Halo Finder Research Articles

The e-MANTIS emulator: Fast and accurate predictions of the halo mass function in f(R)CDM and wCDM cosmologies

In this work, we present a novel emulator of the halo mass function (HMF), which we implemented in the framework of the e-MANTIS emulator of $f(R)$ gravity models. We also extended e-MANTIS to cover a larger cosmological parameter space and to include models of dark energy with a constant equation of state $w$CDM. We used a Latin hypercube sampling of the $w$CDM and $f(R)$CDM cosmological parameter spaces, over a wide range, and carried out a large suite of more than $10000$ $N$-body simulations with a different volume, mass resolution, and random phase for the initial conditions. For each simulation in the suite, we generated halo catalogues using the friends-of-friends (FoF) halo finder, as well as the spherical overdensity (SO) algorithm for different overdensity thresholds (200, 500, and 1000 times the critical density). We decomposed the corresponding HMFs on a B-spline basis, while adopting a minimal set of assumptions on their shape. We used this decomposition to train an emulator based on Gaussian processes. The resulting emulator is able to predict the HMF for redshifts $ 1.5$ and for halo masses $M_h M_ The typical HMF errors for SO haloes with $ c $ at $z=0$ in $w$CDM (respectively $f(R)$CDM) are of the order of $ up to a transition mass $M_t M_ ($M_t M_ For larger masses, the errors are dominated by the shot noise and scale as $ with $ up to $M_h M_ Independently of this general trend, the emulator is able to provide an estimation of its own error as a function of the cosmological parameters, halo mass, and redshift. We have performed an extensive comparison against analytical parametrizations and shown that e-MANTIS is able to better capture the cosmological dependence of the HMF, while being complementary to other existing emulators. The e-MANTIS emulator, which is publicly available, can be used to obtain fast and accurate predictions of the HMF in the $f(R)$CDM and $w$CDM non-standard cosmological models. As such, it represents a useful theoretical tool to constrain the nature of dark energy using data from galaxy cluster surveys.

Haunted haloes: tracking the ghosts of subhaloes lost by halo finders

Abstract Dark matter subhaloes are key for the predictions of simulations of structure formation, but their existence frequently ends prematurely due to two technical issues, namely numerical disruption in N-body simulations and halo finders failing to identify them. Here we focus on the second issue, using the phase-space friends-of-friends halo finder Rockstar as a benchmark (though we expect our results to translate to comparable codes). We confirm that the most prominent cause for losing track of subhaloes is tidal distortion rather than a low number of particles. As a solution, we present a flexible post-processing algorithm that tracks all subhalo particles over time, computes subhalo positions and masses based on those particles, and progressively removes stripped matter. If a subhalo is lost by the halo finder, this algorithm keeps tracking its so-called ghost until it has almost no particles left or has truly merged with its host. We apply this technique to a large suite of N-body simulations and restore lost subhaloes to the halo catalogues, which has a substantial effect on key summary statistics of large-scale structure. Specifically, the subhalo mass function increases by about 20–30 per cent and the halo correlation function by about 50 per cent at small scales. While these quantitative results are somewhat specific to our algorithm, they demonstrate that particle tracking is a promising way to reliably follow haloes and to reduce the need for orphan models. Our algorithm and augmented halo catalogues are publicly available.

Symfind : Addressing the Fragility of Subhalo Finders and Revealing the Durability of Subhalos

A major question in ΛCDM is what this theory actually predicts for the properties of subhalo populations. Subhalos are difficult to accurately simulate and to find within simulations, and this propagates into uncertainty in theoretical predictions for satellite galaxies. We present Symfind, a new particle-tracking-based subhalo finder, and demonstrate that it can track subhalos to orders-of-magnitude lower masses than commonly used halo-finding tools, with a focus on Rockstar and consistent-trees. These longer survival times mean that at a fixed peak subhalo mass, we find ≈ 15%–40% more subhalos within the virial radius, R vir, and ≈35%–120% more subhalos within R vir/4 in the Symphony dark-matter-only simulation suite. More subhalos are found as the resolution is increased, in contrast to the Rockstar halo finder, which appears to be converged at smaller subhalo counts. We perform extensive numerical testing. In agreement with idealized simulations, we show that the vmax , the maximum circular velocity, is systematically biased low until high resolutions (n peak ≳ 3 × 104) are achieved, but that mass loss itself can be resolved at much more modest resolutions (n peak ≳ 4 × 103). We show that Rockstar converges to false solutions for the mass function, radial distribution, and disruption masses of subhalos. We argue that our new method can trace resolved subhalos until the point of typical galaxy disruption without invoking post hoc orphan modeling. We outline a concrete set of steps for determining whether other subhalo finders meet the same criteria. We publicly release Symfind catalogs and particle data for the Symphony simulation suite at http://web.stanford.edu/group/gfc/symphony.

Self-similar mass accretion history in scale-free simulations

ABSTRACT Using a scale-free N-body simulation generated with the abacusN-body code, we test the robustness of halo mass accretion histories via their convergence to self-similarity. We compare two halo finders, rockstar and compaso. We find superior self-similarity in halo mass accretion histories determined using rockstar, with convergence to 5 per cent or better between $\sim\!\! 10^2$ and $10^5$ particles. For compaso, we find weaker convergence over a similar region, with at least 10 per cent between $\sim\!\! 10^2$ and $10^4$ particles. Furthermore, we find that the convergence to self-similarity improves as the simulation evolves, with the largest and deepest regions of convergence appearing after the scale factor quadrupled from the time at which non-linear structures begin to form. With sufficient time evolution, halo mass accretion histories are converged to self-similarity within 5 per cent with as few as $\sim\!\! 70$ particles for compaso and within 2 per cent for as few as $\sim\!\! 30$ particles for rockstar.

Improving the accuracy of halo mass based statistics for fast approximate N-body simulations

ABSTRACT Approximate N-body methods, such as fastpm and cola, have been successful in modelling halo and galaxy clustering statistics, but their low resolution on small scales is a limitation for applications that require high precision. Full N-body simulations can provide better accuracy but are too computationally expensive for a quick exploration of cosmological parameters. This paper presents a method for correcting distinct haloes identified in fast N-body simulations, so that various halo statistics improve to a percent level accuracy. The scheme seeks to find empirical corrections to halo properties such that the virial mass is the same as that of a corresponding halo in a full N-body simulation. The modified outer density contour of the corrected halo is determined on the basis of the fastpm settings and the number of particles inside the halo. This method only changes some parameters of the halo finder, and does not require any extra CPU-cost. We demonstrate that the adjusted halo catalogues of fastpm simulations significantly improve the precision of halo mass-based statistics from redshifts $z=0.0$ to 1.0, and that our calibration can be applied to different cosmologies without needing to be recalibrated.

The hierarchical structure of galactic haloes: differentiating clusters from stochastic clumping with astrolink

ABSTRACT We present astrolink, an efficient and versatile clustering algorithm designed to hierarchically classify astrophysically relevant structures from both synthetic and observational data sets. We build upon clustar-nd, a hierarchical galaxy/(sub)halo finder, so that astrolink now generates a 2D representation of the implicit clustering structure as well as ensuring that clusters are statistically distinct from the noisy density fluctuations implicit within the n-dimensional input data. This redesign replaces the three cluster extraction parameters from clustar-nd with a single parameter, S – the lower statistical significance threshold of clusters, which can be automatically and reliably estimated via a dynamical model-fitting process. We demonstrate the robustness of this approach compared to astrolink’s predecessors by applying each algorithm to a suite of simulated galaxies defined over various feature spaces. We find that astrolink delivers a more powerful clustering performance while being $\sim 27~{{\ \rm per \, cent}}$ faster and using less memory than clustar-nd. With these improvements, astrolink is ideally suited to extracting a meaningful set of hierarchical and arbitrarily shaped astrophysical clusters from both synthetic and observational data sets – lending itself as a great tool for morphological decomposition within the context of hierarchical structure formation.

DESI mock challenge: constructing DESI galaxy catalogues based on FastPM simulations

ABSTRACT Together with larger spectroscopic surveys such as the Dark Energy Spectroscopic Instrument (DESI), the precision of large-scale structure studies and thus the constraints on the cosmological parameters are rapidly improving. Therefore, one must build realistic simulations and robust covariance matrices. We build galaxy catalogues by applying a halo occupation distribution (HOD) model upon the FastPM simulations, such that the resulting galaxy clustering reproduces high-resolution N-body simulations. While the resolution and halo finder are different from the reference simulations, we reproduce the reference galaxy two-point clustering measurements – monopole and quadrupole – to a precision required by the DESI Year 1 emission line galaxy sample down to non-linear scales, i.e. $k\lt 0.5\, h\, \mathrm{Mpc}^{-1}$ or $s\gt 10\, \mathrm{Mpc}\, h^{-1}$. Furthermore, we compute covariance matrices based on the resulting FastPM galaxy clustering – monopole and quadrupole. We study for the first time the effect of fitting on Fourier conjugate (e.g. power spectrum) on the covariance matrix of the Fourier counterpart (e.g. correlation function). We estimate the uncertainties of the two parameters of a simple clustering model and observe a maximum variation of 20 per cent for the different covariance matrices. Nevertheless, for most studied scales the scatter is between 2 and 10 per cent. Consequently, using the current pipeline we can precisely reproduce the clustering of N-body simulations and the resulting covariance matrices provide robust uncertainty estimations against HOD fitting scenarios. We expect our methodology will be useful for the coming DESI data analyses and their extension for other studies.

SimBIG: mock challenge for a forward modeling approach to galaxy clustering

Simulation-Based Inference of Galaxies (SimBIG) is a forward modeling framework for analyzing galaxy clustering using simulation-based inference. In this work, we present the SimBIG forward model, which is designed to match the observed SDSS-III BOSS CMASS galaxy sample. The forward model is based on high-resolution Quijote N-body simulations and a flexible halo occupation model. It includes full survey realism and models observational systematics such as angular masking and fiber collisions. We present the “mock challenge” for validating the accuracy of posteriors inferred from SimBIG using a suite of 1,500 test simulations constructed using forward models with a different N-body simulation, halo finder, and halo occupation prescription. As a demonstration of SimBIG, we analyze the power spectrum multipoles out to k max = 0.5 h/Mpc and infer the posterior of ΛCDM cosmological and halo occupation parameters. Based on the mock challenge, we find that our constraints on Ω m and σ 8 are unbiased, but conservative. Hence, the mock challenge demonstrates that SimBIG provides a robust framework for inferring cosmological parameters from galaxy clustering on non-linear scales and a complete framework for handling observational systematics. In subsequent work, we will use SimBIG to analyze summary statistics beyond the power spectrum including the bispectrum, marked power spectrum, skew spectrum, wavelet statistics, and field-level statistics.

Euclid preparation

Euclid’s photometric galaxy cluster survey has the potential to be a very competitive cosmological probe. The main cosmological probe with observations of clusters is their number count, within which the halo mass function (HMF) is a key theoretical quantity. We present a new calibration of the analytic HMF, at the level of accuracy and precision required for the uncertainty in this quantity to be subdominant with respect to other sources of uncertainty in recovering cosmological parameters from Euclid cluster counts. Our model is calibrated against a suite of N-body simulations using a Bayesian approach taking into account systematic errors arising from numerical effects in the simulation. First, we test the convergence of HMF predictions from different N-body codes, by using initial conditions generated with different orders of Lagrangian Perturbation theory, and adopting different simulation box sizes and mass resolution. Then, we quantify the effect of using different halo finder algorithms, and how the resulting differences propagate to the cosmological constraints. In order to trace the violation of universality in the HMF, we also analyse simulations based on initial conditions characterised by scale-free power spectra with different spectral indexes, assuming both Einstein–de Sitter and standard ΛCDM expansion histories. Based on these results, we construct a fitting function for the HMF that we demonstrate to be sub-percent accurate in reproducing results from 9 different variants of the ΛCDM model including massive neutrinos cosmologies. The calibration systematic uncertainty is largely sub-dominant with respect to the expected precision of future mass–observation relations; with the only notable exception of the effect due to the halo finder, that could lead to biased cosmological inference.

Rapid simulations of halo and subhalo clustering

The analysis of cosmological galaxy surveys requires realistic simulations for their interpretation. Forward modelling is a powerful method to simulate galaxy clustering without the need for an underlying complex model. This approach requires fast cosmological simulations with a high resolution and large volume, to resolve small dark matter halos associated to single galaxies. In this work, we present fast halo and subhalo clustering simulations based on the Lagrangian perturbation theory code PINOCCHIO, which generates halos and merger trees. The subhalo progenitors are extracted from the merger history and the survival of subhalos is modelled. We introduce a new fitting function for the subhalo merger time, which includes a redshift dependence of the fitting parameters. The spatial distribution of subhalos within their hosts is modelled using a number density profile. We compare our simulations with the halo finder ROCKSTAR applied to the full N-body code GADGET-2. The subhalo velocity function and the correlation function of halos and subhalos are in good agreement. We investigate the effect of the chosen number density profile on the resulting subhalo clustering. Our simulation is approximate yet realistic and significantly faster compared to a full N-body simulation combined with a halo finder. The fast halo and subhalo clustering simulations offer good prospects for galaxy forward models using subhalo abundance matching.

The halo-finding problem revisited: a deep revision of the ASOHF code

Context. New-generation cosmological simulations are providing huge amounts of data, whose analysis becomes itself a pressing computational problem. In particular, the identification of gravitationally bound structures, known as halo finding, is one of the main analyses. Several codes that were developed for this task have been presented during the past years. Aims. We present a deep revision of the code ASOHF. The algorithm was thoroughly redesigned in order to improve its capabilities of finding bound structures and substructures using both dark matter particles and stars, its parallel performance, and its abilities of handling simulation outputs with vast amounts of particles. This upgraded version of ASOHF is conceived to be a publicly available tool. Methods. A battery of idealised and realistic tests are presented in order to assess the performance of the new version of the halo finder. Results. In the idealised tests, ASOHF produces excellent results. It is able to find virtually all the structures and substructures that we placed within the computational domain. When the code is applied to realistic data from simulations, the performance of our finder is fully consistent with the results from other commonly used halo finders. The performance in substructure detection is remarkable. In addition, ASOHF is extremely efficient in terms of computational cost. Conclusions. We present a publicly available deeply revised version of the ASOHF halo finder. The new version of the code produces remarkable results in terms of halo and subhalo finding capabilities, parallel performance, and low computational cost.

The hierarchical structure of galactic haloes: generalized N-dimensional clustering with C luSTAR-ND

ABSTRACT We present C luSTAR-ND, a fast hierarchical galaxy/(sub)halo finder that produces Clustering Structure via Transformative Aggregation and Rejection in N-Dimensions. It is designed to improve upon H alo-OPTICS – an algorithm that automatically detects and extracts significant astrophysical clusters from the 3D spatial positions of simulation particles – by decreasing run-times, possessing the capability for metric adaptivity, and being readily applicable to data with any number of features. We directly compare these algorithms and find that not only does C luSTAR-ND produce a similarly robust clustering structure, it does so in a run-time that is at least 3 orders of magnitude faster. In optimizing C luSTAR-ND’s clustering performance, we have also carefully calibrated 4 of the 7 C luSTAR-ND parameters which – unless specified by the user – will be automatically and optimally chosen based on the input data. We conclude that C luSTAR-ND is a robust astrophysical clustering algorithm that can be leveraged to find stellar satellite groups on large synthetic or observational data sets.

Constructing high-fidelity halo merger trees inabacussummit

ABSTRACTTracking the formation and evolution of dark matter haloes is a critical aspect of any analysis of cosmological N-body simulations. In particular, the mass assembly of a halo and its progenitors, encapsulated in the form of its merger tree, serves as a fundamental input for constructing semi-analytic models of galaxy formation and, more generally, for building mock catalogues that emulate galaxy surveys. We present an algorithm for constructing halo merger trees from abacussummit, the largest suite of cosmological N-body simulations performed to date consisting of nearly 60 trillion particles, and which has been designed to meet the Cosmological Simulation Requirements of the Dark Energy Spectroscopic Instrument (DESI) survey. Our method tracks the cores of haloes to determine associations between objects across multiple time slices, yielding lists of halo progenitors and descendants for the several tens of billions of haloes identified across the entire suite. We present an application of these merger trees as a means to enhance the fidelity of abacussummit halo catalogues by flagging and ‘merging’ haloes deemed to exhibit non-monotonic past merger histories. We show that this cleaning technique identifies portions of the halo population that have been deblended due to choices made by the halo finder, but which could have feasibly been part of larger aggregate systems. We demonstrate that by cleaning halo catalogues in this post-processing step, we remove potentially unphysical features in the default halo catalogues, leaving behind a more robust halo population that can be used to create highly accurate mock galaxy realizations from abacussummit.

Classification algorithms applied to structure formation simulations

Throughout cosmological simulations, the properties of the matter density field in the initial conditions have a decisive impact on the features of the structures formed today. In this paper we use a random-forest classification algorithm to infer whether or not dark matter particles, traced back to the initial conditions, would end up in dark matter halos whose masses are above some threshold. This problem might be posed as a binary classification task, where the initial conditions of the matter density field are mapped into classification labels provided by a halo finder program. Our results show that random forests are effective tools to predict the output of cosmological simulations without running the full process. These techniques might be used in the future to decrease the computational time and to explore more efficiently the effect of different dark matter/dark energy candidates on the formation of cosmological structures.

Halo merger tree comparison: impact on galaxy formation models

ABSTRACT We examine the effect of using different halo finders and merger tree building algorithms on galaxy properties predicted using the galform semi-analytical model run on a high resolution, large volume dark matter simulation. The halo finders/tree builders hbt, rockstar, subfind, and VELOCI raptor differ in their definitions of halo mass, on whether only spatial or phase-space information is used, and in how they distinguish satellite and main haloes; all of these features have some impact on the model galaxies, even after the trees are post-processed and homogenized by galform. The stellar mass function is insensitive to the halo and merger tree finder adopted. However, we find that the number of central and satellite galaxies in galform does depend slightly on the halo finder/tree builder. The number of galaxies without resolved subhaloes depends strongly on the tree builder, with VELOCIraptor, a phase-space finder, showing the largest population of such galaxies. The distributions of stellar masses, cold and hot gas masses, and star formation rates agree well between different halo finders/tree builders. However, because VELOCIraptor has more early progenitor haloes, with these trees galform produces slightly higher star formation rate densities at high redshift, smaller galaxy sizes, and larger stellar masses for the spheroid component. Since in all cases these differences are small we conclude that, when all of the trees are processed so that the main progenitor mass increases monotonically, the predicted galform galaxy populations are stable and consistent for these four halo finders/tree builders.

Compaso: A new halo finder for competitive assignment to spherical overdensities

ABSTRACT We describe a new method (compaso) for identifying groups of particles in cosmological N-body simulations. compaso builds upon existing spherical overdensity (SO) algorithms by taking into consideration the tidal radius around a smaller halo before competitively assigning halo membership to the particles. In this way, the compaso finder allows for more effective deblending of haloes in close proximity as well as the formation of new haloes on the outskirts of larger ones. This halo-finding algorithm is used in the abacussummit suite of N-body simulations, designed to meet the cosmological simulation requirements of the Dark Energy Spectroscopic Instrument (DESI) survey. compaso is developed as a highly efficient on-the-fly group finder, which is crucial for enabling good load-balancing between the GPU and CPU and the creation of high-resolution merger trees. In this paper, we describe the halo-finding procedure and its particular implementation in abacus, accompanying it with a qualitative analysis of the finder. We test the robustness of the compaso catalogues before and after applying the cleaning method described in an accompanying paper and demonstrate its effectiveness by comparing it with other validation techniques. We then visualize the haloes and their density profiles, finding that they are well fit by the NFW formalism. Finally, we compare other properties such as radius–mass relationships and two-point correlation functions with that of another widely used halo finder, rockstar.

The hierarchical structure of galactic haloes: classification and characterization with halo-optics

ABSTRACT We build upon Ordering Points To Identify the Clustering Structure (optics ), a hierarchical clustering algorithm well known to be a robust data miner, in order to produce halo-optics , an algorithm designed for the automatic detection and extraction of all meaningful clusters between any two arbitrary sizes. We then apply halo-optics to the 3D spatial positions of halo particles within four separate synthetic Milky Way-type galaxies, classifying the stellar and dark matter structural hierarchies. Through visualization of the halo-optics output, we compare its structure identification to the state-of-the-art galaxy/(sub)halo finder VELOCIraptor , finding excellent agreement even though halo-optics does not consider kinematic information in this current implementation. We conclude that halo-optics is a robust hierarchical halo finder, although its determination of lower spatial-density features such as the tails of streams could be improved with the inclusion of extra localized information such as particle kinematics and stellar metallicity into its distance metric.

Testing dark matter halo properties using self-similarity

ABSTRACT We use self-similarity in N-body simulations of scale-free models to test for resolution dependence in the mass function and two-point correlation functions of dark matter haloes. We use 10243 particle simulations performed with abacus , and compare results obtained with two halo finders: friends-of-friends (fof ), and rockstar . The fof mass functions show a systematic deviation from self-similarity which is explained by resolution dependence of the fof mass assignment previously reported in the literature. Weak evidence for convergence is observed only starting from haloes of several thousand particles, and mass functions are overestimated by at least as much as $20-25{{\ \rm per\ cent}}$ for haloes of 50 particles. The mass function of the default rockstar halo catalogue (with bound virial spherical overdensity mass), on the other hand, shows good convergence of the order of 50 to 100 particles per halo, with no detectable evidence at the few percent level of any systematic dependence for larger particle number. Tests show that the mass unbinding procedure in rockstar is the key factor in obtaining this much improved resolution. Applying the same analysis to the halo–halo two point correlation function, we find again strong evidence for convergence only for rockstar haloes, at separations sufficiently large so that haloes do not overlap. At these separations, we can exclude dependence on resolution at the $5-10{{\ \rm per\ cent}}$ level once haloes have of the order of 50 to 100 particles. At smaller separations results are not converged even at significantly larger particle number, and bigger simulations would be required to establish the resolution required for convergence.

HIKER: a halo-finding method based on kernel-shift algorithm

We introduce a new halo/subhalo finder, HIKER (a Halo fInder based on KERnel-shift algorithm), which takes advantage of a machine learning method – the mean-shift algorithm combined with the Plummer kernel function, to effectively locate density peaks corresponding to halos/subhalos in density field. Based on these density peaks, dark matter halos are identified as spherical overdensity structures, and subhalos are bound substructures with boundaries at their tidal radius. By testing HIKER code with mock halos, we show that HIKER performs excellently in recovering input halo properties. In particular, HIKER has higher accuracy in locating halo/subhalo centres than most halo finders. With cosmological simulations, we further show that HIKER reproduces the abundance of dark matter halos and subhalos quite accurately, and the HIKER halo/subhalo mass functions and Vmax functions are in good agreement with two widely used halo finders, SUBFIND and AHF.

High mass and halo resolution from fast low resolution simulations

Generating mocks for future sky surveys requires large volumes and high resolutions, which is computationally expensive even for fast simulations. In this work we try to develop numerical schemes to calibrate various halo and matter statistics in fast low resolution simulations compared to high resolution N-body and hydrodynamic simulations. For the halos, we improve the initial condition resolution and develop a halo finder “relaxed-FoF”, where we allow different linking lengths for different halo mass and velocity dispersions. We show that our relaxed-FoF halo finder improves the common statistics, such as halo bias, halo mass function, halo auto power spectrum, cross correlation coefficient with the reference halo catalog, and halo-matter cross power spectrum. We also calibrate small-scale velocities of small halos to improve the power spectrum in redshift space. For the matter statistics, we incorporate the potential gradient descent (PGD) method into fast simulations to improve the matter distribution at nonlinear scales. By building a lightcone output, we show that the PGD method significantly improves the weak lensing convergence tomographic power spectrum. With these improvements FastPM is comparable to the high resolution full N-body simulation of the same mass resolution, with two orders of magnitude fewer time steps. These techniques can be used to improve the halo and matter statistics of FastPM simulations for mock catalogs of future surveys such as DESI and LSST.