EFFECTS OF LARGE-SCALE ENVIRONMENT ON THE ASSEMBLY HISTORY OF CENTRAL GALAXIES

We performed a cosmological dark matter-only simulation using parameters of the standard concordance cold dark matter cosmology using a cosmological constant Ω_Λ = 0.728, a current matter density parameter Ω_m = 0.272, the normalization factor of the initial power spectrum σ₈ = 0.809, the spectral index n = 0.963, and the Hubble constant H₀ = 100 h km s⁻¹ with h = 0.704. These parameter values are based on the seven-year Wlikinson Microwave Anisotropy Probe observations (Jarosik et al. 2011). The cosmological hydrodynamic code used in this work is GADGET-2 (Springel 2005). For the simulation, a periodic box-size was chosen as 100 h⁻¹ Mpc with 1024³ dark matter particles.¹ The dark matter particle mass was 6.9 × 10⁸ h⁻¹ M_☉ and the gravitational softening length was 2.441 h⁻¹ kpc. The dark matter particle position and velocity information were stored for 117 time steps between z = 13 and z = 0. The initial condition of the simulation was produced using MPgrafics (Prunet et al. 2008), which is a parallel version of Grafic1 (Bertschinger 2001).

In order to trace the formation and the mass assembly history of halos, we built dark matter halo merger trees from an N-body simulation. Our treebuilder, ySAMtm, was implemented into the semi-analytic model (ySAM; Lee & Yi 2013).

The first step in building dark matter halo merger trees is structure detection. We used the structure finding code AHF (Knollmann & Knebe 2009) in this work. We define the halo center as the position of the densest region in the halo, as the center of mass is not a proper position for halos undergoing mergers. The halos and subhalos in the simulation are supposed to have at least 20 particles.

From the results of structure detection, we constructed dark matter halo merger trees. Figure 1 briefly describes the definition of dark matter halo mergers. We define the beginning of the halo mergers using the virial radius criterion. A detailed procedure for building halo merger trees can be explained as follows.

• 1.  
  Calculate the shared mass between halos. The shared mass between halos at two subsequent snapshots is calculated by tracing the particle transfer between those halos. At this step, particle transfers between halos in two snapshots are tracked using particle indexes and individual particles should be included in a single halo or subhalo. Particles in a subhalo are not listed in the main halo of the subhalo.
• 2.  
  Define a unique descendant halo. In order to be applicable to semi-analytic models, we find the unique descendant halos of individual progenitor halos. For one progenitor halo, the shared masses of its descendant halos are compared and the descendant halo with the largest shared mass among those descendants is assigned as a unique descendant halo of the progenitor. However, if another descendant halo receives the largest fraction of its mass from the same progenitor, we determine this descendant halo to be a unique descendant of the progenitor, even if the shared mass of the descendant is not the largest compared to the other descendants. This additional process is needed to avoid a situation in which the small descendant halo is considered to be otherwise newly born. Thus far, one descendant halo can be connected to multiple progenitor halos, whereas a single progenitor must have a unique descendant. If one descendant halo has multiple progenitors, the main progenitor halo is determined by maximizing M_{shared, i}/M_descendant, where M_{shared, i} is the shared mass between the descendant halo and the progenitor halo and i is the list index of the progenitor halo. In Figure 1, the black (thin) solid arrows indicate a unique descendant–progenitor relation.
• 3.  
  Find the end of the merger events. The end of the halo mergers is defined as the moment when two progenitor halos have an identical descendant halo at the next snapshot. In Figure 1, the main halo and its subhalo at z = 0.02 have the same descendant halo at z = 0. In this case, we consider z = 0 to be the epoch when a halo merger is complete.
• 4.  
  Detect the beginnings of halo mergers. In order to do this, the progenitors of both the primary main halo and its subhalo are tracked backward, starting from the end of merger. At every output, the distance between the two progenitors is compared to the virial radius of the primary halo. The moment when the small halo crosses the virial radius of the main halo is considered to be the beginning of the halo merger. This is equivalent to the moment when the small halo merges with the larger halo and becomes its substructure. As seen in Figure 1, the small halo becomes a subhalo between z = 0.06 and z = 0.04, which defines the beginning of the halo merger.
• 5.  
  Build the merger trees of individual halos. For each halo at z = 0, the whole merger history is constructed by backward tracking progenitor halos including all progenitors of the halos that have finally merged into the object halo.

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Flyby events between halos can significantly inflate the number of halo mergers by double counting (Fakhouri & Ma 2008; Genel et al. 2009). By considering only the subhalos that were supposed to be finally merged and by tracing backward, we avoided the overestimation of halo mergers caused by flybys.

The goal of this study is to investigate the environmental effects in large scales; therefore, we need to define the large-scale environment of halos. In the literature, there are two ways to measure the large-scale environment. The first is to measure the local overdensity in a sphere of radius R centered at a halo (e.g., Lemson & Kauffmann 1999; Wang et al. 2007; Maulbetsch et al. 2007; Fakhouri & Ma 2009; Hahn et al. 2009; Tillson et al. 2011), and the other is to measure the halo bias using the two-point correlation function (e.g., Sheth & Tormen 2004; Gao et al. 2005; Harker et al. 2006; Wechsler et al. 2006; Gao & White 2007; Croton et al. 2007; Wang et al. 2013). Although the two-point correlation function is widely used to study the relations between halo clustering and halo properties (formation, merger, dynamical structure, etc.), the correlation function itself is only dependent on the number of halo pairs. On the other hand, the local overdensity more directly reflects the matter distribution of both the internal and external regions of halos. Therefore, we chose to use the former method.

The definition of the local overdensity (δ_R) is the same as that in Fakhouri & Ma (2009, 2010) and can be calculated as follows:

$$\begin{eqnarray} &&\delta _{R} \equiv \frac{\rho _{R} - \bar{\rho _{m} } }{\bar{\rho _{m} } }, \end{eqnarray} \tag{ 1 }$$

where ρ_R is the matter density in a sphere with radius R, and $\bar{\rho _{m}}$ is the mean matter density in a simulation box. The contribution of the central halo mass is removed by

$$\begin{eqnarray} &&\delta _{R-\rm Halo} \equiv \delta _{R} - \frac{M_{\rm Halo}}{V_{R} \bar{\rho _{m}}}, \end{eqnarray} \tag{ 2 }$$

where M_Halo is the mass of the central halo and V_R is the volume of the sphere.

It is worth mentioning how we choose the sphere radius for measuring the local overdensity. In order to understand the impact of different sphere radii, we calculated the local overdensity with various values (3 h⁻¹ Mpc, 5 h⁻¹ Mpc, 7 h⁻¹ Mpc, and 9 h⁻¹ Mpc). The results did not differ significantly with different sphere radii, which is consistent with previous studies (Sheth & Tormen 2004; Croton et al. 2007; Maulbetsch et al. 2007). However, similar to the results presented in Fakhouri & Ma (2009), we also found that the centric distance of the farthest particle sometimes exceeded 5 h⁻¹ Mpc for massive halos. Therefore, we used 7 h⁻¹ Mpc in this study.

In order to compare halos at a fixed mass in different large-scale environments, we classified the halos in the present universe into three mass bins: 10^11.0–10^11.5 h⁻¹ M_☉, 10^11.5–10^12.0 h⁻¹ M_☉, and 10^12.0–10^13.0 h⁻¹ M_☉. This range of halo mass roughly covers single galaxies to small clusters. We focused on halos with the mass range 10¹¹–10¹³ h⁻¹ M_☉ at z = 0 because there were not enough massive halos (≳ 10¹³ h⁻¹ M_☉) to be statistically analyzed, and smaller halos (≲ 10¹¹ h⁻¹ M_☉) were excluded due to the resolution limits of our simulation. The definitions of high density and low density in large-scale environments were selected to be the top 20% and the bottom 20% of the local overdensity distribution (δ_{7 − Halo}).

The spatial distribution of halos is only slightly dependent on halo mass; the average mass of halos in high-density regions is slightly larger than that of the halos in low-density regions even at the same mass bin. For all identified halos with the mass range 10^12.0–10^13.0 h⁻¹ M_☉, the average mass of halos in denser regions (the top 20%) is 2.73 × 10¹² h⁻¹ M_☉, while that of halos in less dense regions (the bottom 20%) is 1.87 × 10¹² h⁻¹ M_☉. To minimize the effect of halo mass dependence, we selected the same number of halos for different density groups until the average masses of halos in those groups became virtually identical.

Table 1 presents the number and the average mass of the sample halos for each group, and Figure 2 illustrates the distribution of dark matter halos. As seen In Figure 2, the upper panel displays the distribution of all halos more massive than 10¹¹ h⁻¹ M_☉ in a 30 h⁻¹ Mpc slice in the simulation. The grayscale system represents the local overdensity δ_{7 − Halo}; the darker circles indicate halos in denser regions. In the bottom panel, our sample halos are overplotted on the upper panel image (Table 1). The red and blue circles are halos in high-density (the upper 20%) and low-density (the bottom 20%) regions, respectively.

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The main purpose of this paper is to investigate the effects of the halo assembly bias on real galaxies. For this purpose, we used a semi-analytic model (ySAM; Lee & Yi 2013). In the model, the mass accretion and mergers of galaxies follow the evolution of each halo merger tree, and many processes of baryonic physics (gas cooling, star formation, feedback processes, etc.) are calculated using simple prescriptions. Lee & Yi (2013) demonstrated that their model is calibrated to reproduce recent empirical data, and Yi et al. (2013) showed that the merger history of galaxies predicted by the model is comparable to the observational results of the cluster galaxies in Sheen et al. (2012).

To investigate the impact of various SAM parameters on our results presented in the parer, we varied the efficiencies of active galactic nuclei and supernovae feedbacks, which are considered important mechanisms in galaxy growth, in a factor of two ranges: from half to twice of our fiducial values. These wide ranges of efficiencies made noticeable differences in the galaxy stellar mass function at z = 0. We confirmed, however, that our result is not sensitive at all to the variation of feedback efficiencies.

We perform our test on central galaxies because our research focus is on the assembly bias of host halos reflecting the outer environments of those halos and central galaxies directly follow the formation and the mass growth of their host halos. Satellite galaxies, on the other hand, are more likely to be affected by their host halo environment.

In the current galaxy formation theory, the gas accretion in galaxies is strongly affected by the assembly history of dark matter halos. In this section, we present the assembly history of halos and their central galaxies, comparing the average values between different density environments at a fixed halo mass, as shown in Table 1.

Figure 3 shows the average mass growth of dark matter halo (top), hot gas (middle), and cold gas (bottom) components. The average masses are compared in three different halo mass bins: 10^11.0–10^11.5 h⁻¹ M_☉, 10^11.5–10^12.0 h⁻¹ M_☉, and 10^12.0–10^13.0 h⁻¹ M_☉ at z = 0 (from left to right). The dashed curve was calculated using halos in a high-density environment (the top 20%), and the dotted curve was computed using those in a low-density environment (the bottom 20%). The vertical arrows indicate the formation time² of dark matter halos.

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In the top row of Figure 3, the average mass of the halos shows that halos form earlier in denser regions than in less dense regions, and the difference in the halo formation time is larger in lower-mass halos (panel (a)). This is in agreements with the previous studies (e.g., Gao et al. 2005; Harker et al. 2006; Wechsler et al. 2006; Fakhouri & Ma 2010). In the case of gaseous components, the growth trend of hot gas (middle row) is very similar to that of dark matter halos, and the cold gas component (bottom row) follows the trend of dark matter halos and hot gas. In the semi-analytic model, the amount of hot gas accreted onto dark matter halos follows the global baryonic fraction, Ω_b/Ω_m, and cold gas increases from the cooling of the hot gas component. Thus, the mass growth of hot and cold gas is similar to that of dark matter halos.

Following the growth history of gaseous components, we investigate the star formation history and the mass growth of stellar mass in central galaxies. Figure 4 shows the SFRs (top) and the specific SFRs (SSFRs; bottom) in the same mass bins as in Figure 3.

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In the top row, the SFRs of central galaxies in smaller halos (≲ 10¹² h⁻¹ M_☉) are slightly higher in denser regions than in less dense regions, although they are almost the same in the case of more massive halos. This is because the central galaxies in smaller halos have more cold gas in high-density regions than in low-density regions (see panel (g) in Figure 3), and the SFR is strongly dependent on the amount of cold gas.

On the other hand, the SSFRs, the normalized SFRs, show the same feature in both high- and low-density environments in all of the mass bins (bottom panels in Figure 4), which indicates that the amount of newly formed stars per unit stellar mass is almost the same. This is consistent with a previous observational study on the star formation history by Kauffmann et al. (2004), who concluded that the SSFR minimally depends on environments larger than 1 Mpc from a galaxy.

This section describes the mass growth rates of both halos and their central galaxies in an attempt to more directly search for the evidence of the assembly bias in the baryonic universe. Maulbetsch et al. (2007) investigated halo mass growth using an N-body simulation and concluded that at present, low-mass halos are more apt to accrete their mass in low-density regions than in high-density regions because halos in high-density regions form earlier. This means that halos in denser regions (e.g., filaments) grow faster than those in less dense region (e.g., voids) when halos mass is fixed.

As seen in the first row of Figure 5, we reconfirmed that smaller halos in high-density regions grow faster. However, based on the mass growth rates of central galaxies (middle row), we cannot find evidence of any considerable dependence on the large-scale environment in any mass bins. In particular, in low-mass halos where mass growth shows a stronger assembly bias, the difference between the mass growth rates becomes mostly diminished in galaxies (panel (d)).

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The panels in the bottom row show the stellar mass of central galaxies. The galaxy formation times (vertical arrows) are not sensitive to the large-scale environments, even in smaller halos where halos show a relatively stronger bias for assembly time (see panel (a) of Figure 3). However, as a consequence of the higher SFR in small halos, stellar mass is slightly larger in denser regions than in less-dense regions (panel (g)).