skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Computing three-point correlation function randoms counts without the randoms catalogue

Abstract

As we move towards future galaxy surveys, the three-point statistics will be increasingly leveraged to enhance the constraining power of the data on cosmological parameters. An essential part of the three-point function estimation is performing triplet counts of synthetic data points in random catalogues. Since triplet counting algorithms scale at best as O(N2logN) with the number of particles and the random catalogues are typically at least 50 times denser than the data; this tends to be by far the most time-consuming part of the measurements. Here, we present a simple method of computing the necessary triplet counts involving uniform random distributions through simple one-dimensional integrals. The method speeds up the computation of the three-point function by orders of magnitude, eliminating the need for random catalogues, with the simultaneous pair and triplet counting of the data points alone being sufficient.

Authors:
 [1];  [2]
  1. Department of Physics, Kansas State University, 116 Cardwell Hall, Manhattan, KS 66506, USA
  2. Department of Physics, Kansas State University, 116 Cardwell Hall, Manhattan, KS 66506, USA, National Abastumani Astrophysical Observatory, Ilia State University, 2A Kazbegi Ave., GE-1060 Tbilisi, Georgia
Publication Date:
Research Org.:
Kansas State Univ., Manhattan, KS (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); National Aeronautics and Space Administration (NASA)
OSTI Identifier:
1515796
Alternate Identifier(s):
OSTI ID: 1611674; OSTI ID: 1656952
Grant/Contract Number:  
SC0011840; 12-EUCLID11-0004
Resource Type:
Published Article
Journal Name:
Monthly Notices of the Royal Astronomical Society: Letters
Additional Journal Information:
Journal Name: Monthly Notices of the Royal Astronomical Society: Letters Journal Volume: 486 Journal Issue: 1; Journal ID: ISSN 1745-3925
Publisher:
Royal Astronomical Society
Country of Publication:
United Kingdom
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; Astronomy & Astrophysics; methods: numerical; cosmology: miscellaneous; large-scale structure of Universe

Citation Formats

Pearson, David W., and Samushia, Lado. Computing three-point correlation function randoms counts without the randoms catalogue. United Kingdom: N. p., 2019. Web. https://doi.org/10.1093/mnrasl/slz067.
Pearson, David W., & Samushia, Lado. Computing three-point correlation function randoms counts without the randoms catalogue. United Kingdom. https://doi.org/10.1093/mnrasl/slz067
Pearson, David W., and Samushia, Lado. Tue . "Computing three-point correlation function randoms counts without the randoms catalogue". United Kingdom. https://doi.org/10.1093/mnrasl/slz067.
@article{osti_1515796,
title = {Computing three-point correlation function randoms counts without the randoms catalogue},
author = {Pearson, David W. and Samushia, Lado},
abstractNote = {As we move towards future galaxy surveys, the three-point statistics will be increasingly leveraged to enhance the constraining power of the data on cosmological parameters. An essential part of the three-point function estimation is performing triplet counts of synthetic data points in random catalogues. Since triplet counting algorithms scale at best as O(N2logN) with the number of particles and the random catalogues are typically at least 50 times denser than the data; this tends to be by far the most time-consuming part of the measurements. Here, we present a simple method of computing the necessary triplet counts involving uniform random distributions through simple one-dimensional integrals. The method speeds up the computation of the three-point function by orders of magnitude, eliminating the need for random catalogues, with the simultaneous pair and triplet counting of the data points alone being sufficient.},
doi = {10.1093/mnrasl/slz067},
journal = {Monthly Notices of the Royal Astronomical Society: Letters},
number = 1,
volume = 486,
place = {United Kingdom},
year = {2019},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1093/mnrasl/slz067

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Computing the three-point correlation function of galaxies in $\mathcal {O}(N^2)$ time
journal, October 2015

  • Slepian, Zachary; Eisenstein, Daniel J.
  • Monthly Notices of the Royal Astronomical Society, Vol. 454, Issue 4
  • DOI: 10.1093/mnras/stv2119

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: baryon acoustic oscillations in the Data Release 9 spectroscopic galaxy sample
journal, December 2012


The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: baryon acoustic oscillations in the correlation function of LOWZ and CMASS galaxies in Data Release 12
journal, February 2016

  • Cuesta, Antonio J.; Vargas-Magaña, Mariana; Beutler, Florian
  • Monthly Notices of the Royal Astronomical Society, Vol. 457, Issue 2
  • DOI: 10.1093/mnras/stw066

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: modelling of the luminosity and colour dependence in the Data Release 10
journal, May 2014

  • Guo, H.; Zheng, Z.; Zehavi, I.
  • Monthly Notices of the Royal Astronomical Society, Vol. 441, Issue 3
  • DOI: 10.1093/mnras/stu763

Analytic model for galaxy and dark matter clustering
journal, October 2000


Modelling galaxy clustering: halo occupation distribution versus subhalo matching
journal, April 2016

  • Guo, Hong; Zheng, Zheng; Behroozi, Peter S.
  • Monthly Notices of the Royal Astronomical Society, Vol. 459, Issue 3
  • DOI: 10.1093/mnras/stw845

The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant: 6dFGS: BAOs and the local Hubble constant
journal, July 2011


Three-Point Correlation Functions of SDSS Galaxies in Redshift Space: Morphology, Color, and Luminosity Dependence
journal, June 2004

  • Kayo, Issha; Suto, Yasushi; Nichol, Robert C.
  • Publications of the Astronomical Society of Japan, Vol. 56, Issue 3
  • DOI: 10.1093/pasj/56.3.415

A New Class of Estimators for the [ITAL]N[/ITAL]-Point Correlations
journal, February 1998

  • Szapudi, István; Szalay, Alexander S.
  • The Astrophysical Journal, Vol. 494, Issue 1
  • DOI: 10.1086/311146

Efficient Computation of Cosmic Microwave Background Anisotropies in Closed Friedmann‐Robertson‐Walker Models
journal, August 2000

  • Lewis, Antony; Challinor, Anthony; Lasenby, Anthony
  • The Astrophysical Journal, Vol. 538, Issue 2
  • DOI: 10.1086/309179

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
journal, April 2016

  • Rodríguez-Torres, Sergio A.; Chuang, Chia-Hsun; Prada, Francisco
  • Monthly Notices of the Royal Astronomical Society, Vol. 460, Issue 2
  • DOI: 10.1093/mnras/stw1014

Statistics of primordial density perturbations from discrete seed masses
journal, November 1991

  • Scherrer, Robert J.; Bertschinger, Edmund
  • The Astrophysical Journal, Vol. 381
  • DOI: 10.1086/170658

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: single-probe measurements from CMASS anisotropic galaxy clustering
journal, June 2016

  • Chuang, Chia-Hsun; Prada, Francisco; Pellejero-Ibanez, Marcos
  • Monthly Notices of the Royal Astronomical Society, Vol. 461, Issue 4
  • DOI: 10.1093/mnras/stw1535

On the Mass‐to‐Light Ratio of Large‐Scale Structure
journal, September 2005

  • Tinker, Jeremy L.; Weinberg, David H.; Zheng, Zheng
  • The Astrophysical Journal, Vol. 631, Issue 1
  • DOI: 10.1086/432084

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: RSD measurement from the LOS-dependent power spectrum of DR12 BOSS galaxies
journal, May 2016

  • Gil-Marín, Héctor; Percival, Will J.; Brownstein, Joel R.
  • Monthly Notices of the Royal Astronomical Society, Vol. 460, Issue 4
  • DOI: 10.1093/mnras/stw1096

Halo occupation numbers and galaxy bias
journal, November 2000


The large-scale three-point correlation function of the SDSS BOSS DR12 CMASS galaxies
journal, February 2017

  • Slepian, Zachary; Eisenstein, Daniel J.; Beutler, Florian
  • Monthly Notices of the Royal Astronomical Society, Vol. 468, Issue 1
  • DOI: 10.1093/mnras/stw3234

A Detection of the Baryon Acoustic Oscillation features in the SDSS BOSS DR12 Galaxy Bispectrum
journal, May 2018

  • Pearson, David W.; Samushia, Lado
  • Monthly Notices of the Royal Astronomical Society, Vol. 478, Issue 4
  • DOI: 10.1093/mnras/sty1266

Exploring the squeezed three-point galaxy correlation function with generalized halo occupation distribution models
journal, April 2018

  • Yuan, Sihan; Eisenstein, Daniel J.; Garrison, Lehman H.
  • Monthly Notices of the Royal Astronomical Society, Vol. 478, Issue 2
  • DOI: 10.1093/mnras/sty1089

Detection of baryon acoustic oscillation features in the large-scale three-point correlation function of SDSS BOSS DR12 CMASS galaxies
journal, March 2017

  • Slepian, Zachary; Eisenstein, Daniel J.; Brownstein, Joel R.
  • Monthly Notices of the Royal Astronomical Society, Vol. 469, Issue 2
  • DOI: 10.1093/mnras/stx488

The bispectrum in the Effective Field Theory of Large Scale Structure
journal, May 2015

  • Baldauf, Tobias; Mercolli, Lorenzo; Mirbabayi, Mehrdad
  • Journal of Cosmology and Astroparticle Physics, Vol. 2015, Issue 05
  • DOI: 10.1088/1475-7516/2015/05/007

Spatial Correlation Function and Pairwise Velocity Dispersion of Galaxies: Cold Dark Matter Models versus the Las Campanas Survey
journal, February 1998

  • Jing, Y. P.; Mo, H. J.; Borner, G.
  • The Astrophysical Journal, Vol. 494, Issue 1
  • DOI: 10.1086/305209

How Many Galaxies Fit in a Halo? Constraints on Galaxy Formation Efficiency from Spatial Clustering
journal, January 2001

  • Scoccimarro, Roman; Sheth, Ravi K.; Hui, Lam
  • The Astrophysical Journal, Vol. 546, Issue 1
  • DOI: 10.1086/318261

The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample
journal, March 2017

  • Alam, Shadab; Ata, Metin; Bailey, Stephen
  • Monthly Notices of the Royal Astronomical Society, Vol. 470, Issue 3
  • DOI: 10.1093/mnras/stx721

The power spectrum and bispectrum of SDSS DR11 BOSS galaxies – II. Cosmological interpretation
journal, July 2015

  • Gil-Marín, Héctor; Verde, Licia; Noreña, Jorge
  • Monthly Notices of the Royal Astronomical Society, Vol. 452, Issue 2
  • DOI: 10.1093/mnras/stv1359

The power spectrum and bispectrum of SDSS DR11 BOSS galaxies – I. Bias and gravity
journal, May 2015

  • Gil-Marín, Héctor; Noreña, Jorge; Verde, Licia
  • Monthly Notices of the Royal Astronomical Society, Vol. 451, Issue 1
  • DOI: 10.1093/mnras/stv961

The Halo Occupation Distribution: Toward an Empirical Determination of the Relation between Galaxies and Mass
journal, August 2002

  • Berlind, Andreas A.; Weinberg, David H.
  • The Astrophysical Journal, Vol. 575, Issue 2
  • DOI: 10.1086/341469

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: RSD measurement from the power spectrum and bispectrum of the DR12 BOSS galaxies
journal, October 2016

  • Gil-Marín, Héctor; Percival, Will J.; Verde, Licia
  • Monthly Notices of the Royal Astronomical Society, Vol. 465, Issue 2
  • DOI: 10.1093/mnras/stw2679

A lognormal model for the cosmological mass distribution
journal, January 1991

  • Coles, Peter; Jones, Bernard
  • Monthly Notices of the Royal Astronomical Society, Vol. 248, Issue 1
  • DOI: 10.1093/mnras/248.1.1

Erratum: A Detection of the Baryon Acoustic Oscillation Features in the SDSS BOSS DR12 Galaxy Bispectrum
journal, November 2018

  • Pearson, David W.; Samushia, Lado
  • Monthly Notices of the Royal Astronomical Society, Vol. 483, Issue 1
  • DOI: 10.1093/mnras/sty3173

Halo Occupation Distribution Modeling of Clustering of Luminous red Galaxies
journal, November 2009


The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: BAO measurement from the LOS-dependent power spectrum of DR12 BOSS galaxies
journal, May 2016

  • Gil-Marín, Héctor; Percival, Will J.; Cuesta, Antonio J.
  • Monthly Notices of the Royal Astronomical Society, Vol. 460, Issue 4
  • DOI: 10.1093/mnras/stw1264