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Title: Computing the small-scale galaxy power spectrum and bispectrum in configuration space

Abstract

ABSTRACT We present a new class of estimators for computing small-scale power spectra and bispectra in configuration space via weighted pair and triple counts, with no explicit use of Fourier transforms. Particle counts are truncated at $$R_0\sim 100\, h^{-1}\, \mathrm{Mpc}$$ via a continuous window function, which has negligible effect on the measured power spectrum multipoles at small scales. This gives a power spectrum algorithm with complexity $$\mathcal {O}(NnR_0^3)$$ (or $$\mathcal {O}(Nn^2R_0^6)$$ for the bispectrum), measuring N galaxies with number density n. Our estimators are corrected for the survey geometry and have neither self-count contributions nor discretization artefacts, making them ideal for high-k analysis. Unlike conventional Fourier-transform-based approaches, our algorithm becomes more efficient on small scales (since a smaller R0 may be used), thus we may efficiently estimate spectra across k-space by coupling this method with standard techniques. We demonstrate the utility of the publicly available power spectrum algorithm by applying it to BOSS DR12 simulations to compute the high-k power spectrum and its covariance. In addition, we derive a theoretical rescaled-Gaussian covariance matrix, which incorporates the survey geometry and is found to be in good agreement with that from mocks. Computing configuration- and Fourier-space statistics in the same manner allows us to consider joint analyses, which can place stronger bounds on cosmological parameters; to this end we also discuss the cross-covariance between the two-point correlation function and the small-scale power spectrum.

Authors:
ORCiD logo [1];  [2]
  1. Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA, Center for Astrophysics | Harvard & Smithsonian, 60 Garden St, MA 02138, USA
  2. Center for Astrophysics | Harvard & Smithsonian, 60 Garden St, MA 02138, USA
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1582078
Grant/Contract Number:  
SC0013718
Resource Type:
Published Article
Journal Name:
Monthly Notices of the Royal Astronomical Society
Additional Journal Information:
Journal Name: Monthly Notices of the Royal Astronomical Society Journal Volume: 492 Journal Issue: 1; Journal ID: ISSN 0035-8711
Publisher:
Oxford University Press
Country of Publication:
United Kingdom
Language:
English

Citation Formats

Philcox, Oliver H. E., and Eisenstein, Daniel J. Computing the small-scale galaxy power spectrum and bispectrum in configuration space. United Kingdom: N. p., 2019. Web. doi:10.1093/mnras/stz3335.
Philcox, Oliver H. E., & Eisenstein, Daniel J. Computing the small-scale galaxy power spectrum and bispectrum in configuration space. United Kingdom. doi:10.1093/mnras/stz3335.
Philcox, Oliver H. E., and Eisenstein, Daniel J. Thu . "Computing the small-scale galaxy power spectrum and bispectrum in configuration space". United Kingdom. doi:10.1093/mnras/stz3335.
@article{osti_1582078,
title = {Computing the small-scale galaxy power spectrum and bispectrum in configuration space},
author = {Philcox, Oliver H. E. and Eisenstein, Daniel J.},
abstractNote = {ABSTRACT We present a new class of estimators for computing small-scale power spectra and bispectra in configuration space via weighted pair and triple counts, with no explicit use of Fourier transforms. Particle counts are truncated at $R_0\sim 100\, h^{-1}\, \mathrm{Mpc}$ via a continuous window function, which has negligible effect on the measured power spectrum multipoles at small scales. This gives a power spectrum algorithm with complexity $\mathcal {O}(NnR_0^3)$ (or $\mathcal {O}(Nn^2R_0^6)$ for the bispectrum), measuring N galaxies with number density n. Our estimators are corrected for the survey geometry and have neither self-count contributions nor discretization artefacts, making them ideal for high-k analysis. Unlike conventional Fourier-transform-based approaches, our algorithm becomes more efficient on small scales (since a smaller R0 may be used), thus we may efficiently estimate spectra across k-space by coupling this method with standard techniques. We demonstrate the utility of the publicly available power spectrum algorithm by applying it to BOSS DR12 simulations to compute the high-k power spectrum and its covariance. In addition, we derive a theoretical rescaled-Gaussian covariance matrix, which incorporates the survey geometry and is found to be in good agreement with that from mocks. Computing configuration- and Fourier-space statistics in the same manner allows us to consider joint analyses, which can place stronger bounds on cosmological parameters; to this end we also discuss the cross-covariance between the two-point correlation function and the small-scale power spectrum.},
doi = {10.1093/mnras/stz3335},
journal = {Monthly Notices of the Royal Astronomical Society},
number = 1,
volume = 492,
place = {United Kingdom},
year = {2019},
month = {11}
}

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