The relation between velocity dispersion and mass in simulated clusters of galaxies: dependence on the tracer and the baryonic physics

We present an analysis of the relation between the masses of cluster-and group-sized haloes, extracted from Lambda cold dark matter (Lambda CDM) cosmological N-body and hydrodynamic simulations, and their velocity dispersion at different redshifts from z = 2 to 0. The main aim of this analysis is to understand how the implementation of baryonic physics in simulations affects such relations, i.e. to what extent the use of the velocity dispersion as a proxy for cluster mass determination is hampered by the imperfect knowledge of the baryonic physics. In our analysis, we use several sets of simulations with different physics implemented: one DM-only simulation, one simulation with non-radiative gas, and two radiative simulations, one of which with feedback from active galactic nuclei. Velocity dispersions are determined using three different tracers: DM particles, subhaloes and galaxies. We confirm that DM particles trace a relation that is fully consistent with the theoretical expectations based on the virial theorem, sigma(v) proportional to M-alpha with alpha = 1/3, and with previous results presented in the literature. On the other hand, subhaloes and galaxies trace steeper relations, with velocity dispersion scaling with mass with alpha > 1/3, and with larger values of the normalization. Such relations imply that galaxies and subhaloes have a similar to 10 per cent velocity bias relative to the DM particles, which can be either positive or negative, depending on the halo mass, redshift and physics implemented in the simulation. We explain these differences as due to dynamical processes, namely dynamical friction and tidal disruption, acting on substructures and galaxies, but not on DM particles. These processes appear to be more or less effective, depending on the halo masses and the importance of baryon cooling, and may create a non-trivial dependence of the velocity bias and the sigma(1D)-M-200 relation on the tracer, the halo mass and its redshift. These results are relevant in view of the application of velocity dispersion as a proxy for cluster masses in ongoing and future large redshift surveys.