Analytic Gaussian covariance matrices for galaxy <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>-point correlation functions
Jiamin Hou, R. N. Cahn, Oliver H. E. Philcox, Zachary Slepian
Abstract
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 $3j$ 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.