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Traditionally, the pair instability (PI) mass gap is located between 50 and 130 M⊙, with stellar mass black holes (BHs) expected to 'pile up' towards the lower PI edge. However, this lower PI boundary is based on the assumption that the star has already lost its hydrogen (H) envelope. With the announcement of an 'impossibly' heavy BH of 85 M⊙ as part of GW 190521 located inside the traditional PI gap, we realized that blue supergiant (BSG) progenitors with small cores but large hydrogen envelopes at low metallicity (Z) could directly collapse to heavier BHs than had hitherto been assumed. The question of whether a single star can produce such a heavy BH is important, independent of gravitational wave events. Here, we systematically investigate the masses of stars inside the traditional PI gap by way of a grid of 336 detailed mesa stellar evolution models calculated across a wide parameter space, varying stellar mass, overshooting, rotation, semiconvection, and Z. We evolve low Z stars in the range 10−3 < Z /Z⊙ < Z SMC, making no prior assumption regarding the mass of an envelope, but instead employing a wind mass-loss recipe to calculate it. We compute critical carbon–oxygen and helium core masses to determine our lower limit to PI physics, and we provide two equations for M core and M final that can also be of use for binary population synthesis. Assuming the H envelope falls into the BH, we confirm the maximum BH mass below PI is M BH ≃ 93.3 M⊙. Our grid allows us to populate the traditional PI gap, and we conclude that the distribution of BHs above the traditional boundary is not solely due to the shape of the initial mass function, but also to the same stellar interior physics (i.e. mixing) that which sets the BH maximum. [ABSTRACT FROM AUTHOR]

The most massive stars provide an essential source of recycled material for young clusters and galaxies. While very massive stars (VMSs, M>100  |$\rm {\rm M}_{\odot }$|⁠) are relatively rare compared to O stars, they lose disproportionately large amounts of mass already from the onset of core H-burning. VMS have optically thick winds with elevated mass-loss rates in comparison to optically thin standard O-star winds. We compute wind yields and ejected masses on the main sequence, and we compare enhanced mass-loss rates to standard ones. We calculate solar metallicity wind yields from MESA stellar evolution models in the range 50–500  |$\rm {\rm M}_{\odot }$|⁠ , including a large nuclear network of 92 isotopes, investigating not only the CNO-cycle, but also the Ne–Na and Mg–Al cycles. VMS with enhanced winds eject 5–10 times more H-processed elements (N, Ne, Na, Al) on the main sequence in comparison to standard winds, with possible consequences for observed anticorrelations, such as C–N and Na–O, in globular clusters. We find that for VMS 95 per cent of the total wind yields is produced on the main sequence, while only ∼ 5 per cent is supplied by the post-main sequence. This implies that VMS with enhanced winds are the primary source of 26Al, contrasting previous works where classical Wolf–Rayet winds had been suggested to be responsible for galactic 26Al enrichment. Finally, 200  |$\rm {\rm M}_{\odot }$| stars eject 100 times more of each heavy element in their winds than 50  |$\rm {\rm M}_{\odot }$| stars, and even when weighted by an IMF their wind contribution is still an order of magnitude higher than that of 50  |$\rm {\rm M}_{\odot }$| stars. [ABSTRACT FROM AUTHOR]

Very massive stars (VMS) up to 200–300 M⊙ have been found in the Local Universe. If they would lose little mass, they produce intermediate-mass black holes or pair-instability supernovae (PISNe). Until now, VMS modellers have extrapolated mass-loss versus metallicity (Z) exponents from optically thin winds, resulting in a range of PISN thresholds that might be unrealistically high in Z , as VMS develop optically thick winds. We utilize the transition mass-loss rate of Vink and Gräfener (2012) that accurately predicts mass-loss rates of Of/WNh ('slash') stars that characterize the morphological transition from absorption-dominated O-type spectra to emission-dominated WNh spectra. We develop a wind efficiency framework, where optically thin winds transition to enhanced winds, enabling us to study VMS evolution at high redshift where individual stars cannot be resolved. We present a MESA grid covering Z ⊙/2 to Z ⊙/100. VMS above the transition evolve towards lower luminosity, skipping the cool supergiant phase but directly forming pure He stars at the end of hydrogen burning. Below the transition, VMS evolve as cooler luminous blue variables (LBVs) or yellow hypergiants (YHGs), naturally approaching the Eddington limit. Strong winds in this YHG/LBV regime – combined with a degeneracy in luminosity – result in a mass-loss runaway, where a decrease in mass increases wind mass loss. Our models indicate an order-of-magnitude lower metallicity threshold for PISN than usually assumed, at Z ⊙/20 due to our mass-loss runaway. While future work on LBV mass loss could affect the PISN threshold, our framework will be critical for establishing definitive answers on the PISN threshold and galactic chemical evolution modelling. [ABSTRACT FROM AUTHOR]

The ages of stars have historically relied on isochrone fitting of standardized grids of models. While these stellar models have provided key constraints on observational samples of massive stars, they inherit many systematic uncertainties, mainly in the internal mixing mechanisms applied throughout the grid, fundamentally undermining the isochrone method. In this work, we utilize the mass–lumiosity (M–L) plane of Higgins & Vink as a method of determining stellar age, with mixing-corrected models applying a calibrated core overshooting αov and rotation rate to fit the observational data. We provide multiple test-beds to showcase our new method, while also providing comparisons to the commonly used isochrone method, highlighting the dominant systematic errors. We reproduce the evolution of individual O stars, and analyse the wider sample of O and B supergiants from the VLT-FLAMES Tarantula Survey, providing dedicated models with estimates for αov, Ω/Ωcrit, and ultimately stellar ages. The M–L plane highlights a large discrepancy in the spectroscopic masses of the O supergiant sample. Furthermore the M–L plane also demonstrates that the evolutionary masses of the B supergiant sample are inappropriate. Finally, we utilize detached eclipsing binaries, VFTS 642 and VFTS 500, and present their ages resulting from their precise dynamical masses, offering an opportunity to constrain their interior mixing. For the near-TAMS system, VFTS 500, we find that both components require a large amount of core overshooting (αov ≃ 0.5), implying an extended main-sequence width. We hence infer that the vast majority of B supergiants are still burning hydrogen in their cores. [ABSTRACT FROM AUTHOR]

The most massive stars dominate the chemical enrichment, mechanical and radiative feedback, and energy budget of their host environments. Yet how massive stars initially form and how they evolve throughout their lives is ambiguous. The mass loss of the most massive stars remains a key unknown in stellar physics, with consequences for stellar feedback and populations. In this work, we compare grids of very massive star (VMS) models with masses ranging from 80 to 1000 M⊙, for a range of input physics. We include enhanced winds close to the Eddington limit as a comparison to standard O-star winds, with consequences for present-day observations of ∼50–100 M⊙ stars. We probe the relevant surface H abundances (X s) to determine the key traits of VMS evolution compared to O stars. We find fundamental differences in the behaviour of our models with the enhanced-wind prescription, with a convergence on the stellar mass at 1.6 Myr, regardless of the initial mass. It turns out that X s is an important tool in deciphering the initial mass due to the chemically homogeneous nature of VMS above a mass threshold. We use X s to break the degeneracy of the initial masses of both components of a detached binary, and a sample of WNh stars in the Tarantula Nebula. We find that for some objects, the initial masses are unrestricted and, as such, even initial masses of the order 1000 M⊙ are not excluded. Coupled with the mass turnover at 1.6 Myr, X s can be used as a 'clock' to determine the upper stellar mass. [ABSTRACT FROM AUTHOR]

Classical Wolf-Rayet (WR) stars mark an important stage in the late evolution of massive stars. As hydrogen-poor massive stars, these objects have lost their outer layers, while still losing further mass through strong winds indicated by their prominent emission line spectra. Wolf-Rayet stars have been detected in a variety of different galaxies. Their strong winds are a major ingredient of stellar evolution and population synthesis models. Yet, a coherent theoretical picture of their strong mass-loss is only starting to emerge. In particular, the occurrence of WR stars as a function of metallicity (Z) is still far from being understood. To uncover the nature of the complex and dense winds of Wolf-Rayet stars, we employ a new generation of model atmospheres including a consistent solution of the wind hydrodynamics in an expanding non-LTE situation. With this technique, we can dissect the ingredients driving the wind and predict the resulting mass-loss for hydrogen-depleted massive stars. Our modelling efforts reveal a complex picture with strong, non-linear dependencies on the luminosity-to-mass ratio and Z with a steep, but not totally abrupt onset for WR-type winds in helium stars. With our findings, we provide a theoretical motivation for a population of helium stars at low Z, which cannot be detected via WR-type spectral features. Our study of massive He-star atmosphere models yields the very first mass-loss recipe derived from first principles in this regime. Implementing our first findings in stellar evolution models, we demonstrate how traditional approaches tend to overpredict WR-type mass loss in the young Universe. [ABSTRACT FROM AUTHOR]

Very massive stars (VMS) dominate the physics of young clusters due to their ionizing radiation and extreme stellar winds. It is these winds that determine their lifepaths until expiration. Observations in the Arches Cluster show that VMS all have similar temperatures. The VLT-FLAMES Tarantula Survey analysed VMS in the 30 Doradus (30 Dor) region of the Large Magellanic Cloud (LMC) also finding a narrow range of temperatures, albeit at higher values – likely a metallicity effect. Using mesa , we study the main-sequence evolution of VMS with a new mass-loss recipe that switches from optically thin O-star winds to optically thick Wolf–Rayet-type winds through the model-independent transition mass-loss rate of Vink & Gräfener. We examine the temperature evolution of VMS with mass loss that scales with the luminosity-over-mass (L / M) ratio and the Eddington parameter (Γe), assessing the relevance of the surface hydrogen (H) abundance that sets the number of free electrons. We present grids of VMS models at Galactic and LMC metallicity and compare our temperature predictions with empirical results. Models with a steep Γe dependence evolve horizontally in the Hertzsprung–Russel (HR) diagram at nearly constant luminosities, requiring a delicate and unlikely balance between envelope inflation and enhanced mass loss over the entire VMS mass range. By contrast, models with a steep L / M -dependent mass loss are shown to evolve vertically in the HR diagram at nearly constant T eff, naturally reproducing the narrow range of observed temperatures, as well as the correct trend with metallicity. This distinct behaviour of a steeply dropping luminosity is a self-regulatory mechanism that keeps temperatures constant during evolution in the HR diagram. [ABSTRACT FROM AUTHOR]

The Humphreys–Davidson (HD) limit sets the boundary between evolutionary channels of massive stars that end their lives either as the red supergiants (RSGs) or as the hotter blue supergiants (BSGs) and Wolf–Rayet stars. Mixing in the envelopes of massive stars close to their Eddington limit is crucial for investigating the upper luminosity limit of the coolest supergiants. We study the effects of excess mixing in superadiabatic layers that are dominated by radiation pressure, and we critically investigate the effects of mixing and mass-loss on the evolution of RSGs with log (T eff/K) < 3.68 – as a function of metallicity. Using MESA, we produce grids of massive star models at three metallicities: Galactic (Z⊙), LMC |$(\frac{1}{2}{\rm Z}_\odot)$|⁠ , and SMC |$(\frac{1}{5}{\rm Z}_\odot)$|⁠ , with both high and low amounts of overshooting to study the upper luminosity limit of RSGs. We systematically study the effects of excess mixing in the superadiabatic layers of post-main-sequence massive stars, overshooting above the hydrogen core and yellow supergiant (YSG) mass-loss rates on the fraction of core helium burning time spent as a RSG. We find that the excess mixing in the superadiabatic layers is stronger at lower metallicities, as it depends on the opacities in the hydrogen bump at log (T eff/K) ≈ 4, which become more pronounced at lower metallicity. This shifts the cut-off luminosities to lower values at lower metallicities, thus balancing the first-order effect of mass-loss. The opposing effects of mass-loss and excess envelope mixing during post-main-sequence evolution of stars with higher overshooting potentially results in a metallicity-independent upper luminosity limit. [ABSTRACT FROM AUTHOR]

At the end of its life, a very massive star is expected to collapse into a black hole (BH). The recent detection of an 85  M⊙ BH from the gravitational wave event GW 190521 appears to present a fundamental problem as to how such heavy BHs exist above the approximately 50  M⊙ pair-instability (PI) limit where stars are expected to be blown to pieces with no remnant left. Using mesa , we show that for stellar models with non-extreme assumptions, 90–100  M⊙ stars at reduced metallicity (⁠|$Z/\mbox{ $\mathrm{Z}_{\odot }$}\le 0.1$|⁠) can produce blue supergiant progenitors with core masses sufficiently small to remain below the fundamental PI limit, yet at the same time lose an amount of mass via stellar winds that is small enough to end up in the range of an 'impossible' 85  M⊙ BH. The two key points are the proper consideration of core overshooting and stellar wind physics with an improved scaling of mass-loss with iron (Fe) contents characteristic for the host galaxy metallicity. Our modelling provides a robust scenario that not only doubles the maximum BH mass set by PI, but also allows us to probe the maximum stellar BH mass as a function of metallicity and cosmic time in a physically sound framework. [ABSTRACT FROM AUTHOR]

Context. Current massive star evolution grids are not able to simultaneously reproduce the empirical upper luminosity limit of red supergiants, the Humphrey-Davidson (HD) limit, nor the blue-to-red (B/R) supergiant ratio at high and low metallicity. Although previous studies have shown that the treatment of convection and semi-convection plays a role in the post-main-sequence (MS) evolution to blue or red supergiants (RSGs), a unified treatment for all metallicities has not been achieved so far. Aims. We focus on developing a better understanding of what drives massive star evolution to blue and red supergiant phases, with the ultimate aim of reproducing the HD limit at varied metallicities. We discuss the consequences of classifying B and R in the B/R ratio and clarify what is required to quantify a relatable theoretical B/R ratio for comparison with observations. Methods. For solar, Large Magellanic Cloud (50% solar), and Small Magellanic Cloud (20% solar) metallicities, we develop eight grids of MESA models for the mass range 20-60 M⊙ to probe the effect of semi-convection and overshooting on the core heliumburning phase. We compare rotating and non-rotating models with efficient (ffsemi = 100) and inefficient semi-convection (ffsemi = 0:1), with high and low amounts of core overshooting (ffov of 0.1 or 0.5). The red and blue supergiant evolutionary phases are investigated by comparing the fraction of core He-burning lifetimes spent in each phase for a range of masses and metallicities. Results. We find that the extension of the convective core by overshooting ffov = 0:5 has an effect on the post-MS evolution that can disable semi-convection, leading to more RSGs, but a lack of BSGs. We therefore implement ffov = 0:1, which switches on semi-convective mixing, but for standard ffsemi = 1 would result in an HD limit that is higher than observed at low Z (Large and Small Magellanic Clouds). Therefore, we need to implement very efficient semi-convection of ffsemi = 100, which reproduces the HD limit at log L=Lβ ~ 5:5 for the Magellanic Clouds while simultaneously reproducing the Galactic HD limit of log L=Lβ ~ 5:8 naturally. The effect of semi-convection is not active at high metallicities because the envelope structure is depleted by strong mass loss such that semi-convective regions could not form. Conclusions. Metallicity-dependent mass loss plays an indirect, yet decisive role in setting the HD limit as a function of Z. For a combination of efficient semi-convection and low overshooting with standard Ṁ(Z), we find a natural HD limit at all metallicities. [ABSTRACT FROM AUTHOR]

Context. Massive star evolution is dominated by various physical effects, including mass loss, overshooting, and rotation, but the prescriptions of their effects are poorly constrained and even affect our understanding of the main sequence. Aims. We aim to constrain massive star evolution models using the unique test-bed eclipsing binary HD 166734 with new grids of MESA stellar evolution models, adopting calibrated prescriptions of overshooting, mass loss, and rotation. Methods. We introduce a novel tool, called the mass-luminosity plane or M−L plane, as an equivalent to the traditional HR diagram, utilising it to reproduce the test-bed binary HD 166734 with newly calibrated MESA stellar evolution models for single stars. Results. We can only reproduce the Galactic binary system with an enhanced amount of core overshooting (αov = 0.5), mass loss, and rotational mixing. We can utilise the gradient in the M−L plane to constrain the amount of mass loss to 0.5–1.5 times the standard prescription test-bed, and we can exclude extreme reduction or multiplication factors. The extent of the vectors in the M−L plane leads us to conclude that the amount of core overshooting is larger than is normally adopted in contemporary massive star evolution models. We furthermore conclude that rotational mixing is mandatory to obtain the correct nitrogen abundance ratios between the primary and secondary components (3:1) in our test-bed binary system. Conclusions. Our calibrated grid of models, alongside our new M−L plane approach, present the possibility of a widened main sequence due to an increased demand for core overshooting. The increased amount of core overshooting is not only needed to explain the extended main sequence, but the enhanced overshooting is also needed to explain the location of the upper-luminosity limit of the red supergiants. Finally, the increased amount of core overshooting has – via the compactness parameter – implications for supernova explodability. [ABSTRACT FROM AUTHOR]