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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!!

HD 129929 is a slowly-rotating $\beta$ Cephei pulsator with a rich spectrum of detected oscillations, including two rotational multiplets. The asteroseismic interpretation revealed the presence of radial differential rotation in this massive star of $\sim$9.35 M . The stellar core is indeed estimated to spin $\sim$3.6 times faster than the surface. The surface rotation was consequently derived as $\sim$2 km/s. This massive star represents an ideal counter-part to the wealth of space-based photometry results for main-sequence and evolved low-mass stars. Those latter have revealed a new, and often unexpected, picture of the angular momentum transport processes acting in stellar interiors. We investigate in a new way the constraints on the internal rotation of HD 129929, focusing on their interpretation for the evolution of the internal rotation during the main sequence of a massive star. We test separately hydrodynamic and magnetic instability transport processes of angular momentum. We used the best asteroseismic model obtained in an earlier work. We calibrated stellar models including rotation, with different transport processes, to reproduce that reference model. We then looked whether one process is favoured to reproduce the rotation profile of HD 129929, based on the fit of the asteroseismic multiplets. The impact of the Tayler magnetic instability on the angular momentum transport predicts a ratio of the core-to-surface rotation rate of only 1.6, while the recently revised prescription of this mechanism predicts solid-body rotation. Both are too low in comparison with the asteroseismic inference. The models with only hydrodynamic processes are in good agreement with the asteroseismic measurements. Strikingly, we can also get a constraint on the profile of rotation on the zero age main sequence: likely, the ratio between the core and surface rotation was at least $\sim$1.7., Comment: 5 pages, 3 figures, accepted for publication as a letter in A&A

Radiative feedback from massive Population III (Pop III) stars in the form of ionising and photodissociating photons is widely believed to play a central role in shutting off accretion onto these stars. Understanding whether and how this occurs is vital for predicting the final masses reached by these stars and the form of the Pop III stellar initial mass function. To help us better understand the impact of UV radiation from massive Pop III stars on the gas surrounding them, we carry out high resolution simulations of the formation and early evolution of these stars, using the AREPO moving-mesh code coupled with the innovative radiative transfer module SPRAI. Contrary to most previous results, we find that the ionising radiation from these stars is trapped in the dense accretion disk surrounding them. Consequently, the inclusion of radiative feedback has no significant impact on either the number or the total mass of protostars formed during the 20 kyr period that we simulate. We show that the reason that we obtain qualitatively different results from previous studies of Pop III stellar feedback lies in how the radiation is injected into the simulation. HII region trapping only occurs if the photons are injected on scales smaller than the local scale height of the accretion disk, a criterion not fulfilled in previous 3D simulations of this process. Finally, we speculate as to whether outflows driven by the magnetic field or by Lyman-alpha radiation pressure may be able to clear enough gas away from the star to allow the HII region to escape from the disk., Comment: 22 pages, 20 figures, 4 tables. Accepted by MNRAS

Context: Grids of stellar models, computed with the same physical ingredients, allow one to study the impact of a given physics on a broad range of initial conditions and are a key ingredient for modeling the evolution of galaxies. Aims: We present a grid of single star models for masses between 0.8 and 120 $M_\odot$, with and without rotation for a mass fraction of heavy element Z=0.006, representative of the Large Magellanic Cloud (LMC). Methods: We used the Geneva stellar evolution code. The evolution was computed until the end of the central carbon-burning phase, the early asymptotic giant branch phase, or the core helium-flash for massive, intermediate, and low mass stars, respectively. Results: The outputs of the present stellar models are well framed by the outputs of the two grids obtained by our group for metallicities above and below the one considered here. The models of the present work provide a good fit to the nitrogen surface enrichments observed during the main sequence for stars in the LMC with initial masses around 15 $M_\odot$. They also reproduce the slope of the luminosity function of red supergiants of the LMC well, which is a feature that is sensitive to the time-averaged mass loss rate over the red supergiant phase. The most massive black hole that can be formed from the present models at Z=0.006 is around 55 $M_\odot$. No model in the range of mass considered will enter into the pair-instability supernova regime, while the minimal mass to enter the region of pair pulsation instability is around 60 $M_\odot$ for the rotating models and 85 $M_\odot$ for the nonrotating ones. Conclusions: The present models are of particular interest for comparisons with observations in the LMC and also in the outer regions of the Milky Way. We provide public access to numerical tables that can be used for computing interpolated tracks and for population synthesis studies., Comment: 11 pages, 11 figures, published in A&A

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.

Understanding the nature of the first stars is key to understanding the early universe. With new facilities such as JWST we may soon have the first observations of the earliest stellar populations, but to understand these observations we require detailed theoretical models. Here we compute a grid of stellar evolution models using the Geneva code with the aim to improve our understanding of the evolution of zero-metallicity stars, with particular interest in how rotation affects surface properties, interior structure, and metal enrichment. We produce a range of models of initial masses (Mini) from 1.7 Msun to 120 Msun, focusing on massive models of 9 Msun < Mini < 120 Msun. Our grid includes models with and without rotation, with rotating models having an initial velocity of 40% of the critical velocity. We find that rotation strongly impacts the evolution of the first stars, mainly through increased core size and stronger H-burning shells during core He-burning. Without radiative mass loss, angular momentum builds at the surface in rotating models, thus models of initial masses Mini > 60 Msun reach critical rotation on the main sequence and experience mass loss. We find that rotational mixing strongly affects metal enrichment, but does not always increase metal production as we see at higher metallicities. This is because rotation leads to an earlier CNO boost to the H shell during He-burning, which may hinder metal enrichment depending on initial mass and rotational velocity. Electronic tables of this new grid of Population III models are publicly available., Comment: 20 pages, 15 figures. Accepted for publication in MNRAS

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.

We address the origin of the observed bimodal rotational distribution of stars in massive young and intermediate age stellar clusters. This bimodality is seen as split main sequences at young ages and also has been recently directly observed in the $Vsini$ distribution of stars within massive young and intermediate age clusters. Previous models have invoked binary interactions as the origin of this bimodality, although these models are unable to reproduce all of the observational constraints on the problem. Here we suggest that such a bimodal rotational distribution is set up early within a cluster's life, i.e., within the first few Myr. Observations show that the period distribution of low-mass ($\la 2 M_\odot$) pre-main sequence (PMS) stars is bimodal in many young open clusters and we present a series of models to show that if such a bimodality exists for stars on the PMS that it is expected to manifest as a bimodal rotational velocity (at fixed mass/luminosity) on the main sequence for stars with masses in excess of $\sim1.5$~\msun. Such a bimodal period distribution of PMS stars may be caused by whether stars have lost (rapid rotators) or been able to retain (slow rotators) their circumstellar discs throughout their PMS lifetimes. We conclude with a series of predictions for observables based on our model., Comment: 6 pages, 2 figures, accepted for publication in MNRAS

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

We review the current status of knowledge concerning the early phases of star formation during cosmic dawn. This includes the first generations of stars forming in the lowest mass dark matter halos in which cooling and condensation of gas with primordial composition is possible at very high redshift ($z > 20$), namely metal-free Population III stars, and the first generation of massive black holes forming at such early epochs, the so-called black hole seeds. The formation of black hole seeds as end states of the collapse of Population III stars, or via direct collapse scenarios, is discussed. In particular, special emphasis is given to the physics of supermassive stars as potential precursors of direct collapse black holes, in light of recent results of stellar evolution models, and of numerical simulations of the early stages of galaxy formation. Furthermore, we discuss the role of the cosmic radiation produced by the early generation of stars and black holes at high redshift in the process of reionization.

Supermassive stars (SMSs) are candidates for being progenitors of supermassive quasars at high redshifts. However, their formation process requires strong mechanisms that would be able to extract the angular momentum of the gas that the SMSs accrete. We investigate under which conditions the magnetic coupling between an accreting SMS and its winds can remove enough angular momentum for accretion to proceed from a Keplerian disc. We numerically computed the rotational properties of accreting SMSs that rotate at the $\Omega\Gamma$-limit and estimated the magnetic field that is required to maintain the rotation velocity at this limit using prescriptions from magnetohydrodynamical simulations of stellar winds. We find that a magnetic field of 10 kG at the stellar surface is required to satisfy the constraints on stellar rotation from the $\Omega\Gamma$-limit. Magnetic coupling between the envelope of SMSs and their winds could allow for SMS formation by accretion from a Keplerian disc, provided the magnetic field is at the upper end of present-day observed stellar fields. Such fields are consistent with primordial origins.

The collapse of supermassive primordial stars in hot, atomically-cooled halos may have given birth to the first quasars at $z \sim$ 15 - 20. Recent numerical simulations of these rapidly accreting stars reveal that they are cool, red hypergiants shrouded by dense envelopes of pristine atomically-cooled gas at 6,000 - 8,000 K, with luminosities $L$ $\gtrsim$ 10$^{10}$ L$_{\odot}$. Could such luminous but cool objects be detected as the first stage of quasar formation in future near infrared (NIR) surveys? We have now calculated the spectra of supermassive primordial stars in their birth envelopes with the Cloudy code. We find that some of these stars will be visible to JWST at $z \lesssim$ 20 and that with modest gravitational lensing Euclid and WFIRST could detect them out to $z \sim$ 10 - 12. Rather than obscuring the star, its accretion envelope enhances its visibility in the NIR today by reprocessing its short-wavelength flux into photons that are just redward of the Lyman limit in the rest frame of the star., Comment: 6 pages, 4 figures, accepted by ApJL

Context. The origin of the fossil magnetic fields detected in 5 to 10% of intermediate-mass main sequence stars is still highly debated. Aims. We want to bring observational constraints to a large population of intermediate-mass pre-main sequence (PMS) stars in order to test the theory that convective-dynamo fields generated during the PMS phases of stellar evolution can occasionally relax into fossil fields on the main sequence. Methods. Using distance estimations, photometric measurements, and spectropolarimetric data from HARPSpol and ESPaDOnS of 38 intermediate-mass PMS stars, we determined fundamental stellar parameters (Teff, L and v sin i) and measured surface magnetic field characteristics (including detection limits for non-detections, and longitudinal fields and basic topologies for positive detections). Using PMS evolutionary models, we determined the mass, radius, and internal structure of these stars. We compared different PMS models to check that our determinations were not model-dependant. We then compared the magnetic characteristics of our sample accounting for their stellar parameters and internal structures. Results. We detect magnetic fields in about half of our sample. About 90% of the magnetic stars have outer convective envelopes larger than ~25% of the stellar radii, and heavier than ~2% of the stellar mass. Going to higher mass, we find that the magnetic incidence in intermediate-mass stars drops very quickly, within a time-scale of the order of few times 0.1 Myr. Finally, we propose that intermediate-mass T Tauri stars with large convective envelopes, close to the fully convective limit, have complex fields and that their dipole component strengths may decrease as the sizes of their convective envelopes decrease, similar to lower-mass T Tauri stars., Comment: accepted by A&A

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

We explore the initial conditions that lead to detached binary evolution of massive pre-MS binaries and ask how large a fraction of the observed binary systems may have been initially formed as low-mass protobinaries and later undergone a significant accretion phase while remaining detached. We develop a family of analytic models to describe the orbital separation, $a$, and mass ratio, $q$, evolution. For a given mass accretion rate onto the binary system, we define a recipe for distributing this mass between the two components. For this we introduce a parameter $\eta$, such that $\frac{\dot{M}_2}{\dot{M}_1}=q^\eta$ at any time, to determine the binary mass ratio evolution. Depending on the choice of $\eta$, any type of mass ratio evolution is possible. Furthermore, we use MESA, a detailed stellar structure code, to calculate an extensive grid of binary sequences where a protobinary undergoes accretion, and we identify the initial conditions that separates detached from non-detached pre-MS binary evolution. A value of $\eta$ around 2 allows accretion growth in detached systems to form close massive binaries on the Zero Age Main-Sequence with minimum orbital periods down to about 1.2 days for $M_{\rm 1, ZAMS}=20-30M_{\odot}$ twin-binaries. $\eta=2$ can also reproduce the observed population of binary systems with primary stars above $6M_{\odot}$. The whole observed range of massive close binaries can form via accretion growth in detached systems, making the binary formation channel of accretion growth a strong contender to explain the formation of massive close binaries, including progenitors of coalescing binary black holes., Comment: 27 pages, 19 figures, 3 tables, submitted to A&A. Abstract context removed to to fit arXiv

When planets are formed from the protoplanetary disk and after the disk has dissipated, the evolution of their orbits is governed by tidal interactions, friction, and gravitational drag, and also by changes in the mass of the star and planet. These interactions may change the initial distribution of the distances between the planets and their host star by expanding the original orbit, by contracting it (which may cause an engulfment of the planet by the star), or by destroying the planet. We study the evolution of the orbit of a planet orbiting its host star under the effects of equilibrium tides, dynamical tides, drag (frictional and gravitational), and stellar mass loss. We used the Geneva stellar evolution code to compute the evolution of stars with initial masses of 1 and 1.5 solar mass with different rotation rates at solar metallicity. The star is evolved from the pre-main-sequence (PMS) up to the tip of the red giant branch. We used these models as input for computing the evolution of the planetary orbits. We explored the effects of changing the planet masses (of 1 Earth mass up to 20 Jupiter masses), the distance between the planet and the star (of 0.015 and more than 3 au), the mass, and the spin of the star. We present results when only the equilibrium tide was accounted for and when both equilibrium and dynamical tides were accounted for. The expression for the dynamical tide is a frequency-averaged dissipation of tidally excited inertial waves, obtained from a piecewise homogeneous two-layer stellar model. Gravity wave damping was neglected. Dynamical tides in convective zones have a significant effect on planetary orbits only during the PMS phase and only for fast-rotating stars. They have no significant effects during the PMS phase for initially slow-rotating stars and during the red giant branch phase, regardless of the initial rotation (abridged)., Comment: 12 pages, 7 figures, in press for Astronomy in Astrophysics

Supermassive stars born from pristine gas in atomically-cooled haloes are thought to be the progenitors of supermassive black holes at high redshifts. However, the way they accrete their mass is still an unsolved problem. In particular, for accretion to proceed, a large amount of angular momentum has to be extracted from the collapsing gas. Here, we investigate the constraints stellar evolution imposes on this angular momentum problem. We present an evolution model of a supermassive Population III star including simultaneously accretion and rotation. We find that, for supermassive stars to form by accretion, the accreted angular momentum has to be about 1% of the Keplerian angular momentum. This tight constraint comes from the $\Omega\Gamma$-limit, at which the combination of radiation pressure and centrifugal force cancels gravity. It implies that supermassive stars are slow rotators, with a surface velocity less than 10-20% of their first critical velocity, at which the centrifugal force alone cancels gravity. At such low velocities, the deformation of the star due to rotation is negligible.

Supermassive primordial stars forming in atomically-cooled halos at $z \sim15-20$ are currently thought to be the progenitors of the earliest quasars in the Universe. In this picture, the star evolves under accretion rates of $0.1 - 1$ $M_\odot$ yr$^{-1}$ until the general relativistic instability triggers its collapse to a black hole at masses of $\sim10^5$ $M_\odot$. 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 $0.001 - 10$ $M_\odot$ 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 $0.001$ $M_\odot$ yr$^{-1}$ the stars evolve as red, cool supergiants with surface temperatures below $10^4$ K towards masses $>10^5$ $M_\odot$, and become blue and hot, with surface temperatures above $10^5$ K, only for rates $\lesssim0.001$ $M_\odot$ 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.

Rotation plays a key role in the star-formation process, from pre-stellar cores to pre-main-sequence (PMS) objects. Understanding the formation of massive stars requires taking into account the accretion of angular momentum during their PMS phase. We study the PMS evolution of objects destined to become massive stars by accretion, focusing on the links between the physical conditions of the environment and the rotational properties of young stars. In particular, we look at the physical conditions that allow the production of massive stars by accretion. We present PMS models computed with a new version of the Geneva Stellar Evolution code self-consistently including accretion and rotation according to various accretion scenarios for mass and angular momentum. We describe the internal distribution of angular momentum in PMS stars accreting at high rates and we show how the various physical conditions impact their internal structures, evolutionary tracks, and rotation velocities during the PMS and the early main sequence. We find that the smooth angular momentum accretion considered in previous studies leads to an angular momentum barrier and does not allow the formation of massive stars by accretion. A braking mechanism is needed in order to circumvent this angular momentum barrier. This mechanism has to be efficient enough to remove more than 2/3 of the angular momentum from the inner accretion disc. Due to the weak efficiency of angular momentum transport by shear instability and meridional circulation during the accretion phase, the internal rotation profiles of accreting stars reflect essentially the angular momentum accretion history. As a consequence, careful choice of the angular momentum accretion history allows circumvention of any limitation in mass and velocity, and production of stars of any mass and velocity compatible with structure equations.

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

Massive star formation requires the accretion of gas at high rate while the star is already bright. Its actual luminosity depends sensitively on the stellar structure. We compute pre-main-sequence tracks for massive and intermediate-mass stars with variable accretion rates and study the evolution of stellar radius, effective temperature and ionizing luminosity, starting at $2\,M_\odot$ with convective or radiative structures. The radiative case shows a much stronger swelling of the protostar for high accretion rates than the convective case. For radiative structures, the star is very sensitive to the accretion rate and reacts quickly to accretion bursts, leading to considerable changes in photospheric properties on timescales as short as 100 - 1000 yr. The evolution for convective structures is much less influenced by the instantaneous accretion rate, and produces a monotonically increasing ionizing flux that can be many orders of magnitude smaller than in the radiative case. For massive stars, it results in a delay of the HII region expansion by up to 10,000 yr. In the radiative case, the HII region can potentially be engulfed by the star during the swelling, which never happens in the convective case. We conclude that the early stellar structure has a large impact on the radiative feedback during the pre-main-sequence evolution of massive protostars and introduces an important uncertainty that should be taken into account. Because of their lower effective temperatures, our convective models may hint at a solution to an observed discrepancy between the luminosity distribution functions of massive young stellar objects and compact HII regions.

Massive stars likely form by accretion and the evolutionary track of an accreting forming star corresponds to what is called the birthline in the HR diagram. The shape of this birthline is quite sensitive to the evolution of the entropy in the accreting star. We first study the reasons why some birthlines published in past years present different behaviours for a given accretion rate. We then revisit the question of the accretion rate, which allows us to understand the distribution of the observed pre-main-sequence (pre-MS) stars in the Hertzsprung-Russell (HR) diagram. Finally, we identify the conditions needed to obtain a large inflation of the star along its pre-MS evolution that may push the birthline towards the Hayashi line in the upper part of the HR diagram. We present new pre-MS models including accretion at various rates and for different initial structures of the accreting core. From the observed upper envelope of pre-MS stars in the HR diagram, we deduce the accretion law that best matches the accretion history of most of the intermediate-mass stars. In the case of cold disc accretion, the existence of a significant swelling during the accretion phase, which leads to radii $\gtrsim100\,R_\odot$ and brings the star back to the red part of the HR diagram, depends sensitively on the initial conditions. For an accretion rate of $10^{-3}\,M_\odot\rm\,yr^{-1}$, only models starting from a core with a significant radiative region evolve back to the red part of the HR diagram. We also obtain that, in order to reproduce the observed upper envelope of pre-MS stars in the HR diagram with an accretion law deduced from the observed mass outflows in ultra-compact HII regions, the mass effectively accreted onto the star with respect to the total in falling matter decreases when the mass of the star increases.

The database of intermediate mass rotating stellar models presented in the past years by the Geneva Stellar Evolution Group can be used to build synthetic stellar populations that fully account for the effects of stellar rotation. However, up to now we still lacked stellar evolutionary tracks that rotate close to the critical limit during the whole MS phase. This occurs because the flat internal profile of rotation imposed at the Zero-Age MS (ZAMS) is modified by the action of meridional currents immediately after the ZAMS, causing the surface rotational velocity to decrease abruptly until it reaches a quasi-stationary state. We compute stellar models with non-solid rotation at the ZAMS to obtain stellar evolutionary tracks with a larger content of angular momentum, that attain rotational equatorial velocities close to the critical limit throughout their MS phase. These models have a longer MS lifetime and a higher surface chemical enrichment already at the end of the MS, particularly at Z=0.002. Stellar models with solid rotation at the ZAMS adequately represent the overall characteristics and evolution of differentially rotating models of identical angular momentum content, but with a lower initial surface rotational velocity. For these models we recommend to use as the initial rotational rate the values derived once the quasi-stationary state is reached, after the abrupt decrease in surface velocity. Interestingly, the initial equatorial rotational velocities are virtually metallicity independent for the stellar models we computed with the same mass and angular momentum content at the ZAMS. If, as some observational evidence indicates, B-type stars at Z=0.002 rotate with a higher equatorial velocity at the ZAMS than stars with Z=0.014, our finding would indicate that the angular momentum content of B-type stars in the SMC is higher than their Galactic counterparts., Comment: 15 pages, Accepted for publication in A&A

We discuss the physics and the evolution of a typical massive star passing through an evolutionary stage similar to that of Betelgeuse. After a brief introduction recalling various observed parameters of Betelgeuse, we discuss the Pre-Main-Sequence phase (PMS), the Main-Sequence (MS) phase, the physics governing the duration of the first crossing of the HR diagram, the red supergiant stage (RSG), the post-red supergiant phases and the final fate of solar metallicity stars with masses between 9 and 25 M$_\odot$. We examine the impact of different initial rotation and of various prescriptions for the mass loss rates during the red supergiant phase. We show that, whatever the initial rotation rate (chosen between 0 and 0.7$\times\upsilon_{\rm crit}$, $\upsilon_{\rm crit}$ being the surface equatorial velocity producing a centrifugal acceleration balancing exactly the gravity) and the mass loss rates during the RSG stage (varied between a standard value and 25 times that value), a 15 M$_\odot$ star always ends its lifetime as a RSG and explodes as a type II-P or II-L supernova., Comment: 12 pages, 5 figures, Betelgeuse workshop, November 2012, Paris. To be published in the European Astronomical Society Publications Series, editors: Pierre Kervella, Thibaut Le Bertre & Guy Perrin

The rotation of stars has many interesting and important consequences for the photometric and chemical evolution of galaxies. Many of the predictions of models of stellar rotation are now compared with observations of surface abundances and velocities, with interferometric studies of fast rotating stars, with internal rotation profiles as they can be deduced by asteroseismology, to cite just a few observational constraints. In this paper, we investigate how the outputs of models depend on the prescriptions used for the diffusion coefficients included in the shellular rotating models. After recalling the various prescriptions found in the literature, we discuss their impacts on the evolutionary tracks and lifetimes of the Main-Sequence (MS) phase, the changes of the surface composition and velocities during the MS phase, the distribution of the core helium lifetime in the blue and the red part of the HR diagram, the extensions of the blue loops, the evolution of the angular momentum of the core, and the synthesis of primary nitrogen in fast-rotating metal-poor massive stars. While some of these outputs depend only slightly on the prescriptions used (for instance, the evolution of the surface velocities), most of them show a significant dependence. The models which best fit the changes of the surface abundances are those computed with the vertical shear diffusion coefficient of Maeder (1997) and the horizontal shear diffusion coefficient by Zahn (1992)., Comment: 19 pages, 4 figures, to appear in "SeIsmology for studies of stellar Rotation and Convection", Lecture Notes in Physics (Springer Verlag, Berlin), M.J. Goupil, K. Belkacem, C. Neiner, F. Ligni\`eres, and J. J. Green (eds)