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

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 2022 April and identify key areas where further dialog can bring about radical changes in how we view the relationship between stars and the universe they live in.

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., Accepted for publication in MNRAS. 15 pages, 13 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., MNRAS Accepted. 9 pages, 3 figures. Prior Submission in September 2020 to Nature (see Research Square)

At the end of its life, a very massive star is expected to collapse into a black hole. The masses of these black holes are pivotal for our understanding of the evolution and fate of these stars, as well as for galaxy evolution and the build-up of black hole masses through Cosmic time. The recent detection of an 85 solar mass 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 solar mass pair-instability limit where stars are expected to be blown to pieces with no remnant left. Here we show that for stellar models at reduced heavy element content, 90-100 solar mass stars can produce core masses sufficiently small to remain below the fundamental pair-instability limit, yet at the same time lose an amount of mass small enough to end up in an 85 solar mass black hole. A key point is that the amount of mass-loss scales with the host galaxy heavy element fraction, and not with the total amount of element enrichment that occurs naturally during the life of massive stars. Our study shows how our Universe is capable of producing heavy black holes, which are important seeds for the production of supermassive black holes that regulate the evolution of galaxies. Our evolutionary channel to the formation of an 85 solar mass black hole is of fundamental relevance for the manner in which metals are released in the outflows and explosions of the most massive stars, which is shown to be a strong function of Cosmic time.

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., 11pages, 7 figures, accepted for publication in A&A

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 (αov=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 αov=0.5 (rather than αov=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.

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., Revised version, 14 pages, 19 figures, accepted for publication by Astronomy & Astrophysics

Inositol 1,4,5-trisphosphate (IP(3)R) receptor channels control release of Ca(2+) from the endoplasmic reticulum into the cytosol of a cell. The binding of both 1,4,5-trisphosphate (IP(3)) and activating Ca(2+) is required for the channel to open. At high Ca(2+) concentrations, IP(3)Rs are inhibited. IP(3)Rs are composed of four identical subunits and form in clusters. Many models have been proposed to describe how the binding of IP(3) and Ca(2+) to subunits results in the opening and closing of IP(3)Rs. Here we compare the opening and closing probability distributions for clusters of IP(3)Rs, resulting from three different models. The distributions are calculated both analytically, using a method we have developed, and with simulations. We found significant differences in the behavior of the three models as the Ca(2+) and IP(3) concentrations are varied.

Many cells use oscillations in calcium concentration to transmit messages. The oscillations largely result from an influx of calcium into the cytosol from the endoplasmic reticulum (ER), followed by an efflux of calcium from the cytosol back into the ER. The sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA) pump pumps calcium into the ER. It binds calcium on the cytosolic side and releases it on the ER side and in the delay between binding and release, calcium is buffered by the pump. We developed a model of a buffering SERCA pump and investigated whether including this in a model of calcium oscillations has any significant effects. We found that the oscillations produced when using the SERCA pump, which does not buffer calcium, have a larger amplitude and a slightly smaller period than when using the buffering SERCA pump. We show that the buffering SERCA pump shows adaptation to a stimulus, and we demonstrate that, by using a bidirectional SERCA pump, we are able to eliminate futile cycling of calcium between the cytosol and ER when the cell is at rest.

Inositol 1,4,5-trisphosphate (IP(3)R) receptor channels control release of Ca(2+) from the endoplasmic reticulum into the cytosol of a cell. The binding of both 1,4,5-trisphosphate (IP(3)) and activating Ca(2+) is required for the channel to open. At high Ca(2+) concentrations, IP(3)Rs are inhibited. IP(3)Rs are composed of four identical subunits and form in clusters. Many models have been proposed to describe how the binding of IP(3) and Ca(2+) to subunits results in the opening and closing of IP(3)Rs. Here we compare the opening and closing probability distributions for clusters of IP(3)Rs, resulting from three different models. The distributions are calculated both analytically, using a method we have developed, and with simulations. We found significant differences in the behavior of the three models as the Ca(2+) and IP(3) concentrations are varied.

Microdomains of calcium (i.e., areas on the nanometer scale that have qualitatively different calcium concentrations from that in the bulk cytosol) are known to be important in many situations. In cardiac cells, for instance, a calcium microdomain between the L-type channels and the ryanodine receptors, the so-called diadic cleft, is where the majority of the control of calcium release occurs. In other cell types that exhibit calcium oscillations and waves, the importance of microdomains in the vicinity of clusters of inositol trisphosphate receptors, or between the endoplasmic reticulum (ER) and other internal organelles or the plasma membrane, is clear. Given the limits of computational power, it is not currently realistic to model an entire cellular cytoplasm by incorporating detailed structural information about the ER throughout the entire cytoplasm. Hence, most models use a homogenised approach, assuming that both cytoplasm and ER coexist at each point of the domain. Conversely, microdomain models can be constructed, in which detailed structural information can be incorporated, but, until now, methods have not been developed for linking such a microdomain model to a model at the level of the entire cell. Using the homogenisation approach we developed in an earlier paper [Goel, P., Friedman, A., Sneyd, J., 2006. Homogenization of the cell cytoplasm: the calcium bidomain equations. SIAM J. Multiscale Modeling Simulation, in press] we show how a multiscale model of a calcium microdomain can be constructed. In this model a detailed model of the microdomain (in which the ER and the cytoplasm are separate compartments) is coupled to a homogenised model of the entire cell in a rigorous way. Our method is illustrated by a simple model of the diadic cleft of a cardiac half-sarcomere.