Gravitational redshift and asymmetric redshift-space distortions for stacked clusters

TL;DR

This paper derives the relativistic redshift expression, applies it to simulations of galaxy clusters, and identifies systematic biases affecting gravitational redshift measurements in stacked clusters.

Contribution

It introduces a detailed relativistic model for redshift in galaxy clusters and uncovers key systematics impacting gravitational redshift signals in observational data.

Findings

GRedshift signal is reduced by halo morphology and cosmic-web effects.

Significant differences between real and velocity space profiles.

Signal-to-noise ratio increases with decreasing halo mass.

Abstract

We derive the expression for the observed redshift in the weak field limit in the observer's past light cone, including all relativistic terms up to second order in velocity. We then apply it to compute the cluster-galaxy cross-correlation functions (CGCF) using N-body simulations. The CGCF is asymmetric along the line of sight (LOS) owing to the presence of the small second order terms such as the gravitational redshift (GRedshift). We identify two systematics in the modelling of the GRedshift signal in stacked clusters. First, it is affected by the morphology of dark matter haloes and the large-scale cosmic-web. The non-spherical distribution of galaxies around the central halo and the presence of neighbouring clusters systematically reduce the GRedshift signal. This bias is approximately 20% for $M_{\rm min}\simeq 10^{14} {\rm M_{\odot}}/h$, and is more than 50% for haloes with $M_{\rm min}\simeq 2\times 10^{13} {\rm M_{\odot}}/h$ at $r>$4 Mpc/$h$. Second, the best-fit gravitational redshift profiles as well as the profiles of all other relativistic terms are found to be significantly different in velocity space compared to their real space versions. We discuss some subtleties relating to these effects in velocity space. We also find that the S/N of the GRedshift signal increases with decreasing halo mass.