Building merger trees from cosmologicalN-body simulations

Context. In the past decade or so, using numerical N-body simulations to describe the gravitational clustering of dark matter (DM) in an expanding universe has become the tool of choice for tackling the issue of hierarchical galaxy formation. As mass resolution increases with the power of supercomputers, one is able to grasp finer and finer details of this process, resolving more and more of the inner structure of collapsed objects. This begs one to revisit time and again the post-processing tools with which one transforms particles into “invisible” dark matter haloes and from thereon into luminous galaxies.Aims. Although a fair amount of work has been devoted to growing Monte-Carlo merger trees that resemble those built from an N-body simulation, comparatively little effort has been invested in quantifying the caveats one necessarily encounters when one extracts trees directly from such a simulation. To somewhat revert the tide, this paper seeks to provide its reader with a comprehensive study of the problems one faces when following this route.Methods. The first step in building merger histories of dark matter haloes and their subhaloes is to identify these structures in each of the time outputs (snapshots) produced by the simulation. Even though we discuss a particular implementation of such an algorithm (called AdaptaHOP) in this paper, we believe that our results do not depend on the exact details of the implementation but instead extend to most if not all (sub)structure finders. To illustrate this point in the appendix we compare AdaptaHOP's results to the standard friend-of-friend (FOF) algorithm, widely utilised in the astrophysical community. We then highlight different ways of building merger histories from AdaptaHOP haloes and subhaloes, contrasting their various advantages and drawbacks.Results. We find that the best approach to (sub)halo merging histories is through an analysis that goes back and forth between identification and tree building rather than one that conducts a straightforward sequential treatment of these two steps. This is rooted in the complexity of the merging trees that have to depict an inherently dynamical process from the partial temporal information contained in the collection of instantaneous snapshots available from the N-body simulation. However, we also propose a simpler sequential “Most massive Substructure Method” (MSM) whose trees approximate those obtained via the more complicated non sequential method.