Examining Baryonic Faber-Jackson Relation in Galaxy Groups

We investigate the Baryonic Faber-Jackson Relation (BFJR), examining the correlation between baryonic mass and velocity dispersion in galaxy groups and clusters. Originally analysed in elliptical galaxies, the BFJR is derivable from the empirical Radial Acceleration Relation (RAR) and MOdified Newtonian Dynamics (MOND), both showcasing a characteristic acceleration scale $g_\mathrm{\dagger}=1.2\times10^{-10}\,\mathrm{m}\,\mathrm{s}^{-2}$. Recent interpretations within MOND suggest that galaxy group dynamics can be explained solely by baryonic mass, hinting at a BFJR with $g_{\dagger}$ in these systems. To explore this BFJR, we combined X-ray and optical measurements for six galaxy clusters and 13 groups, calculating baryonic masses by combining X-ray gas and stellar mass estimates. Simultaneously, we computed spatially resolved velocity dispersion profiles from membership data using the biweight scale in radial bins. Our results indicate that the BFJR in galaxy groups, using total velocity dispersion, aligns with MOND predictions. Conversely, galaxy clusters exhibit a parallel BFJR with a larger acceleration scale. Analysis using tail velocity dispersion in galaxy groups shows a leftward deviation from the BFJR. Additionally, stacked velocity dispersion profiles reveal two distinct types: declining and flat, based on two parallel BFJRs. The declining profile, if not due to the anisotropy parameters or the incomplete membership, suggests a deviation from standard dark matter density profiles. We further identify three galaxy groups with unusually low dark matter fractions.