Assembly bias in the clustering of dark matter haloes

We use a very large simulation of structure growth in a LCDM universe -- the Millennium Simulation -- to study assembly bias, the fact that the large-scale clustering of haloes of given mass varies significantly with their assembly history. We extend earlier work based on the same simulation by superposing results for redshifts from 0 to 3, by defining a less noisy estimator of clustering amplitude, and by considering halo concentration, substructure mass fraction and spin, as well as formation time, as additional parameters. These improvements lead to results with less noise than previous studies and covering a wider range of halo masses and structural properties. We find significant and significantly different assembly bias effects for all the halo properties we consider, although in all cases the dependences on halo mass and on redshift are adequately described as a dependence on equivalent peak height nu(M,z). The nu-dependences for different halo properties differ qualitatively and are not related as might naively be expected given the relations between formation time, concentration, substructure fraction and spin found for the halo population as a whole. These results suggest that it will be difficult to build models for the galaxy populations of dark haloes which can robustly relate the amplitude of large-scale galaxy clustering to that for mass clustering at better than the 10% level.