Analytic Gaussian Covariance Matrices for Galaxy $N$-Point Correlation Functions

TL;DR

This paper derives analytic covariance matrices for galaxy N-Point Correlation Functions in the Gaussian limit, facilitating efficient estimation and comparison with simulations, and addresses survey geometry effects.

Contribution

It provides a general analytic formalism for covariance matrices of galaxy NPCFs for arbitrary N, improving upon previous numerical methods.

Findings

Analytic covariance matrices agree with mock simulations in periodic-box geometries.

Fitting for effective volume and density partially corrects for survey window effects.

The formalism enhances efficiency in galaxy clustering analysis.

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 of Cahn & Slepian (2020), recently shown to facilitate efficient NPCF estimation. 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 non-uniform window function.