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The collapse of supermassive stars (SMSs) via the general-relativistic (GR) instability would provide a natural explanation to the existence of the most extreme quasars. The presence of dark matter in SMSs is thought to potentially impact their properties, in particular their mass at collapse. Dark matter might be made of weakly interacting massive particles (WIMPs) that can be captured by the gravitational potential well of SMSs due to interaction with the baryonic gas. The annihilation of WIMPs can provide fuel to support the star before H-burning ignition, favouring low densities of baryonic gas, long stellar lifetimes and high final masses. Here, we estimate the impact of dark matter on the GR dynamical stability of rapidly accreting SMSs. We add a dark matter term to the relativistic equation of adiabatic pulsations and apply it to hylotropic structures in order to determine the onset point of the GR instability. We find that, in principle, the dark matter gravitational field can remove completely the GR instability. However, for SMSs fuelled by H-burning, the dark matter densities required to stabilise the star against GR are orders of magnitude above the values that are expected for the dark matter background. On the other hand, for SMSs fuelled by WIMP annihilation, we find that the low densities of baryonic gas inhibit the destabilising GR corrections, which shifts the stability limit by typically an order of magnitude towards higher masses. As long as central temperatures $\lesssim10^7$ K are maintained by WIMP annihilation, the GR instability is reached only for stellar masses $>10^6$ M$_\odot$. Dark matter can impact the GR dynamical stability of SMSs only in the case of energetically significant WIMP annihilation. The detection of a SMS with mass $>10^6$ M$_\odot$ in an atomically cooled halo can be interpreted as an evidence of WIMP annihilation in the star's core., Comment: accepted in A&A

Supermassive stars (SMSs), with masses $>10^5$ M$_\odot$, have been proposed as the possible progenitors of the most extreme supermassive black holes observed at redshifts $z>6-7$. In this scenario ('direct collapse'), a SMS accretes at rates $>0.1$ M$_\odot$ yr$^{-1}$ until it collapses to a black hole via the general-relativistic (GR) instability. Rotation plays a crucial role in the formation of such supermassive black hole seeds. The centrifugal barrier appears as particularly strong in this extreme case of star formation. Moreover, rotation impacts sensitively the stability of SMSs against GR, as well as the subsequent collapse. In particular, it might allow for gravitational wave emission and ultra-long gamma-ray bursts at black hole formation, which represents currently the main observational signatures proposed in the literature for the existence of such objects. Here, I present the latest models of SMSs accounting for accretion and rotation, and discuss some of the open questions and future prospects in this research line., Comment: Proceedings of the Sixteenth Marcel Grossmann Meeting

We revisit the conditions present in supermassive discs (SMDs) formed by the merger of gas-rich, metal-enriched galaxies at red-shift $z\sim 10$. We find that SMDs naturally form hydrostatic cores which go through a rapidly accreting supermassive star phase, before directly collapsing into massive black holes via the general relativistic instability. The growth and collapse of the cores occurs within $\sim 5\times 10^5$ yr from the formation of the SMD, producing bright electromagnetic, neutrino and gravitational wave transients with a typical duration of a few minutes and, respectively, a typical flux and a typical strain amplitude at Earth of $\sim 10^{-8}$ erg s$^{-1}$ cm$^{-2}$ and $\sim4\times 10^{-21}$. We provide a simple fitting formula for the the resulting black hole masses, which range from a few $10^6$ M$_{\odot}$ to $10^8$ M$_{\odot}$ depending on the initial SMD configuration. Crucially, our analysis does not require any specific assumption on the thermal properties of the gas, nor on the angular momentum loss mechanisms within the SMD. Led by these findings, we argue that the merger-driven scenario provides a robust pathway for the rapid formation of supermassive black holes at $z > 6$. It provides an explanation for the origin of the brightest and oldest quasars without the need of a sustained growth phase from a much smaller seed. Its smoking gun signatures can be tested directly via multi-messenger observations., Comment: Published by MNRAS. Comments welcome!!

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. Here, we study the stability of rotating, rapidly accreting SMSs against GR and derive the properties of these stars at death. On the basis of hylotropic structures, 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 find that rotation favours the stability of rapidly accreting SMSs as soon as the accreted angular momentum represents a fraction 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 10^7-10^8 Msun. These results imply that, like 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: 10^5 Msun < M < 10^6 Msun for primordial atomically cooled haloes; 10^6 Msun < M < 10^9 Msun 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 as more favorable than those of atomically cooled haloes for detectable gravitational wave emission and ultra-long gamma-ray bursts at black hole formation.

The formation of supermassive black holes by direct collapse would imply the existence of supermassive stars (SMSs) and their collapse through the general-relativistic (GR) instability into massive black hole seeds. However, the final mass of SMSs is weakly constrained by existing models, in spite of the importance this quantity plays in the consistency of the direct collapse scenario. We estimate the final masses of spherical SMSs in the whole parameter space relevant for these objects. We build analytical stellar structures (hylotropes) that mimic existing numerical SMS models accounting for full stellar evolution with rapid accretion. From these hydrostatic structures, we determine ab initio the conditions for GR instability, and compare the results with the predictions of full stellar evolution. We show that hylotropic models predict the onset of GR instability with high precision. The mass of the convective core appears as a decisive quantity. The lower it is, the larger is the total mass required for GR instability. Typical conditions for GR instability are a total mass >10^5 Msun with a core mass >10^4 Msun. If the core mass remains below 10^4 Msun, total masses in excess of 10^6-10^7 Msun can be reached. Our results confirm that spherical SMSs forming in primordial, atomically cooled haloes collapse at masses below 500 000 Msun. On the other hand, accretion rates in excess of 1000 Msun/yr, leading to final stellar masses >10^6 Msun, are required for massive black hole formation in metal-rich gas. Thus, the different channels of direct collapse imply distinct final masses for the progenitor of the black hole seed.

Supermassive black holes might form by direct collapse, with a supermassive star (SMS) as progenitor. In this scenario, the SMS accretes at > 0.1 Msun/yr until it collapses into a massive black hole seed due to the general-relativistic (GR) instability. However, the exact mass at which the collapse occurs is not known, as existing numerical simulations give divergent results. Here, this problem is addressed analytically, which allows for ab initio, reliable determination of the onset point of the GR instability, for given hydrostatic structures. We apply the relativistic equation of radial pulsations in its general form to the hydrostatic GENEC models already published. We show that the mass of spherical SMSs forming in atomically cooled haloes cannot exceed 500 000 Msun, in contrast to previous claims. On the other hand, masses in excess of this limit, up to 10^6 Msun, could be reached in alternative versions of direct collapse. Our method can be used to test the consistency of GR hydrodynamical stellar evolution codes.

Supermassive stars have been proposed as the progenitors of the massive ($\sim 10^{9}\,\rm{M}_{\odot}$) quasars observed at $z\sim7$. Prospects for directly detecting supermassive stars with next-generation facilities depend critically on their intrinsic lifetimes, as well as their formation rates. We use the 1D stellar evolution code Kepler to explore the theoretical limiting case of zero-metallicity, non-rotating stars, formed monolithically with initial masses between $10\,\rm{kM}_{\odot}$ and $190\,\rm{kM}_{\odot}$. We find that stars born with masses between $\sim60\,\rm{kM}_{\odot}$ and $\sim150\,\rm{kM}_{\odot}$ collapse at the end of the main sequence, burning stably for $\sim1.5\,\rm{Myr}$. More massive stars collapse directly through the general relativistic instability after only a thermal timescale of $\sim3\,\rm{kyr}$--$4\,\rm{kyr}$. The expected difficulty in producing such massive, thermally-relaxed objects, together with recent results for currently preferred rapidly-accreting formation models, suggests that such ``truly direct'' or ``dark'' collapses may not be typical for supermassive objects in the early Universe. We close by discussing the evolution of supermassive stars in the broader context of massive primordial stellar evolution and the possibility of supermassive stellar explosions., Comment: 9 pages, 6 figures, 1 table, MNRAS accepted

In recent years, the discovery of massive quasars at z~7 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 discussions held at the Monash Prato Centre from November 20--24, 2017, during the workshop "Titans of the Early Universe: The Origin of the First Supermassive Black Holes.", Comment: Solicited review article (accepted) for Publications of the Astronomical Society of Australia. 38 pages, 15 figures, 1 table

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 solar masses per year, 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 solar masses for accretion rates of 0.1-10 solar masses per year, 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., Comment: 5 pages, 4 figures. Accepted ApJ letters