Mass-Velocity Dispersion Relation in HIFLUGCS Galaxy Clusters
  We investigate the mass-velocity dispersion relation (MVDR) in 29 galaxy
clusters in the HIghest X-ray FLUx Galaxy Cluster Sample (HIFLUGCS). We measure
the spatially resolved, line-of-sight velocity dispersion profiles of these
clusters, which we find to be mostly flat at large radii, reminiscent of the
rotation curves of galaxies. We discover a tight empirical relation between the
baryonic mass $M_\mathrm{bar}$ and the flat velocity dispersion $\sigma$ of the
member galaxies, i.e. MVDR,
$\log(M_\mathrm{bar}/M_\odot)=4.1^{+0.4}_{-0.4}\,\log(\sigma/\mathrm{km}\,\mathrm{s}^{-1})+1.6^{+1.0}_{-1.3}$,
with the lognormal intrinsic scatter of $12^{+3}_{-3}\%$. The residuals of the
MVDR are uncorrelated with other cluster properties like temperature, cluster
radius, baryonic mass surface density, and redshift. These characteristics are
reminiscent of the MVDR for individual galaxies, albeit about ten times larger
characteristic acceleration scale. The cluster baryon fraction falls short of
the cosmic value, exposing a problem: the discrepancy increases systematically
for clusters of lower mass and lower baryonic acceleration.
