Dark matter mounds from the collapse of supermassive stars: a general-relativistic analysis

TL;DR

This paper develops a fully relativistic model of dark matter mound formation from supermassive star collapse, improving predictions of dark matter distribution around black holes for gravitational wave studies.

Contribution

It introduces a new general-relativistic formalism for modeling dark matter around collapsing supermassive stars, extending beyond adiabatic black hole growth scenarios.

Findings

Dark matter distribution is significantly reshaped during non-adiabatic collapse.

Low-binding-energy dark matter regions are depleted post-collapse.

Results enhance predictions for dark matter profiles around supermassive black holes.

Abstract

Recent work has highlighted the importance of a fully relativistic treatment of the dephasing of gravitational waves induced by dark-matter overdensities in extreme mass-ratio inspirals (EMRIs). However, a general-relativistic description of the dark matter phase-space distribution is currently available only for the case of a dark matter "spike" arising from adiabatic black hole growth. Here we develop a fully general-relativistic formalism for the more realistic scenario in which a supermassive stellar progenitor collapses to a black hole and produces a shallower dark matter overdensity, or "mound". We follow self-consistently the evolution of the supermassive star, its collapse, and the subsequent growth of the resulting black hole, together with the collisionless dark matter orbits. We find that in the regime where the collapse becomes non-adiabatic, the dark matter distribution function is significantly reshaped, with a clear depletion in the low-binding-energy region of phase space. Our results provide a more realistic prediction for the dark matter phase-space distribution around supermassive black holes, which is an essential step in our programme to use future EMRI observations to extract information about both the nature of dark matter and the formation history of the black hole.