Gravity theories, Transverse Doppler and Gravitational Redshifts in Galaxy Clusters

TL;DR

This paper examines gravitational redshifts in galaxy clusters, highlighting the importance of transverse Doppler effects, and finds that these signals are insensitive to different gravity theories when equilibrium constraints are considered.

Contribution

It introduces a self-consistent equilibrium model accounting for transverse Doppler effects and demonstrates that gravitational redshift signals cannot distinguish between gravity theories under these conditions.

Findings

Transverse Doppler effect is significant and often neglected in models.

Gravitational redshift signals are insensitive to gravity theories when equilibrium is enforced.

N-body simulations show non-equilibrium effects amplify the transverse Doppler shift.

Abstract

There is growing interest in testing alternative gravity theories using the subtle gravitational redshifts in clusters of galaxies. However, current models all neglect a transverse Doppler redshift of similar magnitude, and some models are not self-consistent. An equilibrium model would fix the gravitational and transverse Doppler velocity shifts to be about 6sigma^2/c and 3sigma^2/2c in order to fit the observed velocity dispersion sigma self-consistently. This result comes from the Virial Theorem for a spherical isotropic cluster, and is insensitive to the theory of gravity. A gravitational redshift signal also does not directly distinguish between the Einsteinian and f(R) gravity theories, because each theory requires different dark halo mass function to keep the clusters in equilibrium. When this constraint is imposed, the gravitational redshift has no sensitivity to theory. Indeed our N-body simulations show that the halo mass function differs in f(R), and that the transverse Doppler effect is stronger than analytically predicted due to non-equilibrium.