The 2dF Galaxy Redshift Survey: stochastic relative biasing between galaxy populations

It is well known that the clustering of galaxies depends on galaxy type. Such relative bias complicates the inference of cosmological parameters from galaxy redshift surveys, and is a challenge to theories of galaxy formation and evolution. In this paper we perform a joint counts-in-cells analysis on galaxies in the 2dF Galaxy Redshift Survey, classified by both colour and spectral type, eta, as early- or late-type galaxies. We fit three different models of relative bias to the joint probability distribution of the cell counts, assuming Poisson sampling of the galaxy density field. We investigate the non-linearity and stochasticity of the relative bias, with cubic cells of side 10 less than or equal toLless than or equal to 45 Mpc (h= 0.7). Exact linear bias is ruled out with high significance on all scales. Power-law bias gives a better fit, but likelihood ratios prefer a bivariate lognormal distribution, with a non-zero 'stochasticity', i.e. scatter that may result from physical effects on galaxy formation other than those from the local density field. Using this model, we measure a correlation coefficient in log-density space (r(LN)) of 0.958 for cells of length L= 10 Mpc, increasing to 0.970 by L= 45 Mpc. This corresponds to a stochasticity sigma(b)/(b) over cap of 0.44 +/- 0.02 and 0.27 +/- 0.05, respectively. For smaller cells, the Poisson-sampled lognormal distribution presents an increasingly poor fit to the data, especially with regard to the fraction of completely empty cells. We compare these trends with the predictions of semi-analytic galaxy formation models: these match the data well in terms of the overall level of stochasticity, variation with scale and the fraction of empty cells.