On the Maximum Mass of Accreting Primordial Supermassive Stars

Abstract

Supermassive primordial stars are suspected to be the progenitors of the most massive quasars at z ∼ 6. Previous studies of such stars were either unable to resolve hydrodynamical timescales or considered stars in isolation, not in the extreme accretion flows in which they actually form. Therefore, they could not self-consistently predict their final masses at collapse, or those of the resulting supermassive black hole seeds, but rather invoked comparison to simple polytropic models. Here, we systematically examine the birth, evolution and collapse of accreting non-rotating supermassive stars under accretion rates of 0.01 − 10 M ⊙ yr −1 using the stellar evolution code Kepler. Our approach includes post-Newtonian corrections to the stellar structure and an adaptive nuclear network, and can transition to following the hydrodynamic evolution of supermassive stars after they encounter the general relativistic instability. We find that this instability triggers the collapse of the star at masses of 150, 000 − 330, 000 M ⊙ for accretion rates of 0.1 − 10 M ⊙ yr −1 , and that the final mass of the star scales roughly logarithmically with the rate. The structure of the star, and thus its stability against collapse, is sensitive to the treatment of convection, and the heat content of the outer accreted envelope. Comparison with other codes suggests differences here may lead to small deviations in the evolutionary state of the star as a function of time, that worsen with accretion rate. Since the general relativistic instability leads to the immediate death of these stars, our models place an upper limit on the masses of the first quasars at birth.

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).…”

Formation of the First Stars and Black Holes

“…The limit in mass above which accreting SMSs become GR unstable has been investigated in numerical simulations (Umeda et al, 2016;Woods et al, 2017;Haemmerlé et al, 2018b), and are shown on Fig. 5.…”

On monolithic supermassive stars

“…Convective heat transport is included only when a zone is convective by the Ledoux criterion. For accreting models, accretion is carried out as described in Woosley et al (2004) and Woods et al (2017).…”

“…In the atomic-cooling halo scenario (e.g., Bromm & Loeb 2003;Dijkstra et al 2008; Regan et al 2017), photo-destruction of the molecular hydrogen in a primordial halo at z ∼ 10-20 by an intense Lyman-Werner flux permits the halo gas to reach ∼ 8 kK before radiative losses from atomic hydrogen line transitions can lock in the temperature, bringing the Jeans mass and typical infall rates up to ∼ 100 kM ⊙ and 0.1-10 M ⊙ yr −1 . The fates of the resulting objects have been examined in increasing detail in the last few years (e.g., Hosokawa et al 2013;Woods et al 2017;Haemmerlé et al 2018b). Large baryonic streaming velocities may be able to assist in suppressing star formation in the process, and may even be sufficient in the absence of a substantial Lyman-Werner flux (e.g., Tanaka et al 2013).…”