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

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Analytical relations concerning the collapse time in hierarchically clustered cosmological models

M. Gambera 1, 2 and A. Pagliaro 1

1 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


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 [FORMULA] of the shell depends on these parameters. We give a formula that links the dynamical friction coefficient [FORMULA] to the parameters mentioned above and an analytical relation between the collapse time and [FORMULA]. Finally, we obtain an analytical relation between [FORMULA] and the mean overdensity [FORMULA] 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