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

Abstract

Accreting supermassive stars of $ 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\ We determined the final mass by solving the differential equation for GR linear adiabatic radial pulsations. We find that models with accretion rates $ experience the GR instability at masses depending on the accretion rates. The critical masses are larger for higher accretion rates, ranging from $8 for $0.05\ to $ for $1000\ The $0.05\ model reaches the GR instability at the end of the core hydrogen burning. The higher-mass models with higher accretion rates reach the GR instability during the hydrogen burning stage.