On The Assembly History of Dark Matter Haloes

(abridged) 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. Using a suite of 55 PINOCCHIO simulations, with 256^3 particles each, we study the MAHs of 12,924 cold dark matter haloes in a \LambdaCDM concordance cosmology. 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 \pm 2 major mergers since its main progenitor had a mass equal to one percent 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.