UC Berkeley

Using the combined results of the Millennium and Millennium II numerical simulations we compute a number of robust statistics for the growth of dark matter haloes in the ΛCDM concordance model. With an unprecedented 1.35 billion subhaloes we compute, and provide a fit to, the halo merger rate over five orders of magnitude in descendant halo mass (10¹⁰ < M₀ < 10¹⁵M_sun) and progenitor mass ratio (10^-5< ξ < 1) over a redshift range spanning z = 0 to 15. We also compute and categorize halo mass accretion histories and quantify the relative contributions made by the mergers of resolved progenitors and the accretion of unresolved diffuse material to the halo growth rate. In addition, we perform a detailed quantitative study of the environmental dependence of halo growth, finding a higher merger rate among halos in denser regions and, curiously, a negative correlation between environment density and the diffuse component of halo growth. Throughout, we pay special attention to the problem of extracting self-consistent merger trees from the Millennium simulations: numerical issues abound and the problem of halo fragmentation in particular is shown to be important at the 20% level, but tractable via a variety of post-processing algorithms which we describe. Finally, we apply the insight obtained from our analysis to the problem of generating self- consistent Monte Carlo merger trees in the extended Press-Schechter framework.