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The treatment of convection remains a major weakness in the modelling of stellar evolution with one-dimensional (1D) codes. The ever increasing computing power makes now possible to simulate in 3D part of a star for a fraction of its life, allowing us to study the full complexity of convective zones with hydrodynamics codes. Here, we performed state-of-the-art hydrodynamics simulations of turbulence in a neon-burning convective zone, during the late stage of the life of a massive star. We produced a set of simulations varying the resolution of the computing domain (from 1283 to 10243 cells) and the efficiency of the nuclear reactions (by boosting the energy generation rate from nominal to a factor of 1000). We analysed our results by the mean of Fourier transform of the velocity field, and mean-field decomposition of the various transport equations. Our results are in line with previous studies, showing that the behaviour of the bulk of the convective zone is already well captured at a relatively low resolution (2563), while the details of the convective boundaries require higher resolutions. The different boosting factors used show how various quantities (velocity, buoyancy, abundances, abundance variances) depend on the energy generation rate. We found that for low boosting factors, convective zones are well mixed, validating the approach usually used in 1D stellar evolution codes. However, when nuclear burning and turbulent transport occur on the same timescale, a more sophisticated treatment would be needed. This is typically the case when shell mergers occur., Comment: 17 pages, 20 figures, accepted for publication in MNRAS

A common property of globular clusters (GC) is to host multiple populations characterized by peculiar chemical abundances. Recent photometric studies suggest that the He content could vary between the populations of a GC by up to $\Delta$He $\sim$ 0.13, in mass fraction. The initial He content impacts the evolution of low-mass stars by ultimately modifying their lifetimes, luminosity, temperatures, and, more generally, the morphology of post-RGB evolutionary tracks in the Hertzsprung-Russell diagram. We present new physically accurate isochrones with different initial He-enrichments and metallicities, with a focus on the methods implemented to deal with the post-RGB phases. The isochrones are based on tracks computed with the stellar evolution code STAREVOL for different metallicities (Z = 0.0002, 0.0009, 0.002, and 0.008) and with different He-enrichment (from 0.25 to 0.6 in mass fraction). We describe the effect of He-enrichment on the morphology of the isochrones and test these by comparing the predicted number counts of HB and AGB stars with those of selected GCs. Comparing the number ratios, we find that our new theoretical ones agree with the observed values within $1\sigma$ in most cases. The work presented here sets the ground for future studies on stellar populations in globular clusters, in which the abundances of light elements in He-enhanced models will rely on different assumptions for the causes of this enrichment. The developed methodology permits the computation of isochrones from new stellar tracks with non-canonical stellar processes. The checked number counts ensure that, at least in this reference set, the contribution of the luminous late stages of stellar evolution to the integrated light of a GC is represented adequately., Comment: 15 pages, 12 figures, accepted for publication in Astronomy & Astrophysics

This article presents new colored link invariants by introducing the concepts of multi-quandles and topological multi-quandles.

Classical Be stars are fast rotating, near main sequence B-type stars. The rotation and the presence of circumstellar discs profoundly modify the observables of active Be stars. Our goal is to infer stellar and disc parameters, as well as distance and interstellar extinction, using the currently most favoured physical models for these objects. We present BeAtlas, a grid of 61.600 NLTE radiative transfer models for Be stars, calculated with the HDUST code. The grid was coupled with a Monte Carlo Markov chain code to sample the posterior distribution. We test our method on two well-studied Be stars, $\alpha$ Eri and $\beta$ CMi, using photometric, polarimetric and spectroscopic data as input to the code. We recover literature determinations for most of the parameters of the targets, in particular the mass and age of $\alpha$ Eri, the disc parameters of $\beta$ CMi, and their distances and inclinations. The main discrepancy is that we estimate lower rotational rates than previous works. We confirm previously detected signs of disc truncation in $\beta$ CMi and note that its inner disc seems to have a flatter density slope than its outer disc. The correlations between the parameters are complex, further indicating that exploring the entire parameter space simultaneously is a more robust approach, statistically. The combination of BeAtlas and Bayesian-MCMC techniques proves successful, and a powerful new tool for the field: the fundamental parameters of any Be star can now be estimated in a matter of hours or days.

In addition to being spectacular objects, Very Massive Stars (VMS) are suspected to have a tremendous impact on their environment and on the whole cosmic evolution. The nucleosynthesis both during their advanced stages and their final explosion may contribute greatly to the overall enrichment of the Universe. Their resulting supernovae are candidates for the most superluminous events and their extreme conditions also lead to very important radiative and mechanical feedback effects, from local to cosmic scale. We explore the impact of rotation and metallicity on the evolution of very massive stars across cosmic times. With the recent implementation of an equation of state in the GENEC stellar evolution code, appropriate for describing the conditions in the central regions of very massive stars in the advanced phases, we present new results on VMS evolution from Population III to solar metallicity. Low metallicity VMS models are highly sensitive to rotation, while the evolution of higher metallicity models is dominated by mass loss effects. The mass loss affects strongly their surface velocity evolution, breaking quickly at high metallicity while reaching the critical velocity for low metallicity models. The comparison to observed VMS in the LMC shows that the mass loss prescriptions used for these models are compatible with observed mass loss rates. In our framework for modelling rotation, our models of VMS need a high initial velocity to reproduce the observed surface velocities. The surface enrichment of these VMS is difficult to explain with only one initial composition, and could suggest multiple populations in the R136 cluster. At a metallicity typical of R136, only our non- or slowly rotating VMS models may produce Pair Instability supernovae. The most massive black holes that can be formed are less massive than about 60 M$_\odot$., Comment: 13 pages, 11 figures

Our knowledge of stellar evolution is driven by one-dimensional (1D) simulations. 1D models, however, are severely limited by uncertainties on the exact behaviour of many multi-dimensional phenomena occurring inside stars, affecting their structure and evolution. Recent advances in computing resources have allowed small sections of a star to be reproduced with multi-D hydrodynamic models, with an unprecedented degree of detail and realism. In this work, we present a set of 3D simulations of a convective neon-burning shell in a 20 M$_\odot$ star run for the first time continuously from its early development through to complete fuel exhaustion, using unaltered input conditions from a 321D-guided 1D stellar model. These simulations help answer some open questions in stellar physics. In particular, they show that convective regions do not grow indefinitely due to entrainment of fresh material, but fuel consumption prevails over entrainment, so when fuel is exhausted convection also starts decaying. Our results show convergence between the multi-D simulations and the new 321D-guided 1D model, concerning the amount of convective boundary mixing to include in stellar models. The size of the convective zones in a star strongly affects its structure and evolution, thus revising their modelling in 1D will have important implications for the life and fate of stars. This will thus affect theoretical predictions related to nucleosynthesis, supernova explosions and compact remnants., Comment: 12 pages, 15 figures. Accepted for publication in MNRAS

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., Comment: to appear in "Winds of Stars and Exoplanets" Proceedings IAUS 370, 2022, eds.: A.A. Vidotto, L. Fossati, J.S. Vink

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., Comment: Accepted for publication in MNRAS. A full reproduction package is available on Zenodo at https://doi.org/10.5281/zenodo.7069766

A homology and cohomology theory for topological quandles are introduced. The relation between these (co)homology groups and quandle (co)homology groups are studied. The 1 - topological quandle cocycles are used to compute state sum invariants corresponding to knot diagrams.

Our understanding of stellar structure and evolution coming from one-dimensional (1D) stellar models is limited by uncertainties related to multi-dimensional processes taking place in stellar interiors. 1D models, however, can now be tested and improved with the help of detailed three-dimensional (3D) hydrodynamics models, which can reproduce complex multi-dimensional processes over short timescales, thanks to the recent advances in computing resources. Among these processes, turbulent entrainment leading to mixing across convective boundaries is one of the least understood and most impactful. Here we present the results from a set of hydrodynamics simulations of the neon-burning shell in a massive star, and interpret them in the framework of the turbulent entrainment law from geophysics. Our simulations differ from previous studies in their unprecedented degree of realism in reproducing the stellar environment. Importantly, the strong entrainment found in the simulations highlights the major flaws of the current implementation of convective boundary mixing in 1D stellar models. This study therefore calls for major revisions of how convective boundaries are modelled in 1D, and in particular the implementation of entrainment in these models. This will have important implications for supernova theory, nucleosynthesis, neutron stars and black holes physics., Comment: 7 pages, 6 figures, accepted for publication in MNRAS

The $^{26}$Al short-lived radioactive nuclide is the source of the observed galactic diffuse $\gamma$-ray emission at 1.8 MeV. While different sources of $^{26}$Al have been explored, such as AGB stars, massive stars winds, and supernovae, the contribution of very massive stars has never been studied. We study the stellar wind contribution of very massive stars, i.e stars with initial masses between 150 and 300 M$_\odot$, to the enrichment in $^{26}$Al of the galactic interstellar medium. We discuss the production of $^{26}$Al by studying rotating and non-rotating very massive stellar models with initial masses between 150 and 300 M$_\odot$ for metallicities Z=0.006, 0.014, and 0.020. We confront this result to a simple Milky Way model taking into account both the metallicity and the star formation rate gradients. We obtain that very massive stars in the Z=0.006-0.020 metallicity range might be very significant contributors to the $^{26}$Al enrichment of the interstellar medium. Typically, the contribution of the winds of massive stars to the total quantity of $^{26}$Al in the Galaxy increases by 150\% when very massive stars are considered. Very massive stars, despite their rarity, might be important contributors to $^{26}$Al and overall very important actors for nucleosynthesis in the Galaxy., Comment: 10 pages, 6 figures

Sigma Ori E, a massive helium B-type star, shows a high surface rotation and a strong surface magnetic field potentially challenging the process of wind magnetic braking. The Gaia satellite provides an accurate distance to that star and confirms its membership to the sigma Ori cluster. We account for these two key pieces of information to investigate whether single star models can reproduce the observed properties of sigma Ori E and provide new estimates for its metallicity, mass, and age. We compute rotating stellar models accounting for wind magnetic braking and magnetic quenching of the mass loss. We obtain that sigma Ori E is a very young star (age less than 1 Myr) with an initial mass around 9 Msol, a surface equatorial magnetic field around 7 kG and having a metallicity Z (mass fraction of heavy elements) around 0.020. No solution is obtained with the present models for a metallicity Z=0.014. The initial rotation of the models fitting sigma Ori E is not much constrained and can be anywhere in the range studied in the present work. Because of its very young age, models predict no observable changes of the surface abundances due to rotational mixing. The simultaneous high surface rotation and high surface magnetic field of sigma Ori E may simply be a consequence of its young age. This young age implies that the processes responsible for producing the chemical inhomogeneities that are observed at its surface should be rapid. Thus for explaining the properties of sigma Ori E, there is no necessity to invoke a merging event although such a scenario cannot be discarded. Other stars (HR 5907, HR 7355, HR 345439, HD 2347, CPD -50^{o}3509$) showing similar properties as sigma Ori E (fast rotation and strong surface magnetic field) may also be very young stars, although determination of the braking timescales is needed to confirm such a conclusion., Comment: 13 pages, 8 figures, paper accepted for publication in Astronomy and Astrophysics

3D hydrodynamics models of deep stellar convection exhibit turbulent entrainment at the convective-radiative boundary which follows the entrainment law, varying with boundary penetrability. We implement the entrainment law in the 1D Geneva stellar evolution code. We then calculate models between 1.5 and 60 M$_{\odot}$ at solar metallicity ($Z=0.014$) and compare them to previous generations of models and observations on the main sequence. The boundary penetrability, quantified by the bulk Richardson number, $Ri_{\mathrm{B}}$, varies with mass and to a smaller extent with time. The variation of $Ri_{\mathrm{B}}$ with mass is due to the mass dependence of typical convective velocities in the core and hence the luminosity of the star. The chemical gradient above the convective core dominates the variation of $Ri_{\mathrm{B}}$ with time. An entrainment law method can therefore explain the apparent mass dependence of convective boundary mixing through $Ri_{\mathrm{B}}$. New models including entrainment can better reproduce the mass dependence of the main sequence width using entrainment law parameters $A \sim 2 \times 10^{-4}$ and $n=1$. We compare these empirically constrained values to the results of 3D hydrodynamics simulations and discuss implications., Comment: 14 pages, 11 figures, accepted for publication in MNRAS

Spectroscopic studies of Galactic O and B stars show that many stars with masses above 8 M$_{\odot}$ are observed in the HR diagram just beyond the Main-Sequence (MS) band predicted by stellar models computed with a moderate overshooting. This may be an indication that the convective core sizes in stars in the upper part of the HR diagram are larger than predicted by these models. Combining stellar evolution models and spectroscopic parameters derived for a large sample of Galactic O and B stars, including brand new information about their projected rotational velocities, we reexamine the question of the convective core size in MS massive stars. We confirm that for stars more massive than about 8 M$_{\odot}$, the convective core size at the end of the MS phase increases more rapidly with the mass than in models computed with a constant step overshoot chosen to reproduce the main sequence width in the low mass range (around 2 M$_{\odot}$). This conclusion is valid for both the cases of non-rotating models and rotating models either with a moderate or a strong angular momentum transport. The increase of the convective core mass with the mass obtained from the TAMS position is, however, larger than the one deduced from the surface velocity drop for masses above about 15 M$_{\odot}$. Although observations available at the moment cannot decide what is the best choice between the core sizes given by the TAMS and the velocity drop, we discuss different methods to get out of this dilemma. At the moment, comparisons with eclipsing binaries seem to favor the solution given by the velocity drop. While we confirm the need for larger convective cores at higher masses, we find tensions in-between different methods for stars more massive than 15 M$_{\odot}$. The use of single-aged stellar populations (non-interacting binaries or stellar clusters) would be a great asset to resolve this tension., Comment: 13 pages, 8 figures

The time evolution of angular momentum and surface rotation of massive stars is strongly influenced by fossil magnetic fields via magnetic braking. We present a new module containing a simple, comprehensive implementation of such a field at the surface of a massive star within the Modules for Experiments in Stellar Astrophysics (MESA) software instrument. We test two limiting scenarios for magnetic braking: distributing the angular momentum loss throughout the star in the first case, and restricting the angular momentum loss to a surface reservoir in the second case. We perform a systematic investigation of the rotational evolution using a grid of OB star models with surface magnetic fields ($M_\star=5-60$ M$_\odot$, $\Omega/\Omega_{\rm crit} =0.2-1.0$, $B_{\rm p} =1-20$ kG). We then employ a representative grid of B-type star models ($M_\star=5, 10, 15$ M$_\odot$, $\Omega/\Omega_{\rm crit} =0.2 , 0.5, 0.8$, $B_{\rm p} = 1, 3 ,10, 30$ kG) to compare to the results of a recent self-consistent analysis of the sample of known magnetic B-type stars. We infer that magnetic massive stars arrive at the zero age main sequence with a range of rotation rates, rather than with one common value. In particular, some stars are required to have close-to-critical rotation at the ZAMS. However, magnetic braking yields surface rotation rates converging to a common low value, making it difficult to infer the initial rotation rates of evolved, slowly-rotating stars., Comment: accepted for publication in MNRAS, a zenodo record is available at: https://zenodo.org/record/3250412

We present an extended grid of state-of-the art stellar models for low-mass stars including updated physics (nuclear reaction rates, surface boundary condition, mass-loss rate, angular momentum transport, torque and rotation-induced mixing prescriptions). We aim at evaluating the impact of wind braking, realistic atmospheric treatment, rotation and rotation-induced mixing on the structural and rotational evolution from the pre-main sequence to the turn-off. Using the STAREVOL code, we provide an updated PMS grid. We compute stellar models for 7 different metallicities, from [Fe/H] = -1 dex to [Fe/H] = +0.3 dex with a solar composition corresponding to $Z=0.0134$. The initial stellar mass ranges from 0.2 to 1.5\Ms with extra grid refinement around one solar mass. We also provide rotating models for three different initial rotation rates (slow, median and fast) with prescriptions for the wind braking and disc-coupling timescale calibrated on observed properties of young open clusters. The rotational mixing includes an up-to-date description of the turbulence anisotropy in stably stratified regions. The overall behaviour of our models at solar metallicity -- and its constitutive physics -- is validated through a detailed comparison with a variety of distributed evolutionary tracks. The main differences arise from the choice of surface boundary conditions and initial solar composition. The models including rotation with our prescription for angular momentum extraction and self-consistent formalism for angular momentum transport are able to reproduce the rotation period distribution observed in young open clusters over a broad mass-range. These models are publicly available and may be used to analyse data coming from present and forthcoming asteroseismic and spectroscopic surveys such as Gaia, TESS and PLATO., Comment: 21 pages, 13 figures, accepted in A&A

Grids of stellar models are useful tools to derive the properties of stellar clusters, in particular young clusters hosting massive stars, and to provide information on the star formation process in various mass ranges. Because of their short evolutionary timescale, massive stars end their life while their low-mass siblings are still on the pre-main sequence (pre-MS) phase. Thus the study of young clusters requires consistent consideration of all the phases of stellar evolution. But despite the large number of grids that are available in the literature, a grid accounting for the evolution from the pre-MS accretion phase to the post-MS phase in the whole stellar mass range is still lacking. We build a grid of stellar models at solar metallicity with masses from 0.8 $M_\odot$ to 120 $M_\odot$, including pre-MS phase with accretion. We use the {\sc genec} code to run stellar models on this mass range. The accretion law is chosen to match the observations of pre-MS objects on the Hertzsprung-Russell diagram. We describe the evolutionary tracks and isochrones of our models. The grid is connected to previous MS and post-MS grids computed with the same numerical method and physical assumptions, which provides the widest grid in mass and age to date. Numerical tables of our models and corresponding isochrones are available online.

Surface magnetic fields have a strong impact on stellar mass loss and rotation and, as a consequence, on the evolution of massive stars. In this work we study the influence of an evolving dipolar surface fossil magnetic field with an initial field strength of 4 kG on the characteristics of 15 M$_{\odot}$ solar metallicity models using the Geneva stellar evolution code. Non-rotating and rotating models considering two different scenarios for internal angular momentum transport are computed, including magnetic field evolution, mass-loss quenching, and magnetic braking. Magnetic field evolution results in weakening the initially strong magnetic field, however, in our models an observable magnetic field is still maintained as the star evolves towards the red supergiant phase. At the given initial mass of the models, mass-loss quenching is modest. Magnetic braking greatly enhances chemical element mixing if radial differential rotation is allowed for, on the other hand, the inclusion of surface magnetic fields yields a lower surface enrichment in the case of near solid-body rotation. Models including surface magnetic fields show notably different trends on the Hunter diagram (plotting nitrogen abundance vs $v \sin i$) compared to those that do not. The magnetic models agree qualitatively with the anomalous `Group 2 stars', showing slow surface rotation and high surface nitrogen enhancement on the main sequence., Comment: accepted for publication in MNRAS

Convective boundary mixing is one of the major uncertainties in stellar evolution. In order to study its dependence on boundary properties and turbulence strength in a controlled way, we computed a series of 3D hydrodynamical simulations of stellar convection during carbon burning with a varying boosting factor of the driving luminosity. Our 3D implicit large eddy simulations were computed with the PROMPI code. We performed a mean field analysis of the simulations within the Reynolds-averaged Navier-Stokes framework. Both the vertical RMS velocity within the convective region and the bulk Richardson number of the boundaries are found to scale with the driving luminosity as expected from theory. The positions of the convective boundaries were estimated through the composition profiles across them, and the strength of convective boundary mixing was determined by analysing the boundaries within the framework of the entrainment law. We find that the entrainment is approximately inversely proportional to the bulk Richardson number. Although the entrainment law does not encompass all the processes occurring at boundaries, our results support the use of the entrainment law to describe convective boundary mixing in 1D models, at least for the advanced phases. The next steps and challenges ahead are also discussed., Comment: Accepted for publication in MNRAS

Extended MS turn-offs are features commonly found in the colour-magnitude diagrams of young and intermediate age (less than about 2 Gyr) massive star clusters, where the MS turn-off is broader than can be explained by photometric uncertainties, crowding, or binarity. Rotation is suspected to be the cause of this feature, by accumulating fast rotating stars, strongly affected by gravity darkening and rotation-induced mixing, near the MS turn-off. This scenario successfully reproduces the tight relation between the age and the actual extent in luminosity of the extended MS turn-off of observed clusters. Below a given mass (dependent on the metallicity), stars are efficiently braked early on the MS due to the interaction of stellar winds and the surface magnetic field, making their tracks converge towards those of non-rotating tracks in the HRD. When these stars are located at the turn-off of a cluster, their slow rotation causes the extended MS turn-off feature to disappear. We investigate the maximal mass for which this braking occurs at different metallicities, and determine the age above which no extended MS turn-off is expected in clusters. Our models predict that the extended MS turn-off phenomenon disappears at ages older than about 2 Gyr. There is a trend with the metallicity, the age at which the disappearance occurs becoming older at higher metallicity. These results are robust between the two codes used in this work, despite some differences in the input physics and in particular in the detailed description of rotation-induced internal processes and of angular momentum extraction by stellar winds. Comparing our results with clusters in the LMC and Galaxy shows a very good fit to the observations. This strengthens the rotation scenario to explain the cause of the extended MS turn-off phenomenon., Comment: 7 pages, 4 figures, accepted for publication in A&A

Context: The observations of solar-like oscillations in evolved stars have brought important constraints on their internal rotation rates. To correctly reproduce these data, an efficient transport mechanism is needed in addition to meridional circulation and shear instability. Aims: We study the efficiency of the transport of angular momentum during the subgiant phase. Results: The precise asteroseismic measurements of both core and surface rotation rates available for the six Kepler targets enable a precise determination of the efficiency of the transport of angular momentum needed for each of these subgiants. These results are found to be insensitive to all the uncertainties related to the modelling of rotational effects before the post-main sequence phase. An interesting exception in this context is the case of young subgiants (typical values of log(g) close to 4), because their rotational properties are sensitive to the degree of radial differential rotation on the main sequence. These young subgiants constitute therefore perfect targets to constrain the transport of angular momentum on the main sequence from asteroseismic observations of evolved stars. As for red giants, we find that the efficiency of the additional transport process increases with the mass of the star during the subgiant phase. However, the efficiency of this undetermined mechanism decreases with evolution during the subgiant phase, contrary to what is found for red giants. Consequently, a transport process with an efficiency that increases with the degree of radial differential rotation cannot account for the core rotation rates of subgiants, while it correctly reproduces the rotation rates of red giant stars. This suggests that the physical nature of the additional mechanism needed for the internal transport of angular momentum may be different in subgiant and red giant stars., Comment: 10 pages, 11 figures, accepted for publication in A&A

We present an analysis of the relatively low mass ($\sim2400$~M$_{\odot}$), $\sim800$~Myr, Galactic open cluster, NGC~2818, using Gaia DR2 results combined with VLT/FLAMES spectroscopy. Using Gaia DR2 proper motions and parallax measurements we are able to select a clean sample of cluster members. This cluster displays a clear extended main sequence turn-off (eMSTO), a phenomenon previously studied mainly in young and intermediate age massive clusters in the Magellanic clouds. The main sequence of NGC~2818 is extremely narrow, with a width of $\sim0.01$ magnitudes (G$_{\rm BP} - $ G$_{\rm RP}$), suggesting very low levels of differential extinction. Using VLT/FLAMES spectroscopy of 60 cluster members to measure the rotational velocity of the stars (Vsini) we find that stars on the red side of the eMSTO have high Vsini ($>160$~km/s) while stars on the blue side have low Vsini ($<160$~km/s), in agreement with model predictions. The cluster also follows the previously discovered trend between the age of the cluster and the extent of the eMSTO. We conclude that stellar rotation is the likely cause of the eMSTO phenomenon., Comment: 7 pages, 5 figures, MNRAS in press

We present the initial results of the Large Impact of magnetic Fields on the Evolution of hot stars (LIFE) project. The focus of this project is the search for magnetic fields in evolved OBA giants and supergiants with visual magnitudes between 4 and 8, with the aim to investigate how the magnetic fields observed in upper main sequence (MS) stars evolve from the MS until the late post-MS stages. In this paper, we present spectropolarimetric observations of 15 stars observed using the ESPaDOnS instrument of the CFHT. For each star, we have determined the fundamental parameters and have used stellar evolution models to calculate their mass, age and radius. Using the LSD technique, we have produced averaged line profiles for each star. From these profiles, we have measured the longitudinal magnetic field strength and have calculated the detection probability. We report the detection of magnetic fields in two stars of our sample: a weak field of $B_l=1.0\pm0.2\,$G is detected in the post-MS A5 star 19$\,$Aur and a stronger field of $B_l=-230\,\pm\,10\,$G is detected in the MS/post-MS B8/9 star HR$\,$3042., Comment: 17 pages, 9 figures, accepted for publication in MNRAS

Through the modelling of near-infrared photometry of star plus disk systems with the codes BEDISK/BERAY, we successfully describe the WISE photometric characteristics of Be stars in five young open clusters, NGC 663, NGC 869, NGC 884, NGC 3766 and NGC 4755, broadly studied in the literature. WISE photometry allows previously known Be stars to be detected and to find new Be candidates which could be confirmed spectroscopically. The location of Be stars in the WISE colour-magnitude diagram, separates them in two groups; active (Be stars hosting a developed circumstellar disk) and quiescent objects (Be stars in a diskless phase), and this way, we can explore how often stars are observed in these different stages. The variability observed in most active variable Be stars is compatible with a disk dissipation phase. We find that 50 percent of Be stars in the studied open clusters are in an active phase. We can interpret this as Be stars having a developed circumstellar disk half of the time. The location of Be stars with a developed disk in the CMD require mass loss rates in agreement with values recently reported in the literature. For these objects, we expect to have a tight relation between the equivalent width of the H{\alpha} line and the mass of the disk, if the inclination is known. Also, near-infrared photometry of Be stars in stellar clusters has the potential of being useful to test whether there is a preferential viewing angle., Comment: 25 pages, 14 figures, Accepted for publication in AJ

Massive stars with solar metallicity lose important amounts of rotational angular momentum through their winds. When a magnetic field is present at the surface of a star, efficient angular momentum losses can still be achieved even when the mass-loss rate is very modest, at lower metallicities, or for lower-initial-mass stars. In a close binary system, the effect of wind magnetic braking also interacts with the influence of tides, resulting in a complex evolution of rotation. We study the interactions between the process of wind magnetic braking and tides in close binary systems. We discuss the evolution of a 10 M$_\odot$ star in a close binary system with a 7 M$_\odot$ companion using the Geneva stellar evolution code. The initial orbital period is 1.2 days. The 10 M$_\odot$ star has a surface magnetic field of 1 kG. Various initial rotations are considered. We use two different approaches for the internal angular momentum transport. In one of them, angular momentum is transported by shear and meridional currents. In the other, a strong internal magnetic field imposes nearly perfect solid-body rotation. The evolution of the primary is computed until the first mass-transfer episode occurs. The cases of different values for the magnetic fields and for various orbital periods and mass ratios are briefly discussed. We show that, independently of the initial rotation rate of the primary and the efficiency of the internal angular momentum transport, the surface rotation of the primary will converge, in a time that is short with respect to the main-sequence lifetime, towards a slowly evolving velocity that is different from the synchronization velocity. (abridged)., Comment: 11 pages, 13 figures, accepted for publication in Astronomy and Astrophysics

All ten LIGO/Virgo binary black hole (BH-BH) coalescences reported from the O1/O2 runs have near zero effective spins. There are only three potential explanations of this fact. If the BH spin magnitudes are large then (i) either both BH spin vectors must be nearly in the orbital plane or (ii) the spin angular momenta of the BHs must be oppositely directed and similar in magnitude. Or, (iii) the BH spin magnitudes are small. We test the third hypothesis within the framework of the classical isolated binary evolution scenario of the BH-BH merger formation. We test three models of angular momentum transport in massive stars: a mildly efficient transport by meridional currents (as employed in the Geneva code), an efficient transport by the Tayler-Spruit magnetic dynamo (as implemented in the MESA code), and a very-efficient transport (as proposed by Fuller et al.) to calculate natal BH spins. We allow for binary evolution to increase the BH spins through accretion and account for the potential spin-up of stars through tidal interactions. Additionally, we update the calculations of the stellar-origin BH masses, include revisions to the history of star formation and to the chemical evolution across cosmic time. We find that we can match simultaneously the observed BH-BH merger rate density, BH masses, and effective spins. Models with efficient angular momentum transport are favored. The updated stellar-mass weighted gas-phase metallicity evolution now used in our models appears to be a key in better reproducing the LIGO/Virgo merger rate estimate. Mass losses during the pair-instability pulsation supernova phase are likely overestimated if the merger GW170729 hosts a BH more massive than 50 Msun. We also estimate rate of BH-NS mergers from recent LIGO/Virgo observations. Our updated models of BH-BH, BH-NS and NS-NS mergers are now publicly available at www.syntheticuniverse.org., Comment: A&A accepted: revised comparison with LIGO/Virgo (41 pages)

We study the pulsational properties of rapidly rotating main-sequence B-type stars using linear non-adiabatic analysis of non-radial low-frequency modes taking into account the effect of rotation. We compare the properties of prograde sectoral $g$ and retrograde $r$ modes excited by the $\kappa$ mechanism at the Fe opacity peak with the newly discovered period-luminosity relation that is obeyed by a group of fast-rotating B-type stars in the young open cluster NGC 3766. The observed relation consists of two sequences in the period versus magnitude diagram, at periods shorter than 0.5 days. We find that this property is consistent with similar period-luminosity relations predicted for excited sectoral prograde $g$-modes of azimuthal orders $m=-1$ and $m=-2$ in fast-rotating stars along an isochrone. We further show that some of the rapidly rotating stars that have photometric variability with periods longer than a day may be caused by $r$-mode pulsation predicted to be excited in these stars. One fast-rotating star, in particular, shows both short and long periods that can be explained by the simultaneous excitation of $g$- and $r$-mode pulsations in models of fast-rotating stars., Comment: 11 pages, 10 figures, accepted for publication in MNRAS

Context: Constraints on the internal rotation of red giants are now available thanks to asteroseismic observations. Preliminary comparisons with rotating stellar models indicate that an undetermined additional process for the internal transport of angular momentum is required in addition to purely hydrodynamic processes. Aims: We investigate how asteroseismic measurements of red giants can help us characterize the additional transport mechanism. Methods: We first determine the efficiency of the missing transport mechanism for the low-mass red giant KIC 7341231 by computing rotating models that include an additional viscosity corresponding to this process. We then discuss the change in the efficiency of this transport of angular momentum with the mass, metallicity and evolutionary stage. Results: In the case of the low-mass red giant KIC 7341231, we find that the viscosity corresponding to the additional mechanism is constrained to the range 1 x 10^3 - 1.3 x 10^4 cm^2/s. This constraint on the efficiency of the unknown additional transport mechanism during the post-main sequence is obtained independently of any specific assumption about the modelling of rotational effects during the pre-main sequence and the main sequence (in particular, the braking of the surface by magnetized winds and the efficiency of the internal transport of angular momentum before the post-main-sequence phase). When we assume that the additional transport mechanism is at work during the whole evolution of the star together with a solar-calibrated braking of the surface by magnetized winds, the range of nu_add is reduced to 1 - 4 x 10^3 cm^2/s. In addition to being sensitive to the evolutionary stage of the star, we show that the efficiency of the unknown process for internal transport of angular momentum increases with the stellar mass., Comment: 12 pages, 14 figures, accepted for publication in A&A

Recent photometric analysis of the colour-magnitude diagrams (CMDs) of young massive clusters (YMCs) have found evidence for splitting in the main sequence and extended main sequence turn-offs, both of which have been suggested to be caused by stellar rotation. Comparison of the observed main sequence splitting with models has led various authors to suggest a rather extreme stellar rotation distribution, with a minority ($10-30$\%) of stars with low rotational velocities and the remainder ($70-90$\%) of stars rotating near the critical rotation (i.e., near break-up). We test this hypothesis by searching for Be stars within two YMCs in the LMC (NGC 1850 and NGC 1856), which are thought to be critically rotating stars with decretion disks that are (partially) ionised by their host stars. In both clusters we detect large populations of Be stars at the main sequence turn-off ($\sim30-60$\% of stars), which supports previous suggestions of large populations of rapidly rotating stars within massive clusters., Comment: 6 pages, 3 figures, accepted for publication in MNRAS

$Context.$ Pulsating stars are windows to the physics of stars enabling us to see glimpses of their interior. Not all stars pulsate, however. On the main sequence, pulsating stars form an almost continuous sequence in brightness, except for a magnitude range between $\delta$ Scuti and slowly pulsating B stars. Against all expectations, 36 periodic variables were discovered in 2013 in this luminosity range in the open cluster NGC 3766, the origins of which was a mystery. $Aims.$ We investigate the properties of those new variability class candidates in relation to their stellar rotation rates and stellar multiplicity. $Methods.$ We took multi-epoch spectra over three consecutive nights using ESO's Very Large Telescope. $Results.$ We find that the majority of the new variability class candidates are fast-rotating pulsators that obey a new period-luminosity relation. We argue that the new relation discovered here has a different physical origin to the period-luminosity relations observed for Cepheids. $Conclusions.$ We anticipate that our discovery will boost the relatively new field of stellar pulsation in fast-rotating stars, will open new doors for asteroseismology, and will potentially offer a new tool to estimate stellar ages or cosmic distances., Comment: Accepted for publication in A&A Letters

We present Hubble Space Telescope photometry of NGC1850, a ~100 Myr, ~10^5 Msun cluster in the Large Magellanic Cloud. The colour magnitude diagram clearly shows the presence of an extended main sequence turnoff (eMSTO). The use of non-rotating stellar isochrones leads to an age spread of ~40 Myr. This is in good agreement with the age range expected when the effects of rotation in MSTO stars are wrongly interpreted in terms of age spread. We also do not find evidence for multiple, isolated episodes of star-formation bursts within the cluster, in contradiction to scenarios that invoke actual age spreads to explain the eMSTO phenomenon. NGC 1850 therefore continues the trend of eMSTO clusters where the inferred age spread is proportional to the age of the cluster. While our results confirm a key prediction of the scenario where stellar rotation causes the eMSTO feature, direct measurements of the rotational rate of MSTO stars is required to definitively confirm or refute whether stellar rotation is the origin of the eMSTO phenomenon or if it is due to an as yet undiscovered effect., Comment: MNRAS letters, in press

Key physical ingredients governing the evolution of massive stars are mass losses, convection and mixing in radiative zones. These effects are important both in the frame of single and close binary evolution. The present paper addresses two points: 1) the differences between two families of rotating models, i.e. the family of models computed with and without an efficient transport of angular momentum in radiative zones; 2) The impact of the mass losses in single and in close binary models., Comment: 5 pages, 4 figures, to appear in the proceedings of the international Wolf-Rayet stars workshop held in Potsdam (2015)

We present late-time Hubble Space Telescope (HST) ultraviolet (UV) and optical observations of the site of SN 2011dh in the galaxy M51, ~1164 days post-explosion. At the SN location, we observe a point source that is visible at all wavelengths, that is significantly fainter than the spectral energy distribution (SED) of the Yellow Supergiant progenitor observed prior to explosion. The previously reported photometry of the progenitor is, therefore, completely unaffected by any sources that may persist at the SN location after explosion. In comparison with the previously reported late-time photometric evolution of SN 2011dh, we find that the light curve has plateaued at all wavelengths. The SED of the late-time source is clearly inconsistent with a SED of stellar origin. Although the SED is bright at UV wavelengths, there is no strong evidence that the late-time luminosity originates solely from a stellar source corresponding to the binary companion, although a partial contribution to the observed UV flux from a companion star can not be ruled out., Comment: 7 pages, 5 figures, MNRAS accepted

We use the Geneva Syclist isochrone models that include the effects of stellar rotation to investigate the role that rotation has on the resulting colour-magnitude diagram (CMD) of young and intermediate age clusters. We find that if a distribution of rotation velocities exists within the clusters, rotating stars will remain on the main sequence (MS) for longer, appearing to be younger than non-rotating stars within the same cluster. This results in an extended main sequence turn-off (eMSTO) that appears at young ages ($\sim30$~Myr) and lasts beyond 1~Gyr. If this eMSTO is interpreted as an age spread, the resulting age spread is proportional to the age of the cluster, i.e. young clusters ($<100$~Myr) appear to have small age spreads (10s of Myr) whereas older clusters ($\sim1$~Gyr) appear to have much larger spreads, up to a few hundred Myr. We compare the predicted spreads for a sample of rotation rates to observations of young and intermediate age clusters, and find a strong correlation between the measured 'age spread' and the age of the cluster, in good agreement with models of stellar rotation. This suggests that the 'age spreads' reported in the literature may simply be the result of a distribution of stellar rotation velocities within clusters., Comment: 6 pages, 4 figures, accepted for publication in MNRAS

Massive stars burn hydrogen through the CNO cycle during most of their evolution. When mixing is efficient, or when mass transfer in binary systems happens, chemically processed material is observed at the surface of O and B stars. ON stars show stronger lines of nitrogen than morphologically normal counterparts. Whether this corresponds to the presence of material processed through the CNO cycle or not is not known. Our goal is to answer this question. We perform a spectroscopic analysis of a sample of ON stars with atmosphere models. We determine the fundamental parameters as well as the He, C, N, and O surface abundances. We also measure the projected rotational velocities. We compare the properties of the ON stars to those of normal O stars. We show that ON stars are usually helium-rich. Their CNO surface abundances are fully consistent with predictions of nucleosynthesis. ON stars are more chemically evolved and rotate - on average - faster than normal O stars. Evolutionary models including rotation cannot account for the extreme enrichment observed among ON main sequence stars. Some ON stars are members of binary systems, but others are single stars as indicated by stable radial velocities. Hence, mass transfer is not a simple explanation for the observed chemical properties. We conclude that ON stars show extreme chemical enrichment at their surface, consistent with nucleosynthesis through the CNO cycle. Its origin is not clear at present., Comment: 18 pages, 10 figures (+ appendix). A&A accepted

The post main-sequence evolution of massive stars is very sensitive to many parameters of the stellar models. Key parameters are the mixing processes, the metallicity, the mass-loss rate and the effect of a close companion. We study how the red supergiant lifetimes, the tracks in the Hertzsprung-Russel diagram (HRD), the positions in this diagram of the pre-supernova progenitor as well as the structure of the stars at that time change for various mass-loss rates during the red supergiant phase (RSG), and for two different initial rotation velocities. The surface abundances of RSGs are much more sensitive to rotation than to the mass-loss rates during that phase. A change of the RSG mass-loss rate has a strong impact on the RSG lifetimes and therefore on the luminosity function of RSGs. At solar metallicity, the enhanced mass-loss rate models do produce significant changes on the populations of blue, yellow and red supergiants. When extended blue loops or blue ward excursions are produced by enhanced mass-loss, the models predict that a majority of blue (yellow) supergiants are post RSG objects. These post RSG stars are predicted to show much smaller surface rotational velocities than similar blue supergiants on their first crossing of the HR gap. The position in the HRD of the end point of the evolution depends on the mass of the hydrogen envelope. More precisely, whenever, at the pre-supernova stage, the H-rich envelope contains more than about 5\% of the initial mass, the star is a red supergiant, and whenever the H-rich envelope contains less than 1\% of the total mass the star is a blue supergiant. For intermediate situations, intermediate colors/effective temperatures are obtained. Yellow progenitors for core collapse supernovae can be explained by the enhanced mass-loss rate models, while the red progenitors are better fitted by the standard mass-loss rate models., Comment: 19 pages, 11 figures, 6 tables, accepted for publication in Astronomy and Astrophysics

Recent stellar evolution computations indicate that massive stars in the range ~ 20 - 30 Msun are located in the blue supergiant (BSG) region of the Hertzsprung-Russell diagram at two different stages of their life: immediately after the main sequence (MS, group 1) and during a blueward evolution after the red supergiant phase (group 2). From the observation of the pulsationnal properties of a subgroup of variable BSGs (alpha Cyg variables), one can deduce that these stars belongs to group 2. It is however difficult to simultaneously fit the observed surface abundances and gravity for these stars, and this allows to constrain the physical processes of chemical species transport in massive stars. We will show here that the surface abundances are extremely sensitive to the physics of convection, particularly the location of the intermediate convective shell that appears at the ignition of the hydrogen shell burning after the MS. Our results show that the use of the Ledoux criterion to determine the convective regions in the stellar models leads to a better fit of the surface abundances for alpha Cyg variables than the Schwarzschild one., Comment: 5 pages, 2 figures, to appear in IAUS 307 proceedings

[Abridged] We aim to improve the understanding of Cepheids from an evolutionary perspective and establish the role of rotation in the Cepheid paradigm. In particular, we are interested in the contribution of rotation to the problem of Cepheid masses, and explore testable predictions of quantities that can be confronted with observations. Evolutionary models including a homogeneous and self-consistent treatment of rotation are studied in detail during the crossings of the classical instability strip (IS). The dependence of several parameters on initial rotation is studied. These parameters include mass, luminosity, temperature, lifetimes, equatorial velocity, surface abundances, and rates of period change. Several key results are obtained: i) mass-luminosity (M-L) relations depend on rotation, particularly during the blue loop phase; ii) luminosity increases between crossings of the IS. Hence, Cepheid M-L relations at fixed initial rotation rate depend on crossing number (faster rotation yields greater luminosity difference between crossings); iii) the Cepheid mass discrepancy problem vanishes when rotation and crossing number are taken into account, without a need for high core overshooting values or enhanced mass loss; iv) rotation creates dispersion around average parameters predicted at fixed mass and metallicity. This is of particular importance for the period-luminosity-relation, for which rotation is a source of intrinsic dispersion; v) enhanced surface abundances do not unambiguously distinguish Cepheids occupying the Hertzsprung gap from ones on blue loops (after dredge-up), since rotational mixing can lead to significantly enhanced Main Sequence (MS) abundances; vi) rotating models predict greater Cepheid ages than non-rotating models due to longer MS lifetimes. Rotation has a significant evolutionary impact on classical Cepheids and should no longer be neglected in their study., Comment: 13 pages, 13 figures, accepted for publication in Astronomy & Astrophysics

Even though it is broadly accepted that single Be stars are rapidly rotating stars surrounded by a flat rotating circumstellar disk, there is still a debate about how fast these stars rotate and also about the mechanisms involved in the angular-momentum and mass input in the disk. We study the properties of stars that rotate near their critical-rotation rate and investigate the properties of the disks formed by equatorial mass ejections. We used the most recent Geneva stellar evolutionary tracks for rapidly rotating stars that reach the critical limit and used a simple model for the disk structure. We obtain that for a 9 Msun star at solar metallicity, the minimum average velocity during the Main Sequence phase to reach the critical velocity is around 330 km/s, whereas it would be 390 km/s at the metallicity of the Small Magellanic Cloud (SMC). Red giants or supergiants originating from very rapid rotators rotate six times faster and show N/C ratios three times higher than those originating from slowly rotating stars. This difference becomes stronger at lower metallicity. It might therefore be very interesting to study the red giants in clusters that show a large number of Be stars on the MS band. On the basis of our single-star models, we show that the observed Be-star fraction with cluster age is compatible with the existence of a temperature-dependent lower limit in the velocity rate required for a star to become a Be star. The mass, extension, and diffusion time of the disks produced when the star is losing mass at the critical velocity, obtained from simple parametrized expressions, are not too far from those estimated for disks around Be-type stars. At a given metallicity, the mass and the extension of the disk increase with the initial mass and with age on the MS phase. Denser disks are expected in low-metallicity regions., Comment: Accepted for publication in A&A, language edited

Optical and infrared interferometers definitively established that the photometric standard Vega (alpha Lyrae) is a rapidly rotating star viewed nearly pole-on. Recent independent spectroscopic analyses could not reconcile the inferred inclination angle with the observed line profiles, preferring a larger inclination. In order to resolve this controversy, we observed Vega using the six-beam Michigan Infrared Combiner on the Center for High Angular Resolution Astronomy Array. With our greater angular resolution and dense (u,v)-coverage, we find Vega is rotating less rapidly and with a smaller gravity darkening coefficient than previous interferometric results. Our models are compatible with low photospheric macroturbulence and also consistent with the possible rotational period of ~0.71 days recently reported based on magnetic field observations. Our updated evolutionary analysis explicitly incorporates rapid rotation, finding Vega to have a mass of 2.15+0.10_-0.15 Msun and an age 700-75+150 Myrs, substantially older than previous estimates with errors dominated by lingering metallicity uncertainties (Z=0.006+0.003-0.002)., Comment: Accepted for publication in ApJ Letters

The research of exoplanets has entered an era in which we characterize extrasolar planets. This has become possible with measurements of radii and luminosities. Meanwhile, radial velocity surveys discover also very low-mass planets. Uniting all this observational data into one coherent picture to better understand planet formation is an important, but difficult undertaking. Our approach is to develop a model which can make testable predictions for all these observational methods. We continue to describe how we have extended our formation model into a self-consistently coupled formation and evolution model. We show how we calculate the internal structure of the solid core and radiogenic heating. We also improve the protoplanetary disk model. Finally, we conduct population synthesis calculations. We present how the planetary mass-radius relationship of planets with primordial H/He envelopes forms and evolves in time. The basic shape of the M-R relation can be understood from the core accretion model. Low-mass planets cannot bind massive envelopes, while super-critical cores necessarily trigger runway gas accretion, leading to "forbidden" zones in the M-R plane. For a given mass, there is a considerable diversity of radii. We compare the synthetic M-R relation with the observed one, finding good agreement for a>0.1 AU. The synthetic radius distribution is characterized by a strong increase towards small R, and a second, lower local maximum at ~1 Jovian radius. The increase towards small radii reflects the increase of the mass function towards low M. The second local maximum is due to the fact that radii are nearly independent of mass for giant planets. A comparison of the synthetic radius distribution with Kepler data shows agreement for R>2 Earth radii, but divergence for smaller radii. We predict that in the next few years, Kepler should find the second, local maximum at ~1 Jovian radius., Comment: Accepted to A&A. Minor revisions only relative to v1

We present dense grids of stellar models suitable for comparison with observable quantities measured with great precision, such as those derived from binary systems or planet-hosting stars. We computed new Geneva models without rotation at metallicities Z=0.006, 0.01, 0.014, 0.02, 0.03 and 0.04 (i.e. [Fe/H] from -0.33 to +0.54) and with mass in small steps from 0.5 to 3.5 Msun. Great care was taken in the procedure for interpolating between tracks in order to compute isochrones. Several properties of our grids are presented as a function of stellar mass and metallicity. Those include surface properties in the Hertzsprung-Russell diagram, internal properties including mean stellar density, sizes of the convective cores, and global asteroseismic properties. We checked our interpolation procedure and compared interpolated tracks with computed tracks. The deviations are less than 1% in radius and effective temperatures for most of the cases considered. We also checked that the present isochrones provide nice fits to four couples of observed detached binaries and to the observed sequences of the open clusters NGC 3532 and M67. Including atomic diffusion in our models with M<1.1 Msun leads to variations in the surface abundances that should be taken into account when comparing with observational data of stars with measured metallicities. For that purpose, iso-Zsurf lines are computed. These can be requested for download from a dedicated web page together with tracks at masses and metallicities within the limits covered by the grids. The validity of the relations linking Z and FeH is also re-assessed in light of the surface abundance variations in low-mass stars., Comment: Accepted for publication in A&A

Since the external regions of the envelopes of rapidly rotating early-type stars are unstable to convection, a coupling may exist between the convection and the internal rotation. We explore what can be learned from spectroscopic and interferometric observations about the properties of the rotation law in the external layers of these objects. Using simple relations between the entropy and specific rotational quantities, some of which are found to be efficient at accounting for the solar differential rotation in the convective region, we derived analytical solutions that represent possible differential rotations in the envelope of early-type stars. A surface latitudinal differential rotation may not only be an external imprint of the inner rotation, but induces changes in the stellar geometry, the gravitational darkening, the aspect of spectral line profiles, and the emitted spectral energy distribution. By studying the equation of the surface of stars with non-conservative rotation laws, we conclude that objects undergo geometrical deformations that are a function of the latitudinal differential rotation able to be scrutinized both spectroscopically and by interferometry. The combination of Fourier analysis of spectral lines with model atmospheres provides independent estimates of the surface latitudinal differential rotation and the inclination angle. Models of stars at different evolutionary stages rotating with internal conservative rotation laws were calculated to show that the Roche approximation can be safely used to account for the gravitational potential. The surface temperature gradient in rapid rotators induce an acceleration to the surface angular velocity. A non-zero differential rotation parameter may indicate that the rotation is neither rigid nor shellular underneath the stellar surface., Comment: Paper in press

When the surface angular velocity is above about 70% of the critical angular velocity, many interesting features appear which may be tested by interferometric observations, like significant deformation of stars, variation of the effective temperature with the latitude. Also polar winds become important and equatorial disks may appear. Near the critical limit, convection is also favored in the outer layers. In the present paper, we emphasize the need for a proper estimate of the critical velocity since this is the ratio of the actual velocity of the star to that critical velocity which determines the amplitude of the above effects. We recall the existence of two critical velocities. The first one, also called the classical critical velocity is the one to consider when the star has an Eddington factor inferior to 0.639, while the second one is the one to be considered when the Eddington factor is above 0.639. The features of the star at these two critical limits may be very different., Comment: 4 pages, 3 figures, conference proceedings "Interferometric view of hot stars", Rev. Mexi. de Astron. y Astrofis

AGB stars have long been held responsible for the important star-to-star variations in light elements observed in Galactic globular clusters. We analyse the main impacts of a first generation of rotating intermediate-mass stars on the chemical properties of second-generation globular cluster stars. The rotating models were computed without magnetic fields and without the effects of internal gravity waves. They account for the transports by meridional currents and turbulence. We computed the evolution of both standard and rotating stellar models with initial masses between 2.5 and 8 Msun within the metallicity range covered by Galactic globular clusters. During central He-burning, rotational mixing transports fresh CO-rich material from the core towards the hydrogen-burning shell, leading to the production of primary 14N. In stars more massive than M > 4 Msun, the convective envelope reaches this reservoir during the second dredge-up episode, resulting in a large increase in the total C+N+O content at the stellar surface and in the stellar wind. The corresponding pollution depends on the initial metallicity. At low- and intermediate-metallicity, it is at odds with the constancy of C+N+O observed among globular cluster low-mass stars. With the given input physics, our models suggest that massive rotating AGB stars have not shaped the abundance patterns observed in low- and intermediate-metallicity globular clusters. Our non-rotating models, on the other hands, do not predict surface C+N+O enhancements, hence are in a better position as sources of the chemical anomalies in globular clusters showing the constancy of the C+N+O. However at the moment, there is no reason to think that intermediate mass stars were not rotating., Comment: Accepted in Astronomy and Astrophysics, 7 pages, 3 figures