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

¹ Astronomical Institute, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan
² Département d’Astronomie, Université de Genève, Chemin Pegasi 51, 1290 Versoix, Switzerland
e-mail: deveshnandal@yahoo.com

Received: 14 March 2024
Accepted: 25 June 2024

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.