Analytical relations concerning the collapse time in hierarchically clustered cosmological models
Abstract
By means of numerical methods, we solve the equations of motion for the collapse of a shell of baryonic matter, made of galaxies and substructure falling into the central regions of a cluster of galaxies, taking into account effect of the dynamical friction. The parameters on which the dynamical friction mainly depends are: the peaks' height, the number of peaks inside a protocluster multiplied by the correlation function evaluated at the origin, the filtering radius and the nucleus radius of the protocluster of galaxies. We show how the collapse time tau of the shell depends on these parameters. We give a formula that links the dynamical friction coefficient eta to the parameters mentioned above and an analytical relation between the collapse time and eta . Finally, we obtain an analytical relation between tau and the mean overdensity {/line delta } within the shell. All the analytical relations that we find are in excellent agreement with the numerical integration.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 June 1998
 arXiv:
 arXiv:astroph/9708173
 Bibcode:
 1998A&A...334..381G
 Keywords:

 COSMOLOGY: THEORY;
 LARGE SCALE STRUCTURE OF UNIVERSE;
 GALAXIES: FORMATION;
 Astrophysics
 EPrint:
 16 pages with 5 figures included, (Latex, laa style). Accepted by Astronomy &