Does gravitational clustering stabilize on small scales?

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Abstract
The stable clustering hypothesis is a key analytical anchor for the non-linear 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. N-body simulations have only recently achieved sufficient resolution to probe the regime of correlation function amplitudes ξ ∼ 100−104 in which stable clustering might be valid. In this paper we use N-body simulations of scale-free spectra P(k) ∝ kn with −2≤n ≤0 and of the CDM spectrum to apply two tests for stable clustering: the time evolution and shape of ξ (x, t), and the mean pair velocity on small scales. We solve the pair conservation equation to measure the mean pair velocity, as it provides a more accurate estimate from the simulation data. For all spectra the results are consistent with the stable clustering predictions on the smallest scales probed, x < 0.07 xnl(t), where xnl(t) is the correlation length. The measured stable clustering regime corresponds to a typical range of 200 ≾ ξ ≾ 2000, although spectra with more small-scale power (n ≃ 0) approach the stable clustering asymptote at larger values of ξ. We test the amplitude of ξ predicted by the analytical model of Sheth & Jain, and find agreement to within 20 per cent in the stable clustering regime for nearly all spectra. For the CDM spectrum the non-linear ξ is accurately approximated by this model with n ≃ −2 on physical scales ≾ 100–300 h−1 kpc for σ8 = 0.5–1, and on smaller scales at earlier times. The growth of ξ for CDM-like models is discussed in the context of a power-law parametrization often used to describe galaxy clustering at high redshifts. The growth parameter ∊ is computed as a function of time and length-scale, and is found to be larger than 1 in the moderately non-linear regime —thus the growth of ξ is much faster on scales of interest than is commonly assumed.
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