Mathematics – Probability
Scientific paper
Dec 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997aas...191.8707l&link_type=abstract
American Astronomical Society, 191st AAS Meeting, #87.07; Bulletin of the American Astronomical Society, Vol. 29, p.1355
Mathematics
Probability
Scientific paper
An analytic estimation of the mass function for gravitationally bound objects is presented. We use the Zel'dovich approximation to extend the Press-Schecter formalism to a nonspherical dynamical model. In the Zel'dovich approximation, the gravitational collapse along all three directions which will eventually lead 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 M_{*}, and that the probability of lambda_ {3} > 0 is almost unity in the highly overdense regions (delta > 3sigma ). Finally the analytic mass function of clumps is derived with a help of one simple ansatz which is employed to approach the multistream regimes 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-Schecter one, having a lower peak and predicting more small-mass objects.
Lee Julian
Shandarin Sergei F.
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