Mass loss and the Eddington parameter: a new mass-loss recipe for hot and massive stars

Mass loss through stellar winds plays a dominant role in the evolution of massive stars. In particular, the mass-loss rates of very massive stars (⁠>100M⊙⁠) are highly uncertain. Such stars display Wolf–Rayet spectral morphologies (WNh), whilst on the main sequence. Metal-poor very massive stars are progenitors of gamma-ray bursts and pair instability supernovae. In this study, we extended the widely used stellar wind theory by Castor, Abbott & Klein from the optically thin (O star) to the optically thick main-sequence (WNh) wind regime. In particular, we modify the mass-loss rate formula in a way that we are able to explain the empirical mass-loss dependence on the Eddington parameter (Γe). The new mass-loss recipe is suitable for incorporation into current stellar evolution models for massive and very massive stars. It makes verifiable predictions, namely how the mass-loss rate scales with metallicity and at which Eddington parameter the transition from optically thin O star to optically thick WNh star winds occurs. In the case of the star cluster R136 in the Large Magellanic Cloud we find in the optically thin wind regime M˙∝Γ3e⁠, while in the optically thick wind regime M˙∝1/(1−Γe)3.5⁠. The transition from optically thin to optically thick winds occurs at Γe, trans ≈ 0.47. The transition mass-loss rate is logM˙ (M⊙yr−1)≈−4.76±0.18⁠, which is in line with the prediction by Vink & Gräfener assuming a volume filling factor of fV=0.23+0.40−0.15⁠

Massive main-sequence stars evolving at the Eddington limit

Context. Massive stars play a vital role in the Universe, however, their evolution even on the main-sequence is not yet well understood. Aims. Because of the steep mass-luminosity relation, massive main-sequence stars become extremely luminous. This brings their envelopes very close to the Eddington limit. We analyse stellar evolutionary models in which the Eddington limit is reached and exceeded, explore the rich diversity of physical phenomena that take place in their envelopes, and investigate their observational consequences. Methods. We use published grids of detailed stellar models, computed with a state-of-the-art, one-dimensional hydrodynamic stellar evolution code using LMC composition, to investigate the envelope properties of core hydrogen burning massive stars. Results. We find that the Eddington limit is almost never reached at the stellar surface, even for stars up to 500 M⊙. When we define an appropriate Eddington limit locally in the stellar envelope, we can show that most stars more massive than ~40 M⊙ actually exceed this limit, in particular, in the partial ionisation zones of iron, helium, or hydrogen. While most models adjust their structure such that the local Eddington limit is exceeded at most by a few per cent, our most extreme models do so by a factor of more than seven. We find that the local violation of the Eddington limit has severe consequences for the envelope structure, as it leads to envelope inflation, convection, density inversions, and, possibly to, pulsations. We find that all models with luminosities higher than 4 × 105L⊙, i.e. stars above ~40 M⊙ show inflation, with a radius increase of up to a factor of about 40. We find that the hot edge of the S Dor variability region coincides with a line beyond which our models are inflated by more than a factor of two, indicating a possible connection between S Dor variability and inflation. Furthermore, our coolest models show highly inflated envelopes with masses of up to several solar masses, and appear to be candidates for producing major luminous blue variable eruptions. Conclusions. Our models show that the Eddington limit is expected to be reached in all stars above ~40 M⊙ in the LMC, even in lower mass stars in the Galaxy, or in close binaries or rapid rotators. While our results do not support the idea of a direct super-Eddington wind driven by continuum photons, the consequences of the Eddington limit in the form of inflation, pulsations and possibly eruptions may well give rise to a significant enhancement of the time averaged mass-loss rate

Line luminosities of Galactic and Magellanic Cloud Wolf–Rayet stars

We provide line luminosities and spectroscopic templates of prominent optical emission lines of 133 Galactic Wolf–Rayet (WR) stars by exploiting Gaia DR3 parallaxes and optical spectrophotometry, and provide comparisons with 112 counterparts in the Magellanic Clouds. Average line luminosities of the broad blue (He II λ4686, C III λλ4647,51, N III λλ4634,41, and N V λλ4603,20) and yellow (C IV λλ5801,12) emission features for WN, WN/C, WC, and WO stars have application in characterizing the WR populations of star-forming regions of distant, unresolved galaxies. Early-type WN stars reveal lower line luminosities in more metal-poor environments, but the situation is less clear for late-type WN stars. LMC WC4–5 line luminosities are higher than their Milky Way counterparts, with line luminosities of Magellanic Cloud WO stars higher than Galactic stars. We highlight other prominent optical emission lines, N IV λλ3478,85 for WN and WN/C stars, O IV λλ3403,13 for WC and WO stars, and O VI λλ3811,34 for WO stars. We apply our calibrations to representative metal-poor and metal-rich WR galaxies, IC 4870 and NGC 3049, respectively, with spectral templates also applied based on a realistic mix of subtypes. Finally, the global blue and C IV λλ5801,12 line luminosities of the Large Magellanic Clouds or LMCs (Small Magellanic Clouds) are 2.6 × 1038 erg s−1 (9 × 1036 erg s−1) and 8.8 × 1037 erg s−1 (4 × 1036 erg s−1), respectively, with the cumulative WR line luminosity of the Milky Way estimated to be an order of magnitude higher than the LMC

Discovery of a new Galactic bona fide luminous blue variable with Spitzer

We report the discovery of a circular mid-infrared shell around the emission-line star Wray 16- 137 using archival data of the Spitzer Space Telescope. Follow-up optical spectroscopy of Wray 16-137 with the Southern African Large Telescope revealed a rich emission spectrum typical of the classical luminous blue variables (LBVs) like P Cygni. Subsequent spectroscopic and photometric observations showed drastic changes in the spectrum and brightness during the last three years, meaning that Wray 16-137 currently undergoes an S Dor-like outburst. Namely, we found that the star has brightened by ≈1 mag in the V and Ic bands, while its spectrum became dominated by Fe II lines. Taken together, our observations unambiguously show that Wray 16-137 is a new member of the family of Galactic bona fide LBVs

Spectroscopic analysis of hot, massive stars in large spectroscopic surveys with de-idealized models

Upcoming large-scale spectroscopic surveys with e.g. WEAVE (William herschel telescope Enhanced Area Velocity Explorer) and 4MOST (4-metre Multi-Object Spectroscopic Telescope) will provide thousands of spectra of massive stars, which need to be analysed in an efficient and homogeneous way. Usually, studies of massive stars are limited to samples of a few hundred objects, which pushes current spectroscopic analysis tools to their limits because visual inspection is necessary to verify the spectroscopic fit. Often uncertainties are only estimated rather than derived and prior information cannot be incorporated without a Bayesian approach. In addition, uncertainties of stellar atmospheres and radiative transfer codes are not considered as a result of simplified, inaccurate, or incomplete/missing physics or, in short, idealized physical models. Here, we address the question of ‘How to compare an idealized model of complex objects to real data?’ with an empirical Bayesian approach and maximum a posteriori approximations. We focus on application to large-scale optical spectroscopic studies of complex astrophysical objects like stars. More specifically, we test and verify our methodology on samples of OB stars in 30 Doradus region of the Large Magellanic Clouds using a grid of FASTWIND model atmospheres. Our spectroscopic model de-idealization analysis pipeline takes advantage of the statistics that large samples provide by determining the model error to account for the idealized stellar atmosphere models, which are included into the error budget. The pipeline performs well over a wide parameter space and derives robust stellar parameters with representative uncertainties

Oxygen abundance of γ Vel from [O III] 88 μm Herschel/PACS spectroscopy

We present Herschel PACS spectroscopy of the [O III] 88.4 μm fine-structure line in the nearby WC8+O binary system γ Vel to determine its oxygen abundance. The critical density of this line corresponds to several 105R∗ such that it is spatially extended in PACS observations at the 336 pc distance to γ Vel. Two approaches are used, the first involving a detailed stellar atmosphere analysis of γ Vel using CMFGEN, extending to Ne ∼ 100 cm−3 in order to fully sample the line formation region of [O III] 88.4 μm. The second approach involves the analytical model introduced by Barlow et al. and revised by Dessart et al., additionally exploiting ISO LWS spectroscopy of [O III] 51.8 μm. We obtain higher luminositiesfor the WR and O components of γ Vel with respect to De Marco et al., log L/L⊙ = 5.31 and 5.56, respectively, primarily due to the revised (higher) interferometric distance. We obtain an oxygen mass fraction of XO = 1.0 ± 0.3 per cent for an outer wind volume filling factor of f = 0.5 ± 0.25, favouring either standard or slightly reduced Kunz et al. rates for the 12C(α, γ ) 16O reaction from comparison with BPASS binary population synthesis models. We also revisit neon and sulphur abundances in the outer wind of γ Vel from ISO SWS spectroscopy of [S IV] 10.5 μm, [Ne II] 12.8 μm, and [Ne III] 15.5 μm. The inferred neon abundance XNe = 2.0+0.4 −0.6 per cent is in excellent agreement with BPASS predictions, while the sulphur abundance of XS = 0.04 ± 0.01 per cent agrees with the solar abundance, as expected for unprocessed elements

Summary of IAU GA SpS 5 II: Stellar and Wind Parameters

The development of infrared observational facilities has revealed a number of massive stars in obscured environments throughout the Milky Way and beyond. The determination of their stellar and wind properties from infrared diagnostics is thus required to take full advantage of the wealth of observations available in the near and mid infrared. However, the task is challenging. This session addressed some of the problems encountered and showed the limitations and successes of infrared studies of massive stars

The R136 star cluster dissected with Hubble Space Telescope/STIS. II. Physical properties of the most massive stars in R136

We present an optical analysis of 55 members of R136, the central cluster in the Tarantula Nebula of the Large Magellanic Cloud. Our sample was observed with STIS aboard the Hubble Space Telescope, is complete down to about 40 M⊙, and includes 7 very massive stars with masses over 100 M⊙. We performed a spectroscopic analysis to derive their physical properties. Using evolutionary models we find that the initial mass function (IMF) of massive stars in R136 is suggestive of being top-heavy with a power-law exponent γ ≈ 2 ± 0.3, but steeper exponents cannot be excluded. The age of R136 lies between 1 and 2 Myr with a median age of around 1.6 Myr. Stars more luminous than log L/L⊙ = 6.3 are helium enriched and their evolution is dominated by mass loss, but rotational mixing or some other form of mixing could be still required to explain the helium composition at the surface. Stars more massive than 40 M⊙ have larger spectroscopic than evolutionary masses. The slope of the wind-luminosity relation assuming unclumped stellar winds is 2.41 ± 0.13 which is steeper than usually obtained (∼1.8). The ionising (log Q0 [ph/s] = 51.4) and mechanical (log LSW [erg/s] = 39.1) output of R136 is dominated by the most massive stars (>100 M⊙). R136 contributes around a quarter of the ionising flux and around a fifth of the mechanical feedback to the overall budget of the Tarantula Nebula. For a census of massive stars of the Tarantula Nebula region we combined our results with the VLT-FLAMES Tarantula Survey plus other spectroscopic studies. We observe a lack of evolved Wolf-Rayet stars and luminous blue and red supergiants

Weighing Melnick 34: the most massive binary system known

Here, we confirm Melnick 34, an X-ray bright star in the 30 Dor region of the Large Magellanic Cloud, as an SB2 binary comprising WN5h + WN5h components. We present orbital solutions using 26 epochs of VLT/UVES spectra and 22 epochs of archival Gemini/GMOS spectra. Radial velocity monitoring and automated template-fitting methods both reveal a similar high-eccentricity system with a mass ratio close to unity, and an orbital period in agreement with the 155.1 ± 1 d X-ray light-curve period previously derived by Pollock et al. Our favoured solution derived an eccentricity of 0.68 ± 0.02 and mass ratio of 0.92 ± 0.07, giving minimum masses of MAsin3(i) = 65 ± 7 M⊙ and MBsin3(i) = 60 ± 7 M⊙. Spectral modelling using WN5h templates with cmfgen reveals temperatures of T ∼ 53 kK for each component and luminosities of log(LA/L⊙) = 6.43 ± 0.08 and log(LB/L⊙) = 6.37 ± 0.08, from which BONNSAI evolutionary modelling gives masses of MA = 139+21−18 M⊙ and MB = 127+17−17 M⊙ and ages of ∼0.6 Myr. Spectroscopic and dynamic masses would agree if Mk34 has an inclination of i ∼ 50°, making Mk34 the most massive binary known and an excellent candidate for investigating the properties of colliding wind binaries. Within 2–3 Myr, both components of Mk34 are expected to evolve to stellar mass black holes, which, assuming the binary system survives, would make Mk34 a potential binary black hole merger progenitor and a gravitational wave source

GRAVITY Spectro-interferometric Study of the Massive Multiple Stellar System HD 93206 A

Characterization of the dynamics of massive star systems and the astrophysical properties of the interacting components are a prerequisite for understanding their formation and evolution. Optical interferometry at milliarcsecond resolution is a key observing technique for resolving high-mass multiple compact systems. Here, we report on Very Large Telescope Interferometer/GRAVITY, Magellan/Folded-port InfraRed Echellette, and MPG2.2 m/FEROS observations of the late-O/early-B type system HD 93206 A, which is a member of the massive cluster Collinder 228 in the Carina nebula complex. With a total mass of about $90\,{M}_{\odot }$, it is one of the most compact massive quadruple systems known. In addition to measuring the separation and position angle of the outer binary Aa–Ac, we observe Brγ and He i variability in phase with the orbital motion of the two inner binaries. From the differential phase (${{\rm{\Delta }}}_{\phi }$) analysis, we conclude that the Brγ emission arises from the interaction regions within the components of the individual binaries, which is consistent with previous models for the X-ray emission of the system based on wind–wind interaction. With an average 3σ deviation of ${{\rm{\Delta }}}_{\phi }\sim 15^\circ$, we establish an upper limit of p ~ 0.157 mas (0.35 au) for the size of the Brγ line-emitting region. Future interferometric observations with GRAVITY using the 8 m Unit Telescopes will allow us to constrain the line-emitting regions down to angular sizes of 20 μas (0.05 au at the distance of the Carina nebula)