Modelling the evolution of galaxy clustering

Measurements of galaxy clustering are now becoming possible over a range of redshifts out to z̃ 3. We use a semi-analytic model of galaxy formation to compute the expected evolution of the galaxy correlation function with redshift. We illustrate how the degree of clustering evolution is sensitive to the details of sample selection. For a fixed apparent magnitude limit, galaxies selected at higher redshifts are located in progressively rarer dark matter haloes, compared with the general population of galaxies in place at each redshift. As a result these galaxies are highly biased tracers of the underlying dark matter distribution and exhibit stronger clustering than the dark matter. In general, the correlation length measured in comoving units, decreases at first with increasing redshift, before increasing again at higher redshift. We show that the ε-model often used to interpret the angular correlation function of faint galaxies gives an inadequate description of the evolution of clustering, and offers no physical insight into the clustering process. We compare our predictions with those of a simple, popular model in which a one-to-one correspondence between galaxies and dark haloes is assumed. Qualitatively, this model reproduces the correct evolutionary behaviour at high redshift, but the quantitative results can be significantly in error. Our theoretical expectations are in good agreement with the high redshift clustering data of Carlberg et al. and Postman et al. but are higher than the measurements of Le Fèvre et al.