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  <h2 id="publications" class="archive__subtitle">publications</h2>

Very massive stars: a metallicity-dependent upper-mass limit, slow winds, and the self-enrichment of globular clusters

Authors: Jorick S. Vink

One of the key questions in Astrophysics concerns the issue of whether there exists an upper-mass limit to stars, and if so, what physical mechanism sets this limit? The answer to this question might also determine if the upper-mass limit is metallicity (Z) dependent. We argue that mass loss by radiation-driven winds mediated by line opacity is one of the prime candidates setting the upper-mass limit. We present mass-loss predictions (Ṁ_wind) from Monte Carlo radiative transfer models for relatively cool (T_eff = 15 kK) very inflated massive stars (VMS) with large Eddington Γ factors in the mass range 10²-10³ M_⊙ as a function of metallicity down to 1/100 Z/Z_⊙. We employed a hydrodynamic version of our Monte Carlo method, allowing us to predict the rate of mass loss (Ṁ_wind) and the terminal wind velocity (v_∞) simultaneously. Interestingly, we find wind terminal velocities (v_∞) that are low (100-500 km s^-1) over a wide Z-range, and we propose that the slow winds from VMS are an important source of self-enrichment in globular clusters. We also find mass-loss rates (Ṁ_wind), exceeding the typical mass-accretion rate (Ṁ_accr) of 10^-3 M_⊙ yr^-1 during massive-star formation. We have expressed our mass-loss predictions as a function of mass and Z, finding log Ṁ = -9.13 + 2.1 log(M/M_⊙) + 0.74 log(Z/Z_⊙) (M_⊙/yr). Even if stellar winds do not directly halt & reverse mass accretion during star formation, if the most massive stars form by stellar mergers, stellar wind mass loss may dominate over the rate at which stellar growth takes place. We therefore argue that the upper-mass limit is effectively Z-dependent due to the nature of radiation-driven winds. This has dramatic consequences for the most luminous supernovae, gamma-ray bursts, and other black hole formation scenarios at different Cosmic epochs.

Published in Astronomy and Astrophysics, 2018

Massive star evolution: rotation, winds, and overshooting vectors in the mass-luminosity plane. I. A calibrated grid of rotating single star models

Authors: Erin R. Higgins, Jorick S. Vink

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 (α_ov = 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. <P />Evolutionary tracks are also available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/622/A50

Published in Astronomy and Astrophysics, 2019

Massive star evolution revealed in the Mass-Luminosity plane

Authors: Erin R. Higgins, Jorick S. Vink

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 (α_ov=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 α_ov=0.5 (rather than α_ov=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.

Published in High-mass X-ray Binaries: Illuminating the Passage from Massive Binaries to Merging Compact Objects, 2019

Theoretical investigation of the Humphreys-Davidson limit at high and low metallicity

Authors: Erin R. Higgins, Jorick S. Vink

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 helium-burning phase. We compare rotating and non-rotating models with efficient (α_semi = 100) and inefficient semi-convection (α_semi = 0.1), with high and low amounts of core overshooting (α_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 for a range of masses and metallicities.
Results: We find that the extension of the convective core by overshooting α_ov = 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 α_ov = 0.1, which switches on semi-convective mixing, but for standard α_semi = 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 α_semi = 100, which reproduces the HD limit at log L/L_⊙ ∼ 5.5 for the Magellanic Clouds while simultaneously reproducing the Galactic HD limit of log L/L_⊙ ∼ 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.

Published in Astronomy and Astrophysics, 2020

On the nature of massive helium star winds and Wolf-Rayet-type mass-loss

Authors: Andreas A. C. Sander, Jorick S. Vink

The mass-loss rates of massive helium stars are one of the major uncertainties in modern astrophysics. Regardless of whether they were stripped by a binary companion or managed to peel off their outer layers by themselves, the influence and final fate of helium stars - in particular the resulting black hole mass - highly depends on their wind mass-loss as stripped-envelope objects. While empirical mass-loss constraints for massive helium stars have improved over the last decades, the resulting recipes are limited to metallicities with the observational ability to sufficiently resolve individual stars. Yet, theoretical efforts have been hampered by the complexity of Wolf-Rayet (WR) winds arising from the more massive helium stars. In an unprecedented effort, we calculate next-generation stellar atmosphere models resembling massive helium main-sequence stars with Fe-bump driven winds up to 500 M_☉ over a wide metallicity range between 2.0 and 0.02 Z_☉ . We uncover a complex Γ_e-dependency of WR-type winds and their metallicity-dependent breakdown. The latter can be related to the onset of multiple scattering, requiring higher L/M-ratios at lower metallicity. Based on our findings, we derive the first ever theoretically motivated mass-loss recipe for massive helium stars. We also provide estimates for Lyman continuum and HeII ionizing fluxes, finding stripped helium stars to contribute considerably at low metallicity. In sharp contrast to OB-star winds, the mass-loss for helium stars scales with the terminal velocity. While limited to the helium main sequence, our study marks a major step towards a better theoretical understanding of helium star evolution.

Published in Monthly Notices of the Royal Astronomical Society, 2020

Maximum black hole mass across cosmic time

Authors: Jorick S. Vink, Erin R. Higgins, Andreas A. C. Sander, Gautham N. Sabhahit

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 / Z_☉ ≤ 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.

Published in Monthly Notices of the Royal Astronomical Society, 2021

Metallicity-dependent wind parameter predictions for OB stars

Authors: Jorick S. Vink, Andreas A. C. Sander

Mass-loss rates and terminal wind velocities are key parameters that determine the kinetic wind energy and momenta of massive stars. Furthermore, accurate mass-loss rates determine the mass and rotational velocity evolution of mass stars, and their fates as neutron stars and black holes in function of metallicity (Z). Here, we update our Monte Carlo mass-loss Recipe with new dynamically consistent computations of the terminal wind velocity - as a function of Z. These predictions are particularly timely as the Hubble Space Telescope Ultraviolet Legacy Library of Young Stars as Essential Standards (ULLYSES) project will observe ultraviolet spectra with blue-shifted P Cygni lines of hundreds of massive stars in the low-Z Large and Small Magellanic Clouds (SMC), as well as sub-SMC metallicity hosts. Around 35 000 K, we uncover a weak-wind ‘dip’ and we present diagnostics to investigate its physics with ULLYSES and X-Shooter data. We discuss how the dip may provide important information on wind-driving physics, and how this is of key relevance towards finding a new gold-standard for OB star mass-loss rates. For B supergiants below the Fe IV to III bi-stability jump, the terminal velocity is found to be independent of Z and M, while the mass-loss rate still varies as Ṁ ∝ Z^0.85. For O-type stars above the bi-stability jump we, find a terminal-velocity dependence of v_∞ ∝ Z^0.19 and the Z-dependence of the mass-loss rate is found to be as shallow as Ṁ ∝ Z^0.42, implying that to reproduce the ‘heavy’ black holes from LIGO/Virgo, the ‘low Z’ requirement becomes even more stringent than was previously anticipated.

Published in Monthly Notices of the Royal Astronomical Society, 2021

Superadiabaticity and the metallicity independence of the Humphreys-Davidson limit

Authors: Gautham N. Sabhahit, Jorick S. Vink, Erin R. Higgins, Andreas A. C. Sander

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 (1/2 Z_⊙), and SMC (1/5 Z_⊙), 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.

Published in Monthly Notices of the Royal Astronomical Society, 2021

The origin and impact of Wolf-Rayet-type mass loss

Authors: Andreas A. C. Sander, Jorick S. Vink, Erin R. Higgins, Tomer Shenar, Wolf-Rainer Hamann, Helge Todt

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.

Published in The Origin of Outflows in Evolved Stars, 2022

Mass-loss implementation and temperature evolution of very massive stars

Authors: Gautham N. Sabhahit, Jorick S. Vink, Erin R. Higgins, Andreas A. C. Sander

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 (Γ_e), 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 Γ_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 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.

Published in Monthly Notices of the Royal Astronomical Society, 2022

Theory and Diagnostics of Hot Star Mass Loss

Authors: Jorick S. Vink

Massive stars have strong stellar winds that direct their evolution through the upper Hertzsprung-Russell diagram and determine the black hole mass function. Furthermore, wind strength dictates the atmospheric structure that sets the ionizing flux. Finally, the wind directly intervenes with the stellar envelope structure, which is decisive for both single-star and binary evolution, affecting predictions for gravitational wave events. Key findings of current hot star research include: The traditional line-driven wind theory is being updated with Monte Carlo and comoving frame computations, revealing a rich multivariate behavior of the mass-loss rate in terms of M, L, Eddington Γ, T_eff, and chemical composition Z. Concerning the latter, is shown to depend on the iron (Fe) opacity, making Wolf-Rayet populations, and gravitational wave events dependent on host galaxy Z. On top of smooth mass-loss behavior, there are several transitions in the Hertzsprung-Russell diagram, involving bistability jumps around Fe recombination temperatures, leading to quasi-stationary episodic, and not necessarily eruptive, luminous blue variable and pre-SN mass loss. Furthermore, there are kinks. At 100 a high Γ mass-loss transition implies that hydrogen-rich, very massive stars have higher mass-loss rates than commonly considered. At the other end of the mass spectrum, low-mass stripped helium stars no longer appear as Wolf-Rayet stars but as optically thin stars. These stripped stars, in addition to very massive stars, are two newly identified sources of ionizing radiation that could play a key role in local star formation as well as at high redshift.

Published in Annual Review of Astronomy and Astrophysics, 2022

The hydrogen clock to infer the upper stellar mass

Authors: Erin R. Higgins, Jorick S. Vink, Gautham N. Sabhahit, Andreas A. C. Sander

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.

Published in Monthly Notices of the Royal Astronomical Society, 2022

Mass loss implementation and temperature evolution of very massive stars

Authors: Gautham N. Sabhahit, Jorick S. Vink, Erin R. Higgins, Andreas A. C. Sander

Very massive stars (VMS) dominate the physics of young clusters due to their extreme stellar winds. The mass lost by these stars in their winds determine their evolution, chemical yields and their end fates. In this contribution 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.

Published in Winds of Stars and Exoplanets, 2023

Stellar age determination in the mass-luminosity plane

Authors: Erin R. Higgins, Jorick S. Vink

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 α_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 α_ov, Ω/Ω_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 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 (α_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.

Published in Monthly Notices of the Royal Astronomical Society, 2023

Very massive stars and pair-instability supernovae: mass-loss framework for low metallicity

Authors: Gautham N. Sabhahit, Jorick S. Vink, Andreas A. C. Sander, Erin R. Higgins

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.

Published in Monthly Notices of the Royal Astronomical Society, 2023

Exploring the Red Supergiant wind kink. A Universal mass-loss concept for massive stars

Authors: Jorick S. Vink, Gautham N. Sabhahit

Red supergiants (RSG) are key objects in studying the evolution of massive stars and their endpoints, but uncertainties related to their underlying mass-loss mechanism have stood in the way of an appropriate framework for massive star evolution thus far. In this work, we analyse a recently uncovered empirical mass-loss “kink” feature and we highlight its similarity to hot star radiation-driven wind models and observations at the optically thin-to-thick transition point. We motivate a new RSG mass-loss prescription that depends on the Eddington factor, Γ, (including both a steep luminosity, L, dependence and an inverse steep mass, M_cur, dependence). We subsequently implement this new RSG mass-loss prescription in the stellar evolution code MESA. We find that our physically motivated mass-loss behaviour naturally reproduces the Humphreys-Davidson limit without the need for any ad hoc tweaks. It also resolves the RSG supernova “problem”. We argue that a universal behaviour that is seen for radiation-driven winds across the HR diagram, independent of the exact source of opacity, is a key feature of the evolution of the most massive stars.

Published in Astronomy and Astrophysics, 2023

Stellar wind yields of very massive stars

Authors: Erin R. Higgins, Jorick S. Vink, Raphael Hirschi, Alison M. Laird, Gautham N. Sabhahit

The most massive stars provide an essential source of recycled material for young clusters and galaxies. While very massive stars (VMSs, M > 100 M_☉) 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 M_☉, 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 M_☉ stars eject 100 times more of each heavy element in their winds than 50 M_☉ stars, and even when weighted by an IMF their wind contribution is still an order of magnitude higher than that of 50 M_☉ stars.

Published in Monthly Notices of the Royal Astronomical Society, 2023

Very massive stars and nitrogen-emitting galaxies

Authors: Jorick S. Vink

Recent studies of high-redshift galaxies with James Webb Space Telescope (JWST), such as GN-z11 at z = 10.6, show unexpectedly significant amounts of nitrogen (N) in their spectra. As this phenomenology appears to extend to gravitionally lensed galaxies at Cosmic noon such as the Sunburst Arc at z = 2.37, as well as globular clusters overall, we suggest that the common ingredient among them are very massive stars (VMSs) with zero-age main sequence (ZAMS) masses in the range of 100-1000 M_⊙. The He II in the Sunburst Arc might also be the result of the disproportionally large contribution of VMS to the total stellar contribution. We analyse the pros and cons of the previous suggestions, including classical Wolf-Rayet (cWR) stars and supermassive stars (SMSs), to conclude that only our VMS alternative ticks all the relevant boxes. We discuss the VMS mass-loss history via their peculiar vertical evolution in the HR diagram resulting from a self-regulatory effect of these wind-dominated VMSs and we estimate that the large amounts of N present in star-forming galaxies may indeed result from VMSs. We conclude that VMSs should be included in population synthesis and chemical evolution models. Moreover, that it is critical for this to be done self-consistently, as a small error in their mass-loss rates would have dramatic consequences for their stellar evolution, as well as their ionising and chemical feedback.

Published in Astronomy and Astrophysics, 2023

Constraining physical processes in pre-supernovae massive star evolution

Authors: Erin R. Higgins, Jorick S. Vink, Andreas Sander, Raphael Hirschi

While we have growing numbers of massive star observations, it remains unclear how efficient the key physical processes such as mass loss, convection and rotation are, or indeed how they impact each other. We reconcile this with detailed stellar evolution models, yet these models have their own drawbacks with necessary assumptions for 3-dimensional processes like rotation which need to be adapted into 1-dimensional models. The implementation of empirical mass-loss prescriptions in stellar evolution codes can lead to the extrapolation of base rates to unconstrained evolutionary stages leading to a range of uncertain fates. In short, there remain many free parameters and physical processes which need to be calibrated in order to align our theory better with upcoming observations. We have tested various processes such as mass loss and internal mixing, including rotational mixing and convective overshooting, against multiple observational constraints such as using eclipsing binaries, the Humphreys-Davidson limit, and the final masses of Wolf-Rayet stars, across a range of metallicities. In fact, we developed a method of disentangling the effects of mixing and mass loss in the `Mass-Luminosity Plane’ allowing direct calibration of these processes. In all cases, it is important to note that a combined appreciation for both stellar winds and internal mixing are important to reproduce observations.

Published in IAU Symposium, 2024

How to make an 85 Solar Mass Black Hole

Authors: Ethan Winch, Jorick S. Vink, Erin Higgins, Gautham Sabhahit

We present in-progress resolution test and parameter space studies for very massive stars using MESA, showcasing current MESA version convergence studies.

Published in IAU Symposium, 2024

On the Z-(in)dependence of the Humphreys-Davidson Limit

Authors: Gautham N. Sabhahit, Jorick S. Vink, Erin R. Higgins, Andreas A. C. Sander

The temperature independent part of the Humphreys-Davidson (HD) limit sets the boundary for 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. Recent downward revision of most luminous RSGs the Galaxy below log(L / L_⊙) ≈ 5.5, more in line with the Magellanic Clouds, might hint towards a metallicity (Z)-independent HD limit. We present MESA single star models in the 15-40 M_⊙ range and study the different Z-dependent processes that could potentially affect the location of the upper luminosity limit of RSGs.

Published in IAU Symposium, 2024

Predicting the heaviest black holes below the pair instability gap

Authors: Ethan R. J. Winch, Jorick S. Vink, Erin R. Higgins, Gautham N. Sabhahit

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.

Published in Monthly Notices of the Royal Astronomical Society, 2024

The maximum black hole mass at solar metallicity

Authors: Jorick S. Vink, Gautham N. Sabhahit, Erin R. Higgins

We analyse the 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 produce the most massive BHs, we find that the maximum M_BH^Max ≃ 30 ± 10 M_⊙ is found in the canonical intermediate range between M_ZAMS ≃ 30 and 50 M_⊙ instead. The prime reason for this seemingly counter-intuitive finding is that very massive stars (VMS) have increasingly high mass-loss rates that lead to substantial mass evaporation before they expire as stars and end as lighter BHs than their canonical O-star counterparts.

Published in Astronomy and Astrophysics, 2024

New Wolf-Rayet wind yields and nucleosynthesis of Helium stars

Authors: Erin R. Higgins, Jorick S. Vink, Raphael Hirschi, Alison M. Laird, Andreas A. C. Sander

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 (12–50 M_☉), adopting recent hydrodynamical wind rates. 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, 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 (N_n) of a 30 M_☉ cWR compared with a 32 M_☉ 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(α,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.

Published in Monthly Notices of the Royal Astronomical Society, 2024

Stellar expansion or inflation?

Authors: Gautham N. Sabhahit, Jorick S. Vink

While stellar expansion after core-hydrogen exhaustion related to thermal imbalance has been documented for decades, the physical phenomenon of stellar inflation that occurs close to the Eddington limit has only come to the fore in recent years. We aim to elucidate the differences between these physical mechanisms for stellar radius enlargement, especially given that additional terms such as ‘bloated’ and ‘puffed-up’ stars have been introduced in the recent massive star literature. We employ single and binary star MESA structure and evolution models for constant mass, as well as models allowing the mass to change due to winds or binary interaction. We find cases that were previously attributed to stellar inflation in fact to be due to stellar expansion. We also highlight that while the opposite effect of expansion is contraction, the removal of an inflated zone should not be referred to as contraction but rather deflation, as the star is still in thermal balance.

Published in Astronomy and Astrophysics, 2025

A new mass estimate method with hydrodynamical atmospheres for very massive WNh stars

Authors: Gautham N. Sabhahit, Jorick S. Vink, Andreas A. C. Sander, Matheus Bernini-Peron, Paul A. Crowther, Roel R. Lefever, Tomer Shenar

Very massive stars with masses over 100 M_⊙ are key objects in the Universe for our understanding of chemical and energetic feedback in the Universe, but their evolution and fate are almost entirely determined by their wind mass loss. Here, we aim to determine the mass of the most massive star known in the Local Group R136a1. To this end, we computed the first hydrodynamically consistent non-local thermodynamical equilibrium atmosphere models for R136a1 (WN5h), as well as the binary system R144 (WN5/6h+WN6/7h) in the Tarantula Nebula. Using the Potsdam Wolf–Rayet code, we were able to simultaneously empirically derive and theoretically predict their mass-loss rates and wind velocities. By fitting synthetic spectra derived from these models to multi-wavelength observations, we constrained the stellar and wind properties of R144 and R136a1. We first determined the clumping stratification required by our hydro-models to fit the spectra of R144, using the available dynamical mass estimates for the two components. We then utilised this clumping stratification in hydrodynamic models of R136a1 and estimated a mass of M_Hydro of 233 M_⊙. Remarkably, the estimated mass is close to and fully consistent with chemical homogeneous mass relations. This present-day mass of 233 M_⊙ provides a lower limit to the initial stellar mass, which could be far higher due to previous wind mass loss.

Published in Astronomy and Astrophysics, 2025

The black hole - pair instability boundary for high stellar rotation

Authors: Ethan R. J. Winch, Gautham N. Sabhahit, Jorick S. Vink, Erin R. Higgins

The Pair Instability (PI) boundary is crucial for understanding heavy merging Black Holes (BHs) and the second mass gap’s role in galactic chemical evolution. So far, no works have critically and systematically examined how rotation and mass loss affect the PI boundary or BH masses below it. Rapid rotation significantly alters stellar structure and mass loss, which is expected to have significant effects on the evolution of stellar models. We have previously derived a critical core mass independent of stellar evolution parameters, finding the BH (Pulsational) PI boundary at M_{CO, crit} = 36.3M_⊙ for a carbon-oxygen (CO) core. Using MESA, we model massive stars around the PI boundary for varying rotation rates and metallicities. We implement mechanical mass loss in MESA, studying its effects on massive stars in low-metallicity environments. Below 1/100th Z_⊙, mechanical mass loss dominates over radiative winds. We check the BH-PI boundary for rapid rotators to confirm our critical core mass criterion and derive model fits describing rotationâs impact on core and final masses. Fast rotators reach a point (typically Ω/Ω_crit ≈ 0.6) where the entire star becomes chemically homogeneous, evolving like a stripped star. This lowers the maximum BH mass before PI to its critical core mass of M_{CO, crit} = 36.3M_⊙, aligning with the bump feature in the BH mass distribution observed by LIGO/VIRGO.

Published in Monthly Notices of the Royal Astronomical Society, 2025

The impact of wind mass loss on nucleosynthesis and yields of very massive stars at low metallicity

Authors: Erin R. Higgins, Jorick S. Vink, Raphael Hirschi, Alison M. Laird, Gautham N. Sabhahit

The chemical feedback from stellar winds in low metallicity (Z) environments is key for understanding the evolution of globular clusters and the early Universe. With disproportionate mass lost from the most massive stars (M > 100M_⊙ ), and an excess of such stars expected at the lowest metallicities, their contribution to the enrichment of the early pristine clusters could be significant. In this work, we examine the effect of mass loss at low metallicity on the nucleosynthesis and wind yields of (very) massive stars. We calculate stellar models with initial masses ranging from 30 to 500M_⊙ during core Hydrogen and Helium burning phases, at four metallicities ranging from 20% Z_⊙ down to 1% Z_⊙ . The ejected masses and net yields are provided for each grid of models. While mass-loss rates decrease with Z, we find that not only are wind yields significant, but the nucleosynthesis is also altered due to the change in central temperatures and therefore also plays a role. We find that 80-300M_⊙ models can produce large quantities of Na-rich and O-poor material, relevant for the observed Na-O anti-correlation in globular clusters.

Published in arXiv e-prints, 2025

About Us

We are the Massive Star Group at Armagh Observatory, specializing in the wind physics of massive and very massive stars in the local Universe as well as the metal-poor early Universe. Our expertise spans stellar evolution modeling and hydrodynamical atmosphere modeling, enabling us to study stellar winds, mass loss, and the cosmic feedback of the most massive stars.

Group Lead

Professor Jorick S. Vink is a leading astronomer at Armagh Observatory whose models of radiation-driven winds in massive stars have significantly advanced our understanding of stellar wind physics, stellar feedback, chemical enrichment, and the distribution of black hole masses. His research interests include the physics of stellar winds and stellar evolution, with a particular focus on the role of radiation pressure at the upper end of the stellar mass spectrum. On the observational side, much of his work involves spectroscopy and spectro-polarimetry. He also leads the XShooting ULLYSES consortium aimed at obtaining optical and near-IR spectra for hundreds of massive stars in the Magellanic Clouds to complement the UV spectra from ULLYSES.

Current and Past Team Members

Ciaran Furey – PhD Student
Ethan Winch – PhD Student
Gautham Sabhahit – Postdoctoral Researcher
Erin Higgins – Former Postdoctoral Researcher
Andreas Sander – Former Postdoctoral Researcher

Research Highlights from the group

Theory and Diagnostics of Hot Star Mass Loss

Vink (2022) reviews advances in hot star wind theory, highlighting complex dependencies of mass loss on stellar parameters and metallicity. The work discusses wind transitions across the HR diagram and identifies very massive and stripped helium stars as key ionizing sources shaping star formation locally and at high redshift.

Maximum black hole mass across cosmic time

Vink et al. (2021) demonstrate that very massive stars at low metallicity can produce black holes exceeding the pair-instability limit (~50 M⊙) by accounting for core overshooting and metallicity-dependent winds. Their MESA models explain gravitational wave detections of heavy black holes (~85 M⊙) and map maximum BH masses as a function of metallicity and cosmic time.

Predicting the heaviest black holes below the pair instability gap

Winch et al. (2024) challenge the traditional pair-instability mass gap by showing that blue supergiant progenitors with small cores but massive hydrogen envelopes at low metallicity can produce black holes up to ~93 M⊙. Using an extensive grid of MESA models with varying physics, they demonstrate how mixing and envelope retention fill the lower PI gap, impacting predictions for heavy BH formation.

Mass-loss implementation and temperature evolution of very massive stars

Sabhahit et al. (2022) develop a new MESA mass-loss recipe transitioning between O-star and Wolf-Rayet winds, showing that VMS mass loss scaling with luminosity-to-mass reproduces the observed narrow temperature range in Galactic and LMC very massive stars. This reveals a self-regulatory mechanism stabilizing their effective temperatures during evolution.

Massive star evolution: rotation, winds, and overshooting vectors in the mass-luminosity plane

Higgins & Vink (2019) present a calibrated grid of rotating massive star models constrained by the eclipsing binary HD 166734. Their mass-luminosity plane tool requires enhanced core overshooting and rotational mixing to match observations, implying a widened main sequence and influencing red supergiant luminosities and supernova explodability.

Recent Publications

The impact of wind mass loss on nucleosynthesis and yields of very massive stars at low metallicity
Higgins et al. (2025), arXiv e-prints
The black hole - pair instability boundary for high stellar rotation
Winch et al. (2025), MNRAS
A new mass estimate method with hydrodynamical atmospheres for very massive WNh stars
Sabhahit et al. (2025), Astronomy and Astrophysics

More publications →

Contact

Email: Prof. Jorick Vink

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    <h2>Journal papers</h2><hr />

The impact of wind mass loss on nucleosynthesis and yields of very massive stars at low metallicity

Authors: Erin R. Higgins, Jorick S. Vink, Raphael Hirschi, Alison M. Laird, Gautham N. Sabhahit

The chemical feedback from stellar winds in low metallicity (Z) environments is key for understanding the evolution of globular clusters and the early Universe. With disproportionate mass lost from the most massive stars (M > 100M_⊙ ), and an excess of such stars expected at the lowest metallicities, their contribution to the enrichment of the early pristine clusters could be significant. In this work, we examine the effect of mass loss at low metallicity on the nucleosynthesis and wind yields of (very) massive stars. We calculate stellar models with initial masses ranging from 30 to 500M_⊙ during core Hydrogen and Helium burning phases, at four metallicities ranging from 20% Z_⊙ down to 1% Z_⊙ . The ejected masses and net yields are provided for each grid of models. While mass-loss rates decrease with Z, we find that not only are wind yields significant, but the nucleosynthesis is also altered due to the change in central temperatures and therefore also plays a role. We find that 80-300M_⊙ models can produce large quantities of Na-rich and O-poor material, relevant for the observed Na-O anti-correlation in globular clusters.

Published in arXiv e-prints, 2025

The black hole - pair instability boundary for high stellar rotation

Authors: Ethan R. J. Winch, Gautham N. Sabhahit, Jorick S. Vink, Erin R. Higgins

The Pair Instability (PI) boundary is crucial for understanding heavy merging Black Holes (BHs) and the second mass gap’s role in galactic chemical evolution. So far, no works have critically and systematically examined how rotation and mass loss affect the PI boundary or BH masses below it. Rapid rotation significantly alters stellar structure and mass loss, which is expected to have significant effects on the evolution of stellar models. We have previously derived a critical core mass independent of stellar evolution parameters, finding the BH (Pulsational) PI boundary at M_{CO, crit} = 36.3M_⊙ for a carbon-oxygen (CO) core. Using MESA, we model massive stars around the PI boundary for varying rotation rates and metallicities. We implement mechanical mass loss in MESA, studying its effects on massive stars in low-metallicity environments. Below 1/100th Z_⊙, mechanical mass loss dominates over radiative winds. We check the BH-PI boundary for rapid rotators to confirm our critical core mass criterion and derive model fits describing rotationâs impact on core and final masses. Fast rotators reach a point (typically Ω/Ω_crit ≈ 0.6) where the entire star becomes chemically homogeneous, evolving like a stripped star. This lowers the maximum BH mass before PI to its critical core mass of M_{CO, crit} = 36.3M_⊙, aligning with the bump feature in the BH mass distribution observed by LIGO/VIRGO.

Published in Monthly Notices of the Royal Astronomical Society, 2025

A new mass estimate method with hydrodynamical atmospheres for very massive WNh stars

Authors: Gautham N. Sabhahit, Jorick S. Vink, Andreas A. C. Sander, Matheus Bernini-Peron, Paul A. Crowther, Roel R. Lefever, Tomer Shenar

Very massive stars with masses over 100 M_⊙ are key objects in the Universe for our understanding of chemical and energetic feedback in the Universe, but their evolution and fate are almost entirely determined by their wind mass loss. Here, we aim to determine the mass of the most massive star known in the Local Group R136a1. To this end, we computed the first hydrodynamically consistent non-local thermodynamical equilibrium atmosphere models for R136a1 (WN5h), as well as the binary system R144 (WN5/6h+WN6/7h) in the Tarantula Nebula. Using the Potsdam Wolf–Rayet code, we were able to simultaneously empirically derive and theoretically predict their mass-loss rates and wind velocities. By fitting synthetic spectra derived from these models to multi-wavelength observations, we constrained the stellar and wind properties of R144 and R136a1. We first determined the clumping stratification required by our hydro-models to fit the spectra of R144, using the available dynamical mass estimates for the two components. We then utilised this clumping stratification in hydrodynamic models of R136a1 and estimated a mass of M_Hydro of 233 M_⊙. Remarkably, the estimated mass is close to and fully consistent with chemical homogeneous mass relations. This present-day mass of 233 M_⊙ provides a lower limit to the initial stellar mass, which could be far higher due to previous wind mass loss.

Published in Astronomy and Astrophysics, 2025

Stellar expansion or inflation?

Authors: Gautham N. Sabhahit, Jorick S. Vink

While stellar expansion after core-hydrogen exhaustion related to thermal imbalance has been documented for decades, the physical phenomenon of stellar inflation that occurs close to the Eddington limit has only come to the fore in recent years. We aim to elucidate the differences between these physical mechanisms for stellar radius enlargement, especially given that additional terms such as ‘bloated’ and ‘puffed-up’ stars have been introduced in the recent massive star literature. We employ single and binary star MESA structure and evolution models for constant mass, as well as models allowing the mass to change due to winds or binary interaction. We find cases that were previously attributed to stellar inflation in fact to be due to stellar expansion. We also highlight that while the opposite effect of expansion is contraction, the removal of an inflated zone should not be referred to as contraction but rather deflation, as the star is still in thermal balance.

Published in Astronomy and Astrophysics, 2025

New Wolf-Rayet wind yields and nucleosynthesis of Helium stars

Authors: Erin R. Higgins, Jorick S. Vink, Raphael Hirschi, Alison M. Laird, Andreas A. C. Sander

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 (12–50 M_☉), adopting recent hydrodynamical wind rates. 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, 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 (N_n) of a 30 M_☉ cWR compared with a 32 M_☉ 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(α,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.

Published in Monthly Notices of the Royal Astronomical Society, 2024

The maximum black hole mass at solar metallicity

Authors: Jorick S. Vink, Gautham N. Sabhahit, Erin R. Higgins

We analyse the 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 produce the most massive BHs, we find that the maximum M_BH^Max ≃ 30 ± 10 M_⊙ is found in the canonical intermediate range between M_ZAMS ≃ 30 and 50 M_⊙ instead. The prime reason for this seemingly counter-intuitive finding is that very massive stars (VMS) have increasingly high mass-loss rates that lead to substantial mass evaporation before they expire as stars and end as lighter BHs than their canonical O-star counterparts.

Published in Astronomy and Astrophysics, 2024

Predicting the heaviest black holes below the pair instability gap

Authors: Ethan R. J. Winch, Jorick S. Vink, Erin R. Higgins, Gautham N. Sabhahit

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.

Published in Monthly Notices of the Royal Astronomical Society, 2024

Very massive stars and nitrogen-emitting galaxies

Authors: Jorick S. Vink

Recent studies of high-redshift galaxies with James Webb Space Telescope (JWST), such as GN-z11 at z = 10.6, show unexpectedly significant amounts of nitrogen (N) in their spectra. As this phenomenology appears to extend to gravitionally lensed galaxies at Cosmic noon such as the Sunburst Arc at z = 2.37, as well as globular clusters overall, we suggest that the common ingredient among them are very massive stars (VMSs) with zero-age main sequence (ZAMS) masses in the range of 100-1000 M_⊙. The He II in the Sunburst Arc might also be the result of the disproportionally large contribution of VMS to the total stellar contribution. We analyse the pros and cons of the previous suggestions, including classical Wolf-Rayet (cWR) stars and supermassive stars (SMSs), to conclude that only our VMS alternative ticks all the relevant boxes. We discuss the VMS mass-loss history via their peculiar vertical evolution in the HR diagram resulting from a self-regulatory effect of these wind-dominated VMSs and we estimate that the large amounts of N present in star-forming galaxies may indeed result from VMSs. We conclude that VMSs should be included in population synthesis and chemical evolution models. Moreover, that it is critical for this to be done self-consistently, as a small error in their mass-loss rates would have dramatic consequences for their stellar evolution, as well as their ionising and chemical feedback.

Published in Astronomy and Astrophysics, 2023

Stellar wind yields of very massive stars

Authors: Erin R. Higgins, Jorick S. Vink, Raphael Hirschi, Alison M. Laird, Gautham N. Sabhahit

The most massive stars provide an essential source of recycled material for young clusters and galaxies. While very massive stars (VMSs, M > 100 M_☉) 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 M_☉, 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 M_☉ stars eject 100 times more of each heavy element in their winds than 50 M_☉ stars, and even when weighted by an IMF their wind contribution is still an order of magnitude higher than that of 50 M_☉ stars.

Published in Monthly Notices of the Royal Astronomical Society, 2023

Exploring the Red Supergiant wind kink. A Universal mass-loss concept for massive stars

Authors: Jorick S. Vink, Gautham N. Sabhahit

Red supergiants (RSG) are key objects in studying the evolution of massive stars and their endpoints, but uncertainties related to their underlying mass-loss mechanism have stood in the way of an appropriate framework for massive star evolution thus far. In this work, we analyse a recently uncovered empirical mass-loss “kink” feature and we highlight its similarity to hot star radiation-driven wind models and observations at the optically thin-to-thick transition point. We motivate a new RSG mass-loss prescription that depends on the Eddington factor, Γ, (including both a steep luminosity, L, dependence and an inverse steep mass, M_cur, dependence). We subsequently implement this new RSG mass-loss prescription in the stellar evolution code MESA. We find that our physically motivated mass-loss behaviour naturally reproduces the Humphreys-Davidson limit without the need for any ad hoc tweaks. It also resolves the RSG supernova “problem”. We argue that a universal behaviour that is seen for radiation-driven winds across the HR diagram, independent of the exact source of opacity, is a key feature of the evolution of the most massive stars.

Published in Astronomy and Astrophysics, 2023

Very massive stars and pair-instability supernovae: mass-loss framework for low metallicity

Authors: Gautham N. Sabhahit, Jorick S. Vink, Andreas A. C. Sander, Erin R. Higgins

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.

Published in Monthly Notices of the Royal Astronomical Society, 2023

Stellar age determination in the mass-luminosity plane

Authors: Erin R. Higgins, Jorick S. Vink

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 α_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 α_ov, Ω/Ω_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 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 (α_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.

Published in Monthly Notices of the Royal Astronomical Society, 2023

The hydrogen clock to infer the upper stellar mass

Authors: Erin R. Higgins, Jorick S. Vink, Gautham N. Sabhahit, Andreas A. C. Sander

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.

Published in Monthly Notices of the Royal Astronomical Society, 2022

Theory and Diagnostics of Hot Star Mass Loss

Authors: Jorick S. Vink

Massive stars have strong stellar winds that direct their evolution through the upper Hertzsprung-Russell diagram and determine the black hole mass function. Furthermore, wind strength dictates the atmospheric structure that sets the ionizing flux. Finally, the wind directly intervenes with the stellar envelope structure, which is decisive for both single-star and binary evolution, affecting predictions for gravitational wave events. Key findings of current hot star research include: The traditional line-driven wind theory is being updated with Monte Carlo and comoving frame computations, revealing a rich multivariate behavior of the mass-loss rate in terms of M, L, Eddington Γ, T_eff, and chemical composition Z. Concerning the latter, is shown to depend on the iron (Fe) opacity, making Wolf-Rayet populations, and gravitational wave events dependent on host galaxy Z. On top of smooth mass-loss behavior, there are several transitions in the Hertzsprung-Russell diagram, involving bistability jumps around Fe recombination temperatures, leading to quasi-stationary episodic, and not necessarily eruptive, luminous blue variable and pre-SN mass loss. Furthermore, there are kinks. At 100 a high Γ mass-loss transition implies that hydrogen-rich, very massive stars have higher mass-loss rates than commonly considered. At the other end of the mass spectrum, low-mass stripped helium stars no longer appear as Wolf-Rayet stars but as optically thin stars. These stripped stars, in addition to very massive stars, are two newly identified sources of ionizing radiation that could play a key role in local star formation as well as at high redshift.

Published in Annual Review of Astronomy and Astrophysics, 2022

Mass-loss implementation and temperature evolution of very massive stars

Authors: Gautham N. Sabhahit, Jorick S. Vink, Erin R. Higgins, Andreas A. C. Sander

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 (Γ_e), 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 Γ_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 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.

Published in Monthly Notices of the Royal Astronomical Society, 2022

Superadiabaticity and the metallicity independence of the Humphreys-Davidson limit

Authors: Gautham N. Sabhahit, Jorick S. Vink, Erin R. Higgins, Andreas A. C. Sander

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 (1/2 Z_⊙), and SMC (1/5 Z_⊙), 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.

Published in Monthly Notices of the Royal Astronomical Society, 2021

Metallicity-dependent wind parameter predictions for OB stars

Authors: Jorick S. Vink, Andreas A. C. Sander

Mass-loss rates and terminal wind velocities are key parameters that determine the kinetic wind energy and momenta of massive stars. Furthermore, accurate mass-loss rates determine the mass and rotational velocity evolution of mass stars, and their fates as neutron stars and black holes in function of metallicity (Z). Here, we update our Monte Carlo mass-loss Recipe with new dynamically consistent computations of the terminal wind velocity - as a function of Z. These predictions are particularly timely as the Hubble Space Telescope Ultraviolet Legacy Library of Young Stars as Essential Standards (ULLYSES) project will observe ultraviolet spectra with blue-shifted P Cygni lines of hundreds of massive stars in the low-Z Large and Small Magellanic Clouds (SMC), as well as sub-SMC metallicity hosts. Around 35 000 K, we uncover a weak-wind ‘dip’ and we present diagnostics to investigate its physics with ULLYSES and X-Shooter data. We discuss how the dip may provide important information on wind-driving physics, and how this is of key relevance towards finding a new gold-standard for OB star mass-loss rates. For B supergiants below the Fe IV to III bi-stability jump, the terminal velocity is found to be independent of Z and M, while the mass-loss rate still varies as Ṁ ∝ Z^0.85. For O-type stars above the bi-stability jump we, find a terminal-velocity dependence of v_∞ ∝ Z^0.19 and the Z-dependence of the mass-loss rate is found to be as shallow as Ṁ ∝ Z^0.42, implying that to reproduce the ‘heavy’ black holes from LIGO/Virgo, the ‘low Z’ requirement becomes even more stringent than was previously anticipated.

Published in Monthly Notices of the Royal Astronomical Society, 2021

Maximum black hole mass across cosmic time

Authors: Jorick S. Vink, Erin R. Higgins, Andreas A. C. Sander, Gautham N. Sabhahit

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 / Z_☉ ≤ 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.

Published in Monthly Notices of the Royal Astronomical Society, 2021

On the nature of massive helium star winds and Wolf-Rayet-type mass-loss

Authors: Andreas A. C. Sander, Jorick S. Vink

The mass-loss rates of massive helium stars are one of the major uncertainties in modern astrophysics. Regardless of whether they were stripped by a binary companion or managed to peel off their outer layers by themselves, the influence and final fate of helium stars - in particular the resulting black hole mass - highly depends on their wind mass-loss as stripped-envelope objects. While empirical mass-loss constraints for massive helium stars have improved over the last decades, the resulting recipes are limited to metallicities with the observational ability to sufficiently resolve individual stars. Yet, theoretical efforts have been hampered by the complexity of Wolf-Rayet (WR) winds arising from the more massive helium stars. In an unprecedented effort, we calculate next-generation stellar atmosphere models resembling massive helium main-sequence stars with Fe-bump driven winds up to 500 M_☉ over a wide metallicity range between 2.0 and 0.02 Z_☉ . We uncover a complex Γ_e-dependency of WR-type winds and their metallicity-dependent breakdown. The latter can be related to the onset of multiple scattering, requiring higher L/M-ratios at lower metallicity. Based on our findings, we derive the first ever theoretically motivated mass-loss recipe for massive helium stars. We also provide estimates for Lyman continuum and HeII ionizing fluxes, finding stripped helium stars to contribute considerably at low metallicity. In sharp contrast to OB-star winds, the mass-loss for helium stars scales with the terminal velocity. While limited to the helium main sequence, our study marks a major step towards a better theoretical understanding of helium star evolution.

Published in Monthly Notices of the Royal Astronomical Society, 2020

Theoretical investigation of the Humphreys-Davidson limit at high and low metallicity

Authors: Erin R. Higgins, Jorick S. Vink

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 helium-burning phase. We compare rotating and non-rotating models with efficient (α_semi = 100) and inefficient semi-convection (α_semi = 0.1), with high and low amounts of core overshooting (α_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 for a range of masses and metallicities.
Results: We find that the extension of the convective core by overshooting α_ov = 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 α_ov = 0.1, which switches on semi-convective mixing, but for standard α_semi = 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 α_semi = 100, which reproduces the HD limit at log L/L_⊙ ∼ 5.5 for the Magellanic Clouds while simultaneously reproducing the Galactic HD limit of log L/L_⊙ ∼ 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.

Published in Astronomy and Astrophysics, 2020

Massive star evolution: rotation, winds, and overshooting vectors in the mass-luminosity plane. I. A calibrated grid of rotating single star models

Authors: Erin R. Higgins, Jorick S. Vink

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 (α_ov = 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. <P />Evolutionary tracks are also available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/622/A50

Published in Astronomy and Astrophysics, 2019

Very massive stars: a metallicity-dependent upper-mass limit, slow winds, and the self-enrichment of globular clusters

Authors: Jorick S. Vink

One of the key questions in Astrophysics concerns the issue of whether there exists an upper-mass limit to stars, and if so, what physical mechanism sets this limit? The answer to this question might also determine if the upper-mass limit is metallicity (Z) dependent. We argue that mass loss by radiation-driven winds mediated by line opacity is one of the prime candidates setting the upper-mass limit. We present mass-loss predictions (Ṁ_wind) from Monte Carlo radiative transfer models for relatively cool (T_eff = 15 kK) very inflated massive stars (VMS) with large Eddington Γ factors in the mass range 10²-10³ M_⊙ as a function of metallicity down to 1/100 Z/Z_⊙. We employed a hydrodynamic version of our Monte Carlo method, allowing us to predict the rate of mass loss (Ṁ_wind) and the terminal wind velocity (v_∞) simultaneously. Interestingly, we find wind terminal velocities (v_∞) that are low (100-500 km s^-1) over a wide Z-range, and we propose that the slow winds from VMS are an important source of self-enrichment in globular clusters. We also find mass-loss rates (Ṁ_wind), exceeding the typical mass-accretion rate (Ṁ_accr) of 10^-3 M_⊙ yr^-1 during massive-star formation. We have expressed our mass-loss predictions as a function of mass and Z, finding log Ṁ = -9.13 + 2.1 log(M/M_⊙) + 0.74 log(Z/Z_⊙) (M_⊙/yr). Even if stellar winds do not directly halt & reverse mass accretion during star formation, if the most massive stars form by stellar mergers, stellar wind mass loss may dominate over the rate at which stellar growth takes place. We therefore argue that the upper-mass limit is effectively Z-dependent due to the nature of radiation-driven winds. This has dramatic consequences for the most luminous supernovae, gamma-ray bursts, and other black hole formation scenarios at different Cosmic epochs.

Published in Astronomy and Astrophysics, 2018

    <h2>Conference proceedings</h2><hr />

On the Z-(in)dependence of the Humphreys-Davidson Limit

Authors: Gautham N. Sabhahit, Jorick S. Vink, Erin R. Higgins, Andreas A. C. Sander

The temperature independent part of the Humphreys-Davidson (HD) limit sets the boundary for 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. Recent downward revision of most luminous RSGs the Galaxy below log(L / L_⊙) ≈ 5.5, more in line with the Magellanic Clouds, might hint towards a metallicity (Z)-independent HD limit. We present MESA single star models in the 15-40 M_⊙ range and study the different Z-dependent processes that could potentially affect the location of the upper luminosity limit of RSGs.

Published in IAU Symposium, 2024

How to make an 85 Solar Mass Black Hole

Authors: Ethan Winch, Jorick S. Vink, Erin Higgins, Gautham Sabhahit

We present in-progress resolution test and parameter space studies for very massive stars using MESA, showcasing current MESA version convergence studies.

Published in IAU Symposium, 2024

Constraining physical processes in pre-supernovae massive star evolution

Authors: Erin R. Higgins, Jorick S. Vink, Andreas Sander, Raphael Hirschi

While we have growing numbers of massive star observations, it remains unclear how efficient the key physical processes such as mass loss, convection and rotation are, or indeed how they impact each other. We reconcile this with detailed stellar evolution models, yet these models have their own drawbacks with necessary assumptions for 3-dimensional processes like rotation which need to be adapted into 1-dimensional models. The implementation of empirical mass-loss prescriptions in stellar evolution codes can lead to the extrapolation of base rates to unconstrained evolutionary stages leading to a range of uncertain fates. In short, there remain many free parameters and physical processes which need to be calibrated in order to align our theory better with upcoming observations. We have tested various processes such as mass loss and internal mixing, including rotational mixing and convective overshooting, against multiple observational constraints such as using eclipsing binaries, the Humphreys-Davidson limit, and the final masses of Wolf-Rayet stars, across a range of metallicities. In fact, we developed a method of disentangling the effects of mixing and mass loss in the `Mass-Luminosity Plane’ allowing direct calibration of these processes. In all cases, it is important to note that a combined appreciation for both stellar winds and internal mixing are important to reproduce observations.

Published in IAU Symposium, 2024

Mass loss implementation and temperature evolution of very massive stars

Authors: Gautham N. Sabhahit, Jorick S. Vink, Erin R. Higgins, Andreas A. C. Sander

Very massive stars (VMS) dominate the physics of young clusters due to their extreme stellar winds. The mass lost by these stars in their winds determine their evolution, chemical yields and their end fates. In this contribution 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.

Published in Winds of Stars and Exoplanets, 2023

The origin and impact of Wolf-Rayet-type mass loss

Authors: Andreas A. C. Sander, Jorick S. Vink, Erin R. Higgins, Tomer Shenar, Wolf-Rainer Hamann, Helge Todt

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.

Published in The Origin of Outflows in Evolved Stars, 2022

Massive star evolution revealed in the Mass-Luminosity plane

Authors: Erin R. Higgins, Jorick S. Vink

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 (α_ov=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 α_ov=0.5 (rather than α_ov=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.

Published in High-mass X-ray Binaries: Illuminating the Passage from Massive Binaries to Merging Compact Objects, 2019

Scripts

1. Mass–Luminosity Calculator

We provide a Python script and an online calculator that enable users to compute mass–luminosity relations (MLRs), which can predict the minimum, maximum, and pure-helium (He) mass for a given luminosity and surface composition — and vice versa. These results are based on the stellar structure models presented in Sabhahit et al. (2025b) and build upon existing MLRs in the literature by incorporating models that feature a helium core and hydrogen shell. These configurations may result from partial envelope stripping and can break simple homology relations, appearing more luminous than pure-He stars despite having a lower mean molecular weight. A detailed description of our additional structure models by taking into account partial envelope stripping and the resulting new MLRs can be found here.

MLR Python script from Sabhahit et al. (2025b) MLR Online calculator from Sabhahit et al. (2025b)

For comparison, we also provide a Python script implementing the minimum and maximum MLRs from Gräfener et al. 2011 ( NASA ADS).

MLR Python script from Gräfener et al. (2011)

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publications

Very massive stars: a metallicity-dependent upper-mass limit, slow winds, and the self-enrichment of globular clusters

Authors: Jorick S. Vink

One of the key questions in Astrophysics concerns the issue of whether there exists an upper-mass limit to stars, and if so, what physical mechanism sets this limit? The answer to this question might also determine if the upper-mass limit is metallicity (Z) dependent. We argue that mass loss by radiation-driven winds mediated by line opacity is one of the prime candidates setting the upper-mass limit. We present mass-loss predictions (Ṁ_wind) from Monte Carlo radiative transfer models for relatively cool (T_eff = 15 kK) very inflated massive stars (VMS) with large Eddington Γ factors in the mass range 10²-10³ M_⊙ as a function of metallicity down to 1/100 Z/Z_⊙. We employed a hydrodynamic version of our Monte Carlo method, allowing us to predict the rate of mass loss (Ṁ_wind) and the terminal wind velocity (v_∞) simultaneously. Interestingly, we find wind terminal velocities (v_∞) that are low (100-500 km s^-1) over a wide Z-range, and we propose that the slow winds from VMS are an important source of self-enrichment in globular clusters. We also find mass-loss rates (Ṁ_wind), exceeding the typical mass-accretion rate (Ṁ_accr) of 10^-3 M_⊙ yr^-1 during massive-star formation. We have expressed our mass-loss predictions as a function of mass and Z, finding log Ṁ = -9.13 + 2.1 log(M/M_⊙) + 0.74 log(Z/Z_⊙) (M_⊙/yr). Even if stellar winds do not directly halt & reverse mass accretion during star formation, if the most massive stars form by stellar mergers, stellar wind mass loss may dominate over the rate at which stellar growth takes place. We therefore argue that the upper-mass limit is effectively Z-dependent due to the nature of radiation-driven winds. This has dramatic consequences for the most luminous supernovae, gamma-ray bursts, and other black hole formation scenarios at different Cosmic epochs.

Published in Astronomy and Astrophysics, 2018

Massive star evolution: rotation, winds, and overshooting vectors in the mass-luminosity plane. I. A calibrated grid of rotating single star models

Authors: Erin R. Higgins, Jorick S. Vink

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 (α_ov = 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. <P />Evolutionary tracks are also available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/622/A50

Published in Astronomy and Astrophysics, 2019

Massive star evolution revealed in the Mass-Luminosity plane

Authors: Erin R. Higgins, Jorick S. Vink

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 (α_ov=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 α_ov=0.5 (rather than α_ov=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.

Published in High-mass X-ray Binaries: Illuminating the Passage from Massive Binaries to Merging Compact Objects, 2019

Theoretical investigation of the Humphreys-Davidson limit at high and low metallicity

Authors: Erin R. Higgins, Jorick S. Vink

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 helium-burning phase. We compare rotating and non-rotating models with efficient (α_semi = 100) and inefficient semi-convection (α_semi = 0.1), with high and low amounts of core overshooting (α_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 for a range of masses and metallicities.
Results: We find that the extension of the convective core by overshooting α_ov = 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 α_ov = 0.1, which switches on semi-convective mixing, but for standard α_semi = 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 α_semi = 100, which reproduces the HD limit at log L/L_⊙ ∼ 5.5 for the Magellanic Clouds while simultaneously reproducing the Galactic HD limit of log L/L_⊙ ∼ 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.

Published in Astronomy and Astrophysics, 2020

On the nature of massive helium star winds and Wolf-Rayet-type mass-loss

Authors: Andreas A. C. Sander, Jorick S. Vink

The mass-loss rates of massive helium stars are one of the major uncertainties in modern astrophysics. Regardless of whether they were stripped by a binary companion or managed to peel off their outer layers by themselves, the influence and final fate of helium stars - in particular the resulting black hole mass - highly depends on their wind mass-loss as stripped-envelope objects. While empirical mass-loss constraints for massive helium stars have improved over the last decades, the resulting recipes are limited to metallicities with the observational ability to sufficiently resolve individual stars. Yet, theoretical efforts have been hampered by the complexity of Wolf-Rayet (WR) winds arising from the more massive helium stars. In an unprecedented effort, we calculate next-generation stellar atmosphere models resembling massive helium main-sequence stars with Fe-bump driven winds up to 500 M_☉ over a wide metallicity range between 2.0 and 0.02 Z_☉ . We uncover a complex Γ_e-dependency of WR-type winds and their metallicity-dependent breakdown. The latter can be related to the onset of multiple scattering, requiring higher L/M-ratios at lower metallicity. Based on our findings, we derive the first ever theoretically motivated mass-loss recipe for massive helium stars. We also provide estimates for Lyman continuum and HeII ionizing fluxes, finding stripped helium stars to contribute considerably at low metallicity. In sharp contrast to OB-star winds, the mass-loss for helium stars scales with the terminal velocity. While limited to the helium main sequence, our study marks a major step towards a better theoretical understanding of helium star evolution.

Published in Monthly Notices of the Royal Astronomical Society, 2020

Maximum black hole mass across cosmic time

Authors: Jorick S. Vink, Erin R. Higgins, Andreas A. C. Sander, Gautham N. Sabhahit

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 / Z_☉ ≤ 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.

Published in Monthly Notices of the Royal Astronomical Society, 2021

Metallicity-dependent wind parameter predictions for OB stars

Authors: Jorick S. Vink, Andreas A. C. Sander

Mass-loss rates and terminal wind velocities are key parameters that determine the kinetic wind energy and momenta of massive stars. Furthermore, accurate mass-loss rates determine the mass and rotational velocity evolution of mass stars, and their fates as neutron stars and black holes in function of metallicity (Z). Here, we update our Monte Carlo mass-loss Recipe with new dynamically consistent computations of the terminal wind velocity - as a function of Z. These predictions are particularly timely as the Hubble Space Telescope Ultraviolet Legacy Library of Young Stars as Essential Standards (ULLYSES) project will observe ultraviolet spectra with blue-shifted P Cygni lines of hundreds of massive stars in the low-Z Large and Small Magellanic Clouds (SMC), as well as sub-SMC metallicity hosts. Around 35 000 K, we uncover a weak-wind ‘dip’ and we present diagnostics to investigate its physics with ULLYSES and X-Shooter data. We discuss how the dip may provide important information on wind-driving physics, and how this is of key relevance towards finding a new gold-standard for OB star mass-loss rates. For B supergiants below the Fe IV to III bi-stability jump, the terminal velocity is found to be independent of Z and M, while the mass-loss rate still varies as Ṁ ∝ Z^0.85. For O-type stars above the bi-stability jump we, find a terminal-velocity dependence of v_∞ ∝ Z^0.19 and the Z-dependence of the mass-loss rate is found to be as shallow as Ṁ ∝ Z^0.42, implying that to reproduce the ‘heavy’ black holes from LIGO/Virgo, the ‘low Z’ requirement becomes even more stringent than was previously anticipated.

Published in Monthly Notices of the Royal Astronomical Society, 2021

Superadiabaticity and the metallicity independence of the Humphreys-Davidson limit

Authors: Gautham N. Sabhahit, Jorick S. Vink, Erin R. Higgins, Andreas A. C. Sander

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 (1/2 Z_⊙), and SMC (1/5 Z_⊙), 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.

Published in Monthly Notices of the Royal Astronomical Society, 2021

The origin and impact of Wolf-Rayet-type mass loss

Authors: Andreas A. C. Sander, Jorick S. Vink, Erin R. Higgins, Tomer Shenar, Wolf-Rainer Hamann, Helge Todt

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.

Published in The Origin of Outflows in Evolved Stars, 2022

Mass-loss implementation and temperature evolution of very massive stars

Authors: Gautham N. Sabhahit, Jorick S. Vink, Erin R. Higgins, Andreas A. C. Sander

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 (Γ_e), 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 Γ_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 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.

Published in Monthly Notices of the Royal Astronomical Society, 2022

Theory and Diagnostics of Hot Star Mass Loss

Authors: Jorick S. Vink

Massive stars have strong stellar winds that direct their evolution through the upper Hertzsprung-Russell diagram and determine the black hole mass function. Furthermore, wind strength dictates the atmospheric structure that sets the ionizing flux. Finally, the wind directly intervenes with the stellar envelope structure, which is decisive for both single-star and binary evolution, affecting predictions for gravitational wave events. Key findings of current hot star research include: The traditional line-driven wind theory is being updated with Monte Carlo and comoving frame computations, revealing a rich multivariate behavior of the mass-loss rate in terms of M, L, Eddington Γ, T_eff, and chemical composition Z. Concerning the latter, is shown to depend on the iron (Fe) opacity, making Wolf-Rayet populations, and gravitational wave events dependent on host galaxy Z. On top of smooth mass-loss behavior, there are several transitions in the Hertzsprung-Russell diagram, involving bistability jumps around Fe recombination temperatures, leading to quasi-stationary episodic, and not necessarily eruptive, luminous blue variable and pre-SN mass loss. Furthermore, there are kinks. At 100 a high Γ mass-loss transition implies that hydrogen-rich, very massive stars have higher mass-loss rates than commonly considered. At the other end of the mass spectrum, low-mass stripped helium stars no longer appear as Wolf-Rayet stars but as optically thin stars. These stripped stars, in addition to very massive stars, are two newly identified sources of ionizing radiation that could play a key role in local star formation as well as at high redshift.

Published in Annual Review of Astronomy and Astrophysics, 2022

The hydrogen clock to infer the upper stellar mass

Authors: Erin R. Higgins, Jorick S. Vink, Gautham N. Sabhahit, Andreas A. C. Sander

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.

Published in Monthly Notices of the Royal Astronomical Society, 2022

Mass loss implementation and temperature evolution of very massive stars

Authors: Gautham N. Sabhahit, Jorick S. Vink, Erin R. Higgins, Andreas A. C. Sander

Very massive stars (VMS) dominate the physics of young clusters due to their extreme stellar winds. The mass lost by these stars in their winds determine their evolution, chemical yields and their end fates. In this contribution 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.

Published in Winds of Stars and Exoplanets, 2023

Stellar age determination in the mass-luminosity plane

Authors: Erin R. Higgins, Jorick S. Vink

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 α_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 α_ov, Ω/Ω_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 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 (α_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.

Published in Monthly Notices of the Royal Astronomical Society, 2023

Very massive stars and pair-instability supernovae: mass-loss framework for low metallicity

Authors: Gautham N. Sabhahit, Jorick S. Vink, Andreas A. C. Sander, Erin R. Higgins

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.

Published in Monthly Notices of the Royal Astronomical Society, 2023

Exploring the Red Supergiant wind kink. A Universal mass-loss concept for massive stars

Authors: Jorick S. Vink, Gautham N. Sabhahit

Red supergiants (RSG) are key objects in studying the evolution of massive stars and their endpoints, but uncertainties related to their underlying mass-loss mechanism have stood in the way of an appropriate framework for massive star evolution thus far. In this work, we analyse a recently uncovered empirical mass-loss “kink” feature and we highlight its similarity to hot star radiation-driven wind models and observations at the optically thin-to-thick transition point. We motivate a new RSG mass-loss prescription that depends on the Eddington factor, Γ, (including both a steep luminosity, L, dependence and an inverse steep mass, M_cur, dependence). We subsequently implement this new RSG mass-loss prescription in the stellar evolution code MESA. We find that our physically motivated mass-loss behaviour naturally reproduces the Humphreys-Davidson limit without the need for any ad hoc tweaks. It also resolves the RSG supernova “problem”. We argue that a universal behaviour that is seen for radiation-driven winds across the HR diagram, independent of the exact source of opacity, is a key feature of the evolution of the most massive stars.

Published in Astronomy and Astrophysics, 2023

Stellar wind yields of very massive stars

Authors: Erin R. Higgins, Jorick S. Vink, Raphael Hirschi, Alison M. Laird, Gautham N. Sabhahit

The most massive stars provide an essential source of recycled material for young clusters and galaxies. While very massive stars (VMSs, M > 100 M_☉) 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 M_☉, 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 M_☉ stars eject 100 times more of each heavy element in their winds than 50 M_☉ stars, and even when weighted by an IMF their wind contribution is still an order of magnitude higher than that of 50 M_☉ stars.

Published in Monthly Notices of the Royal Astronomical Society, 2023

Very massive stars and nitrogen-emitting galaxies

Authors: Jorick S. Vink

Recent studies of high-redshift galaxies with James Webb Space Telescope (JWST), such as GN-z11 at z = 10.6, show unexpectedly significant amounts of nitrogen (N) in their spectra. As this phenomenology appears to extend to gravitionally lensed galaxies at Cosmic noon such as the Sunburst Arc at z = 2.37, as well as globular clusters overall, we suggest that the common ingredient among them are very massive stars (VMSs) with zero-age main sequence (ZAMS) masses in the range of 100-1000 M_⊙. The He II in the Sunburst Arc might also be the result of the disproportionally large contribution of VMS to the total stellar contribution. We analyse the pros and cons of the previous suggestions, including classical Wolf-Rayet (cWR) stars and supermassive stars (SMSs), to conclude that only our VMS alternative ticks all the relevant boxes. We discuss the VMS mass-loss history via their peculiar vertical evolution in the HR diagram resulting from a self-regulatory effect of these wind-dominated VMSs and we estimate that the large amounts of N present in star-forming galaxies may indeed result from VMSs. We conclude that VMSs should be included in population synthesis and chemical evolution models. Moreover, that it is critical for this to be done self-consistently, as a small error in their mass-loss rates would have dramatic consequences for their stellar evolution, as well as their ionising and chemical feedback.

Published in Astronomy and Astrophysics, 2023

Constraining physical processes in pre-supernovae massive star evolution

Authors: Erin R. Higgins, Jorick S. Vink, Andreas Sander, Raphael Hirschi

While we have growing numbers of massive star observations, it remains unclear how efficient the key physical processes such as mass loss, convection and rotation are, or indeed how they impact each other. We reconcile this with detailed stellar evolution models, yet these models have their own drawbacks with necessary assumptions for 3-dimensional processes like rotation which need to be adapted into 1-dimensional models. The implementation of empirical mass-loss prescriptions in stellar evolution codes can lead to the extrapolation of base rates to unconstrained evolutionary stages leading to a range of uncertain fates. In short, there remain many free parameters and physical processes which need to be calibrated in order to align our theory better with upcoming observations. We have tested various processes such as mass loss and internal mixing, including rotational mixing and convective overshooting, against multiple observational constraints such as using eclipsing binaries, the Humphreys-Davidson limit, and the final masses of Wolf-Rayet stars, across a range of metallicities. In fact, we developed a method of disentangling the effects of mixing and mass loss in the `Mass-Luminosity Plane’ allowing direct calibration of these processes. In all cases, it is important to note that a combined appreciation for both stellar winds and internal mixing are important to reproduce observations.

Published in IAU Symposium, 2024

How to make an 85 Solar Mass Black Hole

Authors: Ethan Winch, Jorick S. Vink, Erin Higgins, Gautham Sabhahit

We present in-progress resolution test and parameter space studies for very massive stars using MESA, showcasing current MESA version convergence studies.

Published in IAU Symposium, 2024

On the Z-(in)dependence of the Humphreys-Davidson Limit

Authors: Gautham N. Sabhahit, Jorick S. Vink, Erin R. Higgins, Andreas A. C. Sander

The temperature independent part of the Humphreys-Davidson (HD) limit sets the boundary for 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. Recent downward revision of most luminous RSGs the Galaxy below log(L / L_⊙) ≈ 5.5, more in line with the Magellanic Clouds, might hint towards a metallicity (Z)-independent HD limit. We present MESA single star models in the 15-40 M_⊙ range and study the different Z-dependent processes that could potentially affect the location of the upper luminosity limit of RSGs.

Published in IAU Symposium, 2024

Predicting the heaviest black holes below the pair instability gap

Authors: Ethan R. J. Winch, Jorick S. Vink, Erin R. Higgins, Gautham N. Sabhahit

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.

Published in Monthly Notices of the Royal Astronomical Society, 2024

The maximum black hole mass at solar metallicity

Authors: Jorick S. Vink, Gautham N. Sabhahit, Erin R. Higgins

We analyse the 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 produce the most massive BHs, we find that the maximum M_BH^Max ≃ 30 ± 10 M_⊙ is found in the canonical intermediate range between M_ZAMS ≃ 30 and 50 M_⊙ instead. The prime reason for this seemingly counter-intuitive finding is that very massive stars (VMS) have increasingly high mass-loss rates that lead to substantial mass evaporation before they expire as stars and end as lighter BHs than their canonical O-star counterparts.

Published in Astronomy and Astrophysics, 2024

New Wolf-Rayet wind yields and nucleosynthesis of Helium stars

Authors: Erin R. Higgins, Jorick S. Vink, Raphael Hirschi, Alison M. Laird, Andreas A. C. Sander

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 (12–50 M_☉), adopting recent hydrodynamical wind rates. 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, 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 (N_n) of a 30 M_☉ cWR compared with a 32 M_☉ 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(α,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.

Published in Monthly Notices of the Royal Astronomical Society, 2024

Stellar expansion or inflation?

Authors: Gautham N. Sabhahit, Jorick S. Vink

While stellar expansion after core-hydrogen exhaustion related to thermal imbalance has been documented for decades, the physical phenomenon of stellar inflation that occurs close to the Eddington limit has only come to the fore in recent years. We aim to elucidate the differences between these physical mechanisms for stellar radius enlargement, especially given that additional terms such as ‘bloated’ and ‘puffed-up’ stars have been introduced in the recent massive star literature. We employ single and binary star MESA structure and evolution models for constant mass, as well as models allowing the mass to change due to winds or binary interaction. We find cases that were previously attributed to stellar inflation in fact to be due to stellar expansion. We also highlight that while the opposite effect of expansion is contraction, the removal of an inflated zone should not be referred to as contraction but rather deflation, as the star is still in thermal balance.

Published in Astronomy and Astrophysics, 2025

A new mass estimate method with hydrodynamical atmospheres for very massive WNh stars

Authors: Gautham N. Sabhahit, Jorick S. Vink, Andreas A. C. Sander, Matheus Bernini-Peron, Paul A. Crowther, Roel R. Lefever, Tomer Shenar

Very massive stars with masses over 100 M_⊙ are key objects in the Universe for our understanding of chemical and energetic feedback in the Universe, but their evolution and fate are almost entirely determined by their wind mass loss. Here, we aim to determine the mass of the most massive star known in the Local Group R136a1. To this end, we computed the first hydrodynamically consistent non-local thermodynamical equilibrium atmosphere models for R136a1 (WN5h), as well as the binary system R144 (WN5/6h+WN6/7h) in the Tarantula Nebula. Using the Potsdam Wolf–Rayet code, we were able to simultaneously empirically derive and theoretically predict their mass-loss rates and wind velocities. By fitting synthetic spectra derived from these models to multi-wavelength observations, we constrained the stellar and wind properties of R144 and R136a1. We first determined the clumping stratification required by our hydro-models to fit the spectra of R144, using the available dynamical mass estimates for the two components. We then utilised this clumping stratification in hydrodynamic models of R136a1 and estimated a mass of M_Hydro of 233 M_⊙. Remarkably, the estimated mass is close to and fully consistent with chemical homogeneous mass relations. This present-day mass of 233 M_⊙ provides a lower limit to the initial stellar mass, which could be far higher due to previous wind mass loss.

Published in Astronomy and Astrophysics, 2025

The black hole - pair instability boundary for high stellar rotation

Authors: Ethan R. J. Winch, Gautham N. Sabhahit, Jorick S. Vink, Erin R. Higgins

The Pair Instability (PI) boundary is crucial for understanding heavy merging Black Holes (BHs) and the second mass gap’s role in galactic chemical evolution. So far, no works have critically and systematically examined how rotation and mass loss affect the PI boundary or BH masses below it. Rapid rotation significantly alters stellar structure and mass loss, which is expected to have significant effects on the evolution of stellar models. We have previously derived a critical core mass independent of stellar evolution parameters, finding the BH (Pulsational) PI boundary at M_{CO, crit} = 36.3M_⊙ for a carbon-oxygen (CO) core. Using MESA, we model massive stars around the PI boundary for varying rotation rates and metallicities. We implement mechanical mass loss in MESA, studying its effects on massive stars in low-metallicity environments. Below 1/100th Z_⊙, mechanical mass loss dominates over radiative winds. We check the BH-PI boundary for rapid rotators to confirm our critical core mass criterion and derive model fits describing rotationâs impact on core and final masses. Fast rotators reach a point (typically Ω/Ω_crit ≈ 0.6) where the entire star becomes chemically homogeneous, evolving like a stripped star. This lowers the maximum BH mass before PI to its critical core mass of M_{CO, crit} = 36.3M_⊙, aligning with the bump feature in the BH mass distribution observed by LIGO/VIRGO.

Published in Monthly Notices of the Royal Astronomical Society, 2025

The impact of wind mass loss on nucleosynthesis and yields of very massive stars at low metallicity

Authors: Erin R. Higgins, Jorick S. Vink, Raphael Hirschi, Alison M. Laird, Gautham N. Sabhahit

The chemical feedback from stellar winds in low metallicity (Z) environments is key for understanding the evolution of globular clusters and the early Universe. With disproportionate mass lost from the most massive stars (M > 100M_⊙ ), and an excess of such stars expected at the lowest metallicities, their contribution to the enrichment of the early pristine clusters could be significant. In this work, we examine the effect of mass loss at low metallicity on the nucleosynthesis and wind yields of (very) massive stars. We calculate stellar models with initial masses ranging from 30 to 500M_⊙ during core Hydrogen and Helium burning phases, at four metallicities ranging from 20% Z_⊙ down to 1% Z_⊙ . The ejected masses and net yields are provided for each grid of models. While mass-loss rates decrease with Z, we find that not only are wind yields significant, but the nucleosynthesis is also altered due to the change in central temperatures and therefore also plays a role. We find that 80-300M_⊙ models can produce large quantities of Na-rich and O-poor material, relevant for the observed Na-O anti-correlation in globular clusters.

Published in arXiv e-prints, 2025