The Halo Bispectrum Multipoles in Redshift Space

TL;DR

This paper analyzes the halo bispectrum multipoles in redshift space using simulations, fitting a perturbation theory model to extract bias parameters and growth rate, and assesses covariance estimation accuracy.

Contribution

It provides a comprehensive analysis of the halo bispectrum multipoles in redshift space, including covariance estimation and model validity range, with implications for cosmological parameter inference.

Findings

Tree-level model valid up to k=0.08 h/Mpc for monopole

Quadrupole improves parameter constraints significantly

Gaussian covariance approximation works well for periodic boxes

Abstract

We present the analysis of the halo bispectrum in redshift-space in terms of its multipoles, monopole, quadrupole and hexadecapole, measured from a large set of simulations. We fit such measurements with a tree-level model in perturbation theory that depends on linear and nonlinear bias parameters as well as on the growth rate $f$ of density fluctuations. The likelihood analysis takes advantage of a very large set of mock catalogs, enabling a robust estimation of the covariance properties for all multipoles. We compare the numerical estimate of the covariance matrix to its Gaussian prediction finding discrepancies of 10% or less for all configurations with the sole exception of the squeezed triangles in the monopole case. We find the range of validity of the tree-level model, for the total simulation volume of about 1000 $h^{-3}\, {\rm Gpc}^3$, reaches a maximum wavenumber of $0.08 \, h \, {\rm Mpc}^{-1}$ for the monopole, while it is limited to $0.06$ and $0.045\, h \, \rm{Mpc}^{-1}$ respectively for quadrupole and hexadecapole. Despite this, the addition of the quadrupole to the analysis allows for significant improvements on the determination of the model parameters and specifically on $f$, similarly to the power spectrum case. Finally, we compare our numerical estimate for the full covariance with its theoretical prediction in the Gaussian approximation and find the latter to work remarkably well in the context of simulation boxes with periodic boundary condition.