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 Mdot ~ 0.1 - 1 Msun/yr 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 1000 Msun. 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 0.01 Msun/yr, 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 Rsun, which increases monotonically with the stellar mass. The mass-radius relation for stellar masses exceeding ~ 100 Msun follows the same track with R_* \propto M_*^0.5 in all cases with accretion rates > 0.01 Msun/yr; at a stellar mass of 1000 Msun the radius is about 7000 Rsun (~= 30 AU). With higher accretion rates the onset of hydrogen burning is shifted towards higher stellar masses. In particular, for accretion rates exceeding Mdot > 0.1 Msun/yr, there is no significant hydrogen burning even after 1000 Msun have accreted onto the protostar. Such "supergiant" protostars have effective temperatures as low as Teff ~= 5000 K throughout their evolution and because they hardly emit ionizing photons, they do not create an HII 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 1000 Msun, as long as material is accreted at rates Mdot > 0.01 Msun/yr. 
Takashi Hosokawa, Kazuyuki Omukai, Harold W. Yorke
astro-ph.CO astro-ph.SR