DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: The Aemulus Project. II. Emulating the Halo Mass Function

Abstract

Existing models for the dependence of the halo mass function on cosmological parameters will become a limiting source of systematic uncertainty for cluster cosmology in the near future. We present a halo mass function emulator and demonstrate improved accuracy relative to state-of-the-art analytic models. In this work, mass is defined using an overdensity criteria of 200 relative to the mean background density. Our emulator is constructed from the Aemulus simulations, a suite of 40 N-body simulations with snapshots from z = 3 to z = 0. These simulations cover the flat wCDM parameter space allowed by recent cosmic microwave background, baryon acoustic oscillation and SNe Ia results, varying the parameters w, Ω m, Ω b, σ 8, N eff, n s, and H 0. We validate our emulator using five realizations of seven different cosmologies, for a total of 35 test simulations. These test simulations were not used in constructing the emulator, and were run with fully independent initial conditions. We use our test simulations to characterize the modeling uncertainty of the emulator, and introduce a novel way of marginalizing over the associated systematic uncertainty. We confirm nonuniversality in our halo mass function emulator as a function of both cosmologicalmore » parameters and redshift. As a result, our emulator achieves better than 1% precision over much of the relevant parameter space, and we demonstrate that the systematic uncertainty in our emulator will remain a negligible source of error for cluster abundance studies through at least the LSST Year 1 data set.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3]; ORCiD logo [4]; ORCiD logo [3];  [5]; ORCiD logo [3]; ORCiD logo [5]
  1. Univ. of Arizona, Tucson, AZ (United States)
  2. Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Stanford, CA (United States); Civic Analytics, Chicago, IL (United States)
  3. Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Stanford, CA (United States)
  4. Univ. of Pittsburgh, Pittsburgh, PA (United States)
  5. New York Univ., New York, NY (United States)
Publication Date:
Research Org.:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1506961
Grant/Contract Number:  
AC02-76SF00515
Resource Type:
Accepted Manuscript
Journal Name:
The Astrophysical Journal (Online)
Additional Journal Information:
Journal Name: The Astrophysical Journal (Online); Journal Volume: 872; Journal Issue: 1; Journal ID: ISSN 1538-4357
Publisher:
Institute of Physics (IOP)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; large-scale structure of universe; methods: numerical; methods: statistical

Citation Formats

McClintock, Thomas, Rozo, Eduardo, Becker, Matthew R., DeRose, Joseph, Mao, Yao -Yuan, McLaughlin, Sean, Tinker, Jeremy L., Wechsler, Risa H., and Zhai, Zhongxu. The Aemulus Project. II. Emulating the Halo Mass Function. United States: N. p., 2019. Web. doi:10.3847/1538-4357/aaf568.
McClintock, Thomas, Rozo, Eduardo, Becker, Matthew R., DeRose, Joseph, Mao, Yao -Yuan, McLaughlin, Sean, Tinker, Jeremy L., Wechsler, Risa H., & Zhai, Zhongxu. The Aemulus Project. II. Emulating the Halo Mass Function. United States. https://doi.org/10.3847/1538-4357/aaf568
McClintock, Thomas, Rozo, Eduardo, Becker, Matthew R., DeRose, Joseph, Mao, Yao -Yuan, McLaughlin, Sean, Tinker, Jeremy L., Wechsler, Risa H., and Zhai, Zhongxu. Fri . "The Aemulus Project. II. Emulating the Halo Mass Function". United States. https://doi.org/10.3847/1538-4357/aaf568. https://www.osti.gov/servlets/purl/1506961.
@article{osti_1506961,
title = {The Aemulus Project. II. Emulating the Halo Mass Function},
author = {McClintock, Thomas and Rozo, Eduardo and Becker, Matthew R. and DeRose, Joseph and Mao, Yao -Yuan and McLaughlin, Sean and Tinker, Jeremy L. and Wechsler, Risa H. and Zhai, Zhongxu},
abstractNote = {Existing models for the dependence of the halo mass function on cosmological parameters will become a limiting source of systematic uncertainty for cluster cosmology in the near future. We present a halo mass function emulator and demonstrate improved accuracy relative to state-of-the-art analytic models. In this work, mass is defined using an overdensity criteria of 200 relative to the mean background density. Our emulator is constructed from the Aemulus simulations, a suite of 40 N-body simulations with snapshots from z = 3 to z = 0. These simulations cover the flat wCDM parameter space allowed by recent cosmic microwave background, baryon acoustic oscillation and SNe Ia results, varying the parameters w, Ω m, Ω b, σ 8, N eff, n s, and H 0. We validate our emulator using five realizations of seven different cosmologies, for a total of 35 test simulations. These test simulations were not used in constructing the emulator, and were run with fully independent initial conditions. We use our test simulations to characterize the modeling uncertainty of the emulator, and introduce a novel way of marginalizing over the associated systematic uncertainty. We confirm nonuniversality in our halo mass function emulator as a function of both cosmological parameters and redshift. As a result, our emulator achieves better than 1% precision over much of the relevant parameter space, and we demonstrate that the systematic uncertainty in our emulator will remain a negligible source of error for cluster abundance studies through at least the LSST Year 1 data set.},
doi = {10.3847/1538-4357/aaf568},
journal = {The Astrophysical Journal (Online)},
number = 1,
volume = 872,
place = {United States},
year = {Fri Feb 08 00:00:00 EST 2019},
month = {Fri Feb 08 00:00:00 EST 2019}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 57 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

First data release of the Hyper Suprime-Cam Subaru Strategic Program
journal, October 2017

  • Aihara, Hiroaki; Armstrong, Robert; Bickerton, Steven
  • Publications of the Astronomical Society of Japan, Vol. 70, Issue SP1
  • DOI: 10.1093/pasj/psx081

Fast Direct Methods for Gaussian Processes
journal, February 2016

  • Ambikasaran, Sivaram; Foreman-Mackey, Daniel; Greengard, Leslie
  • IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 38, Issue 2
  • DOI: 10.1109/TPAMI.2015.2448083

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: baryon acoustic oscillations in the Data Releases 10 and 11 Galaxy samples
journal, April 2014

  • Anderson, Lauren; Aubourg, Éric; Bailey, Stephen
  • Monthly Notices of the Royal Astronomical Society, Vol. 441, Issue 1
  • DOI: 10.1093/mnras/stu523

The Rockstar Phase-Space Temporal halo Finder and the Velocity Offsets of Cluster Cores
journal, December 2012


Mass Function Predictions Beyond Λcdm
journal, April 2011


Galaxy Clusters Discovered via the Sunyaev-Zel'Dovich Effect in the 2500-Square-Degree Spt-Sz Survey
journal, January 2015

  • Bleem, L. E.; Stalder, B.; de Haan, T.
  • The Astrophysical Journal Supplement Series, Vol. 216, Issue 2
  • DOI: 10.1088/0067-0049/216/2/27

Halo mass function: baryon impact, fitting formulae, and implications for cluster cosmology
journal, December 2015

  • Bocquet, Sebastian; Saro, Alex; Dolag, Klaus
  • Monthly Notices of the Royal Astronomical Society, Vol. 456, Issue 3
  • DOI: 10.1093/mnras/stv2657

Transients from initial conditions in cosmological simulations
journal, November 2006


The Dark Energy Survey: more than dark energy – an overview
journal, March 2016

  • Abbott, T.; Abdalla, F. B.; Aleksic, J.
  • Monthly Notices of the Royal Astronomical Society, Vol. 460, Issue 2, p. 1270-1299
  • DOI: 10.1093/mnras/stw641

The third data release of the Kilo-Degree Survey and associated data products
journal, August 2017


The universality of the virial halo mass function and models for non-universality of other halo definitions
journal, December 2015

  • Despali, Giulia; Giocoli, Carlo; Angulo, Raul E.
  • Monthly Notices of the Royal Astronomical Society, Vol. 456, Issue 3
  • DOI: 10.1093/mnras/stv2842

Sunyaev–Zel’dovich effect and X-ray scaling relations from weak lensing mass calibration of 32 South Pole Telescope selected galaxy clusters
journal, December 2018

  • Dietrich, J. P.; Bocquet, S.; Schrabback, T.
  • Monthly Notices of the Royal Astronomical Society, Vol. 483, Issue 3
  • DOI: 10.1093/mnras/sty3088

Galaxy Clusters in Hubble Volume Simulations: Cosmological Constraints from Sky Survey Populations
journal, July 2002

  • Evrard, A. E.; MacFarland, T. J.; Couchman, H. M. P.
  • The Astrophysical Journal, Vol. 573, Issue 1
  • DOI: 10.1086/340551

emcee : The MCMC Hammer
journal, March 2013

  • Foreman-Mackey, Daniel; Hogg, David W.; Lang, Dustin
  • Publications of the Astronomical Society of the Pacific, Vol. 125, Issue 925
  • DOI: 10.1086/670067

Why your model parameter confidences might be too optimistic. Unbiased estimation of the inverse covariance matrix
journal, December 2006


The Mira–Titan Universe: Precision Predictions for dark Energy Surveys
journal, March 2016


The Coyote Universe. ii. Cosmological Models and Precision Emulation of the Nonlinear Matter Power Spectrum
journal, October 2009


NINE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE ( WMAP ) OBSERVATIONS: COSMOLOGICAL PARAMETER RESULTS
journal, September 2013

  • Hinshaw, G.; Larson, D.; Komatsu, E.
  • The Astrophysical Journal Supplement Series, Vol. 208, Issue 2
  • DOI: 10.1088/0067-0049/208/2/19

Matplotlib: A 2D Graphics Environment
journal, January 2007


The mass function of dark matter haloes
journal, February 2001


Cosmological parameters from CMB and other data: A Monte Carlo approach
journal, November 2002


Weighing the giants– V. Galaxy cluster scaling relations
journal, September 2016

  • Mantz, Adam B.; Allen, Steven W.; Morris, R. Glenn
  • Monthly Notices of the Royal Astronomical Society, Vol. 463, Issue 4
  • DOI: 10.1093/mnras/stw2250

Dark Energy Survey Year 1 results: weak lensing mass calibration of redMaPPer galaxy clusters
journal, October 2018

  • McClintock, T.; Varga, T. N.; Gruen, D.
  • Monthly Notices of the Royal Astronomical Society, Vol. 482, Issue 1
  • DOI: 10.1093/mnras/sty2711

The XMM Cluster Survey: optical analysis methodology and the first data release: The XMM Cluster Survey first data release
journal, April 2012


Weak-lensing mass calibration of redMaPPer galaxy clusters in Dark Energy Survey Science Verification data
journal, May 2017

  • Melchior, P.; Gruen, D.; McClintock, T.
  • Monthly Notices of the Royal Astronomical Society, Vol. 469, Issue 4
  • DOI: 10.1093/mnras/stx1053

Hyper Suprime-Cam
conference, October 2012

  • Miyazaki, Satoshi; Komiyama, Yutaka; Nakaya, Hidehiko
  • SPIE Astronomical Telescopes + Instrumentation, SPIE Proceedings
  • DOI: 10.1117/12.926844

The Overdensity and Masses of the Friends-Of-Friends Halos and Universality of halo mass Function
journal, June 2011

  • More, Surhud; Kravtsov, Andrey V.; Dalal, Neal
  • The Astrophysical Journal Supplement Series, Vol. 195, Issue 1
  • DOI: 10.1088/0067-0049/195/1/4

The MCXC: a meta-catalogue of x-ray detected clusters of galaxies
journal, October 2011


Planck 2013 results. XVI. Cosmological parameters
journal, October 2014


Planck 2015 results : XXIV. Cosmology from Sunyaev-Zeldovich cluster counts
journal, September 2016


Formation of Galaxies and Clusters of Galaxies by Self-Similar Gravitational Condensation
journal, February 1974

  • Press, William H.; Schechter, Paul
  • The Astrophysical Journal, Vol. 187
  • DOI: 10.1086/152650

Searching for galaxy clusters in the Kilo-Degree Survey
journal, February 2017


Gaussian Processes for Machine Learning
book, January 2005


The halo mass function from the dark ages through the present day
journal, January 2007


Towards an accurate mass function for precision cosmology
journal, March 2013

  • Reed, D. S.; Smith, R. E.; Potter, D.
  • Monthly Notices of the Royal Astronomical Society, Vol. 431, Issue 2
  • DOI: 10.1093/mnras/stt301

redMaPPer. I. ALGORITHM AND SDSS DR8 CATALOG
journal, April 2014


The Redmapper Galaxy Cluster Catalog from des Science Verification data
journal, May 2016

  • Rykoff, E. S.; Rozo, E.; Hollowood, D.
  • The Astrophysical Journal Supplement Series, Vol. 224, Issue 1
  • DOI: 10.3847/0067-0049/224/1/1

Ellipsoidal collapse and an improved model for the number and spatial distribution of dark matter haloes
journal, May 2001


Large-scale bias and the peak background split
journal, September 1999


Weak lensing measurement of the mass–richness relation of SDSS redMaPPer clusters
journal, December 2016

  • Simet, Melanie; McClintock, Tom; Mandelbaum, Rachel
  • Monthly Notices of the Royal Astronomical Society, Vol. 466, Issue 3
  • DOI: 10.1093/mnras/stw3250

The cosmological simulation code gadget-2
journal, December 2005


Toward a Halo Mass Function for Precision Cosmology: The Limits of Universality
journal, December 2008

  • Tinker, Jeremy; Kravtsov, Andrey V.; Klypin, Anatoly
  • The Astrophysical Journal, Vol. 688, Issue 2
  • DOI: 10.1086/591439

The Large-Scale bias of dark Matter Halos: Numerical Calibration and Model Tests
journal, November 2010

  • Tinker, Jeremy L.; Robertson, Brant E.; Kravtsov, Andrey V.
  • The Astrophysical Journal, Vol. 724, Issue 2
  • DOI: 10.1088/0004-637X/724/2/878

Precision Determination of the Mass Function of Dark Matter Halos
journal, August 2006

  • Warren, Michael S.; Abazajian, Kevork; Holz, Daniel E.
  • The Astrophysical Journal, Vol. 646, Issue 2
  • DOI: 10.1086/504962

Observational probes of cosmic acceleration
journal, September 2013


Cosmological constraints from the large-scale weak lensing of SDSS MaxBCG clusters
journal, February 2014

  • Zu, Ying; Weinberg, David H.; Rozo, Eduardo
  • Monthly Notices of the Royal Astronomical Society, Vol. 439, Issue 2
  • DOI: 10.1093/mnras/stu033

Planck 2015 results : XI. CMB power spectra, likelihoods, and robustness of parameters
journal, September 2016


CASSPER is a semantic segmentation-based particle picking algorithm for single-particle cryo-electron microscopy
journal, February 2021


Planck 2015 results : XIII. Cosmological parameters
journal, September 2016


Towards an accurate mass function for precision cosmology
text, January 2013


Planck 2015 results : VI. LFI mapmaking
journal, September 2016


Planck 2015 results : XVI. Isotropy and statistics of the CMB
journal, September 2016


Planck 2015 results : XXVI. The Second
journal, September 2016


The Rockstar Phase-Space Temporal Halo Finder and the Velocity Offsets of Cluster Cores
text, January 2011


Cosmological Constraints from the Large Scale Weak Lensing of SDSS MaxBCG Clusters
text, January 2012


redMaPPer I: Algorithm and SDSS DR8 Catalog
text, January 2013


Planck 2013 results. XVI. Cosmological parameters
text, January 2013


Fast Direct Methods for Gaussian Processes
preprint, January 2014


Halo mass function: Baryon impact, fitting formulae and implications for cluster cosmology
text, January 2015


The Mira-Titan Universe: Precision Predictions for Dark Energy Surveys
text, January 2015


The Dark Energy Survey: more than dark energy - an overview
text, January 2016


Weak Lensing Measurement of the Mass--Richness Relation of SDSS redMaPPer Clusters
text, January 2016


First Data Release of the Hyper Suprime-Cam Subaru Strategic Program
text, January 2017


The third data release of the Kilo-Degree Survey and associated data products
text, January 2017


Galaxy Clusters in Hubble Volume Simulations: Cosmological Constraints from Sky Survey Populations
text, January 2001


Precision Determination of the Mass Function of Dark Matter Halos
text, January 2005


The halo mass function from the dark ages through the present day
text, January 2006


Works referencing / citing this record:

Methods for cluster cosmology and application to the SDSS in preparation for DES Year 1 release
journal, July 2019

  • Costanzi, M.; Rozo, E.; Simet, M.
  • Monthly Notices of the Royal Astronomical Society, Vol. 488, Issue 4
  • DOI: 10.1093/mnras/stz1949

A novel scheme for Dark Matter Annihilation Feedback in cosmological simulations
journal, August 2019

  • List, Florian; Iwanus, Nikolas; Elahi, Pascal J.
  • Monthly Notices of the Royal Astronomical Society, Vol. 489, Issue 3
  • DOI: 10.1093/mnras/stz2287

Reconstructing probability distributions with Gaussian processes
journal, September 2019

  • McClintock, Thomas; Rozo, Eduardo
  • Monthly Notices of the Royal Astronomical Society, Vol. 489, Issue 3
  • DOI: 10.1093/mnras/stz2426

On the road to per cent accuracy – II. Calibration of the non-linear matter power spectrum for arbitrary cosmologies
journal, September 2019

  • Giblin, Benjamin; Cataneo, Matteo; Moews, Ben
  • Monthly Notices of the Royal Astronomical Society, Vol. 490, Issue 4
  • DOI: 10.1093/mnras/stz2659

Cosmological Evidence Modelling: a new simulation-based approach to constrain cosmology on non-linear scales
journal, September 2019

  • Lange, Johannes U.; van den Bosch, Frank C.; Zentner, Andrew R.
  • Monthly Notices of the Royal Astronomical Society, Vol. 490, Issue 2
  • DOI: 10.1093/mnras/stz2664

Prediction of H α and [O iii] emission line galaxy number counts for future galaxy redshift surveys
journal, October 2019

  • Zhai, Zhongxu; Benson, Andrew; Wang, Yun
  • Monthly Notices of the Royal Astronomical Society, Vol. 490, Issue 3
  • DOI: 10.1093/mnras/stz2844

Weak lensing analysis of codex clusters using dark energy camera legacy survey: mass–richness relation
journal, November 2019

  • Phriksee, Anirut; Jullo, Eric; Limousin, Marceau
  • Monthly Notices of the Royal Astronomical Society, Vol. 491, Issue 2
  • DOI: 10.1093/mnras/stz3049

The Aemulus Project. III. Emulation of the Galaxy Correlation Function
journal, March 2019

  • Zhai, Zhongxu; Tinker, Jeremy L.; Becker, Matthew R.
  • The Astrophysical Journal, Vol. 874, Issue 1
  • DOI: 10.3847/1538-4357/ab0d7b

The Aemulus Project. I. Numerical Simulations for Precision Cosmology
journal, April 2019

  • DeRose, Joseph; Wechsler, Risa H.; Tinker, Jeremy L.
  • The Astrophysical Journal, Vol. 875, Issue 1
  • DOI: 10.3847/1538-4357/ab1085

Dark Quest. I. Fast and Accurate Emulation of Halo Clustering Statistics and Its Application to Galaxy Clustering
journal, October 2019

  • Nishimichi, Takahiro; Takada, Masahiro; Takahashi, Ryuichi
  • The Astrophysical Journal, Vol. 884, Issue 1
  • DOI: 10.3847/1538-4357/ab3719

The Aemulus Project III: Emulation of the Galaxy Correlation Function
text, January 2018


Dark Quest. I. Fast and Accurate Emulation of Halo Clustering Statistics and Its Application to Galaxy Clustering
text, January 2018


Reconstructing Probability Distributions with Gaussian Processes
text, January 2019


A Novel Scheme for Dark Matter Annihilation Feedback in Cosmological Simulations
text, January 2019


Probing Diffuse Gas with Fast Radio Bursts
text, January 2019


Cosmological Evidence Modelling: a new simulation-based approach to constrain cosmology on non-linear scales
text, January 2019