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Home All issues Volume 661 (May 2022) A&A, 661 (2022) A98 Full HTML
Open Access
Issue
A&A
Volume 661, May 2022
Article Number A98
Number of page(s) 14
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361/202142533
Published online 06 May 2022

© S.-Y. Yu et al. 2022

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Open Access funding provided by Max Planck Society.

1. Introduction

Secular evolution describes the slow rearrangement of energy and mass resulting from interactions facilitated by nonaxisymmetric galaxy structures (Combes & Sanders 1981; Kormendy 1982; Pfenniger & Norman 1990; Sellwood & Wilkinson 1993; Kormendy & Kennicutt 2004). Secular processes dominate the evolution of galaxies in the nearby Universe, while violent processes, such as major mergers at high redshift, are less common (e.g., Bertone & Conselice 2009; Duncan et al. 2019; Rodríguez Montero et al. 2019). One of the most important secular processes triggered by disk instability is the driving of gas to the galaxy central regions and subsequent enhancement of the central star formation, leading to the growth of central pseudo bulges (Kormendy & Kennicutt 2004; Athanassoula 2005). Spiral structure, a generic feature in disk galaxies, may play a role.

Approximately 60% of nearby spiral galaxies host a bar (e.g., Aguerri et al. 2009; Li et al. 2011). The role of bars in secular evolution has been widely explored, which may provide hints as to the effects of spirals. A bar imposes a nonaxisymmetric potential on the disk to generate a gravitational torque which drives gas flow toward the galaxy center along the bar dust lanes (Athanassoula 1992; Regan et al. 1999; Fragkoudi et al. 2016). Consistent with bar-driven gas transport, barred galaxies are found to have more centrally concentrated molecular gas distribution than unbarred galaxies (Sakamoto et al. 1999; Sheth et al. 2005; Kuno et al. 2007; Komugi et al. 2008). The degree of gas concentration correlates with bar strength (Kuno et al. 2007). The inflow of gas leads to enhanced central star formation (e.g., Sheth et al. 2005; Regan et al. 2006; Wang et al. 2012, 2020; Combes et al. 2014; Zhou et al. 2015; Díaz-García et al. 2020). In particular, stronger bars tend to have more enhanced central star formation (Zhou et al. 2015; Lin et al. 2017; Chown et al. 2019), due to a higher inflow rate of gas in strong bars than in weak bars (Regan & Teuben 2004). Barred galaxies may have shorter depletion timescales measured for the whole galaxy (e.g., Géron et al. 2021). Still, a recent spatially resolved study found no remarkable differences in the Kennicutt-Schmidt law in the central regions of barred and unbarred galaxies (Díaz-García et al. 2021). Strongly barred galaxies do not necessarily have enhanced central star formation rates (SFRs; Wang et al. 2012, 2020; Consolandi et al. 2017; Díaz-García et al. 2020). Wang et al. (2020) found that disk galaxies hosting strong bars can have both suppressed and enhanced central SFRs. Interestingly, those with enhanced central SFRs tend to connect to strong spiral arms, implying spiral arms may help to drive gas inflow. The suppressed central SFRs could result from a past starburst in which abundant gas may have existed before. Despite the consensus that bars facilitate pseudo bulge formation, bulges in barred galaxies do not have a different Kormendy relation (Kormendy & Kennicutt 2004, reference therein) or different relationships between relative central surface density and other global galaxy properties compared to bulges in unbarred galaxies (Gao et al. 2020; Luo et al. 2020), implying that other disk structures such as spirals also participate in the buildup of pseudo bulges.

Spiral-driven instabilities play a role in secular evolution. In addition to the two well-known secular processes of heating and radial migration of stars caused by spiral arms (e.g., Lynden-Bell & Kalnajs 1972; Athanassoula & Misiriotis 2002; Sellwood & Binney 2002; Roškar et al. 2008; Sellwood 2011, 2014; Martínez-Bautista et al. 2021), the arms could also introduce gas inflow (Kalnajs 1972; Roberts & Shu 1972; Lubow et al. 1986; Hopkins & Quataert 2011; Kim & Kim 2014; Baba et al. 2016; Kim et al. 2020). Theoretical models of quasi-static density waves predict that spiral arms can trigger large-scale shocks on cold gas as they go across the arm (Roberts 1969). The subsequent gravitational collapse induced by the shock accelerates the production of new stars. As stronger spirals trigger stronger shocks, the specific SFRs measured for the whole galaxy are found higher in galaxies with stronger arms than in those with weaker arms (Seigar & James 2002; Kendall et al. 2015; Yu et al. 2021). Studies of global gas depletion time suggest that strong spiral arms enhance star formation efficiency (Yu et al. 2021), although the efficiency does not varying significantly from arm to inter-arm regions (Foyle et al. 2010; Querejeta et al. 2021). The large-scale spiral shocks are an efficient way to transmit angular momentum, causing gas cloud in orbital motions to move radially inward before the corotation radius, and the gravitational torque of the nonaxisymmetric spiral potential acts as a secondary mechanism to drive gas inflow (Kalnajs 1972; Roberts & Shu 1972; Lubow et al. 1986; Hopkins & Quataert 2011; Kim & Kim 2014; Baba et al. 2016; Kim et al. 2020). The gravitational torque of the gaseous component has an additional minor contribution of 10% (Kim & Kim 2014). Inside the corotation radius, the rate of spiral-driven gas mass inflow to the central region follows ∼0.05 − 3.0 M⊙ yr−1, with a more considerable inflow rate corresponding to stronger and slower rotating arms (Kim & Kim 2014).

Another hypothesis for the origin of spirals, in addition to the quasi-static density waves, is that the spiral pattern is recurring and it results from a recurrent cycle of groove modes (Sellwood & Carlberg 2014, 2019; Sellwood & Masters 2022). Traditional N-body simulations of isolated disks present recurring spiral patterns which disappear after a few rotations due to spiral scattering (Sellwood & Carlberg 1984). Recent high-resolution simulations showed that the scattering effect is much less than previously thought and spiral arms exist for much longer (Fujii et al. 2011; D’Onghia et al. 2013). Moreover, longer lived modes, which survive multiple rotations without breaking into pieces, have also been reported (D’Onghia et al. 2013; Sellwood & Carlberg 2014, 2021). Despite their transient nature, the recurring spiral patterns therefore more closely resemble the quasi-static density waves, implying that the gas inflow driven by density waves may be applied to the recurring spiral pattern to some degree. Instructively, simulations of galactic disks subject to spiral-arm perturbations of different origins suggest no apparent difference in the sculpting of the star-forming interstellar medium (ISM) between the different models (Pettitt et al. 2020).

Compared to bars, the connection of spirals to central SFRs and the subsequent secular growth of pseudo bulges is less clear from observations. The photometric images and fiber spectroscopy available from the Sloan Digital Sky Survey (SDSS; York et al. 2020, and references therein) provide us with a good opportunity to statistically test the hypothesis that spiral-driven instabilities drive gas inward to enhance the central star formation in galaxies. As stronger spiral arms are more effective in driving gas inflow (Kim & Kim 2014), we use the strength of spiral arms to characterize the spiral effect. The strengths of spiral arms measured based on SDSS optical r-band images are not significantly affected by emission from young massive stars (Yu et al. 2021). There is a complex web of interdependence between spiral arm strength and other galaxy properties. Spiral arm strength correlates with galaxy mass, global SFR, and concentration (Kendall et al. 2015; Yu & Ho 2020; Yu et al. 2021). Meanwhile, galaxies with lower mass, surface density, and concentration have younger stellar populations in their centers on average (Kauffmann et al. 2003a,b). We therefore aim to probe the effect of spiral arms on secular evolution via the establishment of a true connection between spiral arm strength and central star formation history with the effects from other galaxy parameters removed.

The present paper is organized as follows. Our sample selection and data-reduction methods are described in Sects. 2 and 3, respectively. We present our results in Sect. 4 and discussions in Sect. 5. A summary of the main conclusions appears in Sect. 6.

2. Sample and data

The sample studied here is derived from the NASA Sloan Atlas (NSA; Blanton et al. 2011, reference therein)1, whose background subtraction improved in the SDSS Data Release 8 (Aihara et al. 2011). To probe the properties of central star formation and its enhancement relative to global SFRs, we cross-matched the NSA catalog with the MPA-JHU catalog2 and the catalog of Salim et al. (2018) 3.

We selected the objects with an extinction-corrected r band magnitude from the NSA catalog of brighter than 15 mag at redshifts z of less than 0.05. The magnitude limit is chosen to exclude objects with insufficient signal-to-noise ratio (S/N). The noise drowns out the signal of structure in the outer parts of galaxies if the S/N is too low. The bias caused by noise was also further corrected following the scheme in Yu et al. (2021). An upper redshift limit was chosen to exclude galaxies whose image is degraded due to angular size shrinking caused by long distance and was chosen to ensure robust quantification of spiral arms (Yu et al. 2018). We also exclude all objects at redshifts below 0.01, as the extraction of such low-redshift galaxies is difficult on the basis of SDSS Atlas pipeline images. We exclude galaxies with stellar mass log(M*/M⊙)< 9 to avoid irregular galaxies. Stellar mass (M*) and SFR in actively star-forming galaxies correlate with each other following the relation known as the star formation main sequence (MS; Salim et al. 2007; Renzini & Peng 2015; Saintonge et al. 2016). We make use of the MS defined by Saintonge et al. (2016) and select star-forming MS (SFMS) galaxies by requiring log (SFRglobal/SFRMS)>  − 2 σ, where SFRMS is the SFR along the MS, σ = 0.4 dex is the scatter of the MS, and SFRglobal is the global SFR from Salim et al. (2018). Galaxies in quenched sequence, including ellipticals, S0s, and red spirals are excluded. Red spirals are quenched because of environmental effects such as ram pressure stripping or galaxy harassments (Kormendy & Bender 2012), and their spiral arms no longer influence the gas distribution. The above selection results in 7776 objects. We used the second phase of Galaxy Zoo (Willett et al. 2013; Hart et al. 2016) to identify and exclude barred and edge-on galaxies. We use the redshift bias-corrected vote fraction derived in Hart et al. (2016). We first identify edge-on galaxies as those with a debiased fraction of volunteers that voted that the galaxy is edge-on pedgeon ≥ 0.2, and exclude them. Bars can enhance central star formation and will mix possible effects from spirals if they are included. A galaxy is then classified as barred and removed if the debiased fraction of volunteers that voted that the galaxy has a bar pbar ≥ 0.2 (Skibba et al. 2012; Masters et al. 2012; Willett et al. 2013).

Under our sample selection, the bar fraction fbar reaches 53%, which is significantly higher than fbar ≈ 30% based on the votes without redshift bias correction from Galaxy Zoo (Masters et al. 2011). We verified that this higher bar fraction is due to the fact that the votes we used were redshift-debiased (Hart et al. 2016), that our sample favors massive galaxies (median log M*/M⊙ = 10.5) – which are more likely to host a bar (Erwin 2018) –, and that our sample only contains star-forming galaxies that are disks, meaning that any possible misclassification of ellipticals as disks, or vice versa, has been automatically ruled out. For galaxies not available in the catalog, we visually inspect the r band image to do the classification. To isolate the effect of spirals, we conduct a second inspection to exclude structures such as rings and tidal tails in case these features or processes associated with them may interfere with the inflow of gas driven by spirals. We exclude 26 galaxies severely contaminated by foreground stars or other galaxies, 25 tidally interacting or merger systems, 14 blue ellipticals, 66 galaxies with ring structures, 7 galaxies with peculiar morphology, and 71 more edge-on galaxies.

As some bars may be missed in the visually inspection, we used a second method to exclude them. The profiles of ellipticity (e) and position angle (PA) of isophotes (Sect. 3) are widely adopted to identify and quantify bars (Athanassoula & Misiriotis 2002; Laine et al. 2002; Erwin & Sparke 2003; Menéndez-Delmestre et al. 2007; Aguerri et al. 2009; Li et al. 2011). The e profile generally rises with increasing semi-major axis (SMA) within the bar region and then drops outside of it, and the PA correspondingly suddenly changes at the end of the bar. The difference between e of a particular isophote and the preceding one is denoted Δe and the same for PA is denoted as ΔPA. As in Menéndez-Delmestre et al. (2007), we use the criteria Δe ≥ 0.1 and |ΔPA|≥10° to search for candidates hosting a bar. The PA change does not happen if the bar aligns fortuitously with the major axis of the outer disk. If there exists any isophote presenting Δe ≥ 0.1 and |PAiso − PAdisk|≤20°, the galaxy is also taken as a candidate barred system, even if |ΔPA|< 10°. For these candidates, at each SMA that meets the criteria, we search for an isophote with a local maximum e at and before this location, and set the candidate bar SMAbar, ebar, and PAbar to the same values as those for this isophote. Only if there is a bar-like structure in the r-band image that is consistent with the candidate bar properties is it identified as real and the galaxy classified as barred. The inspection is necessary as we found that the criteria may mistakenly identify distorted spiral arms. Finally, we identify 129 barred galaxies based on the isophotal analysis and exclude them from our sample. The fbar increases to 55%. Short bars are generally weak (Elmegreen et al. 2007). If any bars are missed by Galaxy Zoo and our isophotal analysis, they must be short and weak. Their disks are dominated by spiral arms, and so the possible missing bars may have a weak effect but will not significantly affect our results.

In addition, 55 galaxies with disk ellipticity higher than 0.65 (Sect. 3) are removed to avoid severe projection effects. Excluding an additional 22 galaxies with an S/N of less than 2 (Sect. 3), the selection criterion results in 2779 galaxies, which is the parent sample probed in this work. Our unbarred spirals have a stellar mass that is 0.1 dex lower than the barred galaxies that have been excluded because more massive galaxies tend to have a higher bar fraction (Díaz-García et al. 2016; Erwin 2018). Although SDSS-based studies find a higher frequency of bars toward more massive, gas-poor, and redder galaxies (e.g., Masters et al. 2011, 2012), Erwin (2018) used higher quality images from the Spitzer Survey of Stellar Structure in Galaxies and showed that bars are as common in blue, gas-rich galaxies as they are in red, gas-poor galaxies. Our unbarred spirals therefore do not have significantly different color indices or gas richness compared to barred galaxies. The defined sample is volume-limited because of the redshift and magnitude cuts. As we are mainly interested in the spiral arm characteristics of individual galaxies rather than space densities or abundances, we refrain from applying any incompleteness corrections to the results.

We use the central SFR (SFRfiber) and stellar mass (M*, fiber) within the SDSS 3″-diameter fiber from the MPA-JHU catalog. Considering the redshift, which ranges from 0.01 to 0.05, the 3″fiber covers a physical scale of ∼ 1 to 3 kpc. The SFRfiber was estimated from the attenuation-corrected Hα luminosity for star-forming galaxies (Brinchmann et al. 2004). It traces ongoing star formation averaged over the past ∼10 Myr (Kennicutt & Evans 2012). The M*, fiber is estimated based on the dust-attenuation-corrected z-band magnitude and z-band mass-to-light ratios from a Bayesian analysis (Kauffmann et al. 2003a). The central sSFR is then calculated via sSFRfiber = SFRfiber/M*, fiber.

The SFR and M* based on ultraviolet, optical, and mid-infrared photometry from the catalog of Salim et al. (2018) are used as the measures of SFR and M* for the whole galaxy (SFRglobal and M*). The global sSFR is computed as sSFRglobal = SFRglobal/M*. A ratio of sSFRfiber to sSFRglobal is employed as a measure of relative enhancement of central star formation in Wang et al. (2012). Following the strategy of these latter authors, we define the relative central enhancement of sSFR as:

C ( sSFR ) = log ( sSFR fiber / sSFR global ) . $$ \begin{aligned} C(\mathrm{sSFR}) = \log \,(\mathrm{sSFR_{fiber}/sSFR_{global}}). \end{aligned} $$(1)

A strong Balmer absorption line occurs 0.1–1 Gyr after a burst of star formation. Its absorption line index (HδA) rises to a maximum when hot OB stars have terminated their evolution and A stars are dominated (Worthey & Ottaviani 1997; Poggianti et al. 1999, 2009; Kauffmann et al. 2003a; Dressler et al. 2004). The HδA thus probes SFR on intermediate timescales of 0.1–1 Gyr prior to observation. The 4000 Å break strength, Dn(4000), generated by a combination of metal absorption and the lack of flux from young and hot OB stars (e.g., Poggianti & Barbaro 1997; Balogh et al. 1999; Kauffmann et al. 2003a) traces the current luminosity-weighted mean stellar age; in the case of an instantaneous, solar-metallicity burst of star formation, Dn(4000) increases from ∼1 in young stellar populations with little or no metal absorption at the age of ∼10 Myr to ∼2 in old population with strong metal line absorption at the age of ∼10 Gyr (Kauffmann et al. 2003a). The Dn(4000) thus probes long-timescale star formation history.

It is worth emphasizing that we mostly relate the spiral arms occupying the extended disk to the central-most (1 − 3 kpc) diameter region of the galaxy. In Fig. 1, the comparison between the SDSS fiber size and the disk size is illustrated. In particular, the third (NSAID = 98041) and fifth (NSAID = 51966) panels, respectively, present two extreme cases with a large and small ratio of fiber size to disk size.

thumbnail Fig. 1.

Example r-band galaxy images with spiral arm strength (2 + log sarm) increasing from left to right and top to bottom. The inner circle of 3″ denotes the size of the SDSS fiber. The outer ellipse at a semi-major axis of R90 illustrates the measured mean ellipticity and PA. The ID in the NSA catalog and the arm strength are presented in the top-left corner.

3. Morphological parameters

Our analysis to quantify spiral arm structure is based on the r band cutout images from the NSA. For each galaxy, we first generate a mask of foreground stars and background or nearby galaxies, using both the automatic code Photutils photometry package4 and a manually built mask to exclude stars inside the galaxy that Photutils may have missed. Instead of using the sky background-subtracted image from the NSA directly, we calculate the residual background by averaging the flux over the region in which the intensity profile becomes flat and subtract this value from the NSA r-band cutout images to produce the sky-subtracted image used in this work. We run the IRAF task ellipse with an exponential step of 0.1 to extract isophotes of the galaxy light and then obtain radial profiles of ellipticity e and PA of the isophotes.

We adopt two methods to estimate the average e and PA of the disk (Yu et al. 2018; Yu & Ho 2019, 2020). A combination of incorrect e and PA will cause the round disk to resemble an oval on its face-on viewing angle. The first method is based on the radial profiles of e and PA. The adopted average e and PA for a galaxy is set to the average value over the region where the disk component dominates. This method fails if the disk hosts two prominent spiral arms that extend to the outskirts of the galaxy, resulting in continuously varying e and PA without convergence. In this case, we employ the alternative method, which performs a two-dimensional Fourier transformation of the disk component for a number of groups of e and PA, and then search for a set of parameters that minimize the real part of the m = 2 Fourier spectra at a radial wavenumber of zero (see Grosbøl et al. 2004; Yu & Ho 2020, for more details). We apply the two methods to all galaxies and determine the optimal e and PA for each galaxy by giving preference to that which yields a rounder disk with more logarithmic-shaped spiral arms in the image of their face-on viewing angle. Elliptical apertures with the derived average e and PA are applied to calculate the R20, R50 (effective radius), R80, and R90, which encloses 20%, 50%, 80%, and 90% of the total flux, respectively. We find that 96% of galaxies have spatially resolved R20 ( R 20 > 1 . ″ 4 $ R_{20} > 1{{\overset{\prime\prime}{.}}}4 $); and 20%, 50%, and 80% of galaxies have a SDSS fiber radius of less than 5%, 8%, and 10% of the R90, respectively. The measured e, PA, and R90 for eight example galaxies are illustrated by the outer ellipses in Fig. 1. The galaxy light concentration is defined as C = 5 × log(R80/R20) (Conselice 2003). The stellar surface density is then derived via log ⁡ μ ∗ = log ⁡ ( M ∗ / π R 50 2 ) $ \log\upmu_*=\log (M_*/\pi R^2_{50}) $.

The strength of spiral arms is one of the most fundamental properties of spirals. The two most widely adopted methods to quantify the arm strength are (1) to compute the amplitude of Fourier components relative to the axisymmetric disk (Elmegreen et al. 1989, 2011; Laurikainen et al. 2004; Rix & Zaritsky 1995; Grosbøl et al. 2004; Durbala et al. 2009; Baba 2015; Kendall et al. 2011, 2015; Yu et al. 2018; Yu & Ho 2020), and (2) to choose the arm and interarm region and compare their surface brightnesses (Elmegreen & Elmegreen 1985; Buta et al. 2009; Salo et al. 2010; Elmegreen et al. 2011; Bittner et al. 2017). We make use of the Fourier analysis because of its automatic feature with high efficiency. There are 856 galaxies overlapped with the sample in Yu & Ho (2020), and the measurements for these galaxies are directly acquired from their work. For the rest of the galaxies, we follow the procedure described in Yu et al. (2018) and Yu & Ho (2020) to quantify spiral arms.

We first run ellipse with fixed e and PA determined above with a linear step of R90/30. The intensity distribution, I(r, θ), as a function of azimuthal angle (θ) for an isophote at radius r is extracted and then fitted with a Fourier series following

I ( r , θ ) = I m = 0 ( r ) + ∑ m = 1 6 I m ( r ) cos m ( θ + ϕ m ) , $$ \begin{aligned} I(r, \theta ) = I_{m=0}(r) + \sum _{m=1}^{6} I_{m}(r) \cos m(\theta + \phi _{m}), \end{aligned} $$(2)

where Im and ϕm are the amplitude and phase angle of the mth Fourier component, respectively. In particular, the Im = 0 denotes the axisymmetric disk component. The relative Fourier amplitude is defined as

A m ( r ) = I m ( r ) I 0 . $$ \begin{aligned} A_m(r) = \frac{I_m(r)}{I_0}. \end{aligned} $$(3)

A1 is a measure of galaxy lopsidedness (e.g., Rix & Zaritsky 1995; Reichard et al. 2008) and A2 indicates the strength of spiral arms in grand-design galaxies (e.g., Grosbøl et al. 2004; Elmegreen et al. 2011; Kendall et al. 2011). A3 and A4 reflect the arm strength in multiple-armed or flocculent galaxies (Yu et al. 2018). Higher order modes are not included to avoid the influence of noise. The average relative spiral arm amplitude is therefore defined as the average value of a quadratic sum of the relative amplitude of m = 2, 3, and 4 modes:

s arm = A 2 2 + A 3 2 + A 4 2 , $$ \begin{aligned} s_{\rm arm}=\sqrt{A_2^2+A_3^2+A_4^2}, \end{aligned} $$(4)

over the region occupied by spiral arms. For galaxies with small bulges (C ≤ 3.5), the inner boundary of spiral arms is set to 0.2 R90. In contrast, for galaxies with large bulges (C <  3.5), it is set to a radius where the ellipticity profile drops to e − 0.05, corresponding to the bulge size. Δe = 0.05 is generally small enough. In any case, a minimum inner boundary of 0.2 R90 is applied especially for nearly face-on galaxies. The outer boundary is set as R90, which encloses the majority of the spiral structure at optical wavelengths as shown by the blue ellipse in Fig. 1. Although the relative Fourier amplitude may vary with radius, the uncertainty in calculating arm strength from choosing radial extent is less than 10% (Yu et al. 2018), and thus hardly affects the relationships probed with arm strength (Yu et al. 2021). As the relation between arm amplitude and SFR is highly nonlinear, use of the logarithmic format of the average relative amplitude, log sarm, as the strength of spiral arms is advised (Yu et al. 2021). We further add a constant of 2, which gives 2 + log sarm, in order to make the value greater than zero in this work.

The S/N is defined as the value of average pixel flux between R50 and R90 divided by the sky background Poisson noise. Poisson noise from the sky background causes the spiral arm strength to be systematically overestimated when the S/N is sufficiently low, because the contribution from noise to the Fourier decomposition becomes significant. Yu et al. (2021) studied the noise-induced bias as a function of S/N based on SDSS r band images. We thus correct the bias in our measured spiral arm strength using the result in Yu et al. (2021). In the remainder of the present paper, we refer to the noise-debiased spiral arm strength as simply the spiral arm strength.

We quantify spiral arms in the r band images. A question may arise as to whether or not the Hα emission from star formation regions along the spiral arm in the r band causes severe overestimation in the arm strength. It is found that the arm strength measured in the maps of emission from old stars derived based on the 3.6 μm and 4.5 μm flux from the Spitzer Survey of Stellar Structure in Galaxies (Querejeta et al. 2015) is in good agreement with that in the R band, a bandpass close the r band (Yu et al. 2021). Comparing to the i band, where the Hα emission is free, the r-band strength is only 3% higher (0.015 dex stronger in its logarithm; Yu et al. 2021). These results suggest that the spiral arm strength based on r band images is not significantly affected by Hα emission. Examples of eight galaxies with increasing spiral arm strength from left to right and top to bottom are shown in Fig. 1.

4. Results

We study relationships between spiral arm strength and central star formation history to investigate the possible impact of spiral arms on secular evolution. As spiral arm strength (Yu & Ho 2020; Yu et al. 2021) and central star formation history (Kauffmann et al. 2003b; Brinchmann et al. 2004) are separately correlated with other galaxy structural parameters, we performed an analysis with a control sample to isolate the spiral effect. We used the Pearson correlation coefficient to analyze these relationships. The Pearson correlation coefficient measures the strength of the linear monotonic correlation between two sets of data. In contrast, Spearman’s correlation assesses monotonic relationships, regardless of whether they are linear or not. We calculated the Spearman’s correlation coefficients and found them to be virtually indistinguishable from the Pearson correlation coefficients. As the difference is small and linearity is the first-order approximation of any nonlinear relation, we used the Pearson correlation coefficient throughout this work.

4.1. Dependence on central star formation properties

Figure 2a presents the correlation between spiral arm strength and sSFRfiber. There is a clear bimodal distribution in sSFRfiber with two peaks at ∼ − 12 and ∼ − 10, although these galaxies are star-forming as a whole. We illustrate the distribution in Figure 2b. Our analysis lacks galaxies with sSFRfiber below −12.5 because of the detection limit of central sSFR derived from the SDSS spectra (Brinchmann et al. 2004). The lower value peak in the bimodal distribution suggests that these galaxy centers are quenched (e.g., Kauffmann et al. 2003a; Brinchmann et al. 2004; Luo et al. 2020), which may be caused by inside-out quenching via AGN feedback or morphological or gravitational quenching (Martig et al. 2009). AGN feedback transfers radiation to the surrounding gas to suppress gas accretion (Di Matteo et al. 2005) or kinetic energy and momentum to cause expulsion of gas (Croton et al. 2006). Morphological or gravitational quenching proposes that the growth of stellar spheroids stabilizes the gaseous disk to prevent the formation of bound, star-forming gas clumps (Martig et al. 2009). We find that 25% of the SFMS galaxies of our sample are centrally quenched. In order to avoid any possible influence of these quenching processes on the spiral effect investigated in this work, we separated our sample into two subsamples, 2056 centrally star-forming galaxies and 723 centrally quenched galaxies, according to the valley (log(sSFRfiber/yr−1) = −11.3) of the bimodal distribution, which is marked by the horizon solid line in Fig. 2. We focus on the centrally star-forming galaxies in the rest of this section and come back to the centrally quenched galaxies to discuss bulge types in Sect. 5. A moderate trend of increasing logsSFRfiber with stronger spiral arms occurs, with a Pearson correlation coefficient of ρ = 0.28 and a p value of less than 0.01 (row [1] of Table 1). We consider correlations with coefficients of above 0.4 to be relatively strong. Correlations with coefficients of between 0.2 and 0.4 are considered moderate. Correlations with coefficients of below 0.2 are considered weak.

thumbnail Fig. 2.

Dependence of central sSFR (sSFRfiber) on strength of spiral arms (2 + log sarm). Panel a: the scatter plot of the two parameters. Panel b: shows the number distribution of sSFRfiber. The solid horizon line (logsSFRfiber = −11.3) marks the valley of the number distribution, separating the sample into centrally star-forming and centrally quenched SFMS galaxies. The Pearson correlation coefficient between sSFRfiber and 2 + log sarm is denoted at the top.

Table 1.

Correlation analysis.

Figure 3a presents the connection between spiral arm strength and Dn(4000). The Dn(4000) parameter is extracted from the SDSS 3″-diameter spectra of the galaxy center. As the data points are too crowded to evaluate the data distribution, we do not draw a scatter plot but bin the data and color the bins according to the number of galaxies in each bin. Galaxies with stronger spiral arms tend to have lower Dn(4000), with a Pearson correlation coefficient of ρ = −0.25 and a p value of less than 0.01 (row [6] in Table 1). The Dn(4000) for strong spiral arms could reach ∼1.1, corresponding to very young stellar populations in the centers.

thumbnail Fig. 3.

Dependence of central SFR indicators on spiral arm strength (2 + log sarm). Panels a–c: plot the Dn(4000), HδA, and C(sSFR) against arm strength, respectively. The bin color encodes the number of galaxies in each bin, scaled by the color bar next to the panel. The Pearson correlation coefficient and the corresponding p value are denoted at the top. The confidence ellipses are obtained using the PCA technique described in the text, and they contain approximately 95% of the data. As these ellipses could be distorted due to the different dynamical ranges of the x and y axes, a best-fitted straight line indicating the direction of main principal component is plotted.

In each panel of Fig. 3, the 2σ confidence ellipse approximately marks the regions containing ∼95% of the data. The ellipses are oriented in the direction of maximal variance of the data points, which is denoted by the dashed straight line. These ellipses are obtained using principal component analysis (PCA), which describes the data using a new set of orthonormal bases – the principal components – that successively maximize variance. The orientation of the ellipse and the slope of the straight lines are determined by the direction of the eigenvector with the largest eigenvalue, along which the data show maximum variance in the diagram. The semi-major and semi-minor axes of the ellipse are the root of the larger eigenvalue and smaller eigenvalue, respectively, of the covariance matrix of the data. Therefore, the straight line is the best-fitted linear relation between the two parameters.

Figure 3b plots the HδA as a function of spiral arm strength. The HδA parameter is obtained from the SDSS 3″-diameter spectra of the galaxy center. There is a correlation, with HδA rising from near −1 for weak arms to 7 for strong arms. The Pearson correlation coefficient gives ρ = 0.2 with a p value of less than 0.01 (row [11] in Table 1). The HδA of a few galaxies can even reach a value higher than 7, which can only originate ∼0.1 to 1 Gyr after a star formation burst. However, the connection between HδA and arm strength is only moderate, which is indicated by the low correlation coefficient, meaning that the very high HδA cannot be attributed to the spiral effect.

Yu et al. (2021) report a correlation between spiral arm strength and global sSFR (see also Seigar & James 2002; Kendall et al. 2015), which is likely due to an intertwining process where the shock of spiral arms triggers star formation in the cold gas reservoir, which in turn maintains the arms through gas damping. The C(sSFR) (Eq. (1)), a ratio of fiber sSFR to global sSFR, reflects the relative enhancement of central star formation (Wang et al. 2012, 2020). To test whether or not the correlation between spiral arm strength and central star formation is simply driven by global star formation, we plotted C(sSFR) against arm strength; see Fig. 3c. Likewise, we detect a positive trend that galaxies with stronger spiral arms tend to have higher C(sSFR), that is, more intense central star formation relative to that measured for the whole galaxy (Pearson correlation coefficient ρ = 0.19 with p <  0.01; row [16] in Table 1). Therefore, the spiral arm strength positively correlates with both short-, long-timescale central SFRs and relative central SFR enhancement, with Pearson correlation coefficients ρ ranging from 0.19 to 0.28 and p values < 0.01, suggesting that these relationships are moderate but statistically significant. Our results suggest that spiral arms may play a role in enhancing central star formation.

4.2. Analysis with a control sample

Above, we present results suggesting a dependence of central star formation history on spiral arm strength. However, both the spiral arms and central star formation history correlate with other galaxy structural parameters. Yu & Ho (2020) showed that spiral arms become weaker in earlier-type, more centrally concentrated galaxies. For a given concentration, spiral arms are stronger in more massive galaxies. Kauffmann et al. (2003a,b) showed that galaxy centers are, on average, younger in galaxies with lower mass, surface density, and concentration. These results may lead to an indirect relationship without causality between spiral arm strength and central star formation history. For the sake of establishing a true causal relationship, it is essential to demonstrate that this relationship does not result from the known correlations with stellar mass (log M*), stellar surface density (logμ*), and concentration (C).

One possible concern with using the fixed 3″-diameter aperture of the SDSS fiber is that this size corresponds to a larger physical scale for galaxies at high redshift than those at low redshift. In particular, the 3″ indicates ∼3 kpc at z = 0.05, while it indicates ∼0.6 kpc at z  =  0.01. The fiber could include disk components of galaxies at high redshift and may cause the central star formation history to be biased toward the younger population compared with galaxies at low redshift. The redshift effect therefore needs to be removed when studying the spiral effect. In addition, the physical size (log R50) of disk galaxies can vary by 0.3–0.5 dex at fixed stellar mass according to the mass–size relation (e.g., Shen et al. 2003), which may introduce an aperture effect similar to that induced by redshift. The third and fifth panels of Fig. 1 illustrate the joint effect of redshift and size. The galaxy NSAID = 98041 has z = 0.042 and R50 = 3.2 kpc, and has very large relative fiber aperture (the inner circle). In contrast, the galaxy NSAID = 51966 has z = 0.017 and R50 = 10.9 kpc, and has very small relative fiber aperture. As the size is implicitly involved in logμ* and C, the size effect has already been considered if log M*, logμ*, and C are simultaneously controlled. Nevertheless, we remove the size effect to avoid the possible biases described above.

We perform an analysis using a control sample to isolate the effect of spiral arms. We first define a strong-armed sample with galaxies with spiral arm strengths that occupy the top 20% of the sample of centrally star-forming SFMS galaxies (2 + log sarm ≥ 1.44). The remaining galaxies make up the temporary weak-armed sample (2 + log sarm <  1.44). For each galaxy in the strong-armed sample, we then randomly find within the temporary weak-armed sample a galaxy with almost the same log M*, logμ*, C, and z. The matching criterion follows |Δlogμ*|≤0.1, |Δlog M*|≤0.1, |ΔC|≤0.1, |Δz|≤0.005, and |Δlog R50|≤0.1. If such a galaxy is not found, the strong-armed galaxy is also removed from the strong-armed sample. These newly selected galaxies constitute the control sample, which we refer to as the control weak-armed sample. The strong-armed sample and control weak-armed sample each have 482 objects.

In Fig. 4, we compare the number distribution of log M* in panel (a), logμ* in panel (b), C in panel (c), z in panel (d), and log R50 in panel (e) for the strong-armed sample marked in blue, and the control weak-armed sample marked in gray. For the two distributions in each panel, a two-sample Kolmogorov–Smirnov test gives p values of 0.89, 0.93, 0.89, 0.7, and 0.95 respectively. We cannot therefore reject the null hypothesis that the two samples are drawn from the same parent distribution. In other words, the strong-armed sample and the control weak-armed sample are almost twins concerning z, log M*, logμ*, and C, which, in turn, validates our procedure for generating the control sample.

thumbnail Fig. 4.

Distribution of the parameters used to construct the control sample. Panels a–d: show the distribution of stellar surface density (logμ*), stellar mass (log M*), concentration (C), redshift (z), and effective radius (log R50), respectively. Results for galaxies with strong spiral arms (2 + log sarm ≥ 1.44) are marked in blue histogram, and the same for the control sample with weak spiral arms (2 + log sarm <  1.44) are marked in gray filled histogram. The p value of the Kolmogorov–Smirnov test is presented at the top of each panel.

Panels (a)–(d) of Fig. 5, respectively, show comparisons of the number distribution of log(sSFRfiber), C(sSFR), Dn(4000), and HδA for the strong-armed sample marked in blue, and the control weak-armed sample marked in gray. The p values of Kolmogorov–Smirnov tests for the two samples and the mean difference between the two parameters are denoted at the top of each panel. The p values are all less than 0.01, suggesting that we can reject the null hypothesis that the two samples are drawn from the same parent distribution. The galaxies with strong arms have, on average, 0.4 dex higher log(sSFRfiber), 0.2 dex higher C(sSFR), −0.1 lower Dn(4000), and 1.0 higher HδA than those with weak arms, even after the z, log M*, logμ*, and C have been controlled.

thumbnail Fig. 5.

Distribution of central SFR indicators for galaxies with strong arms and the control sample with weak arms. Panels a–d: show the result of sSFRfiber, C(sSFR), Dn(4000), and HδA, respectively. The distributions for strong-armed galaxies are marked in blue, and the same for the control weak-armed sample are marked in gray. The mean difference between the two distributions and p values from the Kolmogorov–Smirnov test are presented at the top of each panel.

4.3. Partial correlation coefficients

The control experiment demonstrates that the dependence of central star formation on spiral arm strength is intrinsic. The arm strength–central star formation relation may be driven to some extent by the other parameters, or, conversely, diluted. In order to estimate the true strength of the relationships and to make our results statistically more robust, we compute partial correlation coefficients using Python package pingouin (Vallat 2018) based on an inverse covariance matrix and present the results in Table 1. We first separately remove the mutual dependence on log M*, logμ*, and C one by one (z is always included to take into account the nonphysical aperture effect) to calculate the residual dependence of log(sSFRfiber), C(sSFR), Dn(4000), and HδA on arm strength. We did not include log R50 as it is already involved in the definition of logμ* and C. The resulting partial correlation coefficients (rows [2]–[4], [7]–[9], [12]–[14], [17]–[19] in Table 1) are ∼0.01 to 0.08 stronger than the original correlation coefficients (rows [1], [6], [11], [16]). We then simultaneously remove the effects of z, log R50, log M*, logμ*, and C, and find that the resulting partial correlation coefficients increase to 0.39, −0.38, 0.35, and 0.26 with p values < 0.01 (rows [5], [10], [15], [20]). These results are in agreement with the result of the control sample analysis in Fig. 5, namely that neither z, nor log M*, logμ*, or C can explain the connection between arm strength and central star formation. Furthermore, the four parameters dilute the observed relations for spiral arms.

4.4. Spirals induce continuous central star formation

We find more intense ongoing SFRs in the centers of galaxies with stronger spiral arms, and this trend is not driven by other galaxy parameters. To understand if the spiral arms are powerful enough to trigger a central starburst, we define galaxies with log (sSFR/yr−1)≥ − 9 , which corresponds to a mass-doubling time of 1 Gyr, as central starburst galaxies. We thus have 47 central starburst galaxies. The arm strengths 2 + log sarm = 1.03 and 1.64 are respectively critical values containing the bottom and top 5% of the arm strengths in the sample of 2056 centrally star-forming SFMS galaxies. The spiral arm strength of these starburst galaxies spreads over a wide dynamical range (Fig. 2). Four central starburst galaxies have very weak spiral arms (< 1.03). In contrast, ten central starburst galaxies have very strong spiral arms (> 1.64). Likewise, only ∼10% of very strong spiral arms are central starburst galaxies. The wide distribution of arm strength suggests that having a normal (noninteracting) strong spiral arm is neither a sufficient nor a necessary condition to form a central starburst, although we do detect a weak trend in that spiral arms in central starburst galaxies tend to be stronger.

We then investigated the connection between spiral arms and their central post-starburst properties. The combination of Dn(4000) and HδA can be used to identify galaxies that have experienced a burst of star formation ∼1 Gyr prior to the current observation (Kauffmann et al. 2003a). Figure 6a probes HδA plotted as a function of Dn(4000), where the color associated with each data point encodes the average arm strength of its surrounding galaxies within a box of |ΔHδA|≤0.5 and |ΔDn(4000)| ≤ 0.05. Consistent with Fig. 3, HδA increases and Dn(4000) decreases with stronger spiral arms. The curves in Fig. 6a show evolution tracks obtained using the GALAXEV stellar population synthesis code (Bruzual & Charlot 2003) with the provided simple stellar population model of metallicity Z = 0.019 and a Chabrier (2003) initial mass function. Dashed and solid curves are for an instantaneous burst of star formation and continuous star formation that declines exponentially with time with a characteristic timescale of 4 Gyr. For the continuous star formation history, HδA decreases with increasing Dn(4000) following a nearly linear relation. For the burst of star formation, HδA quickly reaches a peak before ∼1 Gyr, beyond which it drops down quickly, while Dn(4000) increases gradually with time. The way that HδA and Dn(4000) respond differently results in a curve in the diagram showing Dn(4000)–HδA where HδA first increases steeply and peaks at HδA ≈ 10 with Dn(4000)≈1.3, before decreasing. If spiral arms can trigger a central burst of star formation overlapped with the existing continuous star formation, the burst will add more HδA with less contribution to Dn(4000) in ∼ 1 Gyr. In this case, we expect a trend whereby higher HδA is associated with stronger spiral arms for a given Dn(4000). However, no such trend is apparent in Fig. 6a.

thumbnail Fig. 6.

HδA plotted as a function of Dn(4000) and spiral arm strength (2 + log sarm). Panels a: the color associated with each data point encodes the average arm strength of the surrounding galaxies with |Δx|≤0.05 and |Δy|≤0.5 (the box is illustrated in the bottom-left corner). The curves show evolution tracks obtained using the GALAXEV stellar population synthesis code (Bruzual & Charlot 2003) with the provided simple stellar population model of a metallicity Z = 0.019 and a Chabrier (2003) initial mass function. Dashed and solid curves respectively show results for an instantaneous burst of star formation and continuous star formation that declines exponentially with time with a characteristic timescale of 4 Gyr. Panel b: the color encodes the different narrow ranges of Dn(4000). The typical scatter in HδA at a given 2 + log sarm and a given Dn(4000) is illustrated in the bottom-left corner.

In Fig. 6b, we plot the HδA as a function of arm strength for several bins of Dn(4000). We only detect a very weak positive trend in the narrow range of 1.3 <  Dn(4000)< 1.5 with a Pearson correlation coefficient of ρ = 0.08 and a p value =0.01. The trends in other narrow ranges of Dn(4000) have overly high p values and are therefore not statistically significant. By removing any mutual dependence on Dn(4000), the partial correlation coefficient between HδA and arm strength gives ρ = 0.02 with a p value =0.45, suggesting that this residual relation does not exist. These results imply that the central star formation related to spiral arms is likely continuous instead of bursty.

5. Discussion

5.1. Gas inflow driven by spiral arms

Secular evolution triggered by disk instabilities is essential to explain the growth of pseudo bulges. Bars and spirals are the most common nonaxisymmetric structures in disk galaxies. Bar-driven instability plays a vital role (Kormendy & Kennicutt 2004). Bars drive the gas in the galactic disk, outward to form a ring and inward to the galaxy centers (Athanassoula 1992; Sellwood & Wilkinson 1993; Patsis & Athanassoula 2000; Regan & Teuben 2004; Combes 2008; Haan et al. 2009; Kim et al. 2012; Combes et al. 2014; Sormani et al. 2015; Prieto et al. 2005). Many observational studies have reported gas inflow caused by bars and associated enhanced central star formation (e.g., Sheth et al. 2005; Regan et al. 2006; Wang et al. 2012, 2020; Lin et al. 2017; Chown et al. 2019; Díaz-García et al. 2020, 2021). In particular, Wang et al. (2012, 2020) used a ratio of fiber sSFR to global sSFR to study the bar effect and found enhancement of central star formation in strongly barred galaxies.

Spiral-driven instabilities are involved in the secular evolution processes. Both in theory (Roberts 1969; Kalnajs 1972; Roberts & Shu 1972; Lubow et al. 1986; Hopkins & Quataert 2011) and simulations (Kim & Kim 2014; Kim et al. 2014, 2020; Baba et al. 2016), spiral arms can induce a shock on gas clouds and drive inflow of gas clouds. Observational evidence supporting the spiral-shock picture has been found. By studying the molecular gas surface density contrasts of 67 star-forming galaxies in the PHANGS-ALMA CO (2–1) survey, Meidt et al. (2021) find that the logarithmic CO contrasts on 150 pc scales are higher than the logarithmic 3.6 μm contrasts in a correlation that is steeper than linear even in the presence of weak or flocculent spiral arms, in agreement with the compression of gas by shocks. The spiral shock could also explain the high number density and mass in the mass spectrum of gas clouds along the arms (Colombo et al. 2014), the shorter gas depletion associated with arms (Rebolledo et al. 2012, but see Foyle et al. 2010), the enhanced global sSFR in strongly armed galaxies (Seigar & James 2002; Kendall et al. 2015; Yu et al. 2021), and the offset in the pitch angle of different tracers (Yu & Ho 2018; Martínez-García et al. 2014; Egusa et al. 2009), although the turbulence and streaming motions in the dense gas reservoir prevent cloud collapse and curtail star formation efficiency (Meidt et al. 2013; Leroy et al. 2017). The relative position, morphology, and kinematics of gaseous and stellar mass in the Milky Way are consistent with models based on the spiral shock (Sakai et al. 2015; Hao et al. 2021). Signatures supporting the inflow of gas driven by spiral arms have been detected, although a small sample size limits these studies. Regan et al. (2006) found that two out of six unbarred spiral galaxies have central excess in the 8 μm and CO emission above the inward extrapolation of an exponential disk. Some unbarred galaxies could have high concentrations of gas, despite being less common than in barred galaxies (Sheth et al. 2005; Komugi et al. 2008). The lower frequency of highly concentrated gas distributions in unbarred spiral galaxies than in barred galaxies may result from the stronger effect of the bar than the spiral. Although simulations comparing the inflow rates driven by bars and spirals are lacking, we may obtain some clues from the statistics of bar and spiral strength. By using arm to interarm contrast, gravitational torque, or Fourier amplitude as a measure of the strength of bars and spirals, it has been shown that bars in barred galaxies are stronger on average than spirals in unbarred galaxies (Buta et al. 2005; Durbala et al. 2009; Bittner et al. 2017). Although the arms may be weaker than bars, and they occupy different radial regions, it is possible that in barred galaxies, arms firstly deliver the gas to the radial range within the bar, which successively drives the gas flow toward the center. This joint effect was highlighted in Wang et al. (2020). Our results suggest that the spiral effect is statistically significant and is thus indispensable for understanding galaxy secular evolution. Future investigations of the influence of the properties of sprial arms on the radial distribution of cold gas with large samples would be worthwhile.

5.2. Implication on secular growth of pseudo bulges

Subsequent star formation followed by gas inflow driven by disk instabilities leads to the growth of central pseudo bulges (Kormendy & Kennicutt 2004). We show in Sect. 4 that spiral arms enhance the central SFR on both short and long timescales in a continuous manner, implying spiral arms may also play a role in the secular growth of pseudo bulges.

Recently, Luo et al. (2020) studied the relative central stellar-mass surface density within 1 kpc (ΔΣ1) and found that classical bulges have high ΔΣ1 (logΣ1 ≥ 0), while pseudo bulges have low ΔΣ1 (logΣ1 <  0). This method to classify bulge types is in line with that based on the Kormendy relation. In order to investigate the spiral effect, we cross-matched our parent sample (including both centrally star-forming and centrally quenched SFMS galaxies) with the sample in Luo et al. (2020) and find 1738 objects in common. Figure 7 compares the ΔΣ1 with arm strength. There is a moderate trend that galaxies with stronger spiral arms tend to have lower ΔΣ1, with a Pearson correlation coefficient of ρ = −0.30 and a p value < 0.01 (row [23] in Table 1). This suggests that galaxies with strong spiral arms tend to have a pseudo bulge in their center.

thumbnail Fig. 7.

Dependence of relative central surface density (ΔΣ1) on spiral arm strength (2 + log sarm). The bin color encodes the galaxy number in each bin. Σ1 is the stellar surface density within the central 1 kpc, while the log ΔΣ1 is calculated via log ΔΣ1 = logΣ1 + 0.275(log M*)2 − 6.445log M* + 28.059, which can be used to distinguish pseudo bulges (log ΔΣ1 <  0) from classical bulges (log ΔΣ1 ≥ 0). The Pearson correlation coefficient is denoted at the top.

The galaxy concentration index C directly reflects the global shape of the surface brightness profile. The larger the bulge relative to the disk (higher bulge fraction), the more prominent the central profile, and the higher C. The quantity ΔΣ1 measures bulge density (thus classical versus pseudo bulges) rather than the bulge fraction, despite the existence of a relation between ΔΣ1 and bulge fraction. The light fraction of a pseudo bulge could be larger than that of a classical bulge (Gadotti 2009; Gao et al. 2020).

The connection between arm strength and ΔΣ1 arises partly due to the classical bulge if this latter weakens the arms. Indeed, a larger classical bulge will decrease the mass fraction of a dynamically active disk to suppress the spiral arms (Bertin et al. 1989), resulting in a trend of increasing concentration with weakening spiral arms (Yu & Ho 2020). We find a similar trend with ρ = −0.23 and p <  0.01 (row [24] in Table 1). Meanwhile, classical bulges tend to reside in more massive galaxies (Luo et al. 2020). When studying the actual dependence of pseudo bulges on spiral arm strength, one needs to control the suppression effect on spiral arms caused by the classical bulge, the significance of which is properly indicated by its bulge fraction (concentration index) and the galaxy stellar mass. We therefore calculated the partial correlation coefficient between arm strength and ΔΣ1 by removing their mutual dependence on log M* and C, yielding ρ = −0.19 with a p value < 0.01 (row [25] in Table 1). The arm strength –ΔΣ1 relation becomes weaker but remains significant after the log M* and C are controlled, and therefore this relation is likely in part driven by suppression of the arms by classical bulges and in part by central star formation triggered by spiral arms.

When the sample is regrouped into pseudo bulges (log ΔΣ1 <  0) and classical bulges (log ΔΣ1 ≥ 0), the correlations between ΔΣ1 and arm strength become much shallower (ρ = −0.06, p = 0.08 >  0.05 for pseudo bulges; ρ = −0.17, p <  0.01 for classical bulges.), perhaps because of the small dynamic range in ΔΣ1 in each subgroup. However, in the subgroup of galaxies hosting pseudo bulges, we detect a positive concentration-arm strength relation (row [28] in Table 1), rather than the suppression of spirals by classical bulges. In galaxies with pseudo bulges, stronger spiral arms tend to have higher galaxy concentration (ρ = 0.11, p <  0.01) for a given log ΔΣ1 and log M*. The concentration of galaxies hosting pseudo bulges is possibly elevated by the larger pseudo bulges, as classical bulges are not included. Consistent with the arm suppression, galaxies hosting classical bulges present a weak inverse correlation with ρ = −0.08 and p = 0.03 (row [29] in Table 1). In Fig. 8, we plot the distribution of C for the strong-armed sample and control sample, which have similar ΔΣ1 and M* (|Δlog M*|≤0.1 and |ΔlogΣ1|≤0.1). For galaxies with pseudo bulges, the strong-armed sample on average has 0.09 higher C than the control weak-armed sample. For those with classical bulges, the C of the strong-armed sample is on average 0.12 lower, although the p-value is greater than 0.05. Our results suggest that spiral arms may help build and grow the pseudo bulges.

thumbnail Fig. 8.

Distribution of concentration index (C) of galaxies with pseudo bulges and those with classical bulges. The blue unfilled and gray filled histograms show results for the strong-armed sample and control weak-armed sample. The mean difference between the two distributions and p values from the Kolmogorov–Smirnov test are presented at the top of each panel.

To shed more light on how spiral arms and bulge types influence each other, we follow the strategy in Luo et al. (2020) to classify 798 pseudo bulges (log ΔΣ1 <  0 and Dn(4000)< 1.6), 369 star-forming classical bulges (log ΔΣ1 ≥ 0 and Dn(4000)< 1.6), and 429 quenched classical bulges (log ΔΣ1 ≥ 0 & Dn(4000)≥1.6). Figure 9 presents C versus M* for the three bulge types. Galaxies with pseudo bulges tend to be less massive and less concentrated. Galaxies with star-forming classical bulges span a relatively wide range. Galaxies with quenched classical bulges tend to have higher mass and be more highly concentrated. In Fig. 10, we illustrate the distribution of arm strength for galaxies hosting pseudo bulges, classical bulges, star-forming classical bulges, and quenched classical bulges. Spiral arms associated with a pseudo bulge tend to be stronger than those with a classical bulge. In the classical bulge population, galaxies with star-forming classical bulges tend to have stronger arms than with quenched classical bulges. Similar behavior can be seen in Fig. 11: the fraction of galaxies hosting pseudo bulges increases with increasing arm strength, while the fraction of classical bulges decreases with increasing arm strength. In the classical bulge population, the fraction of galaxies hosting quenched classical bulges decreases with increasing arm strength, while the fraction of star-forming classical bulges remains relatively unchanged. Classical bulges associated with strong spiral arms (2 + log sarm >  1.35) tend to be star forming.

thumbnail Fig. 9.

Concentration index (C) plotted as a function of galaxy stellar mass (log M*/M⊙) for galaxies with pseudo bulges (blue), star-forming classical bulges (green), and quenched classical bulges (red). The histograms above and to the right show the number distribution of log M*/M⊙ and C, respectively.

thumbnail Fig. 10.

Number distribution of pseudo bulges (blue), classical bulges (black), star-forming classical bulges (green), and quenched classical bulges (red).

thumbnail Fig. 11.

Fraction of galaxies hosting pseudo bulges (blue), classical bulges (black), star-forming classical bulges (green), and quenched classical bulges (red) as a function of spiral arm strength (2 + log sarm).

Classical bulges form through rapid processes of violent relaxation or gaseous dissipation at an early epoch. One proposed scenario is that major mergers provide violent relaxation of preexisting stars and drive rapid gas inflow to trigger central starbursts, resulting in a highly concentrated bulge of randomly moving stars (Hopkins et al. 2009a, 2009b, 2010; Brooks & Christensen 2016; Tonini et al. 2016; Rodriguez-Gomez et al. 2017). Minor mergers play a lesser role in the formation or growth of classical bulges (Aguerri et al. 2001; Eliche-Moral et al. 2006; Hopkins et al. 2010). A second scenario is that gas-rich disks at high redshift are highly turbulent and have giant star-forming clumps formed by gravitational instabilities (Elmegreen & Elmegreen 2005); the bound clumps interact, lose angular momentum, and migrate to the center to form a classical bulge (Noguchi 1999; Bournaud et al. 2007, 2009; Elmegreen et al. 2008; Bournaud 2016). During the coalescence of massive disk clumps and in major mergers, a similar behavior is seen in terms of orbital mixing.

At later stages, there are enough hot stars in a thick disk and bulges arising from the previous stages so that gravitational instabilities produce spirals rather than clumps (Bournaud et al. 2009). The spiral structure in the disks then occurs at 1.4 ≲ z ≲ 1.8, when disks settle down at the point where rotation motion dominates over turbulent motions in the gas and massive clumps become less frequent (Elmegreen & Elmegreen 2014). The onset of spiral arms follows a morphological transformation sequence from clumps to “woolly arms”, to irregular long arms, and finally to normal spiral structure (Elmegreen & Elmegreen 2014). The pre-existing classical bulges and their associated thick hot disks influence the development of spiral structure by reducing the mass fraction of the dynamically active disk that reacts to spiral perturbation (Bertin et al. 1989). Thus, the galaxies with prominent classical bulges have weak spiral arms (Yu & Ho 2020). A fraction of massive star-forming galaxies started inside-out quenching at z ∼ 2 (Tacchella et al. 2015, 2018). In the nearby Universe, more massive galaxies exhibit a greater fraction of inside-out quenching compared to less massive ones in all environments, which may be explained by the morphological quenching (Lin et al. 2019). Perhaps consistent with the inside-out quenching, galaxies with quenched classical bulges have higher mass and higher concentration than galaxies with star-forming classical bulges (Fig. 9). The influence of classical bulges on spiral arms in part explains the correlation between bulge types and arm strength, but not entirely, because a residual interdependence between arm strength and bulge type indicator was detected after removing effects of bulge fraction (concentration index) and galaxy mass (row [24] in Table 1).

Bars appear at about z ∼ 1 (Sheth et al. 2008) and drive secular evolution (Kormendy & Kennicutt 2004). The two-dimensional multi-component decomposition shows that the bulges of barred galaxies do not have a different Kormendy relation from unbarred galaxies (Gao et al. 2020). Likewise, there is no difference in the relationships between relative central surface density and other global galaxy properties for barred and unbarred galaxies (Luo et al. 2020). One possible explanation is that the bar is short-lived (Bournaud & Combes 2002) rather than long-lived (Athanassoula et al. 2013). The compact classical bulges or central black holes may weaken and even destroy bars (Combes 1996; Bournaud et al. 2005), which can re-form through gas accretion (Combes 1996; Block et al. 2002; Bournaud & Combes 2002; Bournaud et al. 2005). Some of the unbarred galaxies observed in our sample may have previously hosted a bar, which facilitates the formation of pseudo bulges during the bar’s lifetime. Alternatively, most of the bars are long-lived, but in unbarred galaxies, nonaxisymmetric structures other than bars, such as spirals, also drive gas inflow and participate in the buildup of pseudo bulges.

When disks have settled down and normal spiral arms have developed, the spiral arms drive gas flow toward the center, primarily by dissipation of angular momentum at spiral shocks, secondarily by gravitational torque of the spiral potential (Kalnajs 1972; Roberts & Shu 1972; Lubow et al. 1986; Hopkins & Quataert 2011; Kim & Kim 2014; Kim et al. 2020), and by self-gravitational torque of the gaseous component in a minor way (Kim & Kim 2014). Stronger arms trigger a higher mass inflow rate of gas (Kim & Kim 2014). The inflowing gas feeds the central star formation so that stronger spiral arms have a higher central SFR even after the effects of stellar mass, surface density, concentration, and redshift have been removed (Sect. 4). The gas inflow is not rapid enough to trigger a central burst of star formation (Sect. 4.4). The subsequent star formation contributes to the buildup of the pseudo bulges, resulting in a connection between relative central stellar surface density and spiral arm strength, irrespective of galaxy mass and concentration (Fig. 7).

In the same vein, spiral arms may enhance central star formation in some less massive galaxies with a pre-existing small classical bulge (green histogram in Fig. 9). Compared with their massive counterparts (red histogram in Fig. 9), less massive galaxies could have a substantial gas reservoir because the gas fraction increases with decreasing stellar mass (Saintonge et al. 2017). Spiral arms are still present, possibly maintained by the cold gas (Bertin et al. 1989; Yu et al. 2021). The arms drive gas to funnel to the center. Assuming that different types of bulges can co-exist (Athanassoula 2005), the newly inflowing gas onto a pre-existing classical bulge should maintain strong in-plane rotational dynamics and therefore form a disky pseudo bulge in addition to the classical bulge. Evidence for the coexistence of classical bulges and disky pseudo bulges has been reported (Erwin et al. 2015). Galaxies with a star-forming classical bulge likely host an additional pseudo bulge, a hypothesis that may be tested in the future. However, this picture is unlikely to apply to massive galaxies with a prominent classical bulge, as the inner gaseous disk, if present, is likely to be stabilized against star formation by the prominent classical bulge (Martig et al. 2009).

Together with the suppression of spiral arm strength by classical bulges, spiral-driven secular evolution leads to the relationship between bulge type and spiral arms (Figs. 10 and 11).

6. Conclusions

We used 2779 nearby relatively face-on unbarred star-forming main-sequence (SFMS) spiral galaxies derived from the SDSS to investigate the hypothesis that spiral-driven instabilities drive gas toward the center of the galaxy, enhancing central star formation. Galactic bars can trigger central star formation and then contribute to the secular growth of galaxy centers (Kormendy & Kennicutt 2004), but less is known about the spiral effect. We derived star formation properties in the central 1–3 kpc region from the SDSS spectra. Specifically, we used sSFRfiber, which is computed based on emission lines, from the MPA-JHU catalog to trace central ongoing star formation averaged over the past ∼10 Myr to probe star formation on intermediate timescales of 0.1–1 Gyr prior to observation, and Dn(4000) to indicate the luminosity-weighted mean stellar age of longer timescales of several gigayears. The ratio of sSFRfiber to sSFRglobal, C(sSFR)=log(sSFRfiber/sSFRglobal), where sSFRglobal is measured for the whole galaxy acquired from Salim et al. (2018), is employed as a measure of enhancement of central star formation relative to global star formation. We are essentially relating the spiral arms occupying the extended optical disk to the central most region of the galaxy. The 2779 SFMS spiral galaxies are further separated into two subsamples of 2056 centrally star-forming SFMS galaxies and 723 centrally quenched SFMS galaxies. To avoid the possible influence of quenching processes, only the centrally star-forming SFMS galaxies are used when studying the impact of spiral arms, but both star-forming and quenched SFMS galaxies are used when studying the bulge types.

The relative amplitude of spiral arms (sarm) is defined as the mean Fourier amplitude relative to an axisymmetric disk over the disk region. The logarithmic form of the relative amplitude (2 + log sarm) is used as a measure of the strength of spiral arms. Biases caused by noise are corrected. We investigate the impact of spiral arms on central star formation by comparing spiral arm strength with central star formation properties. We also isolate the effect of spiral arms by removing effects of redshift (z), stellar mass (log M*), stellar surface density (logμ*), and concentration (C). Our main findings are as follows.

  1. Galaxies with stronger spiral arms not only tend to have more intense central sSFR, larger HδA, and lower Dn(4000), but also have enhanced C(sSFR).

  2. Compared with weak-armed galaxies of similar z, log M*, logμ*, and C, the central star formation enhancement in strong-armed galaxies is still significant. This is further verified by partial correlation coefficients. These results suggest that spiral arms can enhance central star formation and that this is a true effect.

  3. The central starburst galaxies have both weak and strong arms and only ∼10% of galaxies with very strong spiral arms (top 5% of arm strength) have central starburst. Likewise, there is no apparent excess in HδA in strong spirals for a given Dn(4000). Having strong spiral arms is thus not a sufficient nor necessary condition to trigger a central starburst. This implies that the spiral-induced central star formation is continuous instead of bursty.

  4. There is a trend of increasing arm strength with decreasing relative central stellar surface density, suggesting galaxies with strong spiral arms are more likely to have pseudo bulges. Moreover, the pseudo bulges in galaxies with stronger spiral arms are more prominent. These results suggest that spiral arms may play a role in the buildup of pseudo bulges.

  5. Galaxies with increasing spiral arm strength tend to have an increasing fraction of pseudo bulges, a relatively unchanged fraction of star-forming classical bulges, and a decreasing fraction of quenched classical bulges. This relationship is partly attributed to the suppression of spirals by classical bulges (Bertin et al. 1989; Yu & Ho 2020) and partly to the central star formation driven by spirals, which builds the pseudo bulges.

We explain our results in the context of a scenario where spiral arms transport cold gas inward to trigger continuous central star formation. The subsequent star formation contributes to the secular growth of pseudo bulges. Spiral arms thus play an essential role in the secular evolution of disk galaxies.

Acknowledgments

LCH was supported by the National Science Foundation of China (11721303, 11991052), China Manned Space Project (CMS-CSST-2021-A04), and the National Key R&D Program of China (2016YFA0400702). JW thanks support from National Science Foundation of China (12073002, 11721303) and the science research grants from the China Manned Space Project (CMS-CSST-2021-B02). SYY acknowledges the support from the Alexander von Humboldt Foundation. We thank the referee for constructive criticism that helped to improve the quality and presentation of the paper. We benefited from discussions with Veselina Kalinova, Dario Colombo, and Karl Menten. SYY is indebted to Karl Menten for his great support during the pandemic.

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All Tables

Table 1.

Correlation analysis.

In the text

All Figures

thumbnail Fig. 1.

Example r-band galaxy images with spiral arm strength (2 + log sarm) increasing from left to right and top to bottom. The inner circle of 3″ denotes the size of the SDSS fiber. The outer ellipse at a semi-major axis of R90 illustrates the measured mean ellipticity and PA. The ID in the NSA catalog and the arm strength are presented in the top-left corner.
In the text
thumbnail Fig. 2.

Dependence of central sSFR (sSFRfiber) on strength of spiral arms (2 + log sarm). Panel a: the scatter plot of the two parameters. Panel b: shows the number distribution of sSFRfiber. The solid horizon line (logsSFRfiber = −11.3) marks the valley of the number distribution, separating the sample into centrally star-forming and centrally quenched SFMS galaxies. The Pearson correlation coefficient between sSFRfiber and 2 + log sarm is denoted at the top.
In the text
thumbnail Fig. 3.

Dependence of central SFR indicators on spiral arm strength (2 + log sarm). Panels a–c: plot the Dn(4000), HδA, and C(sSFR) against arm strength, respectively. The bin color encodes the number of galaxies in each bin, scaled by the color bar next to the panel. The Pearson correlation coefficient and the corresponding p value are denoted at the top. The confidence ellipses are obtained using the PCA technique described in the text, and they contain approximately 95% of the data. As these ellipses could be distorted due to the different dynamical ranges of the x and y axes, a best-fitted straight line indicating the direction of main principal component is plotted.
In the text
thumbnail Fig. 4.

Distribution of the parameters used to construct the control sample. Panels a–d: show the distribution of stellar surface density (logμ*), stellar mass (log M*), concentration (C), redshift (z), and effective radius (log R50), respectively. Results for galaxies with strong spiral arms (2 + log sarm ≥ 1.44) are marked in blue histogram, and the same for the control sample with weak spiral arms (2 + log sarm <  1.44) are marked in gray filled histogram. The p value of the Kolmogorov–Smirnov test is presented at the top of each panel.
In the text
thumbnail Fig. 5.

Distribution of central SFR indicators for galaxies with strong arms and the control sample with weak arms. Panels a–d: show the result of sSFRfiber, C(sSFR), Dn(4000), and HδA, respectively. The distributions for strong-armed galaxies are marked in blue, and the same for the control weak-armed sample are marked in gray. The mean difference between the two distributions and p values from the Kolmogorov–Smirnov test are presented at the top of each panel.
In the text
thumbnail Fig. 6.

HδA plotted as a function of Dn(4000) and spiral arm strength (2 + log sarm). Panels a: the color associated with each data point encodes the average arm strength of the surrounding galaxies with |Δx|≤0.05 and |Δy|≤0.5 (the box is illustrated in the bottom-left corner). The curves show evolution tracks obtained using the GALAXEV stellar population synthesis code (Bruzual & Charlot 2003) with the provided simple stellar population model of a metallicity Z = 0.019 and a Chabrier (2003) initial mass function. Dashed and solid curves respectively show results for an instantaneous burst of star formation and continuous star formation that declines exponentially with time with a characteristic timescale of 4 Gyr. Panel b: the color encodes the different narrow ranges of Dn(4000). The typical scatter in HδA at a given 2 + log sarm and a given Dn(4000) is illustrated in the bottom-left corner.
In the text
thumbnail Fig. 7.

Dependence of relative central surface density (ΔΣ1) on spiral arm strength (2 + log sarm). The bin color encodes the galaxy number in each bin. Σ1 is the stellar surface density within the central 1 kpc, while the log ΔΣ1 is calculated via log ΔΣ1 = logΣ1 + 0.275(log M*)2 − 6.445log M* + 28.059, which can be used to distinguish pseudo bulges (log ΔΣ1 <  0) from classical bulges (log ΔΣ1 ≥ 0). The Pearson correlation coefficient is denoted at the top.
In the text
thumbnail Fig. 8.

Distribution of concentration index (C) of galaxies with pseudo bulges and those with classical bulges. The blue unfilled and gray filled histograms show results for the strong-armed sample and control weak-armed sample. The mean difference between the two distributions and p values from the Kolmogorov–Smirnov test are presented at the top of each panel.
In the text
thumbnail Fig. 9.

Concentration index (C) plotted as a function of galaxy stellar mass (log M*/M⊙) for galaxies with pseudo bulges (blue), star-forming classical bulges (green), and quenched classical bulges (red). The histograms above and to the right show the number distribution of log M*/M⊙ and C, respectively.
In the text
thumbnail Fig. 10.

Number distribution of pseudo bulges (blue), classical bulges (black), star-forming classical bulges (green), and quenched classical bulges (red).
In the text
thumbnail Fig. 11.

Fraction of galaxies hosting pseudo bulges (blue), classical bulges (black), star-forming classical bulges (green), and quenched classical bulges (red) as a function of spiral arm strength (2 + log sarm).
In the text

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