Gravitational Redshifts in Simulated Galaxy Clusters

We predict the amplitude of the gravitational redshift of galaxies in galaxy clusters using an N-body simulation of a Lambda CDM universe. We examine if it might be possible to detect the gravitational effect on the total redshift observed for galaxies. For clusters of mass M ~10^15 m_sun, the difference in gravitational redshift between the brightest galaxy and the rest of the cluster members is ~10 km/s. The most efficient way to detect gravitational redshifts using information from galaxies only involves using the full gravitational redshift profile of clusters. Massive clusters, while having the largest gravitational redshift suffer from large galaxy peculiar velocities and substructure, which act as a source of noise. This and their low number density make it more reasonable to try averaging over many clusters and groups of relatively low mass. We examine publicly available data for 107 rich clusters from the ESO Nearby Abell Clusters Survey (ENACS), finding no evidence for gravitational redshifts. Tests on our simulated clusters show that we need at least ~2500 clusters/groups with M > 5*10^13 m_sun for a detection of gravitational redshifts at the 2 sigma level.