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

Understand

The merger and accretion probabilities of dark matter halos 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 merger history of a parent halo.
• In this paper we use the random walk formalism to find the merger and accretion probabilities of halos for a finite time interval.
• Specifically, we find the number density of halos at an early redshift that will become part of a halo with a specified final mass at a later redshift, given that they underwent $n$ major mergers, $n=0,1,2,...$ .