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

Accreting supermassive stars of ≳10 5 M ⊙ 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 ⊙ yr −1 . We determined the final mass by solving the differential equation for GR linear adiabatic radial pulsations. We find that models with accretion rates ≳0.05 M ⊙ 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 × 10 4 M ⊙ for 0.05 M ⊙ yr −1 to ∼10 6 M ⊙ for 1000 M ⊙ yr −1 . The 0.05 M ⊙ yr −1 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.