Showing papers by "Ravi K. Sheth published in 1995"

Press–Schechter, thermodynamics and gravitational clustering

Abstract: For the special case of nonlinear gravitational clustering from an initially Poisson distribution , the counts-in-cells distribution function is obtained from the excursion set, Press-Schechter multiplicity function. This Poisson Press-Schechter distribution function has the same form as the gravitational quasi-equilibrium counts-in-cells distribution function, predicted by the Saslaw-Hamilton thermodynamic model of nonlinear gravi-tational clustering, that ts the observed galaxy distribution well. By changing an ad hoc guess in the Saslaw-Hamilton thermodynamic model, the Negative Binomial distribution (which also ts relevant observations well) is derived from the thermodynamic approach. At present, analytic simplicity is the primary reason for preferring one guess over another, so the thermodynamic approach does not, at present, yield a unique prediction for the gravitational counts-in-cells distribution function. Two ways to constrain the parameter space of possible guesses are described; one of these suggests that the Negative Binomial is not a physically reasonable model. One possible relation between the original Saslaw-Hamilton thermodynamic model and the Poisson Press-Schechter approaches is obtained. A system of non-interacting, virialized clusters having a range of masses, the distribution of masses being given by the Poisson Press-Schechter multiplicity function, is shown to be consistent with the original Saslaw-Hamilton thermodynamic model. For this model to work the virialized clusters must be in thermal equilibrium with each other, so that all clusters have the same temperature, independent of their masses. This last requirement, and the idealization that the clusters do not interact gravitationally with each other, are in contradiction with observations.

Constrained realizations and minimum variance reconstruction of non-Gaussian random fields

Abstract: With appropriate modifications, the Hoffman--Ribak algorithm that constructs constrained realizations of Gaussian random fields having the correct ensemble properties can also be used to construct constrained realizations of those non-Gaussian random fields that are obtained by transformations of an underlying Gaussian field. For example, constrained realizations of lognormal, generalized Rayleigh, and chi-squared fields having $n$ degrees of freedom constructed this way will have the correct ensemble properties. The lognormal field is considered in detail. For reconstructing Gaussian random fields, constrained realization techniques are similar to reconstructions obtained using minimum variance techniques. A comparison of this constrained realization approach with minimum variance, Wiener filter reconstruction techniques, in the context of lognormal random fields, is also included. The resulting prescriptions for constructing constrained realizations as well as minimum variance reconstructions of lognormal random fields are useful for reconstructing masked regions in galaxy catalogues on smaller scales than previously possible, for assessing the statistical significance of small-scale features in the microwave background radiation, and for generating certain non-Gaussian initial conditions for $N$-body simulations.

Merging and hierarchical clustering from an initially Poisson distribution

Abstract: The excursion{set, Press{Schechter mass spectrum for a Poisson distribution of identical particles is derived. For the special case of an initially Poisson distribution the spatial distribution of the Press{Schechter clumps is shown to be Poisson. Thus, the distribution function of particle counts in randomly placed cells is easily obtained from the Press{Schechter multiplicity function. This Poisson Press{Schechter distribution function has the same form as the well-studied gravitational quasi-equilibrium counts-in-cells distribution function which ts the observed galaxy distribution well. The description of merging and hierarchical clustering from an initially Poisson distribution is also formulated and solved. These solutions represent the discrete analogue of those already obtained for an initially Gaussian distribution. In addition, physically motivated arguments are used to provide insight about the structure of the partition function that describes all possible merger histories. From this partition function an expression for the number of progenitor clumps as a function of cluster size is obtained. This, with the knowledge that initially Press{Schechter clumps have a Poisson spatial distribution, is used to calculate the subsequent clustering of these clumps. Thus, the growth of hierarchical clustering on all levels of the hierarchy is quantiied. Comparison of the analytic results with relevant N-body simulations of gravitational clustering shows substantial agreement. A method for extending all these results to describe the growth of clustering from more general, non-Gaussian, compound Poisson distributions is also described. For these compound Poisson processes a scaling relation is obtained that greatly clariies the results of relevant N-body simulations in which particles have a range of masses. This scaling solution and the merger history results are consistent with a simple model of the growth of hierarchical clustering. At early times in this model, clustering on all levels of the hierarchy is well approximated by appropriately renormalized Poisson Press{ Schechter forms.