Brisk estimator for the angular multipoles of the redshift space bispectrum

Abstract

The anisotropy of the redshift space bispectrum depends upon the orientation of the triangles formed by three $\mathbf{k}$ modes with respect to the line of sight. For a triangle of fixed size ($k_1$) and shape ($\mu,t$), this orientation dependence can be quantified in terms of angular multipoles $B_\ell^m(k_1,\mu,t)$ which contain a wealth of cosmological information. We propose a fast and efficient FFT-based estimator that computes the bispectrum multipole moments $B_\ell^m$ of a 3D cosmological field for all possible $\ell$ and $m$ (including $m\neq 0$). The time required by the estimator to compute all multipoles from a gridded data cube of volume $N_g^3$ scales as $\sim \mathcal{O}(N_g^4)$ in contrast to the direct computation technique which requires time $\sim \mathcal{O}(N_g^6)$. Here, we demonstrate the formalism and validate the estimator using a simulated non-Gaussian field for which the analytical expressions for all the bispectrum multipoles are known. The estimated results are found to be in good agreement with the analytical predictions for all $16$ non-zero multipoles (up to $\ell= 6, m=6$). We expect the $m \neq 0$ bispectrum multipoles to significantly enhance the information available from galaxy redshift surveys and future redshifted 21-cm observations.