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Maximum accretion rate of supermassive stars


Haemmerlé, L; Klessen, R S; Mayer, L; Zwick, L (2021). Maximum accretion rate of supermassive stars. Astronomy and Astrophysics, 652:L7.

Abstract

Context. The formation of the most massive quasars observed at high redshifts requires extreme inflows of gas down to the length scales of the central compact object.
Aims. Here we estimate the maximum inflow rate allowed by gravity down to the surface of supermassive stars, the possible progenitors of these supermassive black holes.
Methods. We use the continuity equation and the assumption of spherical symmetry and free fall to derive the maximum allowed inflow rates for various density profiles. We apply our approach to the mass–radius relation of rapidly accreting supermassive stars to estimate an upper limit to the accretion rates allowed during the formation of these objects.
Results. We find that, as long as the density of the accreted gas is smaller than or equal to the average density of the accretor, the maximum allowed rate, Ṁ$_{max}$, is given uniquely by the compactness of the accretor. We argue that a density inversion between accreting matter and the accretor is inconsistent with gravitational collapse. For the compactness of rapidly accreting supermassive stars, Ṁ$_{max}$ is related to the stellar mass, M, by a power law, Ṁ$_{max}$ ∝ M$^{3/4}$. The rates of atomically cooled halos (0.1−10 M$_{⊙}$ yr$^{−1}$) are allowed as soon as M ≳ 1 M$_{⊙}$. The largest rates expected in galaxy mergers (10$^{4}$ − 10$^{5}$ M$_{⊙}$ yr$^{−1}$) become accessible once the accretor is supermassive (M ≳ 10$^{4}$ M$_{⊙}$).
Conclusions. These results suggest that supermassive stars can accrete up to masses > 10$^{6}$ M$_{⊙}$ before they collapse via the general-relativistic instability. At such masses, the collapse is expected to lead to the direct formation of a supermassive black hole, even within metal-rich gas, resulting in a black hole seed that is significantly heavier than in conventional direct collapse models for atomic cooling halos.

Abstract

Context. The formation of the most massive quasars observed at high redshifts requires extreme inflows of gas down to the length scales of the central compact object.
Aims. Here we estimate the maximum inflow rate allowed by gravity down to the surface of supermassive stars, the possible progenitors of these supermassive black holes.
Methods. We use the continuity equation and the assumption of spherical symmetry and free fall to derive the maximum allowed inflow rates for various density profiles. We apply our approach to the mass–radius relation of rapidly accreting supermassive stars to estimate an upper limit to the accretion rates allowed during the formation of these objects.
Results. We find that, as long as the density of the accreted gas is smaller than or equal to the average density of the accretor, the maximum allowed rate, Ṁ$_{max}$, is given uniquely by the compactness of the accretor. We argue that a density inversion between accreting matter and the accretor is inconsistent with gravitational collapse. For the compactness of rapidly accreting supermassive stars, Ṁ$_{max}$ is related to the stellar mass, M, by a power law, Ṁ$_{max}$ ∝ M$^{3/4}$. The rates of atomically cooled halos (0.1−10 M$_{⊙}$ yr$^{−1}$) are allowed as soon as M ≳ 1 M$_{⊙}$. The largest rates expected in galaxy mergers (10$^{4}$ − 10$^{5}$ M$_{⊙}$ yr$^{−1}$) become accessible once the accretor is supermassive (M ≳ 10$^{4}$ M$_{⊙}$).
Conclusions. These results suggest that supermassive stars can accrete up to masses > 10$^{6}$ M$_{⊙}$ before they collapse via the general-relativistic instability. At such masses, the collapse is expected to lead to the direct formation of a supermassive black hole, even within metal-rich gas, resulting in a black hole seed that is significantly heavier than in conventional direct collapse models for atomic cooling halos.

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Additional indexing

Item Type:Journal Article, refereed, further contribution
Communities & Collections:07 Faculty of Science > Institute for Computational Science
Dewey Decimal Classification:610 Medicine & health
Scopus Subject Areas:Physical Sciences > Astronomy and Astrophysics
Physical Sciences > Space and Planetary Science
Language:English
Date:1 August 2021
Deposited On:28 May 2024 10:26
Last Modified:30 Jun 2024 01:41
Publisher:EDP Sciences
ISSN:0004-6361
Additional Information:Author, A&A, vol. 652, L7, 2021, Reproduced with permission from Astronomy & Astrophysics, © ESO
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1051/0004-6361/202141376
Related URLs:https://www.zora.uzh.ch/id/eprint/215674/
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)