Brightest group galaxies-II: the relative contribution of BGGs to the total baryon content of groups at z<1.3

We performed a detailed study of the evolution of the star formation rate (SFR) and stellar mass of the brightest group galaxies (BGGs) and their relative contribution to the total baryon budget within R_200 (f^BGG_b,200). The sample comprises 407 BGGs selected from X-ray galaxy groups (M_200=10^12.8-10^14 M_⊙) out to z∼1.3 identified in the COSMOS, XMM-LSS, and AEGIS fields. We find that BGGs constitute two distinct populations of quiescent and star-forming galaxies and their mean SFR is ∼2 dex higher than the median SFR at z<1.3. Both the mean and the median SFRs decline with time by >2 dex. The mean (median) of stellar mass of BGGs has grown by 0.3 dex since z=1.3 to the present day. We show that up to ∼45% of the stellar mass growth in a star-forming BGG can be due to its star-formation activity. With respect to f^BGG_b,200, we find it to increase with decreasing redshift by ∼0.35 dex while decreasing with halo mass in a redshift dependent manner. We show that the slope of the relation between f^BGG_b,200 and halo mass increases negatively with decreasing redshift. This trend is driven by an insufficient star-formation in BGGs, compared to the halo growth rate. We separately show the BGGs with the 20% highest f^BGG_b,200 are generally non-star-forming galaxies and grow in mass by processes not related to star formation (e.g., dry mergers and tidal striping). We present the M_⋆-M_h and M_⋆/M_h-M_h relations and compare them with semi-analytic model predictions and a number of results from the literature. We quantify the intrinsic scatter in stellar mass of BGGs at fixed halo mass (σ_log M_⋆) and find that σ_log M_⋆ increases from 0.3 dex at z∼0.2 to 0.5 dex at z∼1.0 due to the bimodal distribution of stellar mass.