An analytic model for the gravitational clustering of dark matter haloes
Abstract
We develop a simple analytic model for the gravitational clustering of dark haloes. The statistical properties of dark haloes are determined from the initial density field (assumed to be Gaussian) through an extension of the PressSchechter formalism. Gravitational clustering is treated by a spherical model which describes the concentration of dark haloes in collapsing regions. We test this model against results from a variety of Nbody simulations. The autocorrelation function of dark haloes in such simulations depends significantly on how haloes are identified. Our predictions agree well with results based on algorithms which break clusters into subgroups more efficiently than the standard friendsoffriends algorithm. The agreement is better than that found by assuming haloes to lie at the present positions of peaks of the linear density field. We use these techniques to study how the distribution of haloes is biased with respect to that of the mass. The initial (Lagrangian) positions of haloes identified at a given redshift and having circular velocities $v_c=v_c^*(z)$ (i.e. mass equal to the characteristic nonlinear mass $M^*$ at that redshift) are very weakly correlated with the linear density field or among themselves. As a result of dynamical evolution, however, the presentday correlations of these haloes are similar to those of the mass. Haloes with lower $v_c$ are biased toward regions with negative overdensity, while those with higher $v_c$ are biased toward regions with positive overdensity. Among the haloes identified at any given epoch, those with higher circular velocities are more strongly correlated today. Among the haloes of given circular velocity, those at higher redshifts are also more strongly clustered today. In the ``standard CDM'' model, haloes with
 Publication:

arXiv eprints
 Pub Date:
 December 1994
 arXiv:
 arXiv:astroph/9412088
 Bibcode:
 1994astro.ph.12088M
 Keywords:

 Astrophysics
 EPrint:
 28 pages, uuencoded, 12 figs available on request