The 2dF-SDSS LRG and QSO Survey: Evolution of the clustering of luminous red galaxies since z = 0.6

We present an analysis of the small-to-intermediate scale clustering of samples of luminous red galaxies (LRGs) from the Sloan Digital Sky Survey (SDSS) and the 2dF-SDSS LRG and QSO Survey (2SLAQ) survey carefully matched to have the same rest-frame colours and luminosity. We study the spatial two-point autocorrelation function in both redshift space [ξ(s)] and real space [ξ(r)] of a combined sample of over 10 000 LRGs, which represent the most massive galaxies in the universe with stellar masses >10¹¹ h ^-1 M_⊙ and space densities ≃10^-4 h³ Mpc^-3. We find no significant evolution in the amplitude (r₀) of the correlation function with redshift, but do see a slight decrease in the slope (γ) with increasing redshift over 0.19 < z < 0.55 and scales of 0.32 < r < 32 h^-1 Mpc. We compare our measurements with the predicted evolution of dark matter clustering and use the halo model to interpret our results. We find that our clustering measurements are inconsistent (>99.9 per cent significance) with a passive model whereby the LRGs do not merge with one another; a model with a merger rate of 7.5 ± 2.3 per cent from z = 0.55 to 0.19 (i.e. an average rate of 2.4 per cent Gyr^-1) provides a better fit to our observations. Our clustering and number density measurements are consistent with the hypothesis that the merged LRGs were originally central galaxies in different haloes which, following the merger of these haloes, merged to create a single brightest cluster galaxy. In addition, we show that the small-scale clustering signal constrains the scatter in halo merger histories. When combined with measurements of the luminosity function, our results suggest that this scatter is sub-Poisson. While this is a generic prediction of hierarchical models, it has not been tested before.