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**Session 87 - Large Scale Structure.**

*Display session, Friday, January 09*

*Exhibit Hall, *

## [87.07] The Cosmological Mass Distribution Function in the Zel'dovich Approximation

*J. Lee, S. F. Shandarin (U. Kansas)*
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 > 3\sigma).
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.

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