The clustering of dark matter haloes: Scale-dependent bias on quasi-linear scales

Abstract

We investigate the spatial clustering of dark matter haloes, collapsing from 1σ-4σ fluctuations, in the redshift range 0-5 using N-body simulations. The halo bias of high redshift haloes (z ≥ 2) is found to be strongly nonlinear and scale dependent on quasi-linear scales that are larger than their virial radii (0.5-10 Mpc h-1). However, at lower redshifts, the scale dependence of nonlinear bias is weaker and is of the order of a few per cent on quasi-linear scales at z ∼0. We find that the redshift evolution of the scale-dependent bias of dark matter haloes can be expressed as a function of four physical parameters: the peak height of haloes, the nonlinear matter correlation function at the scale of interest, an effective power-law index of the rms linear density fluctuations and the matter density of the universe at the given redshift. This suggests that the scale dependence of halo bias is not a universal function of the dark matter power spectrum, which is commonly assumed. We provide a fitting function for the scale-dependent halo bias as a function of these four parameters. Our fit reproduces the simulation results to an accuracy of better than 4 per cent over the redshift range 0 ≤ z ≤ 5. We also extend our model by expressing the nonlinear bias as a function of the linear matter correlation function. It is important to incorporate our results into the clustering models of dark matter haloes at any redshift, including those hosting early generations of stars and galaxies before reionization.