Sussing Merger Trees: The Merger Trees Comparison Project (original) (raw)

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.

Sussing Merger Trees: the influence of the halo finder

2014

Merger tree codes are routinely used to follow the growth and merger of dark matter haloes in simulations of cosmic structure formation. Whereas in Srisawat et. al. we compared the trees built using a wide variety of such codes here we study the influence of the underlying halo catalogue upon the resulting trees. We observe that the specifics of halo finding itself greatly influences the constructed merger trees. We find that the choices made to define the halo mass are of prime importance. For instance, amongst many potential options different finders select self-bound objects or spherical regions of defined overdensity, decide whether or not to include substructures within the mass returned and vary in their initial particle selection. The impact of these decisions is seen in tree length (the period of time a particularly halo can be traced back through the simulation), branching ratio (essentially the merger rate of subhaloes) and mass evolution. We therefore conclude that the choice of the underlying halo finder is more relevant to the process of building merger trees than the tree builder itself. We also report on some built-in features of specific merger tree codes that (sometimes) help to improve the quality of the merger trees produced.

Sussing merger trees: the impact of halo merger trees on galaxy properties in a semi-analytic model

Monthly Notices of the Royal Astronomical Society, 2014

A halo merger tree forms the essential backbone of a semi-analytic model for galaxy formation and evolution. Recent studies have pointed out that extracting merger trees from numerical simulations of structure formation is non-trivial; different tree building algorithms can give differing merger histories. These differences should be carefully understood before merger trees are used as input for models of galaxy formation. We investigate the impact of different halo merger trees on a semi-analytic model. We find that the z = 0 galaxy properties in our model show differences between trees when using a common parameter set. The star formation history of the universe and the properties of satellite galaxies can show marked differences between trees with different construction methods. Independently calibrating the semi-analytic model for each tree can reduce the discrepancies between the z = 0 global galaxy properties, at the cost of increasing the differences in the evolutionary histories of galaxies. Furthermore, the underlying physics implied can vary, resulting in key quantities such as the supernova feedback efficiency differing by factors of 2. Such a change alters the regimes where star formation is primarily suppressed by supernovae. Therefore, halo merger trees extracted from a common halo catalogue using different, but reliable, algorithms can result in a difference in the semi-analytic model. Given the uncertainties in galaxy formation physics, however, these differences may not necessarily be viewed as significant.

Evaluating Semi-Analytic Halo Merging Histories

We evaluate the accuracy of semi-analytic merger-trees by comparing them with the merging histories of dark-matter halos in N-body simulations, focusing on the joint distribution of the number of progenitors and their masses. We first confirm that the halo mass function as predicted directly by the Press-Schechter (PS) model deviates from the simulations by up to 50% depending on the mass scale and redshift, while the means of the projected distributions of progenitor number and mass for a halo of a given mass are more accurately predicted by the Extended PS model. We then use the full merger trees to study the joint distribution as a function of redshift and parent-halo mass. We find that while the deviation of the mean quantities due to the inaccuracy of the Extended PS model partly propagates into the higher moments of the distribution, the merger-tree procedure does not introduce a significant additional source of error. In particular, certain properties of the merging history such as the mass ratio of the progenitors and the total accretion rate are reproduced quite accurately for galaxy sized halos (∼ 10 12 M ⊙), and less so for larger masses. We conclude that although there could be ∼ 50% deviations in the absolute numbers and masses of progenitors and in the higher order moment of these distributions, the relative properties of progenitors for a given halo are reproduced fairly well by the merger trees. They can thus provide a useful framework for modelling galaxy formation once the above-mentioned limitations are taken into account.

On the reliability of merger-trees and the mass growth histories of dark matter haloes

We have used merger trees realizations to study the formation of dark matter haloes. The construction of merger-trees is based on three different pictures about the formation of structures in the Universe. These pictures include: the spherical collapse (SC), the ellipsoidal collapse (EC) and the non-radial collapse (NR). The reliability of merger-trees has been examined comparing their predictions related to the distribution of the number of progenitors, as well as the distribution of formation times, with the predictions of analytical relations. The comparison yields a very satisfactory agreement. Subsequently, the mass growth histories (MGH) of haloes have been studied and their formation scale factors have been derived. This derivation has been based on two different definitions that are: (a) the scale factor when the halo reaches half its present day mass and (b) the scale factor when the mass growth rate falls below some specific value. Formation scale factors follow approximately power laws of mass. It has also been shown that MGHs are in good agreement with models proposed in the literature that are based on the results of N-body simulations. The agreement is found to be excellent for small haloes but, at the early epochs of the formation of large haloes, MGHs seem to be steeper than those predicted by the models based on N-body simulations. This rapid growth of mass of heavy haloes is likely to be related to a steeper central density profile indicated by the results of some N-body simulations.

Sussing merger trees: stability and convergence

Monthly Notices of the Royal Astronomical Society, 2016

Merger trees are routinely used to follow the growth and merging history of dark matter haloes and subhaloes in simulations of cosmic structure formation. Srisawat et al. compared a wide range of merger-tree-building codes. Here we test the influence of output strategies and mass resolution on tree-building. We find that, somewhat surprisingly, building the tree from more snapshots does not generally produce more complete trees; instead, it tends to shorten them. Significant improvements are seen for patching schemes that attempt to bridge over occasional dropouts in the underlying halo catalogues or schemes that combine the halo-finding and treebuilding steps seamlessly. The adopted output strategy does not affect the average number of branches (bushiness) of the resultant merger trees. However, mass resolution has an influence on both main branch length and the bushiness. As the resolution increases, a halo with the same mass can be traced back further in time and will encounter more small progenitors during its evolutionary history. Given these results, we recommend that, for simulations intended as precursors for galaxy formation models where of the order of 100 or more snapshots are analysed, the tree-building routine should be integrated with the halo finder, or at the very least be able to patch over multiple adjacent snapshots.

Evaluating approximations for halo merging histories

Monthly Notices of the Royal Astronomical Society, 2000

We study the merging history of dark matter haloes in N-body simulations and semianalytical`merger trees' based on the extended Press±Schechter (EPS) formalism. The main focus of our study is the joint distribution of progenitor number and mass as a function of redshift and parent halo mass. We begin by investigating the mean quantities predicted directly by the Press±Schechter (PS) and EPS formalism, such as the halo mass and conditional mass functions, and compare these predictions with the results of the simulations. The higher moments of this distribution are not predicted by the EPS formalism alone and must be obtained from the merger trees. We find that the Press± Schechter model deviates from the simulations at the level of 30±50 per cent on certain mass scales, and that the sense of the discrepancy changes as a function of redshift. We show that this discrepancy is reflected in the higher moments of the distribution of progenitor mass and number. We investigate some related statistics such as the accretion rate and the mass ratio of the largest two progenitors. For galaxy sized haloes M , 10 12 M (Y we find that the merging history of haloes, as represented by these statistics, is well reproduced in the merger trees compared with the simulations. The agreement deteriorates for larger mass haloes. We conclude that merger trees based on the extended Press±Schechter formalism provide a reasonably reliable framework for semi-analytical models of galaxy formation.

Building merger trees from cosmological N -body simulations

Astronomy and Astrophysics, 2009

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 Nbody 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.

Galaxy formation using halo merger histories taken from N-body simulations

Monthly Notices of the Royal Astronomical Society, 2003

We develop a hybrid galaxy formation model which uses outputs from an N-body simulation to follow the merger histories (or "merger trees") of dark matter halos and treats baryonic processes, such as the cooling of gas within halos and subsequent star formation, using the semi-analytic model of Cole et al. We compare this hybrid model to an otherwise identical model which utilises merger tree realisations generated by a Monte-Carlo algorithm and find that, apart from the limited mass resolution imposed by the N-body particle mass, the only significant differences between the models are due to the known discrepancy between the distribution of halo progenitor masses predicted by extended Press Schechter theory and that found in N-body simulations. We investigate the effect of limited mass resolution on the hybrid model by comparing to a purely semi-analytic model with greatly improved mass resolution. We find that the mass resolution of the simulation we use, which has a particle mass of 1.4 × 10 10 h −1 M ⊙ , is insufficient to produce a reasonable luminosity function for galaxies with magnitudes in the b J band fainter than -17.

HBT+: An Improved Code for Finding Subhaloes and Building Merger Trees in Cosmological Simulations

Monthly Notices of the Royal Astronomical Society, 2017

Dark matter subhalos are the remnants of (incomplete) halo mergers. Identifying them and establishing their evolutionary links in the form of merger trees is one of the most important applications of cosmological simulations. The HBT (Hierachical Bound-Tracing) code identifies haloes as they form and tracks their evolution as they merge, simultaneously detecting subhaloes and building their merger trees. Here we present a new implementation of this approach, HBT+ , that is much faster, more user friendly, and more physically complete than the original code. Applying HBT+ to cosmological simulations, we show that both the subhalo mass function and the peak-mass function are well fitted by similar double-Schechter functions. The ratio between the two is highest at the high-mass end, reflecting the resilience of massive subhaloes that experience substantial dynamical friction but limited tidal stripping. The radial distribution of the most-massive subhaloes is more concentrated than the universal radial distribution of lower mass subhaloes. Subhalo finders that work in configuration space tend to underestimate the masses of massive subhaloes, an effect that is stronger in the host centre. This may explain, at least in part, the excess of massive subhaloes in galaxy cluster centres inferred from recent lensing observations. We demonstrate that the peak-mass function is a powerful diagnostic of merger tree defects, and the merger trees constructed using HBT+ do not suffer from the missing or switched links that tend to afflict merger trees constructed from more conventional halo finders. We make the HBT+ code publicly available.