PRIMUS: EFFECTS OF GALAXY ENVIRONMENT ON THE QUIESCENT FRACTION EVOLUTION AT z < 0.8

At intermediate redshifts we use multiwavelength imaging and spectroscopic redshifts from PRIMUS, a faint galaxy survey with ∼120,000 redshifts (${{\sigma }_{z}}/(1+z)\approx 0.5\%$) within the range z ≈ 0–1.2. The survey was conducted using the IMACS spectrograph on the Magellan I Baade 6.5 m telescope with a slitmask and low dispersion prism. For details on the PRIMUS observation methods such as survey design, targeting, and data summary, we refer readers to Coil et al. (2011). For details on redshift fitting, redshift precision and survey completeness we refer readers to Cool et al. (2013).

While the PRIMUS survey targeted seven distinct extragalactic deep fields for a total of $\sim 9\;{{{\rm deg} }^{2}}$, we restrict our sample to five fields that have GALEX and Spitzer/IRAC imaging for a total of $\sim 5.5\;{{{\rm deg} }^{2}}$ (similar to the sample selection in Moustakas et al. 2013). Four of these fields are a part of the Spitzer Wide-area Infrared Extragalactic Survey (SWIRE: ⁹ ) the European Large Area Infrared Space Observatory Survey—South 1 field (ELAIS-S1 ¹⁰ ) the Chandra Deep Field South SWIRE field, and the XMM Large Scale Structure Survey field (XMM-LSS). The XMM-LSS consists of two separate but spatially adjacent fields: the Subaru/XMM-Newton DEEP Survey field (XMM-SXDS ¹¹ ) and the Canadian–France–Hawaii Telescope Legacy Survey field (XMM-CFHTLS ¹² ). Our fifth and final field is the Cosmic Evolution Survey (COSMOS ¹³ ) field. For all of our fields we have near-UV (NUV) and far-UV (FUV) photometry from the GALEX Deep Imaging Survey (DIS; Martin et al. 2005; Morrissey et al. 2005) as well as ground-based optical and Spitzer/IRAC mid-infrared photometric catalogs. Moustakas et al. (2013) provides detailed descriptions of integrated flux calculations in the photometric bands for each of our fields. Furthermore, we derive the K-corrections from the photometry using K-correct (v4.2; Blanton & Roweis 2007).

Finally, using the spectroscopic redshift and broad wavelength photometry we apply iSEDfit, a Bayesian SED modeling code, to calculate stellar masses and SFRs for our sample galaxies (Moustakas et al. 2013). iSEDfit uses the redshift and the observed photometry of the galaxies to determine the statistical likelihood of a large ensemble of generated model SEDs. The model SEDs are generated using Flexible Stellar Population Synthesis models (Conroy et al. 2009; Conroy & Gunn 2010) based on the Chabrier (2003) IMF, along with a time dependent dust attenuation curve of Charlot & Fall (2000) and other prior parameters discussed in Section 4.1 and Appendix A of Moustakas et al. (2013). For details on the effects of prior parameter choices of iSEDfit on physical properties of galaxies we refer readers to the Appendix of Moustakas et al. (2013). For the observed photometry, we use the GALEX FUV and NUV, the two shortest IRAC bands at 3.6 and $4.5\;\mu {\rm m}$ (the two longer-wavelength IRAC channels are excluded because iSEDfit does not model hot dust or polycyclic aromatic hydrocarbons emission lines), and the optical bands.

At low redshifts, we use spectroscopic redshifts and ugriz photometry from the SDSS Data Release 7 (DR7; Abazajian et al. 2009). More specifically we select galaxies from the New York University Value-Added Galaxy Catalog (hereafter VAGC) that satisfy the main sample criterion and have galaxy extinction corrected Petrosian magnitudes $14.5\lt r\lt 17.6$ and spectroscopic redshifts within $0.01\lt z\lt 0.2$ (Blanton et al. 2005b). We further restrict the VAGC sample to only galaxies with medium depth observations with total exposure time greater than $1\;{\rm ks}$ from GALEX Release 6. This leaves 167, 727 galaxies.

Next, we use the MAST/CasJobs ¹⁴ interface and a 4'' diameter search radius, to obtain the NUV and FUV photometry for the SDSS-GALEX galaxies. For optical photometry, we use the ugriz bands from the SDSS model magnitudes scaled to the r-band cmodel magnitude. These photometric bands are then supplemented with integrated JHK_s magnitudes from the 2MASS Extended Source Catalog (XSC; Jarrett et al. 2000) and with photometry at 3.4 and $4.6\;\mu {\rm m}$ from the WISE All-sky Data Release. ¹⁵ Further details regarding the SDSS-GALEX sample photometry can be found in Section 2.4 of Moustakas et al. (2013). As previously done on the PRIMUS data in Section 2.1, we use iSEDfit to obtain the stellar masses and SFRs for the SDSS-GALEX sample.

The SDSS-GALEX data discussed above is derived from the NYU-VAGC based on SDSS DR7, using the standard SDSS photometric measurements. Several investigators have found that the background subtraction techniques used in the standard photometric catalogs introduce a size dependent bias in the galaxy fluxes and consequently stellar masses (Blanton et al. 2005a; West 2005; Bernardi et al. 2007; Lauer et al. 2007; Hyde & Bernardi 2009; West et al. 2010).

In order to quantify the effects of these photometric underestimations in our analysis, we tried replacing our SDSS fluxes in the ugriz band with ugriz fluxes from the NASA-Sloan Atlas catalog, which incorporate the improved background subtraction presented in Blanton et al. (2011) and uses single-Seric fit fluxes rather than the standard SDSS cmodel fluxes. Using the ratio of the luminosity derived from the improved photometry over the luminosity derived from the standard NYU-VAGC photometry, we apply a preliminary correction to the stellar mass values obtained from iSEDfit assuming a consistent mass-to-light ratio. This mass correction leads to a significant increase in the SMF for $\mathcal{M}\gt {{10}^{11}}\;{{\mathcal{M}}_{\odot }}$; however, the effect of the mass correction was negligible for the quiescent fraction evolution results. As a result, for the results presented here we use the standard SDSS fluxes and we do not discuss the issues with photometric measurements any further in this paper. We note that a thorough investigation of these issues to understand their effect on the SMF requires a reanalysis of both the SDSS photometry and the deeper photometry used for PRIMUS targeting.

From the low redshift SDSS-GALEX and intermediate redshift PRIMUS data we define our mass complete galaxy sample. We begin by imposing the parent sample selection criteria from Moustakas et al. (2013). More specifically, we take the statistically complete primary sample from the PRIMUS data (Coil et al. 2011) and impose magnitude limits on optical selection bands as specified in Moustakas et al. (2013), Table 1. These limits are in different optical selection bands and have distinct values for the five PRIMUS target fields. We then exclude stars and broad-line AGN to only select objects spectroscopically classified as galaxies, with high-quality spectroscopic redshifts (Q ≥ 3). Lastly, we impose a redshift range of $0.2\lt z\lt 0.8$ for the PRIMUS galaxy sample, where $z\gt 0.2$ is selected due to limitations from sample variance and $z\lt 0.8$ is selected due to the lack of sufficient statistics in subsamples defined below.

Table 2.  Best Fit Parameters for ${{f}_{{\rm Q}}}({{\mathcal{M}}_{*}})$ Fit

${{z}_{1}}\lt z\lt {{z}_{2}}$	Environment	a	b
$0.05\lt z\lt 0.12$	${{n}_{{\rm env}}}=0.0$	0.410 ± 0.018	0.469 ± 0.007
	${{n}_{{\rm env}}}\gt 3.0$	0.270 ± 0.016	0.620 ± 0.008
$0.2\lt z\lt 0.4$	${{n}_{{\rm env}}}=0.0$	0.340 ± 0.032	0.432 ± 0.015
	${{n}_{{\rm env}}}\gt 3.0$	0.432 ± 0.018	0.544 ± 0.010
$0.4\lt z\lt 0.6$	${{n}_{{\rm env}}}=0.0$	0.263 ± 0.038	0.381 ± 0.018
	${{n}_{{\rm env}}}\gt 3.0$	0.289 ± 0.018	0.446 ± 0.013
$0.6\lt z\lt 0.8$	${{n}_{{\rm env}}}=0.0$	0.284 ± 0.036	0.352 ± 0.019
	${{n}_{{\rm env}}}\gt 3.0$	0.468 ± 0.065	0.429 ± 0.023

Notes. Best fit parameters in Equation (7) for each subsample ${{f}_{{\rm Q}}}({{\mathcal{M}}_{*}})$ in Figure 4 for ${{\mathcal{M}}_{{\rm fid}}}={{10}^{10.5}}\;{{\mathcal{M}}_{\odot }}$.

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For the PRIMUS objects that meet the above criteria, we assign statistical weights (described in Coil et al. 2011 and Cool et al. 2013) in order to correct for targeting incompleteness and redshift failures. The statistical weight, w_i , for each galaxy is given by

$$\begin{eqnarray}&&{{w}_{i}}={{({{f}_{{\rm target}}}\times {{f}_{{\rm collision}}}\times {{f}_{{\rm success}}})}^{-1}},\end{eqnarray} \tag{ 1 }$$

as in Equation (1) in Moustakas et al. (2013).

Since we are ultimately interested in a mass complete galaxy sample to derive SMFs and QFs, next we impose stellar mass completeness limits to our galaxy sample. Stellar mass completeness limits for a magnitude-limited survey such as PRIMUS are functions of redshift, the apparent magnitude limit of the survey, and the typical stellar mass-to-light ratio of galaxies near the flux limit. We use the same procedure as Moustakas et al. (2013), which follows Pozzetti et al. (2010), to empircally determine the stellar mass completeness limits. For each of the target galaxies we compute ${{\mathcal{M}}_{{\rm lim} }}$ using ${\rm log} \;{{\mathcal{M}}_{{\rm lim} }}={\rm log} \;\mathcal{M}+0.4\;(m-{{m}_{{\rm lim} }})$, where $\mathcal{M}$ is the stellar mass of the galaxy in ${{\mathcal{M}}_{\odot }}$, ${{\mathcal{M}}_{{\rm lim} }}$ is the stellar mass of each galaxy if its magnitude was equal to the survey magnitude limit, m is the observed apparent magnitude in the selection band, and ${{m}_{{\rm lim} }}$ is the magnitude limit for our five fields. We construct a cumulative distribution of ${{\mathcal{M}}_{{\rm lim} }}$ for the 15% faintest galaxies in ${\Delta }z=0.04$ bins. In each of these redshift bins, we calculate the minimum stellar mass that includes $95\%$ of the galaxies. Separately for quiescent and SF galaxies, we fit quadratic polynomials to the minimum stellar masses versus redshift (SF or quiescent classification is described in the following section). Finally, we use the polynomials to obtain the minimum stellar masses at the center of redshift bins, 0.2–0.4, 0.4–0.6, and 0.6–0.8, which are then used as PRIMUS stellar mass completeness limits.

For the low redshift portion of our galaxy sample, we start by limiting the SDSS-GALEX data to objects within $0.05\lt z\lt 0.12$, a redshift range later imposed on the volume-limited EDP (Section 2.5). To account for the targeting incompleteness of the SDSS-GALEX sample, we use the statistical weight estimates provided by the NYU-VAGC catalog. Furthermore, we determine a uniform stellar mass completeness limit of ${{10}^{10.2}}\;{{\mathcal{M}}_{\odot }}$ above the stellar mass-to-light ratio completeness limit of the SDSS-GALEX data within the imposed redshift limits (Blanton et al. 2005a; Baldry et al. 2008; Moustakas et al. 2013). We then apply this mass limit in order to obtain our mass-complete galaxy sample at low redshift.

We now have a stellar mass complete sample derived from SDSS-GALEX and PRIMUS data. Since our sample is derived from two different surveys, we account for the disparity in the redshift uncertainty. While PRIMUS provides a large number of redshifts out to z = 1, due to its use of a low dispersion prism, the redshift uncertainties are significantly larger (${{\sigma }_{z}}/(1+z)\approx 0.5\%$) than the uncertainties of the SDSS redshifts. In order to have comparable environment measures throughout our redshift range, we apply PRIMUS redshift uncertainties to our galaxy sample selected from SDSS-GALEX. For each SDSS-GALEX galaxy, we adjust its redshift by randomly sampling a Gaussian distribution with standard deviation $\sigma =0.005(1+{{z}_{{\rm SDSS}}})$, where z_SDSS is the SDSS redshift of the galaxy.

We now classify our mass complete galaxy sample into quiescent or SF using an evolving cut based on specific SFR utilized in Moustakas et al. (2013) Section 3.2. This classification method uses the SF sequence, which is the correlation between SFR and stellar mass in SF galaxies observed at least until $z\sim 2$ (Noeske et al. 2007; Williams et al. 2009; Karim et al. 2011). The PRIMUS sample displays a well-defined SF sequence within the redshift range of our galaxy sample. Using the power-law slope for the SF sequence from Salim et al. (2007) (SFR $\propto \;{{\mathcal{M}}^{0.65}}$) and the minimum of the quiescent/SF bimodality, determined empirically, we obtain the following equation to classify the target galaxies (Equation (2) in Moustakas et al. 2013):

$$\begin{eqnarray}\begin{array}{ccccccccccccccc} {\rm log} ({\rm SF}{{{\rm R}}_{{\rm min} }}) & = & -0.49+0.64{\rm log} (\mathcal{M}-10) \\ {} & {} & +1.07(z-0.1), \\ \end{array}\end{eqnarray} \tag{ 2 }$$

where $\mathcal{M}$ is the stellar mass of the galaxy. If the target galaxy SFR and stellar mass lie above Equation (2) we classify it as SF; if below, as quiescent (Moustakas et al. 2013 Figure 1).

We define the environment of a galaxy as the number of neighboring EDP galaxies (defined below) within a fixed aperture centered around it. We use fixed aperture measurements in order to quantify galaxy environment with an aperture sufficiently large to encompass massive halos (Muldrew et al. 2012; Skibba et al. 2013).

For our aperture, we use a cylinder of dimensions: ${{R}_{{\rm ap}}}=2.5\;{\rm Mpc}$ and ${{H}_{{\rm ap}}}=35\;{\rm Mpc}$. We note that H_ap is the full height of the cylinder and R_ap and H_ap are comoving distances. We use a cylindrical aperture to account for the PRIMUS redshift errors and redshift space distortions (i.e., "Finger of God" effect). As Cooper et al. (2005) and Gallazzi et al. (2009) find, $\pm 1000\;{\rm km}\;{{{\rm s}}^{-1}}$ optimally reduces the effects of redshift space distortions. The PRIMUS redshift uncertainty at $z\sim 0.7$ corresponds to ${{\sigma }_{z}}\lt 0.01$, so our choice of $35\;{\rm Mpc}$ for the aperture height accounts for both of these effects. Our choice of cylinder radius was motivated by scale dependence analyses in the literature (Blanton et al. 2006; Wilman et al. 2010; Muldrew et al. 2012), which suggest that galactic properties such as color and quiescent fractions are most strongly dependent on scales $\lt 2$ Mpc, around the host dark matter halo sizes.

Before we measure the environment for our galaxy sample, we first construct a volume limited EDP with absolute magnitude cut-offs (M_r ) in redshift bins with ${\Delta }z\sim 0.2$. The M_r cut-offs for the EDP are selected such that the cumulative number density over M_r for all redshift bins are equal. We make this choice in order to construct an EDP that contains similar galaxy populations through the redshift range (i.e., accounts for the progenitor bias). In their analysis of this method, Behroozi et al. (2013) and Leja et al. (2013) find that although it does not precisely account for the scatter in mass accretion or galaxy–galaxy mergers, it provides a reasonable means to compare galaxy populations over a wide range of cosmic time.

In constructing the PRIMUS EDP we use the same PRIMUS data used to select our galaxy sample (described in Section 2.3). We again restrict the PRIMUS galaxies to $0.2\lt z\lt 0.8$ and divide them into bins of ${\Delta }z=0.2$. Before we consider the cumulative number densities in the redshift bins, we first determine the M_r limit for the highest redshift bin (z = 0.6–0.8) by examining the M_r distribution with bin size ${\Delta }{{M}_{r}}=0.25$ and select ${{M}_{r,{\rm lim} }}$ near the peak of the distribution where bins with ${{M}_{r}}\gt {{M}_{r,{\rm lim} }}$ have fewer galaxies than the bin at ${{M}_{r,{\rm lim} }}$. We conservatively choose ${{M}_{r,{\rm lim} }}(0.6\lt z\lt 0.8)$ to be ${{M}_{r}}=-20.97$. Then for the lower redshift bins, we impose absolute magnitude limits (${{M}_{r,{\rm lim} }}$) such that the cumulative number density, calculated with the galaxy statistical weights, of the bin ordered by M_r is equal to the cumulative number density of the highest redshift bin with ${{M}_{r,{\rm lim} }}(0.6\lt z\lt 0.8)=-20.97$.

For the SDSS EDP, we do not use the SDSS-GALEX parent data, which is limited to the combined angular selection window of the VAGC and GALEX (Section 2.2). Instead, since FUV, NUV values are not necessary for the EDP, we extend the parent data of the SDSS EDP to the entire NYU-VAGC, including galaxies outside of the GALEX window function. Furthermore, we impose a redshift range of 0.05–0.12 on the SDSS EDP. This redshift range was determined to account for the lack of faint galaxies at $z\sim 0.2$ and the lack of bright galaxies at $z\sim 0.01$ in the VAGC. As with the PRIMUS redshift bins, we determine the SDSS EDP ${{M}_{r,{\rm lim} }}$ by matching the cumulative number density of the highest redshift bin. For redshift bins z = 0.05–0.12, 0.2–0.4, 0.4–0.6, 0.6–0.8 we get ${{M}_{r,{\rm lim} }}=-20.95$, −21.03, −20.98 and −20.97, respectively. These absolute magnitude limits are illustrated in Figure 1, where we present the absolute magnitude (M_r ) versus redshift for the galaxy sample (black squares) ad the EDP (red circles). The left-most panel corresponds to the samples derived from the SDSS-GALEX data while the rest correspond to samples derived from the PRIMUS data divided in bins with ${\Delta }z\sim 0.2$. Figure 1 shows clear M_r cutoffs in the M_r distribution versus redshift for the EDP on top of our galaxy sample.

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For our SDSS-GALEX galaxy sample, in Section 2.3, we apply PRIMUS redshift errors in order to establish a consistent measurement of environment throughout our redshift range. We appropriately apply equivalent redshift adjustments for the SDSS EDP. For the SDSS EDP galaxies that are also contained within the SDSS-GALEX sample, we adjust the redshift by an identical amount. For the rest, we apply the same redshift adjustment procedure described in Section 2.3 in order to obtain PRIMUS level redshift uncertainties.

Finally, we measure the environment for each galaxy in our galaxy sample by counting the number of EDP galaxies, ${{n}_{{\rm env}}}$, with R.A., decl., and z within our cylindrical aperture centered around it. ${{n}_{{\rm env}}}$ accounts for the statistical weights of the EDP galaxies. For our galaxy sample, the expected ${{n}_{{\rm env}}}$ given the uniform number density in each of our EDP redshift bin and volume of our cylindrical aperture is $\langle {{n}_{{\rm env}}}\rangle =1.3$. Once we obtain environment measurements for all the galaxies in our galaxy sample, we classify galaxies with ${{n}_{{\rm env}}}=0.0$ to be in "low" environment densities and galaxies with ${{n}_{{\rm env}}}\gt 3$ to be in "high" environment densities. The high environment cutoff was selected in order to reduce contamination from galaxies in low environment densities while maintaining sufficient statistics. In Section 4.2 we will also explore higher density cutoffs for ${{n}_{{\rm env}}}$.

The analysis we describe below uses a fixed cylindrical aperture with dimensions ${{R}_{{\rm ap}}}=2.5\;{\rm Mpc}$ and ${{H}_{{\rm ap}}}=35\;{\rm Mpc}$ to measure environment. The same analysis was extended for varying aperture dimensions ${{R}_{{\rm ap}}}=1.5,\;2.5,3.0\;{\rm Mpc}$ and ${{H}_{{\rm ap}}}=35,\;70\;{\rm Mpc}$ with adjusted environment classifications. The results obtained from using different apertures and environment classifications are qualitatively consistent with the results presented below.

One of the challenges in obtaining accurate galaxy environments using a fixed aperture method is accounting for the edges of the survey. For galaxies located near the edge of the survey, part of the fixed aperture encompassing it will lie outside the survey regions. In this scenario, n_env only reflects the fraction of the environment within the survey geometry.

To account for these edge effects, we use a Monte Carlo method to impose edge cutoffs on our galaxy sample. First, using ransack from Swanson et al. (2008), we construct a random sample of N_ransack = 1,000,000 points with R.A. and decl. randomly selected within the window function of the EDP (SDSS EDP and PRIMUS EDP separately). We then compute the angular separation, ${{\theta }_{i,{\rm ap}}}$ that corresponds to ${{R}_{{\rm ap}}}$ (Section 2.5) at the redshift of each sample galaxy i. For each sample galaxy we count the number of ransack points within ${{\theta }_{i,{\rm ap}}}$ of the galaxy: ${{n}_{i,{\rm ransack}}}$. Afterwards, we compare ${{n}_{i,{\rm ransack}}}$ to the expected value computed from the angular area of the environment defining aperture and the EDP window function:

$$\begin{eqnarray}&&{{\langle {{n}_{{\rm ransack}}}\rangle }_{i}}=\frac{{{N}_{{\rm ransack}}}}{{{A}_{{\rm EDP}}}}\times \pi \theta _{i,{\rm ap}}^{2}\times {{f}_{{\rm thresh}}}.\end{eqnarray} \tag{ 3 }$$

${{A}_{{\rm EDP}}}$ is the total angular area of the EDP window function and ${{f}_{{\rm thresh}}}$ is the fractional threshold for the edge effect cut-off. For ${{R}_{{\rm ap}}}=2.5\;{\rm Mpc}$, we use ${{f}_{{\rm thresh}}}=0.75$. If ${{n}_{i,{\rm ransack}}}\gt {{\langle {{n}_{{\rm ransack}}}\rangle }_{i}}$ then galaxy i remains in our sample; otherwise, it is discarded. Once the edge effect cuts are applied, we are left with the final galaxy sample. For our SDSS-GALEX galaxy sample, ∼12% of galaxies are removed from the edge effect cuts. For our PRIMUS galaxy sample, ∼40% of galaxies are removed from the edge effect cuts.

In Figure 2 we present the distribution of environment measurements (${{n}_{{\rm env}}}$) for our final galaxy sample in redshift bins: z = 0.05–0.12, 0.2–0.4, 0.4–0.6, and 0.6–0.8. The quiescent galaxy contributions are colored in red while the SF galaxy contributions are colored in blue and patterned. We classify galaxies with ${{n}_{{\rm env}}}=0.0$ to be in low density environments and galaxies with ${{n}_{{\rm env}}}\gt 3.0$ to be in high density environments. We list the number of galaxies (N_gal) in each of the mass complete subsamples classified by redshift, quiescent or SF, and environment in Table 1.

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Although we imposed PRIMUS redshift errors on our SDSS galaxies to consistently measure environment throughout our entire sample, we note a significant discrepancy between the ${{n}_{{\rm env}}}$ distributions of the SDSS and PRIMUS samples. For example, in each of the PRIMUS redshift bins, ∼40% of galaxies in the redshift bin are in low density environments and roughly 30% are in high density environments. In contrast, in the SDSS redshift bin, ∼20% of galaxies in the redshift bin are in low density environments and ∼35% are in high density environments. We remind the reader that this is mainly due to the varying stellar mass-completeness limits imposed on our galaxy sample for each redshift bins and does not affect our results.

To calculate the SMFs we employ a non-parametric $1/{{V}_{{\rm max} }}$ estimator commonly used for galaxy luminosity functions and SMF in order to account for Malmquist bias, as done in Moustakas et al. (2013) and discussed in the review Johnston (2011). The differential SMF is given by the following equation:

$$\begin{eqnarray}&&{\Phi }({\rm log} \mathcal{M}){\Delta }({\rm log} \mathcal{M})=\mathop{\sum }\limits_{i=1}^{N}\frac{{{w}_{i}}}{{{V}_{{\rm max} ,{\rm avail},i}}}.\end{eqnarray} \tag{ 4 }$$

w_i is the statistical weight of galaxy i and ${\Phi }({\rm log} \mathcal{M}){\Delta }({\rm log} \mathcal{M})$ is the number of galaxies (N) per unit volume within the stellar mass range $[{\rm log} \mathcal{M},{\rm log} \mathcal{M}+{\Delta }({\rm log} \mathcal{M})]$. The equation above is the same as Equation (3) in Moustakas et al. (2013) except that we use ${{V}_{{\rm max} ,{\rm avail}}}$ instead than ${{V}_{{\rm max} }}$, to account for the edge effects of the survey discussed in Section 2.6.

${{V}_{{\rm max} ,{\rm i}}}$ is the maximum cosmological volume where it is possible to observe galaxy i given the apparent magnitude limits of the survey. However in Section 2.6 we remove galaxies that lie on the survey edges from our sample. In doing so, we reduce the maximum cosmological volume where a galaxy can be observed, thereby reducing the fraction of ${{V}_{{\rm max} ,i}}$ that is actually available in the sample. We introduce the term ${{V}_{{\rm max} ,{\rm avail},i}}$ to express the maximum volume accounting for the survey edge effects.

To calculate ${{V}_{{\rm max} ,{\rm avail},i}}$, we use a similar Monte Carlo method as the edge effect cutoffs in Section 2.6. First, we generate a sample of points with random R.A., decl. within the window function of our galaxy sample (SDSS-GALEX window function and the five PRIMUS fields) and random z within the redshift range. These points are not to be confused with the ransack sample in Section 2.6. We apply the edge effect cuts on these random points as we did for our galaxy sample using the same method as in Section 2.6. Within redshift bins of ${\Delta }z\sim 0.01$, we calculate the fraction of the random points that remain in the bin after the edge effect cuts over the total number of random points in the bin: ${{f}_{{\rm edge}}}$. We then apply this factor to compute ${{V}_{{\rm max} ,{\rm avail}}}={{V}_{{\rm max} }}\times {{f}_{{\rm edge}}}$. The ${{V}_{{\rm max} }}$ values in the equation above are computed following the method described in Moustakas et al. (2013) Section 4.2 with the same redshift-dependent K-correction from the observed SED and luminosity evolution model.

To calculate the uncertainty of the SMFs from the sample variance, we use a standard jackknife technique (following Moustakas et al. 2013). For the PRIMUS galaxies, we calculate SMFs after excluding one of the five target fields at a time. For the SDSS target galaxies we divide the field into a 12 × 9 rectangular R.A. and decl. grid and calculate the SMFs after excluding one grid at a time. From the calculated SMFs we calculate the uncertainty:

$$\begin{eqnarray}&&{{\sigma }^{j}}=\sqrt{\frac{N-1}{N}\mathop{\sum }\limits_{k=1}^{M}{{({\Phi }_{k}^{j}-\langle {{{\Phi }}^{j}}\rangle )}^{2}}}\end{eqnarray} \tag{ 5 }$$

N in this equation is the number of jackknife SMFs in the stellar mass bin. $\langle {{{\Phi }}^{j}}\rangle$ is the mean number density of galaxies in each stellar mass bin for all of the jackknife ${{{\Phi }}^{j}}$ s.

In Figure 3, we present the SMFs of the quiescent/SF (orange/blue, bottom/top panels) and high/low density environment (left/right panels) subsamples. The redshift evolution of the SMFs in each of these panels are indicated by a darker shade for lower redshift bins. The width of the SMFs represent the sample variance uncertainties derived in Section 3.1.

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While a detailed comparison of the SMFs in each panel for different epochs is complicated by the different stellar mass completeness limits, we present some notable trends in each panel. In panel (a), SF galaxies in low density environments, we find a significant decrease in the high mass end of the SMF ($\mathcal{M}\gt {{10}^{10.75}}\;{{\mathcal{M}}_{\odot }}$) over cosmic time. Meanwhile at lower masses ($\mathcal{M}\lt {{10}^{10.5}}\;{{\mathcal{M}}_{\odot }}$), we observe no noticeable trend in the SMF. In panel (b), SF galaxies in high density environments, we do not observe any clear trends above the knee of the SMF ($\mathcal{M}\sim {{10}^{10.7}}\;{{\mathcal{M}}_{\odot }}$) but an increase in SMF below the knee. For the quiescent population in low density environment, panel (c), we observe a potential decrease at higher masses ($\mathcal{M}\gt {{10}^{10.7}}\;{{\mathcal{M}}_{\odot }}$). Lastly for the quiescent population in high density environments, panel (d), we find significant increase in Φ for lower masses but little trend at higher masses.

Observing the evolutionary trends in SMF for each of these sub-populations provides a narrative of the different galaxy evolutionary tracks involving environment and the end of star formation. For example, the decrease in the massive SF galaxies in low density environments over cosmic time can be attributed to the transition of those galaxies to any of the other panels. The SF galaxies in low density environments that have ended star formation over time are possibly responsible for the increase of the quiescent, low density environment SMF over time. The SF galaxies that fall into higher density environments explain the increase in the SF high density environment SMF below the knee. Finally, SF galaxies in high density environments that have ended their star formation, quiescent galaxies that have transitioned from low to high density environments, and SF galaxies in low density environments that end their star formation while infalling to high density environments all contribute to the overall increase of the high environment quiescent SMF.

In addition to the evolution over cosmic time, we observe noticeable trends when we compare the SMFs for SF and quiescent galaxies between the two environments. Comparison of the SMFs in low versus high density environments reveal a noticeable relation between mass and density, with SMFs in high density environments having more massive galaxies, especially evident in our lowest redshift bin. We further confirm this trend when we compare the median mass between the two environments to find that the median mass for galaxies in high density environments is significantly greater than in low density environments. The relationship between mass and environment observed in our SMFs reflects the well-established mass–density relation and observed mass segregation with environment in the literature (Norberg et al. 2002; Zehavi 2002; Blanton et al. 2005a; Bundy et al. 2006; Scodeggio et al. 2009; Bolzonella et al. 2010).

While our mass complete subsample coupled with robust environment measurements allows us to compare SMF evolution for each of our subsamples out to z = 0.8, we caution readers regarding the photometric biases affecting the SDSS imaging (and perhaps the other imaging sources) and reserve detailed analysis of the SMFs for future investigation.

From the SMF number densities (Φ) computed in the previous section, the quiescent fraction is computed as follows,

$$\begin{eqnarray}&&{{f}_{{\rm Q}}}({{\mathcal{M}}_{*}},z)=\frac{{{{\Phi }}_{{\rm Q}}}}{{{{\Phi }}_{{\rm SF}}}+{{{\Phi }}_{{\rm Q}}}}.\end{eqnarray} \tag{ 6 }$$

${{{\Phi }}_{{\rm Q}}}$ and ${{{\Phi }}_{{\rm SF}}}$ are the total number of galaxies per unit volume in stellar mass bin of ${\Delta }({\rm log} \mathcal{M})=0.20\;{\rm dex}$ for the quiescent and SF subsamples, respectively (Equation (4)). We compute ${{f}_{{\rm Q}}}$ for high and low density environments for all redshift bins as plotted in Figure 4, which shows the evolution of ${{f}_{{\rm Q}}}$ for high (right panel) and low (left panel) density environments. As in Figure 3, the evolution of the quiescent fraction over cosmic time is represented in the shading (darker with lower redshift) and the uncertainty is represented by the width. For the uncertainty in the quiescent fraction, we use the standard jackknife technique, following the same steps as for the SMF uncertainty in Section 3.1.

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Most noticeably in Figure 4, we find ${{f}_{{\rm Q}}}$ increases monotonically as a function of mass at all redshifts and environments. In other words, for galaxies in any environment since $z\sim 0.8$, galaxies with higher masses are more likely to have ceased their star formation. With the roughly linear correlation between galaxy SFR to galaxy color and morphology, we find that this trend reflects the well established color–mass and morphology–mass relations: more massive galaxies are more likely to be red or early-type (Blanton & Moustakas 2009).

Focusing on the redshift evolution of ${{f}_{{\rm Q}}}$, we find that for both environments ${{f}_{{\rm Q}}}$ increases as redshift decreases. For high density environments, this is analogous to the Butcher–Oemler effect (Butcher & Oemler 1984), which states that galaxy populations in groups or clusters have higher ${{f}_{{\rm blue}}}$ (lower ${{f}_{{\rm Q}}}$) at higher redshift. This evolution occurs with roughly the same amplitude in low environments as well.

In addition, when we compare the stellar masses at which ${{f}_{{\rm Q}}}=0.5$ for each subsample, the so-called ${{\mathcal{M}}_{50-50}}$, we find that this quantity decreases over cosmic time. This corresponds to the well-known mass-downsizing pattern found by previous investigators (e.g., Bundy et al. 2006). Furthermore, the mass-downsizing trend observed in each of our environment subsample is qualitatively consistent with the trend observed in zCOSMOS Redshift Survey for isolated and group galaxies (Iovino et al. 2010).

Finally, we compare between our low and high density environment ${{f}_{{\rm Q}}}{\rm s}$ at each redshift bin interval. For our lowest redshift bin, we find that ${{f}_{{\rm Q}}}$ at low density environments ranges from ∼0.4 to ∼0.9 for ${{10}^{10.2}}\;{{\mathcal{M}}_{\odot }}\lt {{\mathcal{M}}_{*}}\lt {{10}^{11.5}}\;{{\mathcal{M}}_{\odot }}$. Over the same mass range, ${{f}_{{\rm Q}}}$ at high density environment ranges from ∼0.55 to ∼0.9. For our SDSS sample, ${{f}_{{\rm Q}}}$ in high density environments is notably higher.

For our PRIMUS sample at $z\sim 0.3$, over ${{10}^{9.5}}\;{{\mathcal{M}}_{\odot }}\lt {{\mathcal{M}}_{*}}\lt {{10}^{11}}\;{{\mathcal{M}}_{\odot }}$ ${{f}_{{\rm Q}}}$ ranges from ∼0.2 to ∼0.65 for low density environment, while at high density environment ${{f}_{{\rm Q}}}$ ranges from ∼0.2 to ∼0.8. Similarly, at $z\sim 0.5$, over ${{10}^{10}}\;{{\mathcal{M}}_{\odot }}\lt {{\mathcal{M}}_{*}}\lt {{10}^{11.2}}\;{{\mathcal{M}}_{\odot }}$ ${{f}_{{\rm Q}}}$ ranges from ∼0.3 to ∼0.6 for low density environment and ${{f}_{{\rm Q}}}$ ranges from ∼0.3 to ∼0.7 for high density environments. Finally in our highest redshift bin $z\sim 0.7$, over the mass range ${{10}^{10.5}}\;{{\mathcal{M}}_{\odot }}\lt {{\mathcal{M}}_{*}}\lt {{10}^{11.5}}\;{{\mathcal{M}}_{\odot }}$, ${{f}_{{\rm Q}}}$ ranges from ∼0.35 to ∼0.6 for low density and ∼0.45 to ∼0.8 for high density. For the entire redshift range of our sample, ${{f}_{{\rm Q}}}$ in high density environment is higher than ${{f}_{{\rm Q}}}$ in low density environments.

We note that for ${{\mathcal{M}}_{*}}\lt {{10}^{10}}\;{{\mathcal{M}}_{\odot }}$ at $z\sim 0.3$, we find no significant difference between f_Q in low and high density environments. Similar quiescent/red fraction studies (e.g., Baldry et al. 2006; Cucciati et al. 2010) find, at these redshifts and mass range, a greater environment dependence in f_Q. Our classification of SF/quiescent galaxies may contribute to this discrepancy with other quiescent fraction studies. We also note that for ${{\mathcal{M}}_{*}}\lt {{10}^{10}}\;{{\mathcal{M}}_{\odot }}$ at $z\sim 0.3$, only three of the five PRIMUS fields used in our analysis (XMM-SXDS, XMM-CFHTLS, and COSMOS; see Section 2.1) contribute galaxies to our sample. As a result our jack-knife method, which calculates uncertainty by excluding one PRIMUS field at a time, may underestimate the uncertainty thereby making an accurate comparison difficult at low masses. For our analysis, we focus on ${{\mathcal{M}}_{*}}\gt {{10}^{10}}\;{{\mathcal{M}}_{\odot }}$.

While there is a significant difference in ${{f}_{{\rm Q}}}$ between the environments, since the difference is observed from our highest redshift bin, it is not necessarily a result of environment dependent mechanisms for ending star formation. In order to isolate any environmental dependence, in the following section we quantitatively compare the evolution of the quiescent fraction between the different environments.

In order to more quantitatively compare the ${{f}_{{\rm Q}}}$ evolution for different epochs and environments, we fit ${{f}_{{\rm Q}}}$ for each subsample to a power-law parameterization as a function of stellar mass,

$$\begin{eqnarray}&&{{f}_{{\rm Q}}}({{\mathcal{M}}_{*}})=a{\rm log} \;\left( \frac{{{\mathcal{M}}_{*}}}{{{\mathcal{M}}_{{\rm fid}}}} \right)+b,\end{eqnarray} \tag{ 7 }$$

where a and b are best-fit parameters using MPFIT (Markwardt 2009) and ${{\mathcal{M}}_{{\rm fid}}}$ represents the empirically selected fiducial mass within the stellar mass limits where there is a sufficiently large number of galaxies. We primarily focus on ${{\mathcal{M}}_{{\rm fid}}}={{10}^{10.5}}\;{{\mathcal{M}}_{\odot }}$. We list the best-fit parameters a and b for each subsample in Table 2.

In Figure 5 we present the evolution of ${{f}_{{\rm Q}}}({{\mathcal{M}}_{{\rm fid}}})$ from $z\sim 0.7$ to ∼0.1 at low (blue) and high (red) density environments for ${{\mathcal{M}}_{{\rm fid}}}={{10}^{10.5}}\;{{\mathcal{M}}_{\odot }}$ (solid fill) and ${{10}^{11}}\;{{\mathcal{M}}_{\odot }}$ (pattern fill). The width of the evolution represents the uncertainty derived from MPFIT. As noted earlier in Section 4.1, ${{f}_{{\rm Q}}}$ in high density environments is significantly greater than ${{f}_{{\rm Q}}}$ in low density environments for both fiducial mass choices. Throughout our sample's redshift range ${{f}_{{\rm Q}}}{{({{\mathcal{M}}_{{\rm fid}}})}_{{\rm high}}}-{{f}_{{\rm Q}}}{{({{\mathcal{M}}_{{\rm fid}}})}_{{\rm low}}}\sim 0.1$.

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In addition, the ${{f}_{{\rm Q}}}({{\mathcal{M}}_{{\rm fid}}})$ evolution illustrates that the quiescent fraction in low density environment increases over cosmic time: ${{f}_{{\rm Q}}}({{\mathcal{M}}_{{\rm fid}}},z\sim 0.1)-{{f}_{{\rm Q}}}({{\mathcal{M}}_{{\rm fid}}},z\sim 0.7)\sim 0.1$. This significant quiescent fraction evolution for low density environments suggests that internal mechanisms, independent of environment, are responsible for a significant amount of star formation cessation. Meanwhile, the ${{f}_{{\rm Q}}}({{\mathcal{M}}_{{\rm fid}}})$ evolution in high density environment (${{f}_{{\rm Q}}}({{\mathcal{M}}_{{\rm fid}}},z\sim 0.1)-{{f}_{{\rm Q}}}({{\mathcal{M}}_{{\rm fid}}},z\sim 0.7)\sim 0.12$) shows little additional evolution.

When we increase our choice of ${{\mathcal{M}}_{{\rm fid}}}$ to ${{10}^{11\,}}{{\mathcal{M}}_{\odot }}$, aside from an overall shift in ${{f}_{{\rm Q}}}({{\mathcal{M}}_{{\rm fid}}})$ by ∼0.2, we observe the same evolutionary trends. ${{f}_{{\rm Q}}}({{\mathcal{M}}_{{\rm fid}}}={{10}^{11\,}}{{\mathcal{M}}_{\odot }})$ for both low and high density environments each increase by ∼0.2 from at all redshifts we study. Increasing the fiducial mass to ${{10}^{11\,}}{{\mathcal{M}}_{\odot }}$ does not significantly alter the evolutionary trends in either environment. Although the varying stellar mass completeness at each redshift bin limits the masses we probe for the ${{f}_{{\rm Q}}}$ evolution, our ${{f}_{{\rm Q}}}$ evolution exhibits little mass dependence.

However, the uncertainties in the PRIMUS redshifts may contaminate our fixed aperture measurements of galaxy environment. Consequently, we consider in Figure 6 more stringent high density environment classifications, extending the cut off to ${{n}_{{\rm env}}}\gt 5$ and 7 (specified in the top right legend and represented by the color of the shading). Aside from the increase in uncertainties that accompany the decrease in sample size of the purer high environment sample, we find an extension of the ${{f}_{{\rm Q}}}$ difference between the environments we stated earlier. A more stringent high environment classification significantly increases the overall ${{f}_{{\rm Q}}}({{\mathcal{M}}_{{\rm fid}}})$, which rises monotonically with the ${{n}_{{\rm env}}}$ limit.

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More importantly, a purer high environment classification reveals a more significant environment dependence on the ${{f}_{{\rm Q}}}$ evolution. While the difference between the ${{f}_{{\rm Q}}}$ evolution in low and high density environment is negligible for the ${{n}_{{\rm env}}}\gt 3$ cut-off, there is a notable difference in ${{f}_{{\rm Q}}}$ evolution between our highest cut-off ${{n}_{{\rm env}}}\gt 7$ and our low density environment. ${{f}_{{\rm Q}}}({{\mathcal{M}}_{{\rm fid}}},z\sim 0.1)-{{f}_{{\rm Q}}}({{\mathcal{M}}_{{\rm fid}}},z\sim 0.7)\sim 0.25$ for ${{n}_{{\rm env}}}\gt 7$ versus ${{f}_{{\rm Q}}}({{\mathcal{M}}_{{\rm fid}}},z\sim 0.1)-{{f}_{{\rm Q}}}({{\mathcal{M}}_{{\rm fid}}},z\sim 0.7)\sim 0.1$ for low density environment. In addition to the environment independent internal mechanisms that can explain the ${{f}_{{\rm Q}}}$ evolution in low density environments, there may be other environment dependent mechanisms that can account for the moderate environment dependence of the ${{f}_{{\rm Q}}}$ evolution. Our measured difference in the ${{f}_{{\rm Q}}}$ evolution between environments provides an important constraint for any environmental models for ending star formation.

Although a direct comparison with other results is difficult due to our sample specific methodology, a number of results from the literature have investigated the quiescent fraction in comparable fashions. In this section we compare our ${{f}_{{\rm Q}}}$ results from above to a number of these results, specifically from SDSS and zCOSMOS, with similarly defined samples and analogous environment classifications.

In Figure 6, we plot best-fit parameterization of ${{f}_{{\rm red}}}$ for high and low density environment from SDSS (panel a), zCOSMOS (panel b), and Peng et al. (2010) (filled square; panel d) from both surveys. From Iovino et al. (2010) (empty square; panel b), we calculate ${{f}_{{\rm red}}}=1-{{f}_{{\rm blue}}}$ using the best-fit ${{f}_{{\rm blue}}}$ from the mass bin $\mathcal{M}={{10}^{10.3}}-{{10}^{10.8}}\;{{\mathcal{M}}_{\odot }}$. From Kovač et al. (2014) (triangle; panel b) we plot an estimated ${{f}_{{\rm Q}}}$ by applying the residual between SFR based and color based galaxy classifications to the best-fit ${{f}_{{\rm red}}}$ at $\mathcal{M}={{10}^{10.5}}\;{{\mathcal{M}}_{\odot }}$ for low ($\delta =0.0$) and high density environments ($\delta =1.5$). Similarly, from Baldry et al. (2006) (diamond; panel a) we plot ${{f}_{{\rm Q}}}$ derived from the best-fit ${{f}_{{\rm red}}}$ at $\mathcal{M}={{10}^{10.5}}{{\mathcal{M}}_{\odot }}$ for low ($\delta =0.0$) and high density environment ($\delta =1.0$). For Geha et al. (2012) (cross; panel a), we plot ${{f}_{{\rm Q}}}$ for their isolated galaxy sample in their mass bin closest to ${{10}^{10.5}}\;{{\mathcal{M}}_{\odot }}$, $\mathcal{M}={{10}^{10.55}}\;{{\mathcal{M}}_{\odot }}$. Finally for Peng et al. (2010) (square; panel c), we plot the parameterized ${{f}_{{\rm red}}}$ at $\mathcal{M}={{10}^{10.5}}\;{{\mathcal{M}}_{\odot }}$ using their best-fit parameters for low ($\delta =0.0$) and high ($\delta =1.4$) density environments.

For our lowest redshift bin SDSS sample, we find that our ${{f}_{{\rm Q}}}$ for low and high environments are consistent with other SDSS ${{f}_{{\rm Q}}}$ (or ${{f}_{{\rm red}}}$) measurements as a function of environment. For example, Baldry et al. (2006) uses projected neighbor density environment measures (${\rm log} \;{\Sigma }$) to obtain ${{f}_{{\rm Q}}}(\mathcal{M})$ for a range of environmental densities. Although the different environment measurements make direct comparisons difficult, in their corresponding higher environments (${\rm log} \;{\Sigma }\gt 0.2$ in Baldry et al. 2006) ${{f}_{{\rm Q}}}(\mathcal{M}\sim {{10}^{10.2}}\;{{\mathcal{M}}_{\odot }})\sim 0.6$ and ${{f}_{{\rm Q}}}(\mathcal{M}\sim {{10}^{11.5}}\;{{\mathcal{M}}_{\odot }})\sim 0.9$, which is in agreement with our high density environment. Likewise, for lower environments (${\rm log} \;{\Sigma }\lt -0.4$ in Baldry et al. 2006) ${{f}_{{\rm Q}}}(\mathcal{M}\sim {{10}^{10.2}}\;{{\mathcal{M}}_{\odot }})\sim 0.4$ and ${{f}_{{\rm Q}}}(\mathcal{M}\sim {{10}^{11.5}}\;{{\mathcal{M}}_{\odot }})\sim 0.8$, which also agree with our low density environment ${{f}_{{\rm Q}}}$. The Baldry et al. (2006) points (diamond) in Figure 6 reflect this agreement.

More recently, Tinker et al. (2011), using a group-finding algorithm on the SDSS DR7, presents the relationship between ${{f}_{{\rm Q}}}$ and overdensity for galaxies within the mass range ${\rm log} \;\mathcal{M}=[9.8,10.1]$. The Tinker et al. (2011) ${{f}_{{\rm Q}}}$ at the lowest and highest overdensities, ${{f}_{{\rm Q}}}\sim 0.4$ and ${{f}_{{\rm Q}}}\sim 0.6$ respectively, are consistent with our ${{f}_{{\rm Q}}}$ for low and high density environment at the lower mass limit (${\rm log} \;\mathcal{M}\sim 10.2$).

A modified Tinker et al. (2011) sample is used in Geha et al. (2012) to obtain ${{f}_{{\rm Q}}}$ for isolated galaxies over a wider mass range (${{10}^{7.4}}\;{{\mathcal{M}}_{\odot }}$ to ${{10}^{11.2\,}}{{\mathcal{M}}_{\odot }}$). Although Geha et al. (2012) probe a slightly lower redshift range ($z\leqslant 0.06$), their ${{f}_{{\rm Q}}}$ is consistent with our low density sample. Within the overlapping mass range, at the low mass end Geha et al. (2012) find ${{f}_{{\rm Q}}}({{\mathcal{M}}_{*}}\sim {{10}^{10.2}}\;{{\mathcal{M}}_{\odot }})\sim 0.3$ and at the high mass end they find ${{f}_{{\rm Q}}}({{\mathcal{M}}_{*}}\sim {{10}^{11.2}}\;{{\mathcal{M}}_{\odot }})\sim 0.8$. Both of these values agree with our lowest redshift ${{f}_{{\rm Q}}}$ results in low density environment. Figure 6 illustrates the ${{f}_{{\rm Q}}}$ agreement for ${{\mathcal{M}}_{*}}={{10}^{10.5}}\;{{\mathcal{M}}_{\odot }}$.

For $z\gt 0.2$, we compare our PRIMUS ${{f}_{{\rm Q}}}$ results to the ${{f}_{{\rm red}}}$ (or $1-{{f}_{{\rm blue}}}$) results from the zCOSMOS Redshift Survey (Iovino et al. 2010; Kovač et al. 2014), which covers a similar redshift range as PRIMUS. Iovino et al. (2010), and Kovač et al. (2014) using a mass-complete galaxy sample derived from zCOSMOS and a group catalog, 3D local density contrast, and overdensity environment measurements, respectively, compare ${{f}_{{\rm red}}}$ with respect to environment. The ${{f}_{{\rm blue}}}$ for group and isolated galaxies from Iovino et al. (2010) are generally inconsistent with our $1-{{f}_{{\rm Q}}}$ for high and low density environments.

Similarly, ${{f}_{{\rm red}}}$ for high and low overdensities in Kovač et al. (2014) are greater overall than the PRIMUS ${{f}_{{\rm Q}}}$ values in high and low density environments. However, Kovač et al. (2014) points out that there is a significant difference between classifying the quiescent population using color and SFR due to dust-reddening in SF galaxies. For their lower redshift bin ($0.1\lt z\lt 0.4$) Kovač et al. (2014) find that their ${{f}_{{\rm Q}}}$ defined by color is greater than ${{f}_{{\rm Q}}}$ defined by SFR by roughly 0.2. While for their higher redshift bin ($0.4\lt z\lt 0.7$) the difference is 0.15–0.19. Although Kovač et al. (2014) does not elaborate on how the galaxy classification discrepancy applies to the different environments, if we simply account for the difference uniformly for ${{f}_{{\rm red}}}$ at all environments, the Kovač et al. (2014) results in their lower redshift bin are roughly consistent with our ${{f}_{{\rm Q}}}$ at high and low density environments. Even accounting for the dust-reddening of ${{f}_{{\rm red}}}$, Kovač et al. (2014) finds a significantly higher ${{f}_{{\rm Q}}}$ in their higher redshift bin.

In Figure 4, the ${{f}_{{\rm Q}}}$ evolution with respect to mass reveals, qualitatively, little mass dependence in the evolution. Moreover, in Figure 5, we illustrated that adjusting the fiducial mass only shifted the overall ${{f}_{{\rm Q}}}({{\mathcal{M}}_{{\rm fid}}})$, but did not change the ${{f}_{{\rm Q}}}$ evolutionary trend. The consistency in the ${{f}_{{\rm Q}}}$ evolutionary trends over change in fiducial mass suggests that ${{f}_{{\rm Q}}}$ evolution exhibit little mass dependence within the mass range probed in our analysis. In contrast to the weak mass dependence we observe in our results, Iovino et al. (2010) find significantly different ${{f}_{{\rm Q}}}$ evolution at $\mathcal{M}\sim {{10}^{11}}\;{{\mathcal{M}}_{\odot }}$ and $\mathcal{M}\sim {{10}^{10.5}}\;{{\mathcal{M}}_{\odot }}$, for both group and isolated galaxies. In fact at their highest mass bin (${{10}^{10.9}}-{{10}^{11.4}}\;{{\mathcal{M}}_{\odot }}$), Iovino et al. (2010) find no evolution for both environments: constant ${{f}_{{\rm blue}}}\sim 0.1$ over z = 0.3–0.8 for both group and isolated galaxy populations.

Meanwhile in their mass bin most comparable to ${{\mathcal{M}}_{{\rm fid}}}\sim {{10}^{10.5}}\;{{\mathcal{M}}_{\odot }}$ (${{10}^{10.3}}\;{{\mathcal{M}}_{\odot }}-{{10}^{10.8}}\;{{\mathcal{M}}_{\odot }}$), Iovino et al. (2010) finds that ${{f}_{{\rm blue}}}$ evolves by ∼0.1 from z = 0.5 to 0.25 for group galaxies and by ∼0.3 from z = 0.55 to 0.3 for isolated galaxies as presented in panel (b) of Figure 6. Altogether, with mass bins beyond the fiducial masses we explore, Iovino et al. (2010) find a strong mass dependence with ${{f}_{{\rm Q}}}$ evolving significantly more in lower mass bins. While our sample from PRIMUS provides larger statistics than zCOSMOS, the mass-completeness limits we impose on our sample limits the mass range we probe (e.g., $\mathcal{M}\gt {{10}^{10.5}}{{\mathcal{M}}_{\odot }}$ for our $z\sim 0.7$ bin). Consequently our results cannot rule out mass dependence in the ${{f}_{{\rm Q}}}$ evolution at lower masses.

In Figures 5 and 6 we quantified that throughout our redshift range, high density environments have a significantly greater ${{f}_{{\rm Q}}}({{\mathcal{M}}_{{\rm fid}}})$ than the low density environments. This finding is in agreement with the zCOSMOS results from Cucciati et al. (2010) and Kovač et al. (2014). As illustrated in panel (b) of Figure 6, Kovač et al. (2014) finds ${{f}_{{\rm Q}}}$ in high density environment significantly greater than ${{f}_{{\rm Q}}}$ at low density environment. Moreover, since galaxy color serves as a proxy for SFR, our results support the existence of the color–density relation (Cooper et al. 2010; Cucciati et al. 2010) and is not consistent with the color–density relation being merely a reflection of the mass–density relationship, as Scodeggio et al. (2009) suggest it is based on the Vimos VLT Deep Survey ($0.2\lt z\lt 1.4$).

In Section 4.2, we showed that ${{f}_{{\rm Q}}}$ in low density environments evolves over cosmic time. From this trend we deduce that internal, environment independent, mechanisms contribute to ending star formation in galaxy evolution. Iovino et al. (2010) from zCOSMOS, plotted in Figure 6 panel (b), also find that ${{f}_{{\rm Q}}}$ in low density environment increases with decreasing redshift. On the other hand Kovač et al. (2014), also from zCOSMOS, presents that ${{f}_{{\rm Q}}}$ in low density environment decreases over cosmic time. While the uncertainties for the parameterized ${{f}_{{\rm Q}}}$ are not listed, and thus not shown in Figure 6, once they are accounted for, Kovač et al. (2014) find no significant ${{f}_{{\rm Q}}}$ evolution over cosmic time. However, once we account for the dust-reddening of the ${{f}_{{\rm red}}}$, we find a more significant decrease over cosmic time (Figure 6 panel b).

Furthermore, in Section 4.2, our comparison of the ${{f}_{{\rm Q}}}$ evolution between the lowest density environment and the highest density environment revealed a modicum of evidence for the existence of environment dependent mechanisms. The same comparison with zCOSMOS results (Iovino et al. 2010; Kovač et al. 2014) present trends inconsistent with our findings. First, comparing the high (red) and low (blue) density environments for Iovino et al. (2010) in Figure 6 shows that there are indeed pronounced discrepancies between the ${{f}_{{\rm Q}}}$ evolution in different environments. Group galaxies in Iovino et al. (2010) have higher overall ${{f}_{{\rm Q}}}$ than isolated galaxies. However, unlike our results, which find a greater ${{f}_{{\rm Q}}}$ evolution at higher density environments, f_Q in Iovino et al. (2010) shows the opposite environment dependence that there is a significantly greater ${{f}_{{\rm Q}}}$ evolution for isolated galaxies. Once the large uncertainties in the f_Q fit are taken into account, Iovino et al. (2010) state that the f_Q is difficult to measure from their sample.

Next, Kovač et al. (2014) also find that overall ${{f}_{{\rm Q}}}$ is greater in high density than in low density environments. Like their low density environment ${{f}_{{\rm Q}}}$ evolution, ${{f}_{{\rm Q}}}$ in high density environment decreases over cosmic time between their two redshift bins. Although the decrease in ${{f}_{{\rm Q}}}$ over cosmic time conflicts with our results, Kovač et al. (2014) finds a greater (less negative) ${{f}_{{\rm Q}}}$ evolution in high density environments relative to low density environments, suggesting an environment dependence that is in the same direction as our results. We note that the negative slopes of the ${{f}_{{\rm Q}}}$ evolution in both environments are enhanced in Figure 6 due to the dust-reddening correction we impose to the Kovač et al. (2014) ${{f}_{{\rm red}}}$ results.

Due to the redshift uncertainties in PRIMUS, our galaxy environment measures are more susceptible to contamination. As discussed in Coil et al. (2011) and Cool et al. (2013), PRIMUS has redshift success rate of $\gt 75\%$; in comparison, zCOSMOS has 88% redshift completeness for the entire sample and 95% complete within the redshift range $0.5\lt z\lt 0.8$ (Lilly et al. 2009). Although the zCOSMOS survey provides more precise spectroscopic redshifts, PRIMUS has higher overall completeness due to its high targeting fraction of ∼80%. zCOSMOS has a spatial sampling rate of ∼30%–50% and a overall completeness rate of 48%–52% (Knobel et al. 2012). Our sample also provides larger statistics and covers a larger portion of the sky. Our SDSS-GALEX sample covers 2505 ${{{\rm deg} }^{2}}$. More comparably, our PRIMUS sample covers $5.5\;{{{\rm deg} }^{2}}$, over three times the sky coverage of zCOSMOS ($1.7\;{{{\rm deg} }^{2}}$). Furthermore, our PRIMUS sample is constructed from five independent fields which allows us to significantly reduce the effects of cosmic variance.

As listed in Table 1, after our edge effect cuts and stellar mass completeness limits, our sample consists of $13,734$ galaxies from PRIMUS over $0.2\lt z\lt 0.8$ and $63,417$ galaxies from SDSS over $0.05\lt z\lt 0.12$. Meanwhile, Iovino et al. (2010) has 914 galaxies with $\mathcal{M}\gt {{10}^{10.3}}\;{{\mathcal{M}}_{\odot }}$ over $0.1\lt z\lt 0.6$ and 1033 galaxies with $\mathcal{M}\gt {{10}^{10.6}}{{\mathcal{M}}_{\odot }}$ over $0.1\lt z\lt 0.8$. For the actual sample used to obtain the best-fit ${{f}_{{\rm Q}}}$ values in Figure 6, Iovino et al. (2010) has 617 galaxies. In comparison, our PRIMUS sample alone contains $\gt 20$ times the number of galaxies. While there is a considerable difference in the overall ${{f}_{{\rm Q}}}$ between our results and those of Iovino et al. (2010), the use of different methodologies, particularly for galaxy classification and environment measurements, make such comparisons ambiguous. On the other hand, the discrepancies in the ${{f}_{{\rm Q}}}$ evolutionary trends with our results may be explained by the limited statistics in the Iovino et al. (2010) sample.

Table 1.  Galaxy Subsamples

	${{n}_{{\rm env}}}$	${{N}_{{\rm gal}}}$		${{\mathcal{M}}_{{\rm lim} }}$		${{M}_{r,{\rm lim} }}$
		Quiescent	Star-forming	Quiescent	Star-forming
$0.05\lt z\lt 0.12$	${{n}_{{\rm env}}}=0.0$	6533	7508	${{10}^{10.2}}\;{{\mathcal{M}}_{\odot }}$	${{10}^{10.2}}\;{{\mathcal{M}}_{\odot }}$	−20.95
	${{n}_{{\rm env}}}\gt 3.0$	14673	9717	⋯	⋯	⋯
	all	33553	29864	⋯	⋯	⋯
$0.2\lt z\lt 0.4$	${{n}_{{\rm env}}}=0.0$	363	1231	${{10}^{9.8}}\;{{\mathcal{M}}_{\odot }}$	${{10}^{9.8}}\;{{\mathcal{M}}_{\odot }}$	−21.03
	${{n}_{{\rm env}}}\gt 3.0$	379	756	⋯	⋯	⋯
	all	1086	2879	⋯	⋯	⋯
$0.4\lt z\lt 0.6$	${{n}_{{\rm env}}}=0.0$	536	1498	${{10}^{10.3}}\;{{\mathcal{M}}_{\odot }}$	${{10}^{10.3}}\;{{\mathcal{M}}_{\odot }}$	−20.98
	${{n}_{{\rm env}}}\gt 3.0$	490	854	⋯	⋯	⋯
	all	1560	3577	⋯	⋯	⋯
$0.6\lt z\lt 0.8$	${{n}_{{\rm env}}}=0.0$	567	1254	${{10}^{10.7}}\;{{\mathcal{M}}_{\odot }}$	${{10}^{10.6}}\;{{\mathcal{M}}_{\odot }}$	−20.97
	${{n}_{{\rm env}}}\gt 3.0$	498	671	⋯	⋯	⋯
	all	1668	2964	⋯	⋯	⋯
Total		77151

Notes. Number of galaxies (${{N}_{{\rm gal}}}$) in the mass complete subsamples within the edges of the survey (Section 2). The subsamples are classified based on environment (${{n}_{{\rm env}}}$) and star formation rate (star-forming or quiescent). The lowest redshift bin is derived from SDSS; the rest are from PRIMUS. We also list the stellar mass completeness limit, ${{\mathcal{M}}_{{\rm lim} }}$, for our sample along with the r-band absolute magnitude limits, ${{M}_{r,{\rm lim} }}$, for the Environment Defining Population.

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The more recent Kovač et al. (2014) provides larger statistics with 2340 galaxies in their lower redshift bin ($0.1\lt z\lt 0.4$) and 2448 galaxies in their higher redshift bin ($0.4\lt z\lt 0.7$). Although their sample is smaller than the PRIMUS sample, which contains over twice times the number of galaxies, the Kovač et al. (2014) sample provides a more stable comparison. Once their results are adjusted for the dust-reddening, we find that their overall ${{f}_{{\rm Q}}}$ is more or less consistent with our overall ${{f}_{{\rm Q}}}$. However, it is difficult to explain the significant discrepancies in the ${{f}_{{\rm Q}}}$ evolutionary trends. The significant overdenities observed in the COSMOS field at $z\sim 0.35$ and $z\sim 0.7$ (Lilly et al. 2009; Kovač et al. 2010) may have a significant effect on the zCOSMOS results and offer a possible explanation for the discrepancies.