Analytic Gaussian covariance matrices for galaxy <math display="inline"><mi>N</mi></math>-point correlation functions

Hou, Jiamin; Cahn, Robert N.; Philcox, Oliver H.E.; Slepian, Zachary

doi:10.1103/PhysRevD.106.043515

Analytic Gaussian covariance matrices for galaxy $N$ -point correlation functions

Aug 3, 2021

31 pages

Published in:

Phys.Rev.D 106 (2022) 4, 043515

Published: Aug 9, 2022

e-Print:

2108.01714 [astro-ph.CO]

DOI:

10.1103/PhysRevD.106.043515 (publication)

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Abstract: (APS)

We derive analytic covariance matrices for the

N

-point correlation functions (NPCFs) of galaxies in the Gaussian limit. Our results are given for arbitrary

N

and projected onto the isotropic basis functions given by spherical harmonics and Wigner

3 j

symbols. A numerical implementation of the 4PCF covariance is compared to the sample covariance obtained from a set of lognormal simulations, Quijote dark matter halo catalogues, and MultiDark-Patchy galaxy mocks, with the latter including realistic survey geometry. The analytic formalism gives reasonable predictions for the covariances estimated from mock simulations with a periodic-box geometry. Furthermore, fitting for an effective volume and number density by maximizing a likelihood based on Kullback-Leibler divergence is shown to partially compensate for the effects of a nonuniform window function. Our result is recently shown to facilitate NPCF analysis on a realistic survey data.

Note:

31 pages, 17 figures

References(114)

Figures(35)

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