## 6. ConclusionsIn 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 while the collapse of density peaks having 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, , which now is larger than that of the top-hat spherical model and depends on . 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 . The
function selects higher and higher density
peaks with increasing value of 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 On clusters scales for we found a value of
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 © European Southern Observatory (ESO) 1998 Online publication: August 6, 1998 |