Quantifying the redshift space distortion of the bispectrum III: detection prospects of the multipole moments

The redshift space anisotropy of the bispectrum is generally quantified using multipole moments. The possibility of measuring these multipoles in any survey depends on the level of statistical fluctuations. We compute the statistical fluctuations in the measurement of bispectrum multipoles for a Euclid like galaxy survey based on second-order perturbation theory and present two quantities: the signal-to-noise ratio (SNR) which quantifies the detectability of a multipole and the rank correlation which quantifies the correlation in measurement errors between any two multipoles. Based on SNR values, we find that Euclid can potentially measure the bispectrum multipoles up to ℓ = 4 across various triangle shapes, formed by the three k vectors in Fourier space. In general, SNR is maximum for the linear triangles. SNR values also depend on the scales and redshifts of observation. While, ℓ ≤ 2 multipoles can be measured with SNR > 5 even at linear/quasi-linear (k₁ ≃ 0.1 Mpc⁻¹) scales, for ℓ > 2 multipoles, we require to go to small scales or need to increase bin sizes. These estimates are based on bins of extent ∆ln k₁ = 0.1, ∆μ = 0.05, and ∆t = 0.05, where k₁ is the length of the largest side, and (μ, t), respectively, quantify the size and shape of the triangles. For most multipole pairs, the errors are only weakly correlated across much of the triangle shapes barring a few in the vicinity of squeezed and stretched triangles. This makes it possible to combine the measurements of different multipoles to increase the effective SNR.