Maximally Rotating Supermassive Stars at the Onset of Collapse: Effects of Gas Pressure. (arXiv:1906.04190v1 [astro-ph.HE])

<a href="http://arxiv.org/find/astro-ph/1/au:+Dennison_K/0/1/0/all/0/1">Kenneth A. Dennison</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Baumgarte_T/0/1/0/all/0/1">Thomas W. Baumgarte</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Shapiro_S/0/1/0/all/0/1">Stuart S. Shapiro</a>

The “direct collapse” scenario has emerged as a promising evolutionary track

for the formation of supermassive black holes early in the Universe. In an

idealized version of such a scenario, a uniformly rotating supermassive star

spinning at the mass-shedding (Keplerian) limit collapses gravitationally after

it reaches a critical configuration. Under the assumption that the gas is

dominated by radiation pressure, this critical configuration is characterized

by unique values of the dimensionless parameters $J/M^2$ and $R_p/M$, where $J$

is the angular momentum, $R_p$ the polar radius, and $M$ the mass. Motivated by

a previous perturbative treatment we adopt a fully nonlinear approach to

evaluate the effects of gas pressure on these dimensionless parameters for a

large range of masses. We find that gas pressure has a significant effect on

the critical configuration even for stellar masses as large as $M simeq 10^6

M_{odot}$. We also calibrate two approximate treatments of the gas pressure

perturbation in a comparison with the exact treatment, and find that one

commonly used approximation in particular results in increasing deviations from

the exact treatment as the mass decreases, and the effects of gas pressure

increase. The other approximation, however, proves to be quite robust for all

masses $M gtrsim 10^4 M_{odot}$.

The “direct collapse” scenario has emerged as a promising evolutionary track

for the formation of supermassive black holes early in the Universe. In an

idealized version of such a scenario, a uniformly rotating supermassive star

spinning at the mass-shedding (Keplerian) limit collapses gravitationally after

it reaches a critical configuration. Under the assumption that the gas is

dominated by radiation pressure, this critical configuration is characterized

by unique values of the dimensionless parameters $J/M^2$ and $R_p/M$, where $J$

is the angular momentum, $R_p$ the polar radius, and $M$ the mass. Motivated by

a previous perturbative treatment we adopt a fully nonlinear approach to

evaluate the effects of gas pressure on these dimensionless parameters for a

large range of masses. We find that gas pressure has a significant effect on

the critical configuration even for stellar masses as large as $M simeq 10^6

M_{odot}$. We also calibrate two approximate treatments of the gas pressure

perturbation in a comparison with the exact treatment, and find that one

commonly used approximation in particular results in increasing deviations from

the exact treatment as the mass decreases, and the effects of gas pressure

increase. The other approximation, however, proves to be quite robust for all

masses $M gtrsim 10^4 M_{odot}$.

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