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# Suppressed or Enhanced Central Star Formation Rates in Late-type Barred Galaxies

Jing Wang, E. Athanassoula, Si-Yue Yu, Christian Wolf, Li Shao, Hua Gao, T. H. Randriamampandry

► To cite this version:

Jing Wang, E. Athanassoula, Si-Yue Yu, Christian Wolf, Li Shao, et al. Suppressed or Enhanced Central Star Formation Rates in Late-type Barred Galaxies. The Astrophysical Journal, 2020, 893 (1), pp.19. 10.3847/1538-4357/ab7fad. hal-03578046

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# Suppressed or Enhanced Central Star Formation Rates in Late-type Barred Galaxies

Jing Wang¹, E. Athanassoula², Si-Yue Yu¹,³, Christian Wolf⁴, Li Shao⁵, Hua Gao¹,³, and T. H. Randriamampandry¹

¹ Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, People's Republic of China

² Aix Marseille Université, CNRS, LAM, Laboratoire d'Astrophysique de Marseille, Marseille, France

³ Department of Astronomy, School of Physics, Peking University, Beijing 100871, People's Republic Of China

⁴ Research School of Astronomy and Astrophysics, Australian National University, Canberra ACT 2611, Australia

⁵ National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District, Beijing, People's Republic of China

Received 2019 December 24; revised 2020 February 19; accepted 2020 March 10; published 2020 April 9

## Abstract

Bars in disk-dominated galaxies are able to drive gas inflow inside the corotation radius, thus enhancing the central star formation rate (SFR). Previous work, however, has found that disk-dominated galaxies with centrally suppressed SFRs frequently host a bar. Here we investigate possible causes for the suppression of central SFRs in such cases. We compare the physical properties of a sample of disk-dominated barred galaxies with high central SFRs (HC galaxies) with those of a sample of disk-dominated barred galaxies with low central SFRs (LC galaxies). We find that the two samples have, on average, similar H I content and bars of similar strength. But we also find that the HCs have bluer colors than the LCs, and that outside the bar region, they host stronger spiral arms than the LCs, where closed rings are more often seen. We discuss and evaluate the possible causes for the suppression of the central SFR in the LC galaxies as opposed to its enhancement in the HC galaxies.

*Unified Astronomy Thesaurus concepts: Disk galaxies (391); Galaxy structure (622); Spiral arms (1559); Star formation (1569); Barred spiral galaxies (136); Interstellar atomic gas (833)*

## 1. Introduction

Disk galaxies evolve both in their morphology and in their stellar population. In the nearby universe, the average evolution of galaxies is no longer violent or driven by major mergers as at higher redshift (e.g., Kraljic et al. 2012). The ways in which nearby galaxies evolve are predominantly secular, via disk instabilities. Bars are believed to play a significant role in the secular evolution of disk galaxies (for reviews of the theoretical and observational aspects, see Athanassoula 2013 and Kormendy 2013, and references therein).

One of the most important mechanisms related to bars is that the nonaxisymmetric potential of strong bars exerts torques on the gas and drives it toward the center of galaxies (Schwarz 1981; Athanassoula 1992b, hereafter A92b; Regan et al. 1999; Sormani et al. 2015; Fragkoudi et al. 2016). This process builds a concentration of cold gas at the center (e.g., Sakamoto et al. 1999; Sheth et al. 2005) and triggers vigorous star formation therein (Ellison et al. 2011; Catalán-Torrecilla et al. 2017). The existence of strong bars may account for nearly half of the central starbursts in massive galaxies at low redshift (Wang et al. 2012, hereafter W12). As the central concentration of stellar mass is built up via star formation, the morphology of the galaxy also changes (but see Laurikainen et al. 2007, for barred early-type disk galaxies in the local universe). Hence, bars play an effective role in shaping the age and morphology of disk galaxies.

Several studies came to the conclusion that bars are able to survive the dissolution effects induced by typical central mass concentrations; i.e., they are long-lived disk phenomena (e.g., Shen & Sellwood 2004; Athanassoula et al. 2005, 2013; Debattista et al. 2006; Berentzen et al. 2007; Aguerri et al. 2009; Kraljic et al. 2012, and references therein), so they would play a major role in the secular evolution of their host galaxies. However, others reached the opposite conclusion (Bournaud & Combes 2002; Bournaud et al. 2005). Note, however, that

central mass concentrations can weaken the bar, even if they cannot completely destroy it (Athanassoula 2013). Furthermore, major or extensive minor mergers can effectively destroy the bar (Pfenniger 1991; Athanassoula 1999; Berentzen et al. 2003; Sheth et al. 2012). Which of these has the upper hand can be found by following the bar fraction of early-type disk galaxies as a function of time. Sheth et al. (2008) and Melvin et al. (2014) found that this fraction remains constant or increases with decreasing redshift, or look-back time, which argues in favor of long-lived bars. Note that bars may play an even more important role in the future evolution of late-type disk galaxies, as the fraction of them that hosts bars continuously increases from $z \sim 0.84$ to the present day (Sheth et al. 2008).

Galaxies that host strong bars are not always found to have high central concentrations of cold gas or star formation rates (SFRs; Martinet & Friedli 1997; Sheth et al. 2005; Cullen et al. 2007; Fisher et al. 2013). Around one-third of barred galaxies are found to have very low densities of cold gas at the center, regardless of their Hubble types (Sheth et al. 2005). There are several possible reasons for the lack of cold gas in the center of barred galaxies. First of all, in order for bars to push gas inward, the gas needs to be available within the radial range where bars are effective (Kuno et al. 2007). In barred disk galaxies, gas is not only driven inward but also outward, with a division line close to the corotation (CR; Kalnajs 1978; Bournaud & Combes 2002; Combes 2008). Thus, the flow of gas strongly depends on the radial distribution of the gas. Second, abundant gas might have been present at the center before but has been efficiently consumed by a past starburst. If we have a large observational sample, we may witness the smoking gun of this process by selecting the post-starburst galaxies. The central star formation may revive if new gas comes in. Some models predict that the onset and quenching of star formation at the center of bars occurs periodically,
regulated by a balance between the inflow rate and the central concentration of mass (Krumholz & Kruijssen 2015). Finally, the complex orbits of the gas strongly depend on a variety of parameters and can rarely reach the center under certain circumstances (Athanassoula 1992a; A92b; Quillen et al. 1995; Sheth et al. 2002). For example, the inner Lindblad resonance (ILR) may stop the gas before it reaches the center if there is no nuclear nonaxisymmetric structure to further tunnel the gas inward.

Bars themselves also evolve while they drive the secular evolution of their host galaxies. Simulations suggest that bars transport angular momentum to the outer disks, the classical bulges and dark matter halos, so that they slow down and grow stronger and longer (Athanassoula 2002, 2003); gas transfers part of its angular momentum to the stellar bar and weakens it (Bournaud & Combes 2002; Berentzen et al. 2007; Athanassoula et al. 2013). Thus, at a fixed central concentration of the optical light, the length of bars over the disk size is found to be correlated with the color of galaxies (W12). The strength of bars is also related to other morphological features: strong bars are shallower in the surface brightness radial distributions and more rectangular in shape, and the contrasts from the underlying disks are stronger than for weak bars (Kim et al. 2015, 2016). In extreme cases, the majority of the stars initially in the disk may be trapped to the bar (Gadotti & de Souza 2003; Gao & Ho 2017). Stronger bars drive stronger gas inflows (Sheth et al. 2005; Kim et al. 2012), in agreement with simulation results (Athanassoula 1994).

The enhancement and suppression of star formation in barred galaxies within one sample, which is selected by the stellar mass, optical central concentration, and redshift, was coherently studied by W12. They found that at the same concentration, disk galaxies that have suppressed or enhanced central SFRs tend to host more bars than galaxies that have intermediate central SFR levels. This result seems to imply a picture where the bars play a role in the star formation quenching at the center of galaxies. However, as W12 focused on the buildup of the central mass concentration of galaxies, the properties of the barred galaxies with centrally suppressed star formation were not thoroughly investigated. It remains unclear whether the suppression of star formation is limited to the center, the suppression is temporary, the total amount of cold gas is significantly reduced in these centrally suppressed galaxies, the bars in the two types of galaxies are of the same type, or another more intrinsic parameter should be responsible for both the quenching of star formation and the formation of bars. Finally, could the enhancement in bar fraction be a consequence instead of a cause of the suppressed central star formation? The answers to these questions may be directly related to the dynamical evolution of bars and stellar evolution of galaxies. We aim to provide better understanding of these questions in this paper.

The paper is organized as follows. We build samples of barred galaxies that have enhanced and suppressed central star formation and describe the data to be analyzed in Section 2. We compare the properties of these different samples in Section 3. We use fiber spectral indices to infer the central star formation history (SFH), color profiles to characterize the radial range of SFR suppression or enhancement, H I richness to indicate the availability of gas reservoirs, and different radial profiles to indicate the strength of the bars and spiral arms. We discuss the results in Section 4. Throughout this paper, we assume a Chabrier initial mass function (Chabrier 2003) and a ΛCDM

cosmology with $\Omega_m = 0.3$, $\Omega_\lambda = 0.7$, and $h = 0.7$. We will refer to the region where the central SFR is clearly enhanced or suppressed as the “central region.” The region beyond it but within the bar radius will be referred to as the main bar region, and the region outside that will be the “outer region.”

## 2. Sample and Analysis

### 2.1. Parameters and the Parent Sample

We select galaxies based on catalogs from the seventh data release (DR7) of the Sloan Digital Sky Survey (SDSS; York et al. 2000) and the sixth data release (GR6) of the Galaxy Evolution Explorer (GALEX; Martin et al. 2005). We extract parameters from the SDSS MPA-JHU catalog,<fnref n="6" /> including redshift ($z$), stellar mass ($M_*$), axis ratio ($b/a$), semimajor axis length ($R_{25}$) of the 25 mag arcsec$^{-2}$ isophotal ellipse, and radius that encloses 90% ($R_{90}$) and 50% ($R_{50}$) of the total flux. We also take as indices the 4000 Å break ($D_n(4000)$) and Balmer absorption index ($H\delta_A$), central SFR, and central stellar mass within the SDSS spectroscopic fiber region (3" in diameter, ~1 kpc in radius). The central SFR was derived from attenuation-corrected $H\alpha$ luminosities for star-forming galaxies and a $D_n(4000)$-based formula for non-star-forming (passive, composite, or active galactic nucleus (AGN)-hosting) galaxies (Brinchmann et al. 2004).

We calculate the central stellar surface densities ($\Sigma_{*,ct}$) with the central stellar mass. The effective stellar mass surface density, $\mu_*$, is calculated as $0.5M_*(\pi R_{50,i}^2)$, where $i$ refers to the $i$ band. The axis ratio is calculated as $b/a$ based on the $g$-band measurements. The concentration index $R_{90}/R_{50}$ is based on the $r$-band measurements.

The total SFR of each galaxy was derived in W12 by fitting the spectral energy distribution (SED) of the optical (from SDSS) and ultraviolet (from GALEX) bands with a library of model SEDs that were built with the stellar population synthesis method and based on the spectral templates from Chabrier (2003). A range of SFHs, metallicities, and dust attenuations was assumed to ensure physically meaningful solutions. More details can be found in W12, Wang et al. (2011), and Saintonge et al. (2011). The SFR central concentration is defined as $C(SF) = \log((SFR/M_*)_{center}/(SFR/M_*)_{total})$, where “center” refers to measurements within the SDSS fiber, and “total” refers to the global measurements. The $C(SF)$ enhancement, $\Delta C(SF)$, is calculated as the excess of $C(SF)$ over the average of galaxies that have similar $M_*$ (differences <0.2 dex), $\Sigma_{*,ct}$ (differences <0.2 dex), $R_{90}/R_{50}$ (differences <0.15), and redshift (differences <0.005). So, a galaxy with a negative $\Delta C(SF)$ has a suppressed central SFR compared to galaxies with similar stellar surface density distributions. The different indicators used to calculate the central and total SFR may cause systematic uncertainties in $\Delta C(SF)$, but we will show in Sections 3.1 and 3.2.2 that subsamples selected with different ranges of $\Delta C(SF)$ show distinct central $D_n(4000)$, $H\delta_A$, and $g-r$ color slopes but less different global SFRs. Hence, on average, $\Delta C(SF)$ works well in selecting samples with different SFR concentrations. Large samples of SFR radial profiles estimated from uniform indicators could ultimately minimize this type of uncertainty and should be available when the MaNGA data are fully released in the future.

<footnote n="6">⁶ http://www.mpa-garching.mpg.de/SDSS/DR7/</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Distribution of semimajor and semiminor axes of bars in the three barred samples. The left and right panels plot the distribution of semimajor axes ($r_{bar}$) and semiminor axes ($r_{bar}(1 - e_{bar})$) of bars, respectively. The red, green, and blue colors are for the LC, HC, and EHC samples (see Section 2.3 for details), respectively. The dashed line marks the SDSS fiber radius of $1''/5$.</figcaption></figure>

After excluding all galaxies with significantly asymmetric morphologies (~3.4%), we select all galaxies with $0.02 < z < 0.05$, $M_* > 10^{10} M_\odot$, $\log\text{SFR}/M_* > -11$, $b/a > 0.75$, and $R_{90}/R_{50} < 2.2$. This makes the parent sample of 1478 massive, face-on, star-forming, and disk-dominated galaxies.

The maximum $R_{90}/R_{50} \approx 2.2$ of the main sample is much lower than the typical threshold of 2.6 for selecting disk-dominated galaxies (see SDSS-based studies; e.g., Kauffmann et al. 2003). By selecting galaxies with very low $R_{90}/R_{50}$, we minimize the potential influence of bulges. From Nair & Abraham (2010), most (>90%) of the galaxies with $R_{90}/R_{50} < 2.2$ have a Hubble type later than S(B)b. But whenever possible in this paper, we avoid discussions based on the relatively subjectively defined Hubble sequence so that the results could be more conveniently extended to other samples at low and high redshifts and compared to simulations in the future.

We list the names of the parameters and the abbreviations of terms that are used in this paper in the Appendix.

## 2.2. The Barred Sample

The bar structures have been identified in W12, based on the standard method of analyzing the shapes of the ellipticity ($e = 1 - b/a$, where b and a are the semimajor and semimajor axis of an isophotal ellipse) and position angle radial profiles. The method is based on the fact that, in a galaxy that hosts a strong bar, the ellipticity in general rises continuously as a function of radius within the bar, reaches its maximum ($e_{bar}$) at a point that we will associate with the end of the bar ($r_{bar}$, the semimajor axis), and then drops to reach the ellipticity of the disk region; the position angle remains roughly constant as a function of radius within the bar and suddenly changes at the end of the bar. It was shown by W12 that the strong bars (with $e_{bar} > 0.5$ and $r_{bar} > 2.5$ kpc) can be more reliably identified (with a reliability of >70%) than the weak bars (with $e_{bar} < 0.5$ or $r_{bar} < 2.5$ kpc), and only strong bars have a significant effect in enhancing the central star formation activities. Following W12, we will only discuss the galaxies with strong bars and refer to them (388 galaxies) as the “barred sample” hereafter in this paper.

From Figure 1, we can see that the SDSS fiber size is smaller than the semimajor and semiminor axes of bars in most of the galaxies analyzed in this paper.

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Top: distribution of relative central SFR concentration ($\Delta C$ (SF); see Section 2.1) for all galaxies with $R_{90}/R_{50} < 2.2$ (magenta) and barred galaxies with $R_{90}/R_{50} < 2.2$ (green). Bottom: distribution of frequency of galaxies hosting bars ($f_{bar}$) as a function of $\Delta C$(SF). In the bottom panel, the parent galaxies are plotted in magenta, and their control samples (matched in $M_*$ and $R_{90}/R_{50}$) are plotted in purple. These two samples are only used in this figure to support our selection of analysis samples LC, HC, and EHC in Section 2.3. The parent sample (magenta) shows a rise of $f_{bar}$ toward low $\Delta C$(SF) (to the left of the first dashed line); this cannot be fully explained by a dependence of these two parameters on $M_*$ or $R_{90}/R_{50}$, for the control sample (purple) shows a much more flattened trend. The error bars represent the 0.683 (1$\sigma$) binomial confidence intervals (Cameron 2011). The two dashed vertical lines mark the selection of the LC and EHC galaxies (see Section 2.3).</figcaption></figure>

## 2.3. The LC, HC, and EHC Samples

The aim of this paper is to understand the possible causes for the suppression of the central SFR in a sample of strongly barred disk-dominated galaxies. To demonstrate the motivation of the criteria used for selecting the sample, we show the relation between $f_{bar}$ and $\Delta C$(SF) (see also W12).

In Figure 2, we confirm the result of W12 that galaxies with $\Delta C(\text{SF}) > 0.2$ or $\Delta C(\text{SF}) < -0.7$ tend to have higher $f_{bar}$
(fraction of galaxies hosting bars) than the galaxies with intermediate $\Delta C(\text{SF})$. While the prevalence of bars in galaxies with high central SFRs has been well accepted (Ellison et al. 2011; Wang et al. 2012; Catalán-Torrecilla et al. 2017), the enhancement of $f_{\text{bar}}$ in galaxies with suppressed central SFRs has not been studied in detail before, especially in disk-dominated galaxies. The trend cannot be explained by the possible dependence of $f_{\text{bar}}$ and $\Delta C(\text{SF})$ on $M_*$ or $R_{90}/R_{50}$, for it is steeper than the trend of corresponding control galaxies matched in $M_*$ and $R_{90}/R_{50}$. When $\Delta C(\text{SF}) < -0.3$, the slopes of the linear fits to the relation between $f_{\text{bar}}$ and $\Delta C(\text{SF})$ are $-0.21 \pm 0.07$ and $-0.10 \pm 0.03$ for the parent sample and the control sample, respectively, suggesting that the difference of the two trends is significant.

The results from Figure 2 motivate us to select the following three analysis samples of barred galaxies.

1. The LC (low central SFR) sample, with $\Delta C(\text{SF}) < -0.7$, a total of 49 galaxies.

2. The HC (high central SFR) sample. We select all galaxies with $\Delta C(\text{SF}) > 0$ from the barred sample and match them in the distribution of $\log M_*, R_{90}/R_{50}$, and redshift $z$ to the LC sample with bin sizes of 0.15, 0.08, and 0.01, respectively. To ensure that the distribution matching is reliable, we require the Kolmogorov–Smirnov (K-S) test probabilities (Press et al. 1992) to be above 0.7 (corresponding to a 70% confidence for similarities) for each of the matching parameters. The resulted HC sample has 48 galaxies. So, the HC sample has similar $M_*$ and concentrations (see first row of Figure 5) but higher (positive, hence enhanced) $\Delta C(\text{SF})$ than the LC sample.

3. The EHC (extremely high central SFR) sample, with $\Delta C(\text{SF}) > 0.7$, a total of 51 galaxies.

We notice that the LC galaxies, on average, have higher $M_*$ than the EHC galaxies (panel (f) of Figure 5). So, in practice, our analysis will be focused on a comparison between the LC and HC samples, but we also include the EHC sample as a reference, for it represents galaxies with the highest $\Delta C(\text{SF})$ in the local universe.

We do not exclude the AGN hosting galaxies to avoid the possible bias against AGN hosts. Due to the selection against significant bulges ($R_{90}/R_{50} < 2.2$), strong AGN hosts (i.e., Seyferts, identified by the criteria of Cid Fernandes et al. 2010) consist only of a small fraction: 8%, 2%, and 2% of the LC, HC, and EHC galaxies, respectively. The AGN feedback hence should not play a significant role in affecting the current nuclear SFR. Due to data limitations, the possible influence of a previously active AGN is outside the scope of this paper.

We point out that although the galaxies with the lowest $\Delta C(\text{SF})$ tend to have higher $f_{\text{bar}}$ than the galaxies that have intermediate $\Delta C(\text{SF})$, their absolute $f_{\text{bar}}$ is low (~35%). Also, we could not conclude that bars directly suppress C(SF); i.e., we could not exclude the possibility that an unidentified third parameter causes both the enhancement of $f_{\text{bar}}$ and suppression of C(SF) in LC galaxies. This paper thus investigates how bars

could be related to the suppression of central SFRs in some disk-dominated galaxies, while they commonly tend to enhance the central SFR, but does not intend to claim bars as a major mechanism that quenches star formation in the center of galaxies in general.

## 2.4. Other Control Samples

There is a possibility that the LC sample differs from the HC sample but not from C(SF)-normal galaxies. So, we also build another control sample (HC2) of 43 galaxies that has $-0.7 < \Delta C(\text{SF}) < 0.7$ and is matched in $M_*, R_{90}/R_{50}$, and $z$ to the LC sample like the HC sample. The main purpose of building HC2 is to confirm the differences found between the LC and HC samples. We find that the behavior of HC2 is close to that of HC in all trends presented in the following part of this paper. For simplicity, we do not further present or discuss results related to HC2.

In order to study the radial enhancement/suppression of SFRs in barred galaxies with respect to general galaxies, we build for each of the LC, HC, and EHC samples a control sample that is matched in $M_*, \mu_*$, and $g-r$ (referred to as the $(g-r)$-control sample hereafter). For each galaxy, we select a random galaxy from the parent sample that differs by no more than 0.1 in $\log M_*$, 0.1 in $\log \Sigma_{*,\text{ct}}$, and 0.05 in $g-r$. The K-S test probabilities are all above 0.9 (corresponding to a 90% confidence for similarities) for each of the matching parameters. We do not specifically select the galaxies without bars, to avoid the danger of being biased against other properties (e.g., low $R_{90}/R_{50}$) favored by the barred galaxies.

## 2.5. Cross-matching to Other Catalogs

In order to investigate the amount of H I gas in galaxies, we cross-match the LC, HC, and EHC samples with the $\alpha$-100 catalog of the Arecibo Legacy Fast ALFA Survey (ALFALFA; Haynes et al. 2011). The nearest ALFALFA counterpart for each galaxy is searched for within a projected distance of 3' and a redshift difference of 0.001. There are 24, 29, and 24 galaxies covered by the ALFALFA footprint, while 16, 17, and 15 galaxies are detected in the LC, HC, and EHC samples, respectively. The specific SFR (sSFR; $\text{SFR}/M_*$) distributions of the ALFALFA-detected subsamples are similar to those of the original samples, with K-S test probabilities of 0.76, 0.96, and 0.99 for the LC, HC, and EHC galaxies, respectively. It suggests that cross-matching with ALFALFA does not result in a significant selection bias toward more star-forming systems.

In order to compare the group environments, we cross-match the three barred samples with the SDSS spectroscopic group catalog of Lim et al. (2017). Lim et al. (2017) identified groups based on a halo-based finder and used stellar masses as a proxy to estimate the dark matter halo mass of each group. There are 33, 35, and 39 of the LC, HC, and EHC galaxies matched to this group catalog, respectively. We take the halo mass ($M_{\text{halo}}$) and group richness (number of members in the group, $N_{\text{member}}$) for each galaxy from the catalog.

## 2.6. Photometric Radial Profiles

We derive the following radial profiles to be analyzed in Section 3.2.

<footnote n="7">⁷ In other words, if the relation between $f_{\text{bar}}$ and $\Delta C(\text{SF})$ is caused by both parameters depending on $M_*$ and/or $R_{90}/R_{50}$, we would observe a similar trend of $f_{\text{bar}}$ varying as a function of $\Delta C(\text{SF})$ in the parent and control samples. This similarity is not observed; hence, there is likely a dependence of $f_{\text{bar}}$ on $\Delta C(\text{SF})$ that is independent of $M_*$ or $R_{90}/R_{50}$. We note that there might be other unidentified parameters that cause the correlation between $f_{\text{bar}}$ and $\Delta C(\text{SF})$. This caveat should be kept in mind and investigated when more abundant observational information becomes available in the future.</footnote>
1. *Ellipticity profiles.* The ellipticity (e) of the r-band surface brightness isophotes as a function of the semimajor axis of ellipses fitted to the isophotes.

2. *Azimuthally averaged profiles*, including the r-band surface brightness ($\Sigma_{r,avg}$), color ((g - r)_{avg}), and stellar mass surface density ($\Sigma_{*,avg}$) profiles. The surface brightness is averaged in elliptical rings that have the same axis ratio and position angle as the global values of the galaxy (see Section 2.1). Here $\Sigma_{*}$ is derived based on the r-band surface brightness and the g - r dependent $M_{*}$-to-light ratio (Bell et al. 2003). We use the subscript “ctrl” to denote measurements for the (g - r)-control galaxies.

3. *Bar profiles.* Profiles along the bar, including $(g - r)_{bar}$ and $\Sigma_{*,bar}$. The properties are averaged in rectangular grids with widths equivalent to the width of the bar ($2 \cdot r_{bar} (1 - e_{bar})$) and aligned in the position angle direction of the bar.

4. *Interbar profiles.* Profiles perpendicular to the bars, including $(g - r)_{int}$ and $\Sigma_{*,int}$. They are derived in a similar way as the profiles along the bar, but the grids are aligned in the direction perpendicular to the position angle of the bar. Because $e_{bar}$ has a minimum value of 0.5 in our sample, part of the interbar profiles can be contaminated by light from the bar regions when the radius is below $0.5 \cdot r_{bar}$.

The profiles derived in this paper may suffer from projection effects. The selection of only weakly inclined (b/a > 0.75) galaxies in the parent sample has mitigated this problem. Considering the potential uncertainties (e.g., thickness of disks and bars, interpolation of data) that might be introduced in deprojection procedures, we only work on these directly derived profiles in this paper.

## 2.7. Azimuthal Fourier Decomposition

In order to quantify the amplitudes of nonaxisymmetric optical structures, we use Fourier decompositions following the technique outlined in Yu et al. (2018). The procedure decomposes the *r*-band light along the ellipse at each radius into a series of Fourier components up to an order of six. The ellipticity and position angle of the disk are determined by averaging their profiles in the region where the disk component dominates, and then the image is deprojected to show the face-on disk. The relative amplitude of each Fourier component is calculated as the absolute amplitude over the azimuthally averaged surface density. The relative amplitudes of the *m* = 2 component ($A_2$) indicate bar strength within $r_{bar}$ (where the position angle does not significantly change) and two-arm spiral strength beyond $r_{bar}$.

The cumulative amplitude $S_{A_2,r}$ is calculated as the integral of $A_2$ over the circular area within the radius *r* of the galaxies. This is also an indicator of bar strength when *r* = $r_{bar}$ and bar strength plus *m* = 2 spiral arm strength when *r* > $r_{bar}$.

The amplitude $A_{\text{tot}}$ is calculated as the square root of the sum of the squares of the relative amplitudes of modes 2, 3, and 4 in the disk-dominated region (beyond $r_{\text{bar}}$). The *m* = 3 and 4 modes are included to account for the multiple-armed structures. Hence, $A_{\text{tot}}$ indicates the nonaxisymmetric potential of the spiral arms and possibly other nonaxisymmetries beyond $r_{\text{bar}}$. We use $A_{\text{tot}}$ > 0.15 to indicate a significant existence of spiral arms.

## 2.8. Error Bars

We derive the error bars of the proportions (fractions) with the formula from Cameron (2011), which estimates the 0.683 (1σ) Bayesian binomial confidence intervals from the quantiles of the beta distribution.

We derive the error bars of other statistical quantities (e.g., median values, K-S test probabilities; Press et al. 1992) through bootstrapping. In the bootstrapping procedure, we randomly resample the original sample with replacement and build 500 new samples, each of which has the same size as the original sample. We derive the given statistical quantity *Q* for each of the 500 new samples and hence obtain a distribution of *Q*. We calculate the standard deviation of this distribution and take it as the error estimate of the *Q* of the original sample.

## 3. Results

We compare properties between the LC, HC, and EHC samples in this section.

Figures 3 and 4 show two atlases<fnref n="8" /> of examples of galaxies in the HC and LC samples, respectively. Comparing them, we can already see some differences between the morphologies of these two samples. Galaxies in the LC sample look red throughout the galaxy and very often show closed ring structures around the end of bars. The galaxies in the HC sample often have blue outer disks, and the ends of bars are more likely to connect with spiral arms than with rings. In the following, we will parameterize the properties of these galaxies.

### 3.1. Global Properties

We first compare the global properties of the whole galaxies.

#### 3.1.1. Histograms

We compare the stellar concentrations, group environments, and global H I richness of the samples.

The SFR surface densities strongly correlate with stellar surface densities in star-forming galaxies (Huang & Kauffmann 2015; Ellison et al. 2018). Central and effective stellar surface densities are also typically used in the literature as a measure of central compactness (bulges) and related to the quenching of the central SFR (Woo et al. 2015). We find that the LC galaxies have a similar distribution of central stellar surface density to the HC and EHC samples. The similarity between the samples is also found in the comparison of effective stellar surface densities (panels (c)–(e) of Figure 5). Hence, the LC galaxies are as similarly disk-dominated as the HC and EHC galaxies (confirming the selection based on $R_{90}/R_{50}$); the different star-forming status of LC and HC (EHC) galaxies is not likely caused by a difference in the central compactness of stars.

The group environmental properties, particularly the halo mass, are key parameters for determining the gas content and star-forming status of galaxies (Catinella et al. 2013; Woo et al. 2015), for theoretically, gas accretion from the circumgalactic medium will be suppressed in more massive halos (Kereš et al. 2005). There are 72<sup>+6</sup><sub>-9</sub>, 62<sup>+7</sup><sub>-9</sub>, and 69<sup>+6</sup><sub>-8</sub>% of the LC, HC, and EHC galaxies identified as central galaxies of groups. The error bars represent the 0.683 (1σ) binomial confidence intervals, derived with the procedure of Cameron (2011). The

<footnote n="8">⁸ Obtained from http://cas.sdss.org/dr7/en/tools chart/list.asp.</footnote>
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Atlas of HC galaxies. The false-color images (of 50" width) are retrieved from the online visual tools of SDSS DR7.</figcaption></figure>

LC galaxies have similar distributions of halo mass and group richness (panels (f) and (g) of Figure 5) as the HC and EHC galaxies. Hence, the group environments are statistically similar between the three samples. The different star-forming status is not likely caused by the current group environments.

The star-forming status of galaxies is strongly correlated with the H I richness (Saintonge et al. 2016, 2017; Catinella et al. 2018). Panel (h) of Figure 5 shows that the three samples have similar H I mass fractions. This is consistent with the comparable detection rates of ALFALFA in the three samples (16/24, 17/29, and 15/24 for the LC, HC, and EHC samples, respectively). Hence, it is unlikely that the difference in the central SFR of the three samples is caused by a difference in the mass of H I reservoirs.

### 3.1.2. *Relations*

This section compares the behavior of the samples in a few sequences and scaling relations.

Here $D_n(4000)$ and $H\delta_A$ are relatively dust-free indicators of the stellar age. Star-forming galaxies have lower values of $D_n(4000)$ and higher values of $H\delta_A$ than passive galaxies. Figure 6 plots the relation between $H\delta_A$ and $D_n(4000)$ for the central 3" of the galaxies. We compare the distribution of galaxies to modeled stellar populations with different SFHs. The average position of the HC galaxies in the diagram can be well modeled by adding starbursts to an SFH that is slowly exponentially declining (purple curve). The single exponentially declining SFH (with or without a starburst) cannot explain the average position of the LC galaxies. Motivated by
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Atlas of LC galaxies. The false-color images (of 50" width) are retrieved from the online visual tools of SDSS DR7.</figcaption></figure>

the average behavior of the low-redshift massive galaxies (Lian et al. 2016), if we force the slowly declining exponential SFH to transit at 10 Gyr to a fast declining exponential function (with a timescale of 0.5 Gyr), then the evolutionary curve reaches the LC galaxies (magenta curve). Indicated by the magenta curve, the central star formation of the LC galaxies should have been quenched more than 1 Gyr ago. The typical stellar age of the LC galaxies should be at least 1 Gyr older than that of the HC (EHC) galaxies if the LC galaxies are evolved from the HC (EHC) galaxies.

The parameter space of $M_*$ and SFR is a useful tool in quantifying the global star-forming status of galaxies: the star-forming galaxies show a tight correlation between SFR and $M_*$ (the star-forming main sequence (SFMS)), and the quenched galaxies show an extended distribution of low SFR at a fixed

$M_*$ (Renzini & Peng 2015). At a fixed $M_*$, galaxies with SFRs deviating by less than ~0.3 dex from the median SFMS are considered star-forming and possibly fluctuating around the median SFMS in cycles driven by a balance between gas depletion and replenishment (Dekel & Burkert 2014; Tacchella et al. 2016). We can see from panel (a) of Figure 7 that the majority of LC galaxies can be classified as star-forming galaxies (i.e., above the curve, which is 0.3 dex below the SFMS), though they have, on average, lower SFRs at a fixed $M_*$ than the other two samples. The LC galaxies are not globally SFR-quenched galaxies.

Panel (b) of Figure 7 plots the relation between sSFR and $M_{H1}/M_*$. On average, the LC galaxies have similar $M_{H1}/M_*$ as the HC and EHC samples (with K-S test probabilities of 0.78 and 0.94, respectively). For the same level of $M_{H1}/M_*$, the LC
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Distribution of global properties of the LC, HC, and EHC galaxies. The first row plots the parameters based on which the HC sample is built, including the redshift (z), stellar mass ($M_*$), and optical concentration ($R_{90}/R_{50}$). The second row shows properties related to the inner stellar surface densities, including the effective stellar mass surface densities ($\mu_*$) and central stellar mass surface densities within a 3" aperture ($\Sigma_{*,ct}$). Panels (f) and (g) in the third row plot properties of the group environment, including the halo mass ($M_{\text{halo}}$) and member richness ($N_{\text{member}}$). Panel (h) plots distributions of the H I mass fraction ($M_{\text{HI}}/M_*$) of the ALFALFA-detected galaxies. The gray filled histograms are for the parent sample. Red, green, and blue are for the LC, HC, and EHC samples, respectively. The K-S test probabilities ($p_{\text{KKS}}$; Press et al. 1992) that indicate the similarity of the distributions between the EHC vs. HC samples (blue) and the HC vs. LC samples (green) are denoted at the upper right corner of each panel. The dashed lines show the medians of the distributions.</figcaption></figure>

galaxies tend to have lower sSFRs than the average behavior (dashed line) of galaxies, while the HC and EHC galaxies are the other way around (with K-S test probabilities of 0.001 and 0.009, respectively, when the distribution of vertical distances from the dashed line in panel (b) of Figure 7 is compared to that of the LC sample). It suggests the very low efficiency of LC galaxies compared to other galaxies in converting the H I gas to SFR.

Theoretical models predict that bars grow in length with increasing age, but gas inflows disturb this process by transferring angular momentum to the bar (Bournaud & Combes 2002; Athanassoula 2003; Athanassoula et al. 2013). We hence expect a correlation between $r_{\text{bar}}/R_{25}$ and $g-r$ when there is no significant gas inflow. Panel (c) of Figure 7 plots the relation between $r_{\text{bar}}/R_{25}$ and $g-r$. We find significant, weak, and no correlations in the LC, HC, and EHC samples, respectively. The higher correlation strength implies that the gas inflow rate is low in the LC sample compared to the HC (EHC) sample.

## 3.2. Radial Profiles

In this section, we compare the distribution of optical light ($M_*$) and color between the different barred samples.

### 3.2.1. Strength of Bars and Spiral Arms

In Figure 8, we present radial profiles of three types of parameters that measure the distribution of the optical light and indicate the strengths of bars and spiral arms.

In panel (b) of Figure 8, we can see that the median *e* profile of the LC sample looks similar to those of the HC and EHC samples within $r_{\text{bar}}$, indicating similar bar strength. The K-S test probability for the comparison between the LC and EHC samples temporarily drops below 0.1 at ~0.5 $r_{\text{bar}}$, indicating a significant difference in the distribution, despite the similarity of the median values of *e* at that radius. But this difference in *e* at ~0.5 $r_{\text{bar}}$ should not be overinterpreted, because the LC and EHC samples have different $M_*$ distributions.

The median *e* profile of the LC sample drops more steeply beyond $r_{\text{bar}}$ than the other two barred samples. It drops to half the maximum values at ~1.2 $r_{\text{bar}}$, while the median *e* profiles of the other two barred samples slowly drops to the same level at ~1.4 $r_{\text{bar}}$. The median *e* profile of the LC sample flattens at ~1.3 $r_{\text{bar}}$, while those of the other two barred samples continuously drop to the last data points at 2 $r_{\text{bar}}$. This is the behavior one would expect, given the morphology of these galaxies, which was discussed in the beginning of this section. Any strong two-armed spirals in the region beyond the end of the bar will influence the ellipse fit so that the best fit will be far
<figure><img src="image_9.png" /><figcaption>**Figure 6.** Relation between optical spectral indexes $H\delta_A$ and $D_n(4000)$ (see Section 2.1). Gray is for the parent sample. The curves show the evolution of stellar populations as a function of age with different SFHs, obtained with the stellar population synthesis codes of Chabrier (2003), assuming the solar metal abundance. The plus signs mark ages of 2, 4, 6, 8, 9, 10, 11, 12, 13, and 14 Gyr on each curve, with larger sizes for older ages. The orange curve is for a single stellar population, and the yellow curve is for an exponentially declining SFH, with a characteristic scale time $\tau$ of 5 Gyr ($SFR(t) = SFR(0)\exp(-t/\tau)$). The purple curve is for a single starburst added (at an age of 10 Gyr, lasting for 0.3 Gyr, contributing to 10% of the total stellar mass formed by 10.3 Gyr) to the SFH of the yellow curve. The magenta curve is for a two-piece wise exponentially declining SFH, with the earlier part (age <10 Gyr) the same as the yellow curve and the later part having a timescale $\tau$ of 0.5 Gyr (motivated by the observed average property of low-redshift massive galaxies; Lian et al. 2016). The yellow, purple, and magenta curves hence overlap when the age is <10 Gyr.</figcaption></figure>

from a circle (see, e.g., Figure 3 in Kalnajs 1973). This would be true particularly in the region near the end of the bar but also considerably further out, depending on the strength of the bar. On the contrary, galaxies with an inner ring and no strong spiral beyond it will leave the disk unperturbed except for the regions very near the end of the bar and have ellipses with much lower ellipticity values. This is indeed what we see in panel (b) of Figure 8.

Panel (d) of Figure 8 compares the median radial distribution of Fourier mode-2 amplitudes ($A_2$) between the samples. The LC and HC galaxies have similar $A_2$ along the bars, except for the innermost regions ($r < 0.3\ r_{bar}$) and the radius close to $r_{bar}$. Beyond $r_{bar}$, HC galaxies have much higher median $A_2$ than LC galaxies. Hence, HC galaxies have similarly strong bars but much stronger spiral arms than LC galaxies. The EHC galaxies have systematically higher $A_2$ (and $S_{A_2, r_{bar}}$) than the other two samples throughout the radius; however, we again refrain from overinterpreting this difference, for EHC galaxies also have systematically lower $M_*$ and only serve as a reference in comparisons between the LC and HC samples.

We show the $\Sigma_*$ contrasts between the bar and interbar regions ($\Sigma_{*,bar} - \Sigma_{*,int}$) in the right column of Figure 8. From panel (f), the median $\Sigma_{*,bar} - \Sigma_{*,int}$ profiles of the three barred samples are all positive within $r_{bar}$, with a comparable peak value of ~0.3 dex, indicating similar bar strength. But the LC median profile starts to drop from a smaller radius and reaches zero (within error bars) at a smaller radius than the HC and EHC median profiles. This difference is caused by the fact that the elliptical bar isophotes of the LC galaxies transit into the intrinsically circular isophotes of the outer disks (in many cases

related to an inner ring around the bar) much more quickly than those of the HC and EHC galaxies (see Athanassoula & Misiriotis 2002) and are consistent with the difference found in the $e$ and $A_2$ profiles.

To summarize, the different radial profiles of light/mass distributions consistently suggest that the LC and HC galaxies have similar bar strength but the HC galaxies have much stronger spiral arms than the LC galaxies. This result is further confirmed in Figure 9 with a comparison in global measures of the bar and spiral arm strengths. The similar bar lengths (panels (a) and (b)) and $S_{A_2, r_{bar}}$ (panel (c)) confirm the similar bar strengths of then LC and HC samples. The EHC galaxies show, on average, higher $S_{A_2, r_{bar}}$ than the other two samples, consistent with the behavior of $A_2$ profiles as discussed above. The on average slightly lower $S_{A_2, 1.5r_{bar}}$ (panel (d)) and significantly lower $A_{tot}$ of the LC galaxies confirm their weaker spiral arms than the HC and EHC galaxies.

### 3.2.2. Radial Distribution of Colors

We use color profiles to indicate the distribution of star-forming activities near the bar regions.

We show the median profiles of azimuthally averaged $g - r$ (panel (a)) and $g - r$ along the bars and perpendicular to them (panel (b)) in Figure 10. We can see from panels (a) and (b) that the median ($g - r$)avg and ($g - r$)bar profiles rise toward the center in the LC sample, flatten near the center in the HC sample, and drop near the center in the EHC sample. The difference in color gradients near the center confirms the selection of the three samples based on $\Delta C(\text{SF})$. In panel (b), ($g - r$)int is almost always bluer than ($g - r$)bar within $r_{bar}$, indicating a common dynamical effect of bars in concentrating or suppressing the SFR within the bar radius. It also implies that when barred disk-dominated galaxies cease their star formation, it preferentially occurs along the bars (in contrast to simple inside-out or outside-in scenarios).

In Figure 11, we compare the ($g - r$)$_{bar}$ profiles of barred galaxies to the ($g - r$)$_{avg,ctrl}$ of the corresponding ($g - r$)-control galaxies (see Section 2.4). It radially investigates the suppression or boosting of SFR in barred galaxies with respect to the general population of galaxies, i.e., barred versus general (not necessarily barred) galactic internal environments. In panel (b), the median ($g - r$)$_{avg}$ - ($g - r$)$_{avg,ctrl}$ profiles of the three barred samples differ significantly within $r_{bar}$: the LC profile is positive with a peak value of ~0.06 mag within $r_{bar}$, the EHC profile is significantly negative near the galactic center (<0.2 $r_{bar}$) with a trough value of ~-0.15 mag, and the HC profile is in between the other two profiles. The outer profiles beyond $r_{bar}$ go the other way from the inner profiles, mostly due to the fact that the barred and control galaxies are matched in the global $g - r$. Similar trends look even clearer along the bars (panel (d)) but are much weaker perpendicular to the bars (panel (f)). To summarize, compared to control galaxies with similar global color, the enhancement of SFR in HC and EHC galaxies occurs close to the galactic center, while the suppression of SFR in LC galaxies occurs within the bar regions.

To summarize, in this subsection, we have shown that the different barred galaxies show similar patterns of SFR distribution around bars; the central SFR is suppressed in LC galaxies not because of the peculiar behavior of bar dynamics but because star formation is suppressed (actually even more seriously) in the whole bar region.
<figure><img src="image_10.png" /></figure>

**Figure 7.** Some relations between galactic and bar properties. Red, green, and blue are for the LC, HC, and EHC samples, respectively. Panel (a): relation between SFR and $M_*$, The dashed and dotted lines mark the mean position and 0.3 dex offset of the SFMS. Gray is for the parent sample. Panel (b): relation between sSFR and $M_{H1}/M_*$, Only the ALFALFA-detected LC, HC, and EHC galaxies (see Section 2.5) are plotted. The GALEX Arecibo SDSS Survey (GASS; Catinella et al. 2010) data, which are an $M_*$ and redshift-defined H I sample, are plotted in gray, with the detected galaxies shown by dots and the upper limits of the nondetected galaxies shown by arrows. The dashed line shows the robust-fit bilinear relation for the detected galaxies in the GASS sample that have logsSFR > −11 yr$^{-1}$. Panel (c): relation between the bar length ($r_{bar}$; see Section 2.2) and the global color of the galaxies. The linear Pearson correlation coefficients ($\rho_{cor}$) are denoted, with error bars derived through bootstrapping.

# 4. Summary and Discussion

## 4.1. Similarities and Differences between the Samples

We have investigated a sample of massive, disk-dominated ($R_{90}/R_{50} < 2.2$), barred galaxies that have suppressed central SFR (LC) by comparing them to barred galaxies that have significantly enhanced central SFRs (HC and EHC).

We found the following common features for these three barred samples, which implies that the differences between their (central) SFRs in galaxies cannot be due to them.

(i) *Stellar central compactness.* The galaxies in these three subsamples have similar distributions of stellar mass central surface densities and optical concentrations (panels (c)–(e) of Figure 5).

(ii) *Group environment.* They have similar distributions of group masses and richness (panels (f) and (g) of Figure 5).

(iii) *H I gas abundance.* They have comparable ALFAFLA detection rates and similar $M_{H1}/M_*$ (panel (h) of Figure 5 and panel (c) of Figure 7).

(iv) *Bar strength.* The HC and LC galaxies have similar bar strengths measured radially (Figure 8) and globally (panels (a)–(c) of Figure 9).

(v) *Distribution of SFR close to bars.* The regions along the bar are redder than the interbar regions (Figure 10), and the central star formation is more enhanced (less

quenched) with respect to control galaxies (indicated by $(g - r) - (g - r)_{ctrl}$) than the star formation in the main bar regions (Figure 11).

There are three major differences found between the LC and HC (EHC) samples that are keys to understanding the suppressed central SFR in the LC galaxies.

(i) *Bar length related to color.* The LC galaxies have a stronger correlation between relative bar sizes and global colors than the other samples (panel (d) of Figure 7).

(ii) *The $g - r$ color out to 2 $r_{bar}$.* The LC galaxies, on average, have redder disks than the HC (EHC) galaxies throughout the radius range (Figure 10). The difference gets smaller when $r > 1.5 r_{bar}$.

(iii) *Spiral arm strength.* The LC galaxies have much weaker spiral structures beyond the bar radius (Figures 3, 4, and 8 and panels (d) and (e) of Figure 9).

Before we discuss possible scenarios, we note that the differences observed between LC and HC (EHC) galaxies can easily be confused with the differences known between early- and late-type galaxies. Early-type galaxies tend to be redder, show weaker spiral arms, and have rings more frequently (Buta et al. 2015, and references therein) than late-type galaxies. Early-type galaxies, however, are also expected to have more prominent classical bulges (higher central surface densities and central concentrations in the stellar distributions) and lower
<figure><img src="image_11.png" /><figcaption>**Figure 8.** Profiles indicating the radial distribution of nonaxisymmetric structures. The LC, HC, and EHC samples are plotted in red, green, and blue, respectively. The left column plots the median profiles of ellipticities (e, panel (b); see Section 2.2 for calculation details) of the three barred samples and the related K-S test probabilities ($P_{KS}$, panel (a)) to indicate the similarity of the distribution of the HC/EHC sample compared to the LC sample at each radius. The middle column plots the median profiles of the relative Fourier amplitudes $A_2$ (panel (d); see Section 2.7 for calculation details) and related K-S test probabilities (panel (c)). The right column plots the median profiles of $\Sigma_*$ differences ($\Sigma_{*,bar} - \Sigma_{*,int}$, panel (f); see Section 2.6 for calculation details) and related K-S test probabilities (panel (e)). In panels (e) and (f), the profiles within 0.5 $r_{bar}$ are specifically plotted in colored dotted lines to warn that in this region, $\Sigma_{*,int}$ can be contaminated by light along the bars. In all panels, error bars are derived through bootstrapping, and the gray vertical lines mark the position of $r_{bar}$. The gray horizontal lines mark 0.1 in panels (a), (c), and (e) and zero in panel (f).</figcaption></figure>

neutral gas content, while both LC and HC (EHC) galaxies are similarly (and highly) disk-dominated and H I-rich. We hence cannot just attribute the difference between LC and HC (EHC) galaxies to a simple difference between different Hubble types.

## 4.2. Indications from the Similarities

There are a few scenarios commonly related to star formation cessation, but we can consider them unlikely because of the similarities of the LC and HC samples.

### 4.2.1. Star Formation Cessation Due to Stellar Compactness and Environments

Observations and theories suggest that compact centers and massive halos are two key conditions for galaxies to cease their central star formation (Dekel & Burkert 2014; Woo et al. 2015). The combination of these two factors is often discussed under the context of the “compaction model,” where star-forming galaxies evolve around the SFMS, regulated by a balance between depletion and replenishment of the neutral gas (Tacchella et al. 2016). The compact centers could be related to feedback from starbursts or the black hole, which quickly deplete or remove the central gas, while the massive, hot halo prevents accretion of the neutral gas (Woo et al. 2015; Zolotov et al. 2015). The similarities in related properties suggest that it is unlikely that these two factors are responsible for the SFR-suppressed center of LC galaxies.

### 4.2.2. Star Formation Cessation Due to Global H I Abundance

Although molecular gas is more directly material or a tracer for star formation than H I gas, its mass is typically a relatively small fraction (~20%) of the neutral gas, and its depletion time is ~1 Gyr for galaxies close to the SFMS (Saintonge et al. 2011, 2017; Catinella et al. 2018). Hence, the H I gas is considered to be a necessary reservoir to sustain the star-forming

status in galaxies. It has been confirmed by previous studies that SFR is strongly correlated with H I mass fraction at a given stellar mass (Saintonge et al. 2016, 2017). The similarity in H I mass fractions between the LC and HC (EHC) samples suggests that the global H I richness is unlikely to be the cause of a suppressed central SFR in the LC galaxies. It is more likely that the large H I reservoir of the LC galaxies for some reason could not efficiently flow in to fuel the star formation within the (relatively) inner disks.

### 4.2.3. Star Formation Cessation Due to Local Star-forming Efficiency of H I Gas

A very low star-forming efficiency may cause a similarly low SFR, even when plenty of H I gas is present. Star formation models predict that the localized star-forming efficiency strongly depends on the stellar mass surface density and metallicity (Krumholz et al. 2009; Ostriker et al. 2010; Krumholz 2013). The LC, HC, and EHC samples have similar $\mu_*$ and $\Sigma_{*,ct}$, and the localized metallicities are strongly correlated with the stellar mass surface densities (Carton et al. 2015). Hence, on average, these three samples are unlikely to have different central star-forming efficiencies due to different metallicities or stellar mass surface densities.

Krumholz & Kruijssen (2015) predicted that strong turbulence caused by gas inflows could temporarily reduce the central star-forming efficiency in barred galaxies until the gas accumulates in the center to very high densities; this cycle runs on a typical timescale of a few tens of Myr. However, the centers of the LC galaxies are, on average, older than the HC and EHC galaxies by >~1 Gyr, and the short-period fluctuations of SFR predicted by Krumholz & Kruijssen (2015) are likely to be averaged out on such long timescales. Hence, the scenario of Krumholz & Kruijssen (2015) is unlikely to explain the formation of the LC galaxies.
<figure><img src="image_12.png" /></figure>

**Figure 9.** Parameters related to the strength of bars and spiral arms. The parameters include the absolute ($r_{bar}$; panel (a)) and relative ($r_{bar}/R_{25}$; panel (b)) bar lengths, the radial cumulative relative amplitude of the *m* = 2 Fourier decomposition component out to $r_{bar}$ ($S_{A_2,r_{bar}}$; panel (c)) and 1.5$bar$ ($S_{A_2,1.5r_{bar}}$; panel (d)), and the sum of the relative amplitudes of the *m* = 2, 3, and 4 components ($A_{tot}$; panel (e)). Please see Sections 2.2 and 2.7 for the details of these parameters. Here $r_{bar}$, $r_{bar}/R_{25}$, and $S_{A_2,r_{bar}}$ are indicators of bar strength, and $S_{A_2,1.5r_{bar}}$ and $A_{tot}$ are indicators of spiral arm strength. Red, green, and blue are for the LC, HC, and EHC samples, respectively. The K-S test probabilities ($p_{K_S}$; Press et al. 1992) that indicate the similarity of the distributions between the HC vs. LC samples (green) and the EHC vs. LC samples (blue) are denoted in the upper right corner of each panel. The dashed lines show the medians of the distributions.

### 4.2.4. Star Formation Cessation Due to Bar Strength

Both observations (e.g., Sakamoto et al. 1999; Sheth et al. 2005; Wang et al. 2012) and simulations (A92b; Piner et al. 1995; Athanassoula et al. 2013; Sormani et al. 2015, etc.) have shown that gas in the region between the CR and ILR moves inward due to the bar torques. The same is true for stars, albeit to a much lesser extent (e.g., Athanassoula & Misiriotis 2002; Valenzuela & Klypin 2003). If the region within the ILR (i.e., the central region) has nonaxisymmetric features—like inner bars, ovals, or spirals—material that has been pushed inward to the ILR can be pushed further inward, yet closer to the center (Shlosman et al. 1989; Peeples & Martini 2006; Schinnerer et al. 2006; Meier et al. 2008; Cole et al. 2014, etc.). In the region outside the CR, the direction of the radial motion has the opposite sign, i.e., outward (Kalnajs 1978), and gas does not cross the CR.

Thus, the gas initially within the CR is accumulated in the central region, while the region between the ILR and CR is steadily depleted of its gas, except for two narrow stripes along the leading sides of the bar, which are the shock loci (A92b). Thus, there should be considerable star formation in the central region but practically none further out in the main bar region, because the shear in the shock loci prevents star formation even in the narrow, high-density regions there, provided the bar is sufficiently strong (A92b; Sorai et al. 2012; Meidt et al. 2013; George et al. 2019). It was shown by A92b (see Figures 6 and 7 and Section 4.2 there) that stronger bars push more material inward and also create more extended and emptier regions between the ILR and CR and more gas concentration in the center (for the latter, see Athanassoula 1994; Athanassoula et al. 2013). It would thus be natural to associate stronger bars with more centrally concentrated star formation.

The LC and HC (EHC) samples show similar SFR distribution near the bar regions (i.e., in the comparisons of bar versus interbar regions and main bar versus central regions), consistent with the

pattern produced by gas inflows along strong bars, as described above. They also have similar bar strength. Hence, the suppressed central SFR in the LC galaxies is unlikely to be caused by bars of different strengths inducing different gas inflows.

### 4.3. Indications from the Differences: Why Is Star Formation Centrally Concentrated in Some Barred Galaxies and Not in Others?

The different properties between the samples are possibly related to the processes that cause the different central SFRs. The strong correlation of relative bar lengths and global color in the LC sample is consistent with both the theoretical prediction that the bar is longer in cases with no gas, or little gas, than in gas-rich cases (Athanassoula et al. 2013, particularly Figures 4 and 5 there, and Athanassoula 2014) and our speculation above, based on the H I abundance, that gas inflows should be weak in the LC galaxies. Below, we discuss a possible cause for LC galaxies to have weak gas inflows.

#### 4.3.1. A Possible Scenario Related to Spiral Arms

The most prominent difference between the samples is in the strength of the spiral arms. The dynamic relation between bars and spiral arms can be complex, and one can distinguish two possibilities. Some theories, such as simple bar-driven spirals (e.g., Athanassoula 1978) or the standard manifold theories (Patsis 2006; Romero-Gómez et al. 2006, 2007; Voglis et al. 2006; Athanassoula et al. 2010; Athanassoula 2012; Efthymiopoulos et al. 2019, etc.) assume that the pattern speed ($\Omega_p$) of the spirals is equal to that of the bar and thus that the spirals are outside their CR. In such cases, the radial motion of the gas will be outward (Kalnajs 1978), so there will be no enhancement of the central SFR due to spiral arms.

This assumption, however, need not be true for all barred galaxies (see, e.g., discussion in Section 6.4 of Athanassoula et al. 2010), and in some cases, the bar and spiral may have
<figure><img src="image_13.png" /><figcaption>**Figure 10.** Color profiles for the three barred samples. The LC, HC, and EHC samples are plotted in red, green, and blue, respectively. Panel (a) plots the median profiles of azimuthally averaged $g - r$. In panel (b), the median profiles of $g - r$ along the bars ("bar") are plotted in colored solid lines; the median profiles of $g - r$ perpendicular to the bars ("int") are plotted in colored dashed lines when $r > 0.5 r_{\text{bar}}$ and colored dotted lines when $r < 0.5 r_{\text{bar}}$. The $r < 0.5 r_{\text{bar}}$ regions of the profiles perpendicular to the bars are specifically plotted in colored dotted lines to warn about the possible contamination of light from the bar regions. Please see Section 2.6 for the details of deriving the color profiles. The error bars of the profiles are calculated through bootstrapping. The vertical gray dotted lines mark the position of $r_{\text{bar}}$.</figcaption></figure>

different pattern speeds and yet exchange energy and angular momentum between them, provided certain conditions are met and two resonances, one from each component, overlap sufficiently (Tagger et al. 1987; Sygnet et al. 1988). In such cases, the spiral continually breaks from and reconnects to the bar, providing a realistic morphology (Sellwood & Sparke 1988). A detailed study by Masset & Tagger (1997) argued that such a nonlinear coupling between the ILR of the spiral and the CR of the bar can be quite efficient and even more relevant than the swing mechanism in accounting for the dynamics of the galaxy beyond the corotation of the bar. Thus, the spiral is within its own CR, and the gas in that region can be pushed inward and therefore produce a larger gas concentration than what would have been achieved by the bar on its own. Thus, the much stronger spiral arms in the HC (EHC) galaxies would help explain the difference between the central SFRs of LC and HC/EHC galaxies.

The second main difference, namely the color, is naturally linked to the spiral strength. Indeed, for a given forcing, i.e., in this case, a given bar strength, the resulting spiral would be

stronger if the stellar population constituting the outer region was kinematically colder (see, e.g., Athanassoula 1984, for a review), i.e., younger and therefore bluer.

## 5. Conclusion and Future Perspective

In this paper, we compared two types of barred galaxies, those with centrally suppressed SFRs (LC) and those with centrally enhanced SFRs (HC/EHC). By making averages over each group, we compared various global quantities related to their mass, density, gas fraction, star formation, colors, and bar properties, as well as various radial profiles. We found which features are common between the two groups and which are clearly different. In the latter, let us mention the star-forming status in the center and inner disks, and the spiral arm strength, while the former includes the group environment, stellar density radial distributions, global H1 richness, etc. We searched for clues under the context of galaxy dynamic theories and simulations. After eliminating a number of alternatives, we proposed one possible scenario to produce the major differences of LC and HC (EHC) galaxies while preserving most of the similarities. This scenario relies on the fact that only gas within the CR can be driven inward by nonaxisymmetric components, such as bars or spirals. The spirals have lower pattern speeds than the bars while being coupled to them via resonances. In such cases, both the spirals and the bar could be driving gas inward, thus increasing the amount of gas driven to the center of HC galaxies.

Our paper contributes considerable new input on the problem at hand but is far from having solved it. We briefly summarize here some possible improvements.

This paper relies on analysis of radial profiles but does not include a decomposition of the light into different components. The selection of low-$R_{90}/R_{50}$ galaxies may have mitigated the contamination from a central bulge; however, the light from the disk may hide structures in the bars, and disk breaks may also affect our analysis. Analysis based on individual components obtained from decompositions, such as achieved by Kim et al. (2015, 2016), Salo et al. (2015), and Gao & Ho (2017), will be helpful and important to confirm the results in this paper. The decompositions will also enable analysis for galaxies with higher $R_{90}/R_{50}$.

Some of our results need confirmation from other types of data in the future. Optical or near-infrared spectroscopy based on either long-slit or integral field unit (MaNGA; e.g., Bundy et al. 2015) equipment will enable us to obtain mean velocities, as well as velocity dispersions of the stellar component, which, in turn, may allow us to get further information (e.g., pattern speed, corotation, kinematical temperature) on the dynamical evolution of our bars. The new radio instruments (e.g., MeerKAT and ALMA) will be useful not only to directly map the distribution of cold gas but also to check whether the radial variation of star-forming efficiency is the same among the different types of galaxies. Kinematical analysis of the cold and ionized gas may directly reveal the inflow and outflow of gas.

Direct comparisons of observations to simulations like those in Athanassoula et al. (2013, 2016) will help us gain more insight into the physics that produces the observables. The most important improvement, however, would be to introduce results not from a single snapshot but from a number of them, all with appropriate properties. Then, averages could be taken over all corresponding simulated galaxies, as we do here with the
<figure><img src="image_14.png" /><figcaption>**Figure 11.** Median profiles of $g - r$ differences from $(g - r)_{\text{avg,ctrl}}$ (see Section 2.6) for the three barred samples. The LC, HC, and EHC samples are plotted in red, green, and blue, respectively. The left column plots the median profiles of $(g - r)_{\text{avg}} - (g - r)_{\text{avg,ctrl}}$ (panel (b)) and related K-S test probabilities ($P_{\text{KS}}$) for the HC and EHC samples to be compared to the LC sample in the similarity of distributions at each radius (panel (a)). The median profiles of $(g - r)_{\text{bar}} - (g - r)_{\text{avg,ctrl}}$ (panel (d)) and related K-S test probabilities (panel (c)) are plotted in the middle column, and the median profiles of $(g - r)_{\text{int}} - (g - r)_{\text{avg,ctrl}}$ (panel (f)) and related K-S test probabilities (panel (e)) are plotted in the right column. The profiles perpendicular to the bars are specifically plotted in dotted lines when $r < 0.5 \ r_{\text{bar}}$ to warn about the possible contamination of light from the bar regions. Error bars are calculated through bootstrapping.</figcaption></figure>

observed galaxies in our sample. We also need to study the SFR in each of these in depth, in order to make more specific comparisons. These will be subjects of future research.

We gratefully thank M. Krumholz, K. Wang, and S. Ellison for useful discussions. J.W., S.Y., and H.G. are thankful for support from the National Science Foundation of China (11721303). S.Y. and H.G. are further thankful for support from the National Science Foundation of China (11991052) and the National Key R&D Program of China (2016YFA0400702). E.A. thanks the CNES for financial support. This work was granted access to the HPC resources of CINES under allocations 2019-A0060407665 and 2018-A0040407665 attributed by Grand Equipement National de Calcul Intensif (GENCI). This work was granted access to the HPC resources of Aix-Marseille Université financed by the project Equip@Meso (ANR-10-EQPX-29-01) of the program Investissements d'Avenir supervised by the Agence Nationale de la Recherche. L.S. is thankful for the support by the China Postdoctoral Science Foundation (2018M641067). J.W. thanks the DoA of Qsinghua University for the host and cookies during the preparation of this paper.

GALEX (Galaxy Evolution Explorer) is a NASA Small Explorer, launched in 2003 April, developed in cooperation

with the Centre National d'Etudes Spatiales of France and the Korean Ministry of Science and Technology.

We thank the many members of the ALFALFA team who have contributed to the acquisition and processing of the ALFALFA data set over the last several years. R.G. and M.P. H. are supported by NSF grant AST-0607007 and a grant from the Brinson Foundation.

Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS website is http://www.sdss.org/.

## Appendix

### Parameters and Abbreviations of Terms Used in the Main Part of the Paper

In Table A1, we list the abbreviations of terms and parameters used in this paper. The terms and parameters of each category are listed in alphabetical order. For each abbreviation or parameter in the table, we give a short description and refer to the section in the main part of the paper where the abbreviation or parameter was defined.
<table><caption>**Table A1**
Parameters and Abbreviations of Terms</caption><thead><tr><th>Definition</th><th>Description</th><th>Section for Definition</th></tr></thead><tbody><tr><td><em>Data Sets</em></td><td></td><td></td></tr><tr><td>ALFALFA</td><td>Arecibo Legacy Fast ALFA Survey</td><td>2.1</td></tr><tr><td>GALEX</td><td>Galaxy Evolution Explorer</td><td>2.1</td></tr><tr><td>GASS</td><td>GALEX Arecibo SDSS Survey</td><td>3.1.2 (Figure 7)</td></tr><tr><td>MPA/JHU</td><td>An advanced parameter catalog for SDSS</td><td>2.1</td></tr><tr><td>SDSS</td><td>Sloan Digital Sky Survey</td><td>2.1</td></tr><tr><td><em>Galactic Abbreviations</em></td><td></td><td></td></tr><tr><td>CR</td><td>Corotation</td><td>1</td></tr><tr><td>ILR</td><td>Inner Lindblad resonance</td><td>1</td></tr><tr><td>SED</td><td>Spectral energy distribution</td><td>2.1</td></tr><tr><td>SFH</td><td>Star formation history</td><td>2.1</td></tr><tr><td>SFMS</td><td>Star-forming main sequence</td><td>3.1.2</td></tr><tr><td><em>Galactic Properties</em></td><td></td><td></td></tr><tr><td>A<sub>2</sub></td><td>Measure of bar and arm strength</td><td>2.7</td></tr><tr><td>A<sub>tot</sub></td><td>Measure of spiral arm strength</td><td>2.7</td></tr><tr><td>C(SF)</td><td>Central concentration of specific SFR</td><td>2.1</td></tr><tr><td>ΔC(SF)</td><td>Enhancement of C(SF) with respect to control galaxies</td><td>2.1</td></tr><tr><td>D<sub>n</sub>(4000)</td><td>4000 Å break</td><td>2.1</td></tr><tr><td>e</td><td>Ellipticity</td><td>2.2</td></tr><tr><td>e<sub>bar</sub></td><td>Maximum ellipticity of the bar</td><td>2.2</td></tr><tr><td>f<sub>bar</sub></td><td>Fraction of galaxies hosting strong bars</td><td>2.3</td></tr><tr><td>g - r</td><td>Optical color</td><td>2.1</td></tr><tr><td>(g - r)<sub>avg</sub></td><td>Azimuthally averaged g - r profile</td><td>2.6</td></tr><tr><td>(g - r)<sub>bar</sub> \ Σ<sub>*,bar</sub></td><td>Radial distribution of g - r \ stellar surface density perpendicular along the bar</td><td>2.6</td></tr><tr><td>(g - r)<sub>int</sub> \ Σ<sub>*,int</sub></td><td>Radial distribution of g - r \ stellar surface density perpendicular to the bar</td><td>2.6</td></tr><tr><td>Hδ<sub>A</sub></td><td>Balmer absorption index</td><td>2.1</td></tr><tr><td>M<sub>*</sub></td><td>Stellar mass</td><td>2.1</td></tr><tr><td>M<sub>halo</sub></td><td>Halo mass</td><td>2.5</td></tr><tr><td>M<sub>H1</sub></td><td>H I mass</td><td>2.5</td></tr><tr><td>μ<sub>*</sub></td><td>Effective stellar mass surface density</td><td>2.1</td></tr><tr><td>N<sub>member</sub></td><td>Number of galaxies in the group</td><td>2.5</td></tr><tr><td>R<sub>90</sub>/R<sub>50</sub></td><td>Central concentration of light</td><td>2.1</td></tr><tr><td>R<sub>25</sub></td><td>Optical disk size</td><td>2.1</td></tr><tr><td>r<sub>bar</sub></td><td>Bar length</td><td>2.2</td></tr><tr><td>S<sub>A2,(1.5)</sub>r<sub>bar</sub></td><td>Measure of bar (and spiral arm) strength</td><td>2.7</td></tr><tr><td>SFR</td><td>Star formation rate</td><td>2.1</td></tr><tr><td>Σ<sub>*,ct</sub></td><td>Stellar mass surface density averaged within the central 3"</td><td>2.1</td></tr><tr><td>z</td><td>Redshift</td><td>2.1</td></tr><tr><td><em>Mathematical Terms</em></td><td></td><td></td></tr><tr><td>K-S test</td><td>Kolmogorov-Smirnov test</td><td>2.3</td></tr><tr><td>P<sub>KS</sub></td><td>K-S test probabilities</td><td>2.3</td></tr><tr><td>ρ<sub>cor</sub></td><td>Pearson correlation coefficient</td><td>3.1.2 (Figure 7)</td></tr></tbody></table>

<table><caption>**Table A1**
(Continued)</caption><thead><tr><th>Definition</th><th>Description</th><th>Section for Definition</th></tr></thead><tbody><tr><td><em>Samples</em></td><td></td><td></td></tr><tr><td>EHC</td><td>Extremely high central SFR, a reference analysis sample</td><td>2.3</td></tr><tr><td>HC</td><td>high central SFR, one of the main analysis sample</td><td>2.3</td></tr><tr><td>LC</td><td>Low central SFR, one of the main analysis sample</td><td>2.3</td></tr><tr><td>(g - r)-control sample</td><td>Control samples that are matched in global g - r to the analysis samples</td><td>2.4</td></tr><tr><td><em>References</em></td><td></td><td></td></tr><tr><td>A92b</td><td>Athanassoula (1992b)</td><td>1</td></tr><tr><td>W12</td><td>Wang et al. (2012)</td><td>1</td></tr></tbody></table>

ORCID iDs

Jing Wang https://orcid.org/0000-0002-6593-8820

E. Athanassoula https://orcid.org/0000-0001-6079-1332

Si-Yue Yu https://orcid.org/0000-0002-3462-4175

Christian Wolf https://orcid.org/0000-0002-4569-016X

Li Shao https://orcid.org/0000-0003-2015-777X

Hua Gao https://orcid.org/0000-0003-1015-5367

T. H. Randriamampandry https://orcid.org/0000-0002-8791-2138

References

Aguerri, J. A. L., Méndez-Abreu, J., & Corsini, E. M. 2009, A&A, 495, 491

Athanassoula, E. 1978, A&A, 69, 395

Athanassoula, E. 1984, PhR, 114, 319

Athanassoula, E. 1992a, MNRAS, 259, 328

Athanassoula, E. 1992b, MNRAS, 259, 345

Athanassoula, E. 1994, in Mass-Transfer Induced Activity in Galaxies, ed. I. Shlosman (Cambridge: Cambridge Univ. Press), 143

Athanassoula, E. 1999, in ASP Conf. Ser. 160, Astrophysical Disks—An EC Summer School, ed. J. A. Sellwood & J. Goodman (San Francisco, CA: ASP), 351

Athanassoula, E. 2002, Ap&SS, 281, 39

Athanassoula, E. 2003, MNRAS, 341, 1179

Athanassoula, E. 2012, MNRAS, 426, L46

Athanassoula, E. 2013, in Secular Evolution of Galaxies, ed. J. Falcón-Barroso & J. H. Knapen (Cambridge: Cambridge Univ. Press), 305

Athanassoula, E. 2014, MNRAS, 438, L81

Athanassoula, E., Lambert, J. C., & Dehnen, W. 2005, MNRAS, 363, 496

Athanassoula, E., Machado, R. E. G., & Rodionov, S. A. 2013, MNRAS, 429, 1949

Athanassoula, E., & Misiriotis, A. 2002, MNRAS, 330, 35

Athanassoula, E., Rodionov, S. A., Peschken, N., & Lambert, J. C. 2016, ApJ, 821, 90

Athanassoula, E., Romero-Gómez, M., Bosma, A., & Masdemont, J. J. 2010, MNRAS, 407, 1433

Bell, E. F., McIntosh, D. H., Katz, N., & Weinberg, M. D. 2003, ApJS, 149, 289

Berentzen, I., Athanassoula, E., Heller, C. H., & Fricke, K. J. 2003, MNRAS, 341, 343

Berentzen, I., Shlosman, I., Martinez-Valpuesta, I., & Heller, C. H. 2007, ApJ, 666, 189

Bournaud, F., & Combes, F. 2002, A&A, 392, 83

Bournaud, F., Combes, F., & Semelin, B. 2005, MNRAS, 364, L18

Brinchmann, J., Charlot, S., White, S. D. M., et al. 2004, MNRAS, 351, 1151
Bundy, K., Bershady, M. A., Law, D. R., et al. 2015, ApJ, 798, 7

Buta, R. J., Sheth, K., Athanassoula, E., et al. 2015, ApJS, 217, 32

Cameron, E. 2011, PASA, 28, 128

Carton, D., Brinchmann, J., Wang, J., et al. 2015, MNRAS, 451, 210

Catalán-Torrecilla, C., Gil de Paz, A., Castillo-Morales, A., et al. 2017, ApJ, 848, 87

Catinella, B., Saintonge, A., Janowiecki, S., et al. 2018, MNRAS, 476, 875

Catinella, B., Schiminovich, D., Cortese, L., et al. 2013, MNRAS, 436, 34

Catinella, B., Schiminovich, D., Kauffmann, G., et al. 2010, MNRAS, 403, 683

Chabrier, G. 2003, PASP, 115, 763

Cid Fernandes, R., Stasińska, G., Schlickmann, M. S., et al. 2010, MNRAS, 403, 1036

Cole, D. R., Debattista, V. P., Erwin, P., Earp, S. W. F., & Roškar, R. 2014, MNRAS, 445, 3352

Combes, F. 2008, in IAU Symp. 245, Formation and Evolution of Galaxy Bulges, ed. M. Bureau, E. Athanassoula, & B. Barbuy (Cambridge: Cambridge Univ. Press), 151

Cullen, H., Alexander, P., Green, D. A., Clemens, M., & Sheth, K. 2007, MNRAS, 374, 1185

Debattista, V. P., Mayer, L., Carollo, C. M., et al. 2006, ApJ, 645, 209

Dekel, A., & Burkert, A. 2014, MNRAS, 438, 1870

Efthymiopoulos, C., Kyziropoulos, P. E., Páez, R. I., Zouloumi, K., & Gravvanis, G. A. 2019, MNRAS, 484, 1487

Ellison, S. L., Nair, P., Patton, D. R., et al. 2011, MNRAS, 416, 2182

Ellison, S. L., Sánchez, S. F., Ibarra-Medel, H., et al. 2018, MNRAS, 474, 2039

Fisher, D. B., Bolatto, A., Drory, N., et al. 2013, ApJ, 764, 174

Fragkoudi, F., Athanassoula, E., & Bosma, A. 2016, MNRAS, 462, L41

Gadotti, D. A., & de Souza, R. E. 2003, ApJL, 583, L75

Gao, H., & Ho, L. C. 2017, ApJ, 845, 114

George, K., Joseph, P., Mondal, C., et al. 2019, A&A, 621, L4

Haynes, M. P., Giovanelli, R., Martin, A. M., et al. 2011, AJ, 142, 170

Huang, M.-L., & Kauffmann, G. 2015, MNRAS, 450, 1375

Kalnajs, A. J. 1973, PASAu, 2, 174

Kalnajs, A. J. 1978, in IAU Symp. 77, Structure and Properties of Nearby Galaxies, ed. E. M. Berkhuijsen & R. Wielebinski (Dordrecht: Reidel), 113

Kauffmann, G., Heckman, T. M., White, S. D. M., et al. 2003, MNRAS, 341, 54

Kereš, D., Katz, N., Weinberg, D. H., & Davé, R. 2005, MNRAS, 363, 2

Kim, T., Gadotti, D. A., Athanassoula, E., et al. 2016, MNRAS, 462, 3430

Kim, T., Sheth, K., Gadotti, D. A., et al. 2015, ApJ, 799, 99

Kim, W.-T., Seo, W.-Y., & Kim, Y. 2012, ApJ, 758, 14

Kormendy, J. 2013, in Secular Evolution of Galaxies, ed. J. Falcón-Barroso & J. H. Knapen (Cambridge: Cambridge Univ. Press), 1

Kraljic, K., Bournaud, F., & Martig, M. 2012, ApJ, 757, 60

Krumholz, M. R. 2013, MNRAS, 436, 2747

Krumholz, M. R., & Kruijssen, J. M. D. 2015, MNRAS, 453, 739

Krumholz, M. R., McKee, C. F., & Tumlinson, J. 2009, ApJ, 699, 850

Kuno, N., Sato, N., Nakanishi, H., et al. 2007, PASJ, 59, 117

Laurikainen, E., Salo, H., Buta, R., & Knapen, J. H. 2007, MNRAS, 381, 401

Lian, J., Yan, R., Zhang, K., & Kong, X. 2016, ApJ, 832, 29

Lim, S. H., Mo, H. J., Lu, Y., Wang, H., & Yang, X. 2017, MNRAS, 470, 2982

Martin, D. C., Fanson, J., Schiminovich, D., et al. 2005, ApJL, 619, L1

Martinet, L., & Friedli, D. 1997, A&A, 323, 363

Masset, F., & Tagger, M. 1997, A&A, 322, 442

Meidt, S. E., Schinnerer, E., García-Burillo, S., et al. 2013, ApJ, 779, 45

Meier, D. S., Turner, J. L., & Hurt, R. L. 2008, ApJ, 675, 281

Melvin, T., Masters, K., Lintott, C., et al. 2014, MNRAS, 438, 2882

Nair, P. B., & Abraham, R. G. 2010, ApJL, 714, L260

Ostriker, E. C., McKee, C. F., & Leroy, A. K. 2010, ApJ, 721, 975

Patsis, P. A. 2006, MNRAS, 369, L56

Peeples, M. S., & Martini, P. 2006, ApJ, 652, 1097

Pfenniger, D. 1991, in Dynamics of Disk Galaxies, ed. B. Sundelius (Gothenburg: Gothenburg University and Chalmers University of Technology), 191

Piner, B. G., Stone, J. M., & Teuben, P. J. 1995, ApJ, 449, 508

Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. 1992, Numerical Recipes in FORTRAN. The Art of Scientific Computing (Cambridge: Cambridge Univ. Press)

Quillen, A. C., Frogel, J. A., Kenney, J. D. P., Pogge, R. W., & Depoy, D. L. 1995, ApJ, 441, 549

Regan, M. W., Sheth, K., & Vogel, S. N. 1999, ApJ, 526, 97

Renzini, A., & Peng, Y.-j. 2015, ApJL, 801, L29

Romero-Gómez, M., Athanassoula, E., Masdemont, J. J., & García-Gómez, C. 2007, A&A, 472, 63

Romero-Gómez, M., Masdemont, J. J., Athanassoula, E., & García-Gómez, C. 2006, A&A, 453, 39

Saintonge, A., Catinella, B., Cortese, L., et al. 2016, MNRAS, 462, 1749

Saintonge, A., Catinella, B., Tacconi, L. J., et al. 2017, ApJS, 233, 22

Saintonge, A., Kauffmann, G., Wang, J., et al. 2011, MNRAS, 415, 61

Sakamoto, K., Okumura, S. K., Ishizuki, S., & Scoville, N. Z. 1999, ApJ, 525, 691

Salo, H., Laurikainen, E., Laine, J., et al. 2015, ApJS, 219, 4

Schinnerer, E., Böker, T., Emsellem, E., & Lisenfeld, U. 2006, ApJ, 649, 181

Schwarz, M. P. 1981, ApJ, 247, 77

Sellwood, J. A., & Sparke, L. S. 1988, MNRAS, 231, 25P

Shen, J., & Sellwood, J. A. 2004, ApJ, 604, 614

Sheth, K., Elmegreen, D. M., Elmegreen, B. G., et al. 2008, ApJ, 675, 1141

Sheth, K., Melbourne, J., Elmegreen, D. M., et al. 2012, ApJ, 758, 136

Sheth, K., Vogel, S. N., Regan, M. W., et al. 2002, AJ, 124, 2581

Sheth, K., Vogel, S. N., Regan, M. W., Thornley, M. D., & Teuben, P. J. 2005, ApJ, 632, 217

Shlosman, I., Frank, J., & Begelman, M. C. 1989, Natur, 338, 45

Sorai, K., Kuno, N., Nishiyama, K., et al. 2012, PASJ, 64, 51

Sormani, M. C., Binney, J., & Magorrian, J. 2015, MNRAS, 449, 2421

Sygnet, J. F., Tagger, M., Athanassoula, E., & Pellat, R. 1988, MNRAS, 232, 733

Tacchella, S., Dekel, A., Carollo, C. M., et al. 2016, MNRAS, 457, 2790

Tagger, M., Sygnet, J. F., Athanassoula, E., & Pellat, R. 1987, ApJL, 318, L43

Valenzuela, O., & Klypin, A. 2003, MNRAS, 345, 406

Voglis, N., Tsoutsis, P., & Efthymiopoulos, C. 2006, MNRAS, 373, 280

Wang, J., Kauffmann, G., Overzier, R., et al. 2011, MNRAS, 412, 1081

Wang, J., Kauffmann, G., Overzier, R., et al. 2012, MNRAS, 423, 3486

Woo, J., Dekel, A., Faber, S. M., & Koo, D. C. 2015, MNRAS, 448, 237

York, D. G., Adelman, J., Anderson, J. E., Jr., et al. 2000, AJ, 120, 1579

Yu, S.-Y., Ho, L. C., Barth, A. J., & Li, Z.-Y. 2018, ApJ, 862, 13

Zolotov, A., Dekel, A., Mandelker, N., et al. 2015, MNRAS, 450, 2327