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Estimating covariance matrices for two- and three-point correlation function moments in Arbitrary Survey Geometries

Journal Article · · Monthly Notices of the Royal Astronomical Society
 [1];  [2]
  1. Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA, Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, USA
  2. Center for Astrophysics | Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA
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ABSTRACT

We present configuration-space estimators for the auto- and cross-covariance of two- and three-point correlation functions (2PCF and 3PCF) in general survey geometries. These are derived in the Gaussian limit (setting higher order correlation functions to zero), but for arbitrary non-linear 2PCFs (which may be estimated from the survey itself), with a shot-noise rescaling parameter included to capture non-Gaussianity. We generalize previous approaches to include Legendre moments via a geometry-correction function calibrated from measured pair and triple counts. Making use of importance sampling and random particle catalogues, we can estimate model covariances in fractions of the time required to do so with mocks, obtaining estimates with negligible sampling noise in ∼10 (∼100) CPU-hours for the 2PCF (3PCF) autocovariance. We compare results to sample covariances from a suite of BOSS DR12 mocks and find the matrices to be in good agreement, assuming a shot-noise rescaling parameter of 1.03 (1.20) for the 2PCF (3PCF). To obtain strongest constraints on cosmological parameters, we must use multiple statistics in concert; having robust methods to measure their covariances at low computational cost is thus of great relevance to upcoming surveys.

Research Organization:
Harvard Univ., Cambridge, MA (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC)
Grant/Contract Number:
SC0013718
OSTI ID:
1574553
Alternate ID(s):
OSTI ID: 1802523
Journal Information:
Monthly Notices of the Royal Astronomical Society, Journal Name: Monthly Notices of the Royal Astronomical Society Journal Issue: 4 Vol. 490; ISSN 0035-8711
Publisher:
Oxford University PressCopyright Statement
Country of Publication:
United Kingdom
Language:
English

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