Maximally accreting supermassive stars: a fundamental limit imposed by hydrostatic equilibrium

TL;DR

This paper explores the maximum accretion rate at which supermassive stars can sustain hydrostatic equilibrium, revealing that only supermassive stars can withstand accretion rates above 10 M$_\odot$ yr$^{-1}$, with implications for SMBH formation.

Contribution

It introduces models of supermassive stars accreting at high rates and establishes a fundamental limit for hydrostatic equilibrium based on accretion rate and stellar mass.

Findings

Stars can only maintain equilibrium if they are supermassive when accreting above 10 M$_\odot$ yr$^{-1}$.

Supermassive stars evolve adiabatically with a hylotropic structure during high accretion.

Maximum sustainable accretion rates for star formation are around 0.1-10 M$_\odot$ yr$^{-1}$.

Abstract

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.