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

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3. How the collapse time depends on the dynamical friction

Like DG97, we have solved Eq. (7) numerically and calculated the collapse time [FORMULA] for different values of the dynamical friction coefficent [FORMULA]. However, DG97 showed the dependence of [FORMULA] on [FORMULA] qualitatively, whilst we have found also an analytical relation [FORMULA] that links [FORMULA] with [FORMULA] in the range of values [FORMULA] (see also Gambera 1997). The results of our calculations are shown in Fig. 5, where we report the collapse time [FORMULA] versus the dynamical friction coefficient. We have determined the function [FORMULA] through a least squares fit method. Our best solution is given by:

[EQUATION]

with:

[EQUATION]

Eq. (21) and our results for [FORMULA] from the numerical integration of Eq. (7) are in excellent agreement. As a matter of fact, the correlation coefficient value obtained is: [FORMULA].

[FIGURE] Fig. 5. Collapse time [FORMULA] of a shell of matter made of galaxies and substructure when dynamical friction is taken into account, versus [FORMULA].

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© European Southern Observatory (ESO) 1998

Online publication: May 15, 1998

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