Einstein Cluster as Central Spiky Distribution of Galactic Dark Matter

TL;DR

This paper models a relativistic, spherically symmetric dark matter distribution near a supermassive black hole using Einstein clusters, exploring how the environment influences the innermost stable orbit.

Contribution

It introduces new toy and realistic models of Einstein clusters with dark matter spikes near black holes, analyzing their stability and orbital properties.

Findings

ISCO depends on environmental details

Inner stable orbit lies between photon sphere and black hole ISCO

Models suggest dark matter spikes significantly affect orbital dynamics

Abstract

Using the Einstein cluster models, we construct a fully relativistic, spherically symmetric, spiky structure of matter distribution near a supermassive black hole. We introduce and discuss three simple toy models, together with a more realistic model, which includes a Hernquist-type distribution with a typical galaxy scale. We find that the innermost stable circular orbit (ISCO) depends on the details of the environment, and lies between the photon radius (at $3M_{\rm BH}$) and the ISCO radius of an isolated black hole of mass $M_{\rm BH}$ (at $6M_{\rm BH}$).