Small scale substructure, collapse time and dynamical friction

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} \div 10^{9} M_{\odot}$, taking into account the dynamical friction and the parameters on which it depends: the peaks’ height ${\nu }_c$, the number of peaks inside a protocluster $N_{tot}$ multiplied by the correlation function $\xi (r)$ evaluated at r=0, the filtering radius $R_f$ and the core radius of the cluster of galaxies, r_0. We show how the collapse time of a shell of baryonic matter depends on those parameters.