Radial and Local Density Dependence of Star Formation Properties in Galaxy Clusters from the Hyper Suprime-Cam Survey

This study examines the impact of cluster environments on galaxy properties using data from the Hyper Suprime-Cam Subaru Strategic Program and an optically selected CAMIRA cluster sample. Specifically, the study analyzes the fractions of quiescent and green valley galaxies with stellar masses above 108.6 M ⊙ at z ∼ 0.2 and 109.8 M ⊙ at z ∼ 1.1, investigating their trends in radius and density. The results indicate that a slow quenching mechanism is at work, as evidenced by a radially independent specific star formation rate reduction of 0.1 dex for star-forming galaxies in a cluster environment. The study also finds that slow quenching dominates fast quenching only for low-mass galaxies (<109.2 M ⊙) near the cluster edge, based on their contributions to the quiescent fraction. After controlling for M *, z, and local overdensity, the study still finds a significant radial gradient in the quiescent fraction, indicating active ram pressure stripping in dense environments. That said, analyzing the density trend of the quiescent fraction with other fixed parameters suggests that radial and density-related quenching processes are equally crucial for low-mass cluster galaxies. The study concludes that ram pressure stripping is the primary environmental quenching mechanism for high stellar mass galaxies in clusters. By contrast, ram pressure stripping and density-related quenching processes act comparably for low-mass cluster galaxies around the center. Near the cluster boundary, starvation and harassment become the leading quenching processes for low stellar mass galaxies.


Introduction
Environmental quenching is a crucial process that affects various galaxy properties such as morphology, colors, and stellar age other than the mass quenching effect (e.g., Dressler 1980;Cooper et al. 2007;Gerke et al. 2007;Peng et al. 2010;Cappellari et al. 2011;Muzzin et al. 2012;Wetzel et al. 2012).Typically, more massive galaxies are older, redder, and earlier in type, while galaxies in denser environments also tend to have older ages, inactive star formation, and elliptical structures.
Environmental quenching scenarios exhibit distinct characteristics in halting the star formation rate (SFR).For example, ram pressure stripping and galaxy-galaxy mergers are fast quenching mechanisms that act on a short timescale of less than 1 Gyr (Gunn & Gott 1972;Lotz et al. 2010;Jian et al. 2012).By contrast, merger studies such as Quai et al. (2023) and Ellison et al. (2022) have shown diverse results.Ellison et al. (2022) have found rapid quenching to be at least 30 times more common in post-mergers, while Quai et al. (2023) have discovered that rapid (within 500 Myr of coalescence) quenching of star formation is rare, but the recently quenched fraction of post-mergers is still higher compared to a control sample by a factor of two in TNG and 11 in EAGLE.In addition, slow quenching processes like starvation and galaxy harassment operate over a timescale of more than 1.5 Gyr (Bekki et al. 2002, McCarthy et al. 2008).
Moreover, understanding the dependence of environmental quenching on host-centric radius and local galaxy number density is crucial in deciphering the underlying physical processes.Ram pressure stripping and starvation, for instance, are influenced by the parent cluster halo's gravitational potential and gas content and vary with the host-centric radii (Fujita 2001).By contrast, galaxy-galaxy mergers and harassment are more related to neighboring galaxies and the local galaxy number density.Besides, galaxy-galaxy mergers display a higher merger rate in dense environments (Lin et al. 2010), with the maximum rate occurring in the group environment (Jian et al. 2012).Galaxy harassment often causes morphological transformations (Moore et al. 1996).Therefore, studying the timescale and type of quenching effects in galaxies in dense environments can provide valuable insights into the physical mechanisms responsible for star formation quenching.
In previous studies, we observed that the specific star formation rate (sSFR) of star-forming galaxies is reduced by around 0.2 dex in dense environments such as groups or clusters compared to the field.This suggests that galaxies in overdense regions experience a slow environmental quenching effect (Lin et al. 2014;Jian et al. 2018).Our sSFR suppression result in the cluster environment is consistent with the findings of previous studies by Vulcani et al. (2010), Haines et al. (2013), and Alberts et al. (2014).In a more recent study (Jian et al. 2020), we examined green valley galaxies in different environments and found a higher effective fraction of green valley galaxies in groups or clusters compared to the field, indicating a slow environmental quenching effect at work in dense environments.
However, some studies have reported no reduction in sSFR between star-forming galaxies in groups and the field, which differs from our findings and suggests a fast environmental quenching mechanism at work in group regions (e.g., Balogh et al. 2004;Vulcani et al. 2010;Koyama et al. 2013;Lin et al. 2014).Disagreements could arise from differences in the definition of galaxy groups and clusters or different sample selections that include galaxies from different environments based on different mass thresholds for groups and clusters and/ or redshifts.
Some previous studies have investigated environmental quenching further by examining the effects of the radial and density factors.In this work, we refer to the radial and density effects as the effects associated with the host-centric radius and the local galaxy density, respectively.For example, Li et al. (2012) studied 905 galaxy groups with redshifts between 0.15 and 0.52 from the first Red-Sequence Cluster Survey, exploring the evolution of the quiescent fraction with respect to galaxy stellar mass, total group stellar mass, group-centric radius, and local galaxy density.They found that the dependence of the quiescent fraction on total group stellar mass, group-centric radius, and local galaxy density is more apparent for galaxies with a mass of M * < 10 10.6 M e compared to more massive galaxies.The radial and density effects are comparable, contributing to halt star formation.However, their sample was limited to galaxy groups, and the redshift range was restricted to values lower than 0.52.Investigating the quenching status in the cluster environment and at higher redshifts may supplement the study as a whole.
Moreover, Jian et al. (2017) used data from two mediumdeep fields of the Pan-STARRS1 survey covering an area of around 14 deg 2 to examine the radial and density effects.The results revealed a minor reduction for the star-forming sequence in groups, implying a fast quenching process, and the ∼0.2 dex reduction in clusters, indicating the slow quenching effect.In addition, by comparing the contribution of the radial and density effects to the quiescent fraction, they found that the density effect is more active in dense environments for more massive galaxies, whereas the radial effect becomes more effective in less massive galaxies.
In groups, the combined result of a slight reduction (or a fast mechanism) and the dominance of the density effect for massive galaxies thus indicates that mergers are their primary quenching mechanism, while the more effective radial effect in less massive galaxies indicates starvation likely is their primary quenching mechanism.That said, in clusters, the reduction is 0.2 dex supporting the slow quenching, with harassment associated with the density process and/or starvation related to the radial effect are the dominant processes in clusters.
In this study, we build on our previous work (Jian et al. 2018(Jian et al. , 2020) ) to extend the analysis for the effects associated with the host-centric radius and local galaxy density.We use the third public data release (PDR3) of Hyper Suprime-Cam (HSC: Miyazaki et al. 2012) Subaru Strategic Program (SSP;Aihara et al. 2022) and the internally released S20A cluster catalog of 6500 clusters to explore environmental quenching in a field of approximately 1470 deg 2 .With the deep and expansive data set of the HSC S20A, we are able to probe environmental effects on low-mass galaxies with stellar masses as low as 10 9.8 M e up to a redshift of z ∼ 1.1, enabling us to distinguish between various environmental effects in clusters.
We outline the remaining sections of our paper as follows.Section 2 briefly describes the HSC-SSP data set, our selection and assignment of cluster and field galaxies, and our analysis methods.In Section 3, we present our main results and discuss our findings.Finally, in Section 4, we provide a summary.Throughout the paper, we use a flat Λ cold dark matter cosmology with the following parameters: H 0 = 100 h km s −1 Mpc −1 , Ω m = 0.3, and Ω Λ = 0.7.We adopt the Hubble constant h = 0.7 in calculating rest-frame magnitudes; all magnitudes are in the AB system (Oke & Gunn 1983).

Galaxy Sample
Our galaxy sample is based on PDR3 of HSC-SSP (Aihara et al. 2022).The HSC-SSP is a ∼5 yr program using the HSC camera in five bands (grizy; Kawanomoto et al. 2018) and four narrowband filters to conduct a three-layered imaging survey, namely Wide, Deep, and UltraDeep.The PDR3 contains a data set acquired from 2014 March through 2020 January on 278 nights in total, and all the data are processed with the updated HscPipe (Bosch et al. 2018, version 8.0-8.4).The quality assurance tests of the PDR3 show that the astrometry is as good as 10-20 mas (s.d.) against GAIA, and the photometry is good to ∼0.01-0.02mag (s.d.).The pointspread function characterization can be found in Miyazaki et al. (2018).For PDR3, the seeing, 5σ depth, and saturation magnitudes for the i band in the Wide layer are 0 61 ± 0 05, -+ 26.2 0.3 0.2 , and 18.3 0.3 0.5 .Information for other bands is listed in Aihara et al. (2022).
Our final galaxy sample is selected with full color, i.e., all grizy bands are detected, and with the i band brighter than 26 (i 26) from data in the S20A Wide layer.In addition, we select sources with the extendedness value of the i band equal to 1 for the extended sources, i.e., i_extendedness_value = 1, to exclude point sources, quasars, and stars.In total, our galaxy data set has roughly 0.26 billion galaxies in the field of ∼1100 deg 2 .
The S20A data release also provides the photometric redshift catalogs, supplying physical quantities derived from several codes, such as photometric redshift and stellar mass.The description and comparison of the codes used to compute photometric redshifts for HSC-SSP, the calibration procedure, and the typical accuracy with the HSC five-band photometry (grizy) can be found in Tanaka et al. (2018) and Nishizawa et al. (2020).In this study, we adopt the photometric redshift and stellar mass estimated using the direct empirical photometric method (DEmP; Hsieh & Yee 2014).Based on the S20A photometric redshift (photoz) release notes, DEmP photoz using the cmodel magnitude quotes a bias of -0.002, a median absolute deviation of 0.028, and an outlier rate of 8.5% relative to the reference spectroscopic redshift (spec-z) for all test samples.The detailed performance evaluation is described in Tanaka et al. (2018) and Nishizawa et al. (2020).In addition, the DEmP stellar mass referenced to COSMOS masses shows a mean of -0.02 dex and a scatter of 0.2 dex.
We follow the empirical method from Lin et al. (2017).We first cross-match the HSC galaxy catalog to the COSMOS2020 catalog (Weaver et al. 2022) and then compute the completeness as functions of mass and redshift, where the completeness is defined as the fraction of the cross-matched HSC galaxies to all galaxies detected in the COSMOS2020 catalog.We then set the lowest stellar mass limits corresponding to the completeness of 90% at a given redshift.Following this approach, we find that in our data set, the log-mass completeness limits in log solar mass are 8.3 (9.1), 8.8 (9.6), and 9.0 (9.9) for star-forming (quiescent) galaxies in redshift ranges of 0.2-0.5, 0.5-0.8, and 0.8-1.1,respectively.

SFR Estimation and Galaxy Classification
To assess the galaxy SFR, we adopt the procedure described in our previous works (Jian et al. 2018(Jian et al. , 2020)).In short, based on empirical templates from Kinney et al. (1996), we apply a K-correction to derive the rest-frame B magnitude M B and (U − B) 0 color for each stacked galaxy.We then employ the fit formula from Mostek et al. (2012) to relate M B , (U − B) 0 , and second-order (U − B) 0 to SFR.We note that the intrinsic scatter of the SFR estimation using the Mostek method (Mostek et al. 2012) is 0.19 and 0.47 dex for star-forming and quiescent galaxies, respectively.The SFR estimation for quiescent galaxies is slightly larger.However, the SFR is utilized mainly for the galaxy classification on the stellar mass versus the SFR plane.The rather considerable uncertainty for quiescent galaxies will not affect our results.Besides, its offset between the mean fitted SFR estimation and spectral energy distribution SFR using templates in Salim et al. (2009) is comparatively small, ∼-0.02 dex.
To study galaxy properties in dense environments, we perform the stacking of two different galaxy physical quantities on a plane for clusters, e.g., SFR versus the cluster-centric radius combined with the background/foreground subtraction technique to recover the properties of cluster galaxies statistically.Our background subtraction method is similar to that in Pimbblet et al. (2002) and Valentinuzzi et al. (2012).
The detailed procedure can be found in our previous works (Jian et al. 2017(Jian et al. , 2018(Jian et al. , 2020)).
As shown in Figure 1, galaxies display two distributions on the SFR versus stellar mass plane.We thus classify galaxy populations based on galaxy location on the SFR-M * plane.Following the classification procedure in our previous works (Jian et al. 2020(Jian et al. , 2022)), galaxies are classified into three populations, i.e., star-forming, green valley, and quiescent galaxies.In Jian et al. (2020Jian et al. ( , 2022)), we locate the star-forming and quiescent sequences and then define the green valley region as the zone enclosed by 0.2 dex above and below the middle point of two sequences.However, this work takes a slightly different approach to defining the green valley galaxies from our previous works.
The main reason for the change in the green valley definition is the improperly defined green valley region for low-mass galaxies below 10 8−9 M e , where our mass completeness limit lies in the range.Our criterion in previous works has included some star-forming galaxies in the green valley, while here we devise the current criterion to mitigate impurities in green valley classifications.The old criterion may not be suitable when the mass completeness limit is as low as in the range of 10 8−9 M e .We thus adopt a new criterion to avoid including star-forming galaxies in the green valley galaxies.
In this work, we first compute the SFR standard deviation σ of star-forming galaxies and define the green valley region as the zone starting from 2σ below the median SFR of the starforming main sequence to 2σ + 0.4 dex below the median SFR of the star-forming main sequence.In other words, the width of the green valley region is 0.4 dex.This new criterion is similar to the definition from Pandya et al. (2017), in which their transition region ranges from 1.5σ to 3.5σ below the starforming median line.
In addition, we also carried out a series of tests to see if our results were robust against the choice of the upper boundary for the green valley, i.e., 2σ-3σ away from the star-forming main sequence, and the width of the green valley (0.2-0.4 dex).The fractions of the three populations change slightly, but the overall trend remains.The best-fit results for the star-forming sequence (blue lines), green valley (white lines), and quiescent sequence (red lines) are summarized in Table 1.

CAMIRA Cluster Catalog
Our cluster sample consists of the HSC S20A cluster catalog produced by the cluster finding algorithm based on the multiband identification of red-sequence galaxies (CAMIRA) developed by Oguri (2014).Utilizing the stellar population synthesis model of Bruzual & Charlot (2003), CAMIRA makes the color prediction of red-sequence galaxies at a given redshift for an arbitrary set of bandpass filters with additional calibration against spectroscopic galaxies.CAMIRA then computes the likelihood of being red-sequence galaxies as a function of redshift.The detailed methodology was presented in Oguri (2014), and the updated CAMIRA algorithm can be found in Oguri et al. (2018).
The public HSC S20A cluster catalog with star mask comprises 7319 clusters with the richness N 15 in the redshift range of 0.1 < z < 1.38. 13The redshift constraints are due to the lack of a high redshift training sample for calibration and the limitation of HSC wave band coverage, and the difficulty of the cluster finding for clusters of large angular sizes at low z and bright member galaxies in the HSC images (Oguri et al. 2018).To be conservative, we construct our cluster sample by selecting clusters in the redshift range between 0.2 and 1.1 and obtain 6442 clusters.We then split the sample into three redshift bins (0.2 < z < 0.5, 0.5 < z < 0.8, and 0.8 < z < 1.1).The information about the number of clusters in the three redshift ranges is listed in Table 2 Similar to Figure 1, we show the density plots for cluster (N > 15) galaxies in three redshift ranges in Figure 2. The sample in Figure 1 is based on all galaxies from the HSC catalog, including cluster, group, field, and void galaxies, while the sample in Figure 2 is based only on cluster galaxies.In other words, the sample of cluster galaxies in Figure 2 is a subset of the sample of Figure 1.The dominance of quiescent cluster galaxies compared to star-forming ones can be seen.We also find that there seems to be an SFR depletion of the star-forming cluster galaxies compared to the SFR of star-forming galaxies in Figure 1, implying that a Figure 1.The normalized color-coded density plot for defining green valley galaxies using all galaxies on the SFR-M * plane in three redshift ranges.Each panel's blue and red open circles represent the median SFR of star-forming and quiescent galaxies.In addition, the blue and red solid lines denote the best-fit results of the median SFR of the star-forming and quiescent galaxies, respectively.The region enclosed by two parallel green lines is the transition area occupied by the green valley galaxies.The green valley zone is defined as 2.0σ away from the star-forming main sequence with a width of 0.4 dex, where σ is the standard deviation of the SFR for star-forming galaxies.The mass completeness limits for star-forming and quiescent galaxies in the corresponding redshift range are marked by the vertical light-blue and red dashed lines, respectively.slow quenching effect likely acts on cluster galaxies.We will explore this issue in detail in Section 3.1.1.

Local Galaxy Density Estimation
For the overdensity estimation, we follow the nth-nearestneighbor approach (Cooper et al. 2007).We first compute the projected sixth-nearest-neighbor surface density, Σ 6 , where Σ 6 is defined as 6/(π R 6 2 ) and R 6 is the projected distance to the sixth-nearest neighbor.To compute Σ 6 , we limit our galaxy redshift range within a slice width of photoz uncertainty 0.055.We then normalize the density to the median density at the corresponding redshift to obtain the overdensity, i.e., log 10 (1 + δ 6 ) = log 10 (S S 6 6 median ).Using mock catalogs from simulations, Lai et al. (2016) have illustrated that the projected overdensity estimation based on photometric redshift is promising for detecting the colordensity relation, and a similar conclusion has been made in Lin et al. (2016) for tests out to redshift z ∼ 2.5.The density measure with photometric redshift is thus reliable and allows us to probe the color-density relation and study density-related issues in this work.

Radial Dependence of Galaxy Properties
Studies of simulations have shown that dynamical friction and tidal stripping effects in a parent halo are expected to correlate satellite radial position with infall time (Gao et al. 2004).It is thus anticipated that the star formation evolution of galaxies inside clusters also likely shows radial gradients.Hence probing galaxy properties relative to its position inside the parent halo may indicate the relative importance of different quenching processes that cease star formation in a dense environment and further help our understanding of galaxy formation and evolution.

Specific Star Formation Rate
One method to distinguish between slow and fast environmental quenching effects is to compute the reduction of the median sSFR (SFR/M * ) of star-forming galaxies in dense environments relative to that in the field.The long timescale of the slow quenching process gradually turns star-forming galaxies into quiescent ones, showing a global sSFR reduction in contrast to galaxies in the field.A fast quenching mechanism quickly ceases the SFR of star-forming galaxies such that they become the quiescent population without changing the mean properties of the star-forming main sequence.In other words, no reduction implies fast quenching while a reduction suggests slow quenching (Lin et al. 2014;Jian et al. 2017Jian et al. , 2018Jian et al. , 2020)).
In our previous studies, the reduction of galaxy median sSFR in dense environments was found to be ∼0.1-0.3 dex with respect to that in the field up to z ∼ 1 (Lin et al. 2014;Jian et al. 2018Jian et al. , 2020)).Our results thus support an ongoing slow quenching process in the dense environment since z ∼ 1.
In this work, we investigate the radial dependence of galaxies' median sSFR to understand whether the slow quenching effects have a radial trend.Following the classification method defined in Section 2.2, we separate galaxies into star-forming, green valley, and quiescent populations.In Figure 3, the median sSFRs of star-forming galaxies are plotted as a function of the host-centric radius (r p ) in the redshift ranges 0.2 < z < 0.5, 0.5 < z < 0.8, and 0.8 < z < 1.1 in the cluster environment.Hereafter, the host-centric Figure 2. The color-coded density plot on the SFR vs. M * plane for clusters (N 15) in three redshift ranges.Two parallel green lines denote the green valley region defined in Figure 1.The vertical light-blue and red dashed lines give the mass completeness limits.It is can be seen that the star-forming main sequence of cluster galaxies is closer to the green valley zone than that of all galaxies in Figure 1, implying an SFR depletion of cluster galaxies.radius (r p ) will be normalized by its r 200m , i.e., in the unit of r 200m .In addition, we note that the shaded regions in all figures in this work denote the error bars estimated using bootstrap resampling from 200 runs.We can see that the reduction (Δ) of the median sSFRs depends weakly on the host-centric radius and redshift.
However, there seems to be a mass dependence on the sSFR reduction.This result may be something other than a natural effect.In Jian et al. (2018), we carried out a simulated test to study the influence of the intrinsic scatter in the SFR estimation using the Mostek method on the sSFR reduction of star-forming galaxies.The tests were done by simulating a log sSFR reduction of 0.2 dex plus an intrinsic scatter of log sSFR ∼ 0.19 dex for different galaxy masses.We found that the intrinsic scatter will not affect the final median sSFR reduction for low-mass galaxies but it smears the sSFR reduction for high-mass galaxies to reveal less or no reduction.Based on the simulated test, we expect that the order of the reduction for high-mass galaxies is similar to that for low-mass ones, i.e., 0.1 dex.
In other words, the mass trend for the sSFR reduction in our results is likely weak or not real.The sSFR reduction is independent of mass and is roughly 0.1 dex for galaxies in the overdense environment.The reduction result implies that cluster galaxies suffer a slow quenching effect.The slow quenching effect is likely starvation (Larson et al. 1980) or galaxy harassment (Moore et al. 1996) in the overdense environment.

Quiescent Fraction
With the galaxy classification defined in Section 2.2, we estimate the quiescent fraction ( f q ), i.e., the fraction of quiescent galaxies to entire galaxies, as a function of the host-centric radius controlling for stellar mass and redshift.The results are shown in Figure 4. We also fit the f q with a linear relation f q = α × (r p /r 200m ) + β for r p /r 200m < 1.25, and the best-fit results of αs and βs are plotted in Figure 5.If the fraction decreases with increasing r p , α will be between 0 and -1.0.
In Figure 4, we find that f q is correlated with host-centric radius, i.e., f q decreases with the increasing radius.The decreasing factor from the center to the field is roughly 1 to 2. The radial trend is weaker for more massive galaxies, while it is stronger for less massive galaxies.The radial gradient of f q can be interpreted as the consequence of the radial effect of quenching mechanisms and/or dynamical friction.However, massive galaxies are more affected by dynamical friction than low-mass ones, implying that a stronger radial gradient for Figure 3. Median log sSFR of star-forming galaxies as a function of the normalized host-centric radius r p /r 200m (top), and the sSFR reduction (Δ) of star-forming galaxies compared to galaxies in the mean field (bottom) in three redshift ranges.Four mass ranges are denoted by yellow, green, blue, and purple solid lines.The vertical black dashed lines mark the cluster border.Due to different mass completeness limits at different redshifts, only four, three, and two mass ranges are displayed in low, medium, and high redshifts, respectively.The shaded regions indicate the error bars estimated using bootstrap resampling from 200 runs.It is evident that there is a reduction of ∼0.1 dex inside clusters, and the reduction appears to be weakly dependent on the host-centric radius.The results suggest a slow quenching mechanism operating in the overdense regions.
Figure 4.The quiescent fractions ( f q ) as a function of the normalized cluster-centric radius in three redshift ranges.Five different color lines represent five different mass ranges.The dashed vertical lines denote the cluster boundary.The error bars are estimated using bootstrap resampling.Normalized for mass and redshift, f q still exhibits an apparent correlation with r p /r 200m , i.e., f q decreases with the increasing r p /r 200m , indicating a significant radial effect.
Figure 5. Best-fit results as a function of mass for the parameter α (the slope) and β (the central f q ) using a linear function of f q = α × (r p /r 200m ) + β.Three different redshift ranges are 0.2 < z < 0.5 (red), 0.5 < z < 0.8 (green), and 0.8 < z < 1.1 (blue).The slope α is generally steeper for low-mass galaxies than for high-mass ones, implying a stronger radial effect for low-mass galaxies.The other trend is that the central f q increases moderately with the decreasing redshift and, apparently, with increasing stellar mass.massive galaxies should be observed.It can be seen that lowmass cluster galaxies appear to exhibit a sharper f q gradient than high-mass ones, suggesting that low-mass cluster galaxies suffer a more substantial environmental quenching and that dynamical friction is likely not the dominant source.
From Figure 5, the best-fit slope α appears to depend on the mass, i.e., lower-mass galaxies tend to have a steeper slope.The most significant radial changes imply that cluster galaxies at the low mass ranges, i.e., ∼10 9.1−9.6 , 10 9.6−10.1 , and 10 10.1−10.6 M e from low to high redshift, suffer the most substantial environmental effects, in agreement with the finding from Li et al. (2012) and Jian et al. (2017).In addition, from the best fit of β, i.e., f q at the center, we find that β depends on mass and moderately depends on redshift.

Green Valley Galaxy Fraction
Examining the green valley galaxy fraction ( f g ) between the dense and field environments also hints at the timescale of environmental quenching.For example, a slow quenching process gradually halts the SFR of star-forming galaxies.The star-forming galaxies gradually pass through the green valley zone as transitional galaxies and finally become quiescent, showing a greater f g than that in the field.By contrast, a fast quenching mechanism quickly turns star-forming galaxies into quiescent populations, showing no green valley galaxies and displaying no difference between f g in the dense region and the field.
Similar to Figure 4, the green valley galaxy fraction ( f g ) is plotted as a function of host-centric radius in Figure 6 on the top row.Due to an insufficient supply of high-mass starforming galaxies in clusters, which could be progenitors of green valley galaxies, the effective green valley galaxy fraction ( fg ), defined as the fraction of star-forming to nonquiescent galaxies, gives a more accurate estimation for green valley galaxies than f g (Jian et al. 2020).Thus, we show the effective green valley galaxy fraction on the bottom row in Figure 6.Similar to Figure 5, the best-fit α and β for f g and fg are shown on the top and bottom row in Figure 7, respectively.
We find that, in general, f g increases with r p for galaxies with log mass > 9.8, and the f g inside the cluster region is smaller than that in the field, consistent with the finding in Jian et al. (2020) that there is a deficit of f g for high-mass galaxies in clusters opposed to that for field galaxies.The effective green valley galaxy fraction fg reveals a decreasing radial trend.The fg is higher in clusters than in the field, suggesting slow Figure 6.The green valley fraction ( f g ) on the top panels and effective green valley fraction ( fg ) on the bottom panels as a function of the normalized host-centric radius in three redshift ranges.From high-mass galaxies, we find an f g deficit in clusters relative to the field, indicating an insufficient supply of progenitors of green valley galaxies, i.e., star-forming galaxies.The fg is the fraction of star-forming to nonquiescent galaxies to account for the deficit issue.The fg decreases with increasing r p and is roughly independent of r p , implying a weakly radial-dependent slow quenching effect in the dense environment, consistent with our results in Section 3.1.1.environmental quenching effects act in the dense environment, in good agreement with results of our previous works (Jian et al. 2020).
In addition, from Figure 7, we find that the best-fit αs and βs for f g and fg depend weakly on redshift and more firmly on stellar mass.The best-fit slopes α of the f g are positive for highmass galaxies in clusters, indicating a deficit of green valley galaxies in clusters as opposed to that in the field.However, when we consider the data points r 200m , the fg shows a slight negative radial gradient, close to a flat radial trend, consistent with the results in Section 3.1.1.This consequence thus suggests that the process acting in dense zones is likely a slow environmental quenching and is radially independent.

Density Effect: Color-Density Relation
The local galaxy density reveals a strong correlation with galaxy type, or a color-density relation, i.e., in the high-density region, passive galaxies dominate star-forming galaxies (Dressler 1980;Balogh et al. 1998;Cooper et al. 2007;Gerke et al. 2007).By contrast, in the low-density environment, most galaxies are found to be star-forming ones.Therefore, the local density effect is expected to play a role in transforming starforming galaxies into passive galaxies.
However, the density effect inevitably couples with the radial effect inside clusters since the galaxy density drops with increasing host-centric radius.When probing galaxy properties, two effects must be directly separated to understand their environmental impact clearly.In addition to the effects of mass, redshift, and radius, we consider the density effect in our further analysis.
We start by probing the color-density relation in the HSC data set.The fractions of star-forming, quiescent, and green valley galaxies are plotted as a function of the local overdensity log 10 (1 + δ 6 ) in three redshift bins from 0.2 to 1.1 and log-mass ranges from 8.6 to 11.6 in Figure 8.We find that the fractions of green valley galaxies are independent of the overdensity and roughly have no dependence or else a mild dependence on redshift and mass.By contrast, the fractions of quiescent galaxies increase with increasing density, similar to what we found previously for the radial dependence results, where f q decreases with increasing r p , and the galaxy density drops with increasing radius.
In addition, we also find that the correlation between the quiescent fractions and overdensity is stronger for galaxies with log mass less than 10.7 and is weaker for higher-mass galaxies.It is roughly consistent with the finding that there is a transition mass at ∼10.4-10.6 such that the mass effect controls the quenching effect above the transition mass, and the environmental effect dominates for galaxies below the mass (Lin et al. 2014;Jian et al. 2017Jian et al. , 2018)).We also see a weak redshift evolution effect at fixed overdensity and mass: the quiescent fraction increases slightly with decreasing redshift, consistent with the Butcher-Oemler effect (Butcher & Oemler 1984).5, the best-fit results of the fitting slope α and fraction at center β for f g (top row) and fg (bottom row).For f g , the radial gradient at low mass is negative and becomes positive at high mass, implying an excess at low mass and a shortage at high mass respective to the field.

Radial and Local Overdensity Effect
To understand the sole impact of these two effects, we need to control one of these two parameters when probing the other one.In Figure 9, the fractions of quiescent galaxies are plotted as a function of the host-centric radius normalized for the overdensity, mass, and redshift in clusters.
Generally, f q exhibits an apparent trend with stellar mass and r p and a weak correlation with overdensity and redshift.At fixed mass, redshift, and overdensity, we find that f q decreases with increasing r p , indicating a significant contribution of environmental quenching purely from the radial effect.We also see that galaxies with different masses all display a radial effect.The mechanism to produce the radial effect is thus likely associated with ram pressure stripping (Gunn & Gott 1972), since it depends on the parent cluster halo's gravitational potential and gas content and is thus linked to the radius effect.
In addition, from Figure 10, we find that the best-fit αs show a weak dependence on mass, redshift, and density, implying that the strength of the environmental quenching effect is associated with radius only.That said, βs display a mass dependence, a moderate redshift trend, and a weak relationship with density, suggesting that more massive galaxies tend to have a higher quiescent fraction.
By contrast, in Figure 11, at fixed redshift and r p , f q shows an increase for low-mass galaxies and roughly no growth for high-mass ones as the overdensity increases, implying a dependence solely on the density effect for low-mass galaxies.The density effect is likely related to the galaxy-galaxy merger mechanism (fast process) or galaxy harassment (slow process).Thus, our results also support a contribution from galaxy-galaxy mergers or galaxy harassment for low-mass galaxies.
Moreover, for low-mass galaxies in clusters, the radial effect has a difference of f q of roughly 0.1-0.2 between the core and the field, comparable to the change due to the density effect from overdense to underdense areas.The result supports the idea that radial and density effects operate similarly in clusters for low-mass galaxies.

Discussions
In Section 3.1.1,our results show that the reduction of the median log sSFR in clusters, as opposed to the field, is roughly 0.1 dex.Following the approach in Lin et al. (2014), we can roughly estimate the percentage contribution from fast and slow quenching separately.Assuming the reduction in log sSFR in cluster galaxies is purely from slow quenching, we manually reduce the log sSFRs of the separation line between star-forming and quiescent galaxies by an amount equal to the log sSFR reduction of ∼0.1 dex found in this work to take into account the reduction effect.Then we recompute the quiescent fraction using the adjusted separation line originating from the Figure 8.The fraction of star-forming, quiescent, and green valley galaxies plotted as a function of overdensity log 10 (1 + δ 6 ) at low (top row), medium (middle row), and high (bottom row) redshift.In each panel, different color lines represent results in different mass ranges.At low mass, the color-density relation, i.e., the fact that f q increases with overdensity, is prominent, while at high mass, the trend becomes weaker.In addition, f q appears to be independent of the overdensity but slightly depends on stellar mass and redshift.reduction to remove quenched galaxies due to the slow quenching effect and obtain the contribution solely due to fast quenching.The contribution from the slow quenching effect to the quiescent fraction is the difference in the quiescent fraction between the quiescent fraction without and with the adjustment of the separation line.
Using the method stated above, for low-mass galaxies in clusters, we find that the slow quenching effect can lead to a ∼20% contribution to the total quiescent fraction at the center, while the contribution from the slow quenching effect at the boundary is ∼65%-75%.In other words, for low-mass galaxies in clusters, the fast quenching process will account for the other 80% at the center and 25%-35% at the boundary.
By contrast, when estimating the slow environmental quenching effect at the high-mass range, the slow process contribution is roughly 15%-25% at the center and 25%-40% at the boundary in clusters.The fast quenching effect appears to dominate the slow one in the cluster environment for high-mass galaxies.
Additionally, from Figure 11, the pure radial effect is visible for low-mass and high-mass galaxies.By contrast, the pure density effect is more effective for low-mass galaxies.The change of f q is roughly 0.1-0.2 over the host-centric radius range from the field to the core from Figure 9.This difference is comparable to the changes in f q from underdensity to overdensity regions for low-mass galaxies from Figure 11.
The results thus support that ram pressure stripping is the leading mechanism for high-mass galaxies in clusters.The finding is consistent with the conclusion from Ando et al. (2023) that a quenching process with a short quenching timescale, such as ram pressure stripping, is needed to account for the anisotropic quenching visible in their study.For lowmass galaxies, starvation and harassment are comparably effective at the cluster boundary.

Summary
We make use of the HSC S20A galaxy catalog for galaxies with i 26 and stellar mass * ( )  M M log 10 completeness 8.6 at z = 0.2 and 9.8 at z = 1.1, and the CAMIRA (Oguri 2014;Oguri et al. 2018) cluster catalog for clusters with the virial mass log 10 (M 200 /M e ) ∼ 14.0 to study the radial and density effects over the redshift range of 0.2-1.1.We adopt the approach of the nth-nearest-neighbor to estimate the galaxy density (Gerke et al. 2007), where n = 6 in this work.We study the quiescent fraction f q as a function of stellar mass (M * ), redshift (z), host-centric radius (r p ), and local overdensity ( ) d + log 1 10 6 .We separate the contributions of the density and the radial effect to f q to understand the dominant quenching mechanisms in overdense regions.We summarize our results as follows:  6, the quiescent fraction f q is plotted as a function of normalized cluster-centric radius in four density ranges, i.e., 0.2 < log 10 (1 + δ 6 ) < 0.5, 0.5 < log 10 (1 + δ 6 ) < 0.8, 0.8 < log 10 (1 + δ 6 ) < 1.1, and 1.1 < log 10 (1 + δ 6 ) < 1.4.In addition, four mass ranges at low z are denoted by four colors and three redshift bins, as indicated in the plot.It is evident that controlling for mass, redshift, and overdensity, the radial trend of f g , i.e., that f g decreases with increasing r p /r 200m , is apparent.The result implies that the quenching contribution from a pure radial effect is significant, and the mechanism is likely to be ram pressure stripping.
1. (Section 3.1.1)We assess the median sSFR of starforming galaxies as a function of r p at fixed M * and z in Figure 3.We find an sSFR reduction of ∼0.1 dex for cluster galaxies with respect to the field galaxies.The sSFR reduction indicates a slow quenching effect.In addition, the sSFR reduction is weakly dependent on r p .It is more significant for less massive galaxies, implying a more substantial environmental effect acting on low-mass galaxies in clusters.2. (Section 3.1.2)The quiescent fraction f q exhibits an apparent radial dependence, i.e., f q decreases with increasing r p normalized for M * and z as shown in Figure 4.In clusters, low-mass galaxies show a larger negative radial gradient of f q , suggesting that low-mass galaxies suffer stronger environmental quenching than high-mass ones (Figure 5). 3. (Section 3.1.3)The effective green valley galaxy fraction ( fg ) defined as the fraction of star-forming to nonquiescent galaxies reveals a weak radial trend such that fg slightly decreases with increasing r p , showing a slight excess of fg in clusters relative to that in the field (the bottom two rows in Figure 6).However, a roughly flat radial trend is visible when considering data points inside the cluster boundary.The finding thus suggests that cluster galaxies experience a slow quenching effect, likely with no radial or density dependency.4. (Section 3.2) The quiescent fraction for low-mass galaxies grows with increasing overdensity, showing the so-called color-density relation.By contrast, the fraction of green valley galaxies is independent of the overdensity and has no dependence or a mild dependence on redshift and mass. 5. (Section 3.3) When exploring f q as a function of r p at fixed M * , z, and ( d + log 1 10 6 ) to isolate the radial effect, we find that the radial trend is still apparent.The contribution from the pure radial effect is visible for all galaxy masses.The dominant environmental quenching process is related to the radial effect and is likely to be ram pressure stripping (Gunn & Gott 1972).6. (Section 3.3) Controlling for M * , z, and r p , the pure density effect is evident for low-mass galaxies and is weak for high-mass galaxies.The change of f q from the density effect is approximately 0.1-0.2,comparable to the change from the radial effect.Thus, the result supports the idea that ram pressure stripping and a density-related process such as harassment are the quenching mechanisms for low-mass galaxies.7. (Section 3.4) Based on the findings in this work, we conclude that ram pressure stripping is the leading quenching mechanism for high-mass galaxies in clusters.For low-mass galaxies in clusters, the quenching effects from ram pressure stripping and a density-related process such as harassment are comparable at the core.At the same time, starvation and harassment dominate at the cluster border.7, the best-fit results of α and β for f q .From left to right, the cluster galaxy subsamples are for the overdensity in the range of 0.2 < log 10 (1 + δ 6 ) < 0.5, 0.5 < log 10 (1 + δ 6 ) < 0.8, 0.8 < log 10 (1 + δ 6 ) < 1.1, and 1.1 < log 10 (1 + δ 6 ) < 1.4.Three different redshift ranges are 0.2 < z < 0.5 (red), 0.5 < z < 0.8 (green), and 0.8 < z < 1.1 (blue).The radial gradient αs are roughly independent of mass, redshift, and overdensity.By contrast, βs moderately depend on redshift and depend on stellar mass but have weak overdensity dependency.
. Adopting the richness-mass relations based on Planck cosmological parameters (Planck Collaboration 2016) from Murata et al. (2019), N = 15 corresponds to the virial halo mass log 10 (M 200m /h −1 M e ) ∼ 13.93 - + 0.32 0.23 in the redshift range of 0.1 < z < 0.4, 14.05 - + 0.26 0.19 in the redshift range of 0.4 < z < 0.7, and 13.96 - + 0.32 0.23 in the redshift range of 0.7 < z < 1.0.In addition, with M 200m from the richness-mass relation, we can then estimate r 200m of CAMIRA clusters in comoving coordinates, where r 200m is the radius within which the halo mass density is 200 times the mean mass density.

Figure 7 .
Figure 7. Similar to Figure5, the best-fit results of the fitting slope α and fraction at center β for f g (top row) and fg (bottom row).For f g , the radial gradient at low mass is negative and becomes positive at high mass, implying an excess at low mass and a shortage at high mass respective to the field.

Figure 9 .
Figure 9. Similar to Figure6, the quiescent fraction f q is plotted as a function of normalized cluster-centric radius in four density ranges, i.e., 0.2 < log 10 (1 + δ 6 ) < 0.5, 0.5 < log 10 (1 + δ 6 ) < 0.8, 0.8 < log 10 (1 + δ 6 ) < 1.1, and 1.1 < log 10 (1 + δ 6 ) < 1.4.In addition, four mass ranges at low z are denoted by four colors and three redshift bins, as indicated in the plot.It is evident that controlling for mass, redshift, and overdensity, the radial trend of f g , i.e., that f g decreases with increasing r p /r 200m , is apparent.The result implies that the quenching contribution from a pure radial effect is significant, and the mechanism is likely to be ram pressure stripping.

Table 1
Best-fit Parameters for the Star-forming Main Sequence, Red Sequence, and Green Valley a α and β are the fitting slope and amplitude, respectively, for the fitting formula,