A fast estimator for quantifying the shape dependence of the 3D bispectrum

TL;DR

This paper introduces a fast FFT-based estimator for the 3D bispectrum that efficiently analyzes its dependence on triangle shape and size, validated against analytical models including redshift space distortions.

Contribution

We developed a computationally efficient estimator that separates size and shape dependence of the 3D bispectrum and validated it against analytical predictions.

Findings

Estimator scales as ~N_g^3 log N_g^3 in computational cost.

Estimated bispectrum agrees within 10% of analytical predictions.

Close agreement for monopole in redshift space distortions.

Abstract

The dependence of the bispectrum on the size and shape of the triangle contains a wealth of cosmological information. Here we consider a triangle parameterization which allows us to separate the size and shape dependence. We have implemented an FFT based fast estimator for the three dimensional (3D) bin averaged bispectrum, and we demonstrate that it allows us to study the variation of the bispectrum across triangles of all possible shapes (and also sizes). The computational requirement is shown to scale as $\sim N_{\rm g}^3~\log{N_{\rm g}^3}$ where $N_g$ is the number of grid points along each side of the volume. We have validated the estimator using a non-Gaussian field for which the bispectrum can be analytically calculated. The estimated bispectrum values are found to be in good agreement ($< 10 \%$ deviation) with the analytical predictions across much of the triangle-shape parameter space. We also introduce linear redshift space distortion, a situation where also the bispectrum can be analytically calculated. Here the estimated bispectrum is found to be in close agreement with the analytical prediction for the monopole of the redshift space bispectrum.