Substructure effects on the collapse of density perturbations

We solve numerically the equations of motion for the collapse of a shell of baryonic matter, made of galaxies and substructure of 10M⊙−10M⊙, falling into the central regions of a cluster of galaxies taking account of dynamical friction. We calculate the evolution of the expansion parameter, a(t), of the perturbation using a coefficient of dynamical friction, η0, calculated for a perturbation in which clustering is absent and a coefficient ηcl obtained from a clustered one. The effect of the dynamical friction is to slow down the collapse (V. AntonuccioDelogu & S. Colafrancesco 1994, hereafter AC) producing an observable variation of the parameter of expansion of the shell. The effect increases with increasing η and with the increasing of clustering. Finally, we show how the collapse time depends on η0 and ηcl.