The clustering of dark matter halos: scale-dependent bias on quasi-linear scales

Abstract

We investigate the spatial clustering of dark matter halos, collapsing from $1-4 σ$ fluctuations, in the redshift range $0 - 5$ using N-body simulations. The halo bias of high redshift halos ($z \geq 2$) is found to be strongly non-linear and scale-dependent on quasi-linear scales that are larger than their virial radii ($0.5-10$ Mpc/h). However, at lower redshifts, the scale-dependence of non-linear bias is weaker and and is of the order of a few percent on quasi-linear scales at $z \sim 0$. We find that the redshift evolution of the scale dependent bias of dark matter halos can be expressed as a function of four physical parameters: the peak height of halos, the non-linear matter correlation function at the scale of interest, an effective power law index of the {\it 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 % over the redshift range $0\leq z \leq 5$. We also extend our model by expressing the non-linear bias as a function of the linear matter correlation function. It is important to incorporate our results into the clustering models of dark matter halos at any redshift, including those hosting early generations of stars and galaxies before reionization.