, sorting and merging the data. This is done by removing strong variations in atmospheric transmission by comparing the recorded successive individual frames of the observations. Those frames having an inconsistent flux compared with the median flux are deleted and replaced by frames of adjacent cycles automatically.

Third, correcting from any telescope drift and/or instrumental flexures along the different successive frames by using reference stars or bright H II regions. According to Sect. 3.1, the wavelength varies with the position across the FoV, thus this correction from telescope drift implies a phase correction for each cycle (i.e. each ≃5 or 8 min for 32 or 48 scanning channels per cycle respectively).

Fourth, obtaining wavelength calibrated cubes. The latter is done by calibrating the interference rings of the galaxy observation by using the phase map. The same wavelength origin is assigned for each pixel.

Fifth, performing a one-spectral-element Hanning smoothing of the spectrum which preserves the flux.

Sixth, subtracting night skylines. The data cube is divided into sky-dominated and galaxy-dominated regions. Then a sky cube is built by fitting the sky dominated regions (polynomial fitting of 2nd order in our case) and then making an interpolation of the sky spectrum on the galaxy-dominated regions. Such a sky cube is finally subtracted.

Seventh, eventually, suppressing ghosts due to reflection at the interfaces air/glass of the interferometer when necessary.

Eighth, computing the astrometry to find the correct World Coordinate System for each galaxy dataset, making use of XDSS R-band images. This is done using KOORDS routine of KARMA⁶ (Gooch 1996) by a systematic comparison between field stars that are present in both the broad-band XDSS images and our continuum images.

Ninth, data processing of adaptive spatial binning based on Voronoi tesselation on the data. The latter preserves the spatial resolution of bright regions while the weak emission of diffuse gas areas is recovered. Due to the small ratio between the number of channels containing continuum and the channels containing the emission line, the criterion used for GHASP data relies on an estimate of the signal-to-noise ratio as the square root of the flux in the line, which is a simple estimation of the Poisson noise at the line flux. We aim to recover a signal-to-noise ratio ≥7 per spatial bin. Two kind of maps are generated: the binned maps with N independent bins, where all the pixels belonging to each bin are affected to the same value and the bin-centroid maps, for which only one pixel per bin corresponding bin-centroid position, contains a value (the other pixels being set to NaN). Those later maps are the ones that are used in practice, in order to provide the same statistical weight to each bin and not to each pixel.

Thenth, computation of the different momenta maps (flux, radial velocity, radial velocity dispersion, continuum).

Eleventh, FSR corrections on velocity fields, since some Hα profiles present FSR overlaps causing velocity jumps at some pixels.

Twelfth, the semi-automatic cleaning system of the velocity fields in order to delimitate the outskirts of the galaxy where there is no more Hα emission. The latter is done by a continuity velocity process on the velocity field, based on a cut-off value between contiguous velocity bins (typically ∼30 km s⁻¹ for a velocity field with an amplitude of ∼300 km s⁻¹). Regions with too low emission and very large bins are also diskarded and thus masked.

Thirteenth, correction of the velocity dispersion from the Line Spread Function (LSF) broadening. This is done by a quadratic difference between the velocity dispersion values of the observation maps and the mean dispersion due to the instrumental contribution.

3.4. Flux calibration and Hα profiles

During the OHP runs, in order to maximize the observing time on the galaxies themselves, we do not observe flux calibration sources but we use instead the high quality Hα photometry, available for the whole HRS sample (Boselli et al. 2015). Thus we perform an indirect calibration of the total Hα flux for the 152 datacubes in a similar way as in Epinat et al. (2008a), but using in our case the calibrated fluxes from Boselli et al. (2015). We correct their Hα + [N II] fluxes for [N II] contamination (6584 and 6548 Å) using the [N II]/Hα ratio derived from spectroscopic observations (Boselli et al. 2013); for galaxies where there is no available [N II]/Hα ratio, we calculate it according to the [N II]/Hα vs. M_star relation in the B-band given in Boselli et al. (2009).

For each galaxy, the total Hα emission is computed by integrating the flux for each spatial element of the datacubes as described in Epinat et al. (2008a), taking into account: the response and the aperture of the instrument, the exposure time (given in Table E.2), the use of the velocity field to disentangle the FSR overlaps when necessary, the shift of the interference filter spectral range due to the tilt (if any) and the temperature, and the subtraction of the continuum contribution.

To minimize the foreground sky contamination, we only consider the spatial elements not masked in the final momenta maps (shown in Appendix D). The integrated Hα profiles per galaxy are shown in Appendix C.1. Figure 2 shows the comparison between the Fabry–Perot fluxes and those from Boselli et al. (2015). The response of the GHASP camera being linear and since we are not comparing quantities having the same units, we use an Ordinary Least Squares (OLS) bisector linear regression, represented on the figure with a solid red line, to calibrate the Fabry–Perot Hα fluxes. The fit is forced to pass through the origin for obvious physical reasons; the calibration coefficient is 1 ph s⁻¹ = 0.50 ± 0.05 × 10⁻¹³ erg cm⁻² s⁻¹. The integrated fluxes estimated for each galaxy using our calibration are given in Table E.3.

We measure the sensitivity of our Fabry–Perot dataset using two methods. The first one consists in computing the detection limits from the isophotes of VESTIGE Hα narrow band images (Boselli et al. 2018a) for galaxies in common with the HRS, while the second method consists in calculating such limits directly on all our Hα monochromatic images using our estimated calibration. We find for each case a surface brightness detection limits of ∼2.5 ± 0.2 × 10⁻¹⁷ erg s⁻¹ cm⁻² arcsec⁻² and ∼2.3 ± 0.2 × 10⁻¹⁷ erg s⁻¹ cm⁻² arcsec⁻² for a typical 2 h exposure time, thus comparable to the typical sensitivity of narrow-band imaging. This sensitivity is close to that reached by Epinat et al. (2008a) using similar integration times and predicted by Fig. 2 in Gach et al. (2002) for a signal-to-noise ratio between 1 and 2.

4. Data analysis

4.1. Kinematical models and rotation curves

Rotation curves are computed from the velocity fields following the method described in Epinat et al. (2008b), which is a synthesis adapted to Hα data between the angular sector method, tilted-ring models and the fitting method used by Barnes & Sellwood (2003). In 21 cm-HI disks where warps are frequently observed at a distance from the center larger than the optical radius, the position angle (PA) and galaxy inclination (i) might vary as a function of the galacto-centric radius. Within the optical radius, the situation is different, as in Epinat et al. (2008b), we do not allow the PA nor i to vary because these variations are slight throughout the optical disk plane and due mainly to non-circular motions and velocity dispersion that behave as oscillations around a median value.

4.1.1. Kinematical Models

For each bin situated in the frame of the galactic plane of a disk, assuming that at first order the expansion velocity component and vertical motions are negligible, the velocity vector projected on the line-of-sight can be described as follows:

$$\begin{array}{c}\hfill V_{\mathrm{obs}}(r)=V_{\mathrm{sys}}+V_{\mathrm{rot}}(r)cos\theta sin\mathit{i}\end{array}$$(1)

where V_sys is the systemic velocity of the galaxy, i is the inclination, and r and θ are the polar coordinates in the plane of the galaxy, both measured from the PA, i and the kinematical center (α, δ) of the galaxy. V_rot(r) is modeled assuming a four-parameters modified Zhao function (Epinat et al. 2008a) on the whole velocity field:

$$\begin{array}{c}\hfill V_{\mathrm{rot}}(r)=v_{\mathrm{t}}\frac{{(r/r_{\mathrm{t}})}^g}{1+{(r/r_{\mathrm{t}})}^a}\end{array}$$(2)

where v_t is the effective “turnover” velocity, r_t is the transition radius between the rising and flat part of the rotation curve g and a are coefficients that parametrise the sharpness of the turnover. This leads to a model of nine free parameters: four projection parameters (PA, i, galaxy center α and δ) and five kinematical parameters (V_sys, v_t, r_t, g, a). The model parameters are obtained with a χ² minimization based on the Levernberg–Marquardt method (Press et al. 1992), computing an iterative 3.5σ clipping on the observed bin-centroid velocity field. The number of unknowns will depend on how many initial guess parameters are fixed or let as free for Eqs. (1) and (2): in our case, the galaxy center is carefully computed from the continuum image and always fixed; PA and/or i are taken from the literature and generally let as free or fixed in some cases (see Sect. 4.2). These initial guesses of projection parameters are used to fit the modified Zhao function to the velocity field in order to obtain the V_rot starting parameters v_t, r_t, g and a, which are then let always as free.

4.1.2. Residual velocity fields

Since the kinematical models are calculated with a prior assumption that circular motions are dominant and those due to non-axisymetric perturbations are not part of a large scale pattern, the residual velocity field computed by subtracting the modeled velocity field to the original one reflects well the deviation from circular velocities. Since our model is simple, the resulting statistical uncertainties of kinematical parameters are too small. For that reason, the calculation of uncertainties is done by computing the power spectrum of the residual velocity fields and then considering several random phases, in order to compute residual fields that present the same kind of structure but placed differently. Through a Monte-Carlo method, we estimate robustly the standard deviations of the kinematical parameters over hundreds of simulated velocity fields (see Epinat et al. 2008a for details). For consistency with Epinat et al. (2008a) and with Sect. 4.1.3, the residual velocities have been computed using the bin centroid maps.

4.1.3. Rotation curves

Once the best set of parameters is derived using the method previously described, the rotation curve is extracted from the velocity field. Since the velocity field is decomposed into rings, we consider the bin centroid velocity fields in order to avoid any artificial oversampling of rings. We use n uncorrelated velocity bins per ring (or annulus) to provide each rotation velocity; n = 25 optimizes the compromise between the higher signal-to-noise ratio and the lower spatial resolution per ring (Epinat et al. 2008a). Rotation curves are computed without correction from the non-circular motions along the disk.

4.1.4. Quality Flags on the rotation curves

With the purpose of quantifying the quality of each rotation curve, we attribute a quality Flag using an automatic classification method extensively described in Appendix A, that goes from Flag “1” (accurate estimation of the rotation curve) to Flag “4” (poor estimation of the rotation curve), and attributing a supplementary Flag “A” and Flag “B”, the latter corresponding to those peculiar cases leading to a non-realistic kinematical fitting, such as the presence of a bar, asymmetries, high or low inclination.

For 11 cases over 152 (HRS 32, 35, 104, 136, 164, 184, 195, 249, 282, 291, and 300), characterized by a poor signal-to-noise ratio, the model does not match the rotation of the galaxy because of lack of Hα emission, thus no model is computed, neither residual velocity field nor rotation curve can be plotted, and no kinematical parameters can be calculated.

4.1.5. Quality checks of the residual velocity fields

For each residual velocity field, the average value ($\overline{\mathrm{Res}}$) and the standard deviation of all the bins (σ_res) are computed (see Table E.3). Figure 3 displays, for the whole dataset, the correlation between σ_res (with a mean value ∼12.6 ± 2.7 km s⁻¹, which is similar to the velocity of 13 km s⁻¹, computed in Epinat et al. 2008a) and the mean amplitude of the velocity field (which is the maximum rotation velocity V_max⁷ multiplied by the sin i_kin). The bisector linear regression traces a trend which indicates that, in general, high velocity amplitude values are correlated with high σ_res values. Nevertheless, many points for which V_max × sin i_kin <  150 km s⁻¹ are situated above the regression line, corresponding to galaxies with quality Flags “3-B” and “4-B”, so that the distribution of such points with respect to the Y-axis seems to be related to the quality of the data and not to the line-of-sight velocity, thus resulting in a high σ_res value (i.e. the outlier with σ_res∼35 km s⁻¹ is the galaxy HRS 59, an almost edge-on object with a chaotic rotation curve and flagged as “3-B”); these specific cases are extensively described in Appendix B. The correlation is in agreement with Epinat et al. (2008a) and Epinat et al. (2008b), and it does not depend on the galaxy type (Epinat et al. 2008a).

4.1.6. Maximum rotation velocity

In order to compute our HαV_max without being perturbed by local variations in the rotation curves due for instance to crossing spiral arms, we fit the rotation curve with analytic functions, between r = 0 and r_RC, the radius corresponding to the last ring of the rotation curve. For this purpose, we select the Courteau profile (Courteau 1997). The original Courteau function describes the line-of-sight velocities from long-slit observations; because we are working with deprojected data, we used the following modified Courteau function:

$$\begin{array}{c}\hfill v(r)=v_{\mathrm{c}}\frac{{(1+\frac{r_{\mathrm{t}}}{r})}^{\beta }}{{(1+{\left(\frac{r_{\mathrm{t}}}{r}\right)}^{\gamma })}^{1/\gamma }}\end{array}$$(3)

where the four free parameters are v_c, the asymptotic velocity; r_t the transition radius between the rising and flat part of the rotation curve ; β, the drop-off or steady rise of the outer part of the rotation curve and γ, the sharpness of turnover beyond the r_t radius. Because it does not affect much the result and decrease by one the degree of freedom, we used β = 0 as suggested by Courteau (1997). Furthermore, V_max is defined by the maximum rotation velocity reached by the fitted modified Courteau profile within the optical radius. The best fit is represented in Fig. 4 and Figures in Appendix D with a black solid curve that goes through the velocity points in each rotation curve.

It is important to mention that the choice of a given fitting function may introduce systematic biases in the estimation of V_max, particularly when extrapolations are necessary where data do not extent further enough at large radii. For instance, modified Zhao and Courteau profiles have four free parameters. A fair comparison of both functions should be done in reducing the degeneracy but in keeping the same number of free parameters, we furthermore set it at three; we fixed the parameters that have the weaker influence on the shape of the rotation curves, namely g = 0, for the modified Zhao function and β = 0 for the modified Courteau function. We conclude that this 3-parameters Zhao function is more sensitive to local oscillations that the 3-parameters Courteau one. In other words, when the modified Zhao function is used to extrapolate the rotation curves outside the last observing radius, V_max tends to follow the trend of the last data points rather than the general trend of the plateaus and, at the opposite, the modified Courteau function averages the mean trend of the whole outer rotation curves. In short, the modified Courteau function tends to extrapolate a flatter rotation curve and flatten local oscillation than the modified Zhao function and this have an impact on V_max. We choose the Courteau function because it provides a more conservative solution, as well as and for consistency with previous works on the GHASP sample.

Alternatively to Zhao and Courteau profiles used in this work, other analytic functions are used in the literature to fit rotation curves like the empirical Polyex function (Giovanelli & Haynes 2002; Catinella et al. 2005, 2006; Masters et al. 2006). Polyex profiles fit well a large variety of rotation curve shapes (94% of the cases, including those declining at large radii, according to Catinella et al. 2005). A comparison between Polyex and the other fitting expressions is beyond the scope of this paper.

4.1.7. Presentation of the data

We present in the Appendix D (online material at the CDS), for each galaxy (as in Fig. 4), six frames per figure containing the XDSS image in the R-band, the Hα line-of-sight velocity field, the Hα monochromatic image (free of continuum, [N II] and night skylines contributions), the line-of-sight velocity dispersion field, the rotation curve of the galaxy and the Hα residual velocity field. The white/black cross indicates the calculated kinematical center, while the solid green line traces the optical radius (called hereafter r_opt. For consistency with previous HRS works we choose r_opt = r₂₄, which is in fact D₂₄/2 in r-band, taken from Cortese et al. 2012. Nevertheless r₂₄ is not available for 5 galaxies, thus we used r₂₅ which is D₂₅/2 in B-band, taken from Boselli et al. 2010) and convert it to r₂₄ following the relation r₂₄ = 0.920 ± 0.01 r₂₅, obtained by comparing both radii for the whole HRS sample and fitting a bisector regression. The black/white solid line traces the kinematical major-axis deduced from our velocity field analysis; the PA is the one calculated from our kinematical models (see Sect. 4.2). In the rotation curve plots (bottom left panel in Fig. 4 and all figures in Appendix D), both sides are superimposed in the same quadrant, using red crosses for the receding side and blue dots for the approaching side. The solid vertical black line represents the r_opt; the black dashed line represents the r₂₅ in B-band, in order to compare the extent between r₂₄ and r₂₅. When available in Cortese et al. (2012), the effective radius r_eff is plotted with a solid blue vertical line. If available in Boselli et al. (2015), the H IV_max is plotted as a horizontal green dashed line. We present the tables of the rotation curves in Appendix E. When no kinematical model can be derived, we plot instead the photometrical center and the PA taken from Cortese et al. (2012) without any residual velocity field nor rotation curve.

4.2. Kinematical projection parameters

As we saw in Sect. 4.1.1, we need a set of initial guess parameters in order to compute our kinematical models. Such a set is composed either by parameters taken from high quality data available in the literature for the HRS (morphological measurements extracted from surface brightness photometry PA_morph, i_morph), systemic velocity from long-slit spectroscopy V_sys, or carefully calculated by us using morphological and kinematic parameters. The galaxy center α and δ is computed either as the nucleus in the continuum image or as the kinematical center of the velocity field. Table E.3 shows the morphological parameters PA_morph and ellipticity ϵ used to compute i_morph for each galaxy, taken from Cortese et al. (2012). We computed i_morph from the ϵ value following the procedure as in Masters et al. (2010):

$$\begin{array}{c}\hfill {cos}^2{i}_{\mathrm{morph}}=\frac{{(1-ϵ)}^2-q^2}{1-q^2}\end{array}$$(4)

where q depends on the galaxy type (Haynes & Giovanelli 1984; Masters et al. 2010).

We use the initial guesses of projection parameters to derive a rotation curve on which is fitted the modified Zhao function to obtain starting parameters v_t, r_t, g and a. The different kinematical projection parameters computed by our models are accurately determined from different symmetry properties of the line-of-sight velocity field: typical accuracy reached by our method are sub-seeing for the coordinates of the galaxy center, ∼0.5 arcsec along the major axis and ∼1 arcsec along the minor one; ∼3 km s⁻¹ for V_sys; ∼2° for PA and 5°–10° for kinematical inclination i_kin. We control those parameters using the method described in Warner et al. (1973), van der Kruit & Allen (1978) and van der Kruit (1990), which is based on the fact that residual velocity fields present characteristic patterns when one of several of those parameters is/are incorrectly determinated. Non-circular motions, mainly due to bar structures, spiral arms, H II complexes, are not considered in the kinematical models since we expect that, except in very low mass dwarf galaxies, such motions are low with respect to rotational ones in rotating systems. The modeled velocity is a purely rotating disk that optimally fits the observed velocity fields. Non-circular motions are thus embedded in the residual velocity field, which is the difference between the observed velocity and the model. For the HRS, the mean velocity dispersion of the residual velocity field is 12.55 ± 2.60 km s⁻¹; such motions may become more important in perturbed galaxies and systems in interaction, which rare in the HRS sample (< 11%, Boselli et al. 2010). However, non-circular motions are taken into account in the determination of the uncertainties (Epinat et al. 2008a,b).

Table E.3 gives also the kinematical output parameters of the models and the best reduced ${\chi }_{\mathrm{red}}^2$ giving the goodness of fit of the Levernberg-Marquardt method. In general, the PA and i values of the galaxy are left as free parameters when computing the best fitting. Nevertheless, for 42 galaxies (out of which 37 are Flag “B” objects), we fix the kinematical PA to the morphological value during the model computation because of the following reasons:

First, i ≥ 70° (39 objects), because galaxies with high inclination have a low spatial coverage along their minor axis; and some of them have a spatial coverage actually too small (i.e., less than 150 velocity bins),

Second, poor signal-to-noise ratio (three galaxies), because their kinematical model easily leads to non-realistic kinematical parameters.

On the other hand, for 78 galaxies, we fix the kinematical i to the morphological value during the fit process because:

First, i ≥ 70° or i ≤ 30° (63 objects), because an underestimation of the inclination leads to a overestimate on velocities and vice versa (Tully & Pierce 2000).

Second, 15 galaxies showing velocity fields dominated by non-circular features.

As already mentioned, some of galaxies relevant from those two later cases have in addition a spatial coverage or/and a signal-to-noise ratio too low.

The details about those special cases are given in the Appendix B, and the parameters PA_kin or i_kin are flagged with an asterisk in Table E.3 when fixed during the model computation.

Figure 5 shows in the top panel the histogram of the | PA_kin − PA_morph| distribution. For 42 galaxies over 140, the PA_kin is fixed to the morphological one (red part of the histogram). Ignoring such galaxies, the peak of the histogram remains at | PA_kin − PA_morph| = 0 because the bin width centered at zero includes 44 galaxies with | PA_kin − PA_morph |≤3°; in fact, | PA_kin − PA_morph | ≤10° for 105 galaxies over 140, and the median of the distribution is 2.47° and the dispersion 7.85°. Figure 5 also displays the comparison of the difference between the kinematical PA_kin and the morphological PA_morph as a function of several parameters:

First, number of bins per velocity field. The | PA_kin − PA_morph| values, as well as the quality flag, depend on the number of bins, which are related to the spatial coverage and signal-to-noise ratio of the galaxy. Objects with a low number of bins are usually Flag “B” for which PA is not fixed, showing a | PA_kin − PA_morph | > 25°, representing 11.4% of the whole sample. Cases for which | PA_kin − PA_morph |> 50° belong to galaxies which are almost face-on with faint emission (HRS 68, HRS 154, HRS 255) or emission concentrated in the inner part (HRS 19, HRS 256); the details about these cases with Flag “3-B” and “4-B” are extensively described in Appendix B; nevertheless their velocity fields are good enough to allow the determination of PA_kin values.

Second, difference between the kinematical and the morphological inclination (i_kin − i_morph). In this plot, if we do not take into account the data for which i_kin has been fixed to the morphological one, we see that a possible under or over-estimation of the inclination does not depend on | PA_kin − PA_morph|. Despite the fact that the median difference between the kinematical and morphological inclinations is almost equal to zero (−0.2°), meaning that we probably do not introduce statistical biais to compute the inclination regardless the method used (morphological or kinematical), the dispersion of the i_kin − i_morph distribution is quite large (8.3°).

Third, the kinematical inclination. | PA_kin − PA_morph| becomes larger as i_kin decreases, showing good agreement with Epinat et al. (2008a,b).

We also compare | PA_kin − PA_morph| as a function of the Galaxy Type and the Distance to the Virgo Cluster (A or B clouds), but we do not find any correlation with these two parameters and we do not show those plots here.

Figure 6 displays the histogram of the variation between the morphological and the kinematical inclinations. For 78 galaxies over 140, i_kin is fixed to the morphological value (red part of the histogram). In order to test whether there was a correlation or not between the galaxy inclination (either i_kin or i_morph) and the maximum rotational velocity V_max, we perform several OLS bisector regressions comparing both i_kin and i_morph values versus V_max (not plotted here). We do not observe any significant relation, on the whole sample neither any of the subsamples as defined by their different quality flags.

Bars and Bulges are usually bright with respect to the disks, nevertheless, bulges contain a low content of warm gas while bars could be warm gas-poor or -rich. In case of low gas content, Voronoi tessellations minimise the impact of the non-rotating bulge and of the bar on the determination of the disk parameters. In case of high gas content, Voronoi techniques do not spread out the impact of non-circular motions to outer regions. On the other hand, despite the accuracy of the PA and i computation, these two parameters may be inadequate in presence of multiple non-axisymmetric structures in the kinematics or/and in the morphology. For instance, in the case of a strong bar, the determination of the i and the PA could vary with the radius within the bar, nevertheless we take this fact into account by measuring the i and PA outside the bar since our rotation curves are extended enough. Indeed, the bar length reaches the outskirt of the warm disk in only 2/152 galaxies. In addition, the estimation of V_max is not significantly biased because of the presence of a bar; indeed, a peak followed by a decrease on the rotation curve is usually linked to the presence of a bar (i.e., galaxy HRS 60) and furthermore identified as such; otherwise the effect of the bar modify the inner slope of the rotation curve and possibly shift V_max at a different radius (i.e. galaxy HRS 287), as described by Dicaire et al. (2008), Randriamampandry et al. (2015) and Korsaga et al. (2019). Finally, we use a model to fit V_max rather than fitting the raw rotation curve, precisely to average local non-circular motions. The position of the galaxy center is usually weakly affected by non-circular motions. In conclusion, the methods we use minimise the effects dues to non-circular motions.

5. Discussion: Dynamical masses

Several models, simulations and multifrequency observations consistently indicate the mass as the principal driver of galaxy evolution (i.e., Cowie et al. 1996; Gavazzi et al. 1996; Boselli et al. 2001 for observations; Navarro et al. 1996; Boissier et al. 2003; Dutton 2012; Moster et al. 2013; Dutton & Macciò 2014 for models and simulations). The mass of galaxies is generally measured through the stellar mass which is derived from optical and near-IR imaging data. Nevertheless other components are present. These include dark matter, which is generally dominant at large radius, the mass of the different gas phases (atomic and molecular hydrogen, helium, ionised and hot gas, metals), and the mass of dust. The unique dataset available for the HRS allows us to directly measure most of the baryonic components: H I and CO data are available for most of the star forming galaxies of the sample (Boselli et al. 2014a), the dust mass has been estimated from SED fitting using the far-IR data by Ciesla et al. (2014), and metallicities have been derived using integrated long slit spectroscopy by Hughes et al. (2013). The kinematical data gathered in this work can be used to roughly estimate the total dynamical mass of a system using relation (9)

In this section, we use the HRS to study the main scaling relations between the dynamical mass, the baryonic mass, and the star formation rate generally used to constrain models of galaxy formation and evolution. The unique multifrequency coverage, which allows at the same time the accurate determination of the different baryonic components, of the star formation activity, and of the dynamical mass, combined with the sample definition (see Sect. 2) and the statistics (∼200 objects spanning a wide range in morphological type and mass), make the HRS the best sample available in the literature for this purpose.

To study the dynamical properties of the sample in the context of galaxy evolution, we proceed as follows:

First, since we lack of Fabry–Perot data for 26.4% of the HRS, we test whether the H I kinematical data can be used to derive the total dynamical mass of the missing galaxies without introducing any systematic bias.

Second, we check the statistical significance of our sample by comparing the Tully-Fisher relations to those derived in other representative samples generally used in the literature.

Third, we then study the stellar and baryonic Tully-Fisher relations, the relation between the baryonic and dynamical mass, and finally we derive the main sequence for the first time using the dynamical mass⁸.

5.1. V_{max, [sans]HI} versus V_{max, [sans]Hα}

Boselli et al. (2014a) published a homogenized catalog of H I data for the whole HRS. Their work provides line widths W_HI measured at 50% of the peak flux per galaxy. We compute V_max, HI assuming that W_HI = 2 V_max, HI sin(i); where V_max, HI is the maximal H I rotation velocity. On the other hand, we compute the maximal Hα rotation velocity V_max, Hα from rotation curves derived from 2D velocity fields, thus intrinsically calculated in a more accurate way.

Uncertainties on V_max, Hα are calculated as the quadratic combination between the i_kin error and the median dispersion of the rotation curve rings beyond r_t, as in Epinat et al. (2008b). This is a much more realistic estimate of the uncertainty on the maximal rotational velocity than the one derived from the integrated H I line profile W_HI, which is very low (< 5 km s⁻¹). For that reason, in order to have comparable errors for both quantities, we derive V_max, HI uncertainties considering the combination of the dispersion between V_max, HI and V_max, Hα values modulated by the inclination (sin i_kin) and the uncertainties associated to inclination.

V_max, HI and V_max, Hα are computed comparing the kinematics of cold and warm gas phases respectively and using different methods; thus likening both quantities might present biases. A bias could come from the way V_max, HI is computed using H I emission lines; such measurements are done at certain percentage of the peak flux, here we measure it at 50% of the peak flux but it could have been done at for instance 20% and this might have an impact on V_max, HI if the edges of H I profiles are not sharp enough. In comparing V_max, HI and V_max, Hα, we check whether systematic biases appear. Fig. 7 shows the comparison between H I and HαV_max values using different symbols according to the quality of the Hα rotation curves. The OSL bisector regression for the whole sample (Flag “A” + “B”) gives V_max, Hα = 0.95 ± 0.02V_max, HI with an intrinsic scatter of 0.82, while for Flag “A”-only galaxies V_max, Hα = 0.9975 ± 0.01 V_max, HI with an intrinsic scatter of 0.11. The two sets of data give consistent results; however, for Flag “A” galaxies the slope of the relation is closer to one and the scatter is smaller than for the whole sample. We conclude that no systematic biases are present in the measurements and to explain the difference of slope between Flag “A”-only and Flag (“A” + “B”) galaxies, we favor an explanation related to galaxy environments. Indeed, Flag “B” galaxies are mainly Virgo cluster objects which can be highly perturbed by their surrounding environment (Boselli & Gavazzi 2006, 2014). There are indeed clear indications that in cluster galaxies the star forming disk is radially truncated with respect to isolated objects (Fossati et al. 2013; Boselli et al. 2015) because of the oustide-in removal of the gas (Boselli & Gavazzi 2006). For this reason, their Hα and H I rotation curves do not always reach the plateau, making the estimate of the maximal rotational velocity quite uncertain. The H I-deficiency parameter is generally used to measure the degree of perturbation in cluster objects: galaxies with H I−Def >  0.4 have a H I gas content at least 2.5 times smaller than similar objects in the field (Haynes & Giovanelli 1984). Most of the Flag “B” galaxies with a rotation curve truncated at r <  0.6 r_opt have indeed an H I-deficiency parameter H I−Def >  0.4 and are thus cluster perturbed galaxies. Since we wish to trace the statistical properties of unperturbed systems, we on purpose avoid H I-deficient cluster galaxies which are known to have a lower baryonic mass than field objects (gas deficient objects, Boselli & Gavazzi 2006; Boselli et al. 2014b). For this reason, we will ignore galaxies with Flag “B” or H I−Def >  0.4 in the following analysis. The resulting sample includes 123 objects, out of which 80 (65%) with Hα rotation curves.

5.2. The optical and NIR Tully-Fisher relation

The Tully–Fisher relation (TF, Tully & Fisher 1977), often used to constrain models and simulations of galaxy evolution, is a tight relation between the baryonic and the dynamical masses of late-type systems. This scaling relation has been derived in different photometric bands using different samples (e.g. Giovanelli et al. 1997a,b; Steinmetz & Navarro 1999; McGaugh et al. 2000; Sakai et al. 2000; Bell & de Jong 2001; McGaugh 2005, 2012; Masters et al. 2006; Cortese et al. 2014b; Sorce et al. 2014; Ponomareva et al. 2017; Aquino-Ortíz et al. 2018), but comparisons with prior studies are really challenging.

In the present study we use maximal rotation velocities derived from homogenous FP Hα rotation curves deduced for 2D velocity fields. Samples available in the literature often come from (i) heterogeneous sources, including Hα long slit spectrography or H I integrated line widths, (ii) they are different in absolute magnitude range, (iii) are based on slightly different photometric bands and (iv) have been studied using different fitting methods. For example, Giovanelli et al. (1997a,b) used rotational velocities derived either from 21 cm spectra or optical emission line long–slit spectra; ∼60% of the galaxies in use in Masters et al. (2006) have their rotational velocities measured using HI, the other ∼40% using Hα long-slit data. Giovanelli et al. (1997a); Giovanelli et al. (1997b) and Masters et al. (2006) used bi-variate fittings in I- and i-bands respectively while Sorce et al. (2014) used inverse fitting methods and photometry in the 3.6 μm-band.

A direct comparison galaxy per galaxy with several previous works is difficult because often galaxy names are not given or the number of galaxies in common is quite reduced. For instance, Aquino-Ortíz et al. (2018) using CALIFA data, and Cortese et al. (2014b), using SAMI data, do not specify the name of the galaxies they used to compute the kinematics of gas. We have only three galaxies in common (NGC 3370, 4535 and 4536) with Ponomareva et al. (2017) who used resolved H I data, for which V_max is respectively 152 ± 4, 195 ± 6 and 161 ± 10 km s⁻¹, while we reach V_max values of 160 ± 9, 201 ± 15 and 160 ± 7 km s⁻¹, thus compatible with our results. On the other hand, rotation curves deduced from IFUs typically only extend up to smaller radius r_opt (e.g. r_opt ∼ r_eff, Cortese et al. 2014b); furthermore, V_max measured from IFU surveys are often measured at radii where the maximum of the rotation curve is not reached yet. While, thanks to the large FoV of our instrument, we know the actual size of the warm disk because it is not limited by the FoV.

Aquino-Ortíz et al. (2018) and Ponomareva et al. (2017) samples are smaller than our HRS one (respectively 42 and 32 galaxies with gas kinematics) while Cortese et al. (2014b) sample, with its 193 galaxies, is comparable to ours. But even more important than the sample size is the galaxy luminosity distribution. To compare different galaxy samples, an important issue is thus to compare the galaxy luminosity distributions of the samples. It is indeed known that the slope of the TF relation is known to slightly change with luminosity (e.g. Schaye et al. 2015). We check hereafter how the statistically limited HRS compares with works which are generally based on several hundreds of galaxies.

We directly compare the HRS data with two other samples, one in the optical (Masters et al. 2006) and the other in the IR (Sorce et al. 2014), see Figs. 8 and 9, Tables 1 and 2. We use the Masters et al. (2006) sample because it has been qualified by these authors as a “template calibrator sample”, by the way this sample is partially extracted from the Giovanelli et al. (1997a); Giovanelli et al. (1997b) sample. It consists of 807 galaxies while the present HRS consists of 123 objects. In order to fairly compare the results we compute the TF relationship on the whole Masters et al. (2006) sample using the OSL bisector. The result we obtain is, as expected, different from the one those authors found using the bivariate method.

We hereafter quantify how the difference in the TF relationships are related to the statistical significance of the sample and mostly, to their galaxy luminosity distribution using the same fitting method, the OSL bisector. To quantify those effects, we randomly pick up one hundred subsamples of 123 galaxies from the Masters et al. (2006) sample with exactly the same luminosity distribution, magnitude bin per magnitude bin, as the HRS. For each of those one hundred subsamples we refit the data and compute the TF slopes and intercepts. Averaging these 100 iterations and computing their rms, we obtained a slope and zero point values closer to the ones obtained with the HRS than the ones for the whole Masters et al. (2006) sample. We see that the values obtained using the HRS sample are within the 1σ uncertainty for both parameters. Both whole sample and subsamples agree quite well, which means that the impact of the sample is not important in this magnitude range.

Using always the OSL bisector method, we make a similar check in the 3.6 μm-band using the sample of Sorce et al. (2014) containing 319 galaxies. The Sorce et al. (2014) sample is larger than the HRS but not large enough to randomly simulate the same galaxy magnitude distribution as the HRS. We furthermore build subsamples of 89 galaxies matching approximatively our magnitude distribution. Despite the impact of sample selection seems larger for the Sorce et al. (2014) sample then for the Masters et al. (2006) sample, the results are nevertheless similar to those obtained for the i-band.

Our TF relationships are in good agreement with the literature. We can thus conclude from these analyses that, despite the difference in luminosity distribution and our smallest sample, the HRS thoroughly represents well other larger samples generally used as references in the literature.

5.3. Stellar and baryonic Tully–Fisher relations

5.3.1. The stellar Tully–Fisher relation

Figure 10 shows the stellar TF relation for the HRS. Stellar masses (from Cortese et al. 2012) have been derived using the i- and g-band SDSS photometry following the prescription of Zibetti et al. (2009) (Chabrier IMF). The OSL bisector regression and the best fit published in the literature are given in Table 3. As for the i- and 3.6 μm-bands, the stellar TF relation derived for the HRS is in good agreement with compute the generally taken as reference in the literature (Bell & de Jong 2001; McGaugh et al. 2000). It well matches also that derived on a much smaller sample with Fabry–Perot data by Torres-Flores et al. (2011).

We also compare our data with the predictions of the EAGLE cosmological hydrodynamical simulations (Schaye et al. 2015, Ferrero et al. 2017) on z ∼ 0.1 late-type galaxies (Fig. 10). The agreement between the slope (4.51 ± 0.68) and intrinsic scatter (∼0.16 dex) of the HRS stellar TF relationship and the EAGLE TF predictions (mean slope ∼4.84 and intrinsic scatter ∼0.14 dex) is very good.

5.3.2. The Baryonic Tully-Fisher Relation

We can also derive the baryonic TF relation (Fig. 11), where the baryonic mass is defined as:

$$\begin{array}{c}\hfill M_{\mathrm{bar}}=M_{\mathrm{star}}+M_{\mathrm{gas}}+M_{\mathrm{dust}},\end{array}$$(5)

and the gas mass is defined as follows:

$$\begin{array}{c}\hfill M_{\mathrm{gas}}=M_{\mathrm{HI}}+M_{{\mathrm{H}}_2}+M_{\mathrm{He}}+M_z,\end{array}$$(6)

where M_HI is the atomic gas mass, M_H2 the molecular gas mass, M_He the helium mass and M_z the metal mass. The hydrogen mass M_H = M_HI + M_H2 is directly measurable (Boselli et al. 2014a, where M_H2 is measured using a luminosity dependent X_CO conversion factor, Boselli et al. 2002). M_He is derived from the primordial nucleosynthesis helium fraction, Y ≡ M_He/M_gas ≃ 0.28 (Pagel 2009), using the relation:

$$\begin{array}{c}\hfill M_{\mathrm{gas}}=\frac{1}{1-Y-Z}\times M_{\mathrm{H}},\end{array}$$(7)

where Z = M_z/M_gas is the metal fraction which can be derived from metallicity measurements using the relation (McGaugh et al. 2000):

$$\begin{array}{c}\hfill log(Z/Z_{\odot })=log(\mathrm{O}/\mathrm{H})-log{(\mathrm{O}/\mathrm{H})}_{\odot },\end{array}$$(8)

taking Z_⊙ = 1.34 × 10⁻² and 12 + log (O/H)_⊙ = 8.69 from Asplund et al. (2009).

As previously mentioned, all baryonic components are directly measurable for the HRS, with the exception of the ionized and hot gas masses which we consider as negligible. Table 4 lists the average contribution of each baryonic component to the total baryonic mass. The mean mass and percentage of each baryonic component has been computed using the whole HRS. We note that the gas (plus dust) content represents more than the half of the stellar content (M_{gas = HI + H2 + He} + M_z + M_dust)/M_star ≃ 56% and the metal content represents 2% of the total gas (plus dust) content (M_z/(M_{gas = HI + H2 + He} + M_z + M_dust)≃0.02).

The OLS bisector regression to the data is compared to the values published in the literature in Table 5. In these published works, the baryonic mass is generally derived summing the contribution of the stellar mass to that of the HI gas mass, and assuming a constant M(H I)/M(H₂) contribution for the molecular gas component. These works also lack of high quality 2D velocity fields. Despite these major differences, these works give results consistent with ours.

We can also compare our results to the predictions of models and simulations. According to Dutton & Macciò (2014), Moster et al. (2013) and Zu & Mandelbaum (2015), N-body simulations predict for the baryonic TF relation an intrinsic scatter of ∼0.15, consistent with the dispersion of our sample (0.16).

5.4. Baryonic versus dynamical masses

Dynamical masses are computed following the prescription of Lequeux (1983), which is a variation of the Virial theorem that attempt to account for a variety of galaxy mass distribution, from a purely flat to a purely spherical model :

$$\begin{array}{c}\hfill M_{\mathrm{dyn}}(M_{\odot })=\alpha r_{\mathrm{opt}}{V}_{\max }^2/G,\end{array}$$(9)

where G is the gravitational constant and α is a coefficient which depends on the model flatness of mass distribution (0.6 ≤ α ≤ 1.0). Figure 12 shows the relationship between baryonic and dynamical masses. Since we are taking into account neither luminosity profiles nor models of mass distribution, we chose for the comparison the spherical model α = 1.0. In order to quantify the impact of this extreme assumption, we plot a cyan shaded area representing the interval 0.6 ≤ α ≤ 1.0. The values of the OLS bisector fit are given in Table 6. The two variables are strongly correlated. The fraction of baryons is lower in low-mass-gas-rich galaxies (∼20–25% of the total dynamical mass) than in high-mass galaxies with low SFR (∼35–45% of the total dynamical mass), consistently with what seen in the previous TF relations (Figs. 8–11). Figure 13 shows how the contribution of each baryonic component changes as a function of the dynamical mass and of the stellar mass (color symbols) within the HRS. Using a simple linear regression (not plotted for clarity), we estimate the trend of the y-axis (respectively, from the top to the bottom: the fraction of stars M_star/M_bar, neutral gas M_H I/M_bar, molecular gas M_H2/M_bar, metals M_z/M_bar and dust M_dust/M_bar) as a function of the dynamical mass (log M_dyn). A positive correlation is only observed between the fraction M_star/M_bar and the dynamical mass, with a statistical coefficient of determination R² ∼ 0.42. Weak negative correlations are found in the fourth next cases. Both slope and R² coefficient become increasingly weaker from the second top panel to the bottom one. The bottom one (M_dust/M_bar) is in fact compatible with a zero slope (R² ∼ 0.03). The gaseous components as well as the metal and dust components, are relatively more abondant, relatively to the baryonic component, in low mass galaxies (log M_dyn <  10.5 M_⊙), while the stellar component does in massive objects. The correlation and the dispersion around this correlation between the stellar and the dynamical masses, already observed in Fig. 12, is again underlined by these plots. This is indeed expected given the rapid evolution in the past of massive galaxies, which already transformed most of the gas into stars, with respect to a fairly constant star formation activity in low mass systems possible thanks to their large gas reservoirs (Sandage 1986; Gavazzi et al. 1996, 2002; Boselli et al. 2001; Boissier et al. 2003).

Dynamical masses are computed within r_opt and furthermore do not provide the total masses since they only account for the visible part of galaxies. In addition, dynamical masses do not take into account possible variation in the bulge-to-disk ratio nor in the actual disk or spherical shape of the baryonic matter distributions. Despite those rough approximations, the observed dispersion in the relation (∼0.12 dex) is comparable to that predicted by semi-analytic models of galaxy formation in a ΛCDM context (∼0.15 dex, Dutton 2012; Dutton & Macciò 2014).

5.5. Baryonic and Dynamical Mass Main Sequences

The tight relationship between SFR and M_star is generally called main sequence (i.e. Guzmán et al. 1997; Brinchmann & Ellis 2000; Bauer et al. 2005; Bell et al. 2005; Papovich et al. 2006; Reddy et al. 2006; Noeske et al. 2007; Salim et al. 2007; Elbaz et al. 2007; Daddi et al. 2007; Pannella et al. 2009; Rodighiero et al. 2010; Peng et al. 2010; Karim et al. 2011; Whitaker et al. 2012; Speagle et al. 2014; Torrey et al. 2014; Gavazzi et al. 2015; Renzini & Peng 2015; Sparre et al. 2015; Cano-Díaz et al. 2016; Hsieh et al. 2017; Medling et al. 2018). The slope of this obvious scaling relation (bigger galaxies have more of everything), its bending at high luminosities, its scatter, and its variation as a function of redshift and environment, are often used to trace the evolution of galaxies with cosmic time. Observational evidence indicates mass as a principal driver of galaxy evolution (e.g. Cowie et al. 1996; Gavazzi et al. 1996; Boselli et al. 2001). Consistently with these obervational results, hydrodynamic cosmological simulations suggest that the evolution of galaxies is mainly gouverned by the dark matter halo in which they reside (Governato et al. 2012; Brooks & Zolotov 2014; Christensen et al. 2014). It would thus be interesting to derive the main sequence using dynamical masses rather than with stellar masses.

The stellar main sequence relation has been derived and analyzed for the HRS by Ciesla et al. (2014), Boselli et al. (2015) and Boselli et al. (2016). Thanks to the unique dataset in our hands, we can compare for the first time in the literature the main sequence relations derived using M_star, M_bar, and M_dyn (Fig. 14).

Consistently with Boselli et al. (2015), we use the whole HRS late-type sample but ignoring the HI-deficient galaxies. The SFR is studied considering the mean value derived using the three tracers M_dyn, M_bar and M_star. The number of galaxies differs for the three cases according to the data available for each tracer. OLS bisector fits to the data have been computed. Figure 14 and Table 7 show that the similar main sequence relations are present using the three different galaxy mass estimators. The slope and the scatter of the three relations are comparable. They obviously differ in their zero points given that M_dyn >  M_bar >  M_star. The best fit values can be taken for comparison with the predictions of models and simulations. We recall that these relations are valid within the mass range 3 × 10⁸ ≲  M_star ≲ 10¹¹ M_⊙, or equivalently 3 × 10⁹ ≲  M_dyn ≲ 4 × 10¹¹ M_⊙. The correlation between the magnitudes (M_i), the three different mass tracers and the SFR is also pointed out on this figure with the expected scatters.

6. Conclusions

We present new high resolution Fabry–Perot observations gathered at the OHP of 152 star-forming galaxies belonging to the Herschel Reference Survey. Combined with those available in the literature (40 objects), previously collected with the same facility, an homogeneous set of kinematical data is now available for 192 objects (73.6% of the sample). By now, this is the first work presenting Hα high resolution spectroscopic data of the HRS, with a typical spatial sampling of ∼2 arcsec and a spectral resolution of R ∼ 10 000. Using improved data reduction pipelines, we compute the Hα momenta, optimizing the spatial resolution given a signal-to-noise ratio through an adaptive binning method based on Voronoi tessellations. We also derive accurate kinematical models and parameters, residual velocity maps, and rotation curves.

We derived the i- and the 3.6 μm-band Tully-Fisher relations and compare them to those obtained for larger samples in the literature. Despite the difference in the kinematic data (Fabry–Perot Hα rotation curves in this work vs. H I line width profiles or long slit optical spectra in the literature), in the dynamical range of the sample, and in the statistics, the different TF relations are very consistent, suggesting that the HRS can be taken as a representative sample for these scaling relations in the local universe.

Thanks to its unique multifrequency coverage, we use this dataset to derive the baryonic TF relation and the relation between the baryonic mass and the dynamical mass of galaxies. The baryonic mass is for the first time measured using direct estimates of the stellar, atomic, molecular, dust and metal mass of galaxies. The intrinsic scatter in the baryonic TF relation (∼0.16 dex) is in agreement with the predictions of cosmological simulations. The baryonic component is dominated by the stellar mass in massive objects and by the total gas mass (H I and H₂) in low mass systems. The dust content is just a very small fraction (∼0.2%) of the total baryonic mass, while the contribution of metals is fairly constant at ∼0.9%.

We computed the baryonic and dynamical main sequence, finding relations with a similar slope and intrinsic scatter than the stellar mass main sequence.

The observations of the whole star-foming galaxy sample will be completed in forthcoming runs. Combined with those available at other frequencies, these 2D-spectroscopic data make the HRS a unique dataset for studying on strong statistical basis the role of gas kinematics on the process of star formation, a major step towards the understanding of the mechanisms that drive galaxy evolution.

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Acknowledgments

Based on observations taken at the Observatoire de Haute Provence (OHP, France), operated by the French CNRS. The authors warmly thank Olivier Boissin from LAM and the OHP team for its technical assistance before and during the observations, namely the night team: Jean Balcaen, Stéphane Favard, Jean-Pierre Troncin, Didier Gravallon and the day team led by François Moreau as well as Dr. Auguste Le Van Suu, the Head of Observatoire de Haute Provence-Institut Pythéas. The authors thank the Mexican grants CONACYT-253085 and DGAPA-UNAM PAPIIT-IN109919 which have extensively supported this work. This work was supported by the Programme National Cosmology et Galaxies (PNCG) of CNRS/INSU with INP and IN2P3, co-funded by CEA and CNES. This research has made use of data from the HRS project. HRS is a Herschel Key Programme utilising guaranteed time from the SPIRE instrument team, ESAC scientists and a mission scientist. This research has also 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. The authors have also made an extensive use of the HyperLeda Data base (http://leda.univ-lyon1.fr). The Digitized Sky Surveys were produced at the Space Telescope Science Institute under U.S. Government grant NAG W-2166. The images of these surveys are based on photographic data obtained using the Oschin Schmidt Telescope on Palomar Mountain and the UK Schmidt Telescope. The plates were processed into the present compressed digital form with the permission of these institutions. JAGL thanks the Consejo Nacional de Ciencia y Tecnologia (CONACYT) of Mexico for the scholarship awarded during the PhD studies at Aix-Marseille University. The authors are very grateful to the referee Dr. Octavio Valenzuela for the very constructive comments and suggestions.

References

Appendix A: Quality flags of the rotation curves

As described in the previous Sect. 4.1.1, the maximum rotational velocity (V_max) per galaxy has been obtained by fitting a modified Courteau function to the rotation curve. We considered as V_max the maximum velocity value reached by the Courteau profile between r = 0 and the radius corresponding the last crown of the rotation curve. The estimated V_max per galaxy are shown in Table E.3, except for those galaxies for which no kinematical model was reached and therefore no rotation curve was obtained.

In order to quantify the quality of each rotation curve and to attribute a quality flag, we used an automatic classification method based on the next parameters:

i) The ratio between r_RC and r_opt. The extension of the rotation curve with respect to the optical radius is directly related to the S/N of the data and the spatial coverage of the distribution of Hα emission, resulting in an accurate or poor estimation of kinematics and thus influencing the quality of the rotation curve.

ii) The number of bins computed by the adaptive spatial binning when obtaining the different momenta (see Fig. A.1). High number of bins means good S/N and/or high spatial coverage of the galaxy, and vice versa, resulting in an accurate or poor estimation of kinematics and thus influencing the quality of the rotation curve.

iii) The mean velocity error of the rotation curve.

iv) The ratio between the radius of the receding and approaching side of the rotation curve. If one side is shorter than the other, its contribution to the Rotation curve will be smaller and the quality of the rotation curve will be affected.

v) We fitted a Spline function to both the receding and the approaching side in order to calculate the root mean square difference (RMSD) between both sides of the Rotation curves. The value of the RMSD is directly related to the symmetry of the velocity field from which we estimate the rotation curve and thus influencing its quality.

All these five quantities were normalized in order to be summed and to obtain a quality classification coefficient to flag the rotation curves (see Fig. A.2). These flags are given in the Table E.3:

Flag 1) Accurate estimation of the rotation curve and V_max,

Flag 2) Reliable estimation of the rotation curve and V_max,

Flag 3) Fairly reliable estimation of the rotation curve and V_max probably reached,

Flag 4) Poor estimation of the rotation curve and V_max probably not reached.

In addition to these 4 flags, we defined a supplementary quality classification flags called Flag “A” and Flag “B”. The Flag “B” corresponds to those peculiar cases leading to a non-realistic kinematical fitting:

a) Galaxies for which i ≥ 70°, since the absorption effects due to high inclination lead to velocity underestimations along the disk, and a little variation in i produces a very high variation in velocity determinations.

b) Objects for which i ≤ 25°, because a little variation in i produces a very high variation in velocity determinations.

c) The difference between the morphological PA and the kinematical PA is bigger than 20°. A low S/N ratio or small spatial coverage lead to poor kinematical fittings and therefore a poor estimation of the PA. On the other hand, a velocity field supported by high velocity dispersion values related to big asymmetries, strong bars, strong defined spiral arms, among other non-circular motions, will influence the determination of the kinematical PA. Finally, morphological PAs have systematically higher uncertainties than kinematical ones, specially in galaxies with low inclination as showed in Epinat et al. (2008b).

d) the r_RC/r_opt ratio is lower than 0.6.

e) The number of bins of the adaptive spatial binning is less than 200. Poor S/N or small spatial coverage lead easily to non-realistic kinematical fittings.

f) the ratio between the HαV_max of our Fabry–Perot dataset and the V_max of HI data (Boselli et al. 2015) is bigger than 1.5 or lower than 0.5. Since the rotation curve is derived from the velocity field, poor S/N or small Hα emission spatial coverage, in addition to asymmetries in the velocity field, could easily lead to an under/over estimation of the V_max of the galaxy.

g) the normalized RMSD between both sides of the RC is lower than 0.6.

Appendix B: Notes on individual galaxies

Galaxy HRS 1, because this galaxy is not far from edge-on, the kinematical inclination was difficult to determine and we adopted the morphological value when computing the rotation curve. Otherwise the agreement between the kinematical and morphological PA of the major axis is very good. The rotation curve is fairly regular and symmetric but does not reach the r₂₄ radius in r-band. Both models (Courteau and Zhao) suggest that it goes on rising beyond that radius.

Galaxy HRS 2, there is a fairly good agreement for the PA of the major axis (4° difference only). Our rotation curve almost reaches the r₂₄ radius in r-band for both sides. Courteau’s model gives the best result since it extrapolates our rotation curve towards the H IV_max whereas Zhao’s model suggests a declining curve beyond the r₂₄ radius.

Galaxy HRS 5, because this galaxy is almost edge-on, the kinematical inclination was difficult to determine and we adopted the morphological value when computing our Hα rotation curve. Otherwise the agreement between the kinematical and morphological PA of the major axis is perfect. The rotation of the redshifted side appears more chaotic because of some faint Hα emission out of the disk which does not seem significant and could be ignored (N.B. It is not seen on the Hα + [N II] image from Boselli et al. 2015.) Our curve exhibits a chaotic behavior of the redshifted side but the blueshifted side is fairly regular and both sides reach the effective radius in r-band where the velocity is close to the H IV_max for both.

Galaxy HRS 6, for this edge-on galaxy we adopted the morphological values for the inclination, as well as for the PA of the major axis, when computing our Hα rotation curve. The rotation of the blueshifted side is more chaotic and the outermost part was not taken into account when tracing the rotation curve. Indeed, the residual velocity field shows exceedingly large values in the outer parts of that side. The Hα + [N II] image from Boselli et al. (2015) confirms that there is almost no emission of ionized gas beyond 30 arcsec from the nucleus on that side of the galaxy. Surprisingly, in spite of this deficiency, our Hα rotation velocity reaches much higher values than the H IV_max for both sides, redshifted as well as blueshifted. This is all the most surprising that our rotation curve barely reaches the effective radius in r-band and both models (but Zhao more than Courteau) suggest that the curve goes on rising beyond that radius.

Galaxy HRS 9, the Hα emission is mainly seen on the southern and western part of the galaxy, where the Hα + [N II] image from Boselli et al. (2015) also shows bright spots. The velocity field is dominated by an almost constant value around 1410 km s⁻¹ which could be due to a contamination of the observed velocities by an OH night-sky line (Osterbrock et al. 1996). As a result, the residual velocity field exhibits strong values on both sides (north and south) of the galaxy and we did not take into account the corresponding velocities when tracing our Hα rotation curve. Also, this contamination of the velocity field could explain the difference observed between kinematical and morphological inclination (9°) as well as for the PA of the major axis (18°). The resulting rotation curve is quite chaotic for both sides and barely reaches the effective radius in r-band for the redshifted side. The velocity we find at this radius is close to the H IV_max.

Galaxy HRS 10, we adopted the morphological value of the inclination for computing our Hα rotation curve. Otherwise there is an excellent agreement between the kinematical and morphological PA of the major axis (2° difference). The velocity field is regular and the resulting rotation curve is pretty good and symmetric, reaching a plateau slightly below the H IV_max. The curve almost reaches the r₂₅ radius in B-band (quasi coincident here with the r₂₄ radius in r-band).

Galaxy HRS 11, there is an excellent agreement between the kinematical and morphological inclination (2° difference) as well as for the PA of the major axis (1° difference). The velocity field is regular, except for some high velocity points on the eastern edge of the disk (probably spurious since the Hα + [N II] image from Boselli et al. (2015) shows no significant emission at that place). Our Hα rotation curve is fairly regular and symmetric, it almost reaches the r₂₅ radius in B-band for the redshifted side. Zhao’s model suggests that the curve goes on rising towards a maximum reached at the r₂₄ radius in r-band, whereas Courteau’s model suggests a continuous rising beyond that radius. However, the velocity reached by our curve at the effective radius is already much higher than the H IV_max.

Galaxy HRS 12, the Hα emission is limited to the inner disk of this galaxy and the outer parts of our velocity field are clearly not significant as suggested by the Hα + [N II] image from Boselli et al. (2015) (showing an abrupt fall of emission on the edge of the inner disk). This is confirmed by the residual velocity field where extreme values are seen all around the disk. This peculiar concentration of the ionized gas in the center of the galaxy probably explains the diskrepancy observed between the kinematical and morphological inclination (9° difference) but, more specifically, that observed between the kinematical and morphological PA of the major axis (21° difference). Anyway the resulting rotation curve is fairly symmetric (when ignoring the outer parts of the velocity field) and steeply rising up to the effective radius in r-band where it reaches the H IV_max. We note however that Zhao’s model exhibits a strange behavior while Courteau’s model suggests that the curve reaches a plateau.

Galaxy HRS 13, the Hα + [N II] image from Boselli et al. (2015) suggests that the southwestern extension of the disk, near the strong spiral arm, is spurious (which is confirmed by the extreme values of the residual velocity field) but the easternmost points, on the major axis, seem real. There is a fairly good agreement between the kinematical and morphological inclination (4° difference), also for the PA of the major axis (7° difference). The resulting rotation curve exhibits a slight asymmetry between redshifted and blueshifted side but the average is satisfying and reaches a plateau close to the H IV_max just after the effective radius in r-band.

Galaxy HRS 17, we find an excellent agreement between the kinematical and morphological inclination (3° difference), also for the PA of the major axis (2° difference) when computing our Hα rotation curve. The resulting curve exhibits a perfect plateau (at the H IV_max) extending between the effective radius and the r₂₄ radius in r-band.

Galaxy HRS 18, although the kinematical and morphological inclinations are in perfect agreement, we find a difference of 17° between the kinematical and morphological PA of the major axis. In fact the agreement is good for the inner part of the disk but the PA changes for the outermost isophotes of this almost face-on galaxy. Anyway the velocity field exhibits a clear gradient and the resulting Hα rotation curve is fairly symmetric but does not go very far beyond the effective radius in r-band. Also, the curve is continuously climbing and bends slightly after the effective radius in r-band, with the outermost points remaining below the H IV_max.

Galaxy HRS 19, this galaxy has a nice spiral structure designed by many H II regions but it is almost face-on and exhibits a very faint velocity gradient, so that its Hα rotation curve is hard to draw. We adopted the morphological value of the inclination when computing the rotation curve and found a huge difference (53°) between the kinematical and morphological PA of the major axis, likely to be explained by the shape of the outermost isophotes of the disk. The resulting rotation curve is quite chaotic and reaches a radius between the effective radius and the r₂₄ radius in r-band. Also, the maximum of this curve is only half of the H IV_max.

Galaxy HRS 21, for this edge-on galaxy, we adopted the morphological values for the inclination as well as for the PA of the major axis, when computing the Hα rotation curve. There is a marked velocity gradient and, athough it looks like a solid body rotation, the rotation curve probably reaches a plateau (as suggested by Courteau’s model) beyond the effective radius in r-band since it reaches the H I maximum there.

Galaxy HRS 23, our continuum image is contaminated by many ghost images of field stars as well as by a ghost image of the galaxy itself (about 20 arcsec below the true image of HRS023) caused by a reflection of light between the Fabry–Perot interferometer and the interference filter. The extension of the Hα emission on the southwestern side of the disk is apparently linked with a ghost image of a field star, otherwise our monochromatic image seems clean when comparing with the Hα + [N II] image from Boselli et al. (2015). The velocity field is rather irregular as confirmed by the residual velocities, displaying extreme values on both sides. Nevertheless the Hα rotation curve is acceptable and continuously rising up to the r₂₅ radius (at least for the blue side) where it reaches velocities 50% above the H IV_max. Moreover, the agreement between the kinematical and morphological inclination is perfect, as well as for the PA of the major axis.

Galaxy HRS 25, this galaxy exhibits a nice velocity field and a fairly regular and symmetric Hα rotation curve, reaching a plateau at the same value as the H IV_max and almost extended up to the r₂₄ radius in r-band (also not far from the r₂₅ radius in B-band). We find an excellent agreement between the kinematical and morphological inclination (2° difference), as well as for the PA of the major axis (less than 1° difference). Both models (Zhao and Courteau) agree that our rotation curve reaches a plateau beyond the optical radius, with a rotation velocity slightly above the H IV_max.

Galaxy HRS 26, for this almost edge-on galaxy, we adopted the morphological values for the inclination as well as for the PA of the major axis, when computing the Hα rotation curve. Although the Hα emission is limited to the inner disk of this galaxy, the rotation curve reaches the effective radius in r-band and climbs up to the H IV_max.

Galaxy HRS 27. despite its faint inclination (29° according to the morphology but 21° only according to the kinematics) this small galaxy exhibits a well marked velocity gradient. The kinematical PA of the major axis is slightly different from the morphological one. The resulting Hα rotation curve almost reaches the r₂₄ radius in r-band (at least for the blueshifted side) and seems to climb up to a plateau at the level of the H I maximum velocity.

Galaxy HRS 28, there is a good agreement between the kinematical and morphological inclination, also for the PA of the major axis, and the resulting Hα rotation curve (ignoring the northeastern extension) is fairly satisfying despite some kinks on the blueshifted side. This curve reaches the r₂₅ radius for both sides and seems to approach a maximum value there, above the H IV_max.

Galaxy HRS 32, this face-on galaxy, although it is of Sb type, has almost none Hα emission, as confirmed by the Hα + [N II] image from Boselli et al. (2015). Our Hα image and velocity field are mainly noise and we could not draw any Hα rotation curve for this galaxy.

Galaxy HRS 35, as for HRS 32, this face-on galaxy has almost none Hα emission. Our Hα image and velocity field are mainly noise and we could not draw any Hα rotation curve for this galaxy.

Galaxy HRS 37, although there is 11° difference between the kinematical and morphological inclination and 16° difference between the kinematical and morphological PA of the major axis, our Hα velocity field produces a very nice and symmetric Hα rotation curve. It just reaches the r₂₅ radius in B-band and probably stays flat afterwards but significantly below the H IV_max (150 km s⁻¹ instead of 200 km s⁻¹).

Galaxy HRS 38, there is a good agreement between the kinematical and morphological inclination and a perfect agreement between the kinematical and morphological PA of the major axis. Our Hα rotation curve is fairly satisfying and reaches the r₂₄ radius in r-band for both sides. The maximum velocity reached there is the same as the H IV_max and the shape of the curve suggests that it is not far from reaching a plateau.

Galaxy HRS 39, for this almost edge-on galaxy, we adopted the morphological values for the inclination as well as for the PA of the major axis, when computing the Hα rotation curve. Although our Hα rotation curve barely reaches the effective radius in r-band, it is not far from the H IV_max there. This is consistent with Courteau’s model suggesting that it reaches a plateau just after, whereas Zhao’s model suggests a continuous rising beyond.

Galaxy HRS 40, the agreement between the kinematical and morphological inclination is good and it is perfect for the PA of the major axis. Our Hα rotation curve shows a solid body rotation up to the effective radius in r-band. The redshifted side suggests however that the curve reaches a plateau slightly after this radius, with a velocity matching the H IV_max. This is consistent with Courteau’s model whereas Zhao’s model suggests a decreasing curve in the outer parts.

Galaxy HRS 44, this galaxy is almost face-on, hence a faint velocity gradient explaining the bad quality of the Hα rotation curve. We adopted the morphological value of the inclination for computing the Hα rotation curve and find a 38° difference between the kinematical and morphological PA of the major axis. Our Hα rotation curve is very chaotic for both sides (especially the blueshifted side) but almost reaches the r₂₄ radius in r-band, with velocities greater than the H IV_max (100 km s⁻¹ instead of 75 km s⁻¹). However, the outermost parts of our Hα map and velocity field are very noisy and must be considered with care.

Galaxy HRS 47, our Hα map and velocity field cover fairly well the optical extent of this galaxy. There is a good agreement between the kinematical and morphological inclination, also for the PA of the major axis. Despite some dispersion, our Hα rotation curve is fairly regular and symmetric; it reaches the r₂₄ radius in r-band where the velocity is close to the H IV_max (150 km s⁻¹). Both models (Courteau and Zhao) suggest however that the curve must go on rising beyond.

Galaxy HRS 48, the spiral pattern of this galaxy is well marked and our Hα map and velocity field follow this structure. The velocity gradient is well marked, despite a faint inclination of the disk. We adopted the morphological value of the inclination for computing our Hα rotation curve and find a 37° difference between the kinematical and morphological PA of the major axis. Our rotation curve is quite chaotic (especially the redshifted side) but seems to reach a plateau before the effective radius in r-band, with a velocity close to the H IV_max (around 120 km s⁻¹).

Galaxy HRS 50, this galaxy has a nice velocity field and Hα rotation curve. We find a good agreement between kinematical and morphological inclination, as well as for the PA of the major axis. The rotation curve is perfectly symmetric and almost reaches the r₂₄ radius in r-band where the velocity is close to the H IV_max. Both models (Courteau and Zhao) suggest that it reaches a plateau just after.

Galaxy HRS 52, the Hα + [N II] image of this galaxy from Boselli et al. (2015) shows many small H II regions dispersed in the disk that we miss here. Indeed our Hα map and velocity field only show the central part of the galaxy and none of these small regions. We find a fairly good agreement between the kinematical and morphological value of the PA of the major axis. Our rotation curve shows a steep rise and bends clearly before reaching the effective radius in r-band. The velocity almost reaches the H IV_max there and both models suggest that the rotation curve reaches its maximum there. However, Courteau’s model suggests a plateau whereas Zhao’s model suggests a decreasing curve beyond the effective radius.

Galaxy HRS 56, the resulting curve is fairly symmetric and reaches a plateau between the effective radius and the r₂₄ radius in r-band, with a velocity close to the H IV_max (around 190 km s⁻¹). Here again Courteau’s model suggests a plateau whereas Zhao’s model suggests a decreasing curve beyond the effective radius.

Galaxy HRS 59, this galaxy is almost edge-on and the blueshifted side (west) on our Hα map seems brighter and more extended than the redshifted side (east), maybe because of dust absorption. We adopted the morphological values for the inclination as well as for the PA of the major axis, when computing our Hα rotation curve. Despite some dispersion, our curve is fairly symmetric up to the effective radius where, after a steep rising, it reaches the H IV_max. Beyond that radius, the curve is mainly traced by the blueshifted side which is quite chaotic. Anyway, the curve seems to follow a plateau at about 200 km s⁻¹, between the effective radius and the r₂₄ radius in r-band (coincident here with the r₂₅ radius in B-band).

Galaxy HRS 60 (KPG 209B), the Hα emission is very faint on the redshifted side (south) of this barred galaxy, as can be seen also on the Hα + [N II] image from Boselli et al. (2015). As a result, our velocity field and Hα rotation curve mainly rely on the blueshifted side (north). The agreement between kinematical and morphological inclination is not very good (13° difference) but it is better for the PA of the major axis (5° difference). Our rotation curve is very chaotic, perhaps also because of the strong bar in the center. The curve barely reaches the effective radius in r-band where its velocity seems to stop rising although it is much smaller than the H IV_max (about 125 km s⁻¹ compared with more than 300 km s⁻¹).

Galaxy HRS 61, this galaxy is almost edge-on and the agreement between kinematical and morphological inclination is not very good (9° difference) but it is perfect for the PA of the major axis. The outermost extension to the north of our Hα map and velocity field is doubtful (there is no hint of any counterpart there on the Hα + [N II] image from Boselli et al. 2015). It gives large values on the residual velocity field and it was not taken into account when tracing our Hα rotation curve. Our curve is asymmetric, with a redshifted side rising steeper than the blueshifted side. The curve almost reaches the r₂₅ radius in B-band where its velocity is slightly above the H IV_max. Both models (Courteau and Zhao) suggest that the rotation curve goes on rising beyond the r₂₅ radius.

Galaxy HRS 62, in spite of a slight disagreement between kinematical and morphological inclination (7° difference) as well as for the PA of the major axis (9° difference) our Hα rotation curve is fairly symmetric and regular. The curve reaches the r₂₅ radius in B-band (coincident with the r₂₄ radius in r-band for this galaxy) and its velocity there is slightly above the H IV_max. The curve extends beyond the r₂₅ on the blueshifted side and both models (Courteau and Zhao) suggest that the plateau is not reached.

Galaxy HRS 63, there is a good agreement between kinematical and morphological inclination, as well as for the PA of the major axis. Our Hα rotation curve is fairly symmetric and regular, almost reaching the r₂₄ radius in r-band for both sides. The curve reaches its maximum there, with a velocity close to the H IV_max (around 160 km s⁻¹) although Courteau’s model suggests that it goes on rising beyond that point.

Galaxy HRS 64, this galaxy is almost edge-on and we adopted the morphological values for the inclination as well as for the PA of the major axis, when computing our Hα rotation curve. In spite of some dispersion, our curve is fairly symmetric and almost reaches the r₂₄ radius in r-band for the blueshifted side. The maximum reached is not far from the H IV_max and both models (Courteau and Zhao) suggest that our curve reaches a plateau at the r₂₄ radius (although slightly declining beyond that point for Zhao).

Galaxy HRS 65, the Hα emission is rather patchy and very faint outside of the spiral pattern of the galaxy. Anyway, we find a fairly good agreement between kinematical and morphological inclination, as well as for the PA of the major axis. Our Hα rotation curve is quite chaotic and asymmetric but reaches the r₂₅ radius in B-band (almost coincident here with the r₂₄ radius in r-band). The velocity there is slightly below the H IV_max but both models (Courteau and Zhao) suggest that the curve, although clearly bending, is still rising beyond that radius.

Galaxy HRS 66, we find a good agreement between kinematical and morphological inclination, as well as for the PA of the major axis. Our Hα rotation curve is fairly regular and symmetric, it almost reaches the r₂₄ radius in r-band for both sides. The maximum velocity is slightly above the H IV_max and both models (but Courteau better than Zhao) suggest that the curve is about to reach a plateau after that radius.

Galaxy HRS 67, the faint extension of our Hα map and velocity field, on the southern side of the galaxy, seems spurious (no counterpart can be seen on the Hα + [N II] image from Boselli et al. 2015). We adopted the morphological value of the inclination for computing our Hα rotation curve and find a 25° difference between the kinematical and morphological PA of the major axis. Anyway our Hα rotation curve, despite some dispersion, is fairly regular and symmetric. The curve barely reaches the effective radius in r-band, where the velocity is found to be close to the H IV_max. Both models (Courteau and Zhao) suggest that the curve goes on rising beyond the r₂₄ radius in r-band but Courteau’s model favors a plateau after that radius.

Galaxy HRS 68, this galaxy is almost face-on and the Hα emission is concentrated in the center of the disk, as confirmed by the Hα + [N II] image from Boselli et al. (2015). As a result, the dispersion is very high in the outer parts of the velocity field, as can be seen also on the residual velocity field where extreme values are reached on both sides (blueshifted and redshifted). Furthermore, we adopted the morphological value of the inclination for computing our Hα rotation curve and find a huge 57° difference between the kinematical and morphological PA of the major axis. The resulting curve is quite chaotic and asymmetric, barely reaching a radius of 5 arcsec (about half the r₂₅ radius in B-band). Also, the velocity remains below 100 km s⁻¹ whereas the H IV_max is around 160 km s⁻¹.

Galaxy HRS 70, we find an acceptable difference (12°) between the kinematical and morphological PA of the major axis. Despite this difference and some dispersion of the velocities in the very center, our rotation curve is fairly regular and symmetric. It reaches the r₂₄ radius in r-band for both sides, with a rotation velocity close to the H IV_max. Both models (but Courteau more than Zhao) suggest that the curve is about to reach a plateau beyond that radius.

Galaxy HRS 72, our Hα velocity field clearly suggests that this galaxy is not as inclined as suggested by its morphology (59° instead of 79°). Also, the kinematical PA of the major axis is found to be 28° different from that suggested by the outermost isophotes of the disk. The resulting Hα rotation curve is fairly regular and symmetric, revealing a pure solid body rotation up to the r₂₄ radius in r-band. The rotation velocity at this radius is significantly higher than the H IV_max (about 160 km s⁻¹ against 110 km s⁻¹).

Galaxy HRS 74, although this galaxy has a rather faint inclination, our Hα velocity field exhibits a marked velocity gradient. We find an acceptable difference (13°) between the kinematical and morphological PA of the major axis. Despite some lack of Hα emission in the very center (confirmed by the Hα + [N II] image from Boselli et al. 2015) the rotation curve can be traced with confidence and clearly shows that a maximum is reached for both sides at the effective radius in r-band. This maximum is significantly higher than the H IV_max (about 190 km s⁻¹ instead of 165 km s⁻¹). Zhao’s model suggests that the curve goes on declining beyond, whereas Courteau’s model favors a plateau.

Galaxy HRS 76, the lack of Hα emission on the northern side (redshifted) of this galaxy is confirmed by the Hα + [N II] image from Boselli et al. (2015). The high inclination of the disk led us to adopt the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. Despite a rather strong dispersion, the rotation curve is acceptable for the blueshifted side and seems to reach a plateau beyond the effective radius (but the redshifted side is difficult to exploit). Our maximum rotation velocity is close to the H IV_max.

Galaxy HRS077, our Hα image and velocity field covers at best the optical disk of this galaxy. The agreement between morphological and kinematical values is excellent for the inclination as well as for the PA of the major axis. Our Hα rotation curve is perfectly symmetric and, after a very steep rise, the velocity remains constant beyond the effective radius and close to the H IV_max. The plateau extends almost out to the r₂₄ radius in r-band (close here to the r₂₅ radius in B-band).

Galaxy HRS 78, the agreement between morphological and kinematical values is rather good for the inclination as well as for the PA of the major axis. The Hα emission is brighter on the northern side (blueshifted) of this galaxy, as can be seen also on the Hα + [N II] image from Boselli et al. (2015). As a result, the rotation curve is better traced by the blueshifted side whereas the redshifted side is quite chaotic (also the residual velocity field shows some extreme values on the redshifted side). Our curve almost reaches the r₂₄ radius in r-band and both models (Courteau and Zhao) suggest that it goes on rising for a while. Indeed the maximum rotation velocity reached by our curve is still much below the H IV_max (almost half).

Galaxy HRS 79, this galaxy is almost edge-on and we adopted the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. The points surrounding the main body of the galaxy on our different maps are but noise and are not taken into account for tracing our Hα rotation curve. The Hα emission is more extended on the blueshifted side and the rotation curve is also more extended on that side, going beyond the r₂₅ radius in B-band whereas it just outpasses the effective radius on the redshifted side. The maximum velocity rotation of our curve is clearly higher than the H IV_max (130 km s⁻¹ instead of 100 km s⁻¹) and both models (but Zhao better than Courteau) suggest that the curve is not far from reaching a plateau beyond the r₂₅ radius.

Galaxy HRS 80, the Hα emission of this galaxy is very patchy and irregular, with only a few H II regions on the redshifted side (south). Furthermore its disk has a faint inclination and the velocity gradient is faint, leading us to adopt the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. Despite some dispersion, our rotation curve is fairly symmetric and both sides exhibit a strange behavior in the central part, with a clear bump within the 10 first arsec. Then the curve is mainly traced by the blueshifted side, rising up steeply before bending slightly. It extends halfway between the effective radius and the r₂₄ radius in r-band where its velocity is close to the H IV_max. Zhao’s model suggests that the rotation curve goes on rising whereas Courteau’s model favors a plateau beyond the effective radius.

Galaxy HRS 82 (KUG 1201+163), the Hα emission is concentrated in some bright spots in the very center of the disk of this galaxy. We find an excellent agreement between the kinematical and morphological PA of the major axis. The central part of our rotation curve rises steeply (steeper for the redshifted side) with a solid body rotation, almost out to the effective radius. Then the redshifted side goes on rising (up to the H IV_max of 80 km s⁻¹) whereas the blueshifted side reaches a plateau at 60 km s⁻¹. Courteau’s model suggests that the rotation curve reaches a plateau at 75 km s⁻¹ beyond the r₂₄ radius in r-band whereas Zhao’s model suggests that the curve reaches a maximum there before declining beyond.

Galaxy HRS 83, the Hα emission is limited to the inner part of the disk of this galaxy. Because of the strong inclination, we adopted the morphological value of the inclination for computing our Hα rotation curve and find a perfect agreement between the kinematical and morphological PA of the major axis. Our rotation curve almost reaches the effective radius in r-band and exhibits a solid body rotation for both sides. Our maximum rotation velocity is close to the H IV_max and it is probable that we reach a plateau there (as suggested by Courteau’s model) whereas Zhao’s model suggests that it goes on rising beyond.

Galaxy HRS 84, the Hα emission is much brighter on the southern part of the disk of this galaxy, as can be seen also on the Hα + [N II] image from Boselli et al. (2015). As a result, our Hα rotation curve is mainly traced by the blueshifted side (south). Also, there is some lack of emission in the very center of the disk, so that we have no points to trace the rising part of the rotation curve which is very steep here. The agreement between morphological and kinematical values is very good for the inclination as well as for the PA of the major axis. Our rotation curve almost reaches the r₂₅ radius in B-band (here slightly shorter than the r₂₄ radius in r-band). We find rotation velocities higher than the H IV_max beyond the effective radius and both models (Courteau and Zhao) suggest that it goes on rising beyond our last measured points.

Galaxy HRS 86 (KPG 322A), the Hα emission covers fairly well the optical disk of this galaxy, although the Hα + [N II] image from Boselli et al. (2015) suggests that we miss some faint H II regions in the southern part of the disk. The agreement between morphological and kinematical values is not too bad for the inclination (10° difference) as well as for the PA of the major axis (7° difference). Our Hα rotation curve is fairly regular and symmetric, with a solid body rotation shape up to the r₂₄ radius in r-band where it reaches a velocity close to the H IV_max. Despite some dispersion, the outermost points of both sides suggest that the curve reaches its maximum there and the blueshifted side exhibits a plateau extending beyond the r₂₅ radius in B-band.

Galaxy HRS 88 (KPG 322B), despite some holes, the Hα emission covers fairly well the optical disk of this galaxy. The agreement between morphological and kinematical values is not too bad for the inclination (13° difference) but rather bad for the PA of the major axis (31° difference). Our Hα rotation curve is quite chaotic in its central rising part, especially for the redshifted side (the residual velocity field shows extreme values on that side, in the inner part of the disk, and more generally all around the nucleus). The rotation curve is more quiet and symmetric beyond the effective radius and reaches the r₂₄ radius in r-band for both sides. Altough we find a rotation velocity significantly higher than the H IV_max, even before reaching the effective radius, both models (Courteau and Zhao) suggest that our curve goes on rising much beyond our last measured points.

Galaxy HRS 92, this galaxy is almost edge-on and we adopted the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. The signal to noise is rather faint, especially on the redshifted side (northwest) and our rotation curve is quite chaotic, barely reaching the effective radius. The curve exhibits a solid body rotation reaching a maximum velocity around 120 km s⁻¹. Courteau’s model suggests a plateau slightly below the H IV_max (150 km s⁻¹) beyond the effective radius whereas Zhao’s model favors a velocity peak at the effective radius.

Galaxy HRS 95, the very thin stripe of Hα emission of this galaxy, as can be seen also on the Hα + [N II] image from Boselli et al. (2015), led to think that its disk is more inclined than suggested by the morphological value (56°). Anyway, we adopted that value when tracing our Hα rotation curve. We find a rather good agreement between morphological and kinematical values for the PA of the major axis (7° difference). Our rotation curve exhibits a solid body rotation for both sides, with a steep rise up to the effective radius in r-band. Then the curve bends clearly and reaches a maximum for both sides (around 85 km s⁻¹ for the redshifted side and 110 km s⁻¹ for the blueshifted side, slightly below the 115 km s⁻¹ of the H IV_max). Courteau’s model suggests that our curve reaches a plateau there, whereas Zhao’s model favors a velocity peak at the effective radius.

Galaxy HRS 98, this galaxy is almost edge-on and we adopted the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. The curve is fairly regular and symmetric but barely reaches the effective radius in r-band. Courteau’s model suggests that the curve clearly bends after the effective radius, reaching a plateau close to the H IV_max at the optical radius, whereas Zhao’s model suggests that it goes on rising much beyond.

Galaxy HRS 104, this Sb type galaxy has no significant Hα emission, as confirmed by the Hα + [N II] image from Boselli et al. (2015). No Hα velocity field nor rotation curve could be extracted from our data. We also note that the isolated spot at about 30 arcsec north from the nucleus is probably but noise (maybe a ghost image).

Galaxy HRS 106, the Hα emission covers fairly well the optical disk of this galaxy. Because of its faint inclination, we adopted the morphological value for the inclination when tracing our Hα rotation curve. We find a rather good agreement between morphological and kinematical values for the PA of the major axis (8° difference). Despite some chaotic behavior in the center (first 5 arcsec), our rotation curve is fairly regular and symmetric. The curve reaches the effective radius for both sides and the blueshifted side (south) extends out to the r₂₄ radius in r-band. The rotation velocity reached there is close to the H IV_max. Anyway both models (Courteau as well as Zhao) suggest that the curve goes on rising beyond that radius.

Galaxy HRS 107, this galaxy is almost edge-on and we adopted the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. The velocity gradient of the velocity field is well marked but the signal to noise is rather bad, so that our rotation curve suffers from dispersion. Our curve does not even reach the effective radius in r-band and the maximum velocity reached is between 100 km s⁻¹ and 110 km s⁻¹, depending on the side, below the H IV_max (close to 130 km s⁻¹).

Galaxy HRS 112, there is some diffuse Hα emission in the disk of this galaxy but its surface brightness is very faint, as can be seen also on the Hα + [N II] image from Boselli et al. (2015). As a result, the signal to noise ratio of our Hα map is also very faint and, despite the relatively high inclination of this galaxy, no velocity gradient can be guessed on our velocity field. We adopted the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve, but no realistic curve could be obtained.

Galaxy HRS 117, this galaxy is almost edge-on and we adopted the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. The Hα emission is limited to a few spots in the central part of the disk of this galaxy, mainly on the southwestern side, as can be seen also on the Hα + [N II] image from Boselli et al. (2015). As a result, our rotation curve is only traced by the blueshifted side (southwest) but nevertheless almost reaches the effective radius in r-band. The rotation velocity reached at this radius is close to the H IV_max and both models (Courteau and Zhao) suggest that the curve goes on rising beyond.

Galaxy HRS 118, apart a few bright spots in the center, the Hα emission of this galaxy is rather faint in this galaxy, as can be seen also on the Hα + [N II] image from Boselli et al. (2015). Nevertheless it covers fairly well the optical disk of the galaxy. We adopted the morphological value for the inclination and find an acceptable agreement between the morphological and kinematical values of the PA of the major axis (26° difference) when tracing our Hα rotation curve. The resulting curve is fairly regular and symmetric, almost reaching the r₂₄ radius in r-band for both sides. The rotation velocity reached there is close to the H IV_max, however some patches of Hα emission northward of the disk enable to extend our Hα rotation curve much beyond the r₂₅ radius in B-band on the redshifted side, suggesting that the rotation curve goes on rising beyond the optical disk. We note that Courteau’s model fails to fit our data correctly, contrary to Zhao’s model.

Galaxy HRS 121, for this galaxy, when tracing our Hα rotation curve, we adopted the morphological values for the inclination as well as for the PA of the major axis. The resulting curve is fairly regular and symmetric, extending midway between the effective radius and the r₂₄ radius in r-band (almost coincident here with the r₂₅ radius in B-band). Both sides of the curve (although blueshifted better than redshifted) almost reach the H IV_max. Zhao’s model suggests that the maximum of our Hα curve is almost reached by our outermost blue point whereas Courteau’s model favors a continuous rising, even beyond the optical radius.

Galaxy HRS 132, the Hα emission is mainly produced by some bright spots lying along the major axis. This galaxy is almost face-on. The rotation curve is quite chaotic for both sides, more especially the redshifted side (northeast) for which there is a counter rotation in the first 5 arcsec, with negative values, before the curve rises steeply. The residual velocity field exhibits high values there, but also extreme values all around the disk. Anyway, both sides of the curve extend beyond the effective radius in r-band, with maximum values of the velocity rotation close to the H IV_max.

Galaxy HRS 133, the comparison of our Hα map with the Hα + [N II] image from Boselli et al. (2015) show that we miss the outermost emission regions on the western side (redshifted) of the disk. This galaxy is almost edge-on and we adopted the morphological values for the inclination as well as for the PA of the major axis when tracing our rotation curve. Both sides of the curve are very chaotic in the central part (first 15 arcsec) then the trend is that of a solid body rotation. The curve barely reaches the effective radius in r-band, where its rotation velocity is clearly below the H IV_max. Indeed both models (Courteau and Zhao) suggest that our Hα curve goes on rising and reaches the H IV_max at the r₂₄ radius in r-band.

Galaxy HRS 134, although this edge-on galaxy is classified as Sc type, its Hα emission is limited to two bright spots on each side of the nucleus, as confirmed by the Hα + [N II] image from Boselli et al. (2015). We adopted the morphological values for the inclination as well as for the PA of the major axis when tracing our Hα rotation curve. However, because of the lack of velocity points, no significant curve could be obtained.

Galaxy HRS 136, this Sa type galaxy has no significant Hα emission, as confirmed by the Hα + [N II] image from Boselli et al. (2015). The spots on our maps are probably more noise than signal and no Hα rotation curve can be obtained for this galaxy.

Galaxy HRS 139, when tracing the Hα rotation curve of this galaxy, we find a fairly good agreement between the morphological and kinematical values of the PA of the major axis (15° difference). The resulting rotation curve is fairly regular and symmetric, with both sides extending midway between the effective radius and the r₂₄ radius in r-band. The rotation velocity reaches the H IV_max at the effective radius and the curve goes on rising beyond although with a smaller slope.

Galaxy HRS 141, the Hα emission of this galaxy is rather faint and patchy but the velocity field is nice. We find a good agreement between the morphological and kinematical values of the inclination (6° difference) and a perfect agreement between the morphological and kinematical values of the PA of the major axis (less than 2° difference). The resulting Hα rotation curve is fairly regular and symmetric and reaches the effective radius in r-band for both sides. The rotation velocity reached there is slightly above the H IV_max and both models (Courteau and Zhao) suggest that it goes on rising beyond, although with a smaller slope.

Galaxy HRS 142, there is a strong Hα emission in the inner disk of this Sa type galaxy but it is very faint beyond the effective radius, as can be seen also on the Hα + [N II] image from Boselli et al. (2015). Despite the relatively high inclination of the disk, the gradient of the Hα velocity is very faint, suggesting that the behavior of the ionized gas do not reflect that of the main body of the galaxy. Also, the outer parts of our velocity field have a very low signal to noise ratio and could be contaminated by a nightskyline. We adopted the morphological value for the inclination when tracing our rotation curve. The first 15 arcsec of the curve show a rising part fairly symmetric for both sides, almost out to the effective radius in r-band. Beyond that point the curve becomes quite chaotic but with a trend to decrease for both sides, casting doubts on the quality of our data in the outer parts of the disk of this galaxy. However, the fact that the rotation velocity reached at the effective radius is much below the H IV_max (20 km s⁻¹ against 120 km s⁻¹) favors our hypothesis of a peculiar behavior of the ionized gas in the very center of this galaxy. It could it be the remnant of a merger.

Galaxy HRS 143, this galaxy is almost edge-on and we adopted the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. The resulting rotation curve is fairly regular and symmetric, with both sides extending midway between the effective radius and the r₂₄ radius in r-band. Courteau’s model suggests that the curve goes on rising beyond and reaches the H IV_max between the r₂₄ radius in r-band and the r₂₅ radius in B-band, whereas Zhao’s model favors a maximum reached at the r₂₄ radius, with a rotation velocity slightly below the H IV_max.

Galaxy HRS 145, we adopted the morphological value for the inclination of the disk of this galaxy and find a good agreement between the morphological and kinematical values of the PA of the major axis (4° difference) when computing our Hα rotation curve. The resulting curve is somewhat chaotic in the center (first 7 arcsec) where the Hα emission is less bright, otherwise it is fairly regular and symmetric, with both sides extending midway between the effective radius and the r₂₄ radius in r-band. The rotation velocity reached at the effective radius is almost equal to the H IV_max but the curve goes on increasing beyond and none of the models (Courteau as well as Zhao) suggests any significant change in the slope beyond that radius.

Galaxy HRS 146, this galaxy is almost edge-on and we adopted the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. Despite some dispersion, the resulting rotation curve is rather regular and symmetric, but barely reaches the effective radius in r-band. The rotation velocity reached there is around 70 km s⁻¹ (against 90 km s⁻¹ for the H IV_max). Courteau’s model suggests that the rotation curve reaches a plateau beyond the optical radius (with a velocity close to the H IV_max) whereas Zhao’s model favors a continuous increase beyond.

Galaxy HRS 148, the disk of this almost edge-on galaxy appears more extended on the southeastern side (redshifted), both on continuum images and Hα images (also on the Hα + [N II] image from Boselli et al. 2015), maybe because of dust absorption. We adopted the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. The resulting rotation curve is fairly regular and symmetric, with both sides extending up to the effective radius in r-band, where the rotation velocity is equal to the H IV_max. The redshifted side enables to draw the curve up to the r₂₅ radius in B-band (here almost coincident with the r₂₄ radius in r-band). This side of the curve seems to reach a plateau at the effective radius but rises again shortly after, with a significant slope, although it seems to diminish when reaching the optical radius.

Galaxy HRS 149, this galaxy is almost edge-on and we adopted the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. The resulting rotation curve is perfectly regular and symmetric, with both sides extending up to the effective radius in r-band, where the rotation velocity is slightly above the H IV_max. The shape of the curve suggests that it goes on rising beyond the effective radius, in agreement with both models (Courteau and Zhao).

Galaxy HRS 151, we find a significant difference between the morphological and kinematical values of the PA of the major axis (21° difference) when computing our Hα rotation curve. The resulting curve is quite chaotic and asymmetric, anyway both sides extend slightly beyond the effective radius in r-band and bend slightly there, suggesting that the curve is about to reach a plateau, with a rotation velocity around the H IV_max. Both models (Courteau as well as Zhao) suggest however that the curve goes on rising much beyond, even after the optical radius.

Galaxy HRS 152, this galaxy is not far from face-on, we adopted the morphological value for the inclination of its disk and find a good agreement between the morphological and kinematical values of the PA of the major axis (6° difference) when computing our Hα rotation curve. The resulting rotation curve is fairly regular and symmetric, extending slightly beyond the effective radius in r-band (N.B. The redshifted side almost extends midway between the effective radius and the r₂₄ radius in r-band.) Courteau’s model suggests that the rotation curve is not far from reaching a plateau beyond the optical radius (with a rotation velocity slightly above the H IV_max) whereas Zhao’s model favors a continuous rising in the outer parts.

Galaxy HRS 153, the disk of this galaxy is peppered with many H II regions covering its whole optical extent. It is faintly inclined and we adopted the morphological value for the inclination of the disk of this galaxy while finding a fairly good agreement between the morphological and kinematical values of the PA of the major axis (10° difference) when computing our Hα rotation curve. The resulting rotation curve is regular and symmetric, extending almost out to the r₂₄ radius in r-band for both sides. Both models (but Courteau better than Zhao) suggest that the rotation curve reaches a plateau after the optical radius, with a rotation velocity close to the H IV_max.

Galaxy HRS 154, this galaxy is not far from face-on, we adopted the morphological value for the inclination of its disk and find a large difference between the morphological and kinematical values of the PA of the major axis (56° difference) when computing our Hα rotation curve. Despite this disagreement, the resulting rotation curve is not so bad and, despite a strong dispersion in the central rising part (especially for the redshifted side) both sides exhibit the same trend and extend out to the r₂₄ radius in r-band, almost reaching a plateau there, with a rotation velocity close to the H IV_max, as suggested by both models (Courteau and Zhao).

Galaxy HRS 156, this galaxy is almost edge-on and we adopted the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. The resulting rotation curve is fairly regular and symmetric, with both sides extending up to the effective radius in r-band, where the rotation velocity is almost twice the H IV_max. Zhao’s model suggests that the maximum of the Hα rotation curve is reached there, whereas Courteau’s model suggests that it continuous rising after the effective radius and reaches a plateau beyond the optical radius.

Galaxy HRS 157, the Hα emission is rich and perfectly covers the whole optical disk of this Sbc type galaxy. We find a perfect agreement between the morphological and kinematical values of the inclination and a rather good agreement between the morphological and kinematical values of the PA of the major axis (7° difference). The resulting Hα rotation curve is fairly regular and symmetric and reaches the r₂₄ radius in r-band for both sides. The rotation velocity reached there is slightly above the H IV_max and both models (Courteau and Zhao) suggest that it goes on rising beyond, although with a smaller slope for Courteau’s model, favoring a plateau beyond the optical radius.

Galaxy HRS159, the Hα emission is limited to the inner disk of this Sa type galaxy, as can be seen also on the Hα + [N II] image from Boselli et al. (2015). Despite the relatively high inclination of the disk, the velocity gradient of the Hα velocity field of this galaxy is rather faint but, most strangely, it suggests that the PA of the major axis is almost at right angle with respect to the morphological value (92° difference). All of this suggests that the behavior of the ionized gas do not reflect that of the main body of the galaxy. Anyway, we traced our Hα rotation curve with the kinematical values suggested by our velocity field (85° for the inclination and 0° for the PA of the major axis, against 62° and 92° respectively for the morphological values). The resulting rotation curve is quite chaotic but suggests a solid body rotation for both sides of the central disk of ionized gas. The curve does not reach the effective radius but its maximum rotation velocity is close to the H IV_max. The strange behavior of the ionized gas in the center of this Sa galaxy leads to think that it could be the remnant of a merger (Boselli et al. 2018b).

Galaxy HRS 160 (KPG 338A), we find a significant difference between the morphological and kinematical values of the inclination (17°) as well as for the PA of the major axis (17° difference) when computing our Hα rotation curve. Despite some chaotic behavior within the first 10 arcsec, the resulting curve is nevertheless fairly regular and symmetric, extending beyond the effective radius in the r-band. The maximum rotation velocity reached is however clearly below the H IV_max. Zhao’s model suggests that the curve goes on rising with an almost constant slope, whereas Courteau’s model suggests that we almost reach a plateau.

Galaxy HRS 164, no significant Hα emission can be detected in this Sa type galaxy, as confirmed by the Hα + [N II] image from Boselli et al. (2015). We could not draw any velocity field nor rotation curve.

Galaxy HRS 165, This galaxy is almost edge-on and we adopted the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. The resulting rotation curve is quite chaotic but reveals a solid body rotation for both sides, extending up to the effective radius in r-band, where the rotation velocity reaches the H IV_max. Zhao’s model suggests that the rotation curve goes on rising beyond, whereas Courteau’s model suggests that it reaches a plateau at this radius.

Galaxy HRS 168, we find a fairly good agreement between the morphological and kinematical values of the PA of the major axis (9° difference) when computing our Hα rotation curve. The resulting curve is regular and symmetric, extending beyond the r₂₄ radius in r-band for both sides. Both models (but Courteau better than Zhao) suggest that our curve reaches a plateau at the optical radius, with a rotation velocity slightly below the H IV_max.

Galaxy HRS 169, we adopted the morphological value for the inclination of the disk of this galaxy and find a good agreement between the morphological and kinematical values of the PA of the major axis (6° difference) when computing our Hα rotation curve. Despite some dispersion for the redshifted side, the resulting curve is fairly regular and symmetric, extending beyond the effective radius in r-band for both sides and almost out to the r₂₅ radius in B-band for the blueshifted side. The rotation velocity reaches the H IV_max at the effective radius but both models (Zhao more than Courteau) suggest that our curve goes on rising much beyond the optical radius.

Galaxy HRS 171, the Hα emission of this Sbc galaxy is very bright but limited to the inner disk. The extension that can be seen on the northern side of the galaxy on our maps seems doubtful when comparing with the Hα + [N II] image from Boselli et al. (2015) and we did not take it into account when tracing our Hα rotation curve (indeed, this extension produces extreme values on the residual velocity field). We adopted the morphological value for the inclination of the disk of this galaxy and find a good agreement between the morphological and kinematical values of the PA of the major axis (6° difference) when computing our Hα rotation curve. The resulting curve is fairly regular and symmetric, it reaches the effective radius in r-band for both sides, with a rotation velocity close to the H IV_max. Zhao’s model suggests that our curve reaches a maximum between the effective radius and the r₂₄ radius, whereas Courteau’s model suggests that it goes on rising much beyond.

Galaxy HRS 172, the Hα emission of this Sb galaxy is very bright but limited to the inner disk. We find a rather good agreement between the morphological and kinematical values of the inclination (10° difference) and a perfect agreement for the PA of the major axis (1° difference) when computing our Hα rotation curve. The resulting curve is fairly regular and symmetric but does not even reach the effective radius in r-band. The rotation velocity reached is close to the H IV_max but both models (Courteau and Zhao) suggest that the curve goes on rising much beyond.

Galaxy HRS 177. this Sa type galaxy has a surprisingly rich Hα emission, covering almost all of its optical disk. We find a good agreement between the morphological and kinematical values of the inclination (5° difference) and a rather good agreement for the PA of the major axis (10° difference) when computing our Hα rotation curve. The resulting curve is fairly regular and symmetric, it extends midway between the effective radius and the r₂₄ radius in r-band. The rotation velocity reached there is slightly below the H IV_max. Zhao’s model suggests that the rotation curve goes on rising beyond the r₂₄ radius, whereas Courteau’s model suggests that it reaches a plateau at this radius, with a rotation velocity remaining below the H IV_max.

Galaxy HRS 182, we find a good agreement between the morphological and kinematical values of the inclination (6° difference) and a perfect agreement for the PA of the major axis (1° difference) when computing our Hα rotation curve. The resulting curve is fairly regular and symmetric, it extends almost out to the r₂₅ radius in B-band (close here from the r₂₄ radius in B-band) at least for the blueshifted side. The rotation velocity reaches the H IV_max at the effective radius in r-band and both models (Zhao and Courteau) suggest that the Hα rotation curve reaches a plateau at the optical radius, with a rotation velocity slightly above the H IV_max.

Galaxy HRS 184, there is but a small patch of Hα emission in the center of this Sa type galaxy, as confirmed by the Hα + [N II] image from Boselli et al. (2015). The other small spots on our maps are but noise or ghost image. We could not draw any realistic velocity field nor rotation curve.

Galaxy HRS 185, the Hα emission of this Sa galaxy has a faint surface brightness and is mainly located in a central ring of about 10 arcsec radius, as can be seen also on the Hα + [N II] image from Boselli et al. (2015). Its disk is almost face-on and we adopted the morphological value for the inclination but find a significant difference between the morphological and kinematical values of the PA of the major axis (36° difference) when computing our H rotation curve. The resulting curve is poorly defined and quite chaotic, with only a few points between 5 and 20 arcsec from the center. It does not even reach the effective radius and the rotation velocity remains much below the H IV_max (about half).

Galaxy HRS 187 (KPG 343A), although this object is a pair of galaxies, both rich in Hα emission, the velocity field of the smaller one (NGC 4496B, located about 1 arcmin southeast from NGC 4496A) seems completely melted in the velocity field of the bigger one. As a result, we reduced the data as if it were a single galaxy. We find a good agreement between the morphological and kinematical values of the inclination (8° difference) as well as for the values of the PA of the major axis (7° difference) when computing our Hα rotation curve. The resulting curve is fairly regular and symmetric, it extends almost out to the r₂₄ radius in r-band for both sides. The rotation velocity reaches the H IV_max at the effective radius in r-band and remains slightly above beyond, with an almost constant value. Both models (Zhao and Courteau) agree that the Hα rotation curve reaches its maximum at the r₂₄ radius.

Galaxy HRS 189, the Hα emission of this galaxy is asymmetric, with a very bright patch north of the nucleus, otherwise it is distributed rather uniformly in the central disk, as can be seen also on the Hα + [N II] image from Boselli et al. (2015). We find a rather good agreement between the morphological and kinematical values of the inclination (14° difference) and an excellent agreement between the values of the PA of the major axis (2° difference) when computing our Hα rotation curve. The resulting curve is quite chaotic, especially for the redshifted side (with extreme values on that side of the residual velocity field) and barely reaches the effective radius in r-band. The rotation velocity there is much below the H IV_max. Zhao’s model suggests that the curve goes on rising beyond, whereas Courteau’s model favors a plateau.

Galaxy HRS 191, we find an excellent agreement between the morphological and kinematical values of the inclination (2° difference) as well as between the values of the PA of the major axis (1° difference) when computing our Hα rotation curve. The resulting curve is fairly regular and symmetric and extends midway between the effective radius and the r₂₄ radius in r-band. Both models (Zhao and Courteau) suggest that it goes on rising, until it reaches the H IV_max at the r₂₅ radius in B-band.

Galaxy HRS 192, the Hα emission of this Sa type galaxy is limited to a few spots in the very center, as can be seen also on the Hα + [N II] image from Boselli et al. (2015). We nevertheless tried to draw the Hα rotation curve, using the morphological values of the inclination and PA of the major axis, but it gives nothing reliable.

Galaxy HRS 193, we adopted the morphological value for the inclination but find a significant difference between the morphological and kinematical values of the PA of the major axis (21° difference) when computing our H rotation curve. Anyway, the resulting curve is fairly regular and symmetric and extends a bit after the effective radius in r-band for both sides (slightly more for the blueshifted side). The rotation velocity reaches the H IV_max after the effective radius and both models (Zhao and Courteau) suggest that it goes on rising much beyond.

Galaxy HRS 195, no significant Hα emission can be seen in this Sab galaxy, as confirmed by the Hα + [N II] image from Boselli et al. (2015). The few spots seen on our maps are probably but noise. We could not draw any realistic velocity field nor rotation curve.

Galaxy HRS 197, this galaxy is almost edge-on and we adopted the morphological value for the inclination. We then find an excellent agreement between the morphological and kinematical values of the PA of the major axis (2° difference) when computing our Hα rotation curve. The resulting rotation curve is fairly regular and symmetric and extends almost out to the effective radius in r-band for both sides. The rotation velocity reaches the H IV_max at the effective radius and both models (Zhao and Courteau) suggest that it goes on rising much beyond.

Galaxy HRS 198, we find a good agreement between the morphological and kinematical values of the inclination (5° difference) as well as between the values of the PA of the major axis (5° difference) when computing our Hα rotation curve. The resulting curve is somewhat chaotic within the first 10 arcsec (for both sides) but becomes more regular and symmetric beyond. It extends almost midway between the effective radius and the r₂₄ radius in r-band where the rotation velocity is close to the H IV_max. Zhao’s model suggests that our Hα curve reaches its maximum there and declines afterwards, whereas Courteau’s model favors a plateau slightly above the H IV_max.

Galaxy HRS 199, the Hα emission of this Sb galaxy is very bright but limited to the inner disk as can be seen also on the Hα + [N II] image from Boselli et al. (2015). We find an acceptable agreement between the morphological and kinematical values of the inclination (16° difference) but a quite large difference between the morphological and kinematical values of the PA of the major axis (25° difference) when computing our Hα rotation curve. Despite some dispersion, the resulting curve shows a solid body rotation for both sides but, because of the small extension of the disk of ionized gas, it is far from reaching the effective radius in r-band. However, the maximum velocity rotation reached is above the H IV_max.

Galaxy HRS 207, we find an excellent agreement between the morphological and kinematical values of the inclination (2° difference) but a quite large difference between the morphological and kinematical values of the PA of the major axis (31° difference) when computing our Hα rotation curve. The resulting curve is somewhat chaotic for the blueshifted side (especially within the 5 first arcsec) but much more regular for the redshifted side. The general shape for both sides is that of a solid body rotation, up to the effective radius in r-band. The blueshifted side of the curve extends a bit further, with a marked bending and a rotation velocity remaining slightly above the H IV_max. Zhao’s model suggests that our Hα curve reaches its maximum there and declines afterwards, whereas Courteau’s model favors a plateau above the H IV_max.

Galaxy HRS 212 (KPG 346A), this galaxy has bright H II regions almost all over its optical disk. We adopted the morphological value for the inclination but find a significant difference between the morphological and kinematical values of the PA of the major axis (22° difference) when computing our Hα rotation curve. The shape of the isovelocity lines of our Hα velocity field suggests that the disk of this galaxy is warped, explaining such a difference. The velocity gradient is very faint in the center, so that our rotation curve is almost flat for both sides, up to a radius of 10 arcsec, then the curve rises very steeply and reaches a plateau at the effective radius in r-band, with different velocities depending on the side. The redshifted side exhibits a higher velocity than the blueshifted side (about 70 km s⁻¹ against 50 km s⁻¹) but both remain much below the H IV_max.

Galaxy HRS 225, the Hα emission of this Sb type galaxy is limited to a fuzzy patch on the southeastern side of the nucleus, as can be seen also on the Hα + [N II] image from Boselli et al. (2015). The faint northern spot seen on our Hα map is probably but noise. We nevertheless tried to draw the Hα rotation curve, using the morphological values of the inclination and PA of the major axis, but it gives nothing reliable.

Galaxy HRS 226, we find an excellent agreement between the morphological and kinematical values of the inclination (1° difference) as well as between the morphological and kinematical values of the PA of the major axis (2° difference) when computing our Hα rotation curve. The resulting rotation curve is fairly regular and symmetric and extends out to the effective radius in r-band for both sides. Both models (Zhao and Courteau) agree that our curve reaches a plateau at the effective radius, with a rotation velocity slightly above the H IV_max.

Galaxy HRS 230, we find an excellent agreement between the morphological and kinematical values of the inclination (less than 1° difference) as well as between the morphological and kinematical values of the PA of the major axis (1° difference) when computing our Hα rotation curve. The resulting rotation curve is fairly regular and symmetric and extends out to the effective radius in r-band for both sides. Both models (but Courteau better than Zhao) agree that our curve reaches a plateau slightly after the effective radius, with a rotation velocity remaining below the H IV_max.

Galaxy HRS 237, except in the very center, the Hα emission of this Im type galaxy has a faint surface brightness. We adopted the morphological value for the inclination when computing our Hα rotation curve. Despite some dispersion, the trend of the curve for both sides is that of a solid body rotation, albeit with a rather faint slope. Both sides extend a bit further than the effective radius in r-band and the rotation velocity remains below the H IV_max.

Galaxy HRS 238, the Hα emission of this Sm galaxy is rather faint and patchy. The large extension bordering the whole northeastern side of the disk has a very faint surface brightness and seems doubtful (N.B. It was not imaged by Boselli et al. 2015.) The fact that all this area appears with the same velocity (coded with blue color on our velocity field map) suggests that our data are polluted there by an OH night skyline insufficiently subtracted. We adopted the morphological value for the inclination but find a large difference between the morphological and kinematical values of the PA of the major axis (27° difference) when computing our Hα rotation curve. The resulting curve is rather poor, because of the faintness of the Hα emission, its trend is that of a solid body rotation for both sides. It reaches the effective radius in r-band, with a rotation velocity which is only half the H IV_max.

Galaxy HRS 239 (KPG 351B), this galaxy is almost edge-on and we adopted the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. The resulting curve is fairly regular and symmetric up to a radius of 20 arcsec, showing a solid body rotation with a steep slope. Then the slope of the blueshifted side diminishes whereas the redshifted side stops for a while before climbing again with about the same slope as the blueshifted side. Both sides of the curve extend slightly after the effective radius in r-band and the models (Zhao as well as Courteau) suggest that our curve reaches a plateau at the optical radius, with a rotation velocity above the H IV_max.

Galaxy HRS 249, the Hα emission of this Sb type galaxy is limited to a bright spot on the left of the nucleus and another (less bright) spot on its right. We could not draw any realistic velocity field nor rotation curve.

Galaxy HRS 252, the disk of this Sd galaxy is peppered with many bright H II regions covering almost completely the southern part of its optical disk, but less numerous on the northern side (redshifted) as can be seen also on the Hα + [N II] image from Boselli et al. (2015). We find an excellent agreement between the morphological and kinematical values of the inclination (less than 1° difference) as well as between the morphological and kinematical values of the PA of the major axis (3° difference) when computing our Hα rotation curve. The resulting curve is fairly regular and symmetric up to the effective radius in r-band for both sides. The blueshifted side then enables to trace the curve up to the r₂₄ radius in r-band (found here slightly beyond the r₂₅ radius in B-band) where it reaches a rotation velocity higher than the H IV_max. Zhao’s model suggests that our curve reaches a maximum there before declining, whereas Courteau’s model favors a continuous rising, although with a smaller slope.

Galaxy HRS 255, the spiral pattern of this Scd galaxy is underlined by many H II regions, as can be seen on the Hα + [N II] image from Boselli et al. (2015). This galaxy is not far from face-on, we adopted the morphological value for the inclination of its disk and find a large difference between the morphological and kinematical values of the PA of the major axis (55° difference) when computing our Hα rotation curve. The resulting curve is quite chaotic, especially in the central part, but the general trend, for both sides, is that of a solid body rotation with a faint slope. Both sides extend beyond the r₂₄ radius in r-band, where the rotation velocity is slightly above the H IV_max. The redshifted side enables to draw the rotation curve almost out to the r₂₅ radius in B-band, keeping the same slope, but with a large uncertainty.

Galaxy HRS 256, the Hα emission is bright but limited to the inner disk of this Sa type galaxy, as can be seen also on the Hα + [N II] image from Boselli et al. (2015). Despite the relatively high inclination of the disk, the velocity gradient of the Hα velocity field of this galaxy is rather faint but, most strangely, it suggests that the PA of the major axis is almost at right angle with respect to the morphological value (95° difference). All of this suggests that the behavior of the ionized gas do not reflect that of the main body of the galaxy. We adopted the morphological value for the inclination of its disk when computing our Hα rotation curve. The resulting curve is quite chaotic for the redshifted side while suggesting a solid body rotation for the blueshifted side of the central disk of ionized gas. The curve does not reach the effective radius and its maximum rotation velocity is very far from the H IV_max. The strange behavior of the ionized gas in the center of this Sa galaxy leads to think that it could be the remnant of a merger (as already seen for HRS142 and HRS159).

Galaxy HRS 261, this galaxy is almost edge-on and we adopted the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. Except some strong dispersion around 10 arcsec radius for the redshifted side, the resulting curve is fairly regular and symmetric, rising up to the effective radius in r-band for both sides. The redshifted side enables to draw the curve a bit further (midway between the effective and r₂₄ radius in r-band) where it reaches the H IV_max. Both models (Zhao as well as Courteau) suggest that our curve goes on rising beyond the optical radius, although with a smaller slope for Courteau’s model.

Galaxy HRS 264, this galaxy is almost edge-on and we adopted the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. The resulting curve is fairly regular and symmetric, almost reaching the effective in r-band for both sides. The rotation velocity at that radius is not far from the H IV_max but both models (Zhao as well as Courteau) suggest that our curve goes on rising beyond the optical radius.

Galaxy HRS 267, the Hα emission of this almost edge-on Scd type galaxy is asymmetric, much brighter on the southwestern side (blueshifted), probably because of absorption by dust in the disk. We adopted the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. The resulting curve is quite chaotic, more especially for the redshifted side that exhibits a marked bump at about 10 arcsec radius before rising again. The curve do not even reach the effective radius in r-band and the rotation velocity remains much below the H IV_max.

Galaxy HRS 268, we adopted the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. The resulting curve is fairly regular for the blueshifted side and extends out to the r₂₅ radius in B-band (which is here slightly larger than the r₂₄ radius in r-band). The redshifted side is shorter and more irregular, although with the same general trend. The rotation velocity reaches the H IV_max and the blueshifted side seems to mark a plateau at this value, although both models (Zhao and Courteau) favor a continuous rising of the rotation curve beyond the optical radius.

Galaxy HRS 271, this galaxy is almost edge-on and we adopted the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. The resulting curve is quite irregular within 10 arcsec radius from the center but the general trend is the same for both sides, that of a solid body rotation with a diminishing slope when reaching the effective radius in r-band. The rotation velocity reached at that radius is equal to the H IV_max. Zhao’s model suggests that our rotation curve reaches a maximum at the optical radius whereas Courteau’s model favors a continuous rising beyond.

Galaxy HRS 273, this galaxy is almost edge-on and we adopted the morphological values for the inclination when computing the rotation curve. We find an excellent agreement between the morphological and kinematical values of the PA of the major axis (less than 2° difference) and, despite some dispersion in the rising part, the resulting curve is fairly regular and symmetric. The curve extends midway between the effective radius and the r₂₄ radius in r-band. The maximum rotation velocity reached is close to the H IV_max and both models (but Courteau better than Zhao) suggest that our rotation curve reaches a plateau at the optical radius.

Galaxy HRS 275, the optical disk of this Sd type galaxy is peppered with many H II regions covering it completely. The inclination of the disk is rather faint and we adopted the morphological value when computing our Hα rotation curve. We find a rather large difference between the morphological and kinematical values of the PA of the major axis (35° difference) but the resulting rotation curve is quite regular and symmetric, despite some dispersion. Indeed both sides show the same trend, that of a solid body rotation, almost out to the r₂₄ radius in r-band where the rotation velocity is about to reach the H IV_max. Zhao’s model suggests that our curve reaches a maximum slightly after the r₂₄ radius, whereas Courteau’s model suggests a continuous rising beyond.

Galaxy HRS 276, the Hα emission of this Sbc type galaxy covers fairly well the northeastern side of the optical disk but is patchy for the southwestern side (redshifted) as can be seen also on the Hα + [N II] image from Boselli et al. (2015). We adopted the morphological value for the inclination of the disk, when computing our Hα rotation curve, and find a rather good agreement between the morphological and kinematical values of the PA of the major axis (7° difference). The redshifted side of the curve is rather ill defined, because of the lack of velocity points, but the blueshifted side is quite regular and enables to trace the rotation curve much beyond the effective radius in r-band, after which it seems to reach a plateau. Indeed Courteau’s model suggests that our curve reaches a plateau after the effective radius, with a velocity close to the H IV_max, whereas Zhao’s model favors a continuous rising beyond that radius.

Galaxy HRS 278, the Hα emission of this edge-on Sb type galaxy has a faint surface brightness and is limited to the inner disk as can be seen also on the Hα + [N II] image from Boselli et al. (2015). We adopted the morphological values for the inclination and for the PA of the major axis when computing our Hα rotation curve. Despite some dispersion, both sides of the curve show the same trend, that of a solid body rotation, and extend out to about 3/4 of the effective radius in r-band. The rotation velocity reached for both sides is clearly above the H IV_max.

Galaxy HRS 279, the optical disk of this Sd type galaxy is peppered with many H II regions covering it completely. We find a fairly good agreement between the morphological and kinematical values of the inclination (7° difference) as well as between the morphological and kinematical values of the PA of the major axis (5° difference) when computing our Hα rotation curve. Despite some dispersion within the first 20 arcsec, the resulting curve is fairly regular and symmetric, almost reaching the r₂₄ radius in r-band (at least for the redshifted side) which is coincident here with the r₂₅ radius in B-band. The rotation velocity reaches the H IV_max for both sides of the curve. Zhao’s model suggests that our curve reaches a maximum before the optical radius and declines strongly beyond, whereas Courteau’s model favors a continuous rising beyond the optical radius, although with a smaller slope.

Galaxy HRS 280, the Hα emission of this Sb type galaxy shows a bright inner disk, with an extension of faint surface brightness on the western extremity of the disk (blueshifted side) as can be seen also on the Hα + [N II] image from Boselli et al. (2015). The inclination of the disk is rather strong and we adopted the morphological value when computing our Hα rotation curve. We find a rather good agreement between the morphological and kinematical values of the PA of the major axis (7° difference) and, despite the relative small number of velocity points, the resulting rotation curve is quite regular and symmetric. The curve extends out to the effective radius in r-band for both sides, reaching there a rotation velocity equal to the H IV_max. The blueshifted side enables to trace our rotation curve a bit further and seems to stop rising. Indeed both models (but Courteau better than Zhao) suggest that our curve reaches a plateau slightly above the H IV_max just after the effective radius.

Galaxy HRS 282, we detected no significant Hα emission in this BCD type galaxy (N.B. It was not imaged by Boselli et al. 2015.) and could not draw any reliable Hα velocity field nor rotation curve.

Galaxy HRS 283, the disk of this galaxy is completely covered by Hα emission and we find an excellent agreement between the morphological and kinematical values of the inclination (1° difference only) as well as between the morphological and kinematical values of the PA of the major axis (2° difference only) when computing our Hα rotation curve. The resulting rotation curve is fairly regular and symmetric, despite some waves on the redshifted side, it extends out to the r₂₄ radius in r-band (almost coincident here with the r₂₅ radius in B-band) for both sides. The rotation velocity reached there is equal to the H IV_max, but both models (Zhao and Courteau) suggest that our curve goes on rising beyond the optical radius, although with a smaller slope for Courteau’s model.

Galaxy HRS 284, the disk of this galaxy is strongly inclined and we adopted the morphological values for the inclination and for the PA of the major axis when computing our rotation curve. The resulting curve is fairly regular and symmetric, with the same trend for both sides, that of a solid body rotation. The curve extends out to about 3/4 of the r₂₄ radius in r-band and the rotation velocity reached is slightly above the H IV_max. Both models (Zhao and Courteau) suggest that our rotation curve reaches a plateau shortly after.

Galaxy HRS 287, this Scd type galaxy has a thick bar and a strong spiral pattern, both underlined by bright H II regions. We adopted the morphological value for the inclination of the disk, when computing our Hα rotation curve, and find a significant difference between the morphological and kinematical values of the PA of the major axis (25° difference). Despite some distortions, the agreement between both sides of our curve is not so bad for the first 10 arcsec (about half the effective radius in r-band), but quite different beyond. The redshifted side then keeps an almost constant rotation velocity, equal to the H IV_max, out to the r₂₄ radius in r-band (almost coincident here with the r₂₅ radius in B-band). The blueshifted side is not so extended and its velocity, after a small pause, goes on rising continuously beyond the effective radius. Zhao’s model suggests that our rotation curve reaches a maximum (close to the H IV_max) between the effective radius and r₂₄ radius before declining very slowly, while Courteau’s model suggests that it reaches a plateau with a rotation velocity close to the H IV_max.

Galaxy HRS 289, this Sbc type galaxy has a nice spiral pattern, underlined by many bright H II regions. We find a reasonable agreement between the morphological and kinematical values of the inclination (10° difference) as well as between the morphological and kinematical values of the PA of the major axis (14° difference) when computing our Hα rotation curve. The resulting rotation curve is fairly regular and symmetric, extending almost out to the r₂₄ radius in r-band (at least for the blueshifted side). The central part of the curve is ill defined, because of the lack of Hα emission there, and the velocity bump seen at about 10 arcsec from the center is likely to be explained by the strong central bulge. Both models (but Courteau better than Zhao) suggest that our curve rapidly reaches a plateau with a rotation velocity slightly above the H IV_max.

Galaxy HRS 290, the Hα emission of this almost edge-on Sa type galaxy is concentrated in the inner disk. We adopted the morphological values for the inclination and for the PA of the major axis when computing our rotation curve. Despite the relatively small number of velocity points, the resulting curve is fairly regular and symmetric, almost reaching the effective radius in r-band. The redshifted side reaches a higher rotation velocity than the blueshifted side and both are clearly above the H IV_max.

Galaxy HRS 291, the Hα emission of this Sab type galaxy is limited to a few faint spots around the nucleus. We cannot check if they are real or mere noise since it was not imaged by Boselli et al. (2015). We could not draw any reliable Hα velocity field nor rotation curve.

Galaxy HRS 292, the Hα emission of this Sb type galaxy is very bright but limited to the inner disk, as can be seen also on the Hα + [N II] image from Boselli et al. (2015). We find an acceptable agreement between the morphological and kinematical values of the PA of the major axis (14° difference). The resulting curve is regular and symmetric, with both sides reaching the effective radius in r-band. The curve rises steeply up to a plateau at the H IV_max as confirmed by both models (Zhao and Courteau).

Galaxy HRS293, the whole optical disk of this Sdm galaxy is well covered by H II regions. We find a reasonable agreement between the morphological and kinematical values of the inclination (7° difference) as well as between the morphological and kinematical values of the PA of the major axis (16° difference) when computing our Hα rotation curve. Despite some waves on the redshifted side, we find a fairly regular and symmetric curve, extending out to the optical radius (the r₂₄ radius in r-band and r₂₅ radius in B-band are coincident here). The rotation velocity reached there is the H IV_max but both models (Zhao and Courteau) suggest that our curve goes on rising beyond the optical radius.

Galaxy HRS 294, apart from a few bright spots, the Hα emission of this edge-on Sb type galaxy has a rather faint surface brightness, as can be seen also on the Hα + [N II] image from Boselli et al. (2015). We adopted the morphological values for the inclination and for the PA of the major axis when computing our rotation curve. Despite the relatively small number of velocity points, the resulting curve is fairly regular and symmetric but do not even reach the effective radius in r-band. Both sides show a solid body rotation that could reach the H IV_max at the effective radius if extrapolated keeping the same slope.

Galaxy HRS 297, the whole optical disk of this Sbc type galaxy is peppered with bright H II regions. It is strongly inclined and we adopted the morphological values for the inclination as well as for the PA of the major axis when computing our rotation curve. Despite some waves on both sides, the resulting curve is fairly regular and symmetric, extending almost out to the r₂₄ radius in r-band where the rotation velocity reaches the H IV_max. Zhaos’s model suggests that our curve goes on rising beyond the optical radius, almost with the same slope, but Courteau’s model apparently fails fitting our data correctly here.

Galaxy HRS 298 (KPG 397A), the Hα emission of this peculiar galaxy is very bright but limited to the inner disk. The large and faint structure surrounding the northern and western side of the disk on our maps seems doubtful since nothing can be seen there on the Hα + [N II] image from Boselli et al. (2015). The fact that it pops out with the same velocity, color coded green on the map of our velocity field, strongly suggests that it is the remnant of an OH night skyline insufficiently subtracted (it also gives extreme values on the residual velocity field). Anyway, it was not taken into account when computing our Hα rotation curve. We adopted the morphological value for the inclination of the disk, when computing our Hα rotation curve, and find a rather good agreement between the morphological and kinematical values of the PA of the major axis (9° difference). The resulting rotation curve is very regular and symmetric, extending almost out to the r₂₅ radius in B-band where it reaches a rotation velocity higher than the H IV_max. Zhao’s model suggests that our curve goes on rising beyond the optical radius but Courteau’s model favors a plateau shortly after.

Galaxy HRS 300, there is no significant Hα emission in this Sab type galaxy, as confirmed by the Hα + [N II] image from Boselli et al. (2015) that shows only a very faint fuzzy spot in the center. The spots on our maps are probably more noise than signal and we could not draw any reliable Hα velocity field nor rotation curve.

Galaxy HRS 301, the whole optical disk of this Sc type galaxy is peppered with numerous H II regions as can be seen also on the Hα + [N II] image from Boselli et al. (2015). We find a good agreement between the morphological and kinematical values of the inclination (8° difference) as well as between the morphological and kinematical values of the PA of the major axis (6° difference) when computing our Hα rotation curve. The resulting rotation curve is fairly regular and symmetric, except some dispersion (for both sides) around the 10 arcsec radius. The curve extends out to the r₂₄ radius in r-band and reaches a rotation velocity higher than the H IV_max. Both models (Zhao and Courteau) suggest that our curve goes on rising beyond the optical radius but with a diminishing slope.

Galaxy HRS 303, the Hα emission of this Sb type galaxy is very bright but limited to the inner disk. We find a rather good agreement between the morphological and kinematical values of the inclination (10° difference) and an excellent agreement between the morphological and kinematical values of the PA of the major axis (2° difference) when computing our Hα rotation curve. The resulting curve is fairly regular and symmetric, with both sides extending a bit further than the effective radius in r-band. Courteau’s model suggests that our rotation curve reaches a plateau at the optical radius with a rotation velocity around 120 km s⁻¹ whereas Zhao’s model favors a continuous rising curve.

Galaxy HRS 304, the disk is strongly inclined and we adopted the morphological values for the inclination as well as for the PA of the major axis when computing our rotation curve. The resulting curve is fairly regular and symmetric, with both sides extending a bit further than the effective radius in r-band. The curve reaches the H IV_max there but both models (Zhao and Courteau) suggest that it goes on rising beyond that radius, although with a smaller slope for Courteau’s model.

Galaxy HRS 305, the Hα emission of this peculiar galaxy is limited to two relatively bright spots on each side of the nucleus, as can be seen also on the Hα + [N II] image from Boselli et al. (2015). Some velocity gradient can be seen anyway on our velocity field and we adopted the morphological values for the inclination as well as for the PA of the major axis when computing our rotation curve. The resulting curve is quite chaotic and limited to one third of the effective radius in r-band. The blueshifted side is less dispersed than the redshifted side but no more extended and its rotation velocity remains much below the H IV_max.

Galaxy HRS 308, the Hα emission of this Sb type galaxy is limited to a faint fuzzy central patch as can be seen also on the Hα + [N II] image from Boselli et al. (2015). Anyway, our velocity field shows some gradient and we tried to draw the rotation curve. The disk is strongly inclined and we adopted the morphological values for the inclination as well as for the PA of the major axis in order to compute our rotation curve. The result is however quite disappointing and not reliable.

Galaxy HRS 309, the optical disk of this Sm type galaxy is peppered with many bright H II regions. We find a rather good agreement between the morphological and kinematical values of the inclination (11° difference) and an excellent agreement between the morphological and kinematical values of the PA of the major axis (3° difference) when computing our Hα rotation curve. Despite a rather faint spatial sampling, the resulting curve is fairly regular and symmetric, with both sides extending a bit further than the r₂₄ radius in r-band. Our curve remains clearly below the H IV_max but both models (Zhao and Courteau) suggest that it goes on rising beyond the optical radius, although with a smaller slope for Courteau’s model.

Galaxy HRS 313, the disk of this Sbc type galaxy is peppered with many bright H II regions. The disk is strongly inclined and we adopted the morphological values for the inclination as well as for the PA of the major axis in order to compute our rotation curve. Despite some dispersion, the resulting curve is fairly regular and symmetric, with both sides extending out halfway between the effective radius and the r₂₄ radius in r-band. Our curve just reaches the H IV_max but both models (Zhao and Courteau) suggest that it goes on rising beyond the optical radius, although with a smaller slope for Courteau’s model which is almost flat in the outer part.

Galaxy HRS 314, the Hα emission of this Sd type galaxy is asymmetric, with brighter H II regions on the northern side (blueshifted) as can be also on the Hα + [N II] image from Boselli et al. (2015). The whole optical disk is nevertheless well covered on both sides by ionized gas. We find a good agreement between the morphological and kinematical values of the inclination (6° difference) and an acceptable agreement between the morphological and kinematical values of the PA of the major axis (13° difference) when computing our Hα rotation curve. The resulting curve is quite chaotic, with a larger dispersion on the redshifted side for which the Hα emission is the less bright. Nevertheless, both sides of the curve exhibit the same general trend, steeply rising up to the effective radius in r-band where the rotation velocity reaches the H IV_max. Beyond that radius, the rotation velocity remains almost constant for both sides, out to the r₂₅ radius in B-band for the redshifted side. Zhao’s model suggests that the curve reaches a maximum (with a rotation velocity close to the H IV_max) before the optical radius and declines beyond, whereas Courteau’s model favors a plateau beyond the optical radius (with a rotation velocity close to the H IV_max).

Galaxy HRS 317, this galaxy is almost edge-on and we adopted the morphological value for the inclination. We then find an excellent agreement between the morphological and kinematical values of the PA of the major axis (less than 1° difference) when computing our Hα rotation curve. Despite the faint sampling and some dispersion, the resulting rotation curve is fairly regular and symmetric and extends almost out to the r₂₅ radius in B-band for both sides. The rotation velocity just reaches the H IV_max but both models (Zhao and Courteau) suggest that it goes on rising beyond the optical radius.

Galaxy HRS318, the faint extension seen on our maps, on the northeastern side of the disk, is doubtful since nothing can be seen there on the Hα + [N II] image from Boselli et al. (2015). We adopted the morphological value for the inclination and find an acceptable agreement between the morphological and kinematical values of the PA of the major axis (16° difference) when computing our Hα rotation curve. The resulting curve is fairly regular and symmetric, despite some waves in the outer part of the redshifted side. The curve extends out to the r₂₅ radius in B-band (almost coincident here with the r₂₄ radius in r-band). Both models (Zhao and Courteau) suggest that our curve goes on rising beyond the optical radius, athough with a lower slope for Courteau’s model.

Galaxy HRS 319, the spiral pattern of this Scd galaxy is underlined by bright H II regions. We find an excellent agreement between the morphological and kinematical values of the inclination (1° difference) as well as between the morphological and kinematical values of the PA of the major axis (3° difference) when computing our Hα rotation curve. However, although the rising part of our curve is fairly regular and symmetric, it becomes quite chaotic and asymmetric beyond the effective radius in r-band. The blueshifted side of the curve rises up to the H IV_max, extending midway between the effective radius and the r₂₄ radius in r-band. The redshifted side extends out to the r₂₅ radius in B-band with velocities remaining clearly below the H IV_max. Zhao’s model suggests a declining curve beyond the effective radius, whereas Courteau’s model favors a plateau after that radius.

Galaxy HRS 321, the Hα emission of this Sb type galaxy is very bright but limited to the inner disk as can be seen also on the Hα + [N II] image from Boselli et al. (2015). We adopted the morphological value for the inclination and find a good agreement between the morphological and kinematical values of the PA of the major axis (4° difference) when computing our Hα rotation curve. The resulting curve is fairly regular and symmetric but extends out only midway between the effective radius in r-band and the r₂₅ radius in B-band (at least for the redshifted side). The rotation velocity remains much below the H IV_max and both models (Zhao and Courteau) suggest that it stops rising beyond the effective radius in r-band. Zhao’s model suggests that our curve declines beyond that radius, whereas Courteau’s model favors a plateau.

Galaxy HRS 322, the spiral pattern of this almost face-on Sa type galaxy is underlined by H II regions tracing a ring with about 1.5 arcmin radius. Because of this peculiar distribution of the Hα emission, our rotation curve has no points in its rising part and it is difficult to optimize the kinematical parameters. We adopted the morphological value of the inclination and choose the value of the PA of the major axis by eye-estimate from the gradient of the velocity field. The resulting curve shows a plateau at about 210 km s⁻¹, above the H IV_max.

Galaxy HRS 323, the Hα emission of this almost edge-on Sb galaxy is asymmetric, much brighter on the northern side (blueshifted), as can be seen also on the Hα + [N II] image from Boselli et al. (2015). We adopted the morphological values for the inclination as well as for the PA of the major axis when computing our rotation curve. The resulting curve is quite chaotic in the central part, out to a radius of 10 arcsec radius, but more regular and symmetric beyond. The blueshifted side (which is the brighter) is better defined than the redshifted side but both sides have about the same slope in their outer part, extending a bit further than the effective radius in r-band. Both models (Zhao and Courteau) suggest that our curve goes on rising with about the same slope and reaches the H IV_max at the r₂₄ radius in r-band.

Appendix C: Hα profiles

Appendix D: Individual Maps

Appendix E: Tables

All Tables

All Figures