Possible Relations between Brightest Central Galaxies and Their Host Galaxies Clusters and Groups

In this section, we explore the relations between physical properties of the BCGs and their host clusters and groups. We consider absolute magnitude and central velocity dispersion as mass representatives of BCGs and BGGs. To measure the mass of cluster and group, we use σ_cl. Figure 1 shows σ_cl of clusters and groups as a function of their redshifts (z). It is clear that most of clusters and groups have σ_cl higher than 300 km s⁻¹.

Fig. 1

In Figure 2, we plot the distribution of BCGs with their spectroscopic redshifts in the r-band.

Fig. 2

Figure 3(a) shows the r-band R_e of BCGs with respect to redshifts of their host clusters and groups. It is clear that galaxies are having larger R_e as the redshift of their host environment increases. Figure 3(b) shows R_e of BCGs as a function of σ_cl of their host clusters and groups. Error bars represent the average values of σ_cl in every R_e bins with errors. There is a tight correlation between R_e of BCGs and σ_cl of their clusters and groups. As a result, the most massive clusters and groups host central galaxies with larger values of R_e.

Fig. 3

Figure 4(a) shows the r-band absolute magnitude of BCGs as a function of the redshift of their host clusters and groups. While BCGs are very bright (M_r < −22 mag) across redshift range, low redshift clusters and groups (z ≤ 0.04) host less luminous BCGs. These low redshift systems have also lower values of σ_cl as clear in Figure 1. Figure 4(b) shows the r-band absolute magnitude of BCGs as a function of σ_cl. It is clear from this figure that clusters or groups with higher velocity dispersions host the brighter central galaxies which is consistent with previous studies [4, 14, 15].

Fig. 4

Figure 5(a) presents σ_o of BCGs in r-band with respect to the redshift of their host clusters and groups. In general, values of σ_o increase along the entire redsift range. In Figure 5(b), we plot σ_o of BCGs as a function of σ_cl of their host clusters and groups. This figure shows that there is a correlation between σ_o of BCGs and σ_cl of their host environment. We can say that σ_o of BCG depends on its host cluster or group mass. The observed relation between σ_o and σ_cl provides an important test for the formation models of galaxies and clusters.

Fig. 5

We found that σ_o of BCG correlates with σ_cl, which represents a cluster and group halo mass proxy. Here we compare the observed relation with predictions from numerical simulations by [3] and [5]. [3] performed their simulation taking into account heating by a UV background, radiative cooling, star formation and feedback. With more than 20 satellite galaxies, they identified 44 clusters. Some star particles were identified which are not bound to any subhalo within the cluster potential. Those star particles are either a diffuse stellar component (DSC) or the BCGs stellar component (cD galaxies). They separated those two components and calculated velocity dispersions for them.

Fig. 6

Figure 6 shows that the relation between σ_o and σ_cl decreases as a function of σ_cl which is also consistent with previous result from [10]. They studied the relation between 227 BCGs and their host clusters in the redshift range 0.02 < z < 0.30. They found a tight relation between BCG velocity dispersion and cluster velocity dispersion. They found that the ratio of BCG velocity dispersion and cluster velocity dispersion decreases as a function of velocity dispersion of the host cluster. On the other side, the simulation of [3] suggests a constant relation between σ_o and σ_cl along a wide range of σ_cl. Also numerical simulations of [5] represents the same constant relation. In Figure 6, error bars represent the average values of σ_o/σ_cl in different σ_cl bins with errors. The black solid and dashed lines represent the relation and the 1σ deviation from simulation. In that simulation of [3], the velocity dispersion of BCGs, DSC, and cluster galaxies are well correlated with virial mass of cluster halo. We can say that the observed σ_o/σ_cl ratio depends on cluster and group mass which suggests that the mass fraction associated with brightest central galaxies indicate the evolution of brightest central galaxies and their host halos.