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

Journal Article · Thu Nov 28 00:00:00 EST 2019 · Monthly Notices of the Royal Astronomical Society

DOI:https://doi.org/10.1093/mnras/stz3335· OSTI ID:1582078

Philcox, Oliver H. E.  ^[1]; Eisenstein, Daniel J. ^[2]

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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

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.

• Research Organization: Harvard Univ., Cambridge, MA (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: SC0013718
• OSTI ID: 1582078
• Alternate ID(s): OSTI ID: 1802525
• Journal Information: Monthly Notices of the Royal Astronomical Society, Journal Name: Monthly Notices of the Royal Astronomical Society Vol. 492 Journal Issue: 1; ISSN 0035-8711
• Publisher: Oxford University Press
• Country of Publication: United Kingdom
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
Astronomy & Astrophysics