Rapidly Accreting Supergiant Protostars: Embryos of Supermassive Black Holes?

Direct collapse of supermassive stars (SMSs) is a possible pathway for generating supermassive black holes in the early universe. It is expected that an SMS could form via very rapid mass accretion with during the gravitational collapse of an atomic-cooling primordial gas cloud. In this paper, we study how stars would evolve under such extreme rapid mass accretion, focusing on the early evolution until the stellar mass reaches 10 3 M ☉ . To this end, we numerically calculate the detailed interior structure of accreting stars with primordial element abundances. Our results show that for accretion rates higher than 10 −2 M ☉ yr −1 , stellar evolution is qualitatively different from that expected at lower rates. While accreting at these high rates, the star always has a radius exceeding 100 R ☉ , which increases monotonically with the stellar mass. The mass–radius relation for stellar masses exceeding ∼100 M ☉ follows the same track with R * ∝ M 1/2 * in all cases with accretion rates ≳ 10 −2 M ☉ yr −1 ; at a stellar mass of 10 3 M ☉ , the radius is ≃ 7000 R ☉ (≃ 30 AU). With higher accretion rates, the onset of hydrogen burning is shifted toward higher stellar masses. In particular, for accretion rates exceeding , there is no significant hydrogen burning even after 10 3 M ☉ have accreted onto the protostar. Such "supergiant" protostars have effective temperatures as low as T eff ≃ 5000 K throughout their evolution and because they hardly emit ionizing photons, they do not create an H ii region or significantly heat their immediate surroundings. Thus, radiative feedback is unable to hinder the growth of rapidly accreting stars to masses in excess of 10 3 M ☉ as long as material is accreted at rates .