Wide-angle effects in multi-tracer power spectra with Doppler corrections
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Date
2023
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
IOP Publishing
Abstract
. We examine the computation of wide-angle corrections to the galaxy power spectrum including redshift-space distortions and relativistic Doppler corrections, and also including multiple tracers with differing clustering, magnification and evolution biases. We show
that the inclusion of the relativistic Doppler contribution, as well as radial derivative terms,
are crucial for a consistent wide-angle expansion for large-scale surveys, both in the single
and multi-tracer cases. We also give for the first time the wide-angle cross-power spectrum
associated with the Doppler magnification-galaxy cross correlation, which has been shown
to be a new way to test general relativity. In the full-sky power spectrum, the wide-angle
expansion allows integrals over products of spherical Bessel functions to be computed analytically as distributional functions, which are then relatively simple to integrate over. We give
for the first time a complete discussion and new derivation of the finite part of the divergent
integrals of the form R ∞
0
drrn
j`(kr)j`
0(qr), which are necessary to compute the wide-angle
corrections when a general window function is included. This facilitates a novel method for
integrating a general analytic function against a pair of spherical Bessel functions.
Description
Keywords
Astronomy, Physics, Power spectrum, Redshift surveys, Galaxies
Citation
Paul, P. et al. (2023). Wide-angle effects in multi-tracer power spectra with Doppler corrections. Journal of Cosmology and Astroparticle Physics, 2023(4), 067. 10.1088/1475-7516/2023/04/067