Bispectrum Supersample Covariance

TL;DR

This paper models the impact of super-survey modes on the bispectrum covariance using response functions, revealing that density contributions dominate and that supersample covariance is significant for cross covariances, with good agreement from halo model predictions.

Contribution

It introduces a response function formalism to quantify supersample covariance effects on the bispectrum and cross covariance, including density and tidal contributions, validated by numerical measurements.

Findings

Tidal contributions are negligible compared to density effects.

Supersample covariance is more significant for cross covariance than for the bispectrum alone.

Halo model response functions accurately predict supersample covariance effects.

Abstract

Modes with wavelengths larger than the survey window can have significant impact on the covariance within the survey window. The supersample covariance has been recognized as an important source of covariance for the power spectrum on small scales, and it can potentially be important for the bispectrum covariance as well. In this paper, using the response function formalism, we model the supersample covariance contributions to the bispectrum covariance and the cross covariance between the power spectrum and the bispectrum. The supersample covariances due to the long wavelength density and tidal perturbations are investigated, and the tidal contribution is a few orders of magnitude smaller than the density one because in configuration space the bispectrum estimator involves angular averaging and the tidal response function is anisotropic. The impact of the super-survey modes is quantified using numerical measurements with periodic box and subbox setups. For the matter bispectrum, the ratio between the supersample covariance correction and the small scale covariance, which can be computed using a periodic box, is roughly an order of magnitude smaller than that for the matter power spectrum. This is because for the bispectrum, the small scale non-Gaussian covariance is significantly larger than that for the power spectrum. For the cross covariance, the supersample covariance is as important as for the power spectrum covariance. The supersample covariance prediction with the halo model response function is in good agreement with numerical results.