Formation and Redshift Evolution of Dark Matter Spikes

TL;DR

This paper develops a semi-analytic model to study the long-term evolution of dark matter density spikes around black holes, considering stellar effects and cosmic evolution, which significantly alters previous predictions.

Contribution

It generalizes adiabatic spike formation to include finite seed masses, stellar cusps, and non-circular orbits, then models their evolution with coupled Fokker-Planck equations.

Findings

Stellar heating drives the inner dark matter slope towards ~1.5 within a few Gyrs.

Overdensities are reduced by 2-4 orders of magnitude from canonical models.

Redshift-dependent benchmarks for detection signals are provided.

Abstract

Dark matter density spikes forming around adiabatically growing black holes can dramatically enhance indirect and direct detection signals. Canonical predictions, however, assume a zero-mass seed in a purely dark matter environment and do not track the long-term dynamical impact of surrounding stars. We present a semi-analytic framework that first generalizes adiabatic spike formation to include finite seed masses, stellar cusps, and non-circular orbits, and then studies the subsequent cosmic evolution by solving coupled Fokker-Planck equations for the dark matter and stellar phase-space distributions, with a heating rate modulated by the cosmic star formation rate. Starting conservatively from canonical Gondolo-Silk spikes and marginalizing over astrophysical uncertainties, we find that stellar gravitational heating drives the inner slope towards $\gamma_\chi \simeq 1.5$ within a few Gyrs (e.g by $z \lesssim 2$ for spikes formed at $z\simeq 10$), yielding overdensities two to four orders of magnitude below canonical expectations but still well above an NFW-like cusp. We provide redshift-dependent benchmarks for the column density and $J$-factor relevant to scattering, decay and annihilation signatures. Any robust interpretation of indirect dark matter signals from galactic nuclei must account for this evolution.