Mass Accretion Rates and Histories of Dark Matter Haloes

We use the extensive catalog of dark matter haloes from the Millennium simulation to investigate the statistics of the mass accretion histories (MAHs) and accretion rates of ~500,000 haloes from redshift z=0 to 6. We find only about 25% of the haloes to have MAHs that are well described by a 1-parameter exponential form. For the rest of the haloes, between 20% (Milky-Way mass) to 50% (cluster mass) experience late-time growth that is steeper than an exponential, whereas the remaining haloes show plateau-ed late-time growth that is shallower than an exponential. The haloes with slower late-time growth tend to reside in denser environments, suggesting that either tidal stripping or the "hotter" dynamics are suppressing the accretion rate of dark matter onto these haloes. These deviations from exponential growth are well fit by introducing a second parameter: M(z) \propto (1+z)^beta exp(-gamma z). The full distribution of beta and gamma as a function of halo mass is provided. From the analytic form of M(z), we obtain a simple formula for the mean accretion rate of dark matter, dM/dt, as a function of redshift and mass. At z=0, this rate is 42 Msun/yr for 1e12 Msun haloes, which corresponds to a mean baryon accretion rate of dMbaryon/dt=7 Msun/yr. This mean rate increases approximately as (1+z)^1.5 at low z and (1+z)^2.5 at high z, reaching dMbaryon/dt = 27, 69, and 140 Msun/yr at z=1, 2, and 3. The specific rate depends on halo mass weakly: dlogM/dt \propto M^0.127. Results for the broad distributions about the mean rates are also discussed.