Tidal Torques Dynamical Friction and the Structure of Clusters of Galaxies

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 eta_{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 show that within high-density environments, such as rich clusters of galaxies, tidal torques and dynamical friction slow down the collapse of low-nu peaks producing an observable variation of the parameter of expansion of the shell. As a consequence a bias of dynamical nature arises because high-density peaks preferentially collapse to form halos within which visible objects eventually will condense. For a standard Cold Dark Matter model this dynamical bias can account for a substantial part of the total bias required by observations on cluster scales.