Velocity Bias in MS1224+20

Abstract

Velocity bias offers a single parameter ($b_v$) description of the likely segregation of mass and light in a galaxy cluster. The relation between the projected mass profile and the light profile, normalized by the virial $M/L$, is presented as a function of $b_v\equivσ_\ell/σ_ρ$, the ratio of the RMS velocity dispersions of the galaxies and the underlying dark matter. The light distribution does not trace the mass at any radius within the cluster. At the apparent harmonic radius the gravitational mass can exceed the virial mass calculated from the light by about a factor of 2 (or more). The data for the MS1224+20 cluster, covering nearly a decade in radius, are well described by a velocity bias value of $b_v=0.85\pm0.05$, comparable to the n-body estimate of $b_v=0.8\pm0.1$. This particular value will remain tentative until more data are available.