Astron. Astrophys. 334, 381-387 (1998)

Analytical relations concerning the collapse time in hierarchically clustered cosmological models

M. Gambera ^{1, 2} and A. Pagliaro <sup>1

1</sup> Istituto di Astronomia dell'Università di Catania, Viale A.Doria 6, I-95125 Catania, Italy
² Osservatorio Astrofisico di Catania and CNR-GNA, Viale A.Doria 6, I-95125 Catania, Italy

Received 2 June 1997 / Accepted 2 September 1997

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 of the shell depends on these parameters. We give a formula that links the dynamical friction coefficient to the parameters mentioned above and an analytical relation between the collapse time and . Finally, we obtain an analytical relation between and the mean overdensity within the shell. All the analytical relations that we find are in excellent agreement with the numerical integration.

Key words: cosmology: theory large scale structure of Universe galaxies: formation

Send offprint requests to: M. Gambera, (mga@sunct.ct.astro.it)

© European Southern Observatory (ESO) 1998

Online publication: May 15, 1998

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