Photometric Objects Around Cosmic Webs (PAC). VII. Disentangling Mass and Environment Quenching with the Aid of Galaxy-halo Connection in Simulations

We use the Jiutian simulation and precise SHMR to build mock catalogs for galaxies with different stellar masses.

The Jiutian suite consists of a sequence of N-body simulations created to satisfy the scientific needs of the Chinese Space Station Telescope optical surveys (Gong et al., 2019). We employ one of the high-resolution main runs based on the Planck 2018 cosmology (Planck Collaboration et al., 2020), as mentioned at the end of the Introduction. This simulation contains $6144^{3}$ dark matter particles within a periodic box of $1000h^{-1}\mathrm{Mpc}$, performed with the GADGET-3 code (Springel et al., 2001). The Friends-of-Friends technique is used to identify dark matter halos, and HBT+ is used to track subhalos (Han et al., 2012, 2018). We use the snapshot at $z_{s}=0.102$ to compare with the SDSS observational data at $z_{s}<0.2$.

We adopt the measurements and a similar methodology from Paper IV to derive the SHMR. Paper IV measured 95 $\bar{n}_{2}w_{\mathrm{p}}(r_{\mathrm{p}})$ across various stellar mass bins, reaching down to $10^{8.0}M_{\odot}$, using the Dark Energy Camera Legacy Survey (DECaLS) photometric catalog and the SDSS Main spectroscopic sample at $z_{s}<0.2$. Here, $\bar{n}_{2}$ represents the mean number density of photometric galaxies, and $w_{\mathrm{p}}$ is the projected cross-correlation function of spectroscopic and photometric galaxies. By modeling these $\bar{n}_{2}w_{\mathrm{p}}(r_{\mathrm{p}})$ measurements using subhalo abundance matching (SHAM) with a parameterized SHMR, Paper IV achieved $1\%$ precision in constraining the parameters. In this work, we follow their methodology and use the same measurements but introduce separate SHMRs for central and satellite galaxies, unlike the unified SHMR approach in Paper IV. We find that this refined model provides a better fit to the measurements and offers a more physically reasonable interpretation (K. Xu et al. 2024, in prep.).

we use the double power law form (the DP model in Paper IV):

Here $M_{\mathrm{acc}}$ refers to the viral mass $M_{\mathrm{vir}}$ of the halo at the specific time when the galaxy was last to be the central dominant object. $M_{*}$ represents the stellar mass. A Gaussian function with width $\sigma$ is adopted to describe the dispersion in $\log(M_{*})$ at a given $M_{\mathrm{acc}}$. The slopes of the SHMR at the high and low mass ends are represented by $\alpha$ and $\beta$, respectively. As we mentioned before, we use two different SHMRs for the central and satellite galaxies separately to model the $\bar{n}_{2}w_{\mathrm{p}}(r_{\mathrm{p}})$ measurements from Paper IV.

The constrained parameters for the DP model for the central and satellite galaxies are given in Table 1 and the corresponding SHMRs are shown in Figure 1. However, in Paper IV, the stellar mass is calculated using the SED code CIGALE (Boquien et al., 2019) based on DECaLS photometry with $g$, $r$ and $z$ bands, while the stellar mass used in Paper V to study galaxy quenching is based on SDSS photometry with five bands $ugriz$. Although the SED fitting code and models are the same, we still find some small differences. In Figure 2, we compare the stellar masses of identical galaxies derived from the two different photometry, and find a linear relation can well describe their differences:

After assigning the DECaLS stellar masses to halos and subhalos in the Jiutian simulation, we further calibrated them to SDSS stellar masses using Equation 2. This calibration ensures a more consistent comparison with observational data from Paper V.

We use the same data and methodology as Paper V to obtain the projected density distribution $\bar{n}_{2}w_{\mathrm{p}}(r_{\mathrm{p}})$ of companion galaxies with different colors and stellar masses around massive central galaxies with varying stellar masses. However, we apply different criteria to select central galaxies to ensure greater consistency with the definition of central galaxies in the simulation.

In this work, we use the SDSS DR7 Main spectroscopic sample (Abazajian et al., 2009) and DR13 datasweep photometric sample (Albareti et al., 2017), focusing on galaxies with redshifts $z_{s}<0.2$. In Paper V, we selected central galaxies in the Main sample as those that do not have more massive neighbors within a distance of $30r^{\rm nb}_{\mathrm{vir}}$ along the line-of-sight (LOS) and within $3r^{\rm nb}_{\mathrm{vir}}$ perpendicular to the LOS, based on our finding that the environmental impact of a halo extends up to approximately $3r_{\mathrm{vir}}$. Here, $r^{\rm nb}_{\mathrm{vir}}$ refers to the virial radius of the more massive galaxies for each comparison. In this paper, to be consistent with the definition used in the simulation, we adjust the selection criteria by applying $r^{\rm nb}_{\mathrm{vir}}$ perpendicular to the LOS as the threshold, while keeping the selection distance along the LOS the same. This adjustment is made because centrals in the simulation are typically defined within each halo, making $r_{\mathrm{vir}}$ a more appropriate choice for comparison. We calculate $r_{\mathrm{vir}}$ for each central stellar mass bin we are interested in based on the SHMR and the Jiutian simulation. The results are $0.47\pm 0.194\,h^{-1}{\rm{Mpc}}$, $0.631\pm 0.263\,h^{-1}{\rm{Mpc}}$, and $0.835\pm 0.329\,h^{-1}{\rm{Mpc}}$ for the central stellar mass bins $[10^{11.1}M_{\odot},10^{11.3}M_{\odot}]$, $[10^{11.3}M_{\odot},10^{11.5}M_{\odot}]$, and $[10^{11.5}M_{\odot},10^{11.7}M_{\odot}]$, respectively.

We use the same color cut as Paper V to define blue and red galaxies based on the rest-frame $u-r$ color:

Then, we calculate $\bar{n}_{2}w_{\mathrm{p}}(r_{\mathrm{p}})$ for the red and the entire companion galaxy sample in four stellar mass bins within $[10^{9.5}M_{\odot},10^{11.0}M_{\odot}]$ around massive central galaxies in four stellar mass bins within $[10^{11.1}M_{\odot},10^{11.7}M_{\odot}]$ . We adopt the jackknife resampling technique to assess the statistical error. The mean value of $\bar{n}_{2}w_{\mathrm{p}}(r_{\mathrm{p}})$ can be obtained by:

The corresponding error is calculated as:

Here, $\bar{n}_{2,k}w_{\mathrm{p},k}\left(r_{\mathrm{p}}\right)$ indicates the excess of the projected density for the $k$th realization, and $N_{\mathrm{sub}}$ signifies the number of jackknife realizations. We use $N_{\mathrm{sub}}=50$ in this work. The measurements are displayed in Figure 3 as dots with error bars.

Although the SDSS Main sample includes lower mass galaxies, we only use centrals with $M_{*}>10^{11.1}M_{\odot}$ due to challenges in selecting central galaxies. However, while we do not use lower mass spectroscopic galaxies to build our 3D quenched fraction model, they serve as a useful tool to verify the extrapolation of our model. Therefore, we also measure the $\bar{n}_{2}w_{\mathrm{p}}(r_{\mathrm{p}})$ of companion galaxies with different colors and stellar masses around the entire lower mass spectroscopic sample, including both central and satellite galaxies. These measurements are then compared to the extrapolated predictions from our 3D quenched fraction model. We believe this approach provides strong validation for the extrapolability of our model.

To derive the 3D quenched fraction profile, we first recover the 3D distributions of the red and the entire companion galaxy sample around massive central galaxies from the projected distributions $\bar{n}_{2}w_{\mathrm{p}}(r_{\mathrm{p}})$. Assuming that the real space correlation function $\xi(r)$ follows the power-law form $\xi(r)=(r/r_{0})^{-\gamma}$, we have:

where $\Gamma$ is the Gamma function. The power-law assumption is a good one for the scales of $<3r_{\mathrm{vir}}$ that are relevant to this paper below. Then, $\bar{n}_{2}w_{\mathrm{p}}(r_{\mathrm{p}})$ can be written as:

where we absorb $n_{2}$ and $r_{0}$ into $r_{1}$. By fitting $\bar{n}_{2}w_{\mathrm{p}}\left(r_{\mathrm{p}}\right)$ of companion galaxies in the range $0.1<r_{\mathrm{p}}<3h^{-1}\mathrm{Mpc}$, we can constrain $r_{1}$ and $\gamma$. We show the fitting results in Figure 3 with lines. It is evident that the data and fit exhibit a relatively good agreement across the whole mass range, both for the entire galaxy samples and for the red ones.

Consequently, the 3D number density distribution can be writen as:

Similarly, for red sub-samples, we can obtain $\bar{n}_{2}^{red}\xi^{red}\left(r\right)$. Finally, we can compute the 3D quenched fraction distributions for companion galaxies:

In Figure 4, we present the 3D quenched fraction distributions. The mass bins for central and companion galaxies are consistent with those shown in Figure 3. For each bin, we list the median values of central stellar mass, companion stellar mass and $r_{\mathrm{vir}}$ derived from the Jiutian catalog, which are subsequently used to build the model. It is clear that the fraction $f^{\rm{com}}_{\mathrm{q}}$ declines as the distance $r/r_{\mathrm{vir}}$ increases, following a power-law relation. This indicates that galaxies located closer to central galaxies are more likely to be quenched, thereby confirming the environmental effect. Additionally, we observe a mass dependence of $f^{\rm{com}}_{\mathrm{q}}$: Higher masses correspond to higher $f^{\rm{com}}_{\mathrm{q}}$, a trend evident for both central and companion stellar masses. The monotonous increase with companion mass highlights the impact of mass quenching, while the gradual increase with central mass suggests a stronger environmental effect in more massive halos, even when scaled distances $r/r_{\text{vir}}$ are taken into account.

Based on these observational results, we construct a fitting formula of $f^{\rm{com}}_{\mathrm{q}}$ as follows:

where

where $A_{1},\eta_{1},\nu_{1}$ and $A_{2},\eta_{2},\nu_{2}$ are free parameters of the model. In order to fit the parameters, we employ the Markov Chain Monte Carlo (MCMC) sampler emcee (Foreman-Mackey et al., 2013). We use the median values of central stellar mass, companion stellar mass, and $r_{\rm{vir}}$ for each mass bin, as previously mentioned, in the fitting process. The posterior probability density functions (PDFs) of the parameters are shown in Figure 5, from which we can conclude that all parameters are well constrained. To validate the fitting, we compare it to the observed $f^{\rm{com}}_{\mathrm{q}}(r;M_{*,\rm{cen}},M_{*,\rm{com}})$ in Figure 4. Overall, the fits of $f^{\rm{com}}_{\mathrm{q}}$ are consistent with the observational data within the error margins.

Although Equation 10 provides $f^{\rm{com}}_{\mathrm{q}}(r;M_{*,\rm{cen}},M_{*,\rm{com}})$ to large scales, in our model, we only apply it to satellite galaxies within the radius $r_{\rm{FOF}}$ of each FOF halo. We define the 3D satellite quenched fraction profile as

We use $f_{\rm{q}}^{\rm{sat}}$ instead of $f_{\rm{q}}^{\rm{com}}$ to ensure the uniqueness of the model prediction, as each satellite galaxy is associated with only one central galaxy, whereas companion galaxies outside $r_{\rm{FOF}}$ can be linked to multiple central galaxies. Moreover, this approach is more physically motivated, as Paper V demonstrated that environmental quenching predominantly occurs within halos, while companion galaxies beyond $r_{\rm{FOF}}$ are primarily influenced by their own host halos.

With the 3D quenched fraction model for satellite galaxies developed above, we can determine the quenched fraction of each satellite galaxy. However, to complete the picture, we still need the quenched fraction of central galaxies, $\bar{f}^{\rm{cen}}_{\rm{q}}(M_{*})$. Additionally, since the quenching of satellite galaxies results from both mass and environmental effects, $\bar{f}^{\rm{cen}}_{\rm{q}}(M_{*})$ is crucial for disentangling these two factors, as it is believed to represent the mass-driven effect.

While we could derive $\bar{f}^{\rm{cen}}_{\rm{q}}(M_{*})$ using the existing $f^{\rm{com}}_{\mathrm{q}}(r;M_{*,\rm{cen}},M_{*,\rm{com}})$ results beyond $r_{\rm{vir}}$ with iterative methods, it would be much simpler to include a new observational quantity, $\bar{f}^{\rm{all}}_{\rm{q}}(M_{*})$, the average quenched fraction for all galaxies in each stellar mass bin. $\bar{f}^{\rm{all}}_{\rm{q}}(M_{*})$ can be easily obtained by counting blue and red galaxies in each stellar mass bin. To account for completeness, during the counting, we employ a weight of $1/V_{\mathrm{max}}$ for each galaxy, where $V_{\mathrm{max}}$ represents the volume corresponding to $z_{\mathrm{max}}$, the maximum redshift at which the galaxy satisfies our selection criteria. The corresponding errors are estimated from the bootstrap resamplings. With $\bar{f}^{\rm{all}}_{\rm{q}}(M_{*})$ and the average quenched fraction of satellite galaxies, $\bar{f}^{\rm{sat}}_{\rm{q}}(M_{*})$, calculated from our model, we can solve for $\bar{f}^{\rm{cen}}_{\rm{q}}(M_{*})$ :

Here, $N_{\mathrm{sat}}$ denotes the number of satellite galaxies in each stellar mass bin, while $N_{\mathrm{cen}}$ represents the number of central galaxies. These values are calculated from our models using the Jiutian simulation. We would like to note that in the calculation of $\bar{f}^{\rm{sat}}(M_{*})$, we have extrapolated our $f^{\rm{sat}}_{\mathrm{q}}(r;M_{*,\rm{cen}},M_{*,\rm{sat}})$ model. This is because the calculation requires the $f^{\rm{sat}}$ values for all satellite galaxies around central galaxies with any stellar mass, while the model is built based on measurements for central galaxies only with $M_{*,{\rm{cen}}}>10^{11.1}M_{\odot}$. This extrapolation will be validated in Section 3.3 by incorporating additional measurements. For now, we assume the extrapolation is reasonable.

In Figure 6, we show the derived $\bar{f_{\rm{q}}}^{\rm{sat}}(M_{*})$, $\bar{f_{\rm{q}}}^{\rm{cen}}(M_{*})$, $\bar{f_{\rm{q}}}^{\rm{all}}(M_{*})$, and the environmental quenched fraction $\bar{f_{\rm{q}}}^{\rm{env}}(M_{*})=\bar{f_{\rm{q}}}^{\rm{all}}(M_{*})-\bar{f_{\rm{q}}}^{\rm{cen}}(M_{*})$, where $\bar{f_{\rm{q}}}^{\rm{cen}}(M_{*})$ also represents the mass quenched fraction, $\bar{f_{\rm{q}}}^{\rm{mass}}(M_{*})$, in our definition. We find that $\bar{f_{\rm{q}}}^{\rm{cen}}$ increases monotonically with stellar mass, suggesting that mass quenching effects become more pronounced in more massive galaxies. To describe $\bar{f_{\rm{q}}}^{\rm{cen}}(M_{*})$, we construct a model as follows:

Here, $\operatorname{erf}$ is the error function, $\mu$ is the central location, and $\sigma$ is the width of the distribution. The fitted values for $\mu$ and $\sigma$ are 10.02 and 0.64, respectively. The fitting model is displayed in Figure 6 with orange line. Using this model, we can assign the value of $\bar{f}_{\mathrm{q}}^{\mathrm{cen}}$ to each central galaxy in the Jiutian simulation. Combined with the $f^{\rm{sat}}_{\rm{q}}$ model, we can now determine the quenched probability of each galaxy in the simulation. We present the model prediction of $f^{\rm{com}}_{\mathrm{q}}(r;M_{*,\rm{cen}},M_{*,\rm{com}})$ from the Jiutian simulation in Figure 4 and find that our model accurately reproduces the measurements.

The 3D quenched fraction model we developed in Equation 10 and Equation 13 can predict the quenched probability for any galaxy with $M_{*}>10^{9.5}M_{\odot}$. However, as mentioned above, this is achieved by extrapolating the $f^{\rm{sat}}_{\mathrm{q}}(r;M_{*,\rm{cen}},M_{*,\rm{sat}})$ model to $M_{*,{\rm{cen}}}<10^{11.1}M_{\odot}$, and this extrapolation still needs to be validated.

Before validate the extrapolation, we first check if we can reproduce the measurements with $M_{*,{\rm{cen}}}>10^{11.1}M_{\odot}$ used to construct our model. The measurements we choose to compare is the projected quenched fraction of companion galaxies $f^{\rm{com}}_{\rm{q}}(r_{\rm{p}};M_{*,{\rm{cen}}},M_{*,\rm{com}})$ as used in Paper V. The $f^{\rm{com}}_{\rm{q}}(r_{\rm{p}};M_{*,{\rm{cen}}},M_{*,\rm{com}})$ of the $k$th jackknifed realization is

Then, the mean value of the $f^{\rm{com}}_{\rm{q}}(r_{\rm{p}};M_{*,{\rm{cen}}},M_{*,\rm{com}})$ and the corresponding error can be expressed as:

We note that the observed $f^{\rm{com}}_{\rm{q}}(r_{\rm{p}};M_{*,{\rm{cen}}},M_{*,\rm{com}})$ is a direct measurement from observations, independent of any model assumptions.

In Figure 7, we compare the observed $f^{\rm{com}}_{\rm{q}}(r_{\rm{p}};M_{*,{\rm{cen}}},M_{*,\rm{com}})$ with predictions from our model across all stellar mass bins used to construct the model, spanning scales of $0.1<r_{\rm{p}}<10\,h^{-1}\,\mathrm{Mpc}$. We find that our model accurately reproduces the measurements across all stellar mass bins, confirming its self-consistency. This test also provides a weak validation of the extrapolation, as $f^{\rm{com}}_{\rm{q}}(r_{\rm{p}})$, particularly at $r_{\rm{p}}>r_{\rm{vir}}$, contains some information about the quenched fraction of satellite galaxies with $M_{*,\rm{cen}}<10^{11.0}M_{\odot}$. This is because companion galaxies at $r>r_{\rm{vir}}$ have the potential to be satellite galaxies of these less massive centrals, contributing to $f^{\rm{com}}_{\rm{q}}(r_{\rm{p}})$. However, since the measurements at $r_{\rm{p}}>r_{\rm{vir}}$ have larger uncertainties, this serves only as a relatively weak validation.

To further validate the extrapolation, we incorporate additional measurements as described below. The reason we initially used only measurements with $M_{*,{\rm{cen}}}>10^{11.1}M_{\odot}$ to construct the model is that identifying lower-mass central galaxies in observations is both challenging and prone to significant uncertainties. However, in the model, we can easily predict $f^{\rm{com}}_{\rm{q}}(r_{\rm{p}};M_{*,{\rm{all}}},M_{*,\rm{com}})$, which represents the quenched fraction of companion galaxies around all galaxies with $M_{*,{\rm{all}}}$, including both central and satellite galaxies. This eliminates the need to isolate central galaxies in observations for comparison. This approach allows us to extend the measurements of $f^{\rm{com}}_{\rm{q}}(r_{\rm{p}};M_{*,{\rm{all}}},M_{*,\rm{com}})$ to $M_{*,{\rm{all}}}<10^{11.1}M_{\odot}$ using the SDSS spectroscopic sample, providing a stronger test for our model.

In Figure 8, we compare the measured and predicted $f^{\rm{com}}_{\rm{q}}(r_{\rm{p}};M_{*,{\rm{all}}},M_{*,\rm{com}})$ for $M_{*,{\rm{all}}}>10^{10.5}M_{\odot}$ and within the same $M_{*,\rm{com}}$ ranges. We refrain from extending to lower $M_{*,{\rm{all}}}$ because the SDSS is only complete at very low redshifts, and the PAC method used in this study has not been fully validated at such low redshifts. This extension can be achieved with next-generation spectroscopic surveys and an improved PAC method (K. Xu et al., in prep.). We find that our model accurately reproduces all the $f^{\rm{com}}_{\rm{q}}(r_{\rm{p}};M_{*,{\rm{all}}},M_{*,\rm{com}})$ measurements down to $M_{*,{\rm{all}}}>10^{10.5}M_{\odot}$, providing a strong test of our model in the environments of $M_{\rm{vir}}>10^{12.0}h^{-1}M_{\odot}$.