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A. de Koter

Publications and source records attributed to A. de Koter.

At least 55 records · Page 3Linked to original sources

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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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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Method and new tabulations for flux-weighted line-opacity and radiation line-force in supersonic media

In accelerating and supersonic media, the interaction of photons with spectral lines can be of ultimate importance. However, fully accounting for such line forces currently can only be done by specialised codes in 1-D steady-state flows. More general cases and higher dimensions require alternative approaches. We presented a comprehensive and fast method for computing the radiation line-force using tables of spectral line-strength distribution parameters, which can be applied in arbitrary (multi-D, time-dependent) simulations, including those accounting for the line-deshadowing instability, to compute the appropriate opacities. We assumed local thermodynamic equilibrium to compute a flux-weighted line opacity from $>4$ million spectral lines. We derived the spectral line strength and tabulated the corresponding line-distribution parameters for a range of input densities $ρ\in[10^{-20},10^{-10}]gcm^{-3}$ and temperatures $T\in[10^4,10^{4.7}]K$. We found that the variation of the line distribution parameters plays an essential role in setting the wind dynamics in our models. In our benchmark study, we also found a good overall agreement between the O-star mass-loss rates of our models and those derived from steady-state studies using more detailed radiative transfer. Our models reinforce that self-consistent variation of the line-distribution parameters is important for the dynamics of line-driven flows. Within a well-calibrated O-star regime, our results support the proposed methodology. In practice, utilising the provided tables, yielded a factor $>100$ speed-up in computational time compared to specialised 1-D model-atmosphere codes of line-driven winds, which constitutes an important step towards efficient multi-D simulations. We conclude that our method and tables are ready to be exploited in various radiation-hydrodynamic simulations where the line force is important.

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Stellar mergers as the origin of the blue main-sequence band in young star clusters

Recent high-quality Hubble Space Telescope (HST) photometry shows that the main sequences (MS) stars of young star clusters form two discrete components in the color-magnitude diagram (CMD). Based on their distribution in the CMD, we show that stars of the blue MS component can be understood as slow rotators originating from stellar mergers. We derive the masses of the blue MS stars, and find that they follow a nearly flat mass function, which supports their unusual formation path. Our results imply that the cluster stars gain their mass in two different ways, by disk accretion leading to rapid rotation, contributing to the red MS, or by binary merger leading to slow rotation and populating the blue MS. We also derive the approximate merger time of the individual stars of the blue MS component, and find a strong early peak in the merger rate, with a lower level merger activity prevailing for tens of Myr. This supports recent binary formation models, and explains new velocity dispersion measurements for members of young star clusters. Our findings shed new light on the origin of the bi-modal mass, spin, and magnetic field distributions of main-sequence stars.

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A dusty veil shading Betelgeuse during its Great Dimming

Red supergiants are the most common final evolutionary stage of stars that have initial masses between 8 and 35 times that of the Sun. During this stage, which lasts roughly 100,000 years1, red supergiants experience substantial mass loss. However, the mechanism for this mass loss is unknown. Mass loss may affect the evolutionary path, collapse and future supernova light curve of a red supergiant, and its ultimate fate as either a neutron star or a black hole. From November 2019 to March 2020, Betelgeuse - the second-closest red supergiant to Earth (roughly 220 parsecs, or 724 light years, away) - experienced a historic dimming of its visible brightness. Usually having an apparent magnitude between 0.1 and 1.0, its visual brightness decreased to 1.614 +/- 0.008 magnitudes around 7-13 February 2020 - an event referred to as Betelgeuse's Great Dimming. Here we report high-angular-resolution observations showing that the southern hemisphere of Betelgeuse was ten times darker than usual in the visible spectrum during its Great Dimming. Observations and modelling support a scenario in which a dust clump formed recently in the vicinity of the star, owing to a local temperature decrease in a cool patch that appeared on the photosphere. The directly imaged brightness variations of Betelgeuse evolved on a timescale of weeks. Our findings suggest that a component of mass loss from red supergiants is inhomogeneous, linked to a very contrasted and rapidly changing photosphere

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ATOMIUM: ALMA tracing the origins of molecules in dust forming oxygen rich M-type stars: Motivation, sample, calibration, and initial results

This overview paper presents ATOMIUM, a Large Programme in Cycle 6 with the Atacama Large Millimeter-submillimeter Array (ALMA). The goal of ATOMIUM is to understand the dynamics and the gas phase and dust formation chemistry in the winds of evolved asymptotic giant branch (AGB) and red supergiant (RSG) stars. A more general aim is to identify chemical processes applicable to other astrophysical environments. 17 oxygen-rich AGB and RSG stars spanning a range in (circum)stellar parameters and evolutionary phases were observed in a homogeneous observing strategy allowing for an unambiguous comparison. Data were obtained between 213.83 and 269.71 GHz at high (0.025-0.050 arcsec), medium (0.13-0.24 arcsec), and low (about 1 arcsec) angular resolution. The sensitivity per 1.3 km/s channel was 1.5-5 mJy/beam. 13 molecules were designated as primary molecules in the survey: CO, SiO, AlO, AlOH, TiO, TiO2, HCN, SO, SO2, SiS, CS, H2O, and NaCl. The scientific motivation, survey design, sample properties, data reduction, and an overview of the data products are described; and we highlight one scientific result - the wind kinematics of the ATOMIUM sources. The ATOMIUM sources often have a slow wind acceleration, and a fraction of the gas reaches a velocity which can be up to a factor of two times larger than previously reported terminal velocities assuming isotropic expansion, and the wind kinematic profiles establish that the radial velocity described by the momentum equation for a spherical wind structure cannot capture the complexity of the velocity field. In 15 sources, some molecular transitions other than 12CO v=0 J=2-1 reach a higher outflow velocity, with a spatial emission zone that is often greater than 30 stellar radii, but much less than the extent of CO. Binary interaction with a (sub)stellar companion might (partly) explain the non-monotonic behaviour of the projected velocity field.

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The Tarantula Massive Binary Monitoring V. R 144: a wind-eclipsing binary with a total mass > 140 Msun

R 144 is the visually brightest WR star in the Large Magellanic Cloud (LMC). R 144 was reported to be a binary, making it potentially the most massive binary thus observed. We perform a comprehensive spectral, photometric, orbital, and polarimetric analysis of R 144. R 144 is an eccentric (e=0.51) 74.2-d binary comprising two relatively evolved (age~2 Myr), H-rich WR stars. The hotter primary (WN5/6h, T=50 kK) and the cooler secondary (WN6/7h,T=45kK) have nearly equal masses. The combination of low rotation and H-depletion observed in the system is well reproduced by contemporary evolution models that include boosted mass-loss at the upper-mass end. The systemic velocity of R 144 and its relative isolation suggest that it was ejected as a runaway from the neighbouring R 136 cluster. The optical light-curve shows a clear orbital modulation that can be well explained as a combination of two processes: excess emission stemming from wind-wind collisions and double wind eclipses. Our light-curve model implies an orbital inclination of i=60.4+-1.5deg, resulting in accurately constrained dynamical masses of 74+-4 and 69+-4 Msun. Assuming that both binary components are core H-burning, these masses are difficult to reconcile with the derived luminosities (logL1,2 = 6.44, 6.39 [Lsun]), which correspond to evolutionary masses of the order of 110 and 100Msun, respectively. Taken at face value, our results imply that both stars have high classical Eddington factors of Gamma_e = 0.78+-0.1. If the stars are on the main sequence, their derived radii (~25Rsun) suggest that they are only slightly inflated, even at this high Eddington factor. Alternatively, the stars could be core-He burning, strongly inflated from the regular size of classical Wolf-Rayet stars (~1Rsun), a scenario that could help resolve the observed mass discrepancy.

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ATOMIUM: Halide molecules around the S-type AGB star W Aquilae

S-type asymptotic giant branch (AGB) stars are thought to be intermediates in the evolution of oxygen- to carbon-rich AGB stars. The chemical compositions of their circumstellar envelopes are also intermediate, but have not been studied in as much detail as their carbon- and oxygen-rich counterparts. We aim to determine the abundances of AlCl and AlF from rotational lines, which have been observed for the first time towards an S-type AGB star, W Aql. In combination with models based on PACS observations, we aim to update our chemical kinetics network based on these results. We analyse ALMA observations towards W Aql of AlCl in the ground and first two vibrationally excited states and AlF in the ground vibrational state. Using radiative transfer models, we determine the abundances and spatial abundance distributions of Al$^{35}$Cl, Al$^{37}$Cl, and AlF. We also model HCl and HF emission and compare these models to PACS spectra to constrain the abundances of these species. AlCl is found in clumps very close to the star, with emission confined within 0.1$^{\prime\prime}$ of the star. AlF emission is more extended, with faint emission extending 0.2$^{\prime\prime}$ to 0.6$^{\prime\prime}$ from the continuum peak. We find peak abundances, relative to H$_2$, of $1.7\times 10^{-7}$ for Al$^{35}$Cl, $7\times 10^{-8}$ for Al$^{37}$Cl and $1\times 10^{-7}$ for AlF. From the PACS spectra, we find abundances of $9.7\times 10^{-8}$ and $\leq 10^{-8}$, relative to H$_2$, for HCl and HF, respectively. The AlF abundance exceeds the solar F abundance, indicating that fluorine synthesised in the AGB star has already been dredged up to the surface of the star and ejected into the circumstellar envelope. From our analysis of chemical reactions in the wind, we conclude that AlF may participate in the dust formation process, but we cannot fully explain the rapid depletion of AlCl seen in the wind.

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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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The young massive SMC cluster NGC 330 seen by MUSE II. Multiplicity properties of the massive-star population

Observations of massive stars in young open clusters (< ~8 Myr) have shown that a majority of them are in binary systems, most of which will interact during their life. Populations of massive stars older than ~20 Myr allow us to probe the outcome of such interactions after many systems have experienced mass and angular momentum transfer. Using multi-epoch integral-field spectroscopy, we investigate the multiplicity properties of the massive-star population in NGC 330 (~40 Myr) in the Small Magellanic Cloud to search for imprints of stellar evolution on the multiplicity properties. From six epochs of VLT/MUSE observations supported by adaptive optics we extract spectra and measure radial velocities for stars brighter than F814W = 19. We identify single-lined spectroscopic binaries through significant RV variability as well as double-lined spectroscopic binaries, and quantify the observational biases for binary detection. The observed spectroscopic binary fraction is 13.2+/-2.0 %. Considering period and mass ratio ranges from log(P)=0.15-3.5, and q = 0.1-1.0, and a representative set of orbital parameter distributions, we find a bias-corrected close binary fraction of 34 +8 -7 %. This seems to decline for the fainter stars, which indicates either that the close binary fraction drops in the B-type domain, or that the period distribution becomes more heavily weighted towards longer orbital periods. Both fractions vary strongly in different regions of the color-magnitude diagram which probably reveals the imprint of the binary history of different groups of stars. We provide the first homogeneous RV study of a large sample of B-type stars at a low metallicity. The overall bias-corrected close binary fraction of B stars in NGC 330 is lower than the one reported for younger Galactic and LMC clusters. More data are needed to establish whether this result from an age or a metallicty effect.

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The effects of surface fossil magnetic fields on massive star evolution: III. The case of $τ$ Sco

$τ$ Sco, a well-studied magnetic B-type star in the Upper Sco association, has a number of surprising characteristics. It rotates very slowly and shows nitrogen excess. Its surface magnetic field is much more complex than a purely dipolar configuration which is unusual for a magnetic massive star. We employ the CMFGEN radiative transfer code to determine the fundamental parameters and surface CNO and helium abundances. Then, we employ MESA and GENEC stellar evolution models accounting for the effects of surface magnetic fields. To reconcile $τ$ Sco's properties with single-star models, an increase is necessary in the efficiency of rotational mixing by a factor of 3 to 10 and in the efficiency of magnetic braking by a factor of 10. The spin down could be explained by assuming a magnetic field decay scenario. However, the simultaneous chemical enrichment challenges the single-star scenario. Previous works indeed suggested a stellar merger origin for $τ$ Sco. However, the merger scenario also faces similar challenges as our magnetic single-star models to explain $τ$ Sco's simultaneous slow rotation and nitrogen excess. In conclusion, the single-star channel seems less likely and versatile to explain these discrepancies, while the merger scenario and other potential binary-evolution channels still require further assessment as to whether they may self-consistently explain the observables of $τ$ Sco.

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Analytic, dust-independent mass-loss rates for red supergiant winds initiated by turbulent pressure

Context. Red supergiants are observed to undergo vigorous mass-loss. However, to date, no theoretical model has succeeded in explaining the origins of these objects' winds. This strongly limits our understanding of red supergiant evolution and Type II-P and II-L supernova progenitor properties. Aims. We examine the role that vigorous atmospheric turbulence may play in initiating and determining the mass-loss rates of red supergiant stars. Methods. We analytically and numerically solve the equations of conservation of mass and momentum, which we later couple to an atmospheric temperature structure, to obtain theoretically motivated mass-loss rates. We then compare these to state-of-the-art empirical mass-loss rate scaling formulae as well as observationally inferred mass-loss rates of red supergiants. Results. We find that the pressure due to the characteristic turbulent velocities inferred for red supergiants is sufficient to explain the mass-loss rates of these objects in the absence of the normally employed opacity from circumstellar dust. Motivated by this initial success, we provide a first theoretical and fully analytic mass-loss rate prescription for red supergiants. We conclude by highlighting some intriguing possible implications of these rates for future studies of stellar evolution, especially in light of the lack of a direct dependence on metallicity.

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The inner circumstellar dust of the red supergiant Antares as seen with VLT/SPHERE/ZIMPOL

The processes by which red supergiants lose mass are not fully understood thus-far and their mass-loss rates lack theoretical constraints. The ambient surroundings of the nearby M0.5 Iab star Antares offers an ideal environment to obtain detailed empirical information on the outflow properties at its onset, and hence indirectly, on the mode(s) of mass loss. We present and analyse optical VLT/SPHERE/ZIMPOL polarimetric imaging with angular resolution down to 23 milli-arcsec, sufficient to spatially resolve both the stellar disk and its direct surroundings. We detect a conspicuous feature in polarised intensity that we identify as a clump containing dust, which we characterise through 3D radiative transfer modelling. The clump is positioned behind the plane of the sky, therefore has been released from the backside of the star, and its inner edge is only 0.3 stellar radii above the surface. The current dust mass in the clump is $1.3^{+0.2}_{-1.0} \times 10^{-8}$ M$_{\odot}$, though its proximity to the star implies that dust nucleation is probably still ongoing. The ejection of clumps of gas and dust makes a non-negligible contribution to the total mass lost from the star which could possibly be linked to localised surface activity such as convective motions or non-radial pulsations.

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A relation between the radial velocity dispersion of young clusters and their age: Evidence for hardening as the formation scenario of massive close binaries

The majority of massive stars ($>8$ $\rm{M_{\odot}}$) in OB associations are found in close binary systems. Nonetheless, the formation mechanism of these close massive binaries is not understood yet. Using literature data, we measured the radial-velocity dispersion ($σ_\mathrm{RV}$) as a proxy for the close binary fraction in ten OB associations in the Galaxy and the Large Magellanic Cloud, spanning an age range from 1 to 6 Myrs. We find a positive trend of this dispersion with the cluster's age, which is consistent with binary hardening. Assuming a universal binary fraction of $f_\mathrm{bin}$ = 0.7, we converted the $σ_\mathrm{RV}$ behavior to an evolution of the minimum orbital period $P_\mathrm{cutoff}$ from $\sim$9.5 years at 1 Myr to $\sim$1.4 days for the oldest clusters in our sample at $\sim$6 Myr. Our results suggest that binaries are formed at larger separations, and they harden in around 1 to 2 Myrs to produce the period distribution observed in few million year-old OB binaries. Such an inward migration may either be driven by an interaction with a remnant accretion disk or with other young stellar objects present in the system. Our findings constitute the first empirical evidence in favor of migration as a scenario for the formation of massive close binaries.

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A dearth of young and bright massive stars in the Small Magellanic Cloud

Massive star evolution at low metallicity is closely connected to many fields in high-redshift astrophysics, but poorly understood. The Small Magellanic Cloud (SMC) is a unique laboratory to study this because of its metallicity of 0.2 Zsol, its proximity, and because it is currently forming stars. We used a spectral type catalog in combination with GAIA magnitudes to calculate temperatures and luminosities of bright SMC stars. By comparing these with literature studies, we tested the validity of our method, and using GAIA data, we estimated the completeness of stars in the catalog as a function of luminosity. This allowed us to obtain a nearly complete view of the most luminous stars in the SMC. When then compared with stellar evolution predictions. We also calculated the extinction distribution, the ionizing photon production rate, and the star formation rate. Our results imply that the SMS hosts only 30 very luminous main-sequence stars (M > 40 Msol; L > 10^5 Lsol), which are far fewer than expected from the number of stars in the luminosity range 3*10^4 < L/Lsol < 3*10^5 and from the typically quoted star formation rate in the SMC. Even more striking, we find that for masses above M > 20 Msol, stars in the first half of their hydrogen-burning phase are almost absent. This mirrors a qualitatively similar peculiarity that is known for the Milky Way and Large Magellanic Cloud. This amounts to a lack of hydrogen-burning counterparts of helium-burning stars, which is more pronounced for higher luminosities. We argue that a declining star formation rate or a steep initial mass function are unlikely to be the sole explanations for the dearth of young bright stars. Instead, many of these stars might be embedded in their birth clouds, although observational evidence for this is weak. We discuss implications for cosmic reionization and the top end of the initial mass function.

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Dynamically inflated wind models of classical Wolf-Rayet stars

Vigorous mass loss in the classical Wolf-Rayet (WR) phase is important for the late evolution and final fate of massive stars. We develop spherically symmetric time-dependent and steady-state hydrodynamical models of the radiation-driven wind outflows and associated mass loss from classical WR stars. The simulations are based on combining the opacities typically used in static stellar structure and evolution models with a simple parametrised form for the enhanced line-opacity expected within a supersonic outflow. Our simulations reveal high mass-loss rates initiated in deep and hot optically thick layers around T\approx 200kK. The resulting velocity structure is non-monotonic and can be separated into three phases: i) an initial acceleration to supersonic speeds ii) stagnation and even deceleration, and iii) an outer region of rapid re-acceleration. The characteristic structures seen in converged steady-state simulations agree well with the outflow properties of our time-dependent models. By directly comparing our dynamic simulations to corresponding hydrostatic models, we demonstrate explicitly that the need to invoke extra energy transport in convectively inefficient regions of stellar structure and evolution models is merely an artefact of enforcing a hydrostatic outer boundary. Moreover, the "dynamically inflated" inner regions of our simulations provide a natural explanation for the often-found mismatch between predicted hydrostatic WR radii and those inferred from spectroscopy. Finally, we contrast our simulations with alternative recent WR wind models based on co-moving frame radiative transfer for computing the radiation force. Since CMF transfer currently cannot handle non-monotonic velocity fields, the characteristic deceleration regions found here are avoided in such simulations by invoking an ad-hoc very high degree of clumping.

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(Sub)stellar companions shape the winds of evolved stars

Binary interactions dominate the evolution of massive stars, but their role is less clear for low- and intermediate-mass stars. The evolution of a spherical wind from an asymptotic giant branch (AGB) star into a nonspherical planetary nebula (PN) could be due to binary interactions. We observed a sample of AGB stars with the Atacama Large Millimeter/submillimeter Array (ALMA) and found that their winds exhibit distinct nonspherical geometries with morphological similarities to planetary nebulae (PNe). We infer that the same physics shapes both AGB winds and PNe; additionally, the morphology and AGB mass-loss rate are correlated. These characteristics can be explained by binary interaction. We propose an evolutionary scenario for AGB morphologies that is consistent with observed phenomena in AGB stars and PNe.

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Properties of OB star-black hole systems derived from detailed binary evolution models

The recent gravitational wave measurements have demonstrated the existence of stellar mass black hole binaries. It is essential for our understanding of massive star evolution to identify the contribution of binary evolution to the formation of double black holes. A promising way to progress is investigating the progenitors of double black hole systems and comparing predictions with local massive star samples such as the population in 30 Doradus in the Large Magellanic Cloud (LMC). Methods. To this purpose, we analyse a large grid of detailed binary evolution models at LMC metallicity with initial primary masses between 10 and 40 Msun, and identify which model systems potentially evolve into a binary consisting of a black hole and a massive main sequence star. We then derive the observable properties of such systems, as well as peculiarities of the OB star component. We find that about 3% of the LMC late O and early B stars in binaries are expected to possess a black hole companion, when assuming stars with a final helium core mass above 6.6 M to form black holes. While the vast majority of them may be X-ray quiet, our models suggest that these may be identified in spectroscopic binaries, either by large amplitude radial velocity variations ( > 50 km s ) and simultaneous nitrogen surface enrichment, or through a moderate radial velocity ( > 10 km/s ) and simultaneously rapid rotation of the OB star. The predicted mass ratios are such that main sequence companions could be excluded in most cases. A comparison to the observed OB+WR binaries in the LMC, Be/X-ray binaries, and known massive BH binaries supports our conclusion. We expect spectroscopic observations to be able to test key assumptions in our models, with important implications for massive star evolution in general, and for the formation of double-black hole mergers in particular.

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