Evolution of supermassive stars as a pathway to black hole formation
  Supermassive stars, with masses greater than a million solar masses, are
possible progenitors of supermassive black holes in galactic nuclei. Because of
their short nuclear burning timescales, such objects can be formed only when
matter is able to accumulate at a rate exceeding ~ 1 solar mass/yr. 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 supermassive stars 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 specific entropy is proportional to the enclosed
mass M(R) to the 2/3-power. 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 ("quasistars") that
result. The seed black holes formed in this way could have typical masses in
the range ~ 10^4-10^5 solar masses, 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 Pop III star formation.
