The Origin and Evolution of Halo Bias in Linear and Nonlinear Regimes

Abstract

We present results from a study of bias and its evolution for galaxy-size halos in a large, high-resolution simulation of a low-density, cold dark matter model with a cosmological constant. In addition to the previous studies of the halo two-point correlation function, we consider the evolution of bias estimated using two different statistics: power spectrum bP and a direct correlation of smoothed halo and matter overdensity fields bδ. We present accurate estimates of the evolution of the matter power spectrum probed deep into the stable clustering regime [k ~ (0.1-200) h Mpc-1 at z = 0] and find that its shape and evolution can be well described, with only a minor modification, by the fitting formula of Peacock & Dodds. The halo power spectrum evolves much slower than the power spectrum of matter and has a different shape which indicates that the bias is time and scale dependent. At z = 0, the halo power spectrum is antibiased (bP < 1) with respect to the matter power spectrum at wavenumbers k ~ (0.15-30) h Mpc-1 and provides an excellent match to the power spectrum of the Automatic Plate Measuring Facility (APM) galaxies at all probed k. In particular, both the halo and matter power spectra show an inflection at k ≈ 0.15 h Mpc-1, which corresponds to the present-day scale of nonlinearity and nicely matches the inflection observed in the APM power spectrum. We complement the power spectrum analysis with a direct estimate of bias using smoothed halo and matter overdensity fields and show that the evolution observed in the simulation in linear and mildly nonlinear regimes can be well described by the analytical model of Mo & White, if the distinction between formation redshift of halos and observation epoch is introduced into the model. We present arguments and evidence that at higher overdensities the evolution of bias is significantly affected by dynamical friction and tidal stripping operating on the satellite halos in high-density regions of clusters and groups; we attribute the strong antibias observed in the halo correlation function and power spectrum to these effects. The results of this study show that despite the apparent complexity, the origin and evolution of bias can be understood in terms of the processes that drive the formation and evolution of dark matter halos. These processes conspire to produce a halo distribution quite different from the overall distribution of matter, yet remarkably similar to the observed distribution of galaxies.