Analytic Gaussian covariance matrices for galaxy N-point correlation functions

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.

Automated summary

This study derives analytic covariance matrices for the N-point correlation functions of galaxies in the Gaussian limit and compares the results with simulated data. The findings suggest that the analytic formalism provides reasonable predictions for the covariances estimated from simulated data and that fitting for an effective volume and number density can compensate for nonuniform window function effects.