The mass function of unprocessed dark matter haloes and merger tree branching rates

Abstract

A common approach in semi-analytic modeling of galaxy formation is to construct Monte Carlo realizations of merger histories of dark matter halos whose masses are sampled from a halo mass function. Both the mass function itself, and the merger rates used to construct merging histories are calibrated to N-body simulations. Typically, "backsplash" halos (those which were once subhalos within a larger halo, but which have since moved outside of the halo) are counted in both the halo mass function, and in the merger rates (or, equivalently, progenitor mass functions). This leads to a double-counting of mass in Monte Carlo merger histories which will bias results relative to N-body results. We measure halo mass functions and merger rates with this double-counting removed in a large, cosmological N-body simulation with cosmological parameters consistent with current constraints. Furthermore, we account for the inherently noisy nature of N-body halo mass estimates when fitting functions to N-body data, and show that ignoring these errors leads to a significant systematic bias given the precision statistics available from state-of-the-art N-body cosmological simulations.

Halo concentrations from extended Press–Schechter merger histories

“…, which may be expected to be valid if the number of particles in each bin obeys Poisson statistics (Benson 2017a). We found that this leads to small but significant differences in the resulting distribution of concentration parameters.…”

“…In the first, we generate spherically symmetric Einasto density profiles with a range of different concentrations, and sample from each profile using different numbers of particles via a Poisson process (Benson 2017a). These N-body representations are then fit using the procedure described above (without any application of the Power et al (2003) convergence criterion, which does not apply in this simple experiment).…”

“…In semi-analytic models of galaxy formation, the density profile of the halo directly affects determinations of galaxy sizes (Cole et al 2000;Jiang et al 2018), and in many models affects the mass loading of outflows from galaxies (Cole et al 2000;Benson 2012). While semi-analytic models of galaxy formation are most often applied to dark matter halo merger trees extracted from N-body simulations, from which dark matter profiles can be measured directly, they can also be applied to merger trees generated using other techniques, such as those based on excursion set theory (Bond et al 1991;Lacey & Cole 1993;Cole et al 2000;Parkinson et al 2008).…”

“…While semi-analytic models of galaxy formation are most often applied to dark matter halo merger trees extracted from N-body simulations, from which dark matter profiles can be measured directly, they can also be applied to merger trees generated using other techniques, such as those based on excursion set theory (Bond et al 1991;Lacey & Cole 1993;Cole et al 2000;Parkinson et al 2008). Such approaches have some advantages over the use of N-body merger trees, for example allowing much finer time resolution to be achieved (which can affect the results of E-mail: abenson@carnegiescience.edu semi-analytic models; Benson et al 2012), rapid exploration of different dark matter physics (Benson et al 2013), and avoidance of numerical noise issues which occur in N-body halos at low particle number (Benson 2017b).…”

hbt+: an improved code for finding subhaloes and building merger trees in cosmological simulations

“…In this case, halos that are temporarily linked together and subhalos that have been ejected from the host can both contribute to the progenitor mass function. The situation can become even worse if these objects fall back into the host and are counted multiple times (Benson 2017). In contrast, our approach of selecting branches located inside the final virial radius produces a progenitor population that can be unambiguiously compared against the final mass function inside the virial radius.…”