General-relativistic instability in rapidly accreting supermassive stars: The impact of rotation

Abstract

Context. Supermassive stars (SMSs) collapsing via the general-relativistic (GR) instability are invoked as the possible progenitors of supermassive black holes. Their mass and angular momentum at the onset of the instability are key in many respects, in particular regarding the possibility for observational signatures of direct collapse. Accretion dominates the evolution of SMSs and, similar to rotation, it has been shown to impact their final properties significantly. However, the combined effect of accretion and rotation on the stability of these objects is not known. Aims. Here, we study the stability of rotating, rapidly accreting SMSs against GR perturbations and derive the properties of these stars at death. Methods. On the basis of hylotropic structures, which are relevant for rapidly accreting SMSs, we define rotation profiles under the assumption of local angular momentum conservation in radiative regions, which allows for differential rotation. We account for rotation in the stability of the structure by adding a Newtonian rotation term in the relativistic equation of stellar pulsation, which is justified by the slow rotations imposed by the ΩΓ-limit. Results. We find that rotation favours the stability of rapidly accreting SMSs as soon as the accreted angular momentum represents a fraction of f ≳ 0.1% of the Keplerian angular momentum. For f ∼ 0.3−0.5%, the maximum masses consistent with GR stability are increased by an order of magnitude compared to the non-rotating case. For f ∼ 1%, the GR instability cannot be reached if the stellar mass does not exceed 107 − 108 M⊙. Conclusions. These results imply that, as in the non-rotating case, the final masses of the progenitors of direct collapse black holes range in distinct intervals depending on the scenario considered: 105 M⊙ ≲ M ≲ 106 M⊙ for primordial atomically cooled haloes and 106 M⊙ ≲ M ≲ 109 M⊙ for metal-rich galaxy mergers. The models suggest that the centrifugal barrier is inefficient to prevent the direct formation of a supermassive black hole at the collapse of a SMS. Moreover, the conditions of galaxy mergers appear to be more favourable than those of atomically cooled haloes for detectable gravitational wave emission and ultra-long gamma-ray bursts at black hole formation.

Pulsations of primordial supermassive stars induced by a general relativistic instability; visible to JWST at z$>$12

“…In this letter, we have assumed the evolutionary models are extremely slow rotators, but in reality, they probably evolve closer to the ΩΓ limit (Haemmerlé et al 2018). Although this would still mean they are slow rotators, even a modest rotation can affect the evolution, and more critically, the GR stability (Haemmerlé 2021b), though much is still unknown about the interplay of rotation and GR.…”

Origin of supermassive black holes in massive metal-poor protoclusters

“…Hosokawa et al 2013; Schleicher Umeda et al 2016), these rates are too low to maintain a very extended envelope of the protostar, and it is more likely to contract on the Kelvin-Helmholtz timescale and form a supermassive star (see also Janka 2002; Begelman 2010). Such objects are expected to subsequently collapse due to the general relativistic instability, as described by Appenzeller & Fricke (1972a); Fuller et al (1986); Haemmerlé (2020Haemmerlé ( , 2021. A summary sketch of the overall scenario considered here is given in Fig.…”

“…The formation of massive black holes could occur directly or through the formation of other types of progenitor objects, such as supermassive stars (e.g. Appenzeller & Fricke 1972a,b;Fuller et al 1986;Begelman 2010; Hosokawa ★ E-mail: dschleicher@astro-udec.cl Schleicher et al 2013b;Umeda et al 2016;Haemmerlé 2020Haemmerlé , 2021.…”

Light-curves and nucleosynthesis of CNO-rp driven general relativistic instability supernovae in metal enriched supermassive protostars

“…Up to this point, we have not considered the effect that an accretion envelope (Hosokawa et al 2013;Umeda et al 2016;Haemmerlé et al 2019) would have on the lightcurve. While the core of an accreting supermassive protostar has constant entropy, the envelope is thought to have entropy increasing as a power law Begelman (2010); Haemmerlé et al (2019); Haemmerlé (2020Haemmerlé ( , 2021b and this structure has been termed a hylotrope (Gk. hyle, 'matter' + tropos, 'turn') in Begelman (2010).…”