On the assembly history of dark matter haloes

We study the mass assembly history (MAH) of dark matter haloes. We compare MAHs obtained using (i) merger trees constructed with the extended Press-Schechter (EPS) formalism, (ii) numerical simulations and (iii) the Lagrangian perturbation code PINOCCHIO. We show that the PINOCCHIO MAHs are in excellent agreement with those obtained using numerical simulations, while the EPS formalism predicts MAHs that occur too late. PINOCCHIO, which is much less CPU intensive than N-body simulation, can be run on a simple personal computer, and does not require any labour intensive post-simulation analysis, therefore provides a unique and powerful tool to investigate the growth history of dark matter haloes. Using a suite of 55 PINOCCHIO simulations, with 256(3) particles each, we study the MAHs of 12 924 cold dark matter (CDM) haloes in a Lambda CDM concordance cosmology. This is by far the largest set of haloes used for any such analysis. For each MAH we derive four different formation redshifts, which characterize different epochs during the assembly history of a dark matter halo. We show that haloes less massive than the characteristic non-linear mass scale establish their potential wells much before they acquire most of their mass. The time when a halo reaches its maximum virial velocity roughly divides its mass assembly into two phases, a fast-accretion phase which is dominated by major mergers, and a slow-accretion phase dominated by minor mergers. Each halo experiences about 3 +/- 2 major mergers since its main progenitor had a mass equal to 1 per cent of the final halo mass. This major merger statistic is found to be virtually independent of halo mass. However, the average redshift at which these major mergers occur is strongly mass dependent, with more massive haloes experiencing their major mergers later.