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Register a new userMaximally accreting supermassive stars: a fundamental limit imposed by hydrostatic equilibrium
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Added by
Lionel Haemmerl\\'e
Publication date
2019
fields
Physics
and research's language is
English
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Major mergers of gas-rich galaxies provide promising conditions for the formation of supermassive black holes (SMBHs; $gtrsim10^5$ M$_odot$) by direct collapse because 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 investigate the limit in accretion rate up to which stars can maintain hydrostatic equilibrium. 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 only maintain hydrostatic equilibrium once they are supermassive. In this case, they evolve adiabatically with a hylotropic structure, that is, entropy is locally conserved and scales with the square root of the mass coordinate. Our results imply that stars can only become supermassive by accretion at the rates of atomically cooled haloes ($sim0.1-10$ M$_odot$ yr$^{-1}$). Once they are supermassive, larger rates are possible.
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The formation of supermassive stars (SMSs) via rapid mass accretion and their direct collapse into black holes (BHs) is a promising pathway for sowing seeds of supermassive BHs in the early universe. We calculate the evolution of rapidly accreting SMSs by solving the stellar structure equations including nuclear burning as well as general relativistic (GR) effects up to the onset of the collapse. We find that such SMSs have less concentrated structure than fully-convective counterpart, which is often postulated for non-accreting ones. This effect stabilizes the stars against GR instability even above the classical upper mass limit $gtrsim 10^5~M_odot$ derived for the fully-convective stars. The accreting SMS begins to collapse at the higher mass with the higher accretion rate. The collapse occurs when the nuclear fuel is exhausted only for cases with $dot M lesssim 0.1~M_odot~{rm yr}^{-1}$. With $dot{M} simeq 0.3 - 1~M_odot~{rm yr}^{-1}$, the star becomes GR-unstable during the helium-burning stage at $M simeq 2 - 3.5~times 10^5~M_odot$. In an extreme case with $10~M_odot~{rm yr}^{-1}$, the star does not collapse until the mass reaches $simeq 8.0times 10^5~M_odot$, where it is still in the hydrogen-burning stage. We expect that BHs with roughly the same mass will be left behind after the collapse in all the cases.
Supermassive stars (SMS; ~ 10^5 M_sun) formed from metal-free gas in the early Universe attract attention as progenitors of supermassive black holes observed at high redshifts. To form SMSs by accretion, central protostars must accrete at as high rates as ~ 0.1-1 M_sun/yr. Such protostars have very extended structures with bloated envelopes, like super-giant stars, and are called super-giant protostars (SGPSs). Under the assumption of hydrostatic equilibrium, SGPSs have density inverted layers, where the luminosity becomes locally super-Eddington, near the surface. If the envelope matter is allowed to flow out, however, a stellar wind could be launched and hinder the accretion growth of SGPSs before reaching the supermassive regime. We examine whether radiation-driven winds are launched from SGPSs by constructing steady and spherically symmetric wind solutions. We find that the wind velocity does not reach the escape velocity in any case considered. This is because once the temperature falls below ~ 10^4 K, the opacity plummet drastically owing to the recombination of hydrogen and the acceleration ceases suddenly. This indicates that, in realistic non-steady cases, even if outflows are launched from the surface of SGPSs, they would fall back again. Such a wind does not result in net mass loss and does not prevent the growth of SGPSs. In conclusion, SGPSs will grow to SMSs and eventually collapse to massive BHs of ~ 10^5 M_sun, as long as the rapid accretion is maintained.
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