Power spectrum in the presence of large-scale overdensity and tidal fields: breaking azimuthal symmetry

Abstract

We consider the power spectrum of a biased tracer observed in a finite volume in the presence of a large-scale overdensity and tidal fields. Expanding both the observed power spectrum and the source fields (linear power spectrum, scalar overdensity and tidal field tensor) in spherical harmonics, we explicitly confirm that each $(\ell ,m)$ source generates just the corresponding $(\ell ,m)$ modes of power spectrum in real space. In redshift space, each $(\ell ,m)$ source additionally couples only to $(\ell +2n,m)$ modes of tracer power spectra. This generalizes the Kaiser formula for monopole, quadrupole and hexadecapole of the power spectrum to all $(\ell ,m)$ modes generated to the second order in perturbation theory. This formalism can find applications in constraining the super-sample covariance and in the local power spectrum based bispectrum estimators. As an example application, we forecast the ability to measure these modes a survey with BOSS-like galaxy number densities.

arXiv comment22 pages, 8 figures; matches JCAP accepted version

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• Measuring the Tidal Response of Structure Formation: Anisotropic Separate Universe Simulations using TreePM
• Local Primordial Non-Gaussianities and Super-Sample Variance
• Lagrangian approach to super-sample effects on biased tracers at field level: galaxy density fields and intrinsic alignments
• Statistical anisotropy in galaxy ellipticity correlations
• Super-sample tidal modes on the celestial sphere
• Minimum variance estimation of statistical anisotropy via galaxy survey
• Clustering redshifts with the 21cm-galaxy cross-bispectrum