Wide-angle and Relativistic effects in Fourier-Space Clustering statistics

Abstract

Galaxy power spectrum and bispectrum signals are distorted by peculiar velocities and other relativistic effects arising from a perturbed spacetime background. In addition, study of correlation functions of tracers in Fourier space is often done in the plane-parallel approximation under which it is assumed that line-of-sight vectors are parallel. In this work we show that a simple perturbative procedure can be employed for a fast evaluation of beyond plane-parallel (wide-angle) corrections to the power spectrum and bispectrum. We also show that evolution of linear matter density fluctuations in a relativistic context can be found from a simple method. For the power spectrum at linear level, we compare leading order wide-angle contributions to multipoles of the galaxy power spectrum with those from non-integrated and integrated relativistic corrections and estimate their possible contamination on local fNL measurements to be of order a few. We also compute wide-angle corrections in the presence of nonlinear terms at one-loop order. For the bispectrum, we show that wide-angle effects alone, even with fully symmetric choices of LOS, give rise to imaginary, oddparity multipoles of the galaxy bispectrum (dipole, octupole, etc.) which are in many cases larger than previously known ones of relativistic origin. We calculate these contributions and provide an estimator for measuring the leading order bispectrum dipole from data, using a symmetric LOS definition. Finally, we calculate the leading order corrections to multipoles of real plane-parallel bispectrum multipoles and estimate the apparent local fNL induced to be of order unity.

Wide-angle effects in multi-tracer power spectra with Doppler corrections

“…Galaxy surveys with wide sky coverage, in particular next-generation surveys, require us to move beyond the flat-sky limit and include wide-angle correlations, with r1 = r2 . This was shown in early work by [1,2] (using a tripolar spherical harmonic expansion) and then further investigated in, e.g., [3][4][5][6][7][8][9][10][11][12][13][14][15]. Our aim is to expand and clarify a number of these results to the multi-tracer power spectrum, including relativistic corrections.…”

“…As a consequence, the leading wide-angle and leading Doppler contributions are of the same order -so that a consistent treatment requires the inclusion of both (e.g. [14,15]). In addition to this, for a consistent treatment we need to include radial derivatives of the growth rate, the biases, and other variables which appear.…”