Gravitational redshift and asymmetric redshift-space distortions for stacked clusters

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 $M_{\min }\simeq 10^{14}{\mathrm{M}}_{\odot }/h$, and is more than 50% for haloes with $M_{\min }\simeq 2\times 10^{13}{\mathrm{M}}_{\odot }/h$ 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.

13 pages, 6 figures, submitted to MNRAS

References in corpus (4)

• New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects
• A GMBCG Galaxy Cluster Catalog of 55,424 Rich Clusters from SDSS DR7
• Gravitational Redshift of Galaxies in Clusters from the Sloan Digital Sky Survey and the Baryon Oscillation Spectroscopic Survey
• Comparing gravitational redshifts of SDSS galaxy clusters with the magnification redshift enhancement of background BOSS galaxies

Cited by in corpus (6)

• Large-scale dark matter simulations
• Relativistic distortions in the large-scale clustering of SDSS-III BOSS CMASS galaxies
• Tests of Gravity with Galaxy Clusters
• N-body simulations of gravitational redshifts and other relativistic distortions of galaxy clustering
• Gravitational redshifting of galaxies in the SPIDERS cluster catalogue
• Perturbed redshifts from N-body simulations