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Session 87 - Large Scale Structure.
Display session, Friday, January 09
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.
Program listing for Friday