Relativistic distortions in galaxy density-ellipticity correlations: gravitational redshift and peculiar velocity effects

TL;DR

This paper models relativistic effects like gravitational redshift and peculiar velocities in galaxy density-ellipticity correlations, showing they produce detectable dipole signals that can reveal relativistic phenomena in future surveys.

Contribution

It provides an analytical model for the relativistic GI correlation, including the covariance matrix, and demonstrates the potential detectability of these effects in upcoming galaxy surveys.

Findings

Relativistic effects induce non-zero odd multipole anisotropies in GI correlations.

Doppler effects dominate at large scales, gravitational redshift at smaller scales.

The GI dipole signal is detectable with future large-volume surveys.

Abstract

We study relativistic effects, arising from the light propagation in an inhomogeneous universe. We particularly investigate the effects imprinted in a cross-correlation function between galaxy positions and intrinsic galaxy shapes (GI correlation). Considering the Doppler and gravitational redshift effects as major relativistic effects, we present an analytical model of the GI correlation function, from which we find that the relativistic effects induce non-vanishing odd multipole anisotropies. Focusing particularly on the dipole anisotropy, we show that the Doppler effect dominates at large scales, while the gravitational redshift effect originated from the halo potential dominates at the scales below $10$-$30\, {\rm Mpc}/h$, with the amplitude of the dipole GI correlation being positive over all the scales. Also, we newly derive the covariance matrix for the modelled GI dipole. Taking into account the full covariance, we estimate the signal-to-noise ratio and show that the GI dipole induced by the relativistic effects is detectable in future large-volume galaxy surveys. We discuss how the measurement of dipole GI correlation could be helpful to detect relativistic effects in combination with the conventional galaxy-galaxy cross correlation.