Euclid: Relativistic effects in the dipole of the 2-point correlation function

TL;DR

This paper investigates the detectability of relativistic effects, specifically gravitational redshift and Doppler effects, in the galaxy correlation dipole within the Euclid survey, demonstrating potential for significant detection.

Contribution

It models relativistic effects in galaxy surveys and shows they can be detected in Euclid data, especially on small scales and at low redshifts.

Findings

Dipole signal detected below 30 h^{-1} Mpc scales

Detection significance of 4σ and 3σ in low redshift bins

Overall detection significance of approximately 6σ in Euclid data

Abstract

Gravitational redshift and Doppler effects give rise to an antisymmetric component of the galaxy correlation function when cross-correlating two galaxy populations or two different tracers. In this paper, we assess the detectability of these effects in the Euclid spectroscopic galaxy survey. We model the impact of gravitational redshift on the observed redshift of galaxies in the Flagship mock catalogue using a Navarro-Frenk-White profile for the host haloes. We isolate these relativistic effects, largely subdominant in the standard analysis, by splitting the galaxy catalogue into two populations of faint and bright objects and estimating the dipole of their cross-correlation in four redshift bins. In the simulated catalogue, we detect the dipole signal on scales below $30\,h^{-1}{\rm Mpc}$, with detection significances of $4\,\sigma$ and $3\,\sigma$ in the two lowest redshift bins, respectively. At higher redshifts, the detection significance drops below $2\,\sigma$. Overall, we estimate the total detection significance in the Euclid spectroscopic sample to be approximately $6\,\sigma$. We find that on small scales, the major contribution to the signal comes from the nonlinear gravitational potential. Our study on the Flagship mock catalogue shows that this observable can be detected in Euclid Data Release 2 and beyond.