Generating merger trees for dark matter haloes: a comparison of methods

Halo merger trees describe the hierarchical assembly of dark matter haloes, and are the backbone for modelling galaxy formation and evolution. Merger trees constructed using Monte Carlo algorithms based on the extended Press-Schechter (EPS) formalism are complementary to using N-body simulations and have the advantage that they are not trammelled by limited numerical resolution and uncertainties in identifying and linking (sub)haloes. This paper compares multiple EPS-based merger tree algorithms to simulation results using four diagnostics: progenitor mass function, mass assembly history (MAH), merger rate per descendant halo and the unevolved subhalo mass function. Spherical collapse-based methods typically overpredict major-merger rates, whereas ellipsoidal collapse dramatically overpredicts the minor-merger rate for massive haloes. The only algorithm in our comparison that yields results in good agreement with simulations is that by Parkinson et al. (P08). We emphasize, though, that the simulation results used as benchmarks in testing the merger trees are hampered by significant uncertainties themselves: MAHs and merger rates from different studies easily disagree by 50 per cent, even when based on the same simulation. Given this status quo, the P08 merger trees can be considered as accurate as those extracted from simulations.