Mass accretion rates and histories of dark matter haloes

We use the extensive catalogue of dark matter haloes from the Millennium Simulation to investigate the statistics of the mass accretion histories (MAHs) and accretion rates of similar to 500 000 haloes from redshift z = 0 to 6. We find only about 25 per cent of the haloes to have MAHs that are well described by a 1-parameter exponential form. For the rest of the haloes, between 20 per cent (Milky Way mass) and 50 per cent (cluster mass) experience late-time growth that is steeper than an exponential, whereas the remaining haloes show plateaued 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 on to these haloes. These deviations from exponential growth are well fit by introducing a second parameter: M(z) proportional to (1 + z)(beta)e(-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, (M) over dot, as a function of redshift and mass. At z = 0, this rate is 42M(circle dot) yr(-1) for 10(12) M-circle dot haloes, which corresponds to a mean baryon accretion rate of (M) over dot(b) = 7M(circle dot) yr(-1). This mean rate increases approximately as (1 + z)(1.5) at low z and (1 + z)(2.5) at high z, reaching (M) over dot(b) = 27, 69 and 140M(circle dot) yr(-1) at z = 1, 2 and 3. The specific rate depends on halo mass weakly:. M/M proportional to M-0.127. Results for the broad distributions about the mean rates are also discussed.