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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

AbacusSummit Cleaned Halo Catalogs

This is a data release from the AbacusSummit suite of cosmological N-body simulations. It contains dark matter halo catalogs and particle samples from those halos. The halo catalogs have been augmented (cleaned) using halo merger tree information. Descriptions of AbacusSummit, the cleaned halo catalogs, and instructions for manipulating these catalogs can be found at the following URL: abacussummit.readthedocs.io/ The halo catalog cleaning is structured as a set of auxiliary files that are ingested by the reader code at runtime. But this release contains both the original catalogs and the auxiliary files, thus forming a self-contained dataset. The files in this release are aggregated by redshift. We define sets of simulations (like all c000 sims or all hugebase sims), and then store one redshift from all simulations per tarball. This is designed to support the use-case where a user wants to analyze multiple simulations at a certain redshift.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

The Mira-Titan Universe. III. Emulation of the Halo Mass Function

We construct an emulator for the halo mass function over group and cluster mass scales for a range of cosmologies, including the effects of dynamical dark energy and massive neutrinos. The emulator is based on the recently completed Mira-Titan Universe suite of cosmological N-body simulations. The main set of simulations spans 111 cosmological models with 2.1 Gpc boxes. We extract halo catalogs in the redshift range z = [0.0, 2.0] and for masses M-200c >= 10(13)M(circle dot)/h. The emulator covers an eight-dimensional hypercube spanned by {Omega(m)h(2), Omega(b)h(2), Omega(nu)h(2), sigma(8), h, n(s), w(0), w(a)}; spatial flatness is assumed. We obtain smooth halo mass functions by fitting piecewise second-order polynomials to the halo catalogs and employ Gaussian process regression to construct the emulator while keeping track of the statistical noise in the input halo catalogs and uncertainties in the regression process. For redshifts z less than or similar to 1, the typical emulator precision is better than 2% for 10(13)-10(14)M(circle dot)/h and <10<^> M similar or equal to 101(circle dot)(54)/h. For comparison, fitting functions using the traditional universal form for the halo mass function can be biased at up to 30% at M similar or equal to 10(144)M(circle dot)/h for z = 0. Our emulator is publicly available at https://github.com/SebastianBocquet/MiraTitanHMFemulator.

cosmology: theory↗
DOE OSTI2020

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. Here 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.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

AbacusSummit: Cosmological N-body Halos, Light Cones, Particles, Merger Trees, Initial Conditions, and Power Spectra

This is the primary data release of the AbacusSummit, a suite of large, high-accuracy cosmological N-body simulations. Documentation describing the suite and code, including links to refereed publications and instructions for manipulating the data contained in this release, may be found at the following URL: https://abacussummit.readthedocs.io/ The primary data products presented in this release are halo catalogs, light cones, and particle data. Several supplemental products are also presented: power spectra, initial conditions, and merger trees. Cleaned halo catalogs are also provided for the subset of simulations that were used in refereed publications at the time of this DOI. This release also contains several large scale-free and high-redshift simulations run as part of the same allocation used to produce AbacusSummit.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

AbacusSummit Halo Light Cone Catalogs

This is a set of halo light cone catalogs from the AbacusSummit suite of cosmological N-body simulations (abacussummit.readthedocs.io/). They are a value-added data product provided by post-processing the simulation output. The main application of the halo light cone catalogs is the construction of realistic mock galaxy catalogues and weak lensing maps on the sky. The algorithm (described in Hadzhiyska et al. 2021) associates CompaSO halos from 29 redshift epochs spanning z = 0.1-2.5 with their particles at the time of light-cone crossing. It then records the halo and particle information into an easily accessible product, which can be read with the CompaSO reader. The 25 base resolution boxes at fiducial cosmology have a halo light cone catalog covering an octant of the sky to z approx 0.8 and about 2000 deg2 extending to z approx 2.4. The huge boxes provide light cone information of the full sky until z approx 2.18 and extend further towards the corners of the box (available until z = 2.25). Galaxy mock catalogs on the sky can be generated easily though the AbacusHOD script providing an extended HOD framework (see Yuan et al. 2021, for details), which has been modified to work with the halo light cone catalogs. The available tracers are luminous red galaxies (LRGs), emission-line galaxies (ELGs), and quasi-stellar objects (QSOs).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

BASS. XXXVI. Constraining the Local Supermassive Black Hole–Halo Connection with BASS DR2 AGNs

We investigate the connection between supermassive black holes (SMBHs) and their host dark matter halos in the local universe using the clustering statistics and luminosity function of active galactic nuclei (AGNs) from the Swift/BAT AGN Spectroscopic Survey (BASS DR2). By forward-modeling AGN activity into snapshot halo catalogs from N -body simulations, we test a scenario in which SMBH mass correlates with dark matter (sub)halo mass for fixed stellar mass. We compare this to a model absent of this correlation, where stellar mass alone determines the SMBH mass. We find that while both simple models are able to largely reproduce the abundance and overall clustering of AGNs, the model in which black hole mass is tightly correlated with halo mass is preferred by the data by 1.8 σ . When including an independent measurement on the black hole mass–halo mass correlation, this model is preferred by 4.6 σ . We show that the clustering trends with black hole mass can further break the degeneracies between the two scenarios and that our preferred model reproduces the measured clustering differences on one-halo scales between large and small black hole masses. These results indicate that the halo binding energy is fundamentally connected to the growth of SMBHs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

The HalfDome multi-survey cosmological simulations: N-body simulations

Upcoming cosmological surveys have the potential to reach groundbreaking discoveries on multiple fronts, including the neutrino mass, dark energy, and inflation. Most of the key science goals require the joint analysis of datasets from multiple surveys to break parameter degeneracies and calibrate systematics. To realize such analyses, a large set of mock simulations that realistically model correlated observables is required. In this paper we present the N-body component of the HalfDome cosmological simulations, designed for the joint analysis of Stage-IV cosmological surveys, such as Rubin LSST, Euclid, SPHEREx, Roman, DESI, PFS, Simons Observatory, CMB-S4, and LiteBIRD. Our 300TB initial data release includes full-sky lightcones and halo catalogs between z = 0–4 for 11 fixed cosmology realizations, as well as an additional run with local primordial non-Gaussianity (f NL = 20). The simulations evolve 61443 particles in a 3.75 h -1 Gpc box, reaching a minimum halo mass of ∼6 × 1012 h -1 M ⊙ and maximum scale of k ∼ h Mpc-1. Our data is publicly available: instructions to access the data and plans for future data releases can be found at https://halfdomesims.github.io.

Bayer, Adrian E↗
DOE OSTI2024

Cosmology with persistent homology: a Fisher forecast

Abstract Persistent homology naturally addresses the multi-scale topological characteristics of the large-scale structure as a distribution of clusters, loops, and voids. We apply this tool to the dark matter halo catalogs from theQuijotesimulations, and build a summary statistic for comparison with the joint power spectrum and bispectrum statistic regarding their information content on cosmological parameters and primordial non-Gaussianity. Through a Fisher analysis, we find that constraints from persistent homology are tighter for 8 out of the 10 parameters by margins of 13–50%. The complementarity of the two statistics breaks parameter degeneracies, allowing for a further gain in constraining power when combined. We run a series of consistency checks to consolidate our results, and conclude that our findings motivate incorporating persistent homology into inference pipelines for cosmological survey data.

Astronomy & Astrophysics↗
DOE OSTI2020

Atacama Cosmology Telescope: Component-separated maps of CMB temperature and the thermal Sunyaev-Zel’dovich effect

Optimal analyses of many signals in the cosmic microwave background (CMB) require map-level extraction of individual components in the microwave sky, rather than measurements at the power spectrum level alone. To date, nearly all map-level component separation in CMB analyses has been performed exclusively using satellite data. In this paper, we implement a component separation method based on the internal linear combination (ILC) approach which we have designed to optimally account for the anisotropic noise (in the 2D Fourier domain) often found in ground-based CMB experiments. Using this method, we combine multi-frequency data from the Planck satellite and the Atacama Cosmology Telescope Polarimeter (ACTPol) to construct the first wide-area, arcminute-resolution component-separated maps (≈ 2100 sq. deg.) of the CMB temperature anisotropy and the thermal Sunyaev-Zel'dovich (tSZ) effect sourced by the inverse-Compton scattering of CMB photons off hot, ionized gas. Our ILC pipeline allows for explicit deprojection of various contaminating signals, including a modified blackbody approximation of the cosmic infrared background (CIB) spectral energy distribution. The cleaned CMB maps will be a useful resource for CMB lensing reconstruction, kinematic SZ cross-correlations, and primordial non-Gaussianity studies. Here, the tSZ maps will be used to study the pressure profiles of galaxies, groups, and clusters through cross-correlations with halo catalogs, with dust contamination controlled via CIB deprojection. The data products described in this paper are available on LAMBDA.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

A Gigaparsec-scale Hydrodynamic Volume Reconstructed with Deep Learning

The next generation of spectroscopic surveys will map the large-scale structure of the Universe at high redshifts (2 ≤ z ≤ 5) using millions of quasar spectra, enabling major advances in constraining both the standard cosmological model and its extensions. Robust cosmological analyses of these data sets require numerical simulations that both cover gigaparsec volumes and resolve features on ∼10 kpc scales and smaller. However, running such large-volume, high-resolution hydrodynamic simulations is computationally prohibitive. We present a generative deep learning model that enhances a low-resolution, gigaparsec-scale (960 h −1 Mpc) hydrodynamic simulation using a smaller (80 h −1 Mpc) high-resolution input hydrodynamic simulation as training data. The resulting enhanced simulation reproduces the line-of-sight power spectrum to within ∼10% and the three-dimensional power spectrum at the ∼20% level at intermediate to small scales (k ≲ 2 h Mpc −1 ). Our method shows strong promise for producing realistic simulations for cosmological analyses with current surveys such as the Dark Energy Spectroscopic Instrument and upcoming next-generation experiments, but further improvements are needed to accurately recover the large-scale modes. We publicly release the enhanced hydrodynamic simulation, along with a halo catalog from a companion N-body dark matter simulation to support the calibration of data analysis pipelines for these large-scale surveys.

Convolutional neural networks↗
NASA NTRS2020

Atacama Cosmology Telescope: Component-separated maps of CMB temperature and the thermal Sunyaev-Zel'dovich effect

Optimal analyses of many signals in the cosmic microwave background (CMB) require map-level extraction of individual components in the microwave sky, rather than measurements at the power spectrum level alone. To date, nearly all map-level component separation in CMB analyses has been performed exclusively using satellite data. In this paper, we implement a component separation method based on the internal linear combination (ILC) approach which we have designed to optimally account for the anisotropic noise (in the 2D Fourier domain) often found in ground-based CMB experiments. Using this method, we combine multi-frequency data from the Planck satellite and the Atacama Cosmology Telescope Polarimeter (ACTPol) to construct the first wide area (≈2100 sq. deg.), arcminute-resolution component-separated maps of the CMB temperature anisotropy and the thermal Sunyaev-Zel'dovich (tSZ) effect sourced by the inverse-Compton scattering of CMB photons off hot, ionized gas. Our ILC pipeline allows for explicit deprojection of various contaminating signals, including a modified blackbody approximation of the cosmic infrared background (CIB) spectral energy distribution. The cleaned CMB maps will be a useful resource for CMB lensing reconstruction, kinematic SZ cross-correlations, and primordial non-Gaussianity studies. The tSZ maps will be used to study the pressure pro les of galaxies, groups, and clusters through cross-correlations with halo catalogs, with dust contamination controlled via CIB deprojection. The data products described in this paper are available on LAMBDA.

Mathew S. Madhavacheril↗
DOE OSTI2023

A Catalog of Distance Determinations for the LAMOST DR8 K Giants in the Galactic Halo

We present a catalog of distances for 19,544 K giants drawn from Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) DR8. Most of them are located in the halo of the Milky Way up to ~120 kpc. There are 15% K giants without Sloan Digital Sky Survey (SDSS) photometry, for which we supplements with Pan-STARRS1 (PS1) photometry calibrated to SDSS photometric system. The possible contamination of the red clumps/horizontal branch are removed according to metallicities and colors before the distance determination. Combining the LAMOST spectroscopic metallicities with the SDSS/PS1 photometry, we estimate the absolute magnitudes in the SDSS r band, the distance moduli, and the corresponding uncertainties through an Bayesian approach devised by Xue et al. for the Sloan Extension for Galactic understanding and exploration halo K giants. The typical distance precision is about 11%. The stars in the catalog lie in a region of 4–126 kpc from the Galactic center, of which with 6320 stars beyond 20 kpc and 273 stars beyond 50 kpc, forming the largest spectroscopic sample of distant tracers in the Milky Way halo so far.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

The DESI Y1 RR Lyrae catalog I: Empirical modeling of the cyclic variation of spectroscopic properties and a chemodynamical analysis of the outer halo

We present the catalog of RR Lyrae stars observed in the first year of operations of the Dark Energy Spectroscopic Instrument (DESI) survey. This catalog contains 6,240 RR Lyrae stars out to $\sim100$ kpc from the Galactic center and over 12,000 individual epochs with homogeneously-derived stellar atmospheric parameters. We introduce a novel methodology to model the cyclical variation of the spectroscopic properties of RR Lyrae from single-epoch measurements. We employ this method to infer the radial velocity and effective temperature variation of fundamental mode and first-overtone RR Lyrae stars and to determine their systemic velocities and mean temperatures. For fundamental mode pulsators, we obtain radial velocity curves with amplitudes of $\sim$30--50 km s$^{-1}$ and effective temperature curves with 300--1,000 K variations, whereas for first-overtone pulsators these amplitudes are $\sim20$ km s$^{-1}$ and $\sim 600$ K, respectively. We use our sample to study the metallicity distribution of the halo and its dependence on Galactocentric distance ($R_{\rm GC}$). Using a radius-dependent mixture model, we split the data into chemodynamically distinct components and find that our inner halo sample ($R_{\rm GC}\lesssim50$ kpc) is predominantly composed of stars with [Fe/H] $\sim-1.5$ dex and largely radial orbits (with an anisotropy parameter $\beta\sim0.94$), that we associate with the Gaia-Sausage-Enceladus merger event. Stars in the outer halo field exhibit a broader and more metal-poor [Fe/H] distribution with more circular orbits ($\beta\sim0.39$). The metallicity gradient of the metal-rich and the metal-poor components is found to be $0.005$ and $0.010$ dex kpc$^{-1}$, respectively. Our catalog highlights DESI's tantalizing potential for studying the Milky Way and the pulsation properties of RR Lyrae stars in the era of large spectroscopic surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

A Hydro-particle-mesh Code for Efficient and Rapid Simulations of the Intracluster Medium

We introduce the cosmological HYPER code based on an innovative hydro-particle-mesh (HPM) algorithm for efficient and rapid simulations of gas and dark matter. For the HPM algorithm, we update the approach of Gnedin & Hui to expand the scope of its application from the lower-density intergalactic medium (IGM) to the higher-density intracluster medium (ICM). While the original algorithm tracks only one effective particle species, the updated version separately tracks the gas and dark matter particles, as they do not exactly trace each other on small scales. For the approximate hydrodynamics solver, the pressure term in the gas equations of motion is calculated using robust physical models. In particular, we use a dark matter halo model, ICM pressure profile, and IGM temperature–density relation, all of which can be systematically varied for parameter-space studies. We show that the HYPER simulation results are in good agreement with the halo model expectations for the density, temperature, and pressure radial profiles. Simulated galaxy cluster scaling relations for Sunyaev–Zel’dovich (SZ) and X-ray observables are also in good agreement with mean predictions, with scatter comparable to that found in hydrodynamic simulations. HYPER also produces lightcone catalogs of dark matter halos and full-sky tomographic maps of the lensing convergence, SZ effect, and X-ray emission. These simulation products are useful for testing data analysis pipelines, generating training data for machine learning, understanding selection and systematic effects, and for interpreting astrophysical and cosmological constraints.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Constraining the galaxy-halo connection of infrared-selected unWISE galaxies with galaxy clustering and galaxy-CMB lensing power spectra

We present the first detailed analysis of the connection between galaxies and their dark matter halos for the unWISE galaxy catalog—a full-sky, infrared-selected sample built from WISE data, containing over 500 million galaxies. Using unWISE galaxy-galaxy autocorrelation and Planck CMB lensing-galaxy cross-correlation measurements down to 10 arcmin angular scales, we constrain the halo occupation distribution (HOD), a model describing how central and satellite galaxies are distributed within dark matter halos, for three unWISE galaxy samples at mean redshifts z ¯ ≈ 0.6 , 1.1, and 1.5, assuming a fixed cosmology at the best-fit Planck Λ CDM values. We constrain the characteristic minimum halo mass to host a central galaxy, M min HOD = 1.8 3 - 1.63 + 0.41 × 10 12 M ⊙ / h , 5.22 - 4.80 + 0.34 × 10 12 M ⊙ / h , 6.60 - 1.11 + 0.30 × 10 13 M ⊙ / h and the mass scale at which one satellite galaxy per halo is found, M 1 ' = 1.1 3 - 0.70 + 0.32 × 10 13 M ⊙ / h , 1.18 - 1.11 + 0.30 × 10 13 M ⊙ / h , 1.23 - 1.17 + 0.14 × 10 14 M ⊙ / h for the unWISE samples at z ¯ ≈ 0.6 , 1.1, and 1.5, respectively. We find that all three samples are dominated by central galaxies, rather than satellites. Using our constrained HOD models, we infer the effective linear galaxy bias for each unWISE sample, and find that it does not evolve as steeply with redshift as found in previous perturbation-theory-based analyses of these galaxies. We discuss possible sources of systematic uncertainty in our results, the most significant of which is the uncertainty on the galaxy redshift distribution. Our HOD constraints provide a detailed, quantitative understanding of how the unWISE galaxies populate the underlying dark matter halo distribution. These constraints will have a direct impact on future studies employing the unWISE galaxies as a cosmological and astrophysical probe, including measurements of ionized gas thermodynamics and dark matter profiles via Sunyaev-Zel’dovich and lensing cross-correlations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

An Extended Halo-based Group/Cluster Finder: Application to the DESI Legacy Imaging Surveys DR8

We extend the halo-based group finder developed by Yang et al. (2005c) to use data simultaneously with either photometric or spectroscopic redshifts. A mock galaxy redshift survey constructed from a high-resolution N-body simulation is used to evaluate the performance of this extended group finder. For galaxies with magnitude z ≤ 21 and redshift 0 < z ≤ 1.0 in the DESI legacy imaging surveys (the Legacy Surveys), our group finder successfully identifies more than 60% of the members in about 90% of halos with mass ≳10 12.5 h –1 M ⊙ . Detected groups with mass ≳10 12.0 h –1 M ⊙ have a purity (the fraction of true groups) greater than 90%. The halo mass assigned to each group has an uncertainty of about 0.2 dex at the high-mass end ≳10 13.5 h –1 M ⊙ and 0.45 dex at the low-mass end. Groups with more than 10 members have a redshift accuracy of ~0.008. We apply this group finder to the Legacy Surveys DR8 and find 6.4 million groups with at least three members. About 500,000 of these groups have at least 10 members. Furthermore, the resulting catalog containing 3D coordinates, richness, halo masses, and total group luminosities is made publicly available.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

The star formation, dust, and abundance of galaxies with unWISE -CIB cross-correlations

Here, the cosmic infrared background (CIB) is the accumulated infrared (IR) radiation mainly from interstellar dust heated up by early stars. In this work, we measure the cross-correlation between galaxies from the unWISE catalog and the CIB maps from the Planck satellite to simultaneously constrain the cosmic star formation rate (SFR), dust spectral energy distribution (SED), and the halo occupation distribution (HOD). The unWISE galaxy catalog is divided into three tomographic bins centered at z ~ 0.6, 1.1, 1.5, and the CIB maps are at 353, 545, and 857 GHz. We measure the cross-correlations between these galaxy samples and CIB maps and get a 194σ signal within an angular scale 100 < ℓ < 2000, from which we constrain two CIB halo models from previous literature and one new model. The SFR, SED, and HOD model parameters are constrained consistently among the three models. Specifically, the dust temperature at z = 0 is constrained T 0 = $21.14^{+1.02}_{-1.34}$ K, which is slightly lower than T 0 = 24.4±1.9 K measured by the Planck collaboration. The halo mass that gives the most efficient star formation is around 10 11.79 $^{+0.73}_{-0.86}$ M ⊙ . From the model parameters, combined with the SFR density at z = 0 synthesized from multi-wavelength observations, we break the degeneracy between SED and SFR and recover the cosmic star formation history that is consistent with multi-wavelength surveys. We also constrain the graybody SED model in agreement with previous measurements from infrared flux stacking. From the HOD constraints, we derive an increasing trend of galaxy linear bias along redshifts that agrees with the results from cross- and auto-correlation with unWISE galaxies. This study indicates the power of using CIB-galaxy cross-correlation to study star formation, dust, and abundance of galaxies across cosmic time.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Dark Energy Survey Year 3 Results: Galaxy mock catalogs for BAO analysis

The calibration and validation of scientific analysis in simulations is a fundamental tool to ensure unbiased and robust results in observational cosmology. In particular, mock galaxy catalogs are a crucial resource to achieve these goals in the measurement of baryon acoustic oscillation (BAO) in the clustering of galaxies. Here we present a set of 1952 galaxy mock catalogs designed to mimic the Dark Energy Survey Year 3 BAO sample over its full photometric redshift range 0.6 < zphoto < 1.1. The mocks are based upon 488 ICE-COLA fast N-body simulations of full-sky light cones and were created by populating halos with galaxies, using a hybrid halo occupation distribution – halo abundance matching model. This model has ten free parameters, which were determined, for the first time, using an automatic likelihood minimization procedure. We also introduced a novel technique to assign photometric redshift for simulated galaxies, following a two-dimensional probability distribution with VIMOS Public Extragalactic Redshift Survey data. The calibration was designed to match the observed abundance of galaxies as a function of photometric redshift, the distribution of photometric redshift errors, and the clustering amplitude on scales smaller than those used for BAO measurements. An exhaustive analysis was done to ensure that the mocks reproduce the input properties. Finally, mocks were tested by comparing the angular correlation function w(θ), angular power spectrum Cℓ, and projected clustering ξp(r⊥) to theoretical predictions and data. The impact of volume replication in the estimate of the covariance is also investigated. The success in accurately reproducing the photometric redshift uncertainties and the galaxy clustering as a function of redshift render this mock creation pipeline as a benchmark for future analyses of photometric galaxy surveys.Key words: catalogs / large-scale structure of Universe / galaxies: distances and redshifts / Galaxy: halo / methods: numerical

79 ASTRONOMY AND ASTROPHYSICS↗