The Final Fates of Accreting Supermassive Stars

Abstract

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 10 5 M 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 withṀ 0.1 M yr −1 . WithṀ 0.3 − 1 M yr −1 , the star becomes GR-unstable during the helium-burning stage at M 2 − 3.5 × 10 5 M . In an extreme case with 10 M yr −1 , the star does not collapse until the mass reaches 8.0 × 10 5 M , 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.

Gravitational collapse of rotating supermassive stars including nuclear burning effects

“…If SMS cores are in nuclear-burning phases, they should be fully convective (e.g., Refs. [8,9]). Hence, it is natural to assume that SMS cores are isentropic (s = constant), its chemical composition is uniform (Y I = constant), and they are rigidly rotating.…”

“…[7,8]) have proposed that a SMS with mass 2 × 10 5 M could be formed if the mass-accretion rate reaches 0.1M /yrs (i.e., the temperature of a primodial gas cloud becomes 10 4 K) and lasts for more than the period of nuclear-burning phases (≈ 2 × 10 6 yrs [9]). To achieve such high virial temperature, there should not exist molecular hydrogen (H 2 ) in a primordial gas cloud.…”

“…[13][14][15]). Also SMS cores seem to be rigidly rotating because convection is strongly enhanced if they are in nuclear-burning phases [8,9,16].…”

Formation of massive seed black holes via collisions and accretion

“…The large accretion rates of 0.1 M yr −1 or more found in the simulations strongly favor protostellar models with cool atmospheres and highly extended envelopes (Hosokawa et al 2013;Schleicher et al 2013;Woods et al 2017;Haemmerlé et al 2017), implying that feedback is rather inefficient. Under such conditions, final black hole masses of 10 5 M can be reached based on the results of cosmological simulations (Latif et al 2013b;Umeda et al 2016).…”

On the Rotation of Supermassive Stars

“…This allows to maintain accretion onto the protostar towards stellar masses in the supermassive range (Hirano et al 2017). The star is thought to accrete until M 3 × 10 5 M , before collapsing into a black hole (Umeda et al 2016;Woods et al 2017;Haemmerlé et al 2017b) due to the general relativistic (GR) instability (Chandrasekhar 1964).…”