Abstract
Accreting supermassive stars of ≳105 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 × 104 M⊙ for 0.05 M⊙ yr−1 to ∼106 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.