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Astron. Astrophys. 337, 96-104 (1998)

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6. Conclusions

In this paper we have studied the role of non-radial motions on the collapse of density peaks solving numerically the equations of motion of a shell of barionic matter falling into the central regions of a cluster of galaxies. We have shown that non-radial motions produce a delay in the collapse of density peaks having a low value of [FORMULA] while the collapse of density peaks having [FORMULA] is not influenced. A first consequence of this effect is a reduction of the mass bound to collapsed perturbations and an increase in the critical threshold, [FORMULA], which now is larger than that of the top-hat spherical model and depends on [FORMULA]. This means that shells of matter of low density have to be subject to a larger gravitational potential, with respect to the homogeneous GG's model, in order to collapse.

The delay in the proto-structures collapse gives rise to a dynamical bias similar to that described in CAD whose bias parameter may be obtained once a proper selection function is defined. The selection function found is not a pure Heaviside function and is different from that used by BBKS to study the statistical properties of clusters of galaxies. Its shape depends on the effect of non-radial motions through its dependence on [FORMULA]. The function [FORMULA] selects higher and higher density peaks with increasing value of [FORMULA] due to the smoothing effect of the density field produced by the filtering procedure. Using this selection function and BBKS prescriptions we have calculated the coefficient of bias b.

On clusters scales for [FORMULA] we found a value of [FORMULA] comparable with that obtained from the mean mass-to-light ratio of clusters, APM survey, or from N-body simulations combined with hydrodynamical models (Frenk et al. 1990). Morever, the value of the coefficient of biasing b that we have calculated is comparable with the values of b given by Kauffmann et al. (1996). This means that non-radial motions play a significant role in determining the bias level. In our next paper (Del Popolo & Gambera, in preparation) we make a more detailed analysis on the problem of the bias.

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© European Southern Observatory (ESO) 1998

Online publication: August 6, 1998