THE PAN-STARRS1 MEDIUM-DEEP SURVEY: THE ROLE OF GALAXY GROUP ENVIRONMENT IN THE STAR FORMATION RATE VERSUS STELLAR MASS RELATION AND QUIESCENT FRACTION OUT TO z ∼ 0.8

Pan-STARRS 1 (hereafter PS1) is a 1.8 m telescopes equipped with a CCD digital camera with 1.4 billion pixels and 3° field of view, located on the summit of Haleakala on Maui in the Hawaii Islands (Onaka et al. 2008; Kaiser et al. 2010). The Pan-STARRS1 observations are obtained through a set of five broadband filters, which we have designated as g_P1, r_P1, i_P1, z_P1, and y_P1. Under certain circumstances Pan-STARRS1 observations are obtained with a sixth, "wide" filter designated as w_P1 that essentially spans g_P1, r_P1, and i_P1. Although the filter system for Pan-STARRS1 has much in common with that used in previous surveys, such as Sloan Digital Sky Survey (SDSS; Abazajian et al. 2009), there are important differences. The g_P1 filter extends 20 nm redward of g_SDSS, paying the price of 5577 Å sky emission for greater sensitivity and lower systematics for photometric redshifts, and the z_P1 filter is cut off at 930 nm, giving it a different response than the detector response defined z_SDSS. SDSS has no corresponding y_P1 filter. Further information on the passband shapes is described in Stubbs et al. (2010).

There are two major components of the PS1 survey which started observations in 2010: the 3π survey and the MDS. The largest portion of time is devoted to the 3π survey (K. Chambers et al., in preparation), which is scanning the entire sky north of declination −30° in five filters, g_P1r_P1i_P1z_P1y_P1 (Tonry et al. 2012), in six separate epochs spanning ∼3.5 yr, each epoch consisting of a pair of exposures taken ∼25 min apart. Each field center is visited by a total of 20 exposures per year in all filters. By stacking all these exposures, PS1 will provide a 30,000 deg² survey of the sky to a depth expected to be somewhat greater than that of the SDSS (York et al. 2000), especially at redder wavelengths. The survey is expected to be completed early in 2014 and publicly released to the world in 2015. More details on the characteristics of the 3π are described in Magnier et al. (2013) and Metcalfe et al. (2013).

This paper uses images and photometry from the Pan-STARRS1 Medium-Deep Field survey. The PS1 Medium Deep Fields (MD fields) consist of 10 spatially well-separated fields, each with 7 deg². MD fields are observed repeatedly with g_P1r_P1i_P1z_P1y_P1 filters (Stubbs et al. 2010; Tonry et al. 2012), with the goal to reach {26.0, 26.0, 26.3, 25.6, 24.3} in AB magnitude respectively for point sources after the 3.5 yr period of the PS1 mission finishes. Observations of the MD fields are taken each night, cycling through the various Pan-STARRS1 filters, during that portion of the year that the fields are accessible at less than 1.3 airmasses. A nightly observation in a given filter consists of eight dithered exposures, with a typical cadence as shown in Table 3 of Tonry et al. (2012).

Nightly stacks of PS1 data are produced by Image Processing Pipeline (IPP; Magnier 2006). The Pan-STARRS1 IPP system performed flatfielding on each of the individual images, using white light flatfield images from a dome screen, in combination with an illumination correction obtained by rastering sources across the field of view. Bad pixel masks were applied, and carried forward for use in the stacking stage. After determining an initial astrometric solution, the flat-fielded images were then warped onto the tangent plane of the sky, using a flux conserving algorithm. The plate scale for the warped images is 0.200 arcsec pixel⁻¹.

Using the "Astromatic" software,¹² SCAMP (Bertin 2006), SWarp (Bertin et al. 2002), and SExtractor (Bertin & Arnouts 1996), we produced our own version of deep stacks and associated catalogs based on all the nightly stacks generated by IPP between 2010 May and 2011 December. The zeropoint of the photometry is calibrated against the SDSS-DR7 catalog. In addition, all PS1 MD fields are covered in Canada–France–Hawaii Telescope (CFHT) MEGACAM u*-band taken by Eugene Magnier et al. as part of the PS1 efforts. We have also downloaded the calibrated u*-band images from the CADC Archive system and produced deep stacks and catalogs following a similar process as for the PS1 images. The final six-band master catalogs based on the i_P1-band detected objects are generated by running SExtractor in dual mode. Because the median seeing varies from 08 to 11 across different bands, the fluxes measured using a fixed size of aperture sample different fractions of lights of galaxies. Therefore we have chosen to use the AUTO magnitude of the i_P1 band to be the total i_P1-band magnitude. The colors are defined as the difference in the ISO magnitude that are output from SExtractor using the isoarea defined by the i_P1 band. Empirically we find that this approach yields the best performance of photometric redshift. This work makes use of data taken in two of the PS1 MD fields, namely MD04 and MD07, which cover well-known multi-wavelength extra-galactic fields, COSMOS and Extended Groth Strip respectively. The choice of these two fields is primarily driven by the availability of large number of redshifts, robust redshift identification, and high sampling rate of the zCOSMOS (Lilly et al. 2007) and DEEP2 (Newman et al. 2013) spectroscopic redshift samples which are crucial for the purpose of calibrating our photometric redshifts (see Section 2.2) and our group-finder algorithm (see Section 2.4). In the current version of the MD07 catalog used in this work, we reach the depth of {25.63, 25.05, 24.95, 25.03, 24.46, 23.18} for {u*g_P1r_P1i_P1z_P1y_P1} at 5σ using the 1'' aperture in radius. The depth of MD04 is comparable to MD07, except for y_P1 which is ∼1 mag shallower. Details are given in a companion paper by S. Foucaud et al. (in preparation).

Photometric redshifts (hereafter photo-z, or sometimes z_ph) are computed by fitting the six optical bands including PS1 grizy-band and CFHT u* photometry with the publicly available EAZY code¹³ (Brammer et al. 2008). The templates adopted in this work are taken from one of the template sets provided by another public photo-z software "LePhare" (Arnouts et al. 1999; Ilbert et al. 2006),¹⁴ called "CFHTLS-SED," which includes 66 templates originally constructed by Ilbert et al. (2006) based on four observed galaxy spectra from Coleman et al. (1980) and two starburst galaxy spectra from Kinney et al. (1996) to optimize the photometric redshift results for the CFHTLS dataset. The details are described in Ilbert et al. (2006) and Coupon et al. (2009).

The computation of photo-z involves several steps. First we ran EAZY only for galaxies with secured spectroscopic redshifts to determine the systematic zeropoint offsets in each band by measuring the medians of the differences in the photometry between the data and the best-fit templates. Then we applied the derived zeropoint offsets back to the data and measured the photo-z for all galaxies. The derived systematic zerpoint offsets are often negligible in u* (−0.01 mag), g_P1 (0.00 mag), r_P1 (−0.01 mag), and z_P1 bands (0.00 mag), and are slightly larger in i_P1 (−0.05 mag) and y_P1 (−0.059 mag) bands. In order to reduce the catastrophic outliers due to the confusion between the Lyman and Balmer breaks in the absence of near-infrared data, we have adopted a prior on the redshift distribution for any given range of i-band magnitude using a mock galaxy catalog constructed based on a semi-analytical model described in Guo et al. (2010).

Two large spectroscopic redshift surveys, the DEEP2 (Newman et al. 2013) and zCOSMOS (Lilly et al. 2007) samples, are used to calibrate the zeropoints and to characterize our photo-z performances in MD07 and MD04 respectively. Figure 1 compares our photo-z results against the spectroscopic redshifts in these two MD fields. Following the definition adopted by Ilbert et al. (2006), we quantify the photo-z accuracy (hereafter $\sigma _{\Delta z/(1+z_{s})}$) using the normalized median absolute deviation (NMAD Hoaglin et al. 1983), defined as 1.48×median (Δz/(1 + z_s)), where z_ph is the photo-z, z_s is the spectroscopic redshifts, and Δz = z_ph − z_s. The outlier rate (hereafter η) is defined as the fraction of galaxies with Δz > 0.15 × (1 + z_s). σ and η are found to be 0.047 and 4% at i < 22.5 in MD04, and 0.051 and 7% at r < 24.1 in MD07.

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A complementary way of assessing the performance of the PS1 z_ph is to use overlapping photometric catalogues using a larger number of filters, thus providing more accurate values of z_ph. In this way, we can reproduce the same selection as in the PS1 catalogues, avoiding the possible biases introduced by the use of spectroscopic redshifts. We used the COSMOS v1.7 catalogue of Ilbert et al. (2009, 2010), which covers 2 deg² in field MD04, and contains photometric redshifts ($z_{{\rm ph}}^{{\rm cosmos}}$) computed with LePhare using 31 broad- and narrow-band filters. The error in the $z_{{\rm ph}}^{{\rm cosmos}}$ (σ ⩽ 0.011 for i⁺ < 24 and z < 1.5) is much smaller than that expected in PS1, so it is a good reference point for our comparison. For the limit used in this work, i_P1 < 24, we found 93, 733 objects which were present in the COSMOS catalogue. We define the dispersion (σ^p) and outlier rate (η^p) of the z_phot in this case in the same way as above, now taking $\Delta z = z_{{\rm ph}} - z_{{\rm ph}}^{{\rm cosmos}}$, and obtain σ^p = 0.083 and η^p = 20.8% for the full catalogue. We also define the bias in the estimation of z_ph as the median of $\Delta z /(1 + z_{{\rm ph}}^{{\rm cosmos}})$, obtaining a value of bias = 0.014. We show the comparison between the PS1 and COSMOS redshifts in Figure 2. When restricting the comparison to objects with i_P1 < 22.5 we found σ^p = 0.050, η^p = 4.5%, bias = 0.012. We can use this comparison to characterize the redshift bins used in this work for galaxies with i_P1 < 24. To this end, we introduce the bin outlier rate η_bin, defined as the fraction of objects selected in a given bin with a value of $z_{{\rm ph}}^{{\rm cosmos}}$ farther than 1σ^p from the bin limits. For the first bin, 0.2 < z_ph < 0.5, we found σ^p = 0.065, bias = 0.027 and η_bin = 9.0%. For the bin in 0.5 < z_ph < 0.8 we obtain σ^p = 0.079, bias = 0.022 and η_bin = 23.5%.

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As a further test, we made a comparison with the "Gold" catalogue of the ALHAMBRA survey (Molino et al. 2013), which provides z_phot down to I < 23 obtained using 23 bands (with an error σ = 0.010), and overlaps an area of ∼0.25 deg² in MD04 and ∼0.5 deg² in MD07. We found, for i_P1 < 22.5, the values σ^p = 0.048, η^p = 5.3% and σ^p = 0.047, η^p = 5.1% for MD04 and MD07, respectively. We therefore conclude that the quality of our z_phot is consistent in the two fields considered. We restrict this study to the two MD catalogs (MD04 and MD07) which consist of 313,997 galaxy-like objects brighter than i_P1 = 24 mag over 14 deg² in the redshift between 0.2 and 0.8.

The K-correction which converts the observed magnitudes to the rest-frame magnitudes is computed following a similar approach as described in Willmer et al. (2006). At a given redshift, we fit a polynomial to the relationship between the K-correction term (using the observed bandpass closest to the desired rest-frame quantity) and a pair of adjacent observed color based on empirical templates taken from Kinney et al. (1996). Depending on the redshift, the corresponding polynomial formula is then applied to each galaxy in the redshift range of 0 < z < 1.45.

We derive stellar masses by fitting the broad-band photometry to the synthesized templates generated with Bruzual & Charlot (2003) models using the spectral energy distribution (SED) fitting code "FAST" (Kriek et al. 2009). During the fitting, we fix the metallicity to be solar value¹⁵ and the redshift to be the photo-z determined from EAZY, while the rest of model properties including the age, star formation time scale τ (assuming an exponentially decaying star formation history), and dust content A_V are treated as free parameters.

For a subset of galaxies overlapped with the COSMOS field, we compared our derived stellar masses based on SED fitting to the six-band PS1 photometry to the ones in the COSMOS v1.7 photometric redshift catalog (Ilbert et al. 2010), computed with LePhare using the 31 broad- plus narrow-band COSMOS photometry data based on the same Bruzual & Charlot (2003) models. The COSMOS stellar masses were previously derived using the Chabier IMF, and hence we have multiplied those by a constant factor of 1.8 to covert them in to Salpeter IMF. In Figure 3 we show the comparison for galaxies (after correcting for the difference in the adopted IMF) whose PS1 z_ph are consistent with COSMOS z_ph within the typical PS1 photo-z uncertainty (i.e., $(z_{{\rm ph}}^{{\rm ps1}} - z_{{\rm ph}}^{{\rm cosmos}})/(1 + z_{{\rm ph}}^{{\rm cosmos}}) < 0.05$). We found that the scatter between the two measurements for "good" photometric redshift sample is ∼0.23 dex.

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To estimate the stellar mass completeness of our sample, we first translate the 5σ limiting magnitudes in the observed PS1 bands into the rest-frame quantities for galaxies at a given redshift, and then estimate the corresponding stellar mass using the empirical formula obtained by Lin et al. (2007) that relates the rest-frame magnitudes and colors to the stellar mass. For a fixed rest-frame magnitudes, the stellar mass is greater for galaxies with redder colors. Therefore we take the reddest colors of star-forming and quiescent populations respectively when computing the mass limit of the above two samples. This yields a mass limit log₁₀(M_*/M_☉) = 9.4 (9.0), 10.1 (9.7), and 10.5 (10.1) for red (blue) galaxies at z ∼ 0.2, z ∼ 0.5, and z ∼ 0.8, respectively. The main sample used in this study contains 244,338 galaxies which have their stellar masses greater than 10⁹ M_☉.

Unlike stellar masses, SFRs are rather sensitive to the degeneracies of the parameters in the SED fitting procedure in the case when there is not enough longer wavelength data. Instead of using the SFR output from FAST, we derived the SFR by adopting the approach described in Mostek et al. (2012) which parameterizes the SFR as a function of rest-frame optical U and B magnitudes (see Equation (1) and Table 3 in their paper) by calibrating against the [O ii] emission line luminosities in the DEEP2 redshift sample (Newman et al. 2013). One caveat of this method is that it may be biased against highly dust-obscured populations (Mostek et al. 2012). However, as illustrated in Mostek et al. (2012), it uncovers the SFR of galaxies with a wide range of star formation activities, including both blue and red galaxies and therefore is suitable for our purposes in a statistically representative way.

Proper identification of galaxy groups is essential to achieve our goals of studying galaxy properties in different environments. While spectroscopic redshift surveys have adequate redshift resolution to secure the group members, in practice it is observationally expensive to conduct a large-volume spectroscopic redshift survey with high sampling rate to yield statistically meaningful large numbers of groups of galaxies. Moreover, the spectroscopic sample has the tendency to be biased toward emission-line galaxies due to the greater signal-to-noise ratio in the line measurement for the redshift identification, which may possibly bias the results in particular for faint galaxies. In contrast, multi-band imaging surveys are relatively efficient at obtaining a large size of galaxy sample. However, group/cluster identification is challenging due to the lack of the redshift precision. One commonly adopted cluster identification method is the so-called red-sequence method which has proven to be successful in finding galaxy clusters by pinpointing the cluster redshifts (Gladders & Yee 2005). Nevertheless, this method relies on identifying the tight sequence in the red population and hence breaks down for group scales and suffers difficulty in recovering blue group members.

An alternative method, the Probability Friend-of-Friend group finder (hereafter PFOF; Liu et al. 2008), attempts to recover both the blue and red populations in groups. PFOF considers the probability distribution function of photometric redshifts of each galaxy and computes the likelihood of a given pair of galaxies being spatially associated. The group sample is then constructed by linking galaxy pairs that have the likelihood exceeding a certain threshold, which is a free parameter determined in the process of optimizing the group memberships to the known spectroscopically identified groups and clusters in the same field.

The PFOF group finder has been tested intensively using galaxy mock catalogs as well as observational datasets (Liu et al. 2008; Jian et al. 2013). In Jian et al. (2013), we applied PFOF to the MD04 and MD07 photometric redshift catalogs, calibrated using the zCOSMOS and DEEP2 spectroscopically identified galaxy groups (Knobel et al. 2009; Gerke et al. 2012) respectively. The details are described in Jian et al. (2013). In this work, we make use of an updated version of the PFOF-generated group samples in MD04 and MD07 with the difference that instead of using different subset training samples in different fields, the two PFOF parameters, linking lengths in both the projected sky plane and the line-of-sight direction, and the probability threshold are trained by optimizing the purity and completeness against the DEEP2 spectroscopic identified group sample in the MD07. The same set of parameters are applied to both MD04 and MD07 as the photometric redshift uncertainty is comparable between the two fields.

Figure 4 shows the histogram of the richness (N_rich) for the 68,180 PFOF groups with N_rich > 2 identified in MD04 and MD07 in the redshift range of 0.2 < z < 0.8, where N_rich is defined as the total number of members brighter than i = 24 in a group. In this work, we divide our PFOF group samples into two subsets, one with 10 < N_rich < 25 (the "group" sample) and the other with N_rich > 25 (the "cluster" sample). For the group sample, the richness cut roughly translates into a group mass of 10^13.2 < M_halo < 10^13.8 M_☉ at z ∼ 0.4 and 10^13.4 < M_halo < 10^14.0 M_☉ at z ∼ 0.8 respectively. We consider field galaxies as those not associated with any groups with N_rich ⩾ 2. For any given group-finding method, it is important to characterize its capability of recovering true group memberships as well as the contamination rate from the field galaxies. Jian et al. (2013) has shown that despite the photo-z uncertainty is in general worse for blue galaxies compared to that for red galaxies, with proper tuning of the linking length and the likelihood threshold, PFOF is able to recover blue members at a similar level as for red members. On the other hand, the contamination from blue galaxies in the field is typically larger than that from red galaxies. The reason for that is because the linking length cannot be too small otherwise we lose many blue members. Therefore the PFOF parameter optimization often leads to a linking length which is large enough to recover both blue and red galaxies at a similar level. The tradeoff is that the contamination rate from blue galaxies would become larger accordingly. This selection effect needs to be corrected when comparing the galaxy properties in different environments.

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Figure 5 shows the SFR–M_* distribution for our sample of galaxies in the PS1 MD04 and MD07 fields, separated into bins of redshift: 0.2 < z < 0.5 (upper panels) and 0.5 < z < 0.8 (lower panels). The colors are scaled according to the numbers of galaxies enclosed in each SFR and M_* grid. The galaxies are further divided into "field" and "group" populations according to the PFOF identification (left-hand and middle panels). The stellar mass limits corresponding to galaxies at the upper- and lower- redshift limits, shown as vertical dashed lines, are computed using the method described in Section 2.3.

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As mentioned in Section 2.4, the PFOF group catalogs are neither complete nor pure in terms of the memberships which may potentially bias our results when comparing the SFR–M_* distribution of galaxies in different environments. To characterize the selection function for star-forming and quiescent group members, we compute the recovery rate R_r and contamination rate R_c for star-forming and quiescent populations separately in bins of redshift and stellar mass, by cross-referencing the MD07 PFOF group catalogs to the spectroscopically identified group catalogs constructed in the EGS field (part of MD07) by Gerke et al. (2012). R_r is calculated as the fraction of spectroscopically identified group members that are also PFOF members, while R_c is computed as the fraction of PFOF group members that are not associated with spectroscopically identified groups. We provide more details in Appendix.

For each of the SFR and M_* grid, we then correct for both the incompleteness and contamination effects by subtracting the field contribution as follows:

$$\begin{equation} n^{g}({\rm SFR},M_{*}) = \frac{1 - R_{c}}{R_{r}}\times n_{{\rm raw}}^{g}({\rm SFR},M_{*}), \end{equation} \tag{ 1 }$$

where n^g(SFR, M_*) denotes the numbers of group galaxies for a given SFR and M_* grid. Ideally R_r and R_c should be computed in a SFR and M_* grid size as small as possible. However, our calibration relies on the limited numbers of spectroscopic group members, so we have chosen to compute R_r and R_c in six regions in the SFR and M_* space, and then for each region we apply the same global value to each SFR and M_* grid. The "corrected" group populations are shown in the right-hand panels of Figure 5.

In Figure 5, it can be seen that the distributions of field and group galaxies in the SFR and M_* plane are distinct. Qualitatively, the stellar masses of group galaxies are systematically shifted toward higher masses for both the star-forming and quiescent populations. In addition, the presence of the quiescent sequence is more prominent in the group environments, especially in the lower-redshift bin. This is in general in good agreement with previous studies concluding that the red fraction of galaxies is greater in the group than in the field (Gerke et al. 2007; Balogh et al. 2009; Giodini et al. 2012). For further analysis used in this work, we define star-forming and quiescent galaxies as those with specific star formation rate (SSFR) greater and lower than 10⁻¹⁰ yr⁻¹, respectively.

It is worth noting that in the high-redshift bin, there exists a class of massive star-forming galaxies with stellar mass >10¹⁰ M_☉ in the group which nevertheless is rare in the field environments in the similar redshift range. The presence of massive blue galaxies (or equivalently massive galaxies with high SFR) in dense environments at z ∼ 1 has also been constantly reported in other studies (Gerke et al. 2007; Cooper et al. 2007; Tran et al. 2010; Koyama et al. 2013), suggesting a more advanced mass assembly stage in high-density regions. Our results suggest that while the fraction of quiescent galaxies in group environments is larger, galaxy groups, on average, are a preferential environment for the formation of massive star-forming galaxies.

To quantitatively describe the SFR–M_* relation of the main-sequence in our sample, we fit the data for the star-forming galaxies with a linear relation between log₁₀ SFR and log₁₀ M_*: log₁₀SFR = α × log₁₀ M_* + log₁₀β, where the slope α and the amplitude β are both fitting parameters. The best-fit results are given in Table 1. The best-fit slopes of the main sequence (star-forming population) in our field sample are between 0.59 and 0.63, in broad agreement with previous results at similar redshifts (Noeske et al. 2007; Whitaker et al. 2012), but slightly shallower compared to those found at z ∼ 2 (Dunne et al. 2009; Pannella et al. 2009; Lin et al. 2012). The amplitude of the SFR–M_* relation in the lower-z bin is also in good agreement with the results from Noeske et al. (2007) who used the AEGIS sample at 0.2 < z < 0.7, after correcting for the difference in the IMF. From Table 1, we also see that both the slope and the amplitude between the field and group "main-sequence" are nearly the same, and the difference is only seen when the quenched population is included. We will discuss this further in the next section.

To have a closer view of the stellar mass dependence of the SFR, we measure the mean of SFR normalized by the stellar mass, namely, SSFR, in each stellar mass bin. These measurements are listed in Table 2. Galaxies are divided into the "star-forming" (SF) and "quiescent" (non-SF) populations by their SSFR with a threshold of 10⁻¹⁰ yr⁻¹. Figure 6 shows the SSFR as a function of M_* for all galaxies (left panels) and for star-forming galaxies (right panels), separated according to their environments (field: purple symbols; groups: orange symbols). The error bars denote the standard errors (standard deviation divided by the square root of sample size in a given stellar mass bin), while the shaded areas show the dispersion of the SSFR at a given stellar mass. The slope of the SSFR–M_* relation becomes steeper when quiescent galaxies are included. While the difference in the median SSFR between field galaxies and group galaxies is apparent for the whole populations (left panels of Figure 6), it becomes more negligible when the quiescent galaxies are excluded (right panels of Figure 6). In other words, the group environment has little effect on the averaged star formation activities for "main-sequence" galaxies, whereas its effect is primarily on moving the galaxies out of the star-forming sequence toward the quiescent populations, leading to a suppressed of the mean SSFR of all (SF plus quiescent) group galaxies.

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The difference in the SSFR–M_* relation for "all" galaxies between field and groups, however, becomes smaller with increasing redshift. This is consistent with the trend found in previous works that suggest a convergence of galaxy properties between field and groups at z ∼ 1 by studying the colors and the red fractions of group galaxies as a function of redshift (Gerke et al. 2007).

In the previous section, we have shown that for a given M_* the mean SSFR of group galaxies is lower compared to field galaxies only if quiescent galaxies are included in the analysis. We next turn to discuss how the fraction of quiescent galaxies depends on the stellar mass and environment (Table 2). Figure 7 displays the quiescent fraction f_q as a function of stellar mass in the field (purple symbols) versus groups (orange symbols). In both the redshift bins (0.2 < z < 0.5 and 0.5 < z < 0.8), it can be seen that f_q increases rapidly with the stellar mass and this trend is independent of environment, consistent with previous works (Quadri et al. 2012; Muzzin et al. 2012; Cheung et al. 2012; Kovac et al. 2013). In addition, f_q is in general higher in groups than in the field at fixed stellar mass.

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To quantify the excess of quenching due to pure environment effects, it is useful to compute the so-called environment quenching efficiency by removing the stellar mass dependence. Assuming that the "mass quenching" and "environment quenching" are independent, the fraction of quenched galaxies in the group environments can be expresses as follows:

$$\begin{equation} f_{q}^{{\rm group}} = 1 - (1 - \epsilon ^{{\rm envi}})*(1 - \epsilon ^{{\rm mass}}), \end{equation} \tag{ 2 }$$

where ^envi is the environment quenching efficiency, and ^mass is the mass quenching efficiency. Assuming that only the mass quenching is in effect in the field environment, ^mass is equivalent to $f_{q}^{{\rm field}}$. Therefore, one can rewrite the environment quenching efficiency ^envi as

$$\begin{equation} \epsilon ^{{\rm envi}} = \left(f_{q}^{{\rm group}} - f_{q}^{{\rm field}} \right) \left/\left(1 - f_{q}^{{\rm field}} \right)\right.. \end{equation} \tag{ 3 }$$

As a result, ^envi is identical to the fraction of galaxies that would be star-forming but which are however quenched in high-density regions as defined in Peng et al. (2010); Quadri et al. (2012).

Previous works have suggested that ^envi has little dependence on stellar mass out to z ∼ 2 (Peng et al. 2010; Quadri et al. 2012), meaning that the environment quenching acts at a similar level regardless of the stellar masses of galaxies. Nevertheless we note that the sample sizes used beyond the local universe were still very small. In the bottom panel of Figure 7, we plot ^envi (red curves) as a function of stellar mass for the PS1MD sample (also see Table 3). In the redshift range we are probing, we find a trend that ^envi slightly increases with increasing stellar mass, different from the weak (or no) stellar mass dependence found in the zCOSMOS sample (Peng et al. 2010) and in the UKIDSS UDS sample (Quadri et al. 2012). We also find that the level of ^envi becomes weaker in the higher-redshift bin, suggesting that the act of environment quenching operates more strongly in local universe than at higher redshifts at a fixed stellar mass.

Table 3. The Mass Quenching Efficiency (^mass) and Environment Quenching Efficiency (^envi) in Groups and Clusters

Redshift	Stellar Mass	mass	envi (Group)	envi (Cluster)
	(log10 (M☉))
0.2 < z < 0.5	9.25	0.05 ± 0.00	0.03 ± 0.01	0.10 ± 0.03
	9.55	0.10 ± 0.00	0.12 ± 0.02	0.18 ± 0.04
	9.85	0.18 ± 0.01	0.22 ± 0.03	0.39 ± 0.07
	10.15	0.31 ± 0.01	0.30 ± 0.05	0.52 ± 0.10
	10.45	0.53 ± 0.02	0.36 ± 0.09	0.52 ± 0.16
	10.75	0.70 ± 0.02	0.44 ± 0.18	0.35 ± 0.30
	11.05	0.84 ± 0.04	0.18 ± 0.52	0.36 ± 0.87
	11.35	0.70 ± 0.05	0.77 ± 0.43	0.73 ± 0.70
0.5 < z < 0.8	9.25	0.02 ± 0.00	0.01 ± 0.01	0.03 ± 0.02
	9.55	0.03 ± 0.00	0.01 ± 0.01	0.07 ± 0.03
	9.85	0.05 ± 0.00	0.03 ± 0.01	0.09 ± 0.04
	10.15	0.13 ± 0.00	0.08 ± 0.02	0.15 ± 0.06
	10.45	0.33 ± 0.01	0.10 ± 0.05	0.24 ± 0.12
	10.75	0.56 ± 0.01	0.07 ± 0.10	0.18 ± 0.23
	11.05	0.77 ± 0.02	0.25 ± 0.26	0.51 ± 0.56
	11.35	0.89 ± 0.03	0.34 ± 0.83	−0.26 ± −1.49

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While the main focus of this work is to study the impact of the group environment on galaxies, we are also able to conduct a similar analysis for clusters that are found in MD04 and MD07 (see Table 2), thanks to the large cosmic volume probed by this catalog. In Figure 8, we again compare the SSFR–M_* relation against field galaxies but for 137 PFOF clusters selected with richness >25, roughly corresponding to M_halo > 10¹⁴ M_☉. We found that the SSFR for star-forming galaxies with M_* >10⁹ M_☉ in the clusters, in contrast to group galaxies, is lower than field star-forming galaxies by 17% with 4σ confidence. Furthermore, the environment quenching efficiency, is in general higher in the cluster case than in the group, as revealed in Figure 9 (see Figure 7 for the group results).

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The higher quiescent fraction seen in the clusters compared to the field may be a result of the global reduction of the SSFR in the cluster galaxies, and/or proportionally more galaxies are being quenched in the groups. To examine the relative importance between the two effects, we also compute the fraction of galaxies below the SSFR threshold value of 10⁻¹⁰ yr⁻¹ in the case where the SSFR of field galaxies are lower by the amount of SSFR difference seen between the field and clusters. The results are shown in green colors in Figure 9. It reveals that the moderate reduction of the SSFR of the star-forming sequence alone cannot fully account for the excess of quiescent galaxies in the clusters. This implies that the influence of cluster environment may consists of both slow and fast quenching mechanisms: the former is responsible for the gradual suppression of the SFR, while the latter must happen in a timescale short enough to produce a notable difference in the quiescent fraction between the field and clusters. We will discuss this issue more in Section 4.

Now that we have shown that both the mass quenching efficiency ^mass (or expressed as $f_{q}^{{\rm field}}$) and the environment quenching efficiency ^envi increase with the stellar mass, we proceed to compare the relative roles of these two effects as a function of stellar mass. The values of ^mass and ^envi are given in Table 3. In the bottom panel of Figures 7 and 9, we overplot ^mass (same as the quantities $f_{q}^{{\rm field}}$ shown on the top panel). In the lower redshift bin (0.2 < z < 0.5), it is clear that the quenching process is dominated by the mass quenching for more massive galaxies whereas the environment is a secondary effect. However, the environment quenching exceeds the mass quenching for galaxies with stellar mass lower than a 1–2 × 10¹⁰ M_☉. This transition mass increases slightly from the group to the cluster environments. In the higher redshift bin (0.5 < z < 0.8), there is also evidence that the mass quenching plays a more important role for massive galaxies, but we cannot pinpoint the transition mass because the sample becomes incomplete below 3 × 10¹⁰ M_☉.