The large-scale monopole of the power spectrum in a Euclid-like survey: wide-angle effects, lensing, and the ‘finger of the observer’

Abstract

ABSTRACT Radial redshift-space distortions due to peculiar velocities and other light-cone effects shape the maps we build of the Universe. We address the open question of their impact onto the monopole moment of the galaxy power spectrum, P0(k). Specifically, we use an upgraded numerical implementation of the liger method to generate 140 mock galaxy density fields for a full Euclid-like survey and we measure P0(k) in each of them utilizing a standard estimator. We compare the spectra obtained by turning on and off different effects. Our results show that wide-angle effects due to radial peculiar velocities generate excess power above the level expected within the plane–parallel approximation. They are detectable with a signal-to-noise ratio of 2.7 for $k\lt 0.02\, h$ Mpc−1. Weak-lensing magnification also produces additional power on large scales which, if the current favourite model for the luminosity function of Hα emitters turns out to be realistic, can only be detected with a signal-to-noise ratio of 1.3 at best. Finally, we demonstrate that measuring P0(k) in the standard of rest of the observer generates an additive component reflecting the kinematic dipole overdensity caused by the peculiar velocity. This component is characterized by a damped oscillatory pattern on large scales. We show that this ‘finger of the observer’ effect is detectable in some redshift bins and suggest that its measurement could possibly open new research directions in connection with the determination of the cosmological parameters, the properties of the galaxy population under study, and the dipole itself.