Gravitational redshifts of clusters and voids

Abstract

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 virialised 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 centre of a void, may make a significant contribution depending on the way the galaxy samples are analysed. The studies on the possible signals of gravitational potential for intracluster gases and voids are performed for the first time.

Tests of Gravity with Galaxy Clusters

“…Measurements of these second-order effects are usually expressed in terms of total redshift difference between a satellite galaxy (S) and the central galaxy (C) in a cluster, that is 153,154…”

“…As a concluding remark note that gravitational redshifts can also in principle be extracted from X-ray spectra of the intracluster medium, with the advantage that owing to the large number of particles only a relatively small number of systems is required to keep the noise within acceptable levels. 150,154 Although such measurements are beyond reach of current X-ray observatories, 162,163 the excellent spectral resolution of future X-ray telescopes will make this possible. 164…”

Gravitational redshift in the void-galaxy cross-correlation function in redshift space

“…We work within the Newtonian gauge of cosmological perturbation theory; however, the results will not depend on this choice because the void relevant to our problem is of the subhorizon scale. Denoting the gravitational potential and the peculiar velocity by ψ and v, respectively, we may express δz up to the order of O(v 2 ) [26],…”

“…We follow the theoretical formulation developed in Ref. [26] by beginning with a brief review of the formulation. When there is no effect from the gravitational potential and the peculiar velocity, the relation between the comoving distance χ and the redshift z is given by…”

“…These works are extensions of precise modeling of galaxy distributions to include higher order effects of redshift-space distortions and other effects. The gravitational redshift and the second order Doppler effect (from the second order peculiar velocity) in the galaxy clusters are one of such topics [22][23][24][25][26][27]. Measurements of the gravitational redshift with galaxies associated with clusters have been reported [22][23][24].…”