The Local Cluster Survey. I. Evidence of Outside-in Quenching in Dense Environments

Galaxy clusters host a smaller fraction of actively star-forming galaxies than the general field (e.g., Balogh et al. 1997; Poggianti et al. 1999; Lewis et al. 2002; Gómez et al. 2003; Finn et al. 2005, 2008, 2010; Postman et al. 2005). Even at fixed stellar mass, the fraction of star-forming galaxies tends to decrease with increasing environmental density (e.g., Peng et al. 2010). The mass accretion rate of clusters (e.g., McGee et al. 2009), combined with the assumption that all accreted galaxies eventually quench their star formation, implies that quenching must take place over a long timescale, 3–7 Gyr (e.g., Balogh et al. 2000; Ellingson et al. 2001; Kimm et al. 2009; Peng et al. 2010; De Lucia et al. 2012; Wetzel et al. 2012).

However, trying to uncover the physics that drives this transformation by studying the properties of galaxies during the transition has proved difficult and controversial. A small fraction of galaxies are found in a post-starburst phase, which implies a rapid truncation timescale (Dressler & Gunn 1983); this fraction may depend on environment and redshift (e.g., Zabludoff et al. 1996; Balogh et al. 1999; Poggianti et al. 1999; Tran et al. 2007; Mok et al. 2013; Muzzin et al. 2013). However, the bulk of the star-forming population in clusters looks very similar to those in the field, in terms of their star formation rate and color distribution (Balogh et al. 2004; Baldry et al. 2006; McGee et al. 2011), with just the relative fraction of star-forming and quiescent galaxies varying with environment. Few galaxies, at least at low redshift, seem to inhabit the green valley region that separates star-forming from quiescent galaxies, which implies that the transition itself must happen rapidly, on timescales <1 Gyr (Wetzel et al. 2012).

To reconcile these facts, Wetzel et al. (2012, 2013) proposed a two-stage model in which star formation truncation happens rapidly, but only after a lengthy delay time following accretion into a cluster or group. In the model as originally proposed, galaxies experience little or no change in their star formation rates during the delay phase. Understanding how galaxies could remain uninfluenced by their environment for so long has been a theoretical challenge. Nonetheless, the model has been used successfully to interpret a range of observations at redshifts out to z = 1 (van der Burg et al. 2013; Mok et al. 2014; Muzzin et al. 2014; Haines et al. 2015; Knobel et al. 2015; Fossati et al. 2017). Following the delay, the process of galaxy quenching proceeds on a rapid timescale of <1 Gyr.

Despite the success of this delay+rapid quenching model, the hypothesis that galaxies are completely unaffected during the delay period remains controversial. Several studies have shown evidence that at a fixed stellar mass, star formation rates of galaxies in dense environments are skewed to lower values than in the general field (e.g., Koopmann & Kenney 2004a; Poggianti et al. 2008; Gallazzi et al. 2009; Wolf et al. 2009; Finn et al. 2010; Vulcani et al. 2010; Haines et al. 2013; Lin et al. 2014; Taranu et al. 2014; Rodríguez del Pino et al. 2017). This would imply that there are environmental processes at work during the several Gyrs after infall. The delay period might then simply be a time during which long-timescale processes are slowly altering the cluster galaxies, prior to the ultimate termination of star formation in a rapid quenching phase (e.g., Haines et al. 2015).

In this paper, we investigate what is happening to galaxies during the delay phase, and we identify delay-phase galaxies as those that have been accreted by a cluster but are still forming stars. Our goal is to measure the relative extent of the gas and stellar disks, because this is a sensitive probe of environmental processing (e.g., Moss & Whittle 2000; Dale et al. 2001; Koopmann et al. 2006; Bamford et al. 2007; Kawata & Mulchaey 2008; Jaffé et al. 2011; Bösch et al. 2013; Bekki 2014; Schaefer et al. 2017). We present a sample of 224 galaxies in 9 low-redshift galaxy groups and clusters, and we map galaxies from the cluster core to the surrounding infall regions. Our galaxy sample spans a large range in stellar mass, which is necessary to help control for any intrinsic quenching mechanisms that may occur independently of environment (e.g., Peng et al. 2010). We use 24 μm imaging from the MIPS camera on Spitzer Space Telescope to measure the size of the star-forming disks, and SDSS r-band imaging to quantify the size of the stellar disk.

Multiple wavelengths can be used to trace the star-forming regions in galaxies, including UV, Hα, and infrared emission. While 24 μm is a reliable star formation indicator that closely traces Paschen alpha (e.g., Calzetti et al. 2007), different wavelength indicators can vary with dust and metallicity, and may therefore result in different measurements of the spatial extent of the gas disk. Furthermore, different components of the ISM will respond differently to environmental processing (e.g., Boselli et al. 2014). To mitigate systematics associated with our choice of wavelength, we normalize the size of the star-forming disk by the size of the stellar disk. Our conclusions are based upon differences in this ratio with environment and intrinsic galaxy properties, rather than absolute measurements.

This paper is organized as follows. We describe the survey and cluster properties in Section 2. In Section 3 we describe the Spitzer observations, and in Section 4 we detail the selection and properties of the galaxies in our sample. In Section 5, we present our methods for quantifying the environment of galaxies, and we discuss our measurements of 24 μm sizes in Section 6. Finally, we present our results in Section 7, which show that the properties of star-forming galaxies are altered during the delay, prior to their final quenching. When calculating distance-dependent quantities, we use H₀ = 70 km s⁻¹, Ω_Λ = 0.7, and Ω_M = 0.3. Stellar masses are calculated as described in Moustakas et al. (2013) and assume a Chabrier initial mass function (Chabrier 2003).

The nine clusters that compose the Local Cluster Survey are listed in Table 1. The sample consists of clusters that have wide-area Spitzer MIPS 24 μm mapping and that lie in the SDSS (York et al. 2000) and ALFALFA (Giovanelli et al. 2005) surveys. The clusters are near enough so that a typical spiral can be resolved in a Spitzer 24 μm image yet far enough so that the SDSS photometry is reliable (0.0137 < z < 0.0433). The clusters purposely span a range of richness, X-ray luminosity, and X-ray temperature so that we can probe the full range of intra-cluster medium properties. In Figure 1, we show X-ray luminosity in the 0.1–2.4 keV band versus cluster velocity dispersion for our sample. For comparison, we show a larger sample of clusters from Mahdavi and Geller (2001), with gray points to illustrate that the scatter seen among Local Cluster Survey clusters is consistent with the scatter seen among a larger population of clusters.

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Table 1.  Cluster Properties and Galaxy Sample Sizes

Cluster	Biweight Central Velocity	Biweight Scale	Ngal	Ngal
	(km s−1)	(km s−1)	Core	External
A1367	${6505}_{-54}^{+55}$	${838}_{-42}^{+31}$	6	5
MKW11	${6904}_{-49}^{+38}$	${383}_{-27}^{+19}$	5	13
Coma	${7011}_{-44}^{+45}$	${1054}_{-29}^{+26}$	28	11
MKW8	${8039}_{-38}^{+40}$	${443}_{-31}^{+29}$	0	11
NGC6107	${9397}_{-53}^{+57}$	${578}_{-34}^{+47}$	6	17
AWM4	${9604}_{-55}^{+61}$	${458}_{-95}^{+107}$	4	17
A2063	${10410}_{-74}^{+72}$	${862}_{-65}^{+42}$	27	8
A2052	${10431}_{-64}^{+57}$	${666}_{-45}^{+37}$	7	34
Hercules	${10917}_{-53}^{+50}$	${790}_{-31}^{+29}$	22	3

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While Figure 1 demonstrates the range in global cluster environments, the galaxies in our sample also span a wide range of local environments. The galaxies in the MIPS scans of the lower-mass clusters sample both low and high density regions, whereas the galaxies in the MIPS scans of Coma, Hercules, and Abell 1367 provide a more complete sampling of the highest-density environments. An important point to keep in mind as we proceed with the analysis is that Coma galaxies dominate the number counts at high local densities. We investigate how this impacts our results in Section 7.4.

While some clusters have average redshift and velocity dispersions available from the literature, we recalculate the biweight location and scale (Beers et al. 1990) and estimate errors using bootstrap resampling. The galaxies for these calculations and throughout are drawn from the NASA-Sloan Atlas (Blanton et al. 2011), which includes SDSS spectroscopic sources along with other spectroscopically confirmed galaxies from ALFALFA and other surveys. We select all galaxies that have redshifts between 0.0137 < z < 0.0433, where the lower limit is set by Coma (recession velocity minus 3σ_v) and the upper limit is set by the most distant cluster, Hercules (recession velocity plus 3σ). We first calculate the biweight location and scale using all galaxies, with a recession velocity within 4000 km s⁻¹ of each cluster and a projected radius less than 1.7 Mpc (this corresponds to a 1 degree radius at the redshift of Coma). We use this biweight location as the new median and recalculate the location and scale. We repeat this until the scale changes by less than 1 km s⁻¹, which usually happens within two iterations. We use the weighting factors suggested by Beers et al. (1990) to minimize the effect of any galaxy whose velocity deviates by more than 4σ_v from the central velocity. We show the results in Figure 2 and in Table 1. The errors listed in Table 1 are the 68% confidence interval as determined by bootstrap resampling. In each panel in Figure 2, we list the number of galaxies with velocity offsets Δv < 3σ that have projected radii less that R₂₀₀, where R₂₀₀ is calculated from the cluster biweight scale according to the relation in Finn et al. (2008).

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Each cluster has 24 μm data from the MIPS instrument (Rieke et al. 2004) on the Spitzer Space Telescope, and we use the 24 μm emission to probe the spatial extent of star formation. In Figure 3, we show the positions of galaxies that lie within the 24 μm scan region and have a redshift in the range of 0.0137 < z < 0.0433. The overall galaxy density is shown with the grayscale, with black and white denoting high and low density areas, respectively. Specifically, white indicates bins with no galaxies, and black indicates regions that contain 10 or more galaxies. The dark gray circles show R₂₀₀, and the green box shows the footprint of the MIPS scan. With the exception of Coma, A1367, and Hercules, the clusters have MIPS data obtained specifically for this project, and each scan covers an area of approximately 1.5 × 2.5 square-degree area around each cluster. The MIPS data for Coma, A1367, and Hercules were pulled from the Spitzer Science Center archive, and the observations are summarized in Table 2. While the areal coverage for these clusters is smaller, the archive clusters provide an important complement by sampling regions of higher local density and X-ray luminosity (see Figure 1).

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Table 2.  Spitzer MIPS Observations

Cluster	z	Date of Obs	Program ID	PI	f80 (MJy/sr)	${\mathrm{log}}_{10}({L}_{80}/{L}_{\odot })$
A1367	0.0217	2006 Jun 07	25	Fazio	3.50 ± 0.25	8.25
MKW11	0.0230	2008 Jul 31	50456	Finn	4.00 ± 0.25	8.38
Coma	0.0234	2004 Jun 22	83	Rieke, G.	2.25 ± 0.25	8.12
MKW8	0.0268	2009 Mar 24	50456	Finn	3.75 ± 0.25	8.45
NGC6107	0.0313	2008 May 16	50456	Finn	3.25 ± 0.25	8.50
AWM4	0.0320	2008 Sep 26	50456	Finn	3.50 ± 0.25	8.56
		2008 Sep 28
A2063	0.0347	2009 Mar 23	50456	Finn	4.00 ± 0.25	8.71
A2052	0.0348	2009 Mar 24	50456	Finn	4.00 ± 0.25	8.71
Hercules	0.0364	2006 Jun 22	25	Fazio	3.25 ± 0.25	8.68

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The MIPS data are reduced using the MOPEX software package, following the procedure outlined in the Spitzer MIPS Data Reduction Cookbook.¹² We use SExtractor (Bertin & Arnouts 1996) to detect galaxies and measure photometry. We measure the noise for each object using the MOPEX-generated standard deviation image. We estimate the depth of each image by placing artificial galaxies on each image and then rerunning SExtractor. We calculate the flux where we recover 80% of the test sources, and we list these flux limits in Table 2. We convert the 80% flux limits to an IR luminosity at the cluster redshift using the templates of Chary and Elbaz (2001) and list these values in the final column of Table 2.

Our parent sample consists of exactly 1800 NSA galaxies that lie on the MIPS 24 μm scans and fall in the redshift range 0.0137 < z < 0.0433. We apply additional selection criteria to ensure that we are sampling the same galaxy population in each cluster. First, to account for the varying sensitivity of the 24 μm scans, we apply a uniform cut in L_IR (L_IR > 5.2 × 10⁸ L_⊙). This limit is set by the depth of the MIPS scans for Abell 2052 and Abell 2063, which have the highest 80% completeness limit of L_IR = 5.13 × 10⁸ L_⊙. Assuming that the 24 μm emission is due to heating from massive stars, this L_IR corresponds to an approximate star formation rate of 0.1 M_⊙ yr⁻¹. We retain 541 galaxies after the L_IR cut.

We use both optical emission-line ratios and infrared colors to eliminate AGN from our sample. The majority of galaxies in the NASA-Sloan Atlas have optical spectra, and we use the Kauffmann et al. (2003) criteria for separating AGN from star-forming galaxies. For those without optical spectra, we use WISE photometry $W1-W2\gt 0.8$ to identify AGN (Stern et al. 2012). (Note that only 10/1800 galaxies in our sample show such red $W1-W2$ colors. This is likely because this color selects only whopping AGN.) Two galaxies have neither optical spectra nor WISE photometry, and so we are not able to classify as AGN versus star-forming; we retain them in the sample nonetheless. After removing AGN, we are left with 351 star-forming galaxies.

We also apply a minimum cut on galaxy size and keep only galaxies with r-band effective radii R_e ≥ 1.3 kpc. This corresponds to 1 pixel on the MIPS detector at the distance of our farthest cluster, Hercules (245 = 1.3 kpc), and we are not confident in measuring sizes that are smaller than a pixel. We retain 332 of the galaxies after applying the size selection.

We attempt to model all of these galaxies using GALFIT (Peng et al. 2002). We remove six galaxies (three pairs) that are close enough to each other to compromise the resulting fits. The modeling fails for another 40 galaxies, and this is usually due to the low signal-to-noise ratio of the 24 μm emission. In addition, we remove 33 galaxies with observed 24 μm surface brightnesses greater than 20 mag/arcsec², because our simulations indicate that the fits are unreliable; we discuss the details of these simulations in the Appendix. We retain 252 galaxies.

Finally, we require galaxies to be in the sample of Simard et al. (2011) because we use their measurements of effective radius and bulge-to-total ratio in our analysis. Simard et al. (2011) perform two-dimensional bulge-to-disk decomposition for more than 1 million galaxies in SDSS DR7 using the GIM2D software. They limit their sample to galaxies with 14 ≤ m_petro,r,corr ≤ 18 and exclude objects that are classified in the DR7 photometry table as saturated or unresolved. We are able to match 89% of our sources to the Simard et al. (2011) catalog, which leaves us with a final sample of 224 galaxies. Of the 28 galaxies not matched to the Simard et al. (2011) catalog, 17 are too bright (m_r < 14), 2 are too faint (m_r > 18), 2 are blended, 2 are saturated, 1 is not in the DR7 catalog, and 1 seems to have bad coordinates in the DR7 catalog. We are not able to identify the reason why the remaining 3 galaxies are not in the Simard catalog.

We will compare the size of the star-forming disk versus environment throughout this paper, and we define environment in two different but related ways. First, we make a simple division in phase space to split the sample into two groups, galaxies in the cluster core versus galaxies external to the core. We adopt the cut used by Oman et al. (2013), $| {\rm{\Delta }}v/\sigma | \,\lt -4/3{\rm{\Delta }}R/{R}_{200}+2$, and we show this cut with the black line in Figure 4. This figure includes galaxies from all clusters, and the black shading shows the phase-space positions of all galaxies. The colored points show the GALFIT sample (Section 6). The region in phase space to the left of the black line contains galaxies that are likely to be true cluster members, whereas the region to the right of this line contains galaxies near the cluster as well as a large fraction (>50%) of interlopers that are not physically associated with the cluster (Oman & Hudson 2016). We denote the sample to the left and right of this line as core and external galaxies, respectively. According to this definition, our sample contains 105 core galaxies and 119 external galaxies, and the breakdown of galaxies by cluster is shown in columns 4 and 5 of Table 1.

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We note that neither the core nor external samples are pure. The core sample is dominated by galaxies that have been in the cluster environment the longest (e.g., Oman et al. 2013) but may still contain galaxies that are physically distant from the cluster center but lie along the line of sight. In addition, the external sample will contain galaxies in the field as well as backsplash galaxies that have already passed through the cluster core (e.g., Balogh et al. 2000; Bahé et al. 2013). Therefore core/external do not translate cleanly into cluster/field, and this cross-contamination will dilute the observational signatures of any environmental processing.

To demonstrate the similarity and therefore comparability of the core and external subsamples, we show the cumulative distributions for stellar mass, bulge-to-total ratio, redshift, and r-band effective radius in Figure 5. The properties of the core and external galaxies are not statistically different according to both the K-S and Anderson-Darling tests, except with regard to redshift. Coma contributes significantly to the core sample, whereas the redshift distribution of the external sample is skewed slightly toward higher redshift. This difference does not impact our results.

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We use local galaxy density as a second metric of galaxy environment. Specifically, we use Σ₅, which is the surface density of galaxies out to the fifth nearest neighbor. When counting neighbors, we use only galaxies in the SDSS spectroscopic sample with M_r < −18.2. The magnitude cut corresponds to the SDSS spectroscopic completeness limit (r < 17.7) at the distance of our farthest cluster. In addition, we require that neighbors must have a velocity offset Δv < 2500 km s⁻¹. We note that our two measures of environment are closely related; Σ₅ is strongly correlated with a galaxy's position in phase space. In effect, Σ₅ provides a continuous measure of environmental density as compared to the dichotomous division of core versus external galaxies.

Two clusters in our sample, A2052 and A2063, lie near each other on the plane of the sky and in redshift space, but we are still confident in our ability to quantify the environment of galaxies in this region. The core/external division is preserved around these two structures because while the MIPS scans overlap slightly, there are no galaxies that are classified as external in one field of view and core in another field of view, or vice versa. In addition, the local density metric will account for any enhanced density between the two clusters (see Figure 3).

Our goal is to measure the size of each galaxy in the optical and infrared to trace the stellar and star-forming components, respectively. Simard et al. (2011) use GIM2D to fit a two-dimensional, single-component Sérsic model for a large fraction of DR7 galaxies, and they also fit two versions of bulge+disk models to each galaxy. One version of the bulge+disk models forces the bulge to have an n = 4 Sérsic profile, and the second set of models allows the Sérsic index of the bulge to vary. We use the r-band disk radius (R_d; see Table 3 for a list of definitions of radial size measurements.) for the n = 4 bulge+disk models to characterize the size of the stellar disk. We use GALFIT (Peng et al. 2002) to fit a Sérsic model to the 24 μm images. To confirm that GALFIT and the GIM2D models are comparable, we fit the r-band images for a subset of the galaxies using GALFIT and find that the GIM2D and GALFIT model parameters are consistent.

6.1. GALFIT Analysis of 24 $\mu m$ Images

6.2. GALFIT Best-fit Model Parameters

We compare the 24 μm and the r-band Sérsic model parameters in Figure 6. The r-band parameters are shown along the horizontal axes, and the GALFIT 24 μm parameters are shown along the vertical axes. The diagonal panels show the corresponding parameters of the r and 24 μm fits. The r and 24 μm effective radii are correlated, as are the model magnitudes. The 24 and r Sérsic indices are not strongly correlated, although the bulk of both r and 24 indices are less than 2. This is consistent with a sample dominated by disk galaxies. The top middle panel shows that galaxies with higher r-band Sérsic index have systematically lower values of R₂₄, a point we will revisit in Section 7.2. We conclude that there are no strange systematics between the 24 μm and r-band model parameters. We discuss the reliability of the GALFIT model parameters in more detail in the Appendix.

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7.1. Relative Sizes of the Star-forming and Stellar Disks

We show examples of the 24 μm Sérsic models in Figures 7–9. In Figure 7, we show five randomly selected galaxies whose 24 μm emission is more compact than the r-band emission, specifically 0.1 < R₂₄/R_d < 0.3. Columns 1 and 2 show the SDSS color and r-band images, respectively. Columns 3 and 4 show the 24 μm image at two different stretches. The first stretch (contrast1) highlights the high surface-brightness features, and the second stretch (contrast2) emphasizes the low surface-brightness features. Columns 5 and 6 show the 24 μm Sérsic model and residual, and both are shown at contrast2. Figure 8 shows five randomly selected galaxies with 0.4 < R₂₄/R_d < 0.7, and Figure 9 shows five randomly selected galaxies with R₂₄/R_d > 0.9. The columns are the same as for Figure 7.

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In Figure 10, we plot the effective radius of the best-fit 24 μm model versus the r-band half-light radius for the disk component from Simard et al. (2011) for each cluster pointing. The clusters are ordered left-to-right and top-to-bottom by increasing X-ray luminosity. The solid black line shows a one-to-one correlation. The circles and squares show core and external galaxies, respectively. For all clusters, the 24 μm and r-band sizes are correlated (see also Figure 6), although the 24 μm half-light radii are systematically smaller than the r-band disk half-light radii R_d.

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We show the distribution of R₂₄/R_d for the core and external galaxies in Figure 11. The mean (median) size ratio for the core galaxies is 0.73 (0.69) ± 0.04, where the uncertainty is the error in the mean. The mean (median) size ratio for the external galaxies is 0.91 (0.94) ± 0.04. We use both the K-S and Anderson-Darling tests to compare the distribution of R₂₄/R_d for the core and external galaxies. Both tests reject the null hypothesis at the 3σ level, which indicates that the core galaxies have significantly smaller values of R₂₄/R_d. We therefore find that the spatial distribution of star formation in core galaxies is more concentrated than in external galaxies.

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Numerous other studies have measured the relative size of the star-forming and stellar disks as a function of environment at both low (Moss & Whittle 2000; Dale et al. 2001; Koopmann et al. 2006; Schaefer et al. 2017) and intermediate redshift (Bamford et al. 2007; Bösch et al. 2013), and most find that the star-forming region is more concentrated among cluster galaxies than the field. Jaffé et al. (2011) find that the outer extent of the emission-line region is systematically smaller in cluster galaxies.

Our quantitative size estimates of R₂₄/R_d for core (mean, median, error in the mean: 0.73, 0.69, 0.04) and external (mean, median, error in the mean: 0.91, 0.94, 0.04) galaxies are in reasonable agreement with previous work. Koopmann et al. (2006) find r_Hα/r_R = 0.91 ± 0.05 and 1.18 ± 0.10 for Virgo cluster and field galaxies, respectively (error is error in the mean). At higher redshift, Bösch et al. (2013) find ∼0.9 and 1.27 for cluster and field galaxies at z = 0.2, and Bamford et al. (2007) find r_em/r_B = 0.92 ± 0.07 and 1.22 ± 0.06 for 0.2 ≲ z ≲ 0.8 cluster and field galaxies. Jaffé et al. (2011) find a ratio of ∼0.8 for 0.4 < z < 1 galaxies that is independent of environment. Interestingly, Jaffé et al. (2011) use the ESO Distant Cluster Survey for their cluster sample, and these are relatively low-mass clusters. With the exception of Jaffé et al. (2011), our values are systematically lower than most previous measurements that have been made using optical emission lines, but the ∼20% offset we find between field and cluster sizes is consistent with previous work.

7.2. R₂₄/R_d  versus B/T, Local Galaxy Density, and Stellar Mass

We show how R₂₄/R_d varies with bulge-to-total ratio in the top row of Figure 12. As mentioned in Section 4, the B/T values are from Simard et al. (2011). The sample is divided into full (left), core (middle), and external (right). The points are colored according to stellar mass. The Spearman rank coefficient and probability of the null hypothesis are shown in the top of each panel. To account for the variation in error among the individual 24 μm best-fit models, we create 1000 Monte-Carlo realizations of the data and calculate the Spearman rank correlation coefficient for each realization, assuming that the GALFIT errors for R₂₄ are normally distributed. We report the 68% confidence interval for the correlation coefficient (ρ) and the probability of no correlation (p). The p-values indicate that R₂₄/R_d and B/T are inversely correlated and that the correlation is strong.

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We use bulge-to-total ratio instead of visually classified morphology because Koopmann and Kenney (1998) show that visual classification is biased by the specific star formation rate. More specifically, when comparing galaxies of a fixed concentration, Koopmann and Kenney (1998) show that galaxies with low star formation rates are systematically classified as having an earlier Hubble type.

The Sérsic index of a single-component fit can also be used as a proxy for morphology, with the index increasing from 1 to 4 as a galaxy profile goes from disk dominated to bulge dominated. We find a similar correlation between R₂₄/R_d versus the r-band Sérsic index, which is not surprising given that B/T and Sérsic index are themselves strongly correlated. The result, then, is that galaxies with more concentrated stellar profiles have smaller R₂₄/R_d, and at a given B/T, core galaxies have smaller R₂₄/R_d ratios than the external galaxies.

The correlation between the radial distribution of star formation and morphology has been known for a long time. Mapping the distribution of H ii regions in 37 nearby galaxies, Hodge and Kennicutt (1983) find that early-type spirals tend to have centrally concentrated, symmetric star formation, whereas later-type spirals have more extended and asymmetric emission. The results were confirmed by Bendo et al. (2007), who use 24 μm emission to quantify the spatial distribution of star formation for the 65 galaxies in the Spitzer Infrared Nearby Galaxy Survey. However, not all previous studies find a link between the spatial distribution of star formation and galaxy morphology (Dale et al. 2001; Koopmann et al. 2006; Fossati et al. 2013). Some of these discrepancies might be due to differences between samples. For example, the Dale et al. (2001) sample is dominated by late-type spirals, and the galaxies were selected to have strong emission-line features; both of these selection effects could hinder their ability to detect a trend with morphology. Koopmann et al. (2006) do not use the central region of each galaxy when fitting the Hα radial profiles, due to possible bulge contamination and extinction problems. Thus no galaxies with weak or severely truncated star formation have measured scale lengths. Interestingly, Bretherton et al. (2013) find a correlation between the relative size of the star-forming disk and morphology among field galaxies but not among cluster galaxies. However, we find a correlation between R₂₄/R_d and B/T for both core and external galaxies.

In the middle panel of Figure 12, we show R₂₄/R_d versus local galaxy density. R₂₄/R_d and Σ₅ are strongly correlated as indicated by a Spearman rank test. A similar effect can be seen in Figure 4; galaxies with smaller R₂₄/R_d ratios are more likely to be found at low projected radii where the projected density of galaxies is high.

Comparison of the core and external panels shows that the core galaxies have lower values of R₂₄/R_d. To further emphasize the offset and to control for the correlation between morphology and environment, we again show the distribution of relative sizes for both core and external galaxies but for B/T < 0.3 galaxies only in the right panel of Figure 11. The core galaxies have R₂₄/R_d ratios that are clearly offset to smaller values.

In the bottom row of Figure 12, we show R₂₄/R_d versus stellar mass, where stellar mass is calculated as described in Moustakas et al. (2013) and assumes a Chabrier IMF (Chabrier 2003). The left column shows the entire GALFIT sample, and the middle and right columns show the core and external samples separately. Using the full sample, we test for a correlation between stellar mass and R₂₄/R_d using a Spearman rank test. The results indicate that R₂₄/R_d and stellar mass are inversely correlated, although the correlation is not particularly strong.

We investigate the dependence of R₂₄/R_d on stellar mass further in Figure 13. To control for morphology, we include only the B/T < 0.3 galaxies. We show the core galaxies in red and the external galaxies in blue. The large red and blue circles show the median R₂₄/R_d for the core and external samples, respectively, in equally spaced bins. The errorbars show the 68% confidence interval on the median, which we calculate using bootstrap resampling of the galaxies in each bin. While R₂₄/R_d is systematically lower for the core galaxies, the difference between the core and external size ratios does not appear to depend on stellar mass.

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We also look at R₂₄/R_d versus several combinations of stellar mass density—namely, stellar mass surface density (Zhang et al. 2013) and M_*/R_e (e.g., Omand et al. 2014). We detect no correlation between R₂₄/R_d and ${M}_{* }/{R}_{e}^{2}$, and a moderate correlation between R₂₄/R_d and M_*/R_e. However, we are testing for a correlation between two correlated variables because both R₂₄/R_d and M_*/R_e have a measure of r-band size in the denominator, and the significance of any detected correlation is thus difficult to interpret.

Table 3.  Definition of Radial Size Symbols

Symbol	Definition
R24	24 μm half-light radius from GALFIT single-component Sérsic model
Re	r-band half-light radius from GIM2D single-component Sérsic model (Simard et al. 2011)
Rd	r-band half-light radius of disk component based on two-component GIM2D model with n = 4 bulge + exponential disk (Simard et al. 2011)

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7.3. Partial Correlation Analysis

7.4. Impact of Coma

7.5. R₂₄/R_d  versus Large-scale Environment

The density of the intra-cluster medium is a key factor in determining the effectiveness with which gas is removed from infalling galaxies by ram-pressure stripping (e.g., Gunn & Gott 1972). We do not have a measure of ρ_ICM, so we use X-ray luminosity as a proxy. We show R₂₄/R_d for B/T < 0.3 cluster galaxies versus the X-ray luminosity of each cluster in Figure 14. Again, we limit the range of B/T in this comparison to help control for the correlation between B/T and environment. We use a box and whisker plot to show the range of values for each cluster. The box extends from the lower to upper quartiles, while the whiskers (errorbars) show the range in each bin. The horizontal line shows the average R₂₄/R_d for the external sample, and the dashed lines show the error in the mean. The MIPS scans for A1367, Hercules, and Coma do not extend to R₂₀₀. We do not attempt to correct for this, however, because if we try to match the areal coverage of these clusters by selecting a smaller radial cut, we run out of galaxies in other clusters. We repeat the same analysis using X-ray temperature in place of X-ray luminosity, and we find similar results.

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Due to the relatively small numbers of galaxies in each cluster, we next look for trends with the large-scale environment by binning the clusters according to X-ray luminosity or velocity dispersion. We combine the galaxy groups (σ < 700 km s⁻¹: MKW11, MKW8, AWM4, and NGC6107) and clusters (σ > 700 km s⁻¹: Hercules, Abell 1367, Abell 2052, and Abell 2063), and leave Coma in a class by itself. For this comparison only, we separate the external sample into near-external and far-external galaxies, where the near-external galaxies have Δv/σ < 3. These galaxies likely live in the large-scale structure surrounding the clusters and may already be affected by environmental process. The far-external galaxies have Δv/σ > 3 and are more likely to be isolated from the cluster environment. We show the median R₂₄/R_d for B/T < 0.3 galaxies versus global environment in Figure 15. Again, we use a box and whisker plot to show the inner quartiles and range of the data. The median R₂₄/R_d decreases as the environmental density increases from the field through to Coma. In addition, the galaxy groups and lower-mass clusters have median R₂₄/R_d that falls between the near-field and Coma, but the differences are not statistically significant. While our results suggest that cluster mass is important, a larger sample of groups and clusters is needed to explore variations between R₂₄/R_d and cluster/group mass. Not many studies have measured R₂₄/R_d as a function of cluster mass or X-ray luminosity. Dale et al. (2001) make a preliminary attempt to measure the effect of cluster X-ray luminosity on stripping, and they find no systematic trend.

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7.6. R₂₄/R_d  versus H i Content

All of the clusters in our sample lie within the ALFALFA survey (Giovanelli et al. 2005). ALFALFA maps H i to a resolution of 35  and with a pointing accuracy better than 30''  for sources with S/N > 6.5, and a total of 43 galaxies in the GALFIT sample have H i detections. We calculate H i mass for these galaxies according to the following relation:

$$\begin{eqnarray}&&{M}_{{\rm{H}}{\rm{I}}}=2.36\times {10}^{5}\ {D}^{2}\int {FdV}\ {M}_{\odot },\end{eqnarray} \tag{ 1 }$$

where D is the distance in Mpc and $\int {FdV}$ is the total H i line flux in Jy km s⁻¹ (e.g., Wild 1952; Roberts 1962). In the left panel of Figure 16, we show R₂₄/R_d versus H i mass fraction M_{H i}/M_*. The squares and circles show external and core galaxies, respectivly, and the color indicates stellar mass. A Spearman rank test indicates that the two quantities are strongly correlated; galaxies with smaller values of R₂₄/R_d have a smaller H i mass fraction.

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Another common way to describe the gas content of spiral galaxies is with H i deficiency (Haynes & Giovanelli 1984; Toribio et al. 2011). This compares the H i content of a galaxy to the H i content of isolated field galaxies of comparable size, and positive values of deficiency indicate that a galaxy has less H i gas than a field galaxy of comparable size (Haynes & Giovanelli 1984; Toribio et al. 2011). We calculate H i deficiency according to the relationship presented in Toribio et al. (2011), using the isophotal r-band diameter from SDSS to measure size. In Figure 16 we show R₂₄/R_d versus H i deficiency. The data show a significant (3.5σ) anti-correlation in the sense that galaxies with smaller R₂₄/R_d also have less H i gas than isolated galaxies of comparable size. We are not able to confirm that the converse (i.e., that H i deficient galaxies will have small R₂₄/R_d ratios) is true; H i deficient galaxies with widespread but low levels of star formation would likely fall below our surface-brightness cut. Figure 16 also shows that core galaxies tend to have lower H i mass fractions and higher H i deficiencies than external galaxies.

Our findings are consistent with previous studies. The Hα 3 survey of nearby galaxies (Fossati et al. 2013; Gavazzi et al. 2013) and Koopmann and Kenney (2004b) for Virgo galaxies find that the relative size of the Hα disk is inversely correlated with H i deficiency. In addition, infrared and CO observations of Virgo galaxies show that H i deficient spirals have smaller dust and molecular gas disks (Cortese et al. 2010; Boselli et al. 2011).

7.7. R₂₄/R_d  versus Color

If Figure 17 we show NUV − r versus R₂₄/R_d, and the points are color-coded by B/T. The core and external galaxies are shown in the middle and right panels, respectively. The horizontal solid line in each panel marks NUV − r = 4, a rough dividing line between blue and red galaxies (e.g., Salim et al. 2007), and the dashed horizontal lines mark the region of the green valley (e.g., Wyder et al. 2007). As before, to account for the variation in error among the individual 24 μm best-fit models, we create 1000 Monte-Carlo realizations of the data and calculate the Spearman rank correlation coefficient for each realization, assuming that the GALFIT errors for R₂₄ are normally distributed. The numbers in Figure 17 show the 68% confidence interval for the correlation coefficient (ρ) and the probability of no correlation (p). R₂₄/R_d is strongly inversely correlated with NUV − r color (>5σ for the combined core+external sample); galaxies that have red NUV − r colors and thus low NUV specific star formation rates have more centrally concentrated star formation.

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Our goal is to investigate the spatial distribution of star formation in galaxies that have been accreted into a cluster but are still forming stars. In Figures 11–15, we show that star-forming galaxies in dense environments have more centrally concentrated star formation. Models of environmentally driven depletion predict that gas is preferentially removed from the outskirts of galaxies (e.g., Gunn & Gott 1972; Kawata & Mulchaey 2008; Bekki 2014), and our observations of smaller star-forming disks in denser environments support this. In addition, we find that galaxies with smaller star-forming disks are more H i deficient (Figure 16) and have redder colors (Figure 17), suggesting that smaller star-forming disks are indicative of the transition phase between blue, gas-rich and red, depleted galaxies.

Centrally concentrated star formation should lead to an increase in B/T, as suggested by Bösch et al. (2013). We can estimate the further evolution of the bulge-to-total ratio for the green valley galaxies if we assume a typical gas mass fraction of 10% (from Figure 16 for galaxies with R₂₄/R_d ≈ 0.5). If we assume a current B/T = 0.2 and M/L = 1, the B/T would increase to 0.3 after all the gas is consumed. This is not a huge effect. However, atomic gas is easier to strip than molecular gas (e.g., Boselli et al. 2014), and so our estimate is likely a lower limit on the final bulge-to-total ratio. We could better predict the growth of the central bulge if we obtain molecular gas masses for the Local Cluster Survey galaxies.

8.1. Outside-in Quenching Timescale

The timescale over which R₂₄/R_d decreases in an important parameter that can help identify the physical mechanism that is causing outside-in quenching. We construct a simple model to constrain this timescale using the observed distribution of R₂₄/R_d for the core and external samples and simulations of cluster infall. Our model assumes that the size of the star-forming disk decreases linearly with time once a galaxy is accreted into a cluster. The distribution of R₂₄/R_d for the core galaxies results from the modification of the external R₂₄/R_d distribution as follows:

$$\begin{eqnarray}&&{\left(\displaystyle \frac{{R}_{24}}{{R}_{d}}\right)}_{\mathrm{core}}={\left(\displaystyle \frac{{R}_{24}}{{Rd}}\right)}_{\mathrm{external}}\times \displaystyle \frac{{dr}}{{dt}}\times {t}_{\mathrm{infall}},\end{eqnarray} \tag{ 2 }$$

where t_infall is the time since accretion into the cluster, and dr/dt is the rate at which the size of the star-forming disk is decreasing in the cluster environment. We assume dr/dt is the same for all galaxies and that the distribution of R₂₄/R_d in the external sample is comparable to that of the core galaxies at the time of infall. (While field galaxies at the time of infall likely had higher star formation rates due to the correlation of galaxy star formation rates with redshift [e.g., Madau & Dickinson 2014, and references therein], there is no compelling evidence to suggest that R₂₄/R_d is larger for intermediate redshift galaxies [e.g., Nelson et al. 2016].) For each galaxy in the external sample, we assign an infall time as αt_max, where α is a random number between zero and 1. In effect, this assumes that the accretion rate is uniform over the time t_max, which is a reasonable approximation to theoretical mass accretion histories for t_max < 5 Gyr (e.g., Neistein & Dekel 2008). To be conservative, we let t_max, the time period over which the star-forming core galaxies have been accreted, range from 1 to 4 Gyr. We note that both the phase space distribution of the core galaxies (e.g., Oman et al. 2013) and simulations of the mass accretion history of clusters (e.g., McGee et al. 2009) suggest that t_max ≃ 3–4 Gyr for the star-forming core galaxies.

To quantify the timescale, we step dr/dt from −2 to zero and calculate the expected distribution of R₂₄/R_d for the core sample according to Equation (2). We compare the resulting distribution of sizes to that of the observed core sample, and compute the probability that the two are drawn from the same population using a Kolmogorov–Smirnov test. For a given value of dr/dt, we repeat the comparison 1000 times, generating a new set of infall times for each trial. We show the distribution of resulting K-S test p-values versus dr/dt in Figure 18, and p-values near 1 indicate that the simulated distribution of R₂₄/R_d is similar to the observed distribution. For t_max = 1 Gyr, dr/dt peaks near −0.6 Gyr⁻¹, and the star-forming disk would be removed in ∼1.7 Gyr. For t_max = 4 Gyr, dr/dt peaks near −0.2 Gyr⁻¹, and the star-forming disks would be completely removed in 5 Gyr. Thus, while a precise estimate of the disk-shrinking time requires a careful comparison with simulations of cluster growth, our simplified model suggests that for a reasonable estimate of infall times, the disk-shrinking timescale is greater than 1 Gyr and likely greater than 2 Gyr.

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This timescale has significant implications for the delay+rapid quenching model of Wetzel et al. (2012, 2013). First, our estimated timescale is significantly longer than expected for the fast-quenching phase of Wetzel et al. (2013). Second, we show that galaxies undergo a significant transformation during the delay phase, in contrast with the delay+rapid model as originally proposed, in which the galaxies remain unchanged in the period before the rapid quenching event.

8.2. The Effect of B/T on Quenching

We present 24 μm size measurements for 224 galaxies in nine nearby galaxy groups and clusters. We normalize the 24 μm effective radius by the disk scale length (Simard et al. 2011) and look for variations in this ratio as a function of morphology, environment, and stellar mass. Our primary results are that (1) R₂₄/R_d is strongly correlated with morphology for star-forming galaxies in the sense that galaxies with higher bulge-to-total ratios or larger Sérsic indices have more centrally concentrated star formation, and (2) star-forming galaxies in more dense environments have more centrally concentrated star formation than galaxies in less dense environments with similar mass and B/T. Furthermore, we find that galaxies with smaller star-forming disks tend to have lower H i mass fractions and redder NUV − r colors, suggesting that at least some galaxies experience a decline in R₂₄/R_d as they transition from blue to red.

We do not detect any trend in the median R₂₄/R_d ratio of cluster galaxies versus X-ray luminosity of the host galaxy cluster. However, when we bin our sample by environment and control for the morphology–density relation by using only B/T < 0.3 galaxies, we do see a trend with large-scale environment that suggests that R₂₄/R_d is highest in the field, lower in our low-mass clusters and groups, and lower still in the extreme environment within the Coma cluster.

We build a toy model to constrain the timescale over which the star-forming disks shrink in the cluster environment. When allowing the galaxies to enter the cluster with a realistic range of infall histories, we find that the star-forming disks in our sample will shrink on a timescale longer than 1 Gyr and likely longer than 2 Gyr.

Our results provide a new piece of information on what is happening to galaxies after they have been accreted by a cluster but while they are still able to form stars. In the context of recent hybrid models of environmental quenching (e.g., Wetzel et al. 2012; Balogh et al. 2016), our core galaxies are considered to be in the delay phase, the period between being accreted into the cluster and complete quenching of star formation. We present clear evidence that the spatial distribution of star formation becomes more concentrated during this delay phase. Our results suggest that the quenching timescale is long (>2 Gyr), which is consistent with mechanisms such as the removal of halo gas through starvation (e.g., Larson et al. 1980) and the slow removal of cold disk gas through extended ram-pressure stripping.

R.A.F. gratefully acknowledges support from NSF grant AST-0847430. R.A.F., G.R., V.D., P.J., and D.Z. thank the International Space Science Institute for facilitating discussions that directly influenced this work. G.R. recognizes the support of NASA grant NNX17AF25G. Many Siena College undergraduate students have contributed to this work, including Corey Snitchler, Trevor Quirk, Erin O'Malley, Amy McCann, Michael Englert, Debra Johnson, and Alissa Earle. R.A.K., R.A.F., and M.P.H. acknowledge support of the Undergraduate ALFALFA Team through NSF AST-1211005, AST-0724918, AST-0725267, and AST-0725380. The ALFALFA team at Cornell is supported by NSF grant AST-1107390 and by the Brinson Foundation. This work is based on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. This research made use of Astropy, a community-developed core Python package for Astronomy (Astropy Collaboration, 2013). We thank the anonymous referee whose suggestions led to significant improvements in this paper.

Facilities: Spitzer - Spitzer Space Telescope satellite, IRSA - , NED - , ADS - .

The MIPS data have lower resolution and lower signal-to-noise ratios than the optical imaging that GALFIT is typically used with; at the median redshift of our cluster sample, 1 pixel on the MIPS camera corresponds to 1.48 kpc. To test the reliability of the GALFIT models, we create 200 model galaxies on each MIPS scan and run them through our analysis. The model galaxies consist of single-component Sérsic models with randomly selected parameters, and the range of parameters are as follows. The effective radius is varied uniformly from 123 to 20'', the Sérsic index is varied uniformly from 0.5 to 4, and the magnitude is varied uniformly from 11.5 to 16. The model galaxy is created by first selecting a region on the MIPS scan that does not have a nearby object within 15 pixels. We create a cutout of this region, generate a model galaxy using GALFIT, and then add the model and noise to the MIPS cutout. The PRF may vary across the final MIPS scan; to incorporate this effect in our simulations, we vary the PRF used to create the model galaxy by randomly selecting from one of the five brightest point sources on each image. We then run GALFIT on the simulated galaxy to compare the recovered versus input parameters. GALFIT requires an initial estimate of the model parameters; we use the model parameters with 20% uncertainty added to the input parameters, except that we keep the axis ratio and position angle fixed to reproduce our fitting procedure. When detecting the galaxy, we use the PRF that we use when modeling the real galaxies (except for Hercules; see below).

We show the results of the simulations in Figure 19, where we plot the ratio of the recovered to input effective radius versus measured surface brightness. We calculate the observed surface brightness, μ, as

$$\begin{eqnarray}&&\mu =m+2.5\,{\mathrm{log}}_{10}(\pi {R}_{e(\mathrm{obs})}^{2}\,B/A),\end{eqnarray} \tag{ 3 }$$

where m, R_e(obs), and B/A are the magnitude, effective radius, and axis ratio of the best-fit Sérsic model. (Area of ellipse is A = πab.) In each panel, the scatter in the recovered size increases significantly beyond a surface brightness of ∼20 mag/arcsec². We give the average and standard deviation of the recovered to input R_e for images with μ > 20. These are consistent with a ratio of one, indicating that GALFIT is able to recover the size of the simulated galaxies with μ > 20.

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In Figure 20 we show the ratio of the recovered to input effective radius versus the effective radius of the input model, just for the models that meet the surface brightness cuts illustrated in Figure 19. The vertical dashed line corresponds to the 245-pixel scale of the MIPS scans. Our convolved models are able to recover the input R_e to this limit, although the recovered values for Hercules are systematically and significantly larger than the input values. When we tried to create a PRF from a source on the Hercules scan, the recovered radii were 20%–30% larger than the input values. When we use the PRF from Spitzer Science Center, the recovered radii are still systematically high, but only by 16%, as shown in Figure 19. The remaining offset is likely due to a mismatch in PRF, but we are not able to further correct for this. The simulations indicate that we will be biased toward measuring larger 24 μm R_e in Hercules.

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The simulation results lead us to apply a surface brightness cut to our sample. In addition to the selection criteria listed in Section 4, we keep only those galaxies whose measured surface brightness is above μ < 20 mag/sq arcsec. In physical units, this surface brightness cut corresponds to ≈0.012 M_⊙ yr⁻¹ kpc⁻² or 7 × 10⁷ erg s⁻¹ kpc⁻².