Non-linear stochastic galaxy biasing in cosmological simulations

We study the biasing relation between dark matter haloes or galaxies and the underlying mass distribution, using cosmological N-body simulations in which galaxies are modelled via semi-analytic recipes. The non-linear, stochastic biasing is quantified in terms of the mean biasing function and the scatter about it as a function of time, scale and object properties. The biasing of galaxies and haloes shows a general similarity and a characteristic shape, with no galaxies in deep voids and a steep slope in moderately underdense regions. At a comoving scale of similar to8 h(-1) Mpc, the non-linearity in the biasing relation is typically less than or similar to 10 per cent and the stochasticity is a few tens of per cent, corresponding to similar to 30 per cent variations in the cosmological parameter beta=Omega (0.6)/b. Biasing depends weakly on halo mass, galaxy luminosity, and scale. The observed trend with luminosity is reproduced when dust extinction is included. The time evolution is rapid, with the mean biasing larger by a factor of a few at z similar to3 compared with z=0, and with a minimum for the non-linearity and stochasticity at an intermediate redshift. Biasing today is a weak function of the cosmological model, reflecting the weak dependence on the power-spectrum shape, but the time evolution is more cosmology-dependent, reflecting the effect of the growth rate. We provide predictions for the relative biasing of galaxies of different type and colour, to be compared with upcoming large redshift surveys. Analytic models in which the number of objects is conserved underestimate the evolution of biasing, while models that explicitly account for merging provide a good description of the biasing of haloes and its evolution, suggesting that merging is a crucial element in the evolution of biasing.