Mass–Velocity Dispersion Relation in MaNGA Brightest Cluster Galaxies

We investigate a kinematic scaling relation between the baryonic mass and the flat velocity dispersion, i.e., mass–velocity dispersion relation (MVDR), from the brightest cluster galaxies (BCGs) to the galaxy clusters. In our studies, the baryonic mass of BCGs is mainly estimated by photometry. The velocity dispersion profiles are explored with the integrated field unit by Mapping Nearby Galaxies at Apache Point Observatory (MaNGA). For the first time, we reveal two significant results with 54 MaNGA BCGs: (1) the flat velocity dispersion profiles; (2) a tight empirical relation on the BCG-cluster scale together with cluster samples, i.e., MVDR, $\mathrm{log}({M}_{\mathrm{bar}}/{M}_{\odot })={4.1}_{-0.1}^{+0.1}$ $\mathrm{log}({\sigma }_{\mathrm{los}}/\mathrm{km}\,{{\rm{s}}}^{-1})\,+{1.6}_{-0.3}^{+0.3}$, with a tiny lognormal intrinsic scatter of ${10}_{-1}^{+2} \% $. This slope is identical to the acceleration relation in galaxy clusters, which is reminiscent of the spiral galaxies, albeit at a larger characteristic acceleration scale. The residuals of the MVDR represent a Gaussian distribution, displaying no correlations with four properties: baryonic mass, scale length, surface density, and redshift. Notably, the MVDR on the BCG-cluster scale provides a strict test, which disfavors the general prediction of the slope of three in the dark matter model.