Dynamical evolution of clusters of galaxies: the effect of high- velocity substructure clumps

In the Cold Dark Matter (hereafter CDM) scenario even isolated density peaks contain a high fraction of small scale clumps having velocities larger than the average escape velocity from the structure. These clumps populate protoclusters, especially in the peripheral regions, r > R_f (where R_f is the filtering scale). During the cluster collapse and the subsequent secondary infall, collapsing or infalling clumps (having v<v_esc) interact with the quoted unbound clumps (or high speed clumps, as we also call them) having v > v_esc. We study the interaction between these two kind of clumps by means of the impulse approximation and we find that the collapse of bound clumps is accelerated with respect to the homogeneous case (Gunn & Gott's model). The acceleration of the collapse increases with decreasing height of the peak, \nu. We finally compare the acceleration produced by this effect to the slowing down effect produced by the gravitational interaction of the quadrupole moment of the system with the tidal field of the matter of the neighboring proto-clusters studied in Del Popolo & Gambera. We find that the magnitude of the slowing down effect is larger than the acceleration produced by the effect studied in this paper, only in the outskirts of the cluster. We want to stress that the one which we study in this paper is also present in an isolated protocluster, being produced by the interaction of the collapsing clumps with the unbound substructure internal to the collapsing clumps itself while that studied in Del Popolo & Gambera (1998) is produced by substructure external to the density peak.