On Einstein clusters as galactic dark matter halos

TL;DR

This paper investigates Einstein clusters as potential galactic dark matter halos, analyzing their stability, gravitational lensing effects, and how they compare to other models, suggesting they could be viable dark matter candidates.

Contribution

The study demonstrates that Einstein clusters are stable, consistent with velocity limits, and produce distinguishable lensing effects, offering a novel dark matter model alternative.

Findings

Einstein clusters are dynamically stable against pulsations.

Velocity limits of particles are consistent with stability.

Lensing effects are slightly smaller than traditional models.

Abstract

We consider global and gravitational lensing properties of the recently suggested Einstein clusters of WIMPs as galactic dark matter halos. Being tangential pressure dominated, Einstein clusters are strongly anisotropic systems which can describe any galactic rotation curve by specifying the anisotropy. Due to this property, Einstein clusters may be considered as dark matter candidates. We analyse the stability of the Einstein clusters against both radial and non-radial pulsations, and we show that the Einstein clusters are dynamically stable. With the use of the Buchdahl type inequalities for anisotropic bodies, we derive upper limits on the velocity of the particles defining the cluster. These limits are consistent with those obtained from stability considerations. The study of light deflection shows that the gravitational lensing effect is slightly smaller for the Einstein clusters, as compared to the singular isothermal density sphere model for dark matter. Therefore lensing observations may discriminate, at least in principle, between Einstein cluster and other dark matter models.