Dark matter halo merger and accretion probabilities in the excursion set formalism

摘要: The merger and accretion probabilities of dark matter haloes have so far only been calculated for an infinitesimal time interval. This means that a Monte Carlo simulation with very small time-steps is necessary to find the history parent halo. In this paper, we use random walk formalism finite Specifically, number density at early redshift will become part halo specified final mass later redshift, given they underwent n major mergers, = 0, 1, 2, ... . We reduce problem into integral equation which then solve numerically. To ensure consistency our formalism, compare results simulations good agreement. Though done calculation assuming flat barrier, more general case can easily be handled using method. derivation used make efficient trees or implemented directly analytical models structure formation evolution.