The concentration–velocity dispersion relation in galaxy groups

Based on results from cold dark matter N ‐body simulations, we develop a dynamical model for the evolution of subhaloes within group‐sized host haloes. Only subhaloes more massive than 5 × 10 8  M ⊙ are considered, because they are massive enough to possibly host luminous galaxies. On their orbits within a growing host potential the subhaloes are subject to tidal stripping and dynamical friction. At the present time ( z = 0) , all model hosts have equal mass ( M vir = 3.9 × 10 13  M ⊙ ) but different concentrations associated with different formation times. We investigate the variation of subhalo (or satellite galaxy) velocity dispersion with host concentration and/or formation time. In agreement with the Jeans equation, the velocity dispersion of subhaloes increases with the host concentration. Between concentrations of ∼5 and ∼20, the subhalo velocity dispersions increase by a factor of ∼1.25. By applying a simplified tidal disruption criterion, that is, rejection of all subhaloes with a tidal truncation radius below 3  kpc at z = 0 , the central velocity dispersion of the ‘surviving’ subhalo sample increases substantially for all concentrations. The enhanced central velocity dispersions in the surviving subhalo samples are caused by a lack of slow tangential motions. Additionally, we present a fitting formula for the anisotropy parameter which does not depend on concentration if the group‐centric distances are scaled by r s , the characteristic radius of the Navarro, Frenk & White profile. Since the expected loss of subhaloes and galaxies due to tidal disruption increases the velocity dispersion of surviving galaxies, the observed galaxy velocity dispersion can substantially overestimate the virial mass.