Dissect two-halo galactic conformity effect for central galaxies: The dependence of star formation activities on the large-scale environment

The sample used for this study is drawn from the Sloan Digital Sky Survey (SDSS) main galaxy sample (MGS), which is a magnitude-limited spectroscopic survey with $r<17$ covering $\sim 8000~{}\rm deg^{2}$ carried on the 2.5 meter wide-angle telescope at Apache Point Observatory (York et al., 2000; Blanton et al., 2005; Abazajian et al., 2009). The SDSS MGS catalogue comprises five bands photometry ($u$, $g$, $r$, $i$, $z$) and accurate redshift measurements from its spectroscopic observation. The central stellar velocity dispersion is measured within the $3^{\prime\prime}$ diameter fiber. Derived quantities, like stellar mass and star formation rate (SFR), are obtained from multi-band photometric measurements and spectra indices (Kauffmann et al., 2003; Salim et al., 2016). In the present work, we adopt the stellar mass and SFR from the GALEX-SDSS-WISE Legacy Catalog (GSWLC) (Salim et al., 2016, 2018), which are estimated by fitting the UV-optical-IR bands photometry using the CIGALE code (Noll et al., 2009; Boquien et al., 2019) with the stellar library of Bruzual & Charlot (2003) and the initial mass function of Chabrier (2003). The specific star formation rate (SSFR) is defined as $\rm SFR/M_{*}$. The middle panel of Fig. 1 shows the distribution of galaxies on the $M_{*}-\rm SFR$ plane where one can clearly see the bimodality. We further separate galaxies into star-forming and quiescent populations, according to the method in Woo et al. (2013). We first fit a linear function to the star-forming main sequence by iteratively applying the least-square fitting and excluding data points 1 dex below the main sequence until convergence. Finally, we define galaxies with SFR lower than the main sequence by more than 1 dex as quiescent, and the remaining ones as star-forming. The separation line is

and shown as the black dashed line in the middle panel of Fig. 1.

Directly calculating the quiescent fraction in stellar mass bins for a magnitude-limited sample, like a $r$-band limited sample, will produce biased results, since star-forming galaxies are brighter in the blue band and hence they are preferentially selected, compared with their quiescent counterparts with similar stellar mass. In previous studies, a $K$-correction procedure is applied to all galaxies to calculate the $V_{\rm max}$ factors (Blanton & Roweis, 2007), which are used for weighting these galaxies (e.g. Peng et al., 2010). A more conservative method is to construct a $M_{*}$-limited sample, which contains a complete sample of galaxies above some stellar mass threshold, which is a function of redshift (see Pozzetti et al., 2010, for more details), after which we can calculate a $V_{\rm max}$ factor for each galaxy in the mass-limited sample. We adopted the latter in this paper. To begin with, we divide galaxies into small redshift bins, i.e. $\Delta z=0.02$. Then, in each redshift bin, we select 20% galaxies with faintest $r$-band magnitude and calculate the rescaled stellar mass, i.e.

where $M_{*}$ and $r$ are the stellar mass and $r$-band apparent magnitude, and $r_{\rm lim}$ is the limit $r$-band magnitude, which ranges from 17.57 to 17.72 for SDSS galaxies. Finally, the stellar mass limit is the envelope assembled by the 95% percentile of $M_{\rm scale}$ in each redshift bin. The envelope is shown as the gray dashed line on the right panel of Fig. 1 and the mass-limited sample is shown in red points. We also weigh each galaxy with $1/V_{\rm max}$ where $V_{\rm max}$ is the volume between $z_{\rm min}$ and $z_{\rm max}$ with $z_{\rm min}=0.02$ and $z_{\rm max}$ inferred from the mass-limited envelop calculated above according to the stellar mass of each galaxy (see also Wang et al., 2023a). In addition, we constructed a volume-limited sample by selecting galaxies with

We emphasize that the central galaxies in the mass-limited sample are the objects for investigation in this work, and the central galaxies in the volume-limited sample only serve as environment tracers, which will be introduced in § 2.3.

We use the morphology classification from the Galaxy Zoo project¹¹1https://data.galaxyzoo.org/ (Lintott et al., 2011). In Galaxy Zoo, galaxies are classified as spiral, elliptical, and uncertain according to their image, and a debiasing process is applied. Here we define spiral galaxies as ones with the flag of SPIRAL set to one.

We use the group catalog of Yang et al. (2007) to select the central galaxy as the most massive one in each galaxy group. The halo mass is calibrated by abundance matching the total stellar mass with the theoretical halo mass function. We note that some studies require the central galaxy to be the most massive and the brightest one simultaneously. This more strict criterion only eliminates $\sim 2\%$ central galaxies from our sample (Peng et al., 2012), and has negligible impact on the results presented in this paper.

The IllustrisTNG project (Pillepich et al., 2018a; Springel et al., 2018; Naiman et al., 2018; Marinacci et al., 2018; Pillepich et al., 2018b; Nelson et al., 2018, 2019) comprises a set of gravo-magnetohydrodynamical cosmological simulations that run with the moving mesh code AREPO (Springel, 2010). It simulates the formation and evolution of galaxies from $z=127$ to $z=0$ based on a cosmology constrained in Planck Collaboration et al. (2016), where $\Omega_{\Lambda,0}=0.6911$, $\Omega_{b,0}=0.3089$, $\sigma_{8}=0.8159$, $n_{s}=0.9667$, and $h=0.6774$. In this paper, we are using the version with a box side length of $\sim 300$Mpc for better statistics. This simulation contains $2500^{3}$ dark matter particles with each weights $\sim 5.9\times 10^{7}\rm M_{\odot}$, and $\sim 2500^{3}$ gas cells with each weights $\sim 1.1\times 10^{7}\rm M_{\odot}$.

The dark matter halos are identified with the friends-of-friends (FoF) algorithm (Davis et al., 1985) using dark matter particles. Substructures are identified with the SUBFIND algorithm using all types of particles (Springel et al., 2001), then the baryonic components are defined as galaxies and the dark matter components are defined as subhalos. In each FoF halo, the central subhalo is defined as the one that is located at the minimum of the gravitational potential, and the galaxy inside this subhalo is defined as the central galaxy, while the remaining subhalos and galaxies are satellites. Subhalo merger trees are constructed using the SUBLINK algorithm (Rodriguez-Gomez et al., 2015), and we identify the main progenitor for each subhalo/galaxy as the one with the most massive progenitor history (De Lucia & Blaizot, 2007).

Here we define the halo mass for each FoF halo as the total mass within a radius within which the average density equals 200 times the critical density, while the radius is used as the halo radius and denoted as $R_{200}$. The stellar mass is calculated by summing all the stellar particle mass within $2R_{*}$, where $R_{*}$ is the stellar half-mass radius for all the stellar particles attributed to the subhalo. The SFR is also calculated from all the star-forming particles within $2R_{*}$. For galaxies in the IllustrisTNG simulation, those with $\rm SSFR<10^{-11}\rm yr^{-1}$ are defined as quiescent, while the remaining ones are star-forming. It is noteworthy that we are using a different criterion to separate star-forming/quiescent galaxies in observation and simulation. Since we do not intend to perform a quantitative comparison between simulation and observation (e.g. Donnari et al., 2019, 2021), it is fine as long as this separation criterion does not bias the environmental dependence of the quiescent fraction.

For all central galaxies at $z=0$, we also identify a sub-sample of backsplash galaxies with the following properties (Wang et al., 2009; Wetzel et al., 2014):

1. 1.

   They are central galaxies at $z=0$.

2. 2.

   Their main progenitors were once satellites of other halos and the satellite state lasts at least two successive snapshots. Here the second requirement is to avoid the central-satellite switching problem (see Figure 1 in Poole et al., 2017).

The formation and evolution of galaxies and their associated dark matter halos are subject to environmental effects (Mo et al., 2010). There are many different metrics to quantify galaxy environments on different spatial scales (e.g. Muldrew et al., 2012). Here we define a novel environment metric that only uses central galaxies as tracers, which is defined as

where $D_{\rm 5th}$ is the projected distance to the fifth nearest central galaxy within $\pm 1000\rm km/s$ in the volume-limited galaxy sample. And each central galaxy in the mass-limited sample has a value of $\Sigma_{\rm cen,5th}$ calculated. The choice of the fifth neighbor is motivated by two reasons. On one side, it cannot be too small which will suffer from the shot noise. On the other side, it cannot be too large where all the information will be smoothed out. Finally, we choose to use the fifth nearest neighbor.

The search of the nearest neighbors can be seriously biased near the edge of survey regions and bright star masks. For the validity of our environment metric, we exclude central galaxies whose 5th nearest neighbor searching is biased. We randomly drop one million points in a rectangular region that enclose the survey footprint on the sphere. Then, we calculate a completeness factor for each central galaxy, which is defined as

where $N(<\theta)$ is the number of random points within the survey mask and within an angular distance of $\theta$ from the central galaxy in question (Blanton et al., 2005), and $\bar{\Sigma}$ is the mean surface density of random points, and $D_{A}$ is the angular distance of the central galaxy in question. In the present work, we restrict our study to central galaxies with $f_{\rm 10Mpc}>0.9$, where 10Mpc is larger than the $D_{\rm 5th}$ for most of the central galaxies in this study, and we present the projected distribution of these selected galaxies with red points on the left panel of Fig. 1. We note that the spatial incompleteness can bias the environment estimation by underestimating the local density for galaxies near masked regions, so we make a conservative cut of 90% completeness to mitigate this effect. It is also noteworthy that this effect can only undermine the environmental dependence of galaxy properties rather than inducing it as long as the spatial mask does not correlate with the galaxy properties in question.

In Fig. 2, we present the distribution of $D_{\rm 5th}$ and $\Sigma_{\rm cen,5th}$ for all central galaxies in the volume-limited sample on the first two panels, with vertical lines indicate the 10%, 40%, 60%, and 90% percentiles. One can see that $D_{\rm 5th}$ spans a large range from $\lesssim 1\rm Mpc$ to $\gtrsim 10\rm Mpc$. The middle panel shows the distribution of $\Sigma_{\rm cen,5th}$. On the right panel, we plot the stellar mass distributions for central galaxies in the $M_{*}$-limited sample with different central-traced densities. One can clearly see that the high-density regions are preferentially occupied by massive galaxies.

Fig. 4 shows that low-mass galaxies with $M_{*}\lesssim 10^{10.5}M_{\odot}$ residing in high-density regions are more quenched than their counterparts in low-density regions. This phenomenon is not only found in observation, but also shown in the semi-analytical models (SAMs) and hydrodynamical simulations of galaxy formation (e.g. Lacerna et al., 2018, 2022; Ayromlou et al., 2022). Lacerna et al. (2022) uses the IllustrisTNG simulation and the SAM of SAG (e.g. Springel et al., 2001; Cora et al., 2018) to demonstrate that this effect is attributed to the vicinity of low-mass central galaxies around massive clusters, so it disappears once these galaxies are removed. Similarly, Ayromlou et al. (2022) find that the original SAM of L-GALAXIES in Henriques et al. (2015) has no conformity signal until a new recipe is adopted, where the ram-pressure stripping effect can also affect the evolution of galaxies beyond the virial radius of massive halos (Ayromlou et al., 2021).

Here we use the IllustrisTNG simulation to see the dependence of central-galaxy properties on large-scale environments and explore their physical origins. Since we intend to study similar signals in IllustrisTNG instead of performing a quantitative comparison with observation, there is no need to include observation effects like the redshift-space distortion effect, which can only undermine the strength of this conformity signal. Here we define a 3D-version large-scale environment metric of equation 4 for each central galaxy, i.e.

where $D_{\rm 5th}$ is the distance to the 5th nearest central galaxy.

Fig. 5 shows the quiescent fraction of central galaxies as a function of stellar mass in different bins of $\rho_{\rm cen,5th}$, where the left panel shows the result for all central galaxies. Clearly, one can see that low-mass central galaxies with $M_{*}\lesssim 10^{10.5}M_{\odot}$ in dense regions are more quenched than their counterparts in under-dense regions and the difference in the quiescent fraction is up to $12\%$. The middle panel of Fig. 5 shows the result after removing all backsplash central galaxies, which are central galaxies at $z=0$ and were satellite galaxies in other halos at $z<1$²²2Here we only consider backsplash galaxies that were satellite galaxies at $z<1$ since, at higher redshift, the progenitor galaxies have very low stellar mass and suffer from resolution problems.. Here one can see that the conformity signal completely disappears on the whole stellar mass range. This result suggests that the conformity signal for low-mass central galaxies in the IllustrisTNG simulation mainly comes from the backsplash galaxies (Wetzel et al., 2014). As suggested in Wetzel et al. (2014), we can also eliminate the impact of backsplash galaxies by removing galaxies within $4R_{200}$ of any other more massive halos, and the result is shown on the right panel of Fig. 5. Here we can see that the conformity signal for galaxies with $M_{*}\lesssim 10^{10.5}M_{\odot}$ also disappears.

Previous studies quantify the two-halo galactic conformity effect with the quiescent fraction difference of neighboring galaxies (secondary galaxies) around star-forming and quiescent central galaxies (primary galaxies). Lacerna et al. (2022) found that galaxies around quiescent central galaxies are more quenched than those around star-forming central galaxies with similar stellar masses in the IllustrisTNG simulation, and this difference is prominent up to $\sim 10$ Mpc (see also Ayromlou et al., 2022). Here we want to see if backsplash galaxies can explain the two-halo galactic conformity signal manifested in this way. In previous studies, the primary galaxies only include centrals, and the secondary galaxies include both centrals and satellites. As we argued in § 1 (see also § 4.3), the mixing of central and satellite galaxies makes the result hard to interpret, so here we only include centrals for both the primary and the secondary galaxies.

Fig. 6 shows the quiescent fraction of central galaxies with $M_{*}\geq 10^{9}M_{\odot}$ (secondary galaxies) as a function of distance to central galaxies in three stellar mass bins (primary galaxies). The primary galaxies are further separated into star-forming and quiescent populations and the results are shown in blue and red colors, respectively. Top panels in Fig. 6 show the results for all central galaxies in the TNG simulation. Here one can see that secondary galaxies around quiescent primary galaxies have higher quiescent fraction by $\lesssim 20\%$, and the difference in the quiescent fraction decreases for more massive primary galaxies and for larger separations, until the difference disappears for the primary galaxies with $M_{*}\gtrsim 10^{10}M_{\odot}$ or for $r>8$ Mpc. Panels on the second row in Fig. 6 show the result after removing all backsplash central galaxies. Here one can see that the difference in the quiescent fraction for star-forming and quiescent primary galaxies disappears, indicating that the two-halo galactic conformity signal comes from these backsplash galaxies. Finally, we tested the method suggested in Wetzel et al. (2014) to eliminate the impact of backsplash galaxies by removing centrals within $4R_{\rm 200}$ of any other more massive halos, and the result is shown on the bottom panels in Fig. 6. Again, the conformity signal completely disappears. It is noteworthy that previous studies have shown that low-mass central galaxies close to more massive halos are more likely to be backsplash galaxies (Wetzel et al., 2014), which is also consistent with the result here.

In order to further understand the distribution of backsplash galaxies around massive halos and their contribution to the two-halo conformity signal for central galaxies, we select all central galaxies around halos with $M_{h}\geq 10^{13}M_{\odot}$ in the IllustrisTNG simulation and calculate their quiescent fractions and backsplash fractions in Fig. 7. The quiescent fractions of central galaxies around these massive halos are shown in gray circles as a function of normalized distance. Here one can see prominent quiescent fraction excess for central galaxies in the vicinity of these massive halos, which is a manifestation of the two-halo conformity effect for central galaxies. Then, we separate these central galaxies into the backsplash ones and non-backsplash ones and plot their quiescent fractions in red and blue colors, respectively. Here one can see that the quiescent fraction for non-backsplash central galaxies shows no excess anymore and coincides with the average quiescent fraction for all non-backsplash galaxies in the simulation volume. This indicates that the quiescent fraction excess around massive halos in the IllustrisTNG simulation, which is responsible for the two-halo conformity effect for central galaxies, all stems from backsplash galaxies. Meanwhile, the right $y$-axis of Fig. 7 shows the fraction of backsplash galaxies among all central galaxies around these massive halos, where the backsplash galaxies range from 20% to 80%. We note that backsplash galaxies dominate (>50%) the central galaxy population within $2R_{\rm 200}$ around these massive systems and gradually declines to $\lesssim 20\%$ around $4R_{\rm 200}$. Eventually, they will approach the average fraction (5%-10%) in the simulation volume, as shown in magenta horizontal dotted lines. We note that those distant backsplash galaxies are not all associated with the halos in question and, instead, from other nearby massive halos (Wetzel et al., 2014). This figure clearly demonstrates that the mere presence of massive halos around central galaxies cannot affect their star formation states, and more violent within-halo environmental processes are required. Nevertheless, it is noteworthy that non-backsplash central galaxies in the vicinity of massive halos may suffer from some other environmental effects, like the termination of gas accretion and the stripping of the circum-galactic medium, as found in previous studies (e.g. Bahé et al., 2013; Behroozi et al., 2014; Ayromlou et al., 2021).

The above results clearly demonstrate that the conformity signal in the IllustrisTNG simulation can be entirely explained by backsplash galaxies. In real observation, since we have no access to their halo merger trees, we can only eliminate the impact of backsplash galaxies by removing galaxies close to any other more massive halos. Here we remove all central galaxies within $4R_{\rm 200}$ of any other more massive halos with $\Delta V<1000\rm km/s$, and Fig. 8 shows the resulting median SSFR and the quiescent fraction for central galaxies as a function of stellar mass and $\Sigma_{\rm cen,5th}$. Here one can see that the dependence of SSFR and quiescent fraction on $\Sigma_{\rm cen,5th}$ are nearly eliminated, indicating this conformity signal is mainly due to the presence of backsplash galaxies. Again, we can still see a weak dependence on $\Sigma_{\rm cen,5th}$. This is consistent with the weak signal presented in Tinker et al. (2017), in which they suggest that this signal is attributed to the correlation between halo formation histories and the star formation activities of central galaxies.

Finally, we want to emphasize that the results in Fig. 5 and Fig. 6 only indicate that the two-halo conformity effect for central galaxies in IllustrisTNG can be explained by backsplash galaxies, but cannot falsify the existence of super-halo-scale environmental effects on low-mass central galaxies. Our results highlight the role played by these backsplash galaxies, even though only $20\%-80\%$ of the central galaxies around massive halos are backsplash galaxies (see Fig. 7). We also emphasize the necessity to control the contribution from these galaxies before we can study the impact of super-halo-scale environmental effects. Finally, investigations on other models can help us better understand the environmental effect, within-halo and super-halo-scale, on galaxies. For example, Ayromlou et al. (2022) performs a similar analysis on the semi-analytical of Ayromlou et al. (2021), where they found that the two-halo conformity effect on central galaxies is still prominent after removing backsplash galaxies from the primary sample and all satellite galaxies are retained in the secondary sample (see their Figure 8).

From Fig. 4, we can also see that massive central galaxies with $M_{*}\gtrsim 10^{11}M_{\odot}$ show strong dependence on $\Sigma_{\rm cen,5th}$, where those in low-density regions are more star-forming than their counterparts in dense regions. Moreover, this dependence is still there after the elimination of the backsplash galaxies (See Fig.8), indicating that this effect cannot be attributed to these backsplash galaxies. A related trend was also pointed out in Tinker et al. (2018a), where they focused on star-forming galaxies and found that star-forming central galaxies preferentially live in low-density regions.

Recently, Zhang et al. (2022) found that star-forming massive central galaxies prefer to reside in low-mass halos than their quiescent counterparts based on weak lensing measurements (see also Mandelbaum et al., 2006; More et al., 2011; Rodriguez-Gomez et al., 2015; Mandelbaum et al., 2016; Zhang et al., 2021a). Consequently, these star-forming central galaxies are less clustered than those quiescent ones (see also Figure 6 of their paper), as expected since massive halos have higher clustering strength (Mo & White, 1996). This result qualitatively agrees with findings in this paper.

To understand the origin of this signal, we investigated their morphology and kinematics, and the results are presented in Fig. 9. On the left panel, we can see that these massive galaxies ($M_{*}\gtrsim 10^{11}M_{\odot}$) in low-density regions are preferentially spiral compared with massive galaxies in dense regions. Meanwhile, from the right panel, one can see that the median central stellar velocity dispersion is also lower for massive galaxies in sparse regions than their counterparts in dense regions by $\sim 15\%$, indicating relatively low-mass bulges and central black holes. All these results together suggest a simple explanation for the conformity signal we observed here. Galaxies in sparse regions experienced fewer merger events (Fakhouri & Ma, 2009; Jian et al., 2012; Kampczyk et al., 2013), thus their spiral morphology keeps intact and the growths of their bulge and central black hole are suppressed. Consequently, they are less likely to be quenched. This explanation is also supported by Posti et al. (2019), where they found that spiral galaxies can convert baryons to stars much more efficiently than galaxies with non-spiral morphology (see also Posti & Fall, 2021; Mancera Piña et al., 2022).

It is noteworthy that the IllustrisTNG simulation cannot reproduce the conformity signal for massive galaxies. In the IllustrisTNG model, the star formation activities of massive central galaxies are mostly determined by the integrated kinetic energy released by the AGN feedback process, or equivalently, the black hole mass (Terrazas et al., 2020; Xu & Peng, 2021; Piotrowska et al., 2022; Bluck et al., 2022). Meanwhile, the mass of central massive black holes strongly correlates with the total stellar mass of their host galaxies (Terrazas et al., 2020; Habouzit et al., 2021). Consequently, the star formation activities of massive central galaxies ($\gtrsim 10^{11}M_{\odot}$) are mostly quenched due to the possession of massive black holes and have no dependence on their large-scale structure. In observation, the star formation activities of central galaxies also mostly depend on the mass of their central black hole (Piotrowska et al., 2022). However, observational results reveal a tight relation between black hole masses and bulge masses (e.g. Magorrian et al., 1998; Kormendy et al., 2011; Kormendy & Ho, 2013), and the relation between bulge masses and the stellar masses of host galaxies is not tight due to a broad distribution of the bulge-to-total mass ratio (B/T) (e.g. Davis et al., 2018), where massive star-forming central galaxies tend to have lower B/T than their quiescent counterparts (Zhang et al., 2021b; Shi et al., 2022).

In this work, we only consider central galaxies in the secondary galaxy sample, while previous studies on the two-halo conformity effect include both central and satellite galaxies. We emphasize that it is helpful to separate these two populations of galaxies for a better understanding of the underlying physical drivers of the two-halo conformity effect.

Before one can study the impact of the two-halo conformity effect on satellite galaxies³³3Satellite galaxies can be within or beyond halo virial radius due to the anisotropic spatial distribution of halos., it is necessary to carefully control the within-halo environmental effect from their own host halos. Previous studies, from both observations and simulations, reveal that the within-halo environmental effect severely affects the properties of satellite galaxies by shutting down the new gas replenishment, stripping the existing cold gas content, and quenching their star formation activities. And the major determinants for the within-halo environmental effect are halo mass and halo-centric distance (e.g. Woo et al., 2013; Wang et al., 2018). Consequently, in order to study the impact of the two-halo conformity on satellite galaxies, one must control the influence of their own host halos, which is beyond the scope of this paper.

Moreover, previous studies found that quiescent central galaxies prefer to live in more massive halos than their star-forming counterparts (e.g. Mandelbaum et al., 2016; Zhang et al., 2022), which is related to the one-halo conformity effect where halos with quiescent central galaxies prefer to host quiescent satellites (Weinmann et al., 2006). Combined with the fact that more massive halos are more clustered (e.g. Mo & White, 1996), satellite galaxies can exhibit the two-halo conformity signal without any new physical processes introduced.