Linear adiabatic analysis for general relativistic instability in primordial accreting supermassive stars

TL;DR

This paper analyzes the stability of accreting supermassive stars under general relativity, determining the critical masses at which they become unstable and collapse into black holes, relevant for early universe black hole formation.

Contribution

It introduces a linear adiabatic radial pulsation method to calculate the final mass of accreting Population III stars before GR instability triggers collapse.

Findings

Critical masses increase with higher accretion rates.

Stars with accretion rates ≥ 0.05 M_sun/yr become unstable during hydrogen burning.

Final masses range from 8×10^4 to 10^6 M_sun depending on accretion rate.

Abstract

Accreting supermassive stars of $\gtrsim 10^{5}\,M_\odot$ will eventually collapse directly to a black hole via the general relativistic (GR) instability. Such direct collapses of supermassive stars are thought to be a possible formation channel for supermassive black holes at $z > 6$. In this work, we investigate the final mass of accreting Population III stars with constant accretion rates between $0.01$ and $1000\,M_\odot$yr$^{-1}$. We determine the final mass by solving the differential equation for the general relativistic linear adiabatic radial pulsations. We find that models with accretion rates $\gtrsim 0.05\,M_\odot$yr$^{-1}$ experience the GR instability at masses depending on the accretion rates. The critical masses are larger for higher accretion rates, ranging from $8\times10^{4}\,M_\odot$ for $0.05\,M_\odot$yr$^{-1}$ to $\sim10^6\,M_\odot$ for $1000\,M_\odot$yr$^{-1}$. The $0.05\,M_\odot$yr$^{-1}$ model reaches the GR instability at the end of the core hydrogen burning. The higher mass models with the higher accretion rates reach the GR instability during the hydrogen burning stage.