Dark Collapse or Supermassive Star: a fundamental limit imposed by hydrostatic equilibrium. (arXiv:1910.04776v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Haemmerle_L/0/1/0/all/0/1">L. Haemmerlé</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Meynet_G/0/1/0/all/0/1">G. Meynet</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Mayer_L/0/1/0/all/0/1">L. Mayer</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Klessen_R/0/1/0/all/0/1">R. S. Klessen</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Woods_T/0/1/0/all/0/1">T. E. Woods</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Heger_A/0/1/0/all/0/1">A. Heger</a>
Major mergers of gas-rich galaxies provide promising conditions for the
formation of supermassive black holes (SMBHs; $gtrsim10^5$ M$_odot$) by
direct collapse, since they can trigger mass inflows as high as $10^4-10^5$
M$_odot$ yr$^{-1}$ on sub-parsec scales. However, the channel of SMBH
formation in this case, either dark collapse (direct collapse without prior
stellar phase) or supermassive star (SMS; $gtrsim10^4$ M$_odot$), remains
unknown. Here, we derive a criterion on mass and accretion rate for SMS
formation by testing the consistency of hydrostatic equilibrium in case of
rapid accretion. We compute hydrostatic models of SMSs accreting at $1-1000$
M$_odot$ yr$^{-1}$, and estimate the departures from equilibrium a posteriori
by taking into account the finite speed of sound. We find that stars accreting
above the atomic cooling limit ($gtrsim10$ M$_odot$ yr$^{-1}$) can maintain
hydrostatic equilibrium only once they are supermassive. In this case, they
evolve adiabatically with a hylotropic structure, i.e. entropy is locally
conserved and scales with the square-root of the mass coordinate. Our results
imply that stars can become supermassive by accretion only at the rates of
atomically cooled haloes ($sim0.1-10$ M$_odot$ yr$^{-1}$). Once they are
supermassive, larger rates are possible. Dark collapse occurs if the accretion
rate exceeds the atomic cooling limit before a SMS already formed.
Major mergers of gas-rich galaxies provide promising conditions for the
formation of supermassive black holes (SMBHs; $gtrsim10^5$ M$_odot$) by
direct collapse, since they can trigger mass inflows as high as $10^4-10^5$
M$_odot$ yr$^{-1}$ on sub-parsec scales. However, the channel of SMBH
formation in this case, either dark collapse (direct collapse without prior
stellar phase) or supermassive star (SMS; $gtrsim10^4$ M$_odot$), remains
unknown. Here, we derive a criterion on mass and accretion rate for SMS
formation by testing the consistency of hydrostatic equilibrium in case of
rapid accretion. We compute hydrostatic models of SMSs accreting at $1-1000$
M$_odot$ yr$^{-1}$, and estimate the departures from equilibrium a posteriori
by taking into account the finite speed of sound. We find that stars accreting
above the atomic cooling limit ($gtrsim10$ M$_odot$ yr$^{-1}$) can maintain
hydrostatic equilibrium only once they are supermassive. In this case, they
evolve adiabatically with a hylotropic structure, i.e. entropy is locally
conserved and scales with the square-root of the mass coordinate. Our results
imply that stars can become supermassive by accretion only at the rates of
atomically cooled haloes ($sim0.1-10$ M$_odot$ yr$^{-1}$). Once they are
supermassive, larger rates are possible. Dark collapse occurs if the accretion
rate exceeds the atomic cooling limit before a SMS already formed.
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