Astronomy and Astrophysics – Astrophysics
Scientific paper
1997-09-19
Astronomy and Astrophysics
Astrophysics
A solution to the normalization problem is added. Latex file, 33 pages, 5 PostScript figures
Scientific paper
10.1086/305710
An analytic approximation to the mass function for gravitationally bound objects is presented. We base on the Zel'dovich approximation to extend the Press-Schechter formalism to a nonspherical dynamical model. A simple extrapolation of that approximation suggests that the gravitational collapse along all three directions which eventually leads to the formation of real virialized objects - clumps occur in the regions where the lowest eigenvalue of the deformation tensor,lambda_{3}, is positive. We derive the conditional probability of lambda_{3}>0 as a function of the linearly extrapolated density contrast, delta, and the conditional probability distribution of delta provided that lambda_{3}>0. These two conditional probability distributions show that the most probable density of the bound regions (lambda_{3}>0) is roughly 1.5 at the characteristic mass scale, and that the probability of lambda_{3}>0 is almost unity in the highly overdense regions (delta>3*sigma). Finally an analytic mass function of clumps is derived with a help of one simple ansatz which is employed to treat the multistream regions beyond the validity of the Zel'dovich approximation. The resulting mass function is renormalized by a factor of 12.5, which we justify with a sharp k-space filter by means of the modified Jedamzik analysis. Our mass function is shown to be different from the Press-Schechter one, having a lower peak and predicting more small-mass objects.
Lee Jounghun
Shandarin Sergei F.
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