Two-body relaxation in simulated cosmological haloes

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This paper aims to quantify, in a general manner that does not directly resort to large-scale calculations, discreteness effects acting on the dynamics of dark matter haloes forming in the context of cosmological simulations. By generalizing the standard formulation of two-body relaxation to the case when the size and mass distributions are variable, and parametrizing the time evolution using established empirical relations, we find that the dynamics of a million-particle halo is noise-dominated within the inner per cent of the final virial radius. Far larger particle numbers (∼108) are required for the rms perturbations to the velocity to drop to the 10 per cent level there. The radial scaling of the relaxation time is simple and strong: t relax ∼ r2, implying that numbers »10 8 are required to faithfully model the very inner regions; artificial relaxation may thus constitute an important factor, contributing to the contradictory claims concerning the persistence of a power-law density cusp to the very centre. The cores of substructure haloes can be many relaxation times old. Since relaxation first causes their expansion before recontraction occurs, it may render them either more difficult or easier to disrupt, depending on their orbital parameters. This may modify the characteristics of the subhalo distribution; and if, as suggested by several authors, it is parent-satellite interactions that determine halo profiles, the overall structure of the system may be affected. We derive simple closed form formulae for the characteristic relaxation time of both parents and satellites, and an elementary argument deducing the weak N-scaling reported by Diemand et al. when the main contribution comes from relaxing subhaloes. © 2006 RAS.

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