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Haloes gone MAD: The Halo-Finder Comparison Project
Alexander Knebe, Steffen R. Knollmann, Stuart I. Muldrew, Frazer R. Pearce, Miguel Angel Aragon-Calvo, Yago Ascasibar, Peter S. Behroozi, Daniel Ceverino, Stephane Colombi, Juerg Diemand, Klaus Dolag, Bridget L. Falck, Patricia Fasel, Jeff Gardner, Stefan Gottloeber, Chung-Hsing Hsu, Francesca Iannuzzi, Anatoly Klypin, Zarija Lukic, Michal Maciejewski, Cameron McBride, Mark C. Neyrinck, Susana Planelles, Doug Potter, Vicent Quilis, Yann Rasera, Justin I. Read, Paul M. Ricker, Fabrice Roy, Volker Springel, Joachim Stadel, Greg Stinson, P. M. Sutter, Victor Turchaninov, Dylan Tweed, Gustavo Yepes, Marcel Zemp
TL;DR
Halo-finder studies lacked a coherent quantitative benchmark despite differing object definitions and increasingly sophisticated codes. The paper compares 18 finders using mock haloes and a cosmological simulation, finding broad agreement on basic halo properties while exposing persistent substructure and particle-assignment limitations.
Problem
The literature lacked a conclusive quantitative comparison of halo-finding techniques based on a well-defined test suite, while halo definitions varied across studies.
Method
The authors compare 18 halo finders across mock-halo tests and a high-resolution cosmological simulation using a publicly available suite of scenarios.
Results
The finders agree well on basic cosmological-halo properties, including mass, velocity, position, and vmax.
Takeaways & Limitations
Phase-space finders locate central and low-particle-number substructure more effectively, but may still assign incorrect particles and derive inaccurate properties.
Takeaways & Limitations
Results can be brought into agreement through appropriate parameter choices, so the comparison concerns codes rather than fixed algorithms.
Abstract
from arXiv · showhide
[abridged] We present a detailed comparison of fundamental dark matter halo properties retrieved by a substantial number of different halo finders. These codes span a wide range of techniques including friends-of-friends (FOF), spherical-overdensity (SO) and phase-space based algorithms. We further introduce a robust (and publicly available) suite of test scenarios that allows halo finder developers to compare the performance of their codes against those presented here. This set includes mock haloes containing various levels and distributions of substructure at a range of resolutions as well as a cosmological simulation of the large-scale structure of the universe. All the halo finding codes tested could successfully recover the spatial location of our mock haloes. They further returned lists of particles (potentially) belonging to the object that led to coinciding values for the maximum of the circular velocity profile and the radius where it is reached. All the finders based in configuration space struggled to recover substructure that was located close to the centre of the host halo and the radial dependence of the mass recovered varies from finder to finder. Those finders based in phase space could resolve central substructure although they found difficulties in accurately recovering its properties. Via a resolution study we found that most of the finders could not reliably recover substructure containing fewer than 30-40 particles. However, also here the phase space finders excelled by resolving substructure down to 10-20 particles. By comparing the halo finders using a high resolution cosmological volume we found that they agree remarkably well on fundamental properties of astrophysical significance (e.g. mass, position, velocity, and peak of the rotation curve).
1 INTRODUCTION
The paper addresses the lack of a coherent, quantitative comparison of halo-finding codes despite their central role in identifying simulation objects. It introduces a broad comparison project and test suite to assess how different approaches recover haloes and substructure.
- The Necessity for a Comparison Project: Halo finders reduce simulation data to gravitationally bound objects that can be compared with the observed Universe.They search simulated matter-density fields and identify locally overdense systems as haloes.
- Halo-finder approaches: The comparison spans density-peak and particle-collector approaches, with spherical-overdensity and FOF methods remaining foundational to many codes.Particle collectors may link particles in configuration space or phase space, whereas density-peak methods grow shells around detected centres.
- The Necessity for a Comparison Project: Quantitative comparison of halo-finding techniques remained lacking, while differing halo definitions made results difficult to compare.Earlier studies did not provide a conclusive inter-comparison based on a well-defined test suite.
- The Workshop: The project compares codes directly rather than tuning them to match theoretical predictions, and provides publicly useful, well-defined test cases.The tests include mock haloes and a state-of-the-art cosmological simulation.
- How to compare Haloes?: Vmax was selected as a stable comparison quantity, although its central measurement is sensitive to resolution and does not directly resolve halo-mass ambiguity.The particle lists supplied by participants were treated mainly as indicators of missing or contaminating particles.
- How to compare Haloes?: Most finders recover mock-halo locations and basic properties well, but central substructure remains difficult, especially for configuration-space methods.Phase-space finders often identify central substructure but can misestimate its associated mass or particle membership.
2 THE CODES
The paper surveys halo finders spanning configuration-space, density-based, FOF, and phase-space methodologies. It emphasizes their object definitions, hierarchy construction, unbinding procedures, and implementation-specific limitations.
- Code organization: The participating codes are organized by methodology, from spherical-overdensity and FOF-based finders to six-dimensional phase-space finders.This organization is used both for presenting the codes and for comparing them.
- FOF methods: The MPI hierarchical FOF implementation constructs fast clusters at arbitrary overdensities and tracks progenitor-descendant relationships between time steps.It uses a minimum spanning tree so subgraphs can be constructed in parallel.
- FOF methods: The hierarchical FOF method identifies subhaloes at 512 times the virial overdensity, but consequently underestimates their mass and size.The velocity of the density peak is estimated correctly, without removing unbound particles.
- Density-based methods: VOBOZ defines haloes as density peaks surrounded by gravitationally bound particles and applies density and statistical-significance thresholds.Its physical density threshold is set to 200 times the mean density and its significance threshold to 4-σ here.
- HOT+FiEstAS: HOT+FiEstAS identifies density-field peaks and assigns boundaries at saddle-point isodensity contours within a hierarchy.It is applied in three-dimensional positions and six-dimensional phase space, but does not use binding energy or virial-radius knowledge.
- HOT+FiEstAS: HOT+FiEstAS can identify filamentary structures as objects, while its current implementation is not applicable to cosmological simulations.Keeping unbound particles is also problematic for subhaloes near host centres.
- Rockstar: Rockstar builds an adaptive hierarchy of phase-space FOF subgroups, renormalizing distances by each subgroup’s position and velocity dispersions.It begins with a large-linking-length 3D FOF group and captures 70% of particles at each successive subgroup level in this analysis.
3 THE DATA
The comparison uses controlled dark-matter-only mock haloes and a cosmological simulation, with standardized and code-native analyses. Mock systems vary density profile, embedded substructure, spatial configuration, and particle resolution to test halo recovery.
- Test suite: The test suite combines isolated and embedded mock haloes with a cosmological simulation focused on large-scale structure.The mock set includes field haloes, subhaloes, and subsubhaloes in larger hosts.
- Data scope: The comparison excludes baryons and gas physics because most participating codes identify objects from dark-matter data alone.A comparison including baryonic physics was postponed to a later study.
- Comparison procedure: For mock haloes, each finder returned particle lists and centres, while one post-processing code derived the studied quantities.This was intended to homogenize the comparison and reduce code-to-code analysis variation.
- Mock profiles: The mock haloes primarily follow NFW profiles, with Plummer-profile tests added to assess sensitivity to density cores and centre determination.The Plummer spheres are academic stability tests rather than observed cosmological counterparts.
- Resolution and blind tests: Resolution tests progressively reduce the particle number sampling a subhalo, thereby reducing its mass at fixed particle mass.A separate blind test used an unknown setup and involved only a small subset of finders.
4 THE COMPARISON
The comparison shows that halo finders generally recover centres and velocities, but differ substantially in particle-based mass estimates, especially for subhaloes near host centres. The maximum circular velocity is a more stable mass proxy, while phase-space methods better recover central substructure and during central passage.
- Recovery of Host and Subhalo Properties: Most NFW centre offsets are below ≈5h−1 kpc, although some FOF-based finders produce outliers.For the large halo, the 100th particle lies 3h−1 kpc from the nominal centre.
- Recovery of Host and Subhalo Properties: Particle counts and M200 estimates vary substantially across finders because halo-edge definitions are unstable, particularly for embedded subhaloes.The comparison therefore favours vmax for cross-comparing halo properties.
- Recovery of Host and Subhalo Properties: vmax agrees considerably better with analytical expectations than M200, although most finders still fail to recover subsubhalo values correctly.The maximum circular velocity is determined mainly by central regions and is less affected by uncertain outer boundaries.
- Radial Dependence of Subhalo Properties: Only phase-space finders disentangle a subhalo placed directly at the host centre, but their recovered particle assignments can still be incomplete or incorrect.For NFW haloes, recovered particle counts decline toward the host centre as the density contrast decreases.
- Radial Dependence of Subhalo Properties: vmax remains nearly unchanged with subhalo position, and all finders recover it equally well from the particle lists used in the radial test.Differences in particle counts mainly arise from the less-contrasted outer regions of the subhalo.
- Dynamical Infall of a Subhalo: During dynamical infall, all non-phase-space finders lose the subhalo when it overlaps the host centre, whereas phase-space finders continue to identify it.After central passage, all finders recover the object again, but with fewer particles than initially.
5 SUMMARY & CONCLUSIONS
The comparison of 18 halo finders shows broadly comparable recovery of fundamental halo properties, while exposing important differences and limitations for subhaloes, especially near host centres and at low particle numbers.
- Comparison design: 18 halo finders were tested across idealized mock haloes and a cosmological large-scale-structure simulation.The mock suite included isolated haloes, subhaloes, and sub-subhaloes with NFW and Plummer profiles; cosmological data primarily contained field haloes.
- Mock haloes: Bulk velocities, virial masses, and vmax generally agreed with analytical inputs for host haloes and subhaloes, while sub-subhalo deviations reached 50% in mass and 20% in vmax.These quantities were computed with common post-processing software from finder-supplied particle lists and centres.
- Mock haloes: Phase-space finders located subhaloes overlapping host centres, but struggled to calculate their properties accurately.Configuration-space methods had greater difficulty in this central-substructure case.
- Resolution study: 30-40 particles were sufficient for most finders to identify a subhalo, whereas most phase-space finders reached 10-20 particles but some configuration-space methods returned incorrect particle lists.Incorrect particle assignments produced subhalo properties differing from analytical values.
- Cosmological simulation: The cosmological simulation showed agreement within the omitted error bars for mass, velocity, position, and vmax, mainly because its haloes were well-defined and isolated.Subhaloes are less well-defined and produced larger inter-finder differences in the mock tests.
- Concluding remarks: Phase-space finders recovered centres and smaller subhaloes more effectively, but still had difficulty assigning the correct particles and deriving subsequent halo properties.The study compares codes rather than abstract algorithms, and appropriate parameter choices can bring results into agreement without making them identical.