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Does Gravitational Clustering Stabilize On Small Scales?  Bhuvnesh Jain
;  Date: 
30 May 1996  Journal:  Mon.Not.Roy.Astron.Soc. 287 (1997) 687  Abstract:  The stable clustering hypothesis is a key analytical anchor on the nonlinear dynamics of gravitational clustering in cosmology. It states that on sufficiently small scales the mean pair velocity approaches zero, or equivalently, that the mean number of neighbours of a particle remains constant in time at a given physical separation. In this paper we use Nbody simulations of scale free spectra P(k) propto k^n with 2 leq n leq 0 and of the CDM spectrum to test for stable clustering using the time evolution and shape of the correlation function xi(x,t), and the mean pair velocity on small scales. For all spectra the results are consistent with the stable clustering predictions on the smallest scales probed, x < 0.07 x_{nl}(t), where x_{nl}(t) is the correlation length. The measured stable clustering regime corresponds to a typical range of 200 lsim xi lsim 2000, though spectra with more small scale power approach the stable clustering asymptote at larger values of xi. We test the amplitude of xi predicted by the analytical model of Sheth & Jain (1996), and find agreement to within 20\% in the stable clustering regime for nearly all spectra. For the CDM spectrum the nonlinear xi is accurately approximated by this model with n simeq 2 on physical scales lsim 100300 h^{1} kpc for sigma_8 = 0.51, and on smaller scales at earlier times. The growth of xi for CDMlike models is discussed in the context of a power law parameterization often used to describe galaxy clustering at high redshifts. The growth parameter epsilon is computed as a function of time and length scale, and found to be larger than 1 in the moderately nonlinear regime  thus the growth of xi is much faster on scales of interest than is commonly assumed.  Source:  arXiv, astroph/9605192  Services:  Forum  Review  PDF  Favorites 


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