Letter to the Editor

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

¹ Département d’Astronomie, Université de Genève, Chemin des Maillettes 51, 1290 Versoix, Switzerland
e-mail: lionel.haemmerle@unige.ch
² Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
³ Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Str. 2, 69120 Heidelberg, Germany
⁴ Universität Heidelberg, Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
⁵ National Research Council of Canada, Herzberg Astronomy & Astrophysics Research Centre, 5071 West Saanich Road, Victoria, BC V9E 2E7, Canada
⁶ School of Physics and Astronomy, Monash University, VIC 3800, Australia
⁷ Tsung-Dao Lee Institute, Shanghai 200240, PR China

Received: 17 September 2019
Accepted: 21 October 2019

Abstract

Context. Major mergers of gas-rich galaxies provide promising conditions for the formation of supermassive black holes (SMBHs; ≳10⁵ M_⊙) by direct collapse because they can trigger mass inflows as high as 10⁴ − 10⁵ M_⊙ 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; ≳10⁴ M_⊙), remains unknown.

Aims. Here, we investigate the limit in accretion rate up to which stars can maintain hydrostatic equilibrium.

Methods. We compute hydrostatic models of SMSs accreting at 1–1000 M_⊙ yr⁻¹, and estimate the departures from equilibrium a posteriori by taking into account the finite speed of sound.

Results. We find that stars accreting above the atomic cooling limit (≳10 M_⊙ 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.

Conclusions. Our results imply that stars can only become supermassive by accretion at the rates of atomically cooled haloes (∼0.1 − 10 M_⊙ yr⁻¹). Once they are supermassive, larger rates are possible.