Evolution of supermassive stars as a pathway to black hole formation

Supermassive stars, with masses ≳106 M⊙, are possible progenitors of supermassive black holes in galactic nuclei. Because of their short nuclear burning time-scales, such objects can be formed only when matter is able to accumulate at a rate exceeding ∼1 M⊙ yr−1. Here we revisit the structure and evolution of rotationally stabilized supermassive stars, taking into account their continuous accumulation of mass and their thermal relaxation. We show that the outer layers of a supermassive star are not thermally relaxed during much of the star's main-sequence lifetime. As a result, they do not resemble n= 3 polytropes, as assumed in previous literature, but rather consist of convective (polytropic) cores surrounded by convectively stable envelopes that contain most of the mass. We compute the structures of these envelopes, in which the equation of state obeys P/ρ4/3∝M2/3(R), where M(R) is the mass enclosed within radius R. By matching the envelope solutions to convective cores, we calculate the core mass as a function of time. We estimate the initial black hole masses formed as a result of core-collapse, and their subsequent growth via accretion from the bloated envelopes (‘quasi-stars’) that result. The seed black holes formed in this way could have typical masses in the range ∼104–105 M⊙, considerably larger than the remnants thought to be left by the demise of Population III stars. Supermassive black holes therefore could have been seeded during an epoch of rapid infall considerably later than the era of Population III star formation.