THE EFFECTS OF THE LOCAL ENVIRONMENT AND STELLAR MASS ON GALAXY QUENCHING TO z ∼ 3

Figure 1 (top left) shows the median SFR of galaxies (star-forming and quiescent) as a function of overdensity for our mass complete samples at different redshifts. Regardless of the environment, we find that at a fixed overdensity, the median SFR is higher for higher-z samples compared to those at lower redshifts. This is consistent with the continuous decline in the global star formation density of the universe since $z\;\;\sim$ 2−3 that has been established by many previous studies (e.g., Sobral et al. 2013; Khostovan et al. 2015; see Madau & Dickinson 2014 for a review).

However, we clearly see that the amount of decline depends on the environment. At $z\;\;\lesssim$ 1, the median SFR of all the galaxies (quiescent and star-forming) strongly depends on the overdensity and decreases with increasing overdensity, particularly for the overdensity values log(1 + δ) ≳ 0.5. For example, for the $0.1\lt z\lt 0.5$ sample, the median SFR decreases by ∼2 orders of magnitude as the overdensity increases by almost the same factor. However, at higher redshifts ($z\;\;\gtrsim$ 1) we do not find a significant relation between the median SFR and overdensity and the median SFR becomes almost independent of the environment. The decline in the median SFR in low-density environments is ∼1.6 dex since $z\;\;\sim$ 3, whereas this decline in dense environments is ∼3.6 dex from $z\;\;\sim$ 3 to the present time.

If the environment was mostly relevant for quenching the less massive galaxies, given the fact that our high-z samples do not contain the less massive systems, the environmental independence of the median SFR at z ≳ 1 might be due to a selection effect. We investigate this by selecting only galaxies that are more massive than the mass completeness limit of our highest-z sample (log($M/{M}_{\odot }$)$\geqslant$ 9.97). We find that our results still hold with the new sample selection. The results are presented in the Appendix.

We find similar results for the relation between sSFR and the environment for all the galaxies (Figure 1 (bottom left panel)). At $z\;\;\lesssim$ 1, there is a tight anti-correlation between the median sSFR and the overdensity for all the galaxies, especially for log(1 + δ) ≳ 0.5. However, for the $z\;\;\gtrsim$ 1 samples, we find that the sSFR becomes independent of the overdensity values.

Using a large sample of galaxies in the COSMOS field at z ≲ 3, Scoville et al. (2013) found a strong anti-correlation between the median SFR and environmental density percentile for their low redshift samples. However, at z ≳ 1.2, Scoville et al. (2013) did not find a strong relation between the environment and the median SFR of the observed galaxies, as shown in their Figures 15 and 16. They found similar trends between the star formation timescale (inverse of the sSFR) and environmental density percentile, in the sense that at z ≲ 1.2, the star formation timescale is larger at higher density percentile levels. These results are fully consistent with what we found in this section and our results confirm the similar previous studies in the COSMOS field.

At low-z (z ≲ 0.2), many studies show a lower SFR or sSFR in denser regions compared to less dense, field-like environments for all galaxies (see e.g., Balogh et al. 2004; Kauffmann et al. 2004; Baldry et al. 2006), which are in agreement with our result in this section for our low-z samples (Figure 1).

However, at intermediate redshifts (z ∼ 1), there is no consistency in the relation between the environment and SFR in galaxies. Some studies retrieve the relations found in the local universe (e.g., Patel et al. 2009; Muzzin et al. 2012), some provide evidence for the flattening of the local relations (e.g., Grützbauch et al. 2011; Scoville et al. 2013), and there are even reports of a reversal of the star formation−density relation (e.g., Elbaz et al. 2007; Cooper et al. 2008; Welikala et al. 2016).

We clearly see no reversal of the star formation−density relation for our z ∼ 1 sample and our results follow the local universe trends, completely consistent with, e.g., Patel et al. (2009) and Muzzin et al. (2012). As already noted by Scoville et al. (2013), the claim of star formation−density reversal by Cooper et al. (2008) is hard to judge according to their Figure 9(b). We argue that the reversal seen in Elbaz et al. (2007) is probably due to the cosmic variance and the small dynamical range of the environments considered in their study, as they only used the GOODS fields. Furthermore, later studies in the GOODS fields by Popesso et al. (2011) attributed this reversal to AGN contamination and Ziparo et al. (2014) found no evidence for the reversal of the star formation activity at z ∼ 1 using a similar data set. At z ∼ 1, Sobral et al. (2011) also found an increase of star formation activity for star-forming galaxies at intermediate densities, likely related to galaxy groups (and/or filaments; Darvish et al. 2014). However, they found that this enhancement is accompanied by a decline of star formation activity in the dense environment and clusters. Sobral et al. (2011) argued that this is likely the reason for inconsistencies at z ∼ 1, as some studies only reach up to intermediate/group environments, while others only focus on rich clusters.

At z ≳ 1, we still see no dependence of the median SFR, sSFR, and the quiescent fraction (see Section 4.2) on the environment. This might be partly due to the larger photo-z uncertainties at higher redshifts and the lack of extremely dense regions in the COSMOS field due to the cosmic variance and how the large-scale structure grows over time, although we can still probe relatively dense environments at z ≳ 1 (log(1 + δ) ∼ 1.4). Moreover, our results represent a median value for SFR, averaged over a variety of environments with similar overdensities but possibly different dynamical states and physics. Nonetheless, the literature results in this redshift range are still controversial as some studies have found a reversal of the star formation−density relation (e.g., Tran et al. 2010; Santos et al. 2015), whereas others have shown that some kind of star formation−density relation still exists well beyond z ∼ 1 (e.g., Quadri et al. 2012; Strazzullo et al. 2013; Kawinwanichakij et al. 2014; Newman et al. 2014; Smail et al. 2014; Hartley et al. 2015; Hung et al. 2016). Part of this controversy might be due to the interpretation of the results and how the environment is selected and its dynamical state. For example, the existence of a large number of star-forming galaxies in clusters does not necessarily mean that the star formation−density relation is reversed. In addition, the selection of relaxed, mature clusters (selected through, e.g., X-ray emission, an overdensity of red galaxies, and the existence of a red sequence) automatically biases the environmental study toward a population of passive, quenched galaxies, whereas the selection of less-mature protoclusters that are still in the formation process (selected through, e.g., Lyα or Hα overdensities; Chiang et al. 2015) leads to a bias in favor of blue star-forming systems.

Therefore, we argue that the cause of the discrepancies might be cosmic variance, the different dynamical range of environments probed, the inclusion of, e.g., AGNs in the study, different SFR measures with different timescales, the interpretation of the results, how the environment is selected, and the dynamical state of the environment. Detection of a large sample of structures with different dynamical states in large-volume surveys such as LSST, Euclid, and WFIRST will shed more light on this topic in the near future.

Although we find a strong SFR−overdensity anti-correlation for the z ≲ 1 samples for all galaxies, this correlation depends on the galaxy type. Figure 1 (top right) shows the median SFR of only the star-forming galaxies as a function of overdensity at different redshifts. When we only consider the star-forming galaxies, the median SFR becomes independent of the environment (overdensity) at all the redshifts considered in this study ($0.1\;\lt z\;\lt \;3.1$). In other words, while a galaxy is star-forming, on average, its star formation activity becomes independent of the environment in which it resides (Figure 1 (top right)). Therefore, the SFR−overdensity trends for the z ≲ 1 samples seen in Figure 1 (top left) are due to the existence of the quiescent galaxies that populate denser environments. Denser environments increase the likelihood of a galaxy becoming quiescent. We also find no relation between the sSFR and the environment (overdensity) for the star-forming galaxies out to z ∼ 3 (Figure 1 (bottom right panel)).

We further divide the star-forming sample into stellar mass bins and investigate the environmental dependence of the median SFR for star-forming systems at fixed stellar mass bins. Figure 2 clearly shows that within the uncertainties, the median SFR of star-forming galaxies is also independent of the overdensity at fixed stellar mass bins. This is unexpected as one might expect an environmental dependence of the SFR for (at least) less massive star-forming galaxies, since several studies at low-z have shown that late-type galaxies in dense environments and clusters are significantly deficient in atomic hydrogen, have lower star formation activity, and have truncated star-forming and atomic hydrogen disks (for a review, see e.g., Boselli & Gavazzi 2006, 2014). We highlight that the environmental dependence of SFR for star-forming galaxies seen in some local universe studies applies mostly to less massive systems ($\mathrm{log}(M/{M}_{\odot }$) ≲ 9)—with a mass range not covered in this study—that are located mostly in dense cluster environments. However, we note that at a given overdensity value, the median SFR for star-forming galaxies is higher for more massive systems out to z ∼ 3, particularly for lower redshift samples.

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The mass dependence of the SFR for star-forming galaxies is not surprising as many studies have established a tight correlation (typical SFR dispersion of ∼0.2–0.3 dex) between SFR and stellar mass of star-forming galaxies, that is, the main-sequence of star-forming galaxies (e.g., Brinchmann et al. 2004; Daddi et al. 2007; Karim et al. 2011; Sobral et al. 2014; Shivaei et al. 2015). We find evidence for the flattening of this relation at higher redshifts (Figure 2). However, the detailed analysis of this is beyond the scope of this work. Moreover, the overdensity independence of the median SFR at fixed stellar mass bins for star-forming galaxies (seen in Figure 2) is another way of presenting the environmental independence of the main-sequence of star-forming galaxies seen in many previous studies (e.g., Peng et al. 2010; Koyama et al. 2013, 2014; Darvish et al. 2014). This indicates that the environment does not significantly affect and regulate the mass build-up of the star-forming galaxies through their star formation activity. However, it decides the probability of a given galaxy becoming quiescent.

The environmental independence of the median SFR for star-forming galaxies (even at fixed stellar mass bins) agrees well with a plethora of observations and simulations at different redshifts, highlighting that, on average, many properties of the star-forming galaxies that are directly or indirectly linked to star formation activity (e.g., SFR, sSFR, EW versus stellar mass, main-sequence of star-forming galaxies) do not depend on their host environment (e.g., Patel et al. 2009; Peng et al. 2010; Muzzin et al. 2012; Wijesinghe et al. 2012; Koyama et al. 2013, 2014; Cen 2014; Darvish et al. 2014, 2015a; Hayashi et al. 2014; Lin et al. 2014; Ricciardelli et al. 2014; Vogelsberger et al. 2014; Sobral et al. 2015; Duivenvoorden et al. 2016; Hung et al. 2016). Indeed, the likelihood of a galaxy becoming quenched increases in denser environments. Therefore, many studies note that the main role of the environment is to set the fraction of quiescent galaxies (e.g., Patel et al. 2009; Peng et al. 2010; Sobral et al. 2011; Muzzin et al. 2012; Darvish et al. 2014; also see Section 4.2), whereas for star-forming systems, on average, their star formation activity is almost independent of the environment. Darvish et al. (2015a) suggested differences in the SFHs as a possible cause of the difference in the fraction of star-forming galaxies in different environments.

However, there is no consensus on this topic, as some studies have found an environmental dependence of SFR, even for star-forming galaxies (e.g., von der Linden et al. 2010; Vulcani et al. 2010; Patel et al. 2011; Haines et al. 2013; Tran et al. 2015; Erfanianfar et al. 2016). We note that the majority of these studies have found a reduction of ∼0.1–0.3 dex in the mean SFR of star-forming galaxies in denser environments. This is well within, or of the order of, the intrinsic SFR dispersion of ∼0.2–0.3 dex around the mean main-sequence of star-forming galaxies. Erfanianfar et al. (2016) attributed this reduction to a large fraction of red, disk-dominated galaxies in denser regions. Tran et al. (2015) found that for a galaxy cluster at z ∼ 1.6, the average SFR for Hα-detected galaxies in the core is half of those in the outer regions. However, their result might have been affected by the incompleteness of their spectroscopic sample in the outer regions. Moreover, the estimated mean sSFR of their sample seems to be independent of the environment. We also note that due to the uncertainties in the SED-based SFRs (∼0.1–0.2 dex; see Section 3.2), in the presence of a weak environmental dependence of the main-sequence we would not be able to see that in our work. Therefore, we conclude that the inconsistencies in the environmental dependence of the SFR for star-forming galaxies could be due to the different selection functions and methods used to define the environment (Muldrew et al. 2012; Darvish et al. 2015b), the inclusion of red galaxies in the sample, sample incompleteness, uncertainties in the SFR indicators, etc.

Nevertheless, recent studies have shown that not all characteristics of the star-forming galaxies are independent of the environment. For example, gas-phase metallicities were found to slightly depend on the environment (e.g., Mouhcine et al. 2007; Shimakawa et al. 2015; also see Genel 2016 for detailed simulations), and electron densities and dust extinction were shown to be a function of the environment (e.g., Koyama et al. 2013; Shimakawa et al. 2015; Sobral et al. 2015; Darvish et al. 2015a; Sobral et al. 2016). In the following section, we focus on the fraction of quiescent/star-forming galaxies as a function of overdensity, stellar mass, and redshift and try to disentangle the partial roles of the environment and stellar mass in star formation quenching in galaxies.

Figure 3 (left panel) shows the fraction of quiescent galaxies (with different stellar masses) as a function of overdensity and for our mass complete samples at different redshifts. The error bars are estimated following Poisson statistics and the uncertainties due to the cosmic variance. At z ≲ 1 we find that the fraction of quiescent galaxies depends on the overdensity. This increases with overdensity from ∼20% at log(1 + δ) ≲ 0.5 to ∼60%–80% at log(1 + δ) ∼ 1.6. The increase is particularly steep at log(1 + δ) ≳ 0.5. However, it does not significantly change with environment (overdensity) at z ≳ 1 (except for the $1.5\lt z\lt 2.0$ sample at the densest regions, although those have large error bars). For example, at $2.0\;\lt z\;\lt \;3.1$, the fraction of quiescent galaxies as a function of overdensity remains at ∼10% at all overdensity levels.

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Additionally, we find that at a fixed overdensity the fraction of quiescent galaxies is higher at lower redshifts. This is a clear manifestation of the Butcher–Oemler effect (Butcher & Oemler 1978), stating that the fraction of blue star-forming galaxies is higher for higher-z galaxy clusters compared to their local counterparts (see e.g., Butcher & Oemler 1978; Couch & Sharples 1987; Aragon-Salamanca et al. 1993; Dressler et al. 1994). Moreover, given the environmental independence of the median SFR for star-forming galaxies (even at fixed stellar mass bins, Section 4.1) and the environmental dependence of their fraction at z ≲ 1, we conclude that quenching of star-forming galaxies (with stellar masses of log($M/{M}_{\odot }$) ≳ 9 covered in this study) due to the environment should happen in a relatively short timescale.

Figure 4 (left panel) shows the quiescent fraction as a function of lookback time for some fixed overdensity values. At lookback times ≳8 Gyr (z ≳ 1), the quiescent fraction increases with cosmic time almost independent of the environment. However, we find that at z ≲ 1 (lookback times ≲8 Gyr) the enhancement in the fraction of quiescent galaxies with cosmic time is larger for galaxies located in denser environments. We quantify the quiescent fraction growth with cosmic time assuming a linear growth in the quiescent fraction at a given overdensity. Figure 4 (right panel) shows the quiescent fraction growth rate as a function of overdensity for galaxies located at lookback times ≲8 and ≳8 Gyr. At look-back times ≳8 Gyr the quiescent fraction growth rate is almost independent of the environment. However, at lookback times ≲8 Gyr and at a given overdensity the quiescent fraction grows monotonically with cosmic time, with the growth rate increasing with density. Galaxies are transferred from the star-forming population to the quiescent system more rapidly in denser environments compared to less dense regions.

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Our result regarding the growth of the quiescent fraction agrees qualitatively with Capak et al. (2007a) and Hahn et al. (2015) who found a faster growth rate of early-type galaxies (and non-star-forming systems) in denser regions at z ≲ 1. Rettura et al. (2010, 2011) also showed that, independent of the environment, stellar mass is the main parameter that regulates the formation epoch of early-type galaxies. However, they found that at a given stellar mass, denser environments can trigger a faster mass assembly event for the early-type systems, fully consistent with our result.

It has been shown that the fraction of quiescent galaxies is also a function of stellar mass (e.g., Baldry et al. 2006; Sobral et al. 2011). We investigate the relation between stellar mass and quiescent fraction, as shown in Figure 3 (right panel).

According to Figure 3 (right panel), the fraction of quiescent galaxies (located at different environments) strongly depends on stellar mass. At all redshifts (for both $z\lt 1$ and $z\gt 1$ samples), the fraction of quiescent galaxies monotonically increases with increasing stellar mass. However, at a fixed stellar mass, this fraction is higher at lower redshifts compared to higher-z samples. For example, at $2.0\lt z\;\lt$ 3.1, the fraction of quiescent galaxies varies from ∼0% for log($M/{M}_{\odot }$) ∼ 10 systems to ∼20% for log($M/{M}_{\odot }$) ∼ 11 galaxies; whereas at $0.1\lt z\;\lt$ 0.5, log($M/{M}_{\odot }$) ∼ 10 galaxies comprise ∼30% of the quiescent population and this fraction increases to ∼80% for log($M/{M}_{\odot }$) ∼ 11 galaxies.

In fact, this is another form of galaxy "mass-downsizing" (e.g., Cowie et al. 1996; Bundy et al. 2006), indicating that higher mass galaxies form and quench their star formation activity earlier than less massive systems. According to Figure 3 (right panel), by $2.0\lt z\;\lt \;3.1$, ∼20% of log($M/{M}_{\odot }$) ∼ 11 have already assembled and quenched their star formation activity, whereas for log($M/{M}_{\odot }$) ∼ 10 this fraction (∼20%) is observed at much later times (at $0.8\lt z\;\lt$ 1.1). Using this, we derive an upper limit for the typical time delay between the quenching of less massive (log($M/{M}_{\odot }$) ∼ 10) and more massive (log($M/{M}_{\odot }$) ∼ 11) galaxies and estimate it to be ${\rm{\Delta }}t\;\sim$ 3.4 ± 0.9 Gyr.

One major difference that is clearly seen in the left and right panels of Figure 3 is that at all redshifts ($0.1\lt z\lt 3.1$), the fraction of quiescent galaxies depends on stellar mass, but this fraction depends on overdensity (environment) only up to z ∼ 1 and not significantly at higher redshifts. This leads us to the conclusion that environmental quenching is only effective at $z\;\lesssim$ 1, whereas mass quenching is the dominant quenching mechanism at $z\;\gtrsim$ 1.

We further investigate this by studying the fraction of quiescent galaxies as a function of overdensity and redshift for fixed stellar mass bins (Figure 5) and the fraction of quiescent galaxies as a function of stellar mass and redshift for fixed overdensity bins (Figure 6). Figure 5 shows the fraction of quiescent galaxies as a function of overdensity for different stellar mass bins and at different redshifts. Different colors correspond to different stellar mass bins. According to Figure 5, at all the redshifts considered (0.1 $\lt z\;\lt$ 3.1) the fraction of quiescent galaxies in a fixed environment strongly depends on stellar mass, i.e., the fraction of quiescent galaxies at all fixed density levels is always higher for more massive galaxies compared to less massive systems out to z ∼ 3. However, as shown in Figure 6, the fraction of quiescent galaxies at a fixed stellar mass depends on overdensity (shown with different colors) only at z ≲ 1 and not significantly at higher redshifts. At a fixed stellar mass and at $z\;\lesssim$ 1 this fraction is higher in denser regions.

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When we combine the results shown in Figures 3, 5, and 6, we conclude that the quenching of galaxies due to environmental effects (external processes) is effective at lower redshifts (z ≲ 1), while the stellar mass of galaxies (internal processes) is the dominant quenching mechanism at higher redshifts (z ≳ 1). We further investigate this in Section 4.3.

Our results in this section are in general agreement with e.g., Peng et al. (2010), Sobral et al. (2011), Muzzin et al. (2012), Iovino et al. (2010), and Lee et al. (2015). Muzzin et al. (2012) showed that at z ∼ 1 the sSFR of star-forming galaxies in a fixed environment depends on stellar mass, but at a fixed stellar mass it is independent of the environment. Peng et al. (2010) studied a sample of galaxies in the SDSS and zCOSMOS (z ∼ 0.7) and showed that for massive galaxies mass quenching is the primary quenching mechanism for all environments and at all redshifts, while environmental quenching becomes predominantly important at lower redshifts, particularly for less massive galaxies. Sobral et al. (2011) showed that stellar mass is the main predictor of star formation activity in galaxies at z ∼ 1, but the environment is responsible for star formation quenching in all galaxies in dense environments. Recently, Lee et al. (2015) found that at $z\;\gt$ 1.4 the quiescent fraction is almost independent of the environment, but it is a strong function of stellar mass. They concluded that the stellar mass is the main parameter controlling galaxy quenching out to z ∼ 2 for log($M/{M}_{\odot }$) > 10 systems, whereas environmental quenching is only relevant at $z\;\lt$ 1. All these results signify the importance of the galaxy environment in suppressing the star formation activity at lower redshifts and stellar mass at higher-z, and they are qualitatively in agreement with the results in this section.

As we already mentioned in Section 3.3, part of the absence of environmental trends at z ∼ 1 might be due to a combination of cosmic variance, how the large-scale structure grows, and the larger photo-z uncertainties at higher redshifts. This sets the need for very large area surveys with large spectroscopic and/or photometric data sets, a possibility that can be achieved in the near future with surveys and facilities such as LSST, Euclid, and WFIRST (see, e.g., Cucciati et al. 2016).

In order to quantify the ability of the environment and stellar mass in quenching the star formation activity in galaxies, we follow the approach proposed by Peng et al. (2010) (also see van den Bosch et al. 2008; Quadri et al. 2012; Lin et al. 2014). At any given redshift, z, we define the environmental quenching efficiency, ${\epsilon }_{\mathrm{env}}(\delta ,{\delta }_{0},m,z)$, as the fraction of galaxies at a given stellar mass, m, which would be star-forming in low-density environments (with overdensity 1 + ${\delta }_{0}$), but have had their star formation quenched in denser environments (with overdensity 1 + δ) due to some physical processes that are related to the environment:

$$\begin{eqnarray}&&{\epsilon }_{\mathrm{env}}(\delta ,{\delta }_{0},m,z)=\displaystyle \frac{{f}_{Q}(\delta ,m,z)-{f}_{Q}({\delta }_{0},m,z)}{1-{f}_{Q}({\delta }_{0},m,z)}\end{eqnarray} \tag{ 1 }$$

where ${f}_{Q}(\delta ,m,z)$ is the fraction of quiescent galaxies with stellar mass m that are located in an environment with overdensity 1 + δ at redshift z and ${f}_{Q}({\delta }_{0},m,z)$ is the fraction of quiescent galaxies with stellar mass m that are located in a low-density environment (field) with overdensity 1 + ${\delta }_{0}$ at redshift z. In this work, we choose the low-density, field-like environment overdensity as log(1 + ${\delta }_{0}$) $\leqslant$ −0.6. However, we note that fine-tuning around this value does not change the results in this section. Similarly, at any given redshift z, we define the mass quenching efficiency, ${\epsilon }_{\mathrm{mass}}(m,{m}_{0},\delta ,z)$, as the fraction of galaxies at a given overdensity value, 1 + δ, which would be star-forming if they were very low-mass systems (with stellar mass m₀), but have had their star formation quenched because of their high stellar mass (with stellar mass m) due to some physical processes that are related to stellar mass:

$$\begin{eqnarray}&&{\epsilon }_{\mathrm{mass}}(m,{m}_{0},\delta ,z)=\displaystyle \frac{{f}_{Q}(m,\delta ,z)-{f}_{Q}({m}_{0},\delta ,z)}{1-{f}_{Q}({m}_{0},\delta ,z)}\end{eqnarray} \tag{ 2 }$$

where ${f}_{Q}(m,\delta ,z)$ is the fraction of quiescent galaxies that is located in the overdensity level 1 + δ and has a stellar mass of m at redshift z, and ${f}_{Q}({m}_{0},\delta ,z)$ is the fraction of quiescent galaxies that is located in the overdensity level 1 + δ and has a stellar mass of m₀ at redshift z. In selecting the low stellar mass level (m₀) we use the stellar mass limit at each redshift.

In general, the environmental and mass quenching efficiencies are functions of both environment and stellar mass. However, we first investigate the environmental quenching efficiency as a function of overdensity only (for all stellar masses) and the mass quenching efficiency as a function of stellar mass only (for all environments). Figure 7 (left) shows the environmental quenching efficiency at redshift z (${\epsilon }_{\mathrm{env}}(z)$) normalized to the same quantity for our z = 0.1–0.5 sample (${\epsilon }_{\mathrm{env}}$ (z = 0.1–0.5)), as a function of overdensity values. For clarity, we only show this for denser regions (log(1 + δ) > 0.8) as for less dense regions the ${\epsilon }_{\mathrm{env}}(z)$ values are around zero and a slight fluctuation around zero results in a large variation in the estimated ratio. We find that at a given overdensity, the ${\epsilon }_{\mathrm{env}}(z)$/${\epsilon }_{\mathrm{env}}$(z = 0.1–0.5) ratio increases with decreasing redshift, showing that the overall efficiency of the environment in quenching galaxies increases with cosmic time, consistent with Lee et al. (2015). We also investigate a similar ratio for mass quenching efficiency (Figure 7 (right)). For massive galaxies (log($M/{M}_{\odot }$) ≳ 10.2), we find that the stellar mass quenching efficiency increases with cosmic time from z ∼ 3 to z ∼ 1 and has flattened out since z ∼ 1. However, for less massive galaxies (log($M/{M}_{\odot }$) ≲ 10.2), the increase in the mass quenching efficiency continues to the present time. Since the overall environmental quenching efficiency is negligible at z ≳ 1, the physical processes related to mass quenching are the main channel for quenching of star formation at z ≳ 1.

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Recently, Hayward & Hopkins (2015) presented an analytical model for how the stellar feedback processes drive outflows and regulate star formation activity in the presence of a turbulent ISM. Their model predicts that in massive galaxies (log($M/{M}_{\odot }$) ≳ 10) at z ≲ 1, stellar feedback-driven outflows are suppressed as the gas fraction of such galaxies decreases to values below which the outflow fraction decreases significantly. They also showed that this is not the case for less massive systems as they still have a large gas fraction even at low redshifts. Since outflows are capable of quenching galaxies and they are linked to the mass quenching process, this model might support our result and explain why the mass quenching efficiency for massive ≳${10}^{10}\;{M}_{\odot }$ galaxies has not changed much since z ∼ 1. Moreover, this also suggests that the physics of the mass quenching process is associated mostly with stellar feedbacks (Hopkins et al. 2014). In addition, cold gas should also be hindered from flowing into the galaxy disk (e.g., through heating). Therefore, the halo quenching process might also play a role.

Furthermore, we study the mass dependence of ${\epsilon }_{\mathrm{env}}$ and the environmental dependence of ${\epsilon }_{\mathrm{mass}}$. Figure 8 shows the environmental quenching efficiency as a function of environment and for several stellar mass bins at different redshifts. We find that within the uncertainties, ${\epsilon }_{\mathrm{env}}$ is almost independent of stellar mass, except for massive galaxies in dense regions and at z ≲ 1. That is, denser environments more efficiently quench galaxies that are more massive, particularly at lower redshifts. Moreover, according to Figure 9, we also see that within the uncertainties, ${\epsilon }_{\mathrm{mass}}$ is almost independent of environment, except for galaxies located in very dense environments at z ≲ 1. This suggests that quenching processes that are associated with higher stellar masses act more efficiently in denser environments.

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Our result regarding the mass dependence of the environmental quenching efficiency is consistent with Lin et al. (2014) who showed that the environmental quenching efficiency depends on stellar mass out to z ∼ 0.8, with ${\epsilon }_{\mathrm{env}}$ greater for more massive galaxies. In agreement with our results, Knobel et al. (2015) showed that "satellite quenching" (the driver of environmental quenching; Peng et al. 2012) is almost independent of stellar mass, except for the most massive satellites (log($M/{M}_{\odot }$) > 11), suggesting some degree of association between mass and environmental quenching. However, several previous studies have suggested that the ability of the environment to quench galaxies does not depend on the mass of galaxies and the ability of stellar mass to quench galaxies is independent of where galaxies are located in different environments, at least out to z ∼ 2 (e.g., Peng et al. 2010 out to z ∼ 1; Quadri et al. 2012 out to z ∼ 2). However, our results show that these fail in very dense environments or for very massive systems. We argue that the disagreement between our results and those of Quadri et al. (2012) in very dense environments and for very massive systems might be due to the smaller dynamical range of environments considered in Quadri et al. (2012) and the association between massive systems and dense environments. Environments in Quadri et al. (2012) only cover up to log(1 + δ) ∼ 0.6 and in this overdensity regime we find a good agreement between our results and those of Quadri et al. (2012). However, the environments probed by Peng et al. (2010) are similar to those investigated in this study and the cause of discrepancy in very dense regions and for massive galaxies is still not clear to us. However, it might be due to their different selection of star-forming and quiescent galaxies, as they only used single color information to separate them.

We note that due to the possible entanglement between very dense environments and very massive galaxies, particularly at z ≲ 1 (see e.g., Bolzonella et al. 2010; Darvish et al. 2015b; Mortlock et al. 2015), the higher environmental quenching efficiency for massive systems and the higher mass quenching efficiency in dense environments might have the same origin which is reflected into two apparently different trends (also see, e.g., Knobel et al. 2015; Carollo et al. 2016).