arXiv subjects

S. A. Brands

Publications and source records attributed to S. A. Brands.

16 recordsLinked to original sources

arXiv2026

X-Shooting ULLYSES: Massive stars at low metallicity XV. On the metallicity dependence of B-supergiant mass-loss rates

Context. For stellar evolution models we rely on mass-loss rate prescriptions that show features that lack empirical confirmation, such as the bi-stability jump. This jump is an increase in mass loss in the decreasing temperature regime Teff 28-21 kK. Although papers compared empirical results to prescriptions,a large observational sample of B stars for which the wind has been scrutinised over different metallicities is still lacking. Aims. By modelling of both ultraviolet (ULLYSES) and optical (XShootU) spectra, we determined the stellar and wind parameters, of 24 SMC B stars ranging in Teff from 13 to 29 kK. By combining this sample with LMC studies, we compared the wind behaviour of B stars in two different metallicity regimes. We compared our results to common mass-loss rate prescriptions to test features present in these models and their metallicity dependence. Methods. We have used the model atmosphere code fastwind and the genetic algorithm code Kiwi-GA to fit the UV and optical spectra simultaneously. This allows us to determine wind properties including clumping behaviour. Results. The metallicity trends present in the mass-loss prescriptions (Z^(0.41-1.4)) explored here overestimate the empirical metallicity dependence in the B-star regime, which appears very weak. We do not find an increase in mass-loss rate at approximately spectral type B1. We show that on average 40% of the wind mass is located in the wind medium between the clumps. We compiled a sample of 80+ O and B stars in the SMC and LMC. From a comparison we find a clear difference in O- and B-type metallicity dependence. Conclusions. The lack of a bi-stability jump in the B-star regime and a weak metallicity dependence for the same stars offers new empirical constraints to models of line-driven winds. As differences between these models are large (reaching orders of magnitude) such constraints are much needed.

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arXiv2025

Evolutionary models for the Very Massive Stars in the R136 cluster of 30 Doradus in the Large Magellanic Cloud

The cluster R136 in the LMC contains a population of stars in excess of 100 M$_\odot$, including R136a1, the most massive star known. Very Massive Stars (VMSs) play an influential role in feedback processes and may potentially produce exotic supernova types and black holes of tens of solar masses. The evolutionary history and final fate of the three most luminous stars, R136a1, R136a2, and R136a3, has been a puzzling issue. We aim to resolve this by rotating single-star MESA models. We produce interpolated model grids and apply a Markov-Chain Monte Carlo analysis to compare our models with observations. The nature of supernova progenitors strongly depends on mass loss and the AM coupling schemes. We predict no pair-instability and no GRB progenitors from our fiducial model grid at LMC metallicity. The onset of Wolf-Rayet-type mass-loss rates on the main sequence leads to a rapid decrease in stellar mass and luminosity. The mass turnover implies that the evolutionary history can only be inferred if additional constraints are available. We utilise the surface helium abundance, which poses a conundrum: R136a1, the most luminous star, is less enriched in helium than R136a2 and R136a3. We propose that this can be explained if both R136a2 and R136a3 were initially more massive than R136a1. From a rigorous confrontation of our models to spectroscopically-derived observables, we estimate an initial mass of 346$\pm41$ M$_\odot$ for R136a1, and $\gtrsim$500 M$_\odot$ for R136a2 and R136a3. Even though VMSs are only present in the youngest clusters below 2 Myr of age, our study strengthens their role in local and galaxy evolution. At LMC metallicity, they will be observable as helium-enriched massive stars after their drastic mass loss, produced via single-star evolution. If the core collapse leads to a supernova, it will be of Type Ib/c. [abridged]

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arXiv2025

X-Shooting ULLYSES: Massive Stars at Low Metallicity: XI. Pipeline-determined Physical Properties of Magellanic Cloud OB Stars

The proximity & low dust extinction of the Magellanic Clouds provides an ideal environment for metal-poor massive stars to be studied in detail. The HST ULLYSES initiative has provided exquisite ultraviolet spectroscopy of a large sample of OB stars in the Magellanic Clouds, and its legacy value has been enhanced through the acquisition of optical VLT/XShooter spectroscopy (XShootU). We aim to determine the spectral types and physical properties of 122 LMC & 103 SMC OB stars observed via XShootU. Physical parameters are required for these to serve as templates in spectral libraries of metal poor massive stars. We also aim to identify double-lined binaries and OeBe stars for which analysis requires non-standard treatment. We apply a pipeline designed to analyse large spectroscopic samples of hot luminous stars to XShootU spectroscopic datasets, together with grids of synthetic model spectra computed with the non-LTE atmospheric code fastwind at LMC & SMC metallicities. We determine physical and wind properties of 97 LMC & 77 SMC massive stars, ranging from O2 to B9 subtypes, representing the majority of the XShootU OB sample (OeBe & candidate SB2 systems are excluded). Results are broadly in agreement with previous optical spectroscopic studies, with evolutionary masses spanning 12-117 Msun in the LMC & 11-74 Msun in the SMC. We determine a revised Teff-spectral type calibration for Magellanic Cloud stars, identify stars with peculiar radial velocities, and compare wind properties of high luminosity O stars with dense winds, revealing ~0.27 dex higher wind momenta of LMC stars with respect to SMC counterparts. Incorporating the recent empirical metallicity dependence of Z^0.22 for wind velocities, this suggests a mass-loss dependence of Z^0.5 for luminous O stars. Studies incorporating ultraviolet mass-loss diagnostics are required for OB stars with weak winds and/or low luminosities.

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arXiv2024

X-Shooting ULLYSES: Massive stars at low metallicity VI. Atmosphere and mass-loss properties of O-type giants in the Small Magellanic Cloud

Mass loss through a stellar wind is an important physical process that steers the evolution of massive stars and controls the properties of their end-of-life products, such as the supernova type and the mass of compact remnants. For an accurate mass loss determination, the inhomogeneities in the wind, known as clumping, needs to be taking into account. We aim to improve empirical estimates of mass loss and wind clumping for hot main-sequence massive stars, study the dependence of both properties on the metallicity, and compare the theoretical predictions to our findings. We analyzed the optical and UV spectra of 13 O-type stars in the Small Magellanic Cloud galaxy, which has a metallicity of $\sim 0.2\,Z_\odot$. We quantified the stellar atmosphere, outflow, and wind-clumping properties. To probe the role of metallicity, we compared our findings to studies of Galactic and Large Magellanic Cloud samples that were analyzed with similar methods. We find significant variations in the wind-clumping properties of the target stars, with clumping starting at flow velocities $0.01 - 0.23$ of the terminal wind velocity and reaching clumping factors $f_{\rm cl} = 2 - 30$. In the luminosity ($\log L / L_{\odot} = 5.0 - 6.0$) and metallicity ($Z/Z_{\odot} = 0.2 - 1$) range we considered, we find that the scaling of the mass loss $\dot{M}$ with metallicity $Z$ varies with luminosity. At $\log L/L_{\odot} = 5.75$, we find $\dot{M} \propto Z^m$ with $m = 1.02 \pm 0.30$, in agreement with pioneering work in the field. For lower luminosities, however, we obtain a significantly steeper scaling of $m > 2$. The monotonically decreasing $m(L)$ behavior adds a complexity to the functional description of the mass-loss rate of hot massive stars. Although the trend is present in the predictions, it is much weaker than we found here.

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arXiv2024

X-Shooting ULLYSES: Massive Stars at low metallicity IX: Empirical constraints on mass-loss rates and clumping parameters for OB supergiants in the Large Magellanic Cloud

Context. Current implementations of mass loss for hot, massive stars in stellar evolution models include a sharp increase in mass loss when blue supergiants become cooler than Teff 20-22kK. This drastic mass-loss jump has been motivated by the potential presence of a so-called bistability ionisation effect, which may occur for line-driven winds in this temperature region due to recombination of important line-driving ions. Aims. We perform quantitative spectroscopy using UV (ULLYSES program) and optical (XShootU collaboration) data for 17 OB-supergiant stars in the LMC (covering the range Teff 14-32kK), deriving absolute constraints on global stellar, wind, and clumping parameters. We examine whether there are any empirical signs of a mass-loss jump in the investigated region, and we study the clumped nature of the wind. Methods. We use a combination of the model atmosphere code fastwind and the genetic algorithm code Kiwi-GA to fit synthetic spectra of a multitude of diagnostic spectral lines in the optical and UV. Results. We find no signs of any upward mass loss jump anywhere in the examined region. Standard theoretical comparison models, which include a strong bistability jump thus severely over predict the empirical mass-loss rates on the cool side of the predicted jump. Additionally, we find that on average about 40% of the total wind mass seems to reside in the diluted medium in between dense clumps. Conclusions. Our derived mass-loss rates suggest that for applications like stellar evolution one should not include a drastic bistability jump in mass loss for stars in the temperature and luminosity region investigated here. The derived high values of interclump density further suggest that the common assumption of an effectively void interclump medium (applied in the vast majority of spectroscopic studies of hot star winds) is not generally valid in this parameter regime.

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arXiv2024

X-Shooting ULLYSES: Massive stars at low metallicity. IV. Spectral analysis methods and exemplary results for O stars

CONTEXT: The spectral analysis of hot, massive stars is a fundamental astrophysical method to obtain their intrinsic properties and their feedback. Quantitative spectroscopy for hot, massive stars requires detailed numerical modeling of the atmosphere and an iterative treatment to obtain the best solution within a given framework. AIMS: We present an overview of different techniques for the quantitative spectroscopy of hot stars employed within the X-Shooting ULLYSES collaboration, from grid-based approaches to tailored fits. By performing a blind test, we gain an overview about the similarities and differences of the resulting parameters. Our study aims to provide an overview of the parameter spread caused by different approaches. METHODS: For three different stars from the sample (SMC O5 star AzV 377, LMC O7 star Sk -69 50, and LMC O9 star Sk -66 171), we employ different atmosphere codes (CMFGEN, Fastwind, PoWR) and strategies to determine their best-fitting model. For our analyses, UV and optical spectra are used to derive the properties with some methods relying purely on optical data for comparison. To determine the overall spectral energy distribution, we further employ additional photometry from the literature. RESULTS: Effective temperatures for each of three sample stars agree within 3 kK while the differences in log g can be up to 0.2 dex. Luminosity differences of up to 0.1 dex result from different reddening assumptions, which seem to be larger for the methods employing a genetic algorithm. All sample stars are nitrogen-enriched. CONCLUSIONS: We find a reasonable agreement between the different methods. Tailored fitting tends to be able to minimize discrepancies obtained with more course or automatized treatments. UV spectral data is essential for the determination of realistic wind parameters. For one target (Sk -69 50), we find clear indications of an evolved status.

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arXiv2024

Properties of intermediate- to high-mass stars in the young cluster M17 -- Characterizing the (pre-)zero-age main sequence

The outcome of the formation of massive stars is an important anchor point in their evolution. It provides insight into the physics of the assembly process, and sets the conditions for stellar evolution. We characterize a population of 18 highly reddened O4.5 to B9 stars in the very young massive star-forming region M17. Their properties allow us to identify the empirical location of the ZAMS, and rotation and mass-loss rate of stars there. We performed quantitative spectroscopic modeling of VLT/X-shooter spectra using NLTE atmosphere code Fastwind and fitting approach Kiwi-GA. The observed SEDs were used to determine the line-of-sight extinction. From a comparison of their positions in the HRD with MIST evolutionary tracks, we inferred the stellar masses and ages. We find an age of $0.4_{-0.2}^{+0.6}$ Myr for our sample, however we also identify a strong relation between the age and the mass of the stars. The extinction towards the sources ranges from $A_V = 3.6$ to 10.6. Stars more massive than 10 M$_{\odot}$ have reached the ZAMS. Their projected ZAMS spin rate distribution extends to 0.3 of the critical velocity; their mass-loss rates agree with those of other main-sequence OB stars. Stars with a mass in the range $3 < M/$M$_{\odot} < 7$ are still on the pre-main sequence (PMS). Evolving their $v \sin i$ to the ZAMS yields values up to $\sim 0.6 v_{\rm crit}$. For PMS stars without disks, we find tentative mass-loss rates up to $10^{-8.5}\,$M$_{\odot}$\,yr$^{-1}$. We constrain the empirical location of the ZAMS for massive ($10 < M/$M$_{\odot} < 50$) stars. The ZAMS rotation rates for intermediate-mass stars are twice as high as for massive stars, suggesting that the angular momentum gain processes differ between the two groups. The relation between the age and mass of the stars suggests a lag in the formation of more massive stars relative to lower mass stars.

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arXiv2024

X-Shooting ULLYSES: Massive stars at low metallicity VII. Stellar and wind properties of B supergiants in the Small Magellanic Cloud

Context. B supergiants (BSGs) represent an important connection between the main sequence and more extreme evolutionary stages of massive stars. Additionally, lying toward the cool end of the hot star regime, determining their wind properties is crucial to constrain the evolution and feedback of massive stars as, for instance, they might manifest the bi-stability jump phenomenon. Aims. We undertake a detailed analysis of a representative sample of 18 Small Magellanic Cloud (SMC) BSGs within the ULLYSES and XShootU datasets. Our UV and optical analysis spans BSGs from B0 to B8 - covering the bi-stability jump region. We aim to evaluate their evolutionary status and verify what their wind properties say about the bi-stability jump in a low-metallicity environment. Methods. We used the CMFGEN to model the spectra and photometry (from UV to infrared) of our sample. We compare our results with different evolutionary models, with previous determinations in the literature of OB stars, and with diverging mass-loss recipes at the bi-stability jump. Additionally, we provide the first BSG models in the SMC including X-rays. Results. (i) Within a single-stellar evolution framework, the evolutionary status of early BSGs seem less clear than that of late BSGs, which agree with H-shell burning models. (ii) UV analysis shows evidence that BSGs contain X-rays in their atmospheres, for which we provide constraints. In general, we find higher X-ray luminosity (close to the standard log(L_X/L) ~ -7) for early BSGs. For cooler BSGs, lower values are preferred, log(L_X/L) ~ -8.5. (iii) The obtained mass-loss rates suggest neither a jump nor a monotonic decrease with temperature. Instead, a rather constant trend is observed, which is at odds with the increase found for Galactic BSGs. (iv) The wind velocity behavior with temperature shows a sharp drop at ~19 kK, similar to what is observed for Galactic BSGs.

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arXiv2024

Empirical mass-loss rates and clumping properties of O-type stars in the LMC

We constrain wind parameters of a sample of 18 O-type stars in the LMC, through analysis with stellar atmosphere and wind models including the effects of optically thick clumping. This allows us to determine the most accurate spectroscopic mass-loss and wind structure properties of massive stars at sub-solar metallicity to date and gain insight into the impact of metallicity on massive stellar winds. Combining high signal to noise (S/N) ratio spectroscopy in the UV and optical gives us access to diagnostics of multiple different physical processes in the stellar wind. We produce synthetic spectra using the stellar atmosphere modelling code FASTWIND, and reproduce the observed spectra using a genetic algorithm based fitting technique. We empirically constrain 15 physical parameters associated with the stellar and wind properties, including temperature, surface gravity, surface abundances, rotation, macroturbulence and wind parameters. We find, on average, mass-loss rates a factor of 4-5 lower than those predicted by Vink et al. 2001, in good agreement with predictions from Bjorklund et al. 2021, and the best agreement with those from Krticka et al. 2018. In the 'weak-wind' regime we find mass-loss rates orders of magnitude below any theoretical predictions. We find a positive correlation of clumping factors (fcl) with effective temperature with an average fcl = 14 +- 8 for the full sample. Above 38 kK an average 46 +- 24% of the wind velocity span is covered by clumps and the interclump density is 10-30% of the mean wind. Below an effective temperature of roughly 38 kK there must be additional light leakage for supergiants. For dwarf stars at low temperatures there is a statistical preference for very low clump velocity spans, however it is unclear if this can be physically motivated as there are no clearly observable wind signatures in UV diagnostics.

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arXiv2024

X-Shooting ULLYSES: Massive stars at low metallicity -- V. Effect of metallicity on surface abundances of O stars

Massive stars rotate faster, on average, than lower mass stars. Stellar rotation triggers hydrodynamical instabilities which transport angular momentum and chemical species from the core to the surface. Models of high-mass stars that include these processes predict that chemical mixing is stronger at lower metallicity. We aim to test this prediction by comparing the surface abundances of massive stars at different metallicities. We performed a spectroscopic analysis of single O stars in the Magellanic Clouds (MCs) based on the ULLYSES and XshootU surveys. We determined the fundamental parameters and helium, carbon, nitrogen, and oxygen surface abundances of 17 LMC and 17 SMC non-supergiant O6-9.5 stars. We complemented these determinations by literature results for additional MCs and also Galactic stars to increase the sample size and metallicity coverage. We investigated the differences in the surface chemical enrichment at different metallicities and compared them with predictions of three sets of evolutionary models. Surface abundances are consistent with CNO-cycle nucleosynthesis. The maximum surface nitrogen enrichment is stronger in MC stars than in Galactic stars. Nitrogen enrichment is also observed in stars with higher surface gravities in the SMC than in the Galaxy. This trend is predicted by models that incorporate chemical transport caused by stellar rotation. The distributions of projected rotational velocities in our samples are likely biased towards slow rotators. A metallicity dependence of surface abundances is demonstrated. The analysis of larger samples with an unbiased distribution of projected rotational velocities is required to better constrain the treatment of chemical mixing and angular momentum transport in massive single and binary stars.

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arXiv2024

X-Shooting ULLYSES: Massive Stars at low metallicity II. DR1: Advanced optical data products for the Magellanic Clouds

Using the medium resolution spectrograph X-shooter, spectra of 235 OB and Wolf-Rayet (WR) stars in sub-solar metallicity environments have been secured. [...]This second paper focuses on the optical observations of 232 Magellanic Clouds targets. It describes the uniform reduction of the UVB (300 - 560 nm) and VIS (550 - 1020 nm) XShootU data as well as the preparation of advanced data products [...] . The data reduction of the raw data is based on the ESO CPL X-shooter pipeline. We paid particular attention to the determination of the response curves [...] We implemented slit-loss correction, absolute flux calibration, (semi-)automatic rectification to the continuum, and a correction for telluric lines. The spectra of individual epochs were corrected for the barycentric motion, re-sampled and co-added, and the spectra from the two arms were merged into a single flux calibrated spectrum covering the entire optical range with maximum signal-to-noise ratio. [...] We provide three types of data products: (i) two-dimensional spectra for each UVB and VIS exposure; (ii) one-dimensional UVB and VIS spectra before and after response-correction, as well as after applying various processing, including absolute flux calibration, telluric removal, normalisation and barycentric correction; and (iii) co-added flux-calibrated and rectified spectra over the full optical range, for which all available XShootU exposures were combined. For many of the targets, the final signal-to-noise ratio per resolution element is above 200 in both the UVB and the VIS co-added spectra. The reduced data and advanced scientific data products will be made available to the community upon publication of this paper. [...]

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arXiv2023

X-Shooting ULLYSES: massive stars at low metallicity. I. Project Description

Observations of individual massive stars, super-luminous supernovae, gamma-ray bursts, and gravitational-wave events involving spectacular black-hole mergers, indicate that the low-metallicity Universe is fundamentally different from our own Galaxy. Many transient phenomena will remain enigmatic until we achieve a firm understanding of the physics and evolution of massive stars at low metallicity (Z). The Hubble Space Telescope has devoted 500 orbits to observe 250 massive stars at low Z in the ultraviolet (UV) with the COS and STIS spectrographs under the ULLYSES program. The complementary ``X-Shooting ULLYSES'' (XShootU) project provides enhanced legacy value with high-quality optical and near-infrared spectra obtained with the wide-wavelength coverage X-shooter spectrograph at ESO's Very Large Telescope. We present an overview of the XShootU project, showing that combining ULLYSES UV and XShootU optical spectra is critical for the uniform determination of stellar parameters such as effective temperature, surface gravity, luminosity, and abundances, as well as wind properties such as mass-loss rates in function of Z. As uncertainties in stellar and wind parameters percolate into many adjacent areas of Astrophysics, the data and modelling of the XShootU project is expected to be a game-changer for our physical understanding of massive stars at low Z. To be able to confidently interpret James Webb Space Telescope (JWST) spectra of the first stellar generations, the individual spectra of low Z stars need to be understood, which is exactly where XShootU can deliver.

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arXiv2023

X-Shooting ULLYSES: Massive stars at low metallicity. III. Terminal wind speeds of ULLYSES massive stars

The winds of massive stars have an impact on stellar evolution and on the surrounding medium. The maximum speed reached by these outflows, the terminal wind speed, is a global wind parameter and an essential input for models of stellar atmospheres and feedback. With the arrival of the ULLYSES programme, a legacy UV spectroscopic survey with HST, we have the opportunity to quantify the wind speeds of massive stars at sub-solar metallicity (in the Large and Small Magellanic Clouds, 0.5Z and 0.2Z) at an unprecedented scale. We empirically quantify the wind speeds of a large sample of OB stars, including supergiants, giants, and dwarfs at sub-solar metallicity. Using these measurements, we investigate trends of terminal wind speed with a number of fundamental stellar parameters, namely effective temperature, metallicity, and surface escape velocity. We empirically determined the terminal wind speed for a sample of 149 OB stars in the Magellanic Clouds either by directly measuring the maximum velocity shift of the absorption component of the Civ 1548-1550 line profile, or by fitting synthetic spectra produced using the Sobolev with exact integration method. Stellar parameters were either collected from the literature, obtained using spectral-type calibrations, or predicted from evolutionary models. We find strong trends of terminal wind speed with effective temperature and surface escape speed when the wind is strong enough to cause a saturated P Cygni profile in Civ 1548-1550. We find evidence for a metallicity dependence on the terminal wind speed proportional to Z^0.22+-0.03 when we compared our results to previous Galactic studies. Our results suggest that effective temperature rather than surface escape speed should be used as a straightforward empirical prediction of terminal wind speed and that the observed metallicity dependence is steeper than suggested by earlier works.

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arXiv2022

Spin-down and reduced mass loss in early-type stars with large-scale magnetic fields

Magnetism can greatly impact the evolution of stars. In some stars with OBA spectral types there is direct evidence via the Zeeman effect for stable, large-scale magnetospheres, which lead to the spin-down of the stellar surface and reduced mass loss. So far, a comprehensive grid of stellar structure and evolution models accounting for these effects was lacking. For this reason, we computed and studied models with two magnetic braking and two chemical mixing schemes in three metallicity environments with the MESA software instrument. We find notable differences between the subgrids, which affects the model predictions and thus the detailed characterisation of stars. We are able to quantify the impact of magnetic fields in terms of preventing quasi-chemically homogeneous evolution and producing slowly-rotating, nitrogen-enriched ("Group 2") stars. Our model grid is fully open access and open source.

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arXiv2022

The effects of surface fossil magnetic fields on massive star evolution: IV. Grids of models at Solar, LMC, and SMC metallicities

Magnetic fields can drastically change predictions of evolutionary models of massive stars via mass-loss quenching, magnetic braking, and efficient angular momentum transport, which we aim to quantify in this work. We use the MESA software instrument to compute an extensive main-sequence grid of stellar structure and evolution models, as well as isochrones, accounting for the effects attributed to a surface fossil magnetic field. The grid is densely populated in initial mass (3-60 M$_\odot$), surface equatorial magnetic field strength (0-50 kG), and metallicity (representative of the Solar neighbourhood and the Magellanic Clouds). We use two magnetic braking and two chemical mixing schemes and compare the model predictions for slowly-rotating, nitrogen-enriched ("Group 2") stars with observations in the Large Magellanic Cloud. We quantify a range of initial field strengths that allow for producing Group 2 stars and find that typical values (up to a few kG) lead to solutions. Between the subgrids, we find notable departures in surface abundances and evolutionary paths. In our magnetic models, chemical mixing is always less efficient compared to non-magnetic models due to the rapid spin-down. We identify that quasi-chemically homogeneous main sequence evolution by efficient mixing could be prevented by fossil magnetic fields. We recommend comparing this grid of evolutionary models with spectropolarimetric and spectroscopic observations with the goals of i) revisiting the derived stellar parameters of known magnetic stars, and ii) observationally constraining the uncertain magnetic braking and chemical mixing schemes.

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arXiv2021

Empirical mass-loss rates and clumping properties of Galactic early-type O supergiants

We investigate the impact of optically thick clumping on stellar wind diagnostics in O supergiants and constrain wind parameters associated with porosity in velocity space. This is the first time the effects of optically thick clumping have been investigated for a sample of massive hot stars, using models including a full optically thick clumping description. We re-analyse spectroscopic observations of a sample of eight O supergiants. Using a genetic algorithm wrapper around the NLTE atmosphere code FASTWIND we obtain simultaneous fits to optical and UV spectra and determine photospheric and wind properties and surface abundances. We provide empirical constraints on a number of wind parameters including the clumping factors, mass-loss rates and terminal wind velocities. Additionally, we establish the first systematic empirical constraints on velocity filling factors and interclump densities. These parameters describe clump distribution in velocity-space and density of the interclump medium in physical-space, respectively. We observe a mass-loss rate reduction of a factor of 3.6 compared to theoretical predictions from Vink et al. (2000), and mass-loss rates within a factor 1.4 of predictions from Björklund et al. (2021). We confirm that including optically thick clumping allows simultaneous fitting of recombination lines and resonance lines, including the unsaturated UV phosphorus lines (Pv 1118-1128), without reducing the phosphorus abundance. We find that, on average, half of the wind velocity field is covered by dense clumps. We also find that these clumps are 25 times denser than the average wind, and that the interclump medium is 3-10 times less dense than the mean wind. The former result agrees well with theoretical predictions, the latter suggests that lateral filling-in of radially compressed gas might be critical for setting the scale of the rarefied interclump matter.

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