Brisk estimator for the angular multipoles of the redshift space bispectrum

The anisotropy of the redshift space bispectrum depends upon the orientation of the triangles formed by three $\mathbit{k}$ modes with respect to the line of sight. For a triangle of fixed size (${k}_{1}$) and shape ($\ensuremath{\mu}$, $t$), this orientation dependence can be quantified in terms of angular multipoles ${B}_{\ensuremath{\ell}}^{m}({k}_{1},\ensuremath{\mu},t)$, which contain a wealth of cosmological information. We propose a fast and efficient Fast Fourier Transform (FFT)-based estimator that computes the bispectrum multipole moments ${B}_{\ensuremath{\ell}}^{m}$ of a three-dimensional cosmological field for all possible $\ensuremath{\ell}$ and $m$ (including $m\ensuremath{\ne}0$). The time required by the estimator to compute all multipoles from a gridded data cube of volume ${N}_{g}^{3}$ scales as $\ensuremath{\sim}\mathcal{O}({N}_{g}^{4})$ in contrast to the direct computation technique, which requires time $\ensuremath{\sim}\mathcal{O}({N}_{g}^{6})$. 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 nonzero multipoles (up to $\ensuremath{\ell}=6$, $m=6$). We expect the $m\ensuremath{\ne}0$ bispectrum multipoles to significantly enhance the information available from galaxy redshift surveys and future redshifted 21 cm observations.