STELLAR POPULATIONS OF BARRED QUIESCENT GALAXIES

The stellar populations of galaxies offer a unique view of the formation and evolution of galaxies. In this work, we use stellar populations to explore the evolution of barred quiescent disk galaxies.

Bars are predicted to affect the properties of their host galaxies through the slow rearrangement of energy and mass, a process called secular evolution (Kormendy & Kennicutt 2004; Athanassoula 2013; Sellwood 2014). This redistribution of material leads to many effects, including the flattening of the initial global abundance gradients of their host galaxies (Friedli et al. 1994; Friedli & Benz 1995; Martinet & Friedli 1997; Minchev & Famaey 2010; Di Matteo et al. 2013; Kubryk et al. 2013), which results in bulge abundances that are dependent on the presence of star formation. Specifically, if star formation is present, then the gaseous metallicities of bulges in barred galaxies are predicted to increase compared to unbarred galaxies (Friedli et al. 1994; Friedli & Benz 1995; Martel et al. 2013), while the bulge stellar metallicities stay relatively unchanged (Friedli et al. 1994). In this case, bars are also predicted to produce younger stellar populations at the center and the ends of the bar structure (Wozniak 2007). But if star formation is absent, then both the gaseous and stellar metallicities of bulges in barred galaxies are predicted to decrease due to dilution by lower-metallicity stars and gas from further galactocentric distances, assuming an initial negative metallicity gradient (Friedli et al. 1994; Di Matteo et al. 2013).

So far, works that have studied the bulge gas-phase metallicities of barred galaxies have only considered star-forming galaxies, which means that the bulge gaseous metallicities of barred galaxies are expected to be enhanced relative to unbarred galaxies. While there are works that agree with this prediction, there are others that do not. For example, Ellison et al. (2011), who used a large sample of galaxies from the Sloan Digital Sky Survey (SDSS), found that the gas-phase metallicities in the inner few kiloparsecs of barred galaxies are higher (by ∼0.06 dex) than unbarred galaxies at a given stellar mass. But Cacho et al. (2014), who also used a large sample of SDSS galaxies, found that for a given stellar mass there are no significant differences in the gas-phase metallicities at the inner few kiloparsecs of barred and unbarred galaxies (see also Henry & Worthey 1999). However, in contrast to all these results, Dutil & Roy (1999) and Considère et al. (2000) found that the central gas-phase metallicities of barred galaxies are lower than those of unbarred galaxies.

Works that have studied the bulge stellar populations of barred galaxies have considered both star-forming and quiescent galaxies. However, in analyzing their results, most of these works did not separate star-forming galaxies from quiescent galaxies, thus producing results that are difficult to interpret. Nonetheless, we summarize their findings for the benefit of the reader: Moorthy & Holtzman (2006) found that barred galaxies have higher bulge stellar metallicities than unbarred galaxies at a given velocity dispersion, which is consistent with the findings of Pérez & Sánchez-Blázquez (2011), who additionally found that the bulges of a sample of barred S0 galaxies are slightly α-enhanced compared to that of unbarred S0 galaxies. These results, however, are in contrast to those of Coelho & Gadotti (2011), Williams et al. (2012), and Cacho et al. (2014); they all found no difference in the stellar metallicity of bulges. Moreover, there is a similar disagreement about the bulge stellar ages of barred and unbarred galaxies: Pérez & Sánchez-Blázquez (2011), Williams et al. (2012), and Cacho et al. (2014) found no difference, while Coelho & Gadotti (2011) did.

Clearly, there is no consensus on whether bars affect the bulge abundances of their host galaxies. However, the lack of any strong bulge abundance differences in these works suggests that any potential effects from bars are probably small.

Turning to global gradients, which are predicted to be flatter in barred galaxies regardless of the presence of star formation, reveals a similarly confused landscape. While some studies found that the gas-phase metallicity gradients of barred galaxies are flatter than unbarred galaxies (Vila-Costas & Edmunds 1992; Martin & Roy 1994; Zaritsky et al. 1994), other studies found no difference (Sánchez et al. 2014; Ho et al. 2015).

Studies on the stellar population gradients of barred galaxies have also found conflicting results. Using slits placed along the bars of 20 galaxies, Pérez et al. (2009) found a variety of stellar metallicity and age gradients, including positive, negative, and null gradients (see also Pérez et al. 2007). For two of these galaxies, Sánchez-Blázquez et al. (2011) found that the stellar metallicity and age gradients are flatter along the bar than along the disk. In agreement, Williams et al. (2012) used a sample of 28 galaxies to show that the stellar metallicity gradients of boxy/peanut-shaped bulges (which are presumably indicative of the presence of a bar; Athanassoula 2005) are shallower than that of a sample of unbarred early-type galaxies. But most recently, using 62 face-on spiral galaxies from the CALIFA survey (Sánchez et al. 2012), Sánchez-Blázquez et al. (2014) found no difference in the stellar metallicity gradient or age gradient (their gradients extend out to the disk region) between barred and unbarred galaxies.

Similar to bulge abundances, there is no consensus on whether bars affect the abundance gradients of their host galaxies, indicating that any potential effects due to bars are small. Therefore, highly accurate and precise chemical analysis is needed to robustly detect them.

This work aims to achieve this goal by using very high signal-to-noise ratio (S/N $\geqslant \;100$ Å⁻¹) stacks of barred and unbarred galaxies, identified by Galaxy Zoo 2 (Willett et al. 2013), to model their stellar populations. Aside from the unprecedented S/N stacks of barred galaxies, an additional important and unique feature of our study is the minimization of emission lines by selecting only quiescent galaxies. The latter feature circumvents the need to model the emission-line contribution, which is complex and introduces more uncertainty to the resulting stellar population parameters (Conroy 2013). Moreover, with quiescent galaxies, we are comparing to predictions that have not been investigated, i.e., simulations without star formation.

We describe the data, sample selection, stacking, and stellar population synthesis (SPS) model in Sections 2 and 3. Section 4 presents our results, which indicates that there are no significant differences in the stellar populations of barred and unbarred quiescent disk galaxies. We present a comparison to past works in Section 5 and discuss our results in Section 6. Finally, we close in Section 7. Throughout this paper, we assume a flat cosmological model with ${H}_{0}=70$ km s⁻¹ Mpc⁻¹, ${{\rm{\Omega }}}_{m}=0.30$, and ${{\rm{\Omega }}}_{{\rm{\Lambda }}}=0.70$, and all magnitudes are given in the AB magnitude system.

Since our study aims to model the stellar populations of barred and unbarred quiescent disk galaxies, we must procure spectra of a large sample of these types of galaxies. Thus, we use the spectroscopic Main Galaxy Sample in the Legacy area of the SDSS Data Release Seven (SDSS DR7; Strauss et al. 2002; Abazajian et al. 2009); these spectra are measured with a 3'' fiber; hence, the results presented in this work only concern the central regions of our galaxies.

2.1. Sample Selection

2.2. Stacking

Because detailed abundance analysis requires high-S/N spectra (S/N $\geqslant 100$ Å⁻¹; Cardiel et al. 1998), we need to stack many SDSS spectra (each SDSS spectrum has a typical S/N ≈ 20 Å⁻¹) to achieve the necessary S/N (e.g., Graves et al. 2009).

We use two stacking schemes that correspond to our two science goals: (1) bins of stellar mass at $0.02\lt z\lt 0.04$ for our bulge analysis and (2) bins of redshift at three mass intervals for our gradient analysis (see Table 1; galaxy stellar masses [not fiber stellar masses] are taken from the MPA-JHU DR7 value-added catalogs); we explain the motivations for these schemes in Section 4.

Table 1.  Properties of Stacked Spectra

	z Bin	M* Bin	Numbera	S/Nb
Stack Name		(${M}_{\odot }$)		(Å−1)
Bulge-barred 1	$0.020\lt z\lt 0.040$	$9.60\lt \mathrm{log}\;{M}_{*}\lt 9.90$	13	80
Bulge-barred 2	$0.020\lt z\lt 0.040$	$9.90\lt \mathrm{log}\;{M}_{*}\lt 10.10$	32	130
Bulge-barred 3	$0.020\lt z\lt 0.040$	$10.10\lt \mathrm{log}\;{M}_{*}\lt 10.25$	39	170
Bulge-barred 4	$0.020\lt z\lt 0.040$	$10.25\lt \mathrm{log}\;{M}_{*}\lt 10.40$	62	257
Bulge-barred 5	$0.020\lt z\lt 0.040$	$10.40\lt \mathrm{log}\;{M}_{*}\lt 10.55$	71	307
Bulge-barred 6	$0.020\lt z\lt 0.040$	$10.55\lt \mathrm{log}\;{M}_{*}\lt 10.70$	66	307
Bulge-barred 7	$0.020\lt z\lt 0.040$	$10.70\lt \mathrm{log}\;{M}_{*}\lt 10.85$	26	189
Bulge-barred 8	$0.020\lt z\lt 0.040$	$10.85\lt \mathrm{log}\;{M}_{*}\lt 11.10$	10	142
Bulge-unbarred 1	$0.020\lt z\lt 0.040$	$9.60\lt \mathrm{log}\;{M}_{*}\lt 9.90$	39	133
Bulge-unbarred 2	$0.020\lt z\lt 0.040$	$9.90\lt \mathrm{log}\;{M}_{*}\lt 10.10$	81	216
Bulge-unbarred 3	$0.020\lt z\lt 0.040$	$10.10\lt \mathrm{log}\;{M}_{*}\lt 10.25$	84	253
Bulge-unbarred 4	$0.020\lt z\lt 0.040$	$10.25\lt \mathrm{log}\;{M}_{*}\lt 10.40$	83	294
Bulge-unbarred 5	$0.020\lt z\lt 0.040$	$10.40\lt \mathrm{log}\;{M}_{*}\lt 10.55$	87	317
Bulge-unbarred 6	$0.020\lt z\lt 0.040$	$10.55\lt \mathrm{log}\;{M}_{*}\lt 10.70$	40	248
Bulge-unbarred 7	$0.020\lt z\lt 0.040$	$10.70\lt \mathrm{log}\;{M}_{*}\lt 10.85$	18	178
Bulge-unbarred 8	$0.020\lt z\lt 0.040$	$10.85\lt \mathrm{log}\;{M}_{*}\lt 11.10$	10	141
Gradient-barred 1	$0.020\lt z\lt 0.040$	$10.10\lt \mathrm{log}\;{M}_{*}\lt 10.40$	101	306
Gradient-barred 2	$0.040\lt z\lt 0.055$	$10.10\lt \mathrm{log}\;{M}_{*}\lt 10.40$	131	272
Gradient-barred 3	$0.055\lt z\lt 0.067$	$10.10\lt \mathrm{log}\;{M}_{*}\lt 10.40$	59	153
Gradient-barred 4	$0.020\lt z\lt 0.040$	$10.40\lt \mathrm{log}\;{M}_{*}\lt 10.70$	137	435
Gradient-barred 5	$0.040\lt z\lt 0.055$	$10.40\lt \mathrm{log}\;{M}_{*}\lt 10.70$	139	338
Gradient-barred 6	$0.055\lt z\lt 0.067$	$10.40\lt \mathrm{log}\;{M}_{*}\lt 10.70$	143	261
Gradient-barred 7	$0.067\lt z\lt 0.077$	$10.40\lt \mathrm{log}\;{M}_{*}\lt 10.70$	148	235
Gradient-barred 8	$0.077\lt z\lt 0.085$	$10.40\lt \mathrm{log}\;{M}_{*}\lt 10.70$	66	158
Gradient-barred 9	$0.020\lt z\lt 0.040$	$10.70\lt \mathrm{log}\;{M}_{*}\lt 11.00$	36	233
Gradient-barred 10	$0.040\lt z\lt 0.055$	$10.70\lt \mathrm{log}\;{M}_{*}\lt 11.00$	90	318
Gradient-barred 11	$0.055\lt z\lt 0.067$	$10.70\lt \mathrm{log}\;{M}_{*}\lt 11.00$	92	262
Gradient-barred 12	$0.067\lt z\lt 0.077$	$10.70\lt \mathrm{log}\;{M}_{*}\lt 11.00$	86	213
Gradient-barred 13	$0.077\lt z\lt 0.085$	$10.70\lt \mathrm{log}\;{M}_{*}\lt 11.00$	94	207
Gradient-unbarred 1	$0.020\lt z\lt 0.040$	$10.10\lt \mathrm{log}\;{M}_{*}\lt 10.40$	167	383
Gradient-unbarred 2	$0.040\lt z\lt 0.055$	$10.10\lt \mathrm{log}\;{M}_{*}\lt 10.40$	509	527
Gradient-unbarred 3	$0.055\lt z\lt 0.067$	$10.10\lt \mathrm{log}\;{M}_{*}\lt 10.40$	341	373
Gradient-unbarred 4	$0.020\lt z\lt 0.040$	$10.40\lt \mathrm{log}\;{M}_{*}\lt 10.70$	127	399
Gradient-unbarred 5	$0.040\lt z\lt 0.055$	$10.40\lt \mathrm{log}\;{M}_{*}\lt 10.70$	429	604
Gradient-unbarred 6	$0.055\lt z\lt 0.067$	$10.40\lt \mathrm{log}\;{M}_{*}\lt 10.70$	687	623
Gradient-unbarred 7	$0.067\lt z\lt 0.077$	$10.40\lt \mathrm{log}\;{M}_{*}\lt 10.70$	842	600
Gradient-unbarred 8	$0.077\lt z\lt 0.085$	$10.40\lt \mathrm{log}\;{M}_{*}\lt 10.70$	441	411
Gradient-unbarred 9	$0.020\lt z\lt 0.040$	$10.70\lt \mathrm{log}\;{M}_{*}\lt 11.00$	26	213
Gradient-unbarred 10	$0.040\lt z\lt 0.055$	$10.70\lt \mathrm{log}\;{M}_{*}\lt 11.00$	152	418
Gradient-unbarred 11	$0.055\lt z\lt 0.067$	$10.70\lt \mathrm{log}\;{M}_{*}\lt 11.00$	292	493
Gradient-unbarred 12	$0.067\lt z\lt 0.077$	$10.70\lt \mathrm{log}\;{M}_{*}\lt 11.00$	423	509
Gradient-unbarred 13	$0.077\lt z\lt 0.085$	$10.70\lt \mathrm{log}\;{M}_{*}\lt 11.00$	472	484

Notes.

^aTotal number of galaxies in the stacked spectrum. ^bEffective median S/N of the stacked spectrum.

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Each individual spectrum was continuum-normalized using Gaussian convolution, smoothed to an effective velocity dispersion of 300 km s⁻¹, corrected for galactic extinction using the parameterization of Cardelli et al. (1989), and flux-calibrated according to Yan (2011). The empirical flux calibration from Yan (2011) results in relative spectrophotometric precision of 0.1%, increasing the accuracy and precision of our model fitting, which we describe in the next section. Each spectrum contributes equally to a stack, but portions of spectra that are 5σ deviations from the initial stack are trimmed. Only a small percentage of spectra are trimmed in this manner, and the exclusion of this trimming does not affect our final results. The typical S/N of our stacks is $\gtrsim 100$ Å⁻¹; see Table 1 for each stack's S/N.

We compare the stacks of our barred and unbarred samples in Figures 8 and 9 of Appendix B. Focusing on the ratio of the stacks at the Lick indices, we find that there are no significant differences, which is supported by Figure 10, which plots several Lick indices as a function of mass for barred and unbarred quiescent disk galaxies. This initial analysis supports our findings using full-spectrum fitting in Section 4.

The total number of barred and unbarred galaxies that make up the stacks for our bulge analysis is 319 and 442, respectively. The total number of barred and unbarred galaxies that make up the stacks for our gradient analysis is 1322 and 4908, respectively.

We fit our high-S/N stacked spectra with the latest version of the SPS model of Conroy & van Dokkum (2012a), which is detailed in Conroy et al. (2014; see also Choi et al. 2014). We follow the methodology of Conroy et al. (2014) in the present work.

Briefly, this SPS model uses three sets of stellar isochrones and the MILES (Sánchez-Blázquez et al. 2006) and IRTF (Cushing et al. 2005; Rayner et al. 2009) empirical stellar spectral libraries to fit for the full inputted spectrum at four wavelength intervals: 4000–4700 Å, 4700–5700 Å, 5700–6400 Å, and 8000–8800 Å. The wavelength range 6400–8000 Å is not included because it is at the edges of the MILES and IRTF wavelength coverage. A two-part Kroupa IMF is assumed. Non-solar abundance patterns are modeled with response functions using the ATLAS12/SYNTHE code suites (Kurucz 1970, 1993) and applied differentially onto the template model galaxy spectrum. A Markov Chain Monte Carlo (MCMC) algorithm was used to explore the 40 free parameters of the model, which include redshift, velocity dispersion, two population ages (the age of the dominant population and the age of the younger population),¹⁶  the mass fraction of the younger population, four nuisance parameters,¹⁷  13 emission line strengths, the velocity broadening of the emission lines, and the abundances of C, N, Na, Mg, Si, Ca, Ti, V, Cr, Mn, Fe, Co, Ni, Sr, and Ba, and O, Ne, and S (the latter three are varied in lockstep). The systematic uncertainties (e.g., incomplete stellar spectral libraries, unknown aspects of stellar evolution, metallicity evolution) are probably ∼0.05 dex (Choi et al. 2014; Conroy et al. 2014).

We illustrate the quality of our model fits in Figures 11 and 12 of Appendix C; it shows that the fits are excellent and, moreover, the quality of the barred and unbarred fits is indistinguishable.

4.1. Stellar Populations of the Bulges of Barred and Unbarred Galaxies

To model the stellar populations of galaxy bulges, our analysis only considers redshifts between $0.02\lt z\lt 0.04$ since the SDSS fiber radius ($1\buildrel{\prime\prime}\over{.} 5$) at z = 0.04 corresponds to $\approx 1$ kpc, which is the typical half-light radii of both classical bulges and disky pseudobulges (Fisher & Drory 2010). The lower limit of z = 0.02 corresponds to the redshift where the SDSS spectrograph starts to cover [O ii] λ3727. The sample for our bulge stellar population analysis is highlighted by the blue hatches in the $\mathrm{log}\;{M}_{*}-z$ distribution of our quiescent sample in Figure 1. The stellar masses we consider range from $\mathrm{log}\;{M}_{*}/{M}_{\odot }=9.6$ to $\mathrm{log}\;{M}_{*}/{M}_{\odot }=11.1$, which we split into eight $\mathrm{log}\;{M}_{*}$ bins; these bins are listed in the top rows of Table 1 and are labeled "Bulge-barred" or "Bulge-unbarred." The barred and unbarred stacked spectra of the highlighted bin ($0.02\lt z\lt 0.04$ and $10.25\lt \mathrm{log}\;{M}_{*}/{M}_{\odot }\lt 10.40$) are shown in the upper and lower panels of Figure 1, with each spectrum plotted in gray. Two images of barred and unbarred galaxies from the highlighted bin are also shown. The ratios of the barred and unbarred stacked spectra at several Lick indices are highlighted in the center right panel. There are extremely subtle differences in these Lick indices, indicating that (1) high S/N is needed to detect these differences and (2) full-spectrum modeling can help bring out features that are not covered by Lick indices. Appendix B presents a more detailed comparison of the stacks and their residuals—they show similar features to the comparison in Figure 1.

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With these high-S/N stacks, we model the bulge stellar populations of our barred and unbarred quiescent disk galaxies at each stellar mass bin. Our results are shown in Figure 2; it displays the stellar age, [Fe/H] (a metallicity indicator), [Mg/Fe] (a star formation timescale indicator), and [N/Fe] (another star formation timescale indicator) versus stellar mass of barred quiescent disks in magenta and unbarred quiescent disks in purple (this is the color scheme throughout the paper). There is a general correlation between all stellar population parameters and stellar mass for both populations, similar to the trends between stellar population parameters and central velocity dispersion of early-type galaxies (e.g., Thomas et al. 2005).

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The error estimates shown in Figure 2 are based on the full posterior distributions of each fitted parameter from the MCMC spectrum-fitting algorithm. Systematic uncertainties are ∼0.05 dex (Choi et al. 2014; Conroy et al. 2014) and should be assumed in addition to the displayed error estimates. Thus, the main result of Figure 2 is that there are no significant differences in the stellar populations of the bulges of barred versus unbarred quiescent disk galaxies, which is supported by the P-values of $\geqslant 0.14$ (based on the Z-score).

4.2. Stellar Population Gradients

Since the SDSS fiber size corresponds to a larger physical size at higher redshift, we can probe stellar populations at larger physical galactocentric radii by analyzing higher-redshift galaxies (e.g., Yan & Blanton 2012). Combining this approach with the assumption that galaxy properties (e.g., galaxy size, bar length, and their abundance patterns) do not evolve significantly at a fixed stellar mass over our redshift range of $0.020\lt z\lt 0.085$, which corresponds to ≈1 Gyr, we can estimate stellar population gradients. Our upper limit of z = 0.085 corresponds to the redshift limit of the debiasing procedure applied to the GZ2 vote fractions (Willett et al. 2013). Therefore, we separate our sample into seven bins of redshift, from z = 0.020 to z = 0.085, at three stellar mass bins: $10.1\lt \mathrm{log}\;{M}_{*}/{M}_{\odot }\lt 10.4$, $10.4\lt \mathrm{log}\;{M}_{*}/{M}_{\odot }\lt 10.7$, and $10.7\lt \mathrm{log}\;{M}_{*}/{M}_{\odot }\lt 11.0$; these bins are listed in the bottom rows of Table 1 and are labeled "Gradient-barred" or "Gradient-unbarred." This sample is highlighted with green hatches in the $\mathrm{log}\;{M}_{*}$ versus z panel of Figure 1.

4.2.1. SDSS Fiber Size versus Typical Galaxy Size

Before we present the stellar population gradients, an important question that needs to be addressed is, "how much of our galaxies is covered by the SDSS fiber?" The answer is shown in Figure 4, which plots semimajor half-light radius (${r}_{{\rm{e}}}$; from the GIM2D single Sérsic fits by Simard et al. 2011) versus redshift (z). Each panel displays the ${r}_{{\rm{e}}}-z$ distribution of our quiescent sample (see Section 2.1) in the gray contours. Overplotted in panels (a)–(c) are the ${r}_{{\rm{e}}}-z$ distributions of the three mass bins considered in the stellar population gradient analysis. The barred and unbarred samples are displayed in solid and dashed contours, respectively; there is no evident difference in their ${r}_{{\rm{e}}}-z$ distribution. Moreover, there is no clear ${r}_{{\rm{e}}}$ evolution at a given mass bin, supporting our assertion of null ${r}_{{\rm{e}}}$ evolution in our redshift range.

Within panels (a)–(c), the colored hatched lines represent the range that is covered by the SDSS fiber at a given mass bin, which, as shown in Figure 1, corresponds to different maximum redshifts. Panel (d) overplots all the ${r}_{{\rm{e}}}-z$ distributions of the three mass bins (combining both barred and unbarred galaxies) and their lines of maximum SDSS fiber physical radius in their respective colors.

Figure 4 shows that for each mass bin, the maximum SDSS fiber physical radius is ≈50%–70% of the median ${r}_{{\rm{e}}}$, meaning that the gradients in Figure 3 extend out to ≈50%–70% the median galaxy semimajor half-light radius. Thus, even at the highest redshift bin, our gradients are still dominated by the central regions of our galaxies, indicating that our gradient analysis is not sensitive to the outskirts of our galaxies.

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4.2.2. SDSS Fiber Size versus Typical Bar Length

A similarly important question is, "how much of our bars is covered by the SDSS fiber?" To illustrate the varying extent of the SDSS fiber with respect to the bar structure as a function of redshift, we present SDSS r-band images of typical barred galaxies for each redshift interval at a given stellar mass bin with the SDSS fiber overplotted in Figure 5. The physical size of the 3'' SDSS fiber is shown at the bottom right of each image. For each mass bin, we reproduce the [Fe/H] gradients from Figure 3 for the reader's convenience.

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Clearly, the SDSS fiber covers more of the bar with increasing redshift. This effect is not likely due to an evolution of the bar length: matching our barred galaxies from the gradient analysis to the bar length catalog of Hoyle et al. (2011)¹⁸ shows that there is no strong bar length evolution, indicating that the SDSS fiber is truly covering a larger fraction of these bars with redshift.

To answer the question posed at the beginning of this section more quantitatively, we need bar length measurements for all our barred galaxies. Unfortunately, as was mentioned above, we only have bar lengths for ≈14% of our sample. Fortunately, this subsample is approximately normally distributed across the mass range used in Section 4.2, and thus it is likely to be a representative sample. Assuming that this subsample is indeed representative of our entire bar sample, we find that most of our bars are 3–7 kpc (in semimajor axis), which is consistent with the findings of other works (Erwin 2005; Durbala et al. 2008; Gadotti 2011). Thus, the SDSS fiber, which ranges from 0.6 to 2.4 kpc in radius, covers ≈8%–80% of the length of the bars in our sample, i.e., the fiber samples a large range of the typical bar lengths in our sample.

But it is clear that our gradients are limited to well within the bar structure, which is an important caveat to consider and is discussed in more detail in Section 6.

4.2.3. Stellar Population Gradients of Barred and Unbarred Galaxies

Given that our gradients do not extend beyond the bars, here we present the stellar population gradients of barred and unbarred quiescent disk galaxies in Figure 3. The top three rows plot [Fe/H], [Mg/Fe], and [N/Fe] as a function of the physical radius of the SDSS fiber (in kpc) in the three bins of stellar mass listed above. The fourth row of Figure 3 superimposes the gradients of all mass bins. At all radii, [Fe/H], [Mg/Fe], and [N/Fe] increase with $\mathrm{log}\;{M}_{*}$, which is consistent with the bulge trends in Figure 2.

We stress that the stellar population parameters at a given fiber radius in Figure 3 are not annular measurements, but rather integrated measurements, i.e., we model the stellar population of the total area covered by the SDSS fiber, which increases with redshift. Despite the fact that our method of estimating gradients is different from that of most other works (which use annular measurements), we still find results that are similar to those works. For example, our [Fe/H] gradients are negative (decrease with radius), while our [Mg/Fe] gradients are nearly flat, both of which are consistent with the findings of past works (Mehlert et al. 2003; Sánchez-Blázquez et al. 2007; Rawle et al. 2008; Kuntschner et al. 2010; Greene et al. 2013).

We do not consider the stellar age gradients because in addition to probing larger physical distances within galaxies with redshift, we are also probing younger galaxies with redshift. Thus, the resulting stellar age gradients can be due to both younger stellar populations at larger physical distances and passive evolution, a degeneracy that we do not attempt to disentangle.

The main result of this section is evident upon examination of Figure 3: there are no differences in the central stellar population gradients of barred and unbarred quiescent disk galaxies that exceed the level of systematic uncertainty.

As summarized in the Introduction, previous works in this topic often disagree—some show that bars affect their host galaxies' stellar populations (e.g., Moorthy & Holtzman 2006; Coelho & Gadotti 2011; Pérez & Sánchez-Blázquez 2011; Sánchez-Blázquez et al. 2011; Williams et al. 2012), while others show that bars do not (e.g., Cacho et al. 2014; Sánchez-Blázquez et al. 2014). While some of these differences can be attributed to the choice of SPS model, Conroy et al. (2014) have shown that there is a broad agreement between their model (the one used in this work) and several other popular models, including EZ_Ages (Graves & Schiavon 2008), which uses Lick indices as opposed to full-spectrum fitting. Thus, assuming that different models produce similar results, we will restrict our comparison to data quantity, data quality, and sample selection.

Comparing our data quantity to previous works shows that there are only a couple of works that are comparable—Coelho & Gadotti (2011) have 251 barred galaxies and 324 unbarred galaxies, and Cacho et al. (2014) have 414 barred galaxies and 1180 unbarred galaxies; both works primarily contained star-forming barred galaxies. Our work contains over 1000 quiescent barred galaxies and over 5000 quiescent unbarred galaxies.

Comparing our data quality to previous works shows that our stacked spectra have the highest S/N ($\gtrsim 100$ Å⁻¹). Previous works have spectra with S/N = 10–50 Å⁻¹, which produces less accurate and less precise stellar population parameters. Of course, in order to achieve such high S/N, we have stacked many spectra, which has not been done in any previous work on this topic. Thus, our work is measuring the average effects of bars in quiescent disk galaxies.

Finally, comparing our sample selection to previous works shows that our sample is unique. While we only select galaxies with SDSS spectra that are bereft of two of the strongest optical emission lines—Hα and [O ii] λ3727—all previous works selected galaxies with a range of star formation states. In fact, most works require the presence of these lines (e.g., Cacho et al. 2014). The main benefit of our selection criteria is that our stacked spectra have minimal emission-line contamination, resulting in highly accurate and precise stellar population modeling, which was one of the main goals of this work. This sample selection, however, is an important consideration in our interpretation, which we discuss in Section 6 (see also Section 2.1).

Based on these three comparisons, it is clear that our work is unlike any of the previous works on this topic. Interestingly though, even with our differences, we find similar results to the latest work on this topic. Namely, like Cacho et al. (2014), we find no strong differences in the stellar populations of barred and unbarred galaxies, indicating that bars do not significantly affect the stellar populations of their host galaxies, regardless of their star formation state.

6.1. Comparison to Predictions of Bar-driven Secular Evolution

In this work, we use the latest SPS model of Conroy & van Dokkum (2012a) to estimate the stellar populations of barred and unbarred quiescent disk galaxies with very high S/N ($\gtrsim 100$ Å⁻¹) stacks drawn from the SDSS. Taking advantage of the variable physical size of the SDSS fiber as a function of redshift, we model the stellar populations at different parts within galaxies. We first focus on the bulges of galaxies, which have a typical half-light radius of 1 kpc (Fisher & Drory 2010), and approximate the physical size of the SDSS fiber at $0.02\lt z\lt 0.04$. We then estimate the stellar population gradients by assuming that galaxies at a fixed stellar mass do not significantly evolve in the redshift range of $0.020\lt z\lt 0.085$, which spans ≈1 Gyr. Our resulting stellar population gradients extend out to 50%–70% of the median semimajor half-light radius of our samples, which is well within the extent of the bars in our sample.

We find that there are no significant differences in the stellar populations of the bulges or the gradients of barred versus unbarred quiescent disk galaxies, suggesting that bars are not a significant influence to the chemical evolution of quiescent disk galaxies.

This publication has been made possible by the participation of more than 200,000 volunteers in the Galaxy Zoo project. Their contributions are individually acknowledged at http://www.galaxyzoo.org/Volunteers.aspx.

Authors from UC Santa Cruz acknowledge financial support from the NSF Grant AST 08-08133. C.C. acknowledges funding from NASA grant NNX13AI46G and NSF grant AST-1313280. E.A. and A.B. acknowledge financial support to the DAGAL network from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme FP7/2007-2013/ under REA grant agreement number PITN-GA-2011-289313, from the CNES (Centre National d'Etudes Spatiales-France), and from the PNCG (Programme National Cosmologie et Galaxies-France). 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/. The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington. E.C. deeply thanks Genevieve J. Graves for sharing her stacking code. E.C. also thanks Jieun Choi and Kevin Bundy for useful discussions. We also thank the anonymous referee for a constructive report. The JavaScript Cosmology Calculator (Wright 2006) was used in the preparation of this paper.

Face-on quiescent disk galaxies, especially those without structures such as bars, are difficult to distinguish from pure elliptical galaxies. In order to illustrate that our unbarred quiescent disk sample is not severely contaminated by pure elliptical galaxies, in this appendix we compare a sample of spheroid-dominated galaxies to our unbarred quiescent disk sample.

To select spheroid-dominated galaxies from our quiescent sample (see Section 2.1), we use the criteria outlined by Cheng et al. (2011). In their work, they offer a way of selecting early-type, bulge-dominated galaxies without sharp edges, which we consider a satisfactory definition of spheroid-dominated galaxies. The selection method of Cheng et al. (2011) depends on GIMD bulge+disk decompositions and standard SDSS photometric parameters. In particular, the criteria are

• 1.  
  $B/T\gt 0.5;$
• 2.  
  $s2\gt 0.08;$
• 3.  
  $b/a\gt 0.65;$
• 4.  
  $C\gt 2.9;$

with B/T representing the bulge-to-total ratio, s2 representing the smoothness parameter, b/a representing the r-band axis ratio, and C representing the r-band concentration. B/T and s2 are from the n = 4 + n = 1 GIM2D catalog (Simard et al. 2011), while b/a and C are from SDSS DR7.

With this spheroid sample, we compare its distributions of global Sérsic index (n), central surface stellar mass density (${{\rm{\Sigma }}}_{1\;\mathrm{kpc}}^{*}$; Cheung et al. 2012), central velocity dispersion (σ), and bulge-to-total ratio (B/T) to those of our unbarred quiescent disk sample at the eight mass bins used in our bulge analysis (see Section 4.1) in Figures 6 and 7. We also include the distributions of our barred quiescent disk sample for a further comparison.

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These distributions show that the spheroids have, on average, a higher n, ${{\rm{\Sigma }}}_{1\;\mathrm{kpc}}^{*}$, σ, and B/T than both the barred and unbarred quiescent disks for the four least massive bins, indicating that our unbarred quiescent disks are not dominated by spheroid-dominated galaxies.

For the more massive bins, however, their distributions become more similar, indicating that the structural properties of these classes of galaxies are almost indistinguishable at high masses. This similarity, though, does not mean that our unbarred quiescent disk sample is severely contained by ellipticals. Indeed, the structural distributions of our barred quiescent disk sample are also similar to that of the spheroid-dominated sample at these massive bins. And since bars are pure disk phenomena (Athanassoula 2013), we conclude that the structural parameters we considered simply cannot distinguish spheroid-dominated galaxies from quiescent disk galaxies at high stellar masses. Therefore, given the ineffectiveness of these structural parameters to distinguish face-on quiescent disks from spheroid-dominated galaxies at high masses, we rely on the visual morphologies of Galaxy Zoo.

Perhaps the most reassuring result of this section, however, is that the structural distributions of our barred and unbarred quiescent face-on disks are similar, indicating that we are selecting similar types of galaxies.

In this section we directly compare the stacked spectra of the barred and unbarred samples. Figures 8 and 9 plot the barred stacks over the unbarred stacks for each stellar mass bin analyzed in the bulge analysis (Section 4.1). The bottom panels show the ratio of the barred to unbarred stacks, highlighting some relevant Lick indices.

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Clearly, there are very small differences in these stacks. To summarize these differences, we plot several Lick indices versus stellar mass in Figure 10. Hβ, a tracer of the stellar age, [MgFe], a tracer for metallicity (Thomas et al. 2003), and Mg b and Mg b/$\lt \mathrm{Fe}\gt$ , a tracer for the α-abundance (Thomas et al. 2003), all show no significant differences between barred and unbarred galaxies, mirroring our main result in Section 4.1.

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In this appendix we illustrate the quality of the model fits by showing the input stacked spectra and the model spectra in Figures 11 and 12 for four mass bins from the bulge analysis (see Section 4.1); the barred stacks are on the left, and unbarred stacks are on the right. At the bottom of each spectrum, we show the residuals of the model and input spectra. The first feature to note is that the residuals are small, about 1%, indicating that the fits are excellent. Second, the residuals for the barred and unbarred model spectra are similar, indicating that the quality of the fits of the two samples is comparable.

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