COSMOS Brightest Group Galaxies -- III: Evolution of stellar ages

The unique characteristics of the brightest group galaxies (BGGs) link the evolutionary continuum between galaxies like the Milky Way and more massive BCGs in dense clusters. This study investigates the stellar properties of BGGs over cosmic time (z = 0.08-1.30), extending our previous work (Gozaliasl et al. 2016, 2018; Paper I and Paper II). We analyze data of 246 BGGs from our X-ray galaxy group catalog in the COSMOS field, examining stellar age, mass, star formation rate (SFR), specific SFR (sSFR), and halo mass. Comparisons are made with Millennium and Magneticum simulations. We explore the variation of stellar properties with the projected offset from the X-ray peak or host halo center. Using a mock galaxy catalog, we evaluated the accuracy of SED-derived stellar ages, finding a mean absolute error of about one Gyr. Observed BGG age distributions show a bias towards younger ages compared to semi-analytical models and the Magneticum simulation. Our analysis of stellar age versus mass reveals trends with a positive slope, suggesting complex evolutionary pathways across redshifts. We observe a negative correlation between stellar age and SFR across all redshift ranges. Using a cosmic-time-dependent main sequence framework, we identify star-forming BGGs, finding that about 20% of BGGs in the local universe exhibit star-forming characteristics, increasing to 50% at $z=1.0$. Our findings support an inside-out formation scenario for BGGs, where older stellar populations are near the X-ray peak and younger populations at larger offsets indicate ongoing star formation. The distribution of stellar ages for lower-mass BGGs ($10^{10-11} M_\odot$) deviates from constant ages predicted by models, highlighting current models' limitations in capturing galaxies' complex star formation histories.