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Modelling the base of the solar convective envelope is a tedious problem. Since the first rotation inversions, solar modellers are confronted with the fact that a region of very limited extent has an enormous physical impact on the Sun. Indeed, it is the transition region from differential to solid body rotation, the tachocline, which furthermore is influenced by turbulence and is also supposed to be the seat of the solar magnetic dynamo. Moreover, solar models show significant disagreement with the sound speed profile in this region. In this paper, we show how helioseismology can provide further constraints on this region by carrying out an inversion of the Ledoux discriminant. We compare these inversions for Standard Solar Models built using various opacity tables and chemical abundances and discuss the origins of the discrepancies between Solar Models and the Sun., Comment: Accepted for publication as a letter in MNRAS

Aims: Past observations of fast-rotating massive stars exhibiting normal nitrogen abundances at their surface have raised questions about the rotational mixing paradigm. We revisit this question thanks to a spectroscopic analysis of a sample of bright fast-rotating OB stars, with the goal of quantifying the efficiency of rotational mixing at high rotation rates. Method: Our sample consists of 40 fast rotators on the main sequence, with spectral types comprised between B0.5 and O4. We compare the abundances of some key element indicators of mixing (He, CNO) with the predictions of evolutionary models for single objects and for stars in interacting binary systems. Results: The properties of half of the sample stars can be reproduced by single evolutionary models, even in the case of probable or confirmed binaries that can therefore be true single stars in a pre-interaction configuration. The main problem for the rest of the sample is a mismatch for the [N/O] abundance ratio (we confirm the existence of fast rotators with a lack of nitrogen enrichment) and/or a high helium abundance that cannot be accounted for by models. Modifying the diffusion coefficient implemented in single- star models does not solve the problem as it cannot simultaneously reproduce the helium abundances and [N/O] abundance ratios of our targets. Since part of them actually are binaries, we also compared their chemical properties with predictions for post-mass transfer systems. We found that these models can explain the abundances measured for a majority of our targets, including some of the most helium-enriched, but fail to reproduce them in other cases. Our study thus reveals that some physical ingredients are still missing in current models.

Massive binary systems are important laboratories in which to probe the properties of massive stars and stellar physics in general. In this context, we analysed optical spectroscopy and photometry of the eccentric short-period early-type binary HD 152218 in the young open cluster NGC 6231. We reconstructed the spectra of the individual stars using a separating code. The individual spectra were then compared with synthetic spectra obtained with the CMFGEN model atmosphere code. We furthermore analysed the light curve of the binary and used it to constrain the orbital inclination and to derive absolute masses of 19.8 +/- 1.5 and 15.0 +/- 1.1 solar masses. Combining radial velocity measurements from over 60 years, we show that the system displays apsidal motion at a rate of (2.04^{+.23}_{-.24}) degree/year. Solving the Clairaut-Radau equation, we used stellar evolution models, obtained with the CLES code, to compute the internal structure constants and to evaluate the theoretically predicted rate of apsidal motion as a function of stellar age and primary mass. In this way, we determine an age of 5.8 +/- 0.6 Myr for HD 152218, which is towards the higher end of, but compatible with, the range of ages of the massive star population of NGC 6231 as determined from isochrone fitting., Comment: Accepted for publication in Astronomy & Astrophysics

Asteroseismology is a powerful tool to access the internal structure of stars. Apart from the important impact of theoretical developments, progress in this field has been commonly associated with the analysis of time-resolved observations. Recently, the so-called macroturbulent broadening has been proposed to be a complementary and less expensive way -- in terms of observational time -- to investigate pulsations in massive stars. We assess to what extent this ubiquitous non-rotational broadening component shaping the line profiles of O stars and B supergiants is a spectroscopic signature of pulsation modes driven by a heat mechanism. We compute stellar main sequence and post-main sequence models from 3 to 70Msun with the ATON stellar evolution code and determine the instability domains for heat-driven modes for degrees l=1-20 using the adiabatic and non-adiabatic codes LOSC and MAD. We use the observational material presented in Sim\'on-D\'iaz et al. (2016) to investigate possible correlations between the single snapshot line-broadening properties of a sample of ~260 O and B-type stars and their location inside/outside the various predicted instability domains. We present an homogeneous prediction for the non-radial instability domains of massive stars for degree l up to 20. We provide a global picture of what to expect from an observational point of view in terms of frequency range of excited modes, and investigate the behavior of the instabilities with stellar evolution and increasing degree of the mode. Furthermore, our pulsational stability analysis, once compared to the empirical results of Sim\'on-D\'iaz et al. (2016), indicates that stellar oscillations originated by a heat mechanism can not explain alone the occurrence of the large non-rotational line-broadening component commonly detected in the O star and B supergiant domain., Comment: 14 pages, 8 figures, Reproduced with permission from Astronomy & Astrophysics, \c{opyright} ESO

We aim to provide new empirical clues about macroturbulent spectral line broadening in O- and B-type stars to evaluate its physical origin. We use high-resolution spectra of ~430 stars with spectral types in the range O4-B9 (all luminosity classes). We characterize the line-broadening of adequate diagnostic metal lines using a combined FT and GOF technique. We perform a quantitative spectroscopic analysis of the whole sample using automatic tools coupled with a huge grid of FASTWIND models. We also incorporate quantitative information about line asymmetries to our observational description of the characteristics of the line-profiles, and present a comparison of the shape and type of line-profile variability found in a small sample of O stars and B supergiants with still undefined pulsational properties and B main sequence stars with variable line-profiles. We present a homogeneous and statistically significant overview of the (single snapshot) line-broadening properties of stars in the whole O and B star domain. We find empirical evidence of the existence of various types of non-rotational broadening agents acting in the realm of massive stars. Even though all of them could be quoted and quantified as a macroturbulent broadening from a practical point of view, their physical origin can be different. Contrarily to the early- to late-B dwarfs/giants, which present a mixture of cases in terms of line-profile shape and variability, the whole O-type and B supergiant domain (or, roughly speaking, stars with M_ZAMS > 15 M_sol) is fully dominated by stars with a remarkable non-rotational broadening component and very similar profiles (including type of variability). We provide some examples illustrating how this observational dataset can be used to evaluate scenarios aimed at explaining the existence of sources of non-rotational broadening in massive stars., Comment: 17 pages, 11 figures, 3 tables. Accepted for publication in A&A

We have advocated in a previous paper (Godart M. arXiv: 1206.2917v2[quant-ph] ) a version of the stochastic theory of quantum mechanics. It is indirectly based on a method proposed by Nelson to associate a Markov process with any solution of the Schroedinger equation. The debate began very soon on the question to know if the new theory based on that stochastic procees was equivalent to the orthodox Copenhagen version. We conclude in this paper that the answer is in the negative in agreement with the opinion of several physicists. We show however that the elementary solutions of the Schroedinger equation can be recovered formally from the stochastic theory in a great number of particular cases. We confirm also that this equation is no longer valid when a magnetic field is at work and that it must then give way to some other equation.

The IACOB project is an ambitious long-term project which is contributing to step forward in our knowledge about the physical properties and evolution of Galactic massive stars. The project aims at building a large database of high-resolution, multi-epoch, spectra of Galactic OB stars, and the scientific exploitation of the database using state-of-the-art models and techniques. In this proceeding, we summarize the latest updates of the IACOB spectroscopic database and highlight some of the first scientific results from the IACOB project; we also announce the first data release and the first public version of the iacob-broad tool for the line-broadening characterization of OB-type spectra., Comment: To appear in Highlights of Spanish Astrophysics VIII, Proceedings of the XI Scientific Meeting of the Spanish Astronomical Society held on September 8-12, 2014, in Teruel, Spain

The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it also relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the classical trajectories of the particles are identical to the sample functions of a diffusion Markov process, whose conditional probability density is proposed as a substitute for the wave function. Along the way, we introduce ad hoc hypotheses for the sole reason that they facilitate and even make possible the further development of the theory. These and the so-called Nelson equations are used to determine the drift vectors and the diffusion tensor characteristic of such a process. It is then possible to write down the Fokker-Planck and Kolmogorov equations that can be used to determine the normal and conditional probability densities. This logical sequence of steps leads to the solution of specific problems and we apply it to the special case of the free particle.

Although playing a key role in the understanding of the supernova phenomenon, the evolution of massive stars still suffers from uncertainties in their structure, even during their "quiet" main sequence phase and later on during their subgiant and helium burning phases. What is the extent of the mixed central region? In the local mixing length theory (LMLT) frame, are there structural differences using Schwarzschild or Ledoux convection criterion? Where are located the convective zone boundaries? Are there intermediate convection zones during MS and post-MS phase, and what is their extent and location? We discuss these points and show how asteroseismology could bring some light on these questions., Comment: 10 pages, 5 figures, IAU Symposium 307, New windows on massive stars: asteroseismology, interferometry, and spectropolarimetry, G. Meynet, C. Georgy, J.H. Groh & Ph. Stee, eds

We used Raman and terahertz spectroscopies to investigate lattice and magnetic excitations and their cross-coupling in the hexagonal YMnO3 multiferroic. Two phonon modes are strongly affected by the magnetic order. Magnon excitations have been identified thanks to comparison with neutron measurements and spin wave calculations but no electromagnon has been observed. In addition, we evidenced two additional Raman active peaks. We have compared this observation with the anti-crossing between magnon and acoustic phonon branches measured by neutron. These optical measurements underly the unusual strong spin-phonon coupling.

The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the classical trajectories of the particles are identical to the sample functions of a diffusion Markov process, whose conditional probability density is proposed as a substitute for the wave function. The Schroedinger equation and the so-called Nelson equations are used to determine the diffusion tensor and the drift vectors characteristic of such a process. It is then possible to write down the forward and backward Kolmogorov equations that are used to determine the conditional probability density, as well as the Fokker-Planck equation that is used to determine the normal probability density. This method is applied to several simple cases and the results obtained are compared with those of the orthodox theory. Among the most important differences let us mention that any system evolving freely from any original state returns spontaneously to its ground state, that the definitions of the particles velocities and momenta are impossible because the sample functions of a diffusion Markov process nowhere possess a derivative with respect to time and that the so-called collapse of the wave function is a mere mirage explained by the updating choice between new and older initial conditions in the resolution of partial differential equations. We finally attempt to extend the proposed theory to the domain of the relativistic quantum mechanics. It is promising but is clearly unfinished because it has not been possible up to now to solve the Nelson and Kolmogorov equations, except in the very simple case of a free particle., Comment: Abstract: corrected typos. Modified content: new paragraph on covariance and no more appendices

Six O-type stars were observed continuously by the CoRoT satellite during a 34.3-day run. The unprecedented quality of the data allows us to detect even low-amplitude stellar pulsations in some of these stars (HD 46202 and the binaries HD 46149 and Plaskett's star). These cover both opacity-driven modes and solar-like stochastic oscillations, both of importance to the asteroseismological modelling of O stars. Additional effects can be seen in the CoRoT light curves, such as binarity and rotational modulation. Some of the hottest O-type stars (HD 46223, HD 46150 and HD 46966) are dominated by the presence of red-noise: we speculate that this is related to a sub-surface convection zone., Comment: 5 pages, 3 figures, conference paper. To be published in "Four decades of Research on Massive Stars", Astronomical Society of the Pacific. Eds. C. Robert, N. St-Louis and L. Drissen

The detection of pulsational frequencies in stellar photometry is required as input for asteroseismological modelling. The second short run (SRa02) of the CoRoT mission has provided photometric data of unprecedented quality and time-coverage for a number of O-type stars. We analyse the CoRoT data corresponding to three hot O-type stars, describing the properties of their light curves and we search for pulsational frequencies, which we then compare to theoretical model predictions. We determine the amplitude spectrum of the data, using the Lomb-Scargle and a multifrequency HMM-like technique. Frequencies are extracted by prewhitening, and their significance is evaluated under the assumption that the light curve is dominated by red noise. We search for harmonics, linear combinations and regular spacings among these frequencies. We use simulations with the same time sampling as the data as a powerful tool to judge the significance of our results. From the theoretical point of view, we use the MAD non-adiabatic pulsation code to determine the expected frequencies of excited modes. A substantial number of frequencies is listed, but none can be convincingly identified as being connected to pulsations. The amplitude spectrum is dominated by red noise. Theoretical modelling shows that all three O-type stars can have excited modes but the relation between the theoretical frequencies and the observed spectrum is not obvious. The dominant red noise component in the hot O-type stars studied here clearly points to a different origin than the pulsations seen in cooler O stars. The physical cause of this red noise is unclear, but we speculate on the possibility of sub-surface convection, granulation, or stellar wind inhomogeneities being responsible., Comment: 13 pages, 8 figures, A&A accepted. Tables 2, 3 and 4 available on ftp://omaftp.oma.be/dist/astro/Blomme.R/CoRoT/

The SRa02 of the CoRoT space mission for Asteroseismology was partly devoted to stars belonging to the Mon OB2 association. An intense monitoring was performed on Plaskett's Star (HD47129) and the unprecedented quality of the light curve allows us to shed new light on this very massive, non-eclipsing binary system. We particularly aimed at detecting periodic variability which might be associated with pulsations or interactions between both components. We also searched for variations related to the orbital cycle which could help to constrain the inclination and the morphology of the binary system. A Fourier-based prewhitening and a multiperiodic fitting procedure were applied to analyse the time series and extract the frequencies of variations. We describe the noise properties to tentatively define an appropriate significance criterion, to only point out the peaks at a certain significance level. We also detect the variations related to the orbital motion and study them by using the NIGHTFALL program. The periodogram exhibits a majority of peaks at low frequencies. Among these peaks, we highlight a list of about 43 values, including notably two different sets of harmonic frequencies whose fundamental peaks are located at about 0.07 and 0.82d-1. The former represents the orbital frequency of the binary system whilst the latter could probably be associated with non-radial pulsations. The study of the 0.07d-1 variations reveals the presence of a hot spot most probably situated on the primary star and facing the secondary. The investigation of this unique dataset constitutes a further step in the understanding of Plaskett's Star. These results provide a first basis for future seismic modelling. The existence of a hot region between both components renders the determination of the inclination ambiguous., Comment: Accepted in A&A, 13 pages, 7 figures, 2 tables

We aim to interpret the photometric and spectroscopic variability of the luminous blue variable supergiant HD\,50064 ($V=8.21$).CoRoT space photometry and follow-up high-resolution spectroscopy, with a time base of 137\,d and 169\,d, respectively, was gathered, analysed and interpreted using standard time series analysis and light curve modelling methods as well as spectral line diagnostics.The space photometry reveals one period of 37\,d, which undergoes a sudden amplitude change with a factor 1.6. The pulsation period is confirmed in the spectroscopy, which additionally reveals metal line radial velocity values differing by $\sim 30\,$km\,s$^{-1}$ depending on the spectral line and on the epoch. We estimate \teff$\sim$13\,500\,K, \logg$\sim$1.5 from the equivalent width of Si lines. The Balmer lines reveal that the star undergoes episodes of changing mass loss on a time scale similar to the changes in the photometric and spectroscopic variability, with an average value of $\log\dot{\rm M}\simeq-5$ (in M$_\odot$\,yr$^{-1}$). We tentatively interpret the 37\,d period as due to a strange mode oscillation., Comment: 4 pages, accepted for publication in Astronomy & Astrophysics Letters

We aimed at finding a physical explanation for the occurrence of macroturbulence in the atmospheres of hot massive stars, a phenomenon found in observations since more than a decade but yet unexplained. We computed time series of line profiles for evolved massive stars broadened by rotation and by hundreds of low-amplitude nonradial gravity-mode pulsations which are predicted to be excited for evolved massive stars. In general, line profiles based on macrotubulent broadening can mimic those subject to pulsational broadening. In several cases, though, good fits require macroturbulent velocities that pass the speed of sound for realistic pulsation amplitudes. Moreover, we find that the rotation velocity can be seriously underestimated by using a simple parameter description for macroturbulence rather than an appropriate pulsational model description to fit the line profiles. We conclude that macroturbulence is a likely signature of the collective effect of pulsations. We provide line diagnostics and their typical values to decide whether or not pulsational broadening is present in observed line profiles, as well as a procedure to avoid an inaccurate estimation of the rotation velocity., Comment: 12 pages, 9 figures, accepted for publication by Astronomy and Astrophysics

Saio et al. (2006) have shown that the presence of an intermediate convective zone (ICZ) in post-main sequence models could prevent the propagation of g-modes in the radiative interior and hence avoid the corresponding radiative damping. The development of such a convective region highly depends on the structure of the star in the mu-gradient region surrounding the convective core during the main sequence phase. In particular,the development of this ICZ depends on physical processes such as mass loss, overshooting (Chiosi & Maeder 1986, Chiosi et al. 1992, see also Godart et al., these proceedings) and convective instability criterion (Schwarzschild's or Ledoux's criteria). In this paper we study the consequences of adopting the Ledoux's criterion on the evolution of the convective regions in massive stars (15 and 20 Msun), and on the pulsation spectrum of these new B-type variables (also called SPBsg)., Comment: Contribution to the Proceedings of the 38th LIAC/HELAS-ESTA/BAG, 2008 Accepted for publication in CoAst

Solar-like oscillations have been observed in numerous red giants from ground and from space. An important question arises: could we expect to detect non-radial modes probing the internal structure of these stars? We investigate under what physical circumstances non-radial modes could be observable in red giants; what would be their amplitudes, lifetimes and heights in the power spectrum (PS)? Using a non-radial non-adiabatic pulsation code including a non-local time-dependent treatment of convection, we compute the theoretical lifetimes of radial and non-radial modes in several red giant models. Next, using a stochastic excitation model, we compute the amplitudes of these modes and their heights in the PS. Very distinct results are found depending on the evolutionary status of the star., Comment: Source tex file : 1713.tex Bibliography file : 1713.bbl 24 figures : 1713f1.eps, ..., 1713f24.eps

Thanks to their past history on the main sequence phase, supergiant massive stars develop a convective shell around the helium core. This intermediate convective zone (ICZ) plays an essential role in governing which g-modes are excited. Indeed a strong radiative damping occurs in the high density radiative core but the ICZ acts as a barrier preventing the propagation of some g-modes into the core. These g-modes can thus be excited in supergiant stars by the kappa-mechanism in the superficial layers due to the opacity bump of iron, at log T=5.2. However massive stars are submitted to various complex phenomena such as rotation, magnetic fields, semiconvection, mass loss, overshooting. Each of these phenomena exerts a significant effect on the evolution and some of them could prevent the onset of the convective zone. We develop a numerical method which allows us to select the reflected, thus the potentially excited, modes only. We study different cases in order to show that mass loss and overshooting, in a large enough amount, reduce the extent of the ICZ and are unfavourable to the excitation of g-modes., Comment: 9 pages, 11 figures, accepted for publication in MNRAS