ON THE ROLE OF THE ΩΓ LIMIT IN THE FORMATION OF POPULATION III MASSIVE STARS

Abstract

ABSTRACT We explore the role of the modified Eddington limit due to rapid rotation (the so-called ΩΓ limit) in the formation of Population III stars. We performed one-dimensional stellar evolution simulations of zero-metallicity protostars accreting mass at a very high rate ( M ˙ ∼ 10 − 3 M ⊙ yr − 1 ?> ) and dealt with stellar rotation as a separate post-process. The protostar would reach the Keplerian rotation very soon after the onset of mass accretion, but mass accretion would continue as stellar angular momentum is transferred outward to the accretion disk by viscous stress. The envelope of the protostar expands rapidly when the stellar mass reaches ~5–7 M ⊙ and the Eddington factor increases sharply. This makes the protostar rotate critically at a rate that is significantly below the Keplerian value (i.e., the ΩΓ limit). The resultant positive gradient of the angular velocity in the boundary layer between the protostar and the Keplerian disk prohibits angular momentum transport from the star to the disk, and consequently further rapid mass accretion. This would prevent the protostar from growing significantly beyond 20–40 M ⊙. Another important consequence of the ΩΓ limit is that the protostar can remain fairly compact (R ≲ 50 R ⊙) and avoid a fluffy structure (R ≳ 500 R ⊙) that is usually found with a very high rate of mass accretion. This effect would make the protostar less prone to binary interactions during the protostar phase. Although our analysis is based on Population III protostar models, this role of the ΩΓ limit would be universal in the formation process of massive stars, regardless of metallicity.