Tidal Torques Dynamical Friction and the Structure of Clusters of Galaxies

Abstract

We study the joint effect of tidal torques and dynamical friction on the collapse of density peaks solving numerically the equations of motion of a shell of barionic matter falling into the central regions of a cluster of galaxies. We calculate the evolution of the expansion parameter, a(t), of the perturbation using a coefficient of dynamical friction η_cl obtained from a clustered system and taking into account the gravitational interaction of the quadrupole moment of the system with the tidal field of the matter of the neighboring proto-galaxies. We find that the tidal torques and the dynamical friction slow down the collapse of low-v (v < 3) peaks producing an observable variation of a(t) (Del Popolo & Gambera 1996,1997). As consequence we have a reduction of the mass bound to collapsed perturbations and a raising of the critical threshold, δ_c. Besides, we have a bias of dynamical nature arises because high-density peaks preferentially collapse to form halos within which visible objects. We calculate the selection function and using it and the prescriptions given by Bardeen et al. 1986 we find a value of the coefficient of bias, b = 2.25 on clusters scales for R_f = 4h^–1Mpc comparable both with that obtained from the mean mass-to-light ratio of clusters, APM survey, or from N-body simulations combined with hydrodynamical models and with the values of b given by Kauffmann et al. 1996. This means that non-radial motions and dynamical friction play a significant role in determining the bias level.