1997/09/30 by Jounghun Lee, Sergei F. Shandarin, S. F. Shandarin · 3 citations
Mathematics · Physics and Astronomy · #Ansatz #Astrophysics #Cosmology and Gravitation Theories #Extrapolation #Function (biology) #Galaxies: Formation, Evolution, Phenomena #Galaxy #Mass distribution #Mathematical analysis #Mathematical physics #Mathematics #Monotonic function #Physics #Probability density function #Probability distribution #Solar and Space Plasma Dynamics #Statistical physics #Statistics #astro-ph
paper · pdf · doi:10.1086/305710
A solution to the normalization problem is added. Latex file, 33 pages, 5 PostScript figures
arxiv created 1997/12/08 · openalex publication_date 1998/06/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
An analytic approximation of the mass function for gravitationally bound objects is presented. Based on the Zeldovich approximation, we 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 object clumps, occurs in the regions where the lowest eigenvalue of the deformation tensor, λ 3 , is positive. We derive the conditional probability of λ 3 > 0 as a function of the linearly extrapolated density contrast δ and the conditional probability distribution of δ, provided that λ 3 > 0. These two conditional probability distributions show that the most probable density of the bound regions (λ 3 > 0) is roughly 1.5 on the characteristic mass scale M * and that the probability of λ 3 > 0 is almost unity in the highly overdense regions (δ > 3σ). Finally, an analytic mass function of clumps is derived with the help of one simple Ansatz , which is employed to treat the multistream regime beyond the validity of the Zeldovich 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.