TheHaloMod: An online calculator for the halo model

The halo model is a successful framework for describing the distribution of matter in the Universe -- from weak lensing observables to galaxy 2-point correlation functions. We review the basic formulation of the halo model and several of its components in the context of galaxy two-point statistics, developing a coherent framework for its application. We use this framework to motivate the presentation of a new Python tool for simple and efficient calculation of halo model quantities, and their extension to galaxy statistics via a \textit{halo occupation distribution}, called \halomod. This tool is efficient, simple to use, comprehensive and importantly provides a great deal of flexibility in terms of custom extensions. This Python tool is complemented by a new web-application at https://thehalomod.app that supports the generation of many halo model quantities directly from the browser -- useful for educators, students, theorists and observers.

[1]  Chris Power,et al.  HMFcalc: An online tool for calculating dark matter halo mass functions , 2013, Astron. Comput..

[2]  S. Kay,et al.  Dark matter halo concentrations in the Wilkinson Microwave Anisotropy Probe year 5 cosmology , 2008, 0804.2486.

[3]  Michael S. Warren,et al.  Toward a Halo Mass Function for Precision Cosmology: The Limits of Universality , 2008, 0803.2706.

[4]  G. Bryan,et al.  Statistical Properties of X-Ray Clusters: Analytic and Numerical Comparisons , 1997, astro-ph/9710107.

[5]  B. Garilli,et al.  The galaxy-halo connection from a joint lensing, clustering and abundance analysis in the CFHTLenS/VIPERS field , 2015, 1502.02867.

[6]  R. Nichol,et al.  Galaxy–galaxy lensing in the Dark Energy Survey Science Verification data , 2015, Monthly Notices of the Royal Astronomical Society.

[7]  D. P. Schneider,et al.  The Luminosity and Color Dependence of the Galaxy Correlation Function , 2005 .

[8]  J. Einasto On the Construction of a Composite Model for the Galaxy and on the Determination of the System of Galactic Parameters , 1965 .

[9]  C. Blake,et al.  Intensity mapping cross-correlations II: HI halo models including shot noise , 2018, Monthly Notices of the Royal Astronomical Society.

[10]  E. Bertschinger,et al.  Statistics of Primordial Density Perturbations from Discrete Seed Masses , 1991 .

[11]  M. White,et al.  Multi-tracer intensity mapping: cross-correlations, line noise & decorrelation , 2021, Journal of Cosmology and Astroparticle Physics.

[12]  S. Giri,et al.  Halo model approach for the 21-cm power spectrum at cosmic dawn , 2020, 2011.12308.

[13]  A. Lapi,et al.  Statistics of dark matter halos in the excursion set peak framework , 2014, 1407.1137.

[14]  Y. Jing,et al.  ACCURATE UNIVERSAL MODELS FOR THE MASS ACCRETION HISTORIES AND CONCENTRATIONS OF DARK MATTER HALOS , 2008, 0811.0828.

[15]  Nonlinear clustering in models with primordial non-Gaussianity: The halo model approach , 2011 .

[16]  Michal Maciejewski,et al.  Haloes gone MAD: The Halo-Finder Comparison Project , 2011, 1104.0949.

[17]  Linear and non-linear contributions to pairwise peculiar velocities , 2000, astro-ph/0009167.

[18]  S. White,et al.  The mass–concentration–redshift relation of cold dark matter haloes , 2013, 1312.0945.

[19]  Concentrations of Dark Halos from Their Assembly Histories , 2001, astro-ph/0108151.

[20]  Michael S. Warren,et al.  THE LARGE-SCALE BIAS OF DARK MATTER HALOS: NUMERICAL CALIBRATION AND MODEL TESTS , 2010, 1001.3162.

[21]  R. Sheth,et al.  Bias deconstructed: unravelling the scale dependence of halo bias using real-space measurements , 2013, 1305.5830.

[22]  U. Seljak,et al.  Halo Zel’dovich model and perturbation theory: Dark matter power spectrum and correlation function , 2015, 1501.07512.

[23]  M. Manera,et al.  Large-scale bias and the inaccuracy of the peak-background split , 2009, 0906.1314.

[24]  R. Smith,et al.  Testing the Warm Dark Matter paradigm with large-scale structures , 2011, 1103.2134.

[25]  A. D. Bray,et al.  DARK MATTER HALO MODELS OF STELLAR MASS-DEPENDENT GALAXY CLUSTERING IN PRIMUS+DEEP2 AT 0.2 < z < 1.2 , 2015, 1503.00731.

[26]  M. Kuhlen,et al.  The Origin of Dark Matter Halo Profiles , 2010, 1010.2539.

[27]  Dark matter and cosmic structure , 2012, 1210.0544.

[28]  C. Blake,et al.  The Gigaparsec WiggleZ simulations: characterizing scale-dependant bias and associated systematics in growth of structure measurements , 2014, 1407.0390.

[29]  A. Myers,et al.  CROSS-CORRELATION OF SDSS DR7 QUASARS AND DR10 BOSS GALAXIES: THE WEAK LUMINOSITY DEPENDENCE OF QUASAR CLUSTERING AT z ∼ 0.5 , 2012, 1212.4526.

[30]  Matias Zaldarriaga,et al.  CMBFAST for Spatially Closed Universes , 1999, astro-ph/9911219.

[31]  Klaus Dolag,et al.  Baryon impact on the halo mass function: Fitting formulae and implications for cluster cosmology , 2015, 1502.07357.

[32]  A. Leauthaud,et al.  A THEORETICAL FRAMEWORK FOR COMBINING TECHNIQUES THAT PROBE THE LINK BETWEEN GALAXIES AND DARK MATTER , 2011, 1103.2077.

[33]  William H. Press,et al.  Formation of Galaxies and Clusters of Galaxies by Self-Similar Gravitational Condensation , 1974 .

[34]  Naoshi Sugiyama Cosmic background anistropies in CDM cosmology , 1994 .

[35]  J. Peacock Testing anthropic predictions for Lambda and the cosmic microwave background temperature , 2007, 0705.0898.

[36]  F. Prada,et al.  MultiDark simulations: the story of dark matter halo concentrations and density profiles , 2014, 1411.4001.

[37]  James E. Taylor Dark Matter Halos from the Inside Out , 2010, 1008.4103.

[38]  Ravi Sheth,et al.  Halo Models of Large Scale Structure , 2002, astro-ph/0206508.

[39]  R. Sheth,et al.  On the streaming motions of haloes and galaxies , 2000, astro-ph/0010137.

[40]  Gaël Varoquaux,et al.  The NumPy Array: A Structure for Efficient Numerical Computation , 2011, Computing in Science & Engineering.

[41]  Shot noise and biased tracers: A new look at the halo model , 2017, 1706.08738.

[42]  Wayne Hu,et al.  Baryonic Features in the Matter Transfer Function , 1997, astro-ph/9709112.

[43]  A. Lewis,et al.  Efficient computation of CMB anisotropies in closed FRW models , 1999, astro-ph/9911177.

[44]  Chung-Pei Ma,et al.  Deriving the Nonlinear Cosmological Power Spectrum and Bispectrum from Analytic Dark Matter Halo Profiles and Mass Functions , 2000, astro-ph/0003343.

[45]  Katrin Heitmann,et al.  MASS FUNCTION PREDICTIONS BEYOND ΛCDM , 2010, 1005.2239.

[46]  Jerzy Neyman,et al.  On the Spatial Distribution of Galaxies: a Specific Model. , 1953 .

[47]  Steven G. Murray,et al.  hankel: A Python library for performing simple and accurate Hankel transformations , 2019, J. Open Source Softw..

[48]  O. Hahn,et al.  Halo mass function and scale-dependent bias from N-body simulations with non-Gaussian initial conditions , 2008, 0811.4176.

[49]  Prasanth H. Nair,et al.  Astropy: A community Python package for astronomy , 2013, 1307.6212.

[50]  Takahiro Nishimichi,et al.  REVISING THE HALOFIT MODEL FOR THE NONLINEAR MATTER POWER SPECTRUM , 2012, 1208.2701.

[51]  R. Smith,et al.  Halo mass function and the free streaming scale , 2013, 1303.0839.

[52]  S. Habib,et al.  DARK MATTER HALO PROFILES OF MASSIVE CLUSTERS: THEORY VERSUS OBSERVATIONS , 2011, 1112.5479.

[53]  F. V. D. Bosch The universal mass accretion history of cold dark matter haloes , 2001, astro-ph/0105158.

[54]  R. Maartens,et al.  The effect of finite halo size on the clustering of neutral hydrogen , 2021, Journal of Cosmology and Astroparticle Physics.

[55]  S. More,et al.  THE OVERDENSITY AND MASSES OF THE FRIENDS-OF-FRIENDS HALOS AND UNIVERSALITY OF HALO MASS FUNCTION , 2011, 1103.0005.

[56]  J. Frieman,et al.  Dark Energy Survey Year 1 Results: Cosmological Constraints from Cluster Abundances, Weak Lensing, and Galaxy Correlations. , 2020, Physical review letters.

[57]  The clustering of Hα emitters at ɀ=2.23 from HiZELS , 2012 .

[58]  C. Giocoli,et al.  Formation times, mass growth histories and concentrations of dark matter haloes , 2011, 1111.6977.

[59]  U. Seljak Analytic model for galaxy and dark matter clustering , 2000, astro-ph/0001493.

[60]  J. R. Bond,et al.  Excursion set mass functions for hierarchical Gaussian fluctuations , 1991 .

[61]  S. More,et al.  A redefinition of the halo boundary leads to a simple yet accurate halo model of large-scale structure , 2020, Monthly Notices of the Royal Astronomical Society.

[62]  A. Dutton,et al.  Cold dark matter haloes in the Planck era: evolution of structural parameters for Einasto and NFW profiles , 2014, 1402.7073.

[63]  V. Morozov,et al.  Halo Profiles and the Concentration–Mass Relation for a ΛCDM Universe , 2018, 1804.10199.

[64]  A. Kravtsov,et al.  ON DETERMINING THE SHAPE OF MATTER DISTRIBUTIONS , 2011, 1107.5582.

[65]  Andrew R. Liddle,et al.  Cosmological Inflation and Large-Scale Structure , 2000 .

[66]  F. Castander,et al.  An algorithm to build mock galaxy catalogues using MICE simulations , 2014, 1411.3286.

[67]  A. Kravtsov,et al.  A UNIVERSAL MODEL FOR HALO CONCENTRATIONS , 2014, 1407.4730.

[68]  J. Schaye,et al.  The accretion history of dark matter haloes - III. A physical model for the concentration-mass relation , 2015, 1502.00391.

[69]  R. Sheth,et al.  Excursion set peaks: a self-consistent model of dark halo abundances and clustering , 2012, 1210.1483.

[70]  C. Medaglia,et al.  A Numerical Study , 2005 .

[71]  M. Blanton,et al.  COSMOLOGICAL CONSTRAINTS FROM GALAXY CLUSTERING AND THE MASS-TO-NUMBER RATIO OF GALAXY CLUSTERS: MARGINALIZING OVER THE PHYSICS OF GALAXY FORMATION , 2013, 1306.4686.

[72]  S. More,et al.  THE PSEUDO-EVOLUTION OF HALO MASS , 2012, 1207.0816.

[73]  Theoretical Models of the Halo Occupation Distribution: Separating Central and Satellite Galaxies , 2004, astro-ph/0408564.

[74]  J. Lesgourgues,et al.  The Cosmic Linear Anisotropy Solving System (CLASS). Part II: Approximation schemes , 2011, 1104.2933.

[75]  A. Amara,et al.  A halo model for cosmological neutral hydrogen : abundances and clustering , 2016, 1611.06235.

[76]  D. Wake,et al.  The clustering of radio galaxies at z≃ 0.55 from the 2SLAQ LRG survey , 2008, 0810.1050.

[77]  A. Bolton,et al.  The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: modelling the clustering and halo occupation distribution of BOSS CMASS galaxies in the Final Data Release , 2015, 1509.06404.

[78]  J. Brownstein,et al.  THE WEAK LENSING SIGNAL AND THE CLUSTERING OF BOSS GALAXIES. II. ASTROPHYSICAL AND COSMOLOGICAL CONSTRAINTS , 2014, 1407.1856.

[79]  Hidenori Ogata,et al.  A Numerical Integration Formula Based on the Bessel Functions , 2005 .

[80]  J. Lesgourgues,et al.  The Cosmic Linear Anisotropy Solving System (CLASS) I: Overview , 2011, 1104.2932.

[81]  H. M. P. Couchman,et al.  The mass function of dark matter haloes , 2000, astro-ph/0005260.

[82]  C. Giocoli,et al.  Halo model description of the non-linear dark matter power spectrum at k≫ 1 Mpc−1 , 2010, 1003.4740.

[83]  D. Nelson Limber,et al.  The Analysis of Counts of the Extragalactic Nebulae in Terms of a Fluctuating Density Field. II , 1953 .

[84]  L. Moustakas,et al.  The Masses, Ancestors, and Descendants of Extremely Red Objects: Constraints from Spatial Clustering , 2001, astro-ph/0110584.

[85]  Kendrick M. Smith,et al.  Characterizing fast radio bursts through statistical cross-correlations , 2019, 1912.09520.

[86]  A. Schneider Structure formation with suppressed small-scale perturbations , 2014, 1412.2133.

[87]  C. Baugh,et al.  The clustering of Hα emitters at z = 2.23 from HiZELS , 2012 .

[88]  John D. Hunter,et al.  Matplotlib: A 2D Graphics Environment , 2007, Computing in Science & Engineering.

[89]  P. Tiwari,et al.  THE CLUSTERING OF RADIO GALAXIES: BIASING AND EVOLUTION VERSUS STELLAR MASS , 2015, 1505.06817.

[90]  Non-linear evolution of cosmological structures in warm dark matter models , 2011, 1112.0330.

[91]  F. Beutler,et al.  The 6dF Galaxy Survey: dependence of halo occupation on stellar mass , 2012, 1212.3610.

[92]  Fast edge-corrected measurement of the two-point correlation function and the power spectrum , 2005, astro-ph/0505389.

[93]  J. Brinkmann,et al.  The environmental dependence of the relations between stellar mass, structure, star formation and nuclear activity in galaxies , 2004, astro-ph/0402030.

[94]  C. Baugh,et al.  How robust are predictions of galaxy clustering , 2013, 1301.3497.

[95]  M. Steinmetz,et al.  The Power Spectrum Dependence of Dark Matter Halo Concentrations , 2000, astro-ph/0012337.

[96]  Galaxy-galaxy lensing : dissipationless simulations versus the halo model , 2004, astro-ph/0410711.

[97]  Christopher D. Martin,et al.  Halo occupation distribution modelling of green valley galaxies , 2012, 1208.6139.

[98]  S. White,et al.  The mass profile and accretion history of cold dark matter haloes , 2013, 1302.0288.

[99]  Tristan L. Smith,et al.  NEW CONSTRAINTS ON THE EVOLUTION OF THE STELLAR-TO-DARK MATTER CONNECTION: A COMBINED ANALYSIS OF GALAXY–GALAXY LENSING, CLUSTERING, AND STELLAR MASS FUNCTIONS FROM z = 0.2 to z = 1 , 2011, 1104.0928.

[100]  Numerical study of halo concentrations in dark-energy cosmologies , 2003, astro-ph/0309771.

[101]  I. Achitouv,et al.  Excursion set halo mass function and bias in a stochastic barrier model of ellipsoidal collapse , 2011, 1107.1251.

[102]  Y. Jing,et al.  Triaxial Modeling of Halo Density Profiles with High-Resolution N-Body Simulations , 2002, astro-ph/0202064.

[103]  THE EXCURSION SET THEORY OF HALO MASS FUNCTIONS, HALO CLUSTERING, AND HALO GROWTH , 2006, astro-ph/0611454.

[104]  Constraining warm dark matter candidates including sterile neutrinos and light gravitinos with WMAP and the Lyman-{alpha} forest , 2005, astro-ph/0501562.

[105]  R. Wechsler,et al.  THE AVERAGE STAR FORMATION HISTORIES OF GALAXIES IN DARK MATTER HALOS FROM z = 0–8 , 2012, 1207.6105.

[106]  How accurate is Limber's equation? , 2006, astro-ph/0609165.

[107]  C. Baugh,et al.  The Halo Occupation Distribution and the Physics of Galaxy Formation , 2002, astro-ph/0212357.

[108]  S. Cole,et al.  The mass–concentration–redshift relation of cold and warm dark matter haloes , 2016, 1601.02624.

[109]  J. Brinkmann,et al.  Galaxy halo masses and satellite fractions from galaxy–galaxy lensing in the Sloan Digital Sky Survey: stellar mass, luminosity, morphology and environment dependencies , 2005, astro-ph/0511164.

[110]  Y. Jing,et al.  Accurate Fitting Formula for the Two-Point Correlation Function of Dark Matter Halos , 1998, astro-ph/9805202.

[111]  J. Comparat,et al.  Accurate mass and velocity functions of dark matter haloes , 2017, 1702.01628.

[112]  M. White,et al.  The Halo Model and Numerical Simulations , 2000, astro-ph/0012518.

[113]  Chris Power,et al.  How well do we know the halo mass function , 2013, 1306.5140.

[114]  O. Lahav,et al.  On combining galaxy clustering and weak lensing to unveil galaxy biasing via the halo model , 2012, 1203.2616.

[115]  R. Nichol,et al.  GALAXY CLUSTERING IN THE COMPLETED SDSS REDSHIFT SURVEY: THE DEPENDENCE ON COLOR AND LUMINOSITY , 2010, 1005.2413.

[116]  M. Maggiore,et al.  The bias and mass function of dark matter haloes in non-Markovian extension of the excursion set theory , 2010, 1007.4201.

[117]  J. Tinker,et al.  On the Mass-to-Light Ratio of Large-Scale Structure , 2004, astro-ph/0411777.

[118]  H. Hoekstra,et al.  Unveiling galaxy bias via the halo model, KiDS, and GAMA , 2018, Monthly Notices of the Royal Astronomical Society.

[119]  E. Rykoff,et al.  Combination of cluster number counts and two-point correlations: validation on mock Dark Energy Survey , 2020, 2008.10757.

[120]  Frank C. van den Bosch,et al.  Concentration, spin and shape of dark matter haloes as a function of the cosmological model: WMAP1, WMAP3 and WMAP5 results , 2008, 0805.1926.

[121]  Joel Nothman,et al.  SciPy 1.0-Fundamental Algorithms for Scientific Computing in Python , 2019, ArXiv.

[122]  O. Lahav,et al.  Halo-model signatures from 380 000 Sloan Digital Sky Survey luminous red galaxies with photometric redshifts , 2007, 0704.3377.

[123]  S. More,et al.  Cosmological inference from an emulator based halo model. I. Validation tests with HSC and SDSS mock catalogs , 2020, Physical Review D.

[124]  B. Jain,et al.  How Many Galaxies Fit in a Halo? Constraints on Galaxy Formation Efficiency from Spatial Clustering , 2000, astro-ph/0006319.

[125]  Miguel de Val-Borro,et al.  The Astropy Project: Building an Open-science Project and Status of the v2.0 Core Package , 2018, The Astronomical Journal.

[126]  Benedikt Diemer,et al.  COLOSSUS: A Python Toolkit for Cosmology, Large-scale Structure, and Dark Matter Halos , 2017, The Astrophysical Journal Supplement Series.

[127]  C. A. Oxborrow,et al.  Planck2015 results , 2015, Astronomy &amp; Astrophysics.

[128]  Masakazu A. R. Kobayashi,et al.  The ν2GC simulations: Quantifying the dark side of the universe in the Planck cosmology , 2014, 1412.2860.

[129]  Zheng Zheng,et al.  Accurate and efficient halo-based galaxy clustering modelling with simulations , 2015, 1506.07523.

[130]  J. Peacock,et al.  Halo occupation numbers and galaxy bias , 2000, astro-ph/0005010.

[131]  L. Hernquist,et al.  An Analytical Model for Spherical Galaxies and Bulges , 1990 .

[132]  Andrew P. Hearin,et al.  The scale-dependence of halo assembly bias , 2015, 1509.06417.

[133]  R. Somerville,et al.  Profiles of dark haloes: evolution, scatter and environment , 1999, astro-ph/9908159.

[134]  J. Peacock,et al.  Stable clustering, the halo model and non-linear cosmological power spectra , 2002, astro-ph/0207664.

[135]  Uros Seljak Michael S. Warren Large‐scale bias and stochasticity of haloes and dark matter , 2004, astro-ph/0403698.

[136]  Interpreting the Observed Clustering of Red Galaxies at z ~ 3 , 2003, astro-ph/0307030.

[137]  Ravi K. Sheth Giuseppe Tormen Large scale bias and the peak background split , 1999 .

[138]  A. Szalay,et al.  The statistics of peaks of Gaussian random fields , 1986 .

[139]  Y. Jing Accurate Determination of the Lagrangian Bias for the Dark Matter Halos , 1999, astro-ph/9901138.

[140]  Yipeng Jing,et al.  The growth and structure of dark matter haloes , 2003 .

[141]  R. Skibba,et al.  A halo model of galaxy colours and clustering in the Sloan Digital Sky Survey , 2008, 0805.0310.

[142]  S. White,et al.  An analytic model for the spatial clustering of dark matter haloes , 1995, astro-ph/9512127.

[143]  S. Cole,et al.  Biased clustering in the cold dark matter cosmogony , 1989 .

[144]  J. R. Bond,et al.  Cosmic background radiation anisotropies in universes dominated by nonbaryonic dark matter , 1984 .

[145]  B. Altieri,et al.  The Uchuu simulations: Data Release 1 and dark matter halo concentrations , 2020, 2007.14720.

[146]  G. Lake,et al.  Resolving the Structure of Cold Dark Matter Halos , 1997, astro-ph/9709051.

[147]  S. More COSMOLOGICAL DEPENDENCE OF THE MEASUREMENTS OF LUMINOSITY FUNCTION, PROJECTED CLUSTERING AND GALAXY–GALAXY LENSING SIGNAL , 2013, 1309.2943.

[148]  Leicester,et al.  The spatial distribution of cold gas in hierarchical galaxy formation models , 2010, 1003.0008.

[149]  R. Wechsler,et al.  Galaxy halo occupation at high redshift , 2001, astro-ph/0106293.

[150]  Durham,et al.  Dark matter halo merger histories beyond cold dark matter – I. Methods and application to warm dark matter , 2012, 1209.3018.

[151]  Ilian T. Iliev,et al.  The halo mass function through the cosmic ages , 2012, 1212.0095.

[152]  B. Diemer,et al.  An Accurate Physical Model for Halo Concentrations , 2018, The Astrophysical Journal.

[153]  S. White,et al.  A Universal Density Profile from Hierarchical Clustering , 1996, astro-ph/9611107.

[154]  G. Kauffmann,et al.  Galaxy formation and large scale bias , 1995, astro-ph/9512009.