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

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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 R₂₀₀ (fBGGb,₂₀₀). The sample comprises 407 BGGs selected from X-ray galaxy groups (M₂₀₀=10¹².⁸-10¹⁴ 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 fBGGb,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 fBGGb,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 fBGGb,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⋆-Mₕ and M⋆/Mₕ-Mₕ 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 (σlog M⋆) and find that σlog 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.