Aims. We study the impact of a subsolar metallicity on various properties of non-rotating and rotating stars, such as surface velocities and abundances, lifetimes, evolutionary tracks, and evolutionary scenarios. Methods. We provide a grid of single star models covering a mass range of 0.8 to 120 M with an initial metallicity Z = 0.002 with and without rotation. We discuss the impact of a change in the metallicity by comparing the current tracks with models computed with exactly the same physical ingredients but with a metallicity Z = 0.014 (solar). Results. We show that the width of the main-sequence (MS) band in the upper part of the Hertzsprung-Russell diagram (HRD), for luminosity above log (L/L ) > 5.5, is very sensitive to rotational mixing. Strong mixing significantly reduces the MS width. Here for the first time over the whole mass range, we confirm that surface enrichments are stronger at low metallicity provided that comparisons are made for equivalent initial mass, rotation, and evolutionary stage. We show that the enhancement factor due to a lowering of the metallicity (all other factors kept constant) increases when the initial mass decreases. Present models predict an upper luminosity for the red supergiants (RSG) of log (L/L ) around 5.5 at Z = 0.002 in agreement with the observed upper limit of RSG in the Small Magellanic Cloud. We show that models using shear diffusion coefficient, which is calibrated to reproduce the surface enrichments observed for MS B-type stars at Z = 0.014, can also reproduce the stronger enrichments observed at low metallicity. In the framework of the present models, we discuss the factors governing the timescale of the first crossing of the Hertzsprung gap after the MS phase. We show that any process favouring a deep localisation of the H-burning shell (steep gradient at the border of the H-burning convective core, low CNO content), and/or the low opacity of the H-rich envelope favour a blue position in the HRD for the whole, or at least a significant fraction, of the core He-burning phase.

Supermassive primordial stars forming in atomically-cooled halos at z ∼ 15 − 20 are currently thought to be the progenitors of the earliest quasars in the Universe. In this picture, the star evolves under accretion rates of 0.1 -1 M yr −1 until the general relativistic instability triggers its collapse to a black hole at masses of ∼ 10 5 M . However, the ability of the accretion flow to sustain such high rates depends crucially on the photospheric properties of the accreting star, because its ionising radiation could reduce or even halt accretion. Here we present new models of supermassive Population III protostars accreting at rates 0.001 -10 M yr −1 , computed with the geneva stellar evolution code including general relativistic corrections to the internal structure. We use the polytropic stability criterion to estimate the mass at which the collapse occurs, which has been shown to give a lower limit of the actual mass at collapse in recent hydrodynamic simulations. We find that at accretion rates higher than 0.001 M yr −1 the stars evolve as red, cool supergiants with surface temperatures below 10 4 K towards masses > 10 5 M , and become blue and hot, with surface temperatures above 10 5 K, only for rates 0.001 M yr −1 . Compared to previous studies, our results extend the range of masses and accretion rates at which the ionising feedback remains weak, reinforcing the case for direct collapse as the origin of the first quasars.

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.

In recent years, the discovery of massive quasars at $z\sim7$ has provided a striking challenge to our understanding of the origin and growth of supermassive black holes in the early Universe. Mounting observational and theoretical evidence indicates the viability of massive seeds, formed by the collapse of supermassive stars, as a progenitor model for such early, massive accreting black holes. Although considerable progress has been made in our theoretical understanding, many questions remain regarding how (and how often) such objects may form, how they live and die, and how next generation observatories may yield new insight into the origin of these primordial titans. This review focusses on our present understanding of this remarkable formation scenario, based on the discussions held at the Monash Prato Centre from November 20 to 24, 2017, during the workshop ‘Titans of the Early Universe: The Origin of the First Supermassive Black Holes’.

Aims. We study the influence of rotation and disc lifetime on lithium depletion of pre-main sequence (PMS) solar-type stars. Methods. The impact of rotational mixing and of the hydrostatic effects of rotation on lithium abundances are investigated by computing non-rotating and rotating PMS models that include a comprehensive treatment of shellular rotation. The influence of the disc lifetime is then studied by comparing the lithium content of PMS rotating models experiencing different durations of the disc-locking phase between 3 and 9 Myr. Results. The surface lithium abundance at the end of the PMS is decreased when rotational effects are included. During the beginning of the lithium depletion phase, only hydrostatic effects of rotation are at work. This results in a decrease in the lithium depletion rate for rotating models compared to non-rotating ones. When the convective envelope recedes from the stellar centre, rotational mixing begins to play an important role due to differential rotation near the bottom of the convective envelope. This mixing results in a decrease in the surface lithium abundance with a limited contribution from hydrostatic effects of rotation, which favours lithium depletion during the second part of the PMS evolution. The impact of rotation on PMS lithium depletion is also found to be sensitive to the duration of the disc-locking phase. When the disc lifetime increases, the PMS lithium abundance of a solar-type star decreases owing to the higher efficiency of rotational mixing in the radiative zone. A relationship between the surface rotation and lithium abundance at the end of the PMS is then obtained: slow rotators on the zero-age main sequence are predicted to be more lithium-depleted than fast rotators due to the increase in the disc lifetime.