Galaxy formation and large-scale bias

We outline a simple approach to understanding the physical origin of bias in the distribution of galaxies relative to that of dark matter. The first step is to specify how collapsed, virialized haloes of dark matter trace the overall matter distribution. if the quantity M* is defined to be the halo mass that has typically just collapsed by the present day, then on large scales, haloes of mass M* are unbiased tracers of the underlying matter distribution. Haloes with masses greater than M* are positively biased, while haloes less massive than M* are antibiased with respect to the dark matter. These conclusions are independent of the assumed shape of the power spectrum. The next step is to make a connection between haloes and the luminous galaxies we observe. We appeal to the results of semi-analytic models of galaxy formation that are tuned to fit the observed luminosity functions of local groups and clusters. Using these models, we are able to specify the luminosities and morphological types of the galaxies contained within a halo of given mass at the present day. We have also used a high-resolution N-body simulation of a cold dark matter (CDM) universe to study the bias relation in more detail. The differences between the galaxy and dark matter distributions are quantified using a number of different clustering statistics, including the power spectrum, the two-point correlation function, the void probability function and the one-point probability density function. Both the semi-analytic and N-body techniques lead to the following general conclusions. A comparison of the galaxy and dark matter density fields shows that linear biasing is a good description on large scales for galaxies of all types and luminosities. The bias factor b depends on the shape and normalization of the power spectrum. The lower the normalization, the larger the bias. More bias is obtained for spectra with more power on large scales. For ‘realistic’ models, b ranges from 1 to 2.5. Galaxies of different luminosity or morphology have different bias factors. The scale dependence of the bias factor is weak.