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

Abstract

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 present a formalism to compute the statistical fluctuations in the measurement of bispectrum multipoles for galaxy surveys. We consider specifications of a {\it Euclid} like galaxy survey 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 {\it Euclid} can potentially measure the bispectrum multipoles up to $\ell =4$ across various triangle shapes, formed by the three {\bf 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, $\ell \le 2$ multipoles can be measured with $\mathrm{SNR}>5$ even at linear/quasi-linear ($k\lesssim 0.1{\mathrm{Mpc}}^{-1}$) scales, for $\ell >2$ multipoles, we require to go to small scales or need to increase bin sizes. 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.

Submitted to MNRAS main journal, 14 Pages, 8 Figures

References in corpus (11)

• The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
• A test of the nature of cosmic acceleration using galaxy redshift distortions
• Constraining $M_{\nu }$ with the Bispectrum II: The Total Information Content of the Galaxy Bispectrum
• The Three-Point Correlation Function of Luminous Red Galaxies in the Sloan Digital Sky Survey
• Information Content of the Angular Multipoles of Redshift-Space Galaxy Bispectrum
• Tensor Non-Gaussianity Search: Current Status and Future Prospects
• Quantifying the Redshift Space Distortion of the Bispectrum I: Primordial Non-Gaussianity
• Modelling redshift-space distortion in the post-reionization $\mathrm{HI}$ 21-cm power spectrum
• Quantifying the Redshift Space Distortion of the Bispectrum II: Induced Non-Gaussianity at Second Order Perturbation
• Redshift space distortions of the {\rm HI} 21-cm intensity mapping signal due to the internal motions within galaxies
• Constraints on Running of Non-Gaussianity from Large Scale Structure Probes

Cited by in corpus (8)

• Cosmology with the Galaxy Bispectrum Multipoles: Optimal Estimation and Application to BOSS Data
• Probing the Anisotropy and Non-Gaussianity in the Redshift Space through the Conditional Moments of the First Derivative
• Brisk estimator for the angular multipoles of the redshift space bispectrum
• The size and shape dependence of the SDSS galaxy bispectrum
• Mixing Bispectrum Multipoles Under Geometric Distortions
• Impact of Redshift Space Distortion on Persistent Homology of cosmic matter density field
• Redshift-space galaxy bispectrum in presence of massive neutrinos: A multipole expansion approach for Euclid
• Tracing Signatures of Modified Gravity in Redshift-Space Galaxy Bispectrum Multipoles: Prospects for Euclid