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Strong metallicity-dependent winds dominate the evolution of core He-burning, classical Wolf-Rayet (cWR) stars, which eject both H and He-fusion products such as 14N, 12C, 16O, 19F, 22Ne and 23Na during their evolution. The chemical enrichment from cWRs can be significant. cWR stars are also key sources for neutron production relevant for the weak s-process. We calculate stellar models of cWRs at solar metallicity for a range of initial Helium star masses (12-50M), adopting the recent hydrodynamical wind rates from Sander & Vink (2020). Stellar wind yields are provided for the entire post-main sequence evolution until core O-exhaustion. While literature has previously considered cWRs as a viable source of the radioisotope 26Al, we confirm that negligible 26Al is ejected by cWRs since it has decayed to 26Mg or proton-captured to 27Al. However, in Paper I, Higgins et al. (2023) we showed that very massive stars eject substantial quantities of 26Al, among other elements including N, Ne, and Na, already from the zero-age-main-sequence. Here, we examine the production of 19F and find that even with lower mass-loss rates than previous studies, our cWR models still eject substantial amounts of 19F. We provide central neutron densities (Nn) of a 30M cWR compared with a 32M post-VMS WR and confirm that during core He-burning, cWRs produce a significant number of neutrons for the weak s-process via the 22Ne(alpha,n)25Mg reaction. Finally, we compare our cWR models with observed [Ne/He], [C/He] and [O/He] ratios of Galactic WC and WO stars., Comment: Accepted for publication in MNRAS. 17 pages, 16 figures

We analyse current knowledge and uncertainties in detailed stellar evolution and wind modelling to evaluate the mass of the most massive stellar black hole (BH) at solar metallicity. Contrary to common expectations that it is the most massive stars that would produce the most massive BHs, we find that the maximum $M_{\rm BH}^{\rm Max} \simeq 30 \pm 10\,M_{\odot}$ is found in the canonical intermediate range between $M_{\rm ZAMS} \simeq 30$ and $50\,M_{\odot}$ instead. The prime reason for this seemingly counter-intuitive finding is that very massive stars (VMS) have increasingly high mass-loss rates, leading to substantial mass evaporation before they expire as stars, ending as lighter BHs than their canonical O-star counterparts., Comment: A&A Letters. Revised after Referee Report. Comments welcome

Traditionally, the pair instability (PI) mass gap is located between 50\,and 130\,$M_{\odot}$, 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\,$M_{\odot}$ as part of GW\,190521 located inside the traditional PI gap, we realised 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, semi-convection, and $Z$. We evolve low $Z$ stars in the range $10^{-3} < Z / Z_{\odot} < Z_{\rm SMC}$, 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 $M_{\text{core}}$ and $M_{\text{final}}$ 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 $M_{\text{BH}} \simeq 93.3$ $M_{\odot}$. 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 (IMF), but also to the same stellar interior physics (i.e. mixing) that which sets the BH maximum., Comment: 24 pages, 14 figures. Accepted in MNRAS

The most massive stars provide an essential source of recycled material for young clusters and galaxies. While very massive stars (VMS, M>100M) 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 - 500M, 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 anti-correlations, such as C-N and Na-O, in globular clusters. We find that for VMS 95% of the total wind yields is produced on the main sequence, while only ~5% 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, 200M stars eject 100 times more of each heavy element in their winds than 50M stars, and even when weighted by an IMF their wind contribution is still an order of magnitude higher than that of 50M stars., Comment: Accepted for publication in MNRAS. 14 pages, 10 figures

Very massive stars (VMS) up to 200-300 $M_\odot$ 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 vs. 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 Gr\"afener (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 $Z_\odot/2$ to $Z_\odot/100$. 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 threshold than usually assumed, at $Z_\odot/20$ 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., Comment: Accepted for publication in MNRAS, 18 pages, 8 figures, 2 appendix

Stars strongly impact their environment, and shape structures on all scales throughout the universe, in a process known as ``feedback''. Due to the complexity of both stellar evolution and the physics of larger astrophysical structures, there remain many unanswered questions about how feedback operates, and what we can learn about stars by studying their imprint on the wider universe. In this white paper, we summarize discussions from the Lorentz Center meeting `Bringing Stellar Evolution and Feedback Together' in April 2022, and identify key areas where further dialogue can bring about radical changes in how we view the relationship between stars and the universe they live in., Comment: Accepted to the Publications of the Astronomical Society of the Pacific

The ages of stars have historically relied on isochrone fitting of standardised 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 utilise the M-L plane of Higgins & Vink as a method of determining stellar age, with mixing-corrected models applying a calibrated core overshooting alpha_ov 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 alpha_ov, Omega/Omega_crit, 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 utilise 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 (alpha_ov ~ 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., Comment: 13 pages, 13 figures. Accepted for publication in MNRAS. Comments welcome

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 80-1000Msun, 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 ~50-100Msun stars. We probe the relevant surface H abundances (Xs) 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 Xs is an important tool in deciphering the initial mass due to the chemically homogeneous nature of VMS above a mass threshold. We use Xs 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 1000Msun are not excluded. Coupled with the mass turnover at 1.6 Myr, Xs can be used as a 'clock' to determine the upper stellar mass., Comment: Accepted for publication in MNRAS, 14 figures

Very massive stars (VMS) dominate the physics of young clusters due to their ionising 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 Dor region of the 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 & Gr\"afener. We examine the temperature evolution of VMS with mass loss that scales with the luminosity-over-mass (L/M) ratio and the Eddington parameter ($\Gamma_{\rm e}$), assessing the relevance of the surface hydrogen (H) abundance which 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 $\Gamma_{\rm e}$-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 Teff, naturally reproducing the narrow range of observed temperatures, as well as the correct trend with metallicity. This distinct behavior of a steeply dropping luminosity is a self-regulatory mechanism that keeps temperatures constant during evolution in the HR-diagram., Comment: Accepted for publication in MNRAS. 18 pages, 16 figures, 1 appendix

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., Comment: 6 pages, 3 figures, to appear in the proceedings of IAUS 366 "The Origin of Outflows in Evolved Stars"

The Humphreys-Davidson (HD) limit sets the boundary between evolutionary channels of massive stars that either end their lives as 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 (Teff/K) < 3.68 - as a function of metallicity. Using MESA, we produce grids of massive star models at three metallicities: Galactic (Zsol), LMC (1/2 Zsol) and SMC (1/5 Zsol), 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 (Teff/K) ~ 4, which become more pronounced at lower metallicity. This shifts the cutoff 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., Comment: Accepted for publication in MNRAS. 15 pages, 13 figures

Evolved Wolf-Rayet stars form a key aspect of massive star evolution, and their strong outflows determine their final fates. In this study, we calculate grids of stellar models for a wide range of initial masses at five metallicities (ranging from solar down to just 2% solar). We compare a recent hydrodynamically-consistent wind prescription with two earlier frequently-used wind recipes in stellar evolution and population synthesis modelling, and we present the ranges of maximum final masses at core He-exhaustion for each wind prescription and metallicity Z. Our model grids reveal qualitative differences in mass-loss behaviour of the wind prescriptions in terms of "convergence". Using the prescription from Nugis & Lamers the maximum stellar black hole is found to converge to a value of 20-30Msun, independent of host metallicity, however when utilising the new physically-motivated prescription from Sander & Vink there is no convergence to a maximum black hole mass value. The final mass is simply larger for larger initial He-star mass, which implies that the upper black hole limit for He-stars below the pair-instability gap is set by prior evolution with mass loss, or the pair instability itself. Quantitatively, we find the critical Z for pair-instability (Z_PI) to be as high as 50% Zsolar, corresponding to the host metallicity of the LMC. Moreover, while the Nugis & Lamers prescription would not predict any black holes above the approx 130Msun pair-instability limit, with Sander & Vink winds included, we demonstrate a potential channel for very massive helium stars to form such massive black holes at ~2% Zsolar or below., Comment: Accepted for publication in MNRAS. 17 pages, 16 figures

At the end of its life, a very massive star is expected to collapse into a black hole. The recent detection of an 85 Msun black hole from the gravitational wave event GW 190521 appears to present a fundamental problem as to how such heavy black holes exist above the approximately 50 Msun pair-instability 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 Msun stars at reduced metallicity (Z/Zsun < 0.1) can produce blue supergiant progenitors with core masses sufficiently small to remain below the fundamental pair-instability 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 Msun black hole. 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 black hole mass set by pair instability, but also allows us to probe the maximum stellar black hole mass as a function of metallicity and Cosmic time in a physically sound framework., Comment: MNRAS Accepted. 9 pages, 3 figures. Prior Submission in September 2020 to Nature (see Research Square)

Current massive star evolution grids are not able to simultaneously reproduce the empirical upper luminosity limit of red supergiants, the Humphrey-Davidson (HD) limit at high and low metallicity. In this study, we provide 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 (Z). For solar, LMC, and SMC Z, we develop eight grids of MESA models for the mass range 20-60M to probe the effect of semiconvection and overshooting. We compare rotating and non-rotating models with efficient (alpha_semi = 100) and inefficient semi-convection (alpha_semi = 0.1), with high and low core overshooting (alpha_ov 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. We find that the extension of the convective core by overshooting alpha_ov = 0.5 has an effect on the post-MS evolution which can disable semiconvection leading to more RSGs, but a lack of BSGs. We therefore implement alpha_ov = 0.1 which switches on semiconvective mixing, though for standard alpha_semi = 1, would result in an HD limit which is higher than observed at low Z. Therefore, we need to implement very efficient semiconvection of alpha_semi = 100 which reproduces the HD limit at log L ~ 5.5 for the Magellanic Clouds while simultaneously reproducing the Galactic HD limit of log L ~ 5.8 naturally. The effect of semiconvection is not active at high Z due to the depletion of the envelope structure by strong mass loss such that semiconvective regions could not form. Z-dependent mass loss plays an indirect, yet decisive role in setting the HD limit as a function of Z. For a combination of efficient semiconvection and low overshooting with standard Z-dependent mass loss, we find a natural HD limit at all metallicities., Comment: 11pages, 7 figures, accepted for publication in A&A

We aim to constrain massive star evolution models using the unique testbed eclipsing binary HD166734 with new grids of MESA stellar evolution models, adopting calibrated prescriptions of overshooting, mass loss, and rotation. We introduce a novel tool: the "mass-luminosity plane" or "M-L plane", as an equivalent to the traditional HR diagram, utilising it to reproduce the testbed binary HD166734 with newly calibrated MESA stellar evolution models for single stars. We can only reproduce the Galactic binary system with an enhanced amount of core overshooting (alpha = 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 Vink et al. 2001 prescriptions, 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 get the nitrogen abundance ratios between the primary and secondary components to be correct (3:1) in our testbed binary system. 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 explodibility., Comment: Revised version, 14 pages, 19 figures, accepted for publication by Astronomy & Astrophysics

Massive star evolution is dominated by key physical processes such as mass loss, convection and rotation, yet these effects are poorly constrained, even on the main sequence. We utilise a detached, eclipsing binary HD166734 as a testbed for single star evolution to calibrate new MESA stellar evolution grids. We introduce a novel method of comparing theoretical models with observations in the 'Mass-Luminosity Plane', as an equivalent to the HRD (see Higgins & Vink, 2018). We reproduce stellar parameters and abundances of HD166734 with enhanced overshooting (alpha=0.5), mass loss and rotational mixing. When comparing the constraints of our testbed to the systematic grid of models we find that a higher value of alpha = 0.5 (rather than 0.1) results in a solution which is more likely to evolve to a neutron star than a black hole, due to a lower value of the compactness parameter.