Stellar mass -- halo mass relation for the brightest central galaxies of X-ray clusters since z~0.65

We present the brightest cluster galaxies (BCGs) catalog for SPectroscoic IDentification of eROSITA Sources (SPIDERS) DR14 cluster program value-added catalog. We list the 416 BCGs identified as part of this process, along with their stellar mass, star formation rates, and morphological properties. We identified the BCGs based on the available spectroscopic data from SPIDERS and photometric data from SDSS. We computed stellar masses and SFRs of the BCGs on the basis of SDSS, WISE, and GALEX photometry using spectral energy distribution fitting. Morphological properties for all BCGs were derived by Sersic profile fitting using the software package SIGMA in different optical bands (g,r,i). We combined this catalog with the BCGs of galaxy groups and clusters extracted from the deeper AEGIS, CDFS, COSMOS, XMM-CFHTLS, and XMM-XXL surveys to study the stellar mass - halo mass relation using the largest sample of X-ray groups and clusters known to date. This result suggests that the mass growth of the central galaxy is controlled by the hierarchical mass growth of the host halo. We find a strong correlation between the stellar mass of BCGs and the mass of their host halos. This relation shows no evolution since z $\sim$ 0.65. We measure a mean scatter of 0.21 and 0.25 for the stellar mass of BCGs in a given halo mass at low ( $0.1<z < 0.3$ ) and high ( $0.3<z<0.65$ ) redshifts, respectively. We further demonstrate that the BCG mass is covariant with the richness of the host halos in the very X-ray luminous systems. We also find evidence that part of the scatter between X-ray luminosity and richness can be reduced by considering stellar mass as an additional variable.