Gravitational redshifts of clusters and voids

We investigate gravitational redshifts (signals of gravitational potential) in measurements of the redshifts of cosmological objects, i.e., central and satellite galaxies in clusters of galaxies, intracluster gas, as well as galaxies associated with voids by developing simple theoretical models. In the analysis with satellite galaxies in clusters, we develop a very simple analytic model for satellite galaxies virialized in halos, which enables us to evaluate the signals depending on the properties of the halo occupation distribution of galaxies. We obtain results consistent with recent previous results, though our results are restricted to the satellite galaxies inside the virial radius. In the analysis of intracluster gas, we develop a simple analytic model including the effect of random motions of gases, which are assumed to generate nonthermal pressure. We demonstrate a possible contribution of the random motions of gases to gravitational potential measurements. We also investigate a possible signature of the gravitational potential in measurements of galaxies associated with voids by utilizing a simple analytic model. We show that the second-order Hubble term, which appears in the expansion of the scale factor around the center of a void, may make a significant contribution depending on the way the galaxy samples are analyzed. The studies on the possible signals of gravitational potential for intracluster gases and voids are performed for the first time.