Bispectrum-window convolution via Hankel transform

TL;DR

This paper introduces an exact convolution method for bispectrum multipoles in redshift space using Hankel transforms and 2D-FFTlog, enabling efficient and accurate modeling of survey window effects.

Contribution

It extends power spectrum convolution techniques to the bispectrum, providing a fast, accurate, and unbiased method for incorporating survey window functions in bispectrum analyses.

Findings

Achieves percent-level accuracy compared to mock catalogs.

Recovers unbiased halo bias parameters in simulations.

Performs convolution in under one second.

Abstract

We present a method to perform the exact convolution of the model prediction for bispectrum multipoles in redshift space with the survey window function. We extend a widely applied method for the power spectrum convolution to the bispectrum, taking advantage of a 2D-FFTlog algorithm. As a preliminary test of its accuracy, we consider the toy model of a spherical window function in real space. This setup provides an analytical evaluation of the 3-point function of the window, and therefore it allows to isolate and quantify possible systematic errors of the method. We find that our implementation of the convolution in terms of a mixing matrix shows differences at the percent level in comparison to the measurements from a very large set of mock halo catalogs. It is also able to recover unbiased constraints on halo bias parameters in a likelihood analysis of a set of numerical simulations with a total volume of $100\, h^{-3} \, {\rm Gpc}^3$. For the level of accuracy required by these tests, the multiplication with the mixing matrix is performed in the time of one second or less.