Non-Equilibrium Relativistic Core Collapse of Self-Interacting Dark Matter Halos -- Limits On Seed Black Hole Mass

TL;DR

This paper models the relativistic collapse of self-interacting dark matter halos to understand seed black hole formation, revealing that additional mechanisms are needed for sufficiently massive SMBH seeds.

Contribution

It introduces the Misner-Sharp formalism into SIDM halo modeling, incorporating relativistic effects and analyzing late-stage collapse behavior.

Findings

Relativistic effects enable tracking to apparent horizon formation.

Late-stage collapse involves outward heat flux causing outer envelope expansion.

Seed black hole mass at horizon formation is about 3×10⁻⁸ of halo mass.

Abstract

Recent observations of supermassive black holes (SMBHs) at high redshifts pose challenges to standard seeding mechanisms. Among competing models, the collapse of self-interacting dark matter (SIDM) halos provide a plausible explanation for early SMBH formation. While previous studies on modeling the gravothermal collapse of SIDM halos have primarily focused on non-relativistic evolution under the assumption of hydrostatic equilibrium, We advance this framework by relaxing the equilibrium assumption and additionally incorporating general-relativistic effects. To this end, we introduce the Misner-Sharp formalism to the SIDM context for the first time. Our model reproduces the standard hydrostatic models in the early long-mean-free-path (LMFP) regime, but displays interesting distinct behavior in the late short-mean-free-path (SMFP) regime, where intense outward heat flux drives a rapid expansion of the outer envelope, removing mass from the core and significantly decelerating the collapse. Our general relativistic treatment enables us to follow halo evolution to the final stage when the apparent horizon forms. Our simulation yields a seed black hole mass of approximately $3\times10^{-8}$ of the halo mass at horizon formation, suggesting that additional mechanisms such as baryonic effects are critical for seeding black holes that are sufficiently massive to account for SMBHs in the early Universe.