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 $ 10^{6} M_{\odot}- 10^{9} M_{\odot}$, 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, $ \eta_{0}$, calculated for a perturbation in which clustering is absent and a coefficient $ \eta_{cl}$ obtained from a clustered one. The effect of the dynamical friction is to slow down the collapse (V. Antonuccio-Delogu \& S. Colafrancesco 1994, hereafter AC) producing an observable variation of the parameter of expansion of the shell. The effect increases with increasing $ \eta $ and with the increasing of clustering. Finally, we show how the collapse time depends on $ \eta_{0}$ and $ \eta_{cl}$. keywords: {cosmology: theory- galaxies: formation} 
A. Del Popolo and M. Gambera (Institute of Astronomy of the University   of Catania)