Author name code: zahn ADS astronomy entries on 2022-09-14 author:"Zahn, Jean-Paul" ------------------------------------------------------------------------ Title: Integrating Single Sign-On into the STScI Archive: Lessons Learned Authors: Alexov, A.; Abney, F.; Kyprianou, M.; Levay, K.; Zahn, J. Bibcode: 2017ASPC..512...93A Altcode: 2017adass..25...93A; 2018ASPC..512...93A The Space Telescope Science Institute (STScI) migrated a handful of web services to a Single Sign-On (SSO) solution in 2014, using the Shibboleth and CAS software solutions. SSO was implemented in order to consolidate usernames and passwords used for a variety of web services, to improve security at STScI and to better the user experience. It took an additional year to integrate the STScI Archive into the SSO Framework, including multiple web services and a non-web service authentication back end which allowed for one set of user credentials. The SSO Framework was expanded to allow external users to register with STScI and use those SSO credentials to access multiple services at STScI, including the Archive. We took great care in migrating and informing over 13,000 STScI Archive users of their new SSO credentials and new user interfaces. We coordinated help desks between IT, the instrument science groups and the Archive to have a successful, seamless transition of the STScI Archive users to their new SSO credentials. We outline our SSO architecture, hurdles, lessons learned and implementation solutions which we have taken in order to migrate STScI's Archive services to using SSO. Title: Confinement of the solar tachocline by a cyclic dynamo magnetic field Authors: Barnabé, Roxane; Strugarek, Antoine; Charbonneau, Paul; Brun, Allan Sacha; Zahn, Jean-Paul Bibcode: 2017A&A...601A..47B Altcode: 2017arXiv170302374B Context. The surprising thinness of the solar tachocline is still not understood with certainty today. Among the numerous possible scenarios suggested to explain its radial confinement, one hypothesis is based on Maxwell stresses that are exerted by the cyclic dynamo magnetic field of the Sun penetrating over a skin depth below the turbulent convection zone.
Aims: Our goal is to assess under which conditions (turbulence level in the tachocline, strength of the dynamo-generated field, spreading mechanism) this scenario can be realized in the solar tachocline.
Methods: We develop a simplified 1D model of the upper tachocline under the influence of an oscillating magnetic field imposed from above. The turbulent transport is parametrized with enhanced turbulent diffusion (or anti-diffusion) coefficients. Two main processes that thicken the tachocline are considered; either turbulent viscous spreading or radiative spreading. An extensive parameter study is carried out to establish the physical parameter regimes under which magnetic confinement of the tachocline that is due to a surface dynamo field can be realized.
Results: We have explored a large range of magnetic field amplitudes, viscosities, ohmic diffusivities and thermal diffusivities. We find that, for large but still realistic magnetic field strengths, the differential rotation can be suppressed in the upper radiative zone (and hence the tachocline confined) if weak turbulence is present (with an enhanced ohmic diffusivity of η> 107-8 cm2/ s), even in the presence of radiative spreading.
Conclusions: Our results show that a dynamo magnetic field can, in the presence of weak turbulence, prevent the inward burrowing of a tachocline subject to viscous diffusion or radiative spreading. Title: New constraints on Saturn's interior from Cassini astrometric data Authors: Lainey, Valéry; Jacobson, Robert A.; Tajeddine, Radwan; Cooper, Nicholas J.; Murray, Carl; Robert, Vincent; Tobie, Gabriel; Guillot, Tristan; Mathis, Stéphane; Remus, Françoise; Desmars, Josselin; Arlot, Jean-Eudes; De Cuyper, Jean-Pierre; Dehant, Véronique; Pascu, Dan; Thuillot, William; Le Poncin-Lafitte, Christophe; Zahn, Jean-Paul Bibcode: 2017Icar..281..286L Altcode: 2015arXiv151005870L Using astrometric observations spanning more than a century and including a large set of Cassini data, we determine Saturn's tidal parameters through their current effects on the orbits of the eight main and four coorbital Moons. We have used the latter to make the first determination of Saturn's Love number from observations, k2=0.390 ± 0.024, a value larger than the commonly used theoretical value of 0.341 (Gavrilov & Zharkov, 1977), but compatible with more recent models (Helled & Guillot, 2013) for which the static k2 ranges from 0.355 to 0.382. Depending on the assumed spin for Saturn's interior, the new constraint can lead to a significant reduction in the number of potential models, offering great opportunities to probe the planet's interior. In addition, significant tidal dissipation within Saturn is confirmed (Lainey et al., 2012) corresponding to a high present-day tidal ratio k2/Q=(1.59 ± 0.74) × 10-4 and implying fast orbital expansions of the Moons. This high dissipation, with no obvious variations for tidal frequencies corresponding to those of Enceladus and Dione, may be explained by viscous friction in a solid core, implying a core viscosity typically ranging between 1014 and 1016 Pa.s (Remus et al., 2012). However, a dissipation increase by one order of magnitude at Rhea's frequency could suggest the existence of an additional, frequency-dependent, dissipation process, possibly from turbulent friction acting on tidal waves in the fluid envelope of Saturn (Ogilvie & Lin, 2004; Fuller et al. 2016). Title: The magnetic fields at the surface of active single G-K giants Authors: Aurière, M.; Konstantinova-Antova, R.; Charbonnel, C.; Wade, G. A.; Tsvetkova, S.; Petit, P.; Dintrans, B.; Drake, N. A.; Decressin, T.; Lagarde, N.; Donati, J. -F.; Roudier, T.; Lignières, F.; Schröder, K. -P.; Landstreet, J. D.; Lèbre, A.; Weiss, W. W.; Zahn, J. -P. Bibcode: 2015A&A...574A..90A Altcode: 2014arXiv1411.6230A
Aims: We investigate the magnetic field at the surface of 48 red giants selected as promising for detection of Stokes V Zeeman signatures in their spectral lines. In our sample, 24 stars are identified from the literature as presenting moderate to strong signs of magnetic activity. An additional 7 stars are identified as those in which thermohaline mixing appears not to have occured, which could be due to hosting a strong magnetic field. Finally, we observed 17 additional very bright stars which enable a sensitive search to be performed with the spectropolarimetric technique.
Methods: We use the spectropolarimeters Narval and ESPaDOnS to detect circular polarization within the photospheric absorption lines of our targets. We treat the spectropolarimetric data using the least-squares deconvolution method to create high signal-to-noise ratio mean Stokes V profiles. We also measure the classical S-index activity indicator for the Ca ii H&K lines, and the stellar radial velocity. To infer the evolutionary status of our giants and to interpret our results, we use state-of-the-art stellar evolutionary models with predictions of convective turnover times.
Results: We unambiguously detect magnetic fields via Zeeman signatures in 29 of the 48 red giants in our sample. Zeeman signatures are found in all but one of the 24 red giants exhibiting signs of activity, as well as 6 out of 17 bright giant stars. However no detections were obtained in the 7 thermohaline deviant giants. The majority of the magnetically detected giants are either in the first dredge up phase or at the beginning of core He burning, i.e. phases when the convective turnover time is at a maximum: this corresponds to a "magnetic strip" for red giants in the Hertzsprung-Russell diagram. A close study of the 16 giants with known rotational periods shows that the measured magnetic field strength is tightly correlated with the rotational properties, namely to the rotational period and to the Rossby number Ro. Our results show that the magnetic fields of these giants are produced by a dynamo, possibly of α-ω origin since Ro is in general smaller than unity. Four stars for which the magnetic field is measured to be outstandingly strong with respect to that expected from the rotational period/magnetic field relation or their evolutionary status are interpreted as being probable descendants of magnetic Ap stars. In addition to the weak-field giant Pollux, 4 bright giants (Aldebaran, Alphard, Arcturus, η Psc) are detected with magnetic field strength at the sub-Gauss level. Besides Arcturus, these stars were not considered to be active giants before this study and are very similar in other respects to ordinary giants, with S-index indicating consistency with basal chromospheric flux.

Tables 6-8 are available in electronic form at http://www.aanda.orgBased on observations obtained at the Télescope Bernard Lyot (TBL) at Observatoire du Pic du Midi, CNRS/INSU and Université de Toulouse, France, and at the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Research Council of Canada, CNRS/INSU and the University of Hawaii. Title: The surface signature of the tidal dissipation of the core in a two-layer planet Authors: Remus, F.; Mathis, S.; Zahn, J. -P.; Lainey, V. Bibcode: 2015A&A...573A..23R Altcode: 2014arXiv1409.8343R Context. Tidal dissipation, which is directly linked to internal structure, is one of the key physical mechanisms that drive the evolution of systems and govern their architecture. A robust evaluation of its amplitude is thus needed to predict the evolution time for spins and orbits and their final states.
Aims: The purpose of this paper is to refine a recent model of the anelastic tidal dissipation in the central dense region of giant planets, which are commonly assumed to retain a large amount of heavy elements, which constitute an important source of dissipation.
Methods: The previous paper evaluated the impact of the static fluid envelope on the tidal deformation of the core and on the associated anelastic tidal dissipation through the tidal quality factor Qc. We examine here its impact on the corresponding effective anelastic tidal dissipation through the effective tidal quality factor Qp.
Results: We show that the strength of this mechanism mainly depends on mass concentration. In the case of Jupiter- and Saturn-like planets, it can increase their effective tidal dissipation by, around, factors 2.4 and 2, respectively. In particular, the range of the rheologies compatible with the observations is enlarged compared to the results issued from previous formulations.
Conclusions: We derive here an improved expression of the tidal effective factor Qp in terms of the tidal dissipation factor of the core Qc, without assuming the commonly used assumptions. When applied to giant planets, the formulation obtained here allows a better match between the anelastic core's tidal dissipation of a two-layer model and the observations. Title: Tidal dissipation in stars and fluid planetary layers and their impact on the evolution of star-planet systems Authors: Mathis, S.; Auclair-Desrotour, P.; Guenel, M.; Remus, F.; Le Poncin-Lafitte, C.; Lainey, V.; Zahn, J. -P. Bibcode: 2014spih.confE...6M Altcode: No abstract at ADS Title: Anelastic Tidal Dissipation in Multi-Layer Planets Authors: Remus, Françcoise; Mathis, Stéphane; Zahn, Jean-Paul; Lainey, Valéry Bibcode: 2014IAUS..293..362R Altcode: Earth-like planets have anelastic mantles, whereas giant planets may have anelastic cores. As for the fluid parts, the tidal dissipation of these regions, gravitationally perturbed by a companion, highly depends on its internal friction and thus its internal structure. Therefore, modeling this kind of interaction presents a high interest to constrain planetary interiors, whose properties are still quite uncertain. Here, we examine the anelastic tidal dissipation in deep planetary interiors, in presence of a fluid envelope, and taking into account its dependence on the rheology.

Taking plausible values for the anelastic parameters, and discussing the frequency-dependence of the anelastic dissipation, we show how this mechanism may compete with the dissipation in fluid layers, when applied to Jupiter- and Saturn-like planets. We also discuss the case of the icy giants Uranus and Neptune. Finally, we show how the results may be implemented to describe the dynamical evolution of planetary systems. Title: Rotation induced mixing in stellar interiors Authors: Zahn, J. -P. Bibcode: 2013EAS....63..245Z Altcode: The standard model of stellar structure is unable to account for various observational facts, such as anomalies in the surface composition, and there is now a broad consensus that some extra mixing must occur in the radiation zones, in addition to the always present convective overshoot or penetration. The search for the causes of this extra mixing started in the late seventies, and it was quickly realized - in particular by Sylvie Vauclair and her co-workers - that some mild turbulence must be present to counteract the effect of gravitational settling and radiative levitation. What could be responsible for this turbulence? One suggestion was the internal gravity waves emitted at the boundary of convection zones, but it is still not established whether these waves will lead to true mixing. However they transport angular momentum, and therefore they generate differential rotation, which may be shear-unstable and thus lead to turbulence. Another way to transport angular momentum and produce an unstable rotation profile is through the large-scale circulation which is induced by the structural adjustments as the star evolves, or by the torques applied to it (due to stellar wind, accretion, tides). These processes participate in what is called the "rotational mixing"; their implementation in stellar evolution codes - again under Sylvie's impulse - has given birth to a new generation of stellar models, which agree much better with the observational constraints, although there is still room for improvement. Title: Seismic diagnostics for transport of angular momentum in stars. I. Rotational splittings from the pre-main sequence to the red-giant branch Authors: Marques, J. P.; Goupil, M. J.; Lebreton, Y.; Talon, S.; Palacios, A.; Belkacem, K.; Ouazzani, R. -M.; Mosser, B.; Moya, A.; Morel, P.; Pichon, B.; Mathis, S.; Zahn, J. -P.; Turck-Chièze, S.; Nghiem, P. A. P. Bibcode: 2013A&A...549A..74M Altcode: 2012arXiv1211.1271M Context. Rotational splittings are currently measured for several main sequence stars and a large number of red giants with the space mission Kepler. This will provide stringent constraints on rotation profiles.
Aims: Our aim is to obtain seismic constraints on the internal transport and surface loss of the angular momentum of oscillating solar-like stars. To this end, we study the evolution of rotational splittings from the pre-main sequence to the red-giant branch for stochastically excited oscillation modes.
Methods: We modified the evolutionary code CESAM2K to take rotationally induced transport in radiative zones into account. Linear rotational splittings were computed for a sequence of 1.3 M⊙ models. Rotation profiles were derived from our evolutionary models and eigenfunctions from linear adiabatic oscillation calculations.
Results: We find that transport by meridional circulation and shear turbulence yields far too high a core rotation rate for red-giant models compared with recent seismic observations. We discuss several uncertainties in the physical description of stars that could have an impact on the rotation profiles. For instance, we find that the Goldreich-Schubert-Fricke instability does not extract enough angular momentum from the core to account for the discrepancy. In contrast, an increase of the horizontal turbulent viscosity by 2 orders of magnitude is able to significantly decrease the central rotation rate on the red-giant branch.
Conclusions: Our results indicate that it is possible that the prescription for the horizontal turbulent viscosity largely underestimates its actual value or else a mechanism not included in current stellar models of low mass stars is needed to slow down the rotation in the radiative core of red-giant stars. Title: Stellar Tides Authors: Zahn, Jean-Paul Bibcode: 2013LNP...861..301Z Altcode: To a first approximation, a binary star behaves as a closed system; therefore it conserves its angular momentum while evolving to its state of minimum kinetic energy, where the orbits are circular, all spins are aligned, and the components rotate in synchronism with the orbital motion. The pace at which this final state is reached depends on the physical processes responsible for the dissipation of the tidal kinetic energy. For stars with an outer convection zone, the dominant mechanism is presumably the turbulent dissipation acting on the equilibrium tide. For stars with an outer radiation zone, the major dissipative process is radiative damping operating on the dynamical tide. Title: The anelastic equilibrium tide in exoplanetary systems Authors: Remus, F.; Mathis, S.; Zahn, J. -P.; Lainey, V. Bibcode: 2012sf2a.conf..245R Altcode: 2012arXiv1208.0377R Earth-like planets have anelastic mantles, whereas giant planets may have anelastic cores. As for the fluid parts of a body, the tidal dissipation of such solid regions, gravitationally perturbed by a companion body, highly depends on its internal friction, and thus on its internal structure. Therefore, modelling this kind of interaction presents a high interest to provide constraints on planet interiors, whose properties are still quite uncertain. Here, we examine the equilibrium tide in the solid central region of a planet, taking into account the presence of a fluid envelope. We discuss how the quality factor Q depends on the rheological parameters, and the size of the core. Taking plausible values for the anelastic parameters, and examinig the frequency-dependence of the solid dissipation, we show how this mechanism may compete with the dissipation in fluid layers, when applied to Jupiter- and Saturn-like planets. We also discuss the case of the icy giants Uranus and Neptune. Title: The Anelastic Equilibrium Tide in Giant Planets Authors: Remus, Francoise; Mathis, S.; Zahn, J.; Lainey, V. Bibcode: 2012DPS....4411319R Altcode: Once a planetary system is formed, its dynamical evolution is governed by gravitational interactions between its components, be it a star-planet or planet-satellite interaction. By converting kinetic energy into heat, the tides pertub their orbital and rotational properties. The rate at which the system evolves depends on the physical properties of tidal dissipation. Therefore, to understand the past history and predict the fate of a binary system, one has to identify the dissipative processes that achieve this conversion of energy. Planetary systems display a large diversity of planets by their composition. Since tidal mechanism is closely related with the internal structure of the perturbed body, one has to investigate its effects on either its fluid and solid layers. Studies have been carried out on tidal effects in fluid bodies such as stars and envelopes of giant planets. However, the planetary solid regions may also contribute to tidal dissipation, be it the mantles of Earth-like planets that have been investigated by many works, or the cores of giant planets. The purpose of our study is to determine the tidal dissipation in the solid central regions of giant planets, taking into account the presence of a fluid envelope. We derive the different Love numbers that describe the anelastic deformation and discuss the dependence of the quality factor Q on the rheological parameters and the size of the core. Taking plausible values for these parameters, and discussing the frequency-dependence of the solid dissipation, we show how this mechanism may compete with the dissipation in fluid layers, when applied to Jupiter- and Saturn-like planets. We also discuss the case of the icy giants Uranus and Neptune. Finally, we present the way to implement the results in the equations that describe the dynamical evolution of planetary systems. Title: Anelastic tidal dissipation in multi-layer planets Authors: Remus, F.; Mathis, S.; Zahn, J. -P.; Lainey, V. Bibcode: 2012epsc.conf..840R Altcode: 2012espc.conf..840R Earth-like planets have anelastic mantles, whereas giant planets may have anelastic cores. As for the fluid parts of a body, the tidal dissipation of such solid regions, gravitationally perturbed by a companion body, highly depends on its internal friction, and thus on its internal structure. Therefore, modelling this kind of interaction presents a high interest to provide constraints on planets interiors, whose properties are still quite uncertain. Here, we examine the equilibrium tide in the solid part of a planet, taking into account the presence of a fluid envelope. We derive the different Love numbers that describe its deformation and discuss the dependence of the quality factor Q on the chosen anelastic model and the size of the core. Taking plausible values for the anelastic parameters, and discussing the frequency-dependence of the solid dissipation, we show how this mechanism may compete with the dissipation in fluid layers, when applied to Jupiter- and Saturn-like planets. We also discuss the case of the icy giants Uranus and Neptune. Finally, we present the way to implement the results in the equations that describe the dynamical evolution of planetary systems. Title: The equilibrium tide in stars and giant planets. I. The coplanar case Authors: Remus, F.; Mathis, S.; Zahn, J. -P. Bibcode: 2012A&A...544A.132R Altcode: 2012arXiv1205.3536R Context. Since 1995, more than 500 extrasolar planets have been discovered orbiting very close to their parent star, where they experience strong tidal interactions. Their orbital evolution depends on the physical mechanisms that cause tidal dissipation, which remain poorly understood.
Aims: We refine the theory of the equilibrium tide in fluid bodies that are partly or entirely convective, to predict the dynamical evolution of the systems. In particular, we examine the validity of modeling the tidal dissipation using the quality factor Q, which is commonly done. We consider here the simplest case where the considered star or planet rotates uniformly, all spins are aligned, and the companion is reduced to a point mass.
Methods: We expand the tidal potential as a Fourier series, and express the hydrodynamical equations in the reference frame, which rotates with the corresponding Fourier component. The results are cast in the form of a complex disturbing function, which may be implemented directly in the equations governing the dynamical evolution of the system.
Results: The first manifestation of the tide is to distort the shape of the star or planet adiabatically along the line of centers. This generates the divergence-free velocity field of the adiabatic equilibrium tide, which is stationary in the frame rotating with the considered Fourier component of the tidal potential; this large-scale velocity field is decoupled from the dynamical tide. The tidal kinetic energy is dissipated into heat by means of turbulent friction, which is modeled here as an eddy-viscosity acting on the adiabatic tidal flow. This dissipation induces a second velocity field, the dissipative equilibrium tide, which is in quadrature with the exciting potential; this field is responsible for the imaginary part of the disturbing function, which is implemented in the dynamical evolution equations, from which one derives the characteristic evolutionary times.
Conclusions: The rate at which the system evolves depends on the physical properties of the tidal dissipation, and specifically on both how the eddy viscosity varies with tidal frequency and the thickness of the convective envelope for the fluid equilibrium tide. At low frequency, this tide is retarded by a constant time delay, whereas it lags behind by a constant angle when the tidal frequency exceeds the convective turnover rate. Title: Strong Tidal Dissipation in Saturn and Constraints on Enceladus' Thermal State from Astrometry Authors: Lainey, Valéry; Karatekin, Özgür; Desmars, Josselin; Charnoz, Sébastien; Arlot, Jean-Eudes; Emelyanov, Nicolai; Le Poncin-Lafitte, Christophe; Mathis, Stéphane; Remus, Françoise; Tobie, Gabriel; Zahn, Jean-Paul Bibcode: 2012ApJ...752...14L Altcode: 2012arXiv1204.0895L Tidal interactions between Saturn and its satellites play a crucial role in both the orbital migration of the satellites and the heating of their interiors. Therefore, constraining the tidal dissipation of Saturn (here the ratio k 2/Q) opens the door to the past evolution of the whole system. If Saturn's tidal ratio can be determined at different frequencies, it may also be possible to constrain the giant planet's interior structure, which is still uncertain. Here, we try to determine Saturn's tidal ratio through its current effect on the orbits of the main moons, using astrometric data spanning more than a century. We find an intense tidal dissipation (k 2/Q = (2.3 ± 0.7) × 10-4), which is about 10 times higher than the usual value estimated from theoretical arguments. As a consequence, eccentricity equilibrium for Enceladus can now account for the huge heat emitted from Enceladus' south pole. Moreover, the measured k 2/Q is found to be poorly sensitive to the tidal frequency, on the short frequency interval considered. This suggests that Saturn's dissipation may not be controlled by turbulent friction in the fluid envelope as commonly believed. If correct, the large tidal expansion of the moon orbits due to this strong Saturnian dissipation would be inconsistent with the moon formations 4.5 Byr ago above the synchronous orbit in the Saturnian subnebulae. But it would be compatible with a new model of satellite formation in which the Saturnian satellites formed possibly over a longer timescale at the outer edge of the main rings. In an attempt to take into account possible significant torques exerted by the rings on Mimas, we fitted a constant rate da/dt on Mimas' semi-major axis as well. We obtained an unexpected large acceleration related to a negative value of da/dt = -(15.7 ± 4.4) × 10-15 AU day-1. Such acceleration is about an order of magnitude larger than the tidal deceleration rates observed for the other moons. If not coming from an astrometric artifact associated with the proximity of Saturn's halo, such orbital decay may have significant implications on the Saturn's rings. Title: Anelastic tidal dissipation in multi-layer planets Authors: Remus, F.; Mathis, S.; Zahn, J. -P.; Lainey, V. Bibcode: 2012A&A...541A.165R Altcode: 2012arXiv1204.1468R Context. Earth-like planets have viscoelastic mantles, whereas giant planets may have viscoelastic cores. The tidal dissipation of these solid regions, which are gravitationally perturbed by a companion body, strongly depends on their rheology and the tidal frequency. Therefore, modeling tidal interactions provides constraints on planets' properties and helps us to understand their history and evolution, in either our solar system or exoplanetary systems.
Aims: We examine the equilibrium tide in the anelastic parts of a planet for every rheology, and by taking into account the presence of a fluid envelope of constant density. We show how to obtain the different Love numbers describing its tidal deformation, and discuss how the tidal dissipation in the solid parts depends on the planet's internal structure and rheology. Finally, we show how our results may be implemented to describe the dynamical evolution of planetary systems.
Methods: We expand in Fourier series the tidal potential exerted by a point mass companion, and express the dynamical equations in the orbital reference frame. The results are cast in the form of a complex disturbing function, which may be implemented directly in the equations governing the dynamical evolution of the system.
Results: The first manifestation of the tide is to distort the shape of the planet adiabatically along the line of centers. The response potential of the body to the tidal potential then defines the complex Love numbers, whose real part corresponds to the purely adiabatic elastic deformation and the imaginary part accounts for dissipation. The tidal kinetic energy is dissipated into heat by means of anelastic friction, which is modeled here by the imaginary part of the complex shear modulus. This dissipation is responsible for the imaginary part of the disturbing function, which is implemented in the dynamical evolution equations, from which we derive the characteristic evolution times.
Conclusions: The rate at which the system evolves depends on the physical properties of the tidal dissipation, and specifically on (1) how the shear modulus varies with tidal frequency, (2) the radius, and (3) the rheological properties of the solid core. The quantification of the tidal dissipation in the solid core of giant planets reveals a possible high dissipation that may compete with dissipation in fluid layers. Title: The fluid equilibrium tide in stars and giant planets Authors: Remus, F.; Mathis, S.; Zahn, J. -P. Bibcode: 2011sf2a.conf..515R Altcode: Many extrasolar planets orbit very close to their parent star, so that they experience strong tidal interactions; by converting mechanical energy into heat, these tides contribute to the dynamical evolution of such systems. This motivates us to seek a deeper understanding of the processes that cause tidal dissipation, which depend both on the internal structure and the physical properties of the considered bodies. Here, we examine the equilibrium tide, i.e. the hydrostatic adjustment to the tidal potential, in a rotating fluid planet or star. We derive the adiabatic velocity field induced by the tidal perturbation and discuss in particular how the quality factor Q characterizing the dissipation is linked whith the turbulent viscosity of convection zones. Finally, we show how the results may be implemented to describe the dynamical evolution of the system. Title: The equilibrium tide in viscoelastic parts of planets Authors: Remus, F.; Mathis, S.; Zahn, J. -P.; Lainey, V. Bibcode: 2011sf2a.conf..519R Altcode: Earth-like planets have viscoelastic mantles, whereas giant planets may have viscoelastic cores. As for the fluid parts of a body, the tidal dissipation of such solid regions, gravitationally perturbed by a companion body, highly depends on the tidal frequency, as well as on the rheology. Therefore, modelling tidal interactions presents a high interest to provide constraints on planet properties, and to understand their history and their evolution. Here, we examine the equilibrium tide in the solid core of a planet, taking into account the presence of a fluid envelope. We explain how to obtain the different Love numbers that describe its deformation. Next, we discuss how the quality factor Q depends on the chosen viscoelastic model. Finally, we show how the results may be implemented to describe the dynamical evolution of planetary systems. Title: Magnetic confinement of the solar tachocline: The oblique dipole Authors: Strugarek , A.; Brun, A. S.; Zahn, J. -P. Bibcode: 2011AN....332..891S Altcode: 2011arXiv1112.1319A 3D MHD global solar simulations coupling the turbulent convective zone and the radiative zone have been carried out. Essential features of the Sun such as differential rotation, meridional circulation and internal waves excitation are recovered. These realistic models are used to test the possibility of having the solar tachocline confined by a primordial inner magnetic field. We find that the initially confined magnetic fields we consider open into the convective envelope. Angular momentum is transported across the two zones by magnetic torques and stresses, establishing the so-called Ferarro's law of isorotation. In the parameter space studied, the confinement of the magnetic field by meridional circulation penetration fails, also implying the failure of the tachocline confinement by the magnetic field. Three-dimensional convective motions are proven responsible for the lack of magnetic field confinement. Those results are robust for the different magnetic field topologies considered, i.e. aligned or oblique dipole. Title: The fluid equilibrium tide in stars and giant planets Authors: Remus, F.; Mathis, S.; Zahn, J. -P. Bibcode: 2011epsc.conf.1366R Altcode: 2011DPS....43.1366R Many extrasolar planets orbit very close to their parent star, so that they experience strong tidal interactions; by converting mechanical energy into heat, these tides contribute to the dynamical evolution of such systems. This motivates us to acquire a deeper understanding of the processes that cause tidal dissipation, which depend both on the structure and the physical properties of the considered body. Here we examine the equilibrium tide, i.e. the hydrostatic adjustment to the tidal potential, in a rotating fluid planet or star. We first present the equations governing the problem, and show how to rigorously separate the equilibrium tide from the dynamical tide, which is due to the excited eigenmodes. We discuss in particular how the quality factor Q is linked whith the turbulent viscosity of the convection zone. Finally we show how the results may be implemented to describe the dynamical evolution of the system. Title: The elasto-viscous equilibrium tide in exoplanetary systems Authors: Remus, F.; Mathis, S.; Zahn, J. -P.; Lainey, V. Bibcode: 2011epsc.conf.1372R Altcode: 2011DPS....43.1372R Earth-like planets have viscoelastic mantles. Moreover, giant planets may have viscoelastic cores. As for the fluid parts of a body, the tidal dissipation of such solid regions, gravitationally perturbed by a companion body, highly depends on its internal friction, and thus on the rheology, as well as on its size. Therefore, modelling this kind of interaction presents a high interest to provide constraints on planets properties. Here, we examine the equilibrium tide in the solid part of a planet, taking into account the presence of a fluid envelope. We first present the equations governing the problem, and show how to obtain the different Love numbers that describe its deformation. We discuss how the quality factor Q depends on the chosen viscoelastic model. Finally we show how the results may be implemented to describe the dynamical evolution of planetary systems. Title: Mixing in Stars Authors: Zahn, Jean-Paul Bibcode: 2011iasa.confE..18Z Altcode: No abstract at ADS Title: The fluid Equilibrium Tide In Stars And Giant Planets Authors: Remus, Françoise; Mathis, S.; Zahn, J. Bibcode: 2011ESS.....2.3401R Altcode: Many extrasolar planets orbit very close to their parent star, so that they experience strong tidal interactions; by converting mechanical energy into heat, these tides contribute to the dynamical evolution of such systems. This motivates us to acquire a deeper understanding of the processes that cause tidal dissipation, which depend both on the structure and the physical properties of the considered body.

Here we examine the equilibrium tide, i.e. the hydrostatic adjustment to the tidal potential, in a rotating fluid planet or star. We first present the equations governing the problem, and show how to rigorously separate the equilibrium tide from the dynamical tide, which is due to the excited eigenmodes. We discuss in particular how the quality factor Q is linked whith the turbulent viscosity of the convection zone. Finally we show how the results may be implemented to describe the dynamical evolution of the system. Title: Magnetic confinement of the solar tachocline: influence of turbulent convective motions Authors: Strugarek, Antoine; Brun, Allan Sacha; Zahn, Jean-Paul Bibcode: 2011IAUS..271..399S Altcode: We present the results of 3D simulations, performed with the ASH code, of the nonlinear, magnetic coupling between the convective and radiative zones in the Sun, through the tachocline. Contrary to the predictions of Gough & McIntyre (1998), a fossil magnetic field, deeply buried initially in the solar interior, will penetrate into the convection zone. According to Ferraro's law of iso-rotation, the differential rotation of the convective zone will thus expand into the radiation zone, along the field lines of the poloidal field. Title: Magnetic confinement of the solar tachocline: II. Coupling to a convection zone Authors: Strugarek, A.; Brun, A. S.; Zahn, J. -P. Bibcode: 2011A&A...532A..34S Altcode: 2011arXiv1107.3665S Context. The reason for the observed thinness of the solar tachocline is still not well understood. One of the explanations that have been proposed is that a primordial magnetic field renders the rotation uniform in the radiation zone.
Aims: We test here the validity of this magnetic scenario through 3D numerical MHD simulations that encompass both the radiation zone and the convection zone.
Methods: The numerical simulations are performed with the anelastic spherical harmonics (ASH) code. The computational domain extends from 0.07R⊙ to 0.97R⊙.
Results: In the parameter regime we explored, a dipolar fossil field aligned with the rotation axis cannot remain confined in the radiation zone. When the field lines are allowed to interact with turbulent unstationary convective motions at the base of the convection zone, 3D effects prevent the field confinement.
Conclusions: In agreement with previous work, we find that a dipolar fossil field, even when it is initially buried deep inside the radiation zone, will spread into the convective zone. According to Ferraro's law of iso-rotation, it then imprints on the radiation zone the latitudinal differential rotation of the convection zone, which is not observed. Title: Juri Toomre and the art of modeling convection zones Authors: Zahn, Jean-Paul Bibcode: 2011IAUS..271..339Z Altcode: Thermal convection plays a very important role in the structure and evolution of stars, as it is one of the main physical processes that transport heat from their interior where it is released, to the surface where it is radiated into space. Much progress has been achieved in modeling that process during the past 60 years, and I shall recall here how Juri Toomre has greatly contributed to it. Title: Rapid rotation and mixing in active OB stars - Physical processes Authors: Zahn, Jean-Paul Bibcode: 2011IAUS..272...14Z Altcode: In the standard description of stellar interiors, O and B stars possess a thoroughly mixed convective core surrounded by a stable radiative envelope in which no mixing occurs. But as is well known, this model disagrees strongly with the spectroscopic diagnostic of these stars, which reveals the presence at their surface of chemical elements that have been synthesized in the core. Hence the radiation zone must be the seat of some mild mixing mechanisms. The most likely to operate there are linked with the rotation: these are the shear instabilites triggered by the differential rotation, and the meridional circulation caused by the changes in the rotation profile accompanying the non-homologous evolution of the star. In addition to these hydrodynamical processes, magnetic stresses may play an important role in active stars, which host a magnetic field. These physical processes will be critically examined, together with some others that have been suggested. Title: On the shape of rapidly rotating stars Authors: Zahn, J. -P.; Ranc, C.; Morel, P. Bibcode: 2010A&A...517A...7Z Altcode:
Aims: The critical surface of a rapidly rotating star is determined, assuming that the rotation is either uniform or shellular (angular velocity constant on level surfaces, but increasing with depth).
Methods: A step beyond the classical Roche model, where the entire mass is assumed to be gathered at the center of the star, here the quadrupolar moment of the mass distribution is taken into account through a linear perturbation method.
Results: The flattening (defined here as the ratio between the equatorial and the polar radius) can somewhat exceed the 3/2 value of the Roche model, depending on the strength of the interior rotation. The result is applied to a star of 7 solar masses, which is the mass of Achernar, the star with the largest flattening detected so far through optical interferometry. Title: The impact of magnetic fields on stellar structure and evolution Authors: Zahn, J. -P. Bibcode: 2009CoAst.158...27Z Altcode: Magnetic fields responsible for various activity phenomena have been detected at the surface of many stars. Presumably they are also present in the stars' deep interior. They channel stellar winds to large distance, thus increasing the loss of angular momentum. In stably stratified radiation zones, they tend to impose uniform rotation, and may thus interfere with the rotational mixing operating in these regions and influence the evolution of the host star. Moreover, certain magnetic configurations are known to be unstable, and they could produce some mixing of their own. We shall discuss these problems in the light of the latest developments. Title: Spanish Relativity Meeting Encuentros Relativistas Espanoles Authors: Mediavilla, Evencio; Oscoz, Alex; Serra-Ricart, Miquel; Zahn, Jean-Paul Bibcode: 2009srme.book.....M Altcode: No abstract at ADS Title: On MHD rotational transport, instabilities and dynamo action in stellar radiation zones Authors: Mathis, Stéphane; Brun, A. -S.; Zahn, J. -P. Bibcode: 2009IAUS..259..421M Altcode: Magnetic field and their related dynamical effects are thought to be important in stellar radiation zones. For instance, it has been suggested that a dynamo, sustained by a m = 1 MHD instability of toroidal magnetic fields (discovered by Tayler in 1973), could lead to a strong transport of angular momentum and of chemicals in such stable regions. We wish here to recall the different magnetic transport processes present in radiative zone and show how the dynamo can operate by recalling the conditions required to close the dynamo loop (BPol → BTor → BPol). Helped by high-resolution 3D MHD simulations using the ASH code in the solar case, we confirm the existence of the m = 1 instability, study its non-linear saturation, but we do not detect, up to a magnetic Reylnods number of 105, any dynamo action. Title: ISSI Workshop on Solar Magnetism: Concluding Remarks Authors: Zahn, Jean-Paul Bibcode: 2009SSRv..144..423Z Altcode: No abstract at ADS Title: Diagnoses to unravel secular hydrodynamical processes in rotating main sequence stars Authors: Decressin, T.; Mathis, S.; Palacios, A.; Siess, L.; Talon, S.; Charbonnel, C.; Zahn, J. -P. Bibcode: 2009A&A...495..271D Altcode: 2008arXiv0812.0363D Context: Recent progress and constraints brought by helio and asteroseismology call for a better description of stellar interiors and an accurate description of rotation-driven mechanisms in stars.
Aims: We present a detailed analysis of the main physical processes responsible for the transport of angular momentum and chemical species in the radiative regions of rotating stars. We focus on cases where meridional circulation and shear-induced turbulence all that are included in the simulations (i.e., no either internal gravity waves nor magnetic fields). We put special emphasis on analysing the angular momentum transport loop and on identifying the contribution of each of the physical process involved.
Methods: We develop a variety of diagnostic tools designed to help disentangle the role of the various transport mechanisms. Our analysis is based on a 2-D representation of the secular hydrodynamics, which is treated using expansions in spherical harmonics. By taking appropriate horizontal averages, the problem reduces to one dimension, making it implementable in a 1D stellar evolution code, while preserving the advective character of angular momentum transport. We present a full reconstruction of the meridional circulation and of the associated fluctuations of temperature and mean molecular weight, along with diagnosis for the transport of angular momentum, heat, and chemicals. In the present paper these tools are used to validate the analysis of two main sequence stellar models of 1.5 and 20 M_⊙, for which the hydrodynamics has previously been extensively studied in the literature.
Results: We obtain a clear visualisation and a precise estimation of the different terms entering the angular momentum and heat transport equations in radiative zones of rotating stars. This enables us to corroborate the main results obtained over the past decade by Zahn, Maeder, and collaborators concerning the secular hydrodynamics of such objects. We focus on the meridional circulation driven by angular momentum losses and structural readjustments. We confirm quantitatively for the first time through detailed computations and separation of the various components that the advection of entropy by this circulation is balanced very well by the barotropic effects and the thermal relaxation during most of the main sequence evolution. This enables us to simplify for the thermal relaxation on this phase. The meridional currents in turn advect heat and generate temperature fluctuations that induce differential rotation through thermal wind, thus closing the transport loop. We plan to make use of our refined diagnosis tools in forthcoming studies of secular (magneto-)hydrodynamics of stars at various evolutionary stages. Title: CoRot observations of active giants: preliminary results Authors: Gondoin, P.; Fridlund, M.; Goupil, M. J.; Baudin, F.; Samadi, R.; Barban, C.; Belkacem, K.; Corbard, T.; Dupret, M. A.; Foing, B.; den Hartog, R.; Lebreton, Y.; Lochard, J.; Mathias, P.; Michel, E.; Morel, P.; Moya, A.; Palacios, A.; Zahn, J. P. Bibcode: 2009AIPC.1094..864G Altcode: 2009csss...15..864G We have analysed rotation modulated light-curves of active giants observed with CoRot using spots model. Preliminary results suggest an increase of the surface spot coverage with decreasing rotation period. A maximum of the surface spot coverage seems to occur on giants with effective temperature around 5100 K. Confirmation and interpretation of these preliminary results require groundbased follow-up observations to measure activity indicators, to identify binary systems, and to determine the stellar parameters and evolutionary status of the sample giants. Title: Stellar Magnetism Authors: Neiner, C.; Zahn, J. -P. Bibcode: 2009EAS....39.....N Altcode: No abstract at ADS Title: The impact of magnetic fields on stellar structure and evolution Authors: Zahn, J. -P. Bibcode: 2009EAS....39..211Z Altcode: Magnetic fields have been detected at the surface of many stars, where they are responsible for various activity phenomena, and presumably they are present also in their deep interior. They channel stellar winds to large distance, thus increasing the loss of angular momentum. In stably stratified radiation zones, they tend to impose uniform rotation, and may thus interfere with the rotational mixing operating in these regions and influence the evolution of the host star. Moreover, certain magnetic configurations are known to be unstable, and they could produce some mixing of their own. We shall discuss these problems in the light of the latest developments. Title: ISSI Workshop on Solar Magnetism: Concluding Remarks Authors: Zahn, Jean-Paul Bibcode: 2009odsm.book..423Z Altcode: No abstract at ADS Title: The Origin and Dynamics of Solar Magnetism Authors: Thompson, M. J.; Balogh, A.; Culhane, J. L.; Nordlund, Å.; Solanki, S. K.; Zahn, J. -P. Bibcode: 2009odsm.book.....T Altcode: No abstract at ADS Title: Foreword Authors: Neiner, Coralie; Zahn, Jean-Paul Bibcode: 2009EAS....39D...3N Altcode: No abstract at ADS Title: The Sun: A Slowly Rotating Star Authors: Zahn, J. -P. Bibcode: 2009LNP...765....1Z Altcode: After a brief historical sketch, we compare the slowly rotating Sun to other stars and explain how it was able to lose so much of its angular momentum. We next discuss the physical processes that may be responsible for its internal rotation profile and conclude that the most efficient of them is the transport of angular momentum by the gravito-inertial waves excited at the base of the convection zone. Title: Effects of rotation on stellar structure: rotation induced mixing Authors: Zahn, J. -P. Bibcode: 2008CoAst.157..196Z Altcode: Standard models of stellar structure are unable to account for various observational facts, such as the appearance at the surface of chemical elements that have been produced in the nuclear core. Thus there is now a large consensus that some ‘extra mixing’ must occur in the radiation zones. This mixing is achieved mainly through the shear-turbulence generated by the differential rotation, which itself results from the transport of angular momentum by a large-scale circulation that is induced either by the structural adjustments accompanying the evolution or by the applied torques (stellar wind, accretion, tides). These processes are now being implemented in stellar evolution codes, and they provide a much better agreement with the observations. Title: Stellar Nucleosynthesis: 50 years after B2FH Authors: Charbonnel, C.; Zahn, J. -P. Bibcode: 2008EAS....32.....C Altcode: No abstract at ADS Title: Dynamical aspects of stellar physics Authors: Zahn, J. -P.; Brun, A. -S.; Mathis, S. Bibcode: 2008sf2a.conf..341Z Altcode: Several manifestations of the dynamics of stellar interiors are briefly presented, with emphasis on the most recent developments in their numerical simulation. Title: Foreword Authors: Charbonnel, C.; Zahn, J. -P. Bibcode: 2008EAS....32D...3C Altcode: No abstract at ADS Title: Thermohaline mixing and fossil magnetic fields in red giant stars Authors: Charbonnel, Corinne; Zahn, Jean-Paul Bibcode: 2008IAUS..252..245C Altcode: We discuss the occurence and consequences of thermohaline mixing in RGB stars, as well as the possible inhibition of this process by a fossil magnetic field in Ap star descendants. Title: On MHD rotational transport, instabilities and dynamo action in stellar radiation zones Authors: Mathis, S.; Zahn, J. -P.; Brun, A. -S. Bibcode: 2008IAUS..252..255M Altcode: Magnetic field is an essential dynamical process in stellar radiation zones. Moreover, it has been suggested that a dynamo action, sustained by a MHD instability which affects the toroidal axisymmetric magnetic field, could lead to a strong transport of angular momentum and of chemicals in such regions. Here, we recall the different magnetic transport and mixing processes in radiative regions. Next, we show that the dynamo cannot operate as described by Spruit (2002) and recall the condition required to close the dynamo loop. We perform high-resolution 3D simulations with the ASH code, where we observe indeed the MHD instability, but where we do not detect any dynamo action, contrary to J. Braithwaite (2006). We conclude on the picture we get for magnetic transport mechanisms in radiation zones and the associated consequences for stellar evolution. Title: Wave transport in stellar radiation zone influenced by the Coriolis acceleration Authors: Mathis, S.; Talon, S.; Pantillon, F. P.; Charbonnel, C.; Zahn, J. P. Bibcode: 2008JPhCS.118a2025M Altcode: Internal gravity waves constitute an efficient process for angular momentum transport over large distances. They are now seen as an important ingredient in understanding the evolution of rotation, and could explain the Sun's quasi-flat rotation profile. Because the Sun's rotation frequency is of the same order as that of the waves, it is necessary to refine our description of wave propagation and to take into account the action of the Coriolis acceleration in a coherent way. To achieve this aim, we adopt the Traditional Approximation which is verified in stellar radiation zones. We present the modified transport equations and their numerical evaluation in a parameter range that is significant for the Sun. The effectiveness of gravity waves, which become gravito-inertial waves, is reduced while new type of waves, namely the Rossby, the Yanai and the Kelvin waves appear with their associated transport. Title: Instabilities and mixing in stellar radiation zones Authors: Zahn, Jean-Paul Bibcode: 2008IAUS..252...47Z Altcode: The standard model of stellar structure is unable to account for various observational facts, and there is now a large consensus that some ‘extra mixing’ must occur in the radiation zones. The possible causes for such mixing are briefly reviewed. The most efficient among them is probably the shear-turbulence generated by the differential rotation, which itself results from the transport of angular momentum that can be mediated through the large-scale circulation induced by structural adjustments or by the applied torques (stellar wind, accretion, tides). In solar-type stars this angular momentum transport is ensured mainly by internal gravity waves that are excited at the boundary with convection zones. Another cause of mixing manifests itself in the red giant phase, namely the thermohaline instability due to an inversion of the molecular weight gradient. The implementation of these processes in stellar evolution codes is giving rise to a new generation of stellar models, which are in much better agreement with the observational constraints. Title: Angular Momentum Transport in the Sun's Radiative Zone by Gravito-Inertial Waves Authors: Mathis, S.; Talon, S.; Pantillon, F. -P.; Zahn, J. -P. Bibcode: 2008SoPh..251..101M Altcode: 2008SoPh..tmp...48M Internal gravity waves constitute an efficient process for angular momentum transport over large distances. They are now seen as an important ingredient in understanding the evolution of stellar rotation and can explain the Sun's quasi-flat internal-rotation profile. Because the Sun's rotation frequency is of the same order as that of the waves, it is now necessary to refine our description of wave propagation and to take into account the action of the Coriolis acceleration in a coherent way. To achieve this goal, we adopt the traditional approximation, which can be applied to stellar radiation zones under conditions that are given. We present the modified transport equations and their numerical evaluation in a parameter range that is significant for the Sun. Consequences for the transport of angular momentum inside solar and stellar radiative regions are discussed. Title: Tidal dissipation in binary systems Authors: Zahn, J. -P. Bibcode: 2008EAS....29...67Z Altcode: 2008arXiv0807.4870Z To first approximation, a binary system conserves its angular momentum while it evolves to its state of minimum kinetic energy: circular orbit, all spins aligned, and components rotating in synchronism with the orbital motion. The pace at which this final state is achieved depends on the physical processes that are responsible for the dissipation of the tidal kinetic energy. For stars (or planets) with an outer convection zone, the dominant mechanism identified so far is the viscous dissipation acting on the equilibrium tide. For stars with an outer radiation zone, it is the radiative damping operating on the dynamical tide.

After a brief presentation of the tides, I shall review these physical processes; I shall discuss the uncertainties of their present treatment, describe the latest developments, and compare the theoretical predictions with the observed properties concerning the orbital circularization of close binaries. Title: Star formation in accretion discs: from the Galactic center to active galactic nuclei Authors: Collin, S.; Zahn, J. -P. Bibcode: 2008A&A...477..419C Altcode: 2007arXiv0709.3772C Context: Keplerian accretion discs around massive black holes (MBHs) are gravitationally unstable beyond a few hundredths of a parsec, and they should collapse to form stars. It has indeed been shown recently that an accretion/star formation episode took place a few million years ago in the Galactic center (GC). This raises the question of how the disc can survive in AGN and quasars and continue to transport matter towards the black hole.
Aims: We study the accretion/star formation process in quasars and AGN with one aim in mind: to show that a spectrum similar to the observed one can be produced by the disc.
Methods: We compute models of stationary accretion discs that are either continuous or clumpy. Continuous discs must be maintained in a state of marginal stability so that the rate of star formation remains modest and the disc is not immediately destroyed. The disc then requires additional heating and additional transport of angular momentum. In clumpy discs, the momentum transport is provided by cloud interactions.
Results: Non-viscous heating can be provided by stellar illumination, but in the case of continuous discs, even momentum transport by supernovae is insufficient for sustaining a marginal state, except at the very periphery of the disc. In clumpy discs it is possible to account for the required accretion rate through interactions between clouds, but this model is unsatisfactory because its parameters are tightly constrained without any physical justification.
Conclusions: Finally one must appeal to non-stationary discs with intermittent accretion episodes like those that occurred in the GC, but such a model is probably not applicable either to luminous high redshift quasars or to radio-loud quasars. Title: Foreword Authors: Goupil, M. -J.; Zahn, J. -P. Bibcode: 2008EAS....29D...3G Altcode: No abstract at ADS Title: Hydrodynamic stability and mode coupling in Keplerian flows: local strato-rotational analysis Authors: Tevzadze, A. G.; Chagelishvili, G. D.; Zahn, J. -P. Bibcode: 2008A&A...478....9T Altcode: 2007arXiv0710.3648T Aims:We present a qualitative analysis of key (but yet unappreciated) linear phenomena in stratified hydrodynamic Keplerian flows: (i) the occurrence of a vortex mode, as a consequence of strato-rotational balance, with its transient dynamics; (ii) the generation of spiral-density waves (also called inertia-gravity or gΩ waves) by the vortex mode through linear mode coupling in shear flows.
Methods: Non-modal analysis of linearized Boussinesq equations were written in the shearing sheet approximation of accretion disk flows.
Results: It is shown that the combined action of rotation and stratification introduces a new degree of freedom, vortex mode perturbation, which is in turn linearly coupled with the spiral-density waves. These two modes are jointly able to extract energy from the background flow, and they govern the disk dynamics in the small-scale range. The transient behavior of these modes is determined by the non-normality of the Keplerian shear flow. Tightly leading vortex mode perturbations undergo substantial transient growth, then, becoming trailing, inevitably generate trailing spiral-density waves by linear mode coupling. This course of events - transient growth plus coupling - is particularly pronounced for perturbation harmonics with comparable azimuthal and vertical scales, and it renders the energy dynamics similar to the 3D unbounded plane Couette flow case.
Conclusions: Our investigation strongly suggests that the so-called bypass concept of turbulence, which has been recently developed by the hydrodynamic community for spectrally stable shear flows, can also be applied to Keplerian disks. This conjecture may be confirmed by appropriate numerical simulations that take the vertical stratification and consequent mode coupling into account in the high Reynolds number regime. Title: Tidal Effects in Stars, Planets and Disks Authors: Goupil, M. -J.; Zahn, J. -P. Bibcode: 2008EAS....29.....G Altcode: No abstract at ADS Title: Meridional circulation in the radiation zones of rotating stars: Origins, behaviors and consequences on stellar evolution Authors: Mathis, S.; Decressin, T.; Palacios, A.; Eggenberger, P.; Siess, L.; Talon, S.; Charbonnel, C.; Turck-Chièze, S.; Zahn, J. -P. Bibcode: 2007AN....328.1062M Altcode: Stellar radiation zones are the seat of meridional currents. This circulation has a strong impact on the transport of angular momentum and the mixing of chemicals that modify the evolution of stars. First, we recall in details the dynamical processes that are taking place in differentially rotating stellar radiation zones and the assumptions which are adopted for their modelling in stellar evolution. Then, we present our new results of numerical simulations which allow us to follow in 2D the secular hydrodynamics of rotating stars, assuming that anisotropic turbulence enforces a shellular rotation law and taking into account the transport of angular momentum by internal gravity waves. The different behaviors of the meridional circulation in function of the type of stars which is studied are discussed with their physical origin and their consequences on the transport of angular momentum and of chemicals. Finally, we show how this work is leading to a dynamical vision of the evolution of rotating stars from their birth to their death. Title: Inhibition of thermohaline mixing by a magnetic field in Ap star descendants: implications for the Galactic evolution of 3He Authors: Charbonnel, C.; Zahn, J. -P. Bibcode: 2007A&A...476L..29C Altcode: 2007arXiv0711.3395C Aims:To reconcile the measurements of ^3He/H in Galactic HII regions with high values of ^3He in a couple of planetary nebulae, we propose that thermohaline mixing is inhibited by a fossil magnetic field in red giant stars that are descendants of Ap stars.
Methods: We examine the effect of a magnetic field on the salt-finger instability, using a local analysis.
Results: We obtain a threshold for the magnetic field of 10^4{-}105 Gauss, above which it inhibits thermohaline mixing in red giant stars located at or above the bump. Fields of that order are expected in the descendants of the Ap stars, taking into account the contraction of their core.
Conclusions: We conclude that in a large fraction of the descendants of Ap stars thermohaline mixing does not occur. As a consequence these objects must produce ^3He as predicted by the standard theory of stellar evolution and as observed in the planetary nebulae NGC 3242 and J320. The relative number of such stars with respect to non-magnetic objects that undergo thermohaline mixing is consistent with the statistical constraint coming from observations of the carbon isotopic ratio in red giant stars. It also satisfies the Galactic requirements for the evolution of the ^3He abundance. Title: On magnetic instabilities and dynamo action in stellar radiation zones Authors: Zahn, J. -P.; Brun, A. S.; Mathis, S. Bibcode: 2007A&A...474..145Z Altcode: 2007arXiv0707.3287Z Context: We examine the MHD instabilities arising in the radiation zone of a differentially rotating star, in which a poloidal field of fossil origin is sheared into a toroidal field.
Aims: We focus on the non-axisymmetric instability that affects the toroidal magnetic field in a rotating star, which was first studied by Pitts and Tayler in the non-dissipative limit. If such an instability were able to mix the stellar material, it could have an impact on the evolution of the star. According to Spruit, it could also drive a dynamo.
Methods: We compare the numerical solutions built with the 3-dimensional ASH code with the predictions drawn from an analytical study of the Pitts & Tayler instability.
Results: The Pitts & Tayler instability is manifestly present in our simulations, with its conspicuous m=1 dependence in azimuth. But its analytic treatment used so far is too simplified to be applied to the real stellar situation. Although the instability generated field reaches an energy comparable to that of the mean poloidal field, that field seems unaffected by the instability: it undergoes Ohmic decline, and is neither eroded nor regenerated by the instability. The toroidal field is produced by shearing the poloidal field and it draws its energy from the differential rotation. The small scale motions behave as Alfvén waves; they cause negligible eddy-diffusivity and contribute little to the net transport of angular momentum.
Conclusions: In our simulations we observe no sign of dynamo action, of either mean field or fluctuation type, up to a magnetic Reynolds number of 10^5. However the Pitts & Tayler instability is sustained as long as the differential rotation acting on the poloidal field is able to generate a toroidal field of sufficient strength. But in the Sun such a poloidal field of fossil origin is ruled out by the nearly uniform rotation of the deep interior. Title: Can a dynamo operate in stellar radiation zones? Authors: Zahn, J. -P.; Brun, A. S.; Mathis, S. Bibcode: 2007sf2a.conf..566Z Altcode: We examine the MHD instabilities arising in the radiation zone of a differentially rotating star, in which a poloidal field of fossil origin is sheared into a toroidal field. The numerical solutions built with the 3-dimensional ASH code are compared with the predictions drawn from an analytical study of the Pitts & Tayler instability. This instability is manifestly present in our simulations, with its conspicuous m=1 dependence in azimuth. However, although the instability generated field reaches an energy comparable to that of the mean poloidal field, that field seems unaffected by the instability: it undergoes Ohmic decline, and is neither eroded nor regenerated by the instability. The instability is sustained as long as the differential rotation acting on the poloidal field is able to generate a toroidal field of sufficient strength but, up to a magnetic Reynolds number of 10^5, we observe no sign of dynamo action, of either mean field or fluctuation type, contrary to what was suggested by Spruit. Title: Transport and mixing by internal waves in stellar interiors: effect of the Coriolis force Authors: Mathis, S.; Zahn, J. -P. Bibcode: 2007arXiv0706.2446M Altcode: We briefly recall the physical background of the transport of angular momentum and the mixing of chemicals inside stellar radiation zones and its importance for stellar evolution. Then, we describe its present modeling, its successes and its weaknesses. Next, we introduce the new theoretical developments that allow us to treat in a self-consistent way the effect of the Coriolis force on the low-frequencies internal waves and its consequences for the transport processes. This research is aimed at improving the modeling of stellar interiors in the perspective of future astero and helioseismology missions such as COROT and GOLF-NG. Title: Thermohaline mixing: a physical mechanism governing the photospheric composition of low-mass giants Authors: Charbonnel, C.; Zahn, J. -P. Bibcode: 2007A&A...467L..15C Altcode: 2007astro.ph..3302C Aims:Numerous spectroscopic observations provide compelling evidence for a non-canonical mixing process that modifies the surface abundances of Li, C and N of low-mass red giants when they reach the bump in the luminosity function. Eggleton and collaborators have proposed that a molecular weight inversion created by the ^3He(^3He, 2p)^4He reaction may be at the origin of this mixing, and relate it to the Rayleigh-Taylor instability. We argue that one is actually dealing with a double diffusive instability referred to as thermohaline convection and we discuss its influence on the red giant branch.
Methods: We compute stellar models of various initial metallicities that include thermohaline mixing, which is treated as a diffusive process based on the prescription given originally by Ulrich for the turbulent diffusivity produced by the thermohaline instability in stellar radiation zones.
Results: Thermohaline mixing simultaneously accounts for the observed behaviour of the carbon isotopic ratio and of the abundances of Li, C and N in the upper part of the red giant branch. It significantly reduces the ^3He production with respect to canonical evolution models as required by measurements of ^3He/H in galactic HII regions.
Conclusions: Thermohaline mixing is a fundamental physical process that must be included in stellar evolution modeling. Title: Concluding remarks Authors: Zahn, Jean-Paul Bibcode: 2007IAUS..239..517Z Altcode: 2006astro.ph.12056Z To be published in the proceedings of IAU Symposium 239 "Convection in Astrophysics" (ed. F. Kupka, I. W. Roxburgh, K. L. Chan). Content: 1. From Nice to Prague, 2. The triumph of 3-D simulations, 3. How to lower the cost - what else can be done? 4. A powerful tool to determine surface abundances, 5. The effects of convection are not confined to convection zones, 6. Towards a realistic model of the solar dynamo, 7. The moment of truth: facing observational tests, 8. On my wish-list. Title: On shear-induced turbulence in rotating stars Authors: Mathis, S.; Palacios, A.; Zahn, J. -P. Bibcode: 2007A&A...462.1063M Altcode: No abstract at ADS Title: Modeling Stellar Interiors with Rotational Mixing Authors: Zahn, J. -P. Bibcode: 2007EAS....26...49Z Altcode: Although it presently includes convective overshoot, microscopic diffusion, gravitational settling and radiative acceleration, the standard model of stellar structure is still unable to account for various observational facts, and there is now a large consensus that some extra mixing must occur in the radiation zones. To account for such mixing, the minimalist approach consists in introducing a parametrized turbulent diffusivity, and to adjust it so as to match the observations. A better way is to strive to implement the physical processes that may be responsible for this mixing, in particular shear-induced turbulence and large-scale meridional circulation, which both are linked with the differential rotation of the star. To describe that rotational mixing, as we call it, one has thus to follow the evolution of the internal rotation profile. By making some plausible assumptions, its is possible to reduce the advection of angular momentum through the 2-D circulation to a 1-D process, and that of the chemical elements to a vertical diffusion. It is then possible to implement these transports in a 1-D stellar evolution code. In massive stars, angular momentum is transported mainly by the meridional circulation, and there is good agreement between the observations and the predictions based on the rotational mixing. This not so for solar-type stars where another, more efficient mechanism is required to transport angular momentum. A fossil magnetic field has been invoked, but recently it has been shown that such a field would connect with the convection zone, and imprint its differential rotation on the radiation zone, which is not observed. The other candidate is the transport of angular momentum by the internal gravity waves that are emitted at the base of the convection zone; although their treatment is still somewhat crude, it appears that they can explain both the quasi-uniform rotation of the solar interior, and the depletion of lithium observed in such stars. Title: On hydrodynamic shear turbulence in spectrally stable Keplerian disks Authors: Lominadze, J. G.; Tevzadze, A. G.; Chagelishvili, G. D.; Zahn, J. -P.; Chanishvili, R. G. Bibcode: 2007acag.conf..335L Altcode: No abstract at ADS Title: Hydrodynamic models of the tachocline Authors: Zahn, Jean-Paul Bibcode: 2007sota.conf...89Z Altcode: No abstract at ADS Title: Advances in Secular Magnetohydrodynamics of Stellar Interiors Dedicated to Asteroseismic Spatial Missions Authors: Mathis, S.; Eggenberger, P.; Decressin, T.; Palacios, A.; Siess, L.; Charbonnel, C.; Turck-Chièze, S.; Zahn, J. -P. Bibcode: 2007EAS....26...65M Altcode: 2007astro.ph..3117M With the first light of COROT, the preparation of KEPLER and the future helioseismology spatial projects such as GOLF-NG, a coherent picture of the evolution of rotating stars from their birth to their death is needed. We describe here the modelling of the macroscopic transport of angular momentum and matter in stellar interiors that we have undertaken to reach this goal. First, we recall in detail the dynamical processes that are driving these mechanisms in rotating stars and the theoretical advances we have achieved. Then, we present our new results of numerical simulations which allow us to follow in 2D the secular hydrodynamics of rotating stars, assuming that anisotropic turbulence enforces a shellular rotation law. Finally, we show how this work is leading to a dynamical vision of the Hertzsprung-Russel diagram with the support of asteroseismology and helioseismology, seismic observables giving constraints on the modelling of the internal transport and mixing processes. In conclusion, we present the different processes that should be studied in the near future to improve our description of stellar radiation zones. Title: Why Bothering to Measure Stellar Rotation with CoRoT? Authors: Goupil, M. J.; Moya, A.; Suarez, J. C.; Lochard, J.; Barban, C.; Dias Do Nascimento, J.; Dupret, M. A.; Samadi, R.; Baglin, A.; Zahn, J. P.; Hubert, A. M.; Brun, S.; Boisnard, L.; Morel, P.; Garrido, R.; Mathis, S.; Michel, E.; Renan de Medeiros, J.; Palacios, A.; Lignières, F.; Rieutord, E. M. Bibcode: 2006ESASP1306...51G Altcode: One important goal of the CoRoT experiment is to obtain information about the internal rotation of stars, in particular the ratio of central to surface rotation rates. This will provide constraints on the modelling of transport mechanisms of angular momentum acting in radiative (rotationally induced turbulent) and convective zones (plumes, extension beyond convectively instable regions). Relations between the surface rotation period and age, magnetic activity, mass loss and other stellar characteristics can also be studied with a statistically significant set of data as will be provided by Corot. We present various theoretical efforts performed over the past years in order to develope the theoretical tools which will enable us to study rotation with Corot. Title: Magnetic confinement of the solar tachocline Authors: Brun, A. S.; Zahn, J. -P. Bibcode: 2006A&A...457..665B Altcode: 2006astro.ph.10069B Context: .We study the physics of the solar tachocline (i.e. the thin transition layer between differential rotation in the convection zone and quasi uniform rotation in the radiative interior), and related MHD instabilities.
Aims: .We have performed 3D MHD simulations of the solar radiative interior to check whether a fossil magnetic field is able to prevent the spread of the tachocline.
Methods: .Starting with a purely poloidal magnetic field and a latitudinal shear meant to be imposed by the convection zone at the top of the radiation zone, we have investigated the interactions between magnetic fields, rotation and shear, using the spectral code ASH on massively parallel supercomputers.
Results: .In all cases we have explored, the fossil field diffuses outward and ends up connecting with the convection zone, whose differential rotation is then imprinted at latitudes above ≈40° throughout the radiative interior, according to Ferraro's law of isorotation. Rotation remains uniform in the lower latitude region which is contained within closed field lines. We find that the meridional flow cannot stop the inward progression of the differential rotation. Further, we observe the development of non-axisymmetric magnetohydrodynamic instabilities, first due to the initial poloidal configuration of the fossil field, and later to the toroidal field produced by shearing the poloidal field through the differential rotation. We do not find dynamo action as such in the radiative interior, since the mean poloidal field is not regenerated. But the instability persists during the whole evolution, while slowly decaying with the mean poloidal field; it is probably sustained by small departures from isorotation.
Conclusions: .According to our numerical simulations, a fossil magnetic field cannot prevent the radiative spread of the tachocline, and thus it is unable to enforce uniform rotation in the radiation zone. Neither can the observed thinness of that layer be invoked as a proof for such an internal fossil magnetic field. Title: The DynaMICS perspective Authors: Turck-Chièze, S.; Schmutz, W.; Thuillier, G.; Jefferies, S.; Pallé; Dewitt, S.; Ballot, J.; Berthomieu, G.; Bonanno, A.; Brun, A. S.; Christensen-Dalsgaard, J.; Corbard, T.; Couvidat, S.; Darwich, A. M.; Dintrans, B.; Domingo, V.; Finsterle, W.; Fossat, E.; Garcia, R. A.; Gelly, B.; Gough, D.; Guzik, J.; Jiménez, A. J.; Jiménez-Reyes, S.; Kosovichev, A.; Lambert, P.; Lefebvre, S.; Lopes, I.; Martic, M.; Mathis, S.; Mathur, S.; Nghiem, P. A. P.; Piau, L.; Provost, J.; Rieutord, M.; Robillot, J. M.; Rogers, T.; Roudier, T.; Roxburgh, I.; Rozelot, J. P.; Straka, C.; Talon, S.; Théado, S.; Thompson, M.; Vauclair, S.; Zahn, J. P. Bibcode: 2006ESASP.624E..24T Altcode: 2006soho...18E..24T No abstract at ADS Title: Dynamical processes in stellar radiation zones: secular magnetohydrodynamics of rotating stars Authors: Mathis, S.; Decressin, T.; Palacios, A.; Siess, L.; Charbonnel, C.; Turck-Chièze, S.; Zahn, J. -P. Bibcode: 2006ESASP.624E..36M Altcode: 2006soho...18E..36M No abstract at ADS Title: Dynamical processes in stellar radiation zones Authors: Mathis, S.; Decressin, T.; Palacios, A.; Siess, L.; Charbonnel, C.; Turck-Chièze, S.; Zahn, J. -P. Bibcode: 2006IAUJD..17E..18M Altcode: With the progress of asteroseismology, we need a coherent picture of the evolution of rotating stars from their birth to their death. We describe here the modelling of the macroscopic transport of matter and angular momentum in stellar interiors that we have undertaken to achieve this goal. First, we briefly recall the dynamical processes that are driving these mechanisms in rotating stars. Then, we present our new results of numerical simulations which allow us to follow in 2D the secular hydrodynamics of rotating stars, assuming that anisotropic turbulence enforces a cellular rotation law. We discuss the different processes such as MHD instabilities that should be studied in the next future to improve our description of dynamical processes in stellar radiation zones. Finally, we show how our new results are leading us to a dynamical vision of Hertzsprung-Russell diagram, in support of asteroseismology. Title: Scientific Objectives of the Novel Formation Flying Mission Aspiics Authors: Turck-Chièze, S.; Schmutz, W.; Thuillier, G.; Jefferies, S.; Pallé; Dewitt, S.; Ballot, J.; Berthomieu, G.; Bonanno, A.; Brun, A. S.; Christensen-Dalsgaard, J.; Corbard, T.; Couvidat, S.; Darwich, A. M.; Dintrans, B.; Domingo, V.; Finsterle, W.; Fossat, E.; Garcia, R. A.; Gelly, B.; Gough, D.; Guzik, J.; Jiménez, A. J.; Jiménez-Reyes, S.; Kosovichev, A.; Lambert, P.; Lefebvre, S.; Lopes, I.; Martic, M.; Mathis, S.; Mathur, S.; Nghiem, P. A. P.; Piau, L.; Provost, J.; Rieutord, M.; Robillot, J. M.; Rogers, T.; Roudier, T.; Roxburgh, I.; Rozelot, J. P.; Straka, C.; Talon, S.; Théado, S.; Thompson, M.; Vauclair, S.; Zahn, J. P. Bibcode: 2006ESASP.617E.164L Altcode: 2006soho...17E.164L No abstract at ADS Title: The EUV Variability Experiment (EVE) on the Solar Dynamics Observatory (SDO): Science Plan and Instrument Overview Authors: Turck-Chièze, S.; Schmutz, W.; Thuillier, G.; Jefferies, S.; Pallé; Dewitt, S.; Ballot, J.; Berthomieu, G.; Bonanno, A.; Brun, A. S.; Christensen-Dalsgaard, J.; Corbard, T.; Couvidat, S.; Darwich, A. M.; Dintrans, B.; Domingo, V.; Finsterle, W.; Fossat, E.; Garcia, R. A.; Gelly, B.; Gough, D.; Guzik, J.; Jiménez, A. J.; Jiménez-Reyes, S.; Kosovichev, A.; Lambert, P.; Lefebvre, S.; Lopes, I.; Martic, M.; Mathis, S.; Mathur, S.; Nghiem, P. A. P.; Piau, L.; Provost, J.; Rieutord, M.; Robillot, J. M.; Rogers, T.; Roudier, T.; Roxburgh, I.; Rozelot, J. P.; Straka, C.; Talon, S.; Théado, S.; Thompson, M.; Vauclair, S.; Zahn, J. P. Bibcode: 2006ESASP.617E.165W Altcode: 2006soho...17E.165W No abstract at ADS Title: The Dynamics Project Authors: Turck-Chièze, S.; Schmutz, W.; Thuillier, G.; Jefferies, S.; Pallé; Dewitt, S.; Ballot, J.; Berthomieu, G.; Bonanno, A.; Brun, A. S.; Christensen-Dalsgaard, J.; Corbard, T.; Couvidat, S.; Darwich, A. M.; Dintrans, B.; Domingo, V.; Finsterle, W.; Fossat, E.; Garcia, R. A.; Gelly, B.; Gough, D.; Guzik, J.; Jiménez, A. J.; Jiménez-Reyes, S.; Kosovichev, A.; Lambert, P.; Lefebvre, S.; Lopes, I.; Martic, M.; Mathis, S.; Mathur, S.; Nghiem, P. A. P.; Piau, L.; Provost, J.; Rieutord, M.; Robillot, J. M.; Rogers, T.; Roudier, T.; Roxburgh, I.; Rozelot, J. P.; Straka, C.; Talon, S.; Théado, S.; Thompson, M.; Vauclair, S.; Zahn, J. P. Bibcode: 2006ESASP.617E.162T Altcode: 2006soho...17E.162T No abstract at ADS Title: Tidal effects in extrasolar planetary systems Authors: Mathis, S.; Zahn, J. -P. Bibcode: 2006sf2a.conf..487M Altcode: With the discovery of new extrasolar planetary systems day after day, we have to understand the physical processes which are driving the dynamical evolution of such systems. We focus here on the tidal processes acting between stars and their giant fluid planets. We describe briefly our new theoretical results on the hydrodynamical tides (equilibrium and dynamical tides). In particular, we present the complete set of dynamical equations governing the tidal evolution which we have derived in a consistent way and for the most general case: eccentric orbits, non synchronized components, general inclination between the orbital spin and those of components. Title: Dynamical processes in stellar radiation zones: secular magnetohydrodynamics of rotating stars Authors: Mathis, S.; Decressin, T.; Palacios, A.; Siess, L.; Charbonnel, C.; Turck-Chièze, S.; Zahn, J. -P. Bibcode: 2006sf2a.conf..491M Altcode: With the imminent launch of COROT and the preparation of new helioseismology instruments such as GOLF-NG (cf. DynaMICS project), we need a coherent picture of the evolution of rotating stars from their birth to their death. We describe here the modeling of the macroscopic transport of angular momentum and matter in stellar interiors that we have undertaken to achieve this goal. First, we recall the dynamical processes that are driving this transport in rotating stars and the theoretical advances we have accomplished. Then, we present our new results of numerical simulations which allow us to follow in 2D the secular hydrodynamics of rotating stars, assuming that anisotropic turbulence enforces a shellular rotation law. Finally, we show how this work is leading to a dynamical vision of the Hertzsprung-Russel diagram in support of asteroseismology and helioseismology. Title: Magnetic instabilities in stellar radiation zones Authors: Brun, A. S.; Zahn, J. -P. Bibcode: 2006sf2a.conf..451B Altcode: Using the 3-dimensional ASH code, we have studied numerically the instabilities that occur in stellar radiation zones in presence of large-scale magnetic fields and differential rotation. We confirm that some configurations are linearly unstable, as predicted by Tayler and collaborators, and we determine the saturation level of the instability. However we found no sign of the dynamo mechanism suggested recently by Spruit. Title: Energy flow in acoustic black holes Authors: Choy, K.; Kruk, T.; Carrington, M. E.; Fugleberg, T.; Zahn, J.; Kobes, R.; Kunstatter, G.; Pickering, D. Bibcode: 2006PhRvD..73j4011C Altcode: 2005gr.qc.....5163C We present the results of an analysis of superradiant energy flow due to scalar fields incident on an acoustic black hole. In addition to providing independent confirmation of the recent results in [E. Berti, V. Cardoso, and J. P. S. Lemos, Phys. Rev. D 70, 124006 (2004).PRVDAQ0556-282110.1103/PhysRevD.70.124006], we determine in detail the profile of energy flow everywhere outside the horizon. We confirm explicitly that in a suitable frame the energy flow is inward at the horizon and outward at infinity, as expected on physical grounds. Title: Rotational mixing in stellar radiation zones: successes and weaknesses Authors: Zahn, J. -P. Bibcode: 2006EAS....19..147Z Altcode: The common way to build stellar models is to treat the radiation zones as inert, stable regions, in contrast with the well mixed convection zones. This allows to account for the main features of stellar evolution, such as the main sequence and the existence of red giants. But there are many indications that some mixing occurs within the radiation zones, and that it has an impact on the later stages. Manuel Forestini was one the first to undertake the implementation of such mixing in his stellar code, and thus to go beyond the standard model. Here I will briefly describe the mixing processes that are likely to operate in stellar radiation zones, as we understand them today, and discuss how well they account for the observed properties of stars. Title: Probing the internal magnetic field of slowly pulsating B-stars through g modes Authors: Hasan, S. S.; Zahn, J. -P.; Christensen-Dalsgaard, J. Bibcode: 2005A&A...444L..29H Altcode: 2005astro.ph.11472H Context: .
Aims: .We suggest that high-order g modes can be used as a probe of the internal magnetic field of SPB (slowly pulsating B) stars. The idea is based on earlier work by the authors hich analytically investigated the effect of a vertical magnetic field on p and g modes in a plane-parallel isothermal stratified atmosphere. It was found that even a weak field can significantly shift the g-mode frequencies - the effect increases with mode order.
Methods: .In the present study we adopt the classical perturbative approach to estimate the internal field of a 4 solar mass SPB star by looking at its effect on a low-degree (l=1) and high-order (n=20) g mode with a period of about 1.5 d.
Results: .We find that a polar field strength of about 110 kG on the edge of the convective core is required to produce a frequency shift of 1%. Frequency splittings of that order have been observed in several SPB variables, in some cases clearly too small to be ascribed to rotation. We suggest that they may be due to a poloidal field with a strength of order 100 kG, buried in the deep interior of the star.
Conclusions: . Title: Transport and mixing by internal waves in stellar interiors: effect of the Coriolis force Authors: Mathis, S.; Zahn, J. -P. Bibcode: 2005sf2a.conf..319M Altcode: We briefly recall the physical background of the transport of angular momentum and the mixing of chemicals inside stellar radiation zones and its importance for stellar evolution. Then, we describe its present modeling, its successes and its weaknesses. Next, we introduce the new theoretical developments that allow us to treat in a self-consistent way the effect of the Coriolis force on the low-frequencies internal waves and its consequences for the transport processes. This research is aimed at improving the modeling of stellar interiors in the perspective of future astero and helioseismology missions such as COROT and GOLF-NG. Title: What did we learn from the tidal evolution theory? Authors: Zahn, J. -P. Bibcode: 2005ASPC..333..280Z Altcode: These notes follow the powerpoint presentation which was prepared to trigger the discussion. I tried my best to incorporate in the text the comments, questions and answers made by the participants. I hope they will forgive me for not quoting them individually. Title: Physical mechanisms for tidal dissipation Authors: Zahn, J. -P. Bibcode: 2005ASPC..333....4Z Altcode: A binary system tends to its state of minimum kinetic energy, for given (and conserved) angular momentum : circular orbit, all spins aligned, and rotation of the components synchronized with the orbital motion. The pace at which this final state is achieved depends on the physical processes which are responsible for the dissipation of the kinetic energy. For stars (or planets) with an outer convection zone, the dominant mechanism identified so far is the viscous dissipation acting on the equilibrium tide. For stars with an outer radiation zone, it is the radiative damping operating on the dynamical tide. I shall review these physical processes, discuss the uncertainties of their present treatment, present the latest developments, and compare the theoretical predictions with the observed properties concerning the orbital circularization of close binaries. Title: Equilibrium tides in differentially rotating stars Authors: Mathis, S.; Zahn, J. -P. Bibcode: 2005ASPC..333..108M Altcode: In this work, we present new theoretical advances in the modelization of the equilibrium tide in the convective envelope of solar-type binary stars. We simplify the problem by assuming that all the spins are aligned but we take into account the two-dimensional character of the rotation law in the convection zone. Following the method of Zahn (1966) we first derive the adiabatic tide which is in phase with the perturbing potential exerted by the companion. Next, we derive the dissipative tide which is in quadrature with it, using the crude MLT eddy-viscosity to model the action of turbulence on the large scale tidal flow. Finally, we discuss the impact of those processes on the dynamical evolution of binary systems. Note that our results may be applied as well to giant planets and to exo-planets, since these possess also a convection zone. Title: Tidal Evolution and Oscillations in Binary Stars Authors: Claret, A.; Giménez, A.; Zahn, J. -P. Bibcode: 2005ASPC..333.....C Altcode: No abstract at ADS Title: Transport and mixing in the radiation zones of rotating stars. II. Axisymmetric magnetic field Authors: Mathis, S.; Zahn, J. -P. Bibcode: 2005A&A...440..653M Altcode: 2005astro.ph..6105M The purpose of this paper is to improve the modeling of the mixing of chemical elements that occurs in stellar radiation zones. In addition to the classical rotational mixing considered in our previous paper, which results of the combined action of the thermally-driven meridional circulation and of the turbulence generated by the shear of differential rotation, we include here the effect of an axisymmetric magnetic field in a self-consistent way. We treat the advection of the field by the meridional circulation, its Ohmic diffusion, and the production of its toroidal component through the shear of differential rotation. The Lorentz force is assumed not to exceed the centrifugal force; it acts on the baroclinic balance and therefore on the meridional flow, and it has a strong impact on the transport of angular momentum. All variables and governing equations are expanded in spherical or spherical vectorial functions, to arbitrary order: this yields a system of partial differential equations in time and in the radial coordinate, which is ready to be implemented in a stellar structure code. Title: Stability and turbulent transport in Taylor-Couette flow from analysis of experimental data Authors: Dubrulle, B.; Dauchot, O.; Daviaud, F.; Longaretti, P. -Y.; Richard, D.; Zahn, J. -P. Bibcode: 2005PhFl...17i5103D Altcode: 2011arXiv1106.1276D This paper provides discussion and prescription about stability and transport in the Taylor-Couette experiment, a rotating shear flow with shear perpendicular to the rotation axis. Such geometry frequently occurs in geophysical or astrophysical context. The prescriptions we obtain are the result of a detailed analysis of the experimental data obtained in several studies of the transition to turbulence and turbulent transport in Taylor-Couette flow. We first introduce a new set of control parameters, based on dynamical rather than geometrical considerations, so that they may be relevant to any rotating shear flows in general and not only to Taylor-Couette flow. We then investigate the transition thresholds in the supercritical and the subcritical regime in order to extract their general dependencies on the control parameters. The inspection of the mean profiles provides us with some general hints on the turbulent to laminar shear ratio. Then the examination of the torque data allows us to propose a decomposition of the torque dependence on the control parameters in two terms, one completely determined by measurements in the case where the outer cylinder is at rest, the other one being a universal function deduced here from experimental fits. As a result, we obtain a general expression for the turbulent viscosity and compare it to existing prescriptions in the literature. Finally, throughout the paper we discuss the influence of additional effects such as stratification or magnetic fields. Title: Circularization in B-Bype Eclipsing Binaries in both Magellanic Clouds Authors: North, P.; Zahn, J. -P. Bibcode: 2005HiA....13..466N Altcode: Making use of detached eclipsing binaries discovered by the OGLE and MACHO teams in the SMC and in the LMC respectively we give the value of the fractional radius above which cirularization occurs. This critical radius is around 0.25 to 0.26 regardless of the mass surface gravity or metallicity and is consistent with that found by Giuricin et al. (1984) for galactic binaries. These empirical facts are shown to be consistent with Zahn's (1975) theory of tidal dissipation. As a by-product of this study we provide approximate stellar parameters of the average component of 148 binaries in the SMC and of 354 binaries (some of which might be non-detached) in the LMC under the assumption of equal components. Title: An hydrodynamic shear instability in stratified disks Authors: Dubrulle, B.; Marié, L.; Normand, Ch.; Richard, D.; Hersant, F.; Zahn, J. -P. Bibcode: 2005A&A...429....1D Altcode: 2004astro.ph.10224D We discuss the possibility that astrophysical accretion disks are dynamically unstable to non-axisymmetric disturbances with characteristic scales much smaller than the vertical scale height. The instability is studied using three methods: one based on the energy integral, which allows the determination of a sufficient condition of stability, one using a WKB approach, which allows the determination of the necessary and sufficient condition for instability and a last one by numerical solution. This linear instability occurs in any inviscid stably stratified differential rotating fluid for rigid, stress-free or periodic boundary conditions, provided the angular velocity Ω decreases outwards with radius r. At not too small stratification, its growth rate is a fraction of Ω. The influence of viscous dissipation and thermal diffusivity on the instability is studied numerically, with emphasis on the case when d ln Ω / d ln r =-3/2 (Keplerian case). Strong stratification and large diffusivity are found to have a stabilizing effect. The corresponding critical stratification and Reynolds number for the onset of the instability in a typical disk are derived. We propose that the spontaneous generation of these linear modes is the source of turbulence in disks, especially in weakly ionized disks. Title: The Spite plateau: a puzzle and a challenge for the stellar physicist Authors: Zahn, Jean-Paul Bibcode: 2005IAUS..228...41Z Altcode: In order to use the lithium abundance of the Spite plateau to constrain the Big Bang Nucleosynthesis, one has to determine how much of the original lithium has been destroyed by the various physical processes that are known to operate in stellar radiation zones. These are briefly reviewed, with emphasis on the mixing occurring in tachoclines and on that generated indirectly by the transport of angular momentum through internal gravity waves. Title: Processes competing with atomic diffusion: mass loss, turbulence, rotation, etc. Authors: Zahn, J. -P. Bibcode: 2005EAS....17..157Z Altcode: Due to radiative acceleration and gravitational settling, stars would display vast differences in their surface composition, if these were not smoothed out, at least partly, by some competing processes. Possible mechanisms have been suggested and examined by Georges Michaud and his collaborators: mass loss, turbulent mixing and meridional circulation. They will be discussed here in the light of more recent developments. Title: Mixing in stellar radiation zones: new theoretical results Authors: Mathis, S.; Zahn, J. -P. Bibcode: 2004sf2a.conf..543M Altcode: 2004sf2a.confE.289M We briefly recall the physical background of the rotational mixing occurring inside stellar radiation zones and its importance for stellar evolution. We describe its present modelization, its successes and its weaknesses. Next, we introduce the new theoretical results which allow us to treat the hydrodynamical processes simultaneously in the bulk of radiation zones and in the tachoclines, and we present our new prescription for the horizontal turbulent transport which has been derived from Couette-Taylor laboratory experiment. Finally, we show how to introduce self-consistently the effect of an axi or non-axisymmetric magnetic field, which may be responsible for the angular momentum transport in low-mass stars (internal gravity waves are another candidate). This research is aimed at improving the modelization of stellar interiors in the perspective of future astero and helioseismology missions such as COROT, EDDINGTON and GOLF-NG, and of new powerful ground-based instruments as ESPADON. Title: Advances in the modelization of binary systems: revisiting the equilibrium tide Authors: Mathis, S.; Zahn, J. -P. Bibcode: 2004sf2a.conf..241M Altcode: 2004sf2a.confE.317M In this work, we present new theoretical advances in the modelization of the equilibrium tide in the convective envelope of solar-type binary stars. We take into account the two-dimensional character of the rotation law in the convection zone and the inclination of the spin of each component with respect to the orbital one. Following the method of Zahn (1966) we first derive the adiabatic tide which is in phase with the perturbing potential exerted by the companion. Next, we derive the dissipative tide which is in quadrature with it, using the crude MLT eddy-viscosity to modelize the action of turbulence on the large scale tidal flow. Finally, we discuss the impact of those processes on the dynamical evolution of binary systems. Note that our results may be applied as well to giant planets and to exo-planets, since these possess also a convection zone. Title: Transport and mixing in the radiation zones of rotating stars. I. Hydrodynamical processes Authors: Mathis, S.; Zahn, J. -P. Bibcode: 2004A&A...425..229M Altcode: 2004astro.ph..6418M The purpose of this paper is to improve the modelization of the rotational mixing which occurs in stellar radiation zones, through the combined action of the thermally driven meridional circulation and of the turbulence generated by the shear of differential rotation. The turbulence is assumed to be anisotropic, due to the stratification, with stronger transport in the horizontal directions than in the vertical. The main difference with the former treatments by Zahn (\cite{Zahn1992}, A&A, 265, 115) and Maeder & Zahn (\cite{Maeder1998}, A&A, 334, 1000) is that we expand here the departures from spherical symmetry to higher order, and include explicitly the differential rotation in latitude, to first order. This allows us to treat simultaneously the bulk of a radiation zone and its tachocline(s). Moreover, we take fully into account the non-stationarity of the problem, which will enable us to tackle the rapid phases of evolution. The system of partial differential equations, which govern the transport of angular momentum, heat and chemical elements, is written in a form which makes it ready to implement in a stellar evolution code. Here the effect of a magnetic field is deliberately ignored; it will be included in forthcoming papers.

Appendices are only available in electronic form at http://www.edpsciences.org Title: On shear-induced turbulence in rotating stars Authors: Mathis, S.; Palacios, A.; Zahn, J. -P. Bibcode: 2004A&A...425..243M Altcode: 2004astro.ph..3580M We review various prescriptions which have been proposed for the turbulent transport of matter and angular momentum in differentially rotating stellar radiation zones. A new prescription is presented for the horizontal transport associated with the anisotropic shear turbulence which is produced by the differential rotation in latitude; this ``β-viscosity'' is drawn from torque measurements in the classical Couette-Taylor experiment (Richard & Zahn \cite{Richard99}, A&A, 347, 734). Its implementation in a stellar evolution code leads to enhanced mixing, as illustrated by models of a rotating main-sequence star of 1.5 solar mass. Title: Circularization in B-type eclipsing binaries in both Magellanic Clouds Authors: North, P.; Zahn, J. -P. Bibcode: 2004NewAR..48..741N Altcode: By making use of detached eclipsing binaries with B-type components discovered by the OGLE and MACHO teams in the SMC and in the LMC, we give the value of the fractional radius above which circularization occurs. This critical radius is around 0.24-0.26, regardless of the mass, surface gravity or metallicity, and is consistent with that found by Giuricin et al. [A&A 134 (1984) 365] for galactic binaries. These empirical facts are shown to be consistent with Zahn's [A&A 41 (1975) 329] theory of tidal dissipation. As a by-product of this study, we provide approximate stellar parameters of the average component of 148 binaries in the SMC and of up to 353 binaries (some of which might be non-detached) in the LMC, under the assumption of equal components. Title: Summary and Concluding Remarks (Invited Review) Authors: Zahn, J. -P. Bibcode: 2004IAUS..215..616Z Altcode: No abstract at ADS Title: Rotational mixing in stellar radiation zones Authors: Zahn, J. -P. Bibcode: 2004EAS....13...63Z Altcode: Contrary to what is assumed in building standard stellar models, all stars undergo some mild mixing in their radiation zones. This mixing is due mainly to a slow thermally driven meridional circulation, and shear turbulence presumably contributes to it. It is the rotation of the star which is responsible for these motions, and therefore the transport of angular momentum must be described in time and space when modeling stellar evolution. This rotational mixing plays an important role in the evolution of massive stars; in particular it determines the late, pre-supernova phases. We review the present state of the problem and discuss briefly the open questions. Title: Evolution of Massive Stars, Mass Loss and Winds Authors: Heydari-Malayeri, M.; Stee, Ph.; Zahn, J. -P. Bibcode: 2004EAS....13.....H Altcode: No abstract at ADS Title: Foreword Authors: Heydari-Malayeri, Mohammad; Stee, Philippe; Zahn, Jean-Paul Bibcode: 2004EAS....13D...3H Altcode: This volume presents a large selection of the lectures which have been given during two consecutive Summer Schools in Stellar Physics (XII and XIII). The first of these schools took place in Aussois, a ski resort in the Alps, on 13-18 October 2002, and it dealt with the formation and the evolution of massive stars. The second was held at Oléron, an island off the Atlantic shore, on 6-10 October 2003, and it focussed on mass loss from stars and on stellar winds. The subjects of these two schools are closely linked, since massive stars lose an important fraction of their mass in the course of their evolution, and that is why we merged the lecture notes in a single volume.In spite of their relatively small number, massive stars play a key role in several aspects. They are the principal sites of nucleosynthesis, and because most of their matter is ejected by their winds and in the final supernova explosion, they are responsible for the chemical evolution of their host galaxy, and thus of the Universe. They are the main energy providers to the interstellar medium, through their winds and their UV radiation. Finally, since they are very luminous, they can be detected in remote galaxies, delivering precious clues about star formation.In recent years, one has become increasingly aware that their evolution strongly depends on the mass they lose, and on the internal mixing which is induced by rotation, as was emphasized by two world experts of the subject: André Maeder in Aussois, and Georges Meynet in Oléron. These effects must be taken into account when modeling these stars, or else one misses completely the late stages of evolution.In massive stars the mass loss occurs through radiation driven winds, whose description has benefited tremendously from the development of new techniques of high angular resolution, and from observation in space. The physical processes involved are now much better understood, and they are being reproduced in the laboratory. Who else than Stan Owocki could we ask to give us such a complete picture of mass ejection, by contrasting these winds blowing from hot stars with those, much less powerful, emitted by solar-type stars?Beside these principal lectures, several others were devoted to various specific topics: the formation of massive stars, the late phases, rotational mixing, the structure of the winds, the role of binarity, colliding winds, wind diagnostics, even laboratory experiments reproducing radiative shocks.We hope that the reader will find as much interest in these proceedings as the participants of these schools did in listening to the lectures. We wish to express our warm thanks to all lecturers for the excellent quality of their talks and and of their proceedings, and for their disponibility. We thank the Formation Permanente du CNRS and the Programme National de Physique Stellaire for funding these annual Schools on Stellar Physics, and to Frédéric Ménadier, Monique Michel and Mireille Petit for taking care of the organisational aspects. Mohammad Heydari-Malayeri, Philippe Stee and Jean-Paul Zahn Title: Direct NumeriSimulations of Penetrative Convection and Generation of Internal Gravity Waves Authors: Kiraga, M.; Jahn, K.; Stȩpień, K.; Zahn, J. -P. Bibcode: 2003AcA....53..321K Altcode: Two-dimensional, direct numerisimulations are used to investigate how thermal convection excites internal gravity waves in the stable layer beneath a convectively unstable zone. The mechanienergy flux carried downwards by the waves strongly depends on the viscosity coefficient. This flux is compared with the energy flux predicted by a simple parametric model of wave generation applied to two models of convection dynamics: one based on the mixing-length treatment and the other on a convective plume model. Numerisimulations always produce substantially larger energy fluxes than the parametric models. This difference may result from shortcomings of the parametric modeling but also from the fact that our simulations are two-dimensional. Title: On hydrodynamic shear turbulence in stratified Keplerian disks: Transient growth of small-scale 3D vortex mode perturbations Authors: Tevzadze, A. G.; Chagelishvili, G. D.; Zahn, J. -P.; Chanishvili, R. G.; Lominadze, J. G. Bibcode: 2003A&A...407..779T Altcode: This is a sequel to Paper I (Chagelishvili et al. \cite{Chagelishvili03}), where we presented the so-called bypass concept for the onset of turbulence in shearing flows. According to this concept, which was worked out during the last decade by the hydrodynamic community for spectrally stable flows, vortical perturbations undergo transient growth by extracting energy from the shear (a linear process), thereby reaching an amplitude which is sufficient to allow for non-linear interactions which, by positive feedback, sustain turbulence. In Paper I we described this transient growth for 2D perturbations in a Keplerian disk; we showed that their kinematics was the same as in plane-parallel flow, and thus that they were not modified by the presence of the Coriolis force. In the present paper, we pursue our goal of applying the bypass scenario to astrophysical disks: we investigate the linear dynamics of 3D small-scale vortical perturbations for single spatial harmonics, in stably stratified, differentially rotating disks, again in the framework of a nonmodal analysis. We find that these 3D perturbations also undergo substantial transient growth, and that they reach a peak amplitude that is comparable to that of 2D perturbations, as long as their vertical scale remains of the order of the azimuthal scale. When the vertical wave-number exceeds the azimuthal one, the amplification rate is reduced, but this may be more than compensated to by the huge Reynolds number and the high shear rate characterizing astrophysical Keplerian disks. Whereas in 2D the Coriolis force had no impact on the transient growth, in 3D this force somewhat constricts the characteristics of the perturbation dynamics in disk flows, and the initial transient growth is followed by some reduction in amplitude. These differences are quantitative, rather than of fundamental character. But the 3D case presents two interesting novelties. In plane parallel flow, the perturbations do not decay after their transient amplification, but their energy stays on a plateau before being dissipated through viscous friction. More importantly, especially for the astrophysicist, in disk flow the 3D vortex mode perturbations excite density-spiral waves, whose energy also settles on a plateau before viscous dissipation. These local vortex mode perturbations fit naturally into the bypass concept of hydrodynamic shear turbulence, which was first developed for plane-parallel flows. We submit that these perturbations will also play an important role in the onset and in the maintenance of turbulence in Keplerian disks. Title: Circularization in B-type eclipsing binariesin the Magellanic Clouds Authors: North, P.; Zahn, J. -P. Bibcode: 2003A&A...405..677N Altcode: Making use of detached eclipsing binaries discovered by the OGLE and MACHO teams in the SMC and in the LMC respectively, we give the value of the fractional radius above which circularization occurs. We show that this critical radius is consistent with that found for galactic binaries by Giuricin et al. (1984) and does not, therefore, depend strongly on metallicity. This conclusion is consistent with Zahn's (1975) theory of tidal dissipation. The critical radius seems slightly larger in the SMC than in the LMC, but this small difference is hardly significant and should be confirmed by a larger sample. We also explore empirically to what extent the critical radius might depend on stellar mass and surface gravity.

This paper utilizes public domain data obtained by the OGLE Project described at http://sirius.astrouw.edu.pl/ ~ ogle/ Title: On hydrodynamic shear turbulence in Keplerian disks: Via transient growth to bypass transition Authors: Chagelishvili, G. D.; Zahn, J. -P.; Tevzadze, A. G.; Lominadze, J. G. Bibcode: 2003A&A...402..401C Altcode: 2003astro.ph..2258C This paper deals with the problem of hydrodynamic shear turbulence in non-magnetized Keplerian disks. Several papers have appeared recently on the subject, on possible linear instabilities which may be due to the presence of a stable stratification, or caused by deviations from cylindrical rotation. Here we wish to draw attention to another route to hydrodynamic turbulence, which seems to be little known by the astrophysical community, but which has been intensively discussed among fluid dynamicists during the past decade. In this so-called bypass concept for the onset of turbulence, perturbations undergo transient growth and if they have initially a finite amplitude they may reach an amplitude that is sufficiently large to allow positive feedback through nonlinear interactions. This transient growth is linear in nature, and thus it differs in principle from the well-known nonlinear instability. We describe the type of perturbations that according to this process are the most likely to lead to turbulence, namely non-axisymmetric vortex mode perturbations in the two dimensional limit. We show that the apparently inhibiting action of the Coriolis force on the dynamics of such vortical perturbations is substantially diminished due to the pressure perturbations, contrary to current opinion. We stress the similarity of the turbulent processes in Keplerian disks and in Cartesian flows and conclude that the prevalent skepticism of the astrophysical community about the occurrence of hydrodynamic shear turbulence in such disks is not founded. Title: Mixing in stellar radiation zones Authors: Zahn, Jean-Paul Bibcode: 2003safd.book..205Z Altcode: Stars undergo some mild mixing in their radiation zones, which is due to a thermally driven large scale circulation, and presumably to turbulence caused by shear instabilities. It is the rotation of the star which is responsible for these motions, and therefore the transport of angular momentum must be described in time and space when modeling stellar evolution. We review the present state of the problem and discuss briefly the open questions. Title: Orbital Circularization in the Magellanic Clouds Authors: North, Pierre; Zahn, Jean-Paul Bibcode: 2003IAUJD..13E..33N Altcode: Making use of detached eclipsing binaries discovered by the OGLE and MACHO teams in the SMC and in the LMC respectively we give the value of the fractional radius above which cirularization occurs. This critical radius is around 0.25 to 0.26 regardless of the mass surface gravity or metallicity and is consistent with that found by Giuricin et al. (1984) for galactic binaries. These empirical facts are shown to be consistent with Zahn's (1975) theory of tidal dissipation. As a by-product of this study we provide approximate stellar parameters of the average component of 148 binaries in the SMC and of 354 binaries (some of which might be non-detached) in the LMC under the assumption of equal components. Title: Transport in stellar radiation zones with magnetic field Authors: Mathis, S.; Zahn, J. -P. Bibcode: 2003sf2a.conf..601M Altcode: 2003sf2a.confE.250M We examine the interaction between meridian circulation and turbulence in rotating stars with an axisymetric magnetic field. In the same way as Zahn (1992) and Spiegel and Zahn (1992), the turbulence is assumed to be anisotropic, due to the stratification, with stronger transport in the horizontal directions than in the vertical. We keep the 'shellular rotation' hypothesis, but we expand the differential rotation in latitude to higher order, which allow us to treat simultaneously the radiative interior and the tachocline(s). We derive the partial differential equations which govern the transport of magnetic field, temperature, angular momentum and chemical elements with taking into account the non-stationarity of the problem, the mu-gradients, the effect of horizontal turbulence in thermal imbalance and a general equation of state like in Maeder and Zahn (1998). Finally, we apply the beta-viscosity prescription which has been derived from Couette-Taylor experiments (Richard and Zahn (1999)) to the problem of transport in stellar interiors to obtain a new expression for the horizontal component of the turbulent viscosity, nuh, and its companion the horizontal diffusivity, Dh.

The next step will be to implement these new equations in existing stellar structure codes, to model the evolution of rotating stars. Title: Jean-Louis Leroy: a pioneer Authors: Zahn, J. -P. Bibcode: 2003EAS.....9....1Z Altcode: This meeting was dedicated to Jean-Louis Leroy, who pioneered polarimetry in French astronomy, and who is one of the leading experts in the field. He applied this diagnostics tool to better understand various astrophysical objects: the Sun, comets, stars, the interstellar medium. Some of his major achievements will be recalled here. Title: Angular Momentum Extraction by Gravity Waves in the Sun Authors: Talon, Suzanne; Kumar, Pawan; Zahn, Jean-Paul Bibcode: 2002ApJ...574L.175T Altcode: 2002astro.ph..6479T We review the behavior of the oscillating shear layer produced by gravity waves below the surface convection zone of the Sun. We show that, under asymmetric filtering produced by this layer, gravity waves of low spherical order that are stochastically excited at the base of the convection zone of late-type stars can extract angular momentum from their radiative interior. The timescale for this momentum extraction in a Sun-like star is on the order of 107 yr. The process is particularly efficient in the central region, and it could produce there a slowly rotating core. Title: Seismic tests for solar models with tachocline mixing Authors: Brun, A. S.; Antia, H. M.; Chitre, S. M.; Zahn, J. -P. Bibcode: 2002A&A...391..725B Altcode: 2002astro.ph..6180B We have computed accurate 1-D solar models including both a macroscopic mixing process in the solar tachocline as well as up-to-date microscopic physical ingredients. Using sound speed and density profiles inferred through primary inversion of the solar oscillation frequencies coupled with the equation of thermal equilibrium, we have extracted the temperature and hydrogen abundance profiles. These inferred quantities place strong constraints on our theoretical models in terms of the extent and strength of our macroscopic mixing, on the photospheric heavy elements abundance, on the nuclear reaction rates such as S11 and S34 and on the efficiency of the microscopic diffusion. We find a good overall agreement between the seismic Sun and our models if we introduce a macroscopic mixing in the tachocline and allow for variation within their uncertainties of the main physical ingredients. From our study we deduce that the solar hydrogen abundance at the solar age is Xinv=0.732+/- 0.001 and that based on the 9Be photospheric depletion, the maximum extent of mixing in the tachocline is 5% of the solar radius. The nuclear reaction rate for the fundamental pp reaction is found to be S11(0)=4.06+/- 0.07 10-25 MeV barns, i.e., 1.5% higher than the present theoretical determination. The predicted solar neutrino fluxes are discussed in the light of the new SNO/SuperKamiokande results. Title: Foreword Authors: Bouvier, Jérôme; Zahn, Jean-Paul Bibcode: 2002EAS.....3D...3B Altcode: How do stars form in molecular clouds? When and how are planetary systems assembled in circumstellar disks? How has the star formation rate varied over cosmological timescales? In the last decade, considerable progress has been made on these fundamental issues linked to the star formation process and the physics of young stellar objects and their circumstellar environment. Improved analytical and numerical models have brought new insight into the phase of cloud collapse and fragmentation as well as into the formation and evolution of circumstellar disks that are prone to form planets. At the same time, the maturation of observational techniques, such as high angular resolution imaging, and the advent of powerful telescopes on the ground and in space, have revealed new exciting aspects of the formation and early evolution of stars from the solar neighborhood to higly redshifted galaxies. The X^th Aussois School on Stellar Physics took place on September 18-22, 2000, and was intended to draw an up-to-date view of current results and concepts in the field of "Star Formation and the Physics of Young Stars". The school is primarily directed towards Ph.D. students in astrophysics and researchers from neighbouring astrophysical fields but is also an opportunity for those who work in this field to meet in a stimulating and yet relaxed atmosphere. Nearly 60 participants attended the school and benefited from week-long high-quality courses that depicted the current state of understanding of the various aspects of star formation, from the local to the cosmological scale: initial conditions in molecular clouds, gravitational collapse, pre-main sequence evolution, theory and observations of accretion disks and of the related mass ejection phenomenon, high energy processes characterizing stellar youth, observational studies of resolved young stellar populations in external galaxies, and the cosmological history of star formation. We hope that the reader will find in these Proceedings as much interest as the audience had in listening to the talks and interacting with the speakers, whom we would like to thank here for their disponibility and the excellent quality of their conferences. We also thank all the participants for the friendly atmosphere they brought to the school, the Formation Permanente du CNRS and the Programme National de Physique Stellaire for funding the annual Aussois School on Stellar Physics, and particularly F. Bouillet, N. Thiéry, M. Michel and M. Petit for taking care of all administrative and organisational aspects, as well as the Director and employees of the Centre Paul Langevin for their competence and hospitality; and, last but not least, Jean-Philippe Beaulieu and Daniele Briot for taking and prodiving the pictures. Title: Convective Overshooting: Physical Properties and Seismic Evidence (invited review) Authors: Zahn, J. -P. Bibcode: 2002ASPC..259...58Z Altcode: 2002IAUCo.185...58Z; 2002rnpp.conf...58Z No abstract at ADS Title: Star formation and the physics of young stars : Summer School on Stellar Physics 10 Authors: Bouvier, Jerome; Zahn, Jean-Paul Bibcode: 2002EAS.....3.....B Altcode: No abstract at ADS Title: Joint Discussion 5 - Mixing and diffusion in stars: introduction and brief overview Authors: Vandenberg, Don A.; Zahn, Jean-Paul Bibcode: 2002HiA....12..259V Altcode: No abstract at ADS Title: Concluding remarks [Mixing and diffusion in stars] Authors: Zahn, Jean-Paul Bibcode: 2002HiA....12..307Z Altcode: No abstract at ADS Title: A powerful local shear instability in stratified disks Authors: Richard, D.; Hersant, F.; Dauchot, O.; Daviaud, F.; Dubrulle, B.; Zahn, J-P. Bibcode: 2001astro.ph.10056R Altcode: In this paper, we show that astrophysical accretion disks are dynamically unstable to non-axisymmetric disturbances. This instability is present in any stably stratified anticyclonically sheared flow as soon as the angular velocity decreases outwards. In the large Froude number limit, the maximal growth rate is proportional to the angular rotation velocity, and is independent of the stratification. In the low Froude number limit, it decreases like the inverse of the Froude number, thereby vanishing for unstratified, centrigugally stable flows. The instability is not sensitive to disk boundaries. We discuss the possible significance of our result, and its implications on the turbulent state achieved by the disks. We conclude that this linear instability is one of the best candidates for the source of turbulence in geometrically thin disks, and that magnetic fields can be safely ignored when studying their turbulent state. The relevance of the instability for thick disks or nearly neutrally stratified disks remains to be explored. Title: Accretion discs models with the β-viscosity prescription derived from laboratory experiments Authors: Huré, J. -M.; Richard, D.; Zahn, J. -P. Bibcode: 2001A&A...367.1087H Altcode: 2000astro.ph.12262H We examine under which conditions one may apply, to steady state Keplerian accretion discs, the beta -viscosity prescription which has been derived from rotating shear flow experiments (nu = beta Omega R2, where Omega is the angular velocity at radius R and beta is a constant of order 10-5; Richard & Zahn \cite{richard99}). Using a vertically averaged model, we show that this law may be suitable for all three families of known systems: in young stellar objects, evolved binary stars and Active Galactic Nuclei discs (except in their outer gas pressure dominated regions where turbulence becomes hypersonic). According to the standard criterion for viscous stability, beta -discs are always stable throughout. Using realistic opacities and equation of state, we demonstrate that these discs are thermally unstable in the temperature domain where hydrogen recombines, when they are optically thick, and this could lead to limit cycle behavior. Radiation pressure dominated regions are thermally stable, in contrast with alpha -discs. This results in a fully stable solution for the innermost parts of AGN discs. Title: Shear turbulence beneath the solar tachocline Authors: Schatzman, E.; Zahn, J. -P.; Morel, P. Bibcode: 2000A&A...364..876S Altcode: 2000astro.ph.10543E; 2000astro.ph.10543S This paper presents a simple and efficient equation of state which can be used for quick and accurate computing of the thermodynamic functions of partly ionized and weakly coupled plasmas. Based on the free energy minimization method, the improvement of the equation of state includes a detailed account of the physical processes of non-ideal effects consisting of electron degeneracy, Coulomb coupling and pressure ionization. The treatment of Coulomb coupling combines the results of the quantum exchange effect of degenerate electrons at finite temperature, N-body semi-analytic theory and the extended Debye-Hückel theory with hard-sphere correction. For the complicated physical processes of pressure ionization an approximate model is adopted. The nonideal corrections to equation of state are calculated under solar interior conditions. Title: Hydrodynamic Instabilities Authors: Zahn, J. Bibcode: 2000eaa..bookE2091Z Altcode: Most of the universe is made of gas, over all scales ranging from the intergalactic medium to stars and giant planets. This fluid rarely remains in static equilibrium or in stationary motion—many forces and processes conspire to render it unstable. When it is unstable, it may oscillate more or less regularly around its equilibrium state, as do variable stars. Alternatively, it may reach a state o... Title: Solar Interior Authors: Zahn, J. Bibcode: 2000eaa..bookE2417Z Altcode: The interior of the Sun is hidden from our sight, because it is opaque to electromagnetic waves: the radiation we receive from it on Earth is emitted in the outermost layers. Our knowledge of the solar interior is based solely on theoretical models which are built with some assumptions about the physical conditions and processes that are likely to prevail there, and on helioseismology, a very pow... Title: Erratum: Standard Solar Models in the Light of New Helioseismic Constraints. II. Mixing below the Convective Zone Authors: Brun, A. S.; Turck-Chièze, S.; Zahn, J. P. Bibcode: 2000ApJ...536.1005B Altcode: In the paper ``Standard Solar Models in the Light of New Helioseismic Constraints. II. Mixing below the Convective Zone'' by A. S. Brun, S. Turck-Chièze, and J. P. Zahn (525, 1032 [1999]), several corrections are required: 1. The words ``greater than'' just after equation (11) for the definition of rbcz should be removed. 2. The beginning of first sentence of the next paragraph should read: ``With the latitudinal dependence of the angular velocity at the base of the convection zone borrowed from Thompson et al. (1996), Ωbcz/2π=456-72x2-42x4 nHz,'' instead of ``Ωbcz>/2π=456-72x2- 42x4.'' 3. In the footnote to Table 1, ``Rbzc'' should be ``Rbcz,'' as it is appears for ``Tbcz'' in the same footnote. 4. In Table 2, in the ``Parameters'' column, ``i0'' should be ``Z0,'' as in Table 1. 5. In Table 3, ``Observaton'' should be ``Observation.'' The Press sincerely regrets these errors. Title: Tidal Dissipation Authors: Zahn, Jean-Paul Bibcode: 2000astu.confE..36Z Altcode: No abstract at ADS Title: Turbulence in Differentially Rotating Flows: New Results from a Couette-Taylor Experiment Authors: Zahn, Jean-Paul; Richard, Denis Bibcode: 2000astu.progE..34Z Altcode: No abstract at ADS Title: Influence of the Tachocline on Solar Evolution. Authors: Brun, A. S.; Zahn, J. -P. Bibcode: 2000NYASA.898..113B Altcode: 2000astro.ph..1510B Recently helioseismic observations have revealed the presence of a shear layer at the base of the convective zone related to the transition from differential rotation in the convection zone to almost uniform rotation in the radiative interior, the tachocline. At present, this layer extends only over a few percent of the solar radius and no definitive explanations have been given for this thiness. Following Spiegel and Zahn (1992, Astron. Astrophys.), who invoke anisotropic turbulence to stop the spread of the tachocline deeper in the radiative zone as the Sun evolves, we give some justifications for their hypothesis by taking into account recent results on rotating shear instability (Richard and Zahn 1999, Astron. Astrophys.). We study the impact of the macroscopic motions present in this layer on the Sun's structure and evolution by introducing a macroscopic diffusivity $D_T$ in updated solar models. We find that a time dependent treatment of the tachocline significantly improves the agreement between computed and observed surface chemical species, such as the $^7$Li and modify the internal structure of the Sun (Brun, Turck-Chièze and Zahn, 1999, in Astrophys. J.). Title: Plumes in Stellar Convection Zones. Authors: Zahn, J. P. Bibcode: 2000NYASA.898...90Z Altcode: 1999astro.ph..9288Z All numerical simulations of compressible convection reveal the presence of strong downwards directed flows. Thanks to helioseismology, such plumes have now been detected also at the top of the solar convection zone, on super- granular scales. Their properties may be crudely described by adopting Taylor's turbulent entrainment hypothesis, whose validity is well established under various conditions. Using this model, one finds that the strong density stratification does not prevent the plumes from traversing the whole convection zone, and that they carry upwards a net energy flux (Rieutord & Zahn 1995). They penetrate to some extent in the adjacent stable region, where they establish a nearly adiabatic stratification. These plumes have a strong impact on the dynamics of stellar convection zones, and they play probably a key role in the dynamo mechanism. Title: Preface (Advances in solar research at eclipses from ground and from space) Authors: Stavinschi, Magda; Zahn, Jean-Paul Bibcode: 2000ASIC..558D...7S Altcode: 2000asre.confD...7S No abstract at ADS Title: Commission 35: Stellar Constitution: (Constitution Des Etoiles) Authors: Zahn, J. -P.; VandenBerg, D.; Canal, R.; Chiosi, C.; Dziembowski, W.; Guzik, J.; Meynet, G.; Michaud, G.; Renzini, A.; Saio, H.; Tutukov, A.; Vauclair, G. Bibcode: 2000IAUTA..24..201Z Altcode: No abstract at ADS Title: Advances in solar research at eclipses from ground and from space Authors: Zahn, Jean-Paul; Stavinschi, Magda Bibcode: 2000ASIC..558.....Z Altcode: 2000asre.conf.....Z No abstract at ADS Title: What we know about the solar interior Authors: Zahn, J. -P. Bibcode: 2000ASIC..558..265Z Altcode: 2000asre.conf..265Z Because the interior of the Sun is opaque to electromagnetic waves, the radiation we receive from it on Earth is emitted in the outermost layers: the photosphere. Therefore our knowledge of the solar interior is based solely on theoretical models, which are built by making some plausible assumptions about the physical conditions and processes that are likely to prevail there. Fortunately, a powerful technique - helioseismology - has been developed in the last twenty years, which permits to probe directly the solar interior by means of acoustic waves, and this had a tremendous impact on solar physics because it provides tight observational constraints on our models. We shall illustrate this here by a few examples of recent advances in modeling the Sun. Title: Mixing by internal waves beneath the convection zone- comparison with analytical models Authors: Kiraga, M.; Jahn, K.; Różyczka, M.; Stěpień, K.; Zahn, J. -P. Bibcode: 2000IAUJD...5E..24K Altcode: The results of 2D hydrodynamical simulations of penetrative convection are presented. Amplitudes, frequencies, and the energy flux transported by the internal gravity waves below the convection layer were determined in several models. We find that these values depend strongly on the value of the adopted viscosity coefficient. However, frequencies and amplitudes of the waves in each computed model were higher than predicted by parametric models of generation of waves, in which the dynamics of the convection zone is based on the MLT, and it was lower than in the `plume' model considered by Schatzman and Montalban. Title: Division IV: Stars: (Etoiles) Authors: Cram, Lawrence; Barbuy, Beatriz; Gerbaldi, Michele; Lambert, David; Pallavicini, Roberto; Zahn, Jean-Paul; Zinnecker, Hans Bibcode: 2000IAUTA..24..173C Altcode: No abstract at ADS Title: Standard Solar Models in the Light of New Helioseismic Constraints. II. Mixing below the Convective Zone Authors: Brun, A. S.; Turck-Chièze, S.; Zahn, J. P. Bibcode: 1999ApJ...525.1032B Altcode: 1999astro.ph..6382B In previous work, we have shown that recent updated standard solar models cannot reproduce the radial profile of the sound speed at the base of the convective zone and fail to predict the photospheric lithium abundance. In parallel, helioseismology has shown that the transition from differential rotation in the convective zone to almost uniform rotation in the radiative solar interior occurs in a shallow layer called the tachocline. This layer is presumably the seat of a large-scale circulation and of turbulent motions. Here we introduce a macroscopic transport term in the structure equations that is based on a hydrodynamical description of the tachocline proposed by Spiegel & Zahn, and we calculate the mixing induced within this layer. We discuss the influence of different parameters that represent the tachocline thickness, the Brunt-Väisälä frequency at the base of the convective zone, and the time dependence of this mixing process along the Sun's evolution. We show that the introduction of such a process inhibits the microscopic diffusion by about 25%. Starting from models including a pre-main-sequence evolution, we obtain (1) a good agreement with observed photospheric chemical abundance of light elements such as 3He, 4He, 7Li, and 9Be; (2) a smooth composition gradient at the base of the convective zone; and (3) a significant improvement of the sound-speed square difference between the seismic Sun and the models in this transition region when we allow the photospheric heavy-element abundance to adjust, within the observational incertitude, as a result of the action of this mixing process. The impact on neutrino predictions is also discussed. Title: Angular Momentum Redistribution by Waves in the Sun Authors: Kumar, Pawan; Talon, Suzanne; Zahn, Jean-Paul Bibcode: 1999ApJ...520..859K Altcode: 1999astro.ph..2309K We calculate the angular momentum transport by gravito-inertial-Alfvén waves and show that, so long as prograde and retrograde gravity waves are excited to roughly the same amplitude, the sign of angular momentum deposit in the radiative interior of the Sun is such as to lead to an exponential growth of any existing small radial gradient of rotation velocity just below the convection zone. This leads to formation of a strong thin shear layer (of thickness about 0.3% Rsolar) near the top of the radiative zone of the Sun on a timescale of order 20 yr. When the magnitude of differential rotation across this layer reaches about 0.1 μHz, the layer becomes unstable to shear instability and undergoes mixing, and the excess angular momentum deposited in the layer is returned to the convection zone. The strong shear in this layer generates a toroidal magnetic field which is also deposited in the convection zone when the layer becomes unstable. This could possibly start a new magnetic activity cycle seen at the surface. Title: Star Formation in Accretion Disks Around Massive Black Holes and Pregalactic Enrichment Authors: Collin, Suzy; Zahn, Jean-Paul Bibcode: 1999Ap&SS.265..501C Altcode: 1999astro.ph..1085C Broad Absorption Lines (BALs) prove the existence of a high velocity outflowing gas with metallicities larger than solar in the central few parsecs of high redshift quasars. At the same distance from the black hole, accretion disks in quasars and Active Galactic Nuclei (AGN) are locally gravitationally unstable, and clumps must form with a size of the order of the scale height of the disk. This is hardly a coincidence, and we have tried to link these two facts. We have assumed that the unstable clumps give rise to protostars, which become massive stars after a rapid stage of accretion, and explode as supernovae, producing strong outflows perpendicular to the disk and inducing outward transfer of angular momentum in the plane of the disk. As a consequence a self-regulated disk made of gas and stars where supernovae sustain the inflow mass rate required by the AGN is a viable solution in this region of the disk. This model could explain the BALs, and could also account for a pregalactic enrichment of the intergalactic medium and of the Galaxy, if massive black holes formed early in the Universe. Title: Turbulence in differentially rotating flows. What can be learned from the Couette-Taylor experiment Authors: Richard, Denis; Zahn, Jean-Paul Bibcode: 1999A&A...347..734R Altcode: 1999astro.ph..3374R The turbulent transport of angular momentum plays an important role in many astrophysical objects, but its modelization is still far from satisfactory. We discuss here what can be learned from laboratory experiments. We analyze the results obtained by Wendt (1933) and Taylor (1936) on the classical Couette-Taylor flow, in the case where angular momentum increases with distance from the rotation axis, which is the most interesting for astrophysical applications. We show that when the gap between the coaxial cylinders is wide enough, the criterion for the onset of the finite amplitude instability can be expressed in terms of a gradient Reynolds number. Based on Wendt's results, we argue that turbulence may be sustained by differential rotation when the angular velocity decreases outward, as in keplerian flows. From the rotation profiles and the torque measurements we deduce a prescription for the turbulent viscosity which is independent of gap width; with some caution it may be applied to stellar interiors and to accretion disks. Title: Star formation and evolution in accretion disks around massive black holes. Authors: Collin, Suzy; Zahn, Jean-Paul Bibcode: 1999A&A...344..433C Altcode: We develop an exploratory model for the outer, gravitationally unstable regions of accretion disks around massive black holes. We consider black holes of mass 10(6) to 10(10) Msun, and primeval or solar abundances. In a first step we study star formation and evolution in a purely gaseous marginally unstable disk, and we show that unstable fragments should collapse rapidly and give rise to compact objects (planets or protostars), which then accrete at a high rate and in less than 10(6) years acquire a mass of a few tens of Msun, according to a mechanism first proposed by Artymowicz et al. (1993). When these stars explode as supernovae, the supernova shells break out of the disk, producing strong outflows. We show that the gaseous disk is able to support a large number of massive stars and supernovae while staying relatively homogeneous. An interesting aspect is that the residual neutron stars can undergo other accretion phases, leading to other (presumably powerful) supernova explosions. In a second step we assume that the regions at the periphery of the disk provide a quasi stationary mass inflow during the lifetime of quasars or of their progenitors, i.e. ~ 10(8) yrs, and that the whole mass transport is ensured by the supernovae, which induce a transfer of angular momentum towards the exterior, as shown by the numerical simulations of Rozyczka et al. (1995). Assuming that the star formation rate is proportional to the growth rate of the gravitational instability, we solve the disk structure and determine the gas and the stellar densities, the heating being provided mainly by the stars themselves. We find self-consistent solutions in which the gas is maintained in a state very close to gravitational instability, in a ring located between 0.1 and 10 pc for a black hole mass of 10(6) M_sun, and between 1 and 100 pc for a black hole mass of 10(8) M_sun or larger, whatever the abundances, and for relatively low accretion rates (<= 10% of the critical accretion rate). For larger accretion rates the number of stars becomes so large that they inhibit any further star formation, and/or the rate of supernovae is so high that they distroy the homogeneity and the marginal stability of the disk. We postpone the study of this case. Several consequences of this model can be envisioned, besides the fact that it proposes a solution to the problem of the mass transport in the intermediate region of the disk where global instabilities do not work. As a first consequence, it could explain the high velocity metal enriched outflows implied by the presence of the broad absorption lines in quasars. As a second consequence it could account for a pregalactic enrichment of the intergalactic medium, if black holes formed early in the Universe. Finally it could provide a triggering mechanism for starbursts in the central regions of galaxies. A check of the model would be to detect a supernova exploding within a few parsecs from the center of an AGN, an observation which can be performed in the near future. Title: Turbulence and differentially rotating flows Authors: Zahn, Jean-Paul Bibcode: 1999bha..progE..51Z Altcode: No abstract at ADS Title: Beyond the Mixing-Length Treatment: Why and How? Authors: Zahn, J. -P. Bibcode: 1999ASPC..173..121Z Altcode: 1999sstt.conf..121Z No abstract at ADS Title: Accretion Disks and Star Formation Authors: Collin, Suzy; Zahn, J. P. Bibcode: 1999IAUS..194..246C Altcode: No abstract at ADS Title: Hydrodynamical Simulations of Penetrative Convection and Generation of Internal Gravity Waves Authors: Kiraga, M.; Zahn, J. -P.; Stȩpień , K.; Jahn, K.; Rózyczka, M.; Muthsam, H. J. Bibcode: 1999ASPC..173..269K Altcode: 1999sstt.conf..269K No abstract at ADS Title: Advances in solar research at eclipses from ground and from space Authors: Zahn, Jean-Paul; Stavinschi, Magda Bibcode: 1999RoAJ....9S....Z Altcode: No abstract at ADS Title: Mixing Below the Solar Convective Zone Authors: Brun, A. S.; Turck-Chièze, S.; Zahn, J. -P. Bibcode: 1999ASPC..173..293B Altcode: 1999sstt.conf..293B No abstract at ADS Title: Star Formation in Accretion Disks Around Massive Black Holes and Pregalactic Enrichment Authors: Collin, S.; Zahn, J. -P. Bibcode: 1999gecd.conf..501C Altcode: High redshift quasars are known to harbour in their very center (~one parsec) high velocity outflows of gas with a metallicity larger than solar (observed as the so-called "Broad Absorption Lines"). We propose that this enrichment takes place in the accretion disk fueling the black holes. In the gravitationally unstable part of the disk, between 0.01 and 1 pc, we show that stars can form and grow by accretion, then evolve to the stage of supernovae and explode in the disk. The gaseous fraction of the disk is maintained in a state of marginal instability by the heating of the stars, and supernovae provide the transfer of momentum required for a large accretion rate. This mechanism is particularly efficient for disks made of primordial gas, and it works as well for small (growing) black holes as for powerful quasars. In the course of the process, the overabundant gas flows out of the disk, enriching in heavy elements the forming host galaxy and the intergalactic medium. This mechanism explains the enrichment and the outflows in quasars, but we propose that it could also be the starting point of heavy element formation in the Universe, provided that massive black holes now present in the centres of galaxies formed early in the past. It can explain without the need to appeal to a pregalactic "Population III", the abundances observed in the oldest stars of the Galactic halo, the abundances in the intergalactic medium (i.e. the L-α forest clouds), and the abundances in the damped L-α and metal systems which are supposed to be tracers of massive galaxies. Title: Stellar evolution with rotation. III. Meridional circulation with MU -gradients and non-stationarity Authors: Maeder, Andre; Zahn, Jean-Paul Bibcode: 1998A&A...334.1000M Altcode: Models of stellar evolution with rotation are very much needed in order to interpret recent stellar properties, in particular for massive stars. For that we proceed to a detailed investigation of some critical physical processes in rotating stars: 1. The equation expressing the transport of angular momentum by circulation and diffusion is revised to also account for expansion and contraction in non-stationary models. 2. We examine the current expressions for the velocity U(r) of the meridional circulation, also taking into account mu -gradients and horizontal turbulence. We show that there are no ``mu -currents'' but just meridional currents which can be sizeably influenced by the gradients of mean molecular weight mu . A proper account of the mu -gradients may reduce U(r) by one or two orders of magnitude with respect to current expressions. 3. While the usual expressions for the meridional circulation would predict an infinite velocity at the edge of a radiative and semiconvective zone and an inverted circulation in a semiconvective zone, the present developments give a continuity of the solutions for the circulation. 4. The approximation of a stationary circulation, which is no longer valid after the main-sequence phase, is also removed and the case of a general equation of state is considered. We notice that in the stationary regime the horizontal fluctuations of mu represent some fixed fraction of the vertical mu -gradient. To first order, this fraction is not dependent on rotation, because the building of horizontal fluctuations by the circulation is compensated by the smoothing due to horizontal turbulence. Title: Macroscopic Transport Large-scale advection, turbulent diffusion, wave transport Authors: Zahn, Jean-Paul Bibcode: 1998SSRv...85...79Z Altcode: While the solar convection zone is very well mixed by its turbulent motions, chemical composition gradients build up in the radiative interior due to microscopic diffusion and settling, and to nuclear burning. Standard models, which ignore any type of macroscopic transport, cannot explain the depletion of lithium in solar-type stars, as they evolve; neither do they account for the observed profile of molecular weight at the base of the solar convection zone. Title: Turbulent Transport in Stellar Interiors Authors: Michaud, G.; Zahn, J. -P. Bibcode: 1998ThCFD..11..183M Altcode: Differential rotation is probably the major cause of turbulence in stably stratified stellar interiors. The boundary of the superficial solar convection zone plays a critical role for both the large scale circulation and the differential rotation. The turbulence arises from the barotropic instability in a vertically stratified medium and is expected to be anisotropic. It tends to suppress one of its causes, namely differential rotation in latitude. It offers an explanation for the thinness of the solar tachocline, the boundary layer beneath the convection zone where solar seismology shows that rotation varies from differential above to apparently uniform below. The anisotropy of turbulence also strongly reduces the efficiency of vertical particle transport. We show that for an anisotropy A of horizontal to vertical velocities, the vertical diffusivity is a factor A2 less than the horizontal diffusivity. Transport by meridional circulation is also reduced, as well as the efficiency of a composition gradient in suppressing meridional circulation. These effects of anisotropy explain the very small upper limit that observations of the concentration of chemical elements impose to vertical transport in stars. However the recent results of helioseismology, that the solar core rotates at nearly the same rate as the whole radiative zone, cannot currently be explained by anisotropic turbulent transport. It suggests the need for an additional transport process such as a magnetic torquing or gravity waves. Furthermore, near the base of the convection zone, magnetic instabilities could provide an alternate mechanism to mix angular momentum preferentially in latitude compared with radial mixing. The quality of the helioseismology data is improving very rapidly. It holds the promise to determine, within the next few years, the velocity field within the Sun to great accuracy. This should allow us to distinguish between the various hydrodynamical and hydromagnetic models. Title: Macroscopic Transport Authors: Zahn, J. -P. Bibcode: 1998sce..conf...79Z Altcode: No abstract at ADS Title: Gravity Waves and the Evolution of the Solar Rotation Profile Authors: Talon, Suzanne; Zahn, Jean-Paul Bibcode: 1998ASPC..154..806T Altcode: 1998csss...10..806T We present here numerical results for the evolution of angular momentum in the Sun, including transport by gravity waves as well as by meridional circulation and shear turbulence which are present in a differentially rotating star. We show that quasi-solid body rotation may be achieved in a timescale shorter than the age of the Sun. Title: Macroscopic Processes in the Solar Interior Authors: Brun, A. S.; Turck-Chièze, S.; Zahn, J. P. Bibcode: 1998ESASP.418..439B Altcode: 1998astro.ph..7090B; 1998soho....6..439B With the recent results of heliseismology aboard SOHO, the solar models are more and more constrained (Brun, Turck-Chièze et Morel 1998) . New physical processes, mainly connected to macroscopic motions, must be introduced to understand these news observations. In this poster, we present solar models with such macroscopic motions, as turbulent pressure in the outer layers, mixing due to the tachocline (Spiegel and Zahn 1992), and some mixing in the core (Morel and Schatzman 1996). From our results, we could say that: (1) Mixing in the core is unlikely (δ c2/c2 > 2%) (2) Turbulent pressure improves the absolute value of the acoustic modes frequencies (~5 μ Hz at 4 mHz) (3) And mixing in a tachocline of thickness of 0.05 plus or minus 0.03 Rodot (Corbard et al. 1997) looks promising. Title: Towards a hydrodynamical model predicting the observed solar rotation profile Authors: Talon, Suzanne; Zahn, Jean-Paul Bibcode: 1998A&A...329..315T Altcode: We present here the results of a numerical study performed to investigate the role of gravity waves in the evolution of the solar rotation profile. We show that, together with meridional circulation and shear turbulence, they may enforce solid body rotation in the solar interior. The transient phase is characterized by an outer portion of the radiative zone rotating at the velocity of the convection zone and an inner portion in strong differential rotation with depth. The gravity waves slow down the outer portion, whereas it is the meridional circulation which dominates the transport of momentum in the interior. With our treatment of the excitation and damping of these waves, solid body rotation is achieved on a timescale of a few giga-years, depending on the initial velocity of the model. Title: Rotation and angular momentum transport Authors: Zahn, J. -P. Bibcode: 1997ASSL..225..187Z Altcode: 1997scor.proc..187Z The internal rotation law of the Sun depends both on the rate at which angular momentum has been lost by the wind, and on the efficiency of the processes which extract that angular momentum from the radiative interior. The transport by the meridian circulation and the associated hydrodynamical instabilities is insufficient to yield the flat profile which is deduced from helioseismology, and therefore other processes must be operating. One possibility is magnetic torquing, but some observations are hard to reconcile with it. Another is the transport through the internal waves emitted by the convection zone and this mechanism seems the most promising: according to recent estimates, it should operate on a timescale of a about $10^7$ years, i.e. three orders of magnitude less than the present spin-down time. Title: Angular momentum transport by internal waves in the solar interior. Authors: Zahn, J. -P.; Talon, S.; Matias, J. Bibcode: 1997A&A...322..320Z Altcode: 1996astro.ph.11189Z The internal gravity waves of low frequency which are emitted at the base of the solar convection zone are able to extract angular momentum from the radiative interior. We evaluate this transport with some simplifying assumptions: we ignore the Coriolis force, approximate the spectrum of turbulent convection by the Kolmogorov law, and couple this turbulence to the internal waves through their pressure fluctuations, following Press (1981ApJ...245..286P) and Garcia Lopez & Spruit (1991ApJ...377..268G). The local frequency of an internal wave varies with depth in a differentially rotating star, and it can vanish at some location, thus leading to enhanced damping (Goldreich & Nicholson 1989ApJ...342.1079G). It is this dissipation mechanism only that we take into account in the exchange of momentum between waves and stellar rotation. The flux of angular momentum is then an implicit function of depth, involving the local rotation rate and an integral representing the cumulative effect of radiative dissipation. We find that the efficiency of this transport process is rather high: it operates on a timescale of 10^7^ years, and is probably responsible for the flat rotation profile which has been detected through helioseismology. Title: Rotational mixing in early-type stars: the main-sequence evolution of a 9Msun_ star. Authors: Talon, S.; Zahn, J. -P.; Maeder, A.; Meynet, G. Bibcode: 1997A&A...322..209T Altcode: 1996astro.ph.11131T We describe the main-sequence evolution of a rotating 9Msun_ star. Its interior rotation profile is determined by the redistribution of angular momentum through the meridian circulation and through the shear turbulence generated by the differential rotation; the possible effect of internal waves is neglected. We examine the mixing of chemicals produced by the same internal motions. Our modelization is based on the set of equations established by Zahn (1992A&A...265..115Z) and completed in Matias, Talon & Zahn (1996, preprint). Our calculations show that the amount of mixing associated with a typical rotation velocity of ~100km/s yields stellar models whose global parameters are very similar to those obtained with the moderate overshooting (d/H_P_=~0.2) which has been invoked until now to fit the observations. Fast rotation (~300km/s) leads to significant changes of the C/N and O/N surface ratios, but the abundance of He is barely increased. The modifications of the internal composition profile due to such rotational mixing will certainly affect the post-main-sequence evolution. Title: Anisotropic diffusion and shear instabilities. Authors: Talon, S.; Zahn, J. -P. Bibcode: 1997A&A...317..749T Altcode: 1996astro.ph..9010T We examine the role of anisotropic turbulence on the shear instabilities in a stratified flow. Such turbulence is expected to occur in the radiative interiors of stars, due to their differential rotation and their strong stratification, and the turbulent transport associated with it will be much stronger in the horizontal than in the vertical direction. It will thus weaken the restoring force which is caused by the gradient of mean molecular weight (μ). We find that the critical shear which is able to overcome the μ-gradient is substantially reduced by this anisotropic turbulence, and we derive an estimate for the resulting turbulent diffusivity in the vertical direction. Title: Stellar rotation and mixing Authors: Zahn, J. P. Bibcode: 1997IAUS..181..175Z Altcode: No abstract at ADS Title: Ekman Pumping and Tidal Dissipation in Close Binaries: A Refutation of Tassoul's Mechanism Authors: Rieutord, Michel; Zahn, Jean-Paul Bibcode: 1997ApJ...474..760R Altcode: We show that the existence of an Ekman boundary layer does not enhance the tidal dissipation in a close binary star because the tides do not exert a stress on the stellar surface. The synchronization timescale is of order (ɛT)-2tadj, where tadj is the (global) viscous damping time and ɛT is the tidal deformation caused by the companion (Darwin 1879; Zahn 1966; Scharlemann 1982; Rieutord & Bonazzola 1987). We thus refute the claim made by Tassoul (1987), who thought to have found a very efficient mechanism for the synchronization and circularization of binary systems. We analyze the paper by Tassoul & Tassoul (1992b) and prove that the alleged magnitude of their Ekman pumping is due to an improper treatment of the surface boundary conditions. Their mechanism would have dramatic, yet unverified consequences, as illustrated by two examples of tidal interaction: between Io and Jupiter, and in the newly discovered planetary system 51 Peg. Title: Chaotic Dynamics of the Solar Cycle Authors: Spiegel, Edward A.; Zahn, Jean-Paul Bibcode: 1996cuny.rept.....S Altcode: The cyclic variation of solar activity is both irregular and intermittent. We have sought to isolate and illuminate the physical mechanisms of this behavior and to provide a mathematical description of it. Our work has brought out three ingredients of the solar cycle that we believe to be central to its operation. (1) The seat of the solar cycle is in a shear layer just below the solar convection zone. We have investigated the structure of this layer (which we call the solar tachocline) in some detail. (2) The spatio-temporal development of the solar cycle is represented by the propagation of robust solitary waves which are affected by dissipation and instability. We have studied the structure and interactions of such waves, which we call solitoids. (3) On top of the simple propagative behavior of the solar solitoids there are intermissions during which the number of sunspots remains quite small. We attribute these intermissions (such as the Maunder minimum) to a form of interaction between the convection zone and the tachocline which is characteristic of a process that we have developed and that we call on/off intermittency. These three ingredients make up some of the key features of the solar cycle and may be expected to play a role in future simulations of the solar cycle. Title: Corot: a Space Project Devoted to the Study of Convection and Rotation in Stars Authors: Catala, C.; Auvergne, M.; Baglin, A.; Bonneau, F.; Magnan, A.; Vuillemin, A.; Goupil, M. J.; Michel, E.; Boumier, P.; Dzitko, H.; Gabriel, A.; Gautier, D.; Lemaire, P.; Mangeney, A.; Mosser, B.; Turck-Chiéze, S.; Zahn, J. P. Bibcode: 1995ESASP.376b.549C Altcode: 1995soho....2..549C; 1995help.confP.549C No abstract at ADS Title: Turbulent plumes in stellar convective envelopes. Authors: Rieutord, M.; Zahn, J. -P. Bibcode: 1995A&A...296..127R Altcode: Recent numerical simulations of compressible convection in a stratified medium suggest that strong downwards directed flows may play an important role in stellar convective envelopes, both in the dynamics and in the energy transport. We transpose this idea to stellar convective envelopes by assuming that these plumes are turbulent plumes which may be described by Taylor's entrainment hypothesis, whose validity is well established in various geophysical conditions. We consider first the ideal case of turbulent plumes occurring in an isentropic atmosphere, and ignore all types of feedback. Thereafter we include the effect of the backflow generated by the plumes, and take into account the contribution of the radiative flux. The main result is that plumes originating from the upper layers of a star are able to reach the base of its convective envelope. Their number is necessarily limited because of their conical shape; the backflow further reduces their number to a maximum of about 1000. In these plumes the flux of kinetic energy is directed downwards, but it is less than the upwards directed enthalpy flux, so that the plumes always carry a net energy flux towards the surface. Our plume model is not applicable near the surface, where the departures from adiabaticity become important due to radiative leaking; therefore it cannot predict the depth of the convection zone, which is determined mainly by the transition from the radiative regime above to the nearly adiabatic conditions below. Neither does it permit to evaluate the extent of penetration, which strongly depends on the (unknown) number of plumes. We conclude that, to be complete, a phenomenological model of stellar convection must have a dual character: it should include both the advective transport through diving plumes, which is outlined in this paper, and the turbulent diffusion achieved by the interstitial medium. Only the latter process is apprehended by the familiar mixing-length treatment. Title: Convective Penetration Authors: Zahn, J. P. Bibcode: 1995LIACo..32..111Z Altcode: 1995sews.book..111Z No abstract at ADS Title: Lithium depletion in late-type stars through wind-driven mixing. Authors: Zahn, J. -P. Bibcode: 1995MmSAI..66..485Z Altcode: No abstract at ADS Title: Lithium Depletion in the Sun Authors: Morel, P.; Provost, J.; Berthomieu, G.; Matias, J.; Zahn, J. P. Bibcode: 1995LIACo..32..395M Altcode: 1995sews.book..395M No abstract at ADS Title: Transport processes in stellar interiors Authors: Zahn, Jean-Paul Bibcode: 1995LNP...458..153Z Altcode: We first recall Evry Schatzman’s pioneering contributions to the theory of transport of matter and angular momentum in the radiative interior of stars. He suggested that this transport could be of turbulent nature and he linked it to the internal rotation state. We then review the major breakthroughs which have been accomplished during the eighties, mainly in the observational domain. Finally, we briefly describe some recent achievements on the theoretical side, and allude to the work in progress. Title: Lithium depletion in late type stars through wind-driven mixing Authors: Zahn, J. -P. Bibcode: 1995HiA....10..461Z Altcode: No abstract at ADS Title: Le monde des etoiles Authors: Benest, Daniel; Froeschle, Claude; Gouguenheim, Lucienne; Loulergue, Michelle; Rozelot, Jean-Pierre; Waelkens, Christoffel; Zahn, Jean-Paul Bibcode: 1995lmde.book.....B Altcode: No abstract at ADS Title: COROT: A Proposal to Study Stellar Convection and Internal Rotation Authors: Catala, C.; Mangeney, A.; Gautier, D.; Auvergne, M.; Baglin, A.; Goupil, M. J.; Michel, E.; Zahn, J. P.; Magnan, A.; Vuillemin, A.; Boumier, P.; Gabriel, A.; Lemaire, P.; Turck-Chieze, S.; Dzitko, H.; Mosser, B.; Bonneau, F. Bibcode: 1995ASPC...76..426C Altcode: 1995gong.conf..426C No abstract at ADS Title: Convective Penetration in the Sun in Presence of Microscopic Diffusion Authors: Provost, J.; Morel, P.; Berthomieu, G.; Zahn, J. P. Bibcode: 1995LIACo..32..201P Altcode: 1995sews.book..201P No abstract at ADS Title: A case study of the quadruple system ξ Ursae Majoris: its activity and lithium depletion. Authors: Cayrel de Strobel, G.; Cayrel, R.; Friel, E.; Zahn, J. -P.; Bentolila, C. Bibcode: 1994A&A...291..505C Altcode: The quadruple system ξ UMa is an interesting test case for the numerous problems encountered when studying the evolutionary status, chromospheric activity and lithium depletion of solar-type stars. We have carried out a detailed analysis of the major components A and B of ξ UMa from high resolution, high signal-to-noise CFHT spectra. We determine accurate temperatures for each of the principal components, neither disturbed by their invisible, much less massive companion, and find that the two differ in temperature by 300 K, one being somewhat hotter than the Sun, the other cooler. The metal abundances derived from iron and a few other elements are identical for the two stars, and the system is moderately metal-deficient, by a factor of two with respect to the Sun. We concur with previous studies that lithium is fairly abundant in A whereas it is below detection in B: we measured log N(Li)=2.33 in A and place a more stringent upper limit log N(Li)<0.8 for B. We discuss this unusual combination of lithium abundances and the position of the stars in the HR diagram in the light of the complex binary nature of the two components, and of current theories of stellar evolution and of lithium depletion. We suggest that B has kept a high level of activity because its rotation is tidally locked with the orbital motion, and that it has therefore lost about ten times more matter than a single star of the same mass, which explains its strong lithium depletion. Title: Rotation and lithium depletion in late-type binaries Authors: Zahn, J. -P. Bibcode: 1994A&A...288..829Z Altcode: Late-type stars possess two firmly established properties: both their rotation speed and their lithium abundance decrease with age. Quite naturally, it has been suggested that the lithium depletion is related with the loss of angular momentum. Such a causal link may just be postulated in the evolutionary calculations, and the free parameters calibrated with the observations (Endal & Sofia 1978; Pinsonneault et al. 1989). But it can also be justified on theoretical reasons, with the meridian circulation playing the major role in the transport of matter and angular momentum (Zahn 1992a). In the present paper, we seek an observational confirmation of this link in the behavior of close binaries. In addition to the torque exerted on them by the stellar wind, which is responsible for the spin-down of single stars, binary stars experience a tidal torque, which tends to synchronize their rotation with the orbital motion. As a result, they exchange lesser amounts of angular momentum than single stars of the same mass and age, and therefore they should retain more of their original lithium. Based on the current tidal theory (Zahn 1989), we calculate the dynamical evolution of close binaries, and infer from it the differences in lithium abundance one should expect between them and single stars. Underdepletion should occur in systems which were tidally locked on the ZAMS, i.e. for orbital periods below =~8 days for solar-type stars of Population I, and 6 days for halo stars. Our theoretical predictions are in good agreement with the latest available data (Soderblom et al. 1993; Thorburn et al. 1993; Spite et al. 1994), and we take this as a proof for the existence of a physical link between the depletion of lithium and the loss of angular momentum. We conclude that the abundance of lithium measured in old disk and halo stars by Spite & Spite (1982) is less than the original one, and cannot be taken as such to constrain the models of the primordial nucleosynthesis. Another implication is that magnetic torquing has played little role in the radiative interior of late-type stars, and that the core of these stars is probably rotating faster than their surface. Title: Penetration below a Convection Zone Authors: Hurlburt, Neal E.; Toomre, Juri; Massaguer, Josep M.; Zahn, Jean-Paul Bibcode: 1994ApJ...421..245H Altcode: Two-dimensional numerical simulations are used to investigate how fully compressible nonlinear convection penetrates into a stably stratified zone beneath a stellar convection zone. Estimates are obtained of the extent of penetration as the relative stability S of the stable to the unstable zone is varied over a broad range. The model deals with a perfect gas possessing a constant dynamic viscosity. The dynamics is dominated by downward-directed plumes which can extend far into the stable material and which can lead to the excitation of a broad spectrum of internal gravity waves in the lower stable zone. The convection is highly time dependent, with the close coupling between the lateral swaying of the plumes and the internal gravity waves they generate serving to modulate the strength of the convection. The depth of penetration delta, determined by the position where the time-averaged kinetic flux has its first zero in the stable layer, is controlled by a balance between the kinetic energy carried into the stable layer by the plumes and the buoyancy braking they experience there. A passive scalar is introduced into the unstable layer to evaluate the transport of chemical species downward. Such a tracer is effectively mixed within a few convective overturning times down to a depth of delta within the stable layer. Analytical estimates based on simple scaling laws are used to interpret the variation of delta with S, showing that it first involves an interval of adiabatic penetration if the local Peclet number of the convection exceeds unity, followed by a further thermal adjustment layer, the depths of each interval scaling in turn as S-1 and S-1/4. These estimates are in accord with the penetration results from the simulations. Title: Mixing processes and stellar evolution. Authors: Zahn, J. -P. Bibcode: 1994ems..conf..285Z Altcode: The author reviews some of the mixing processes that may influence the evolution of massive stars, such as penetrative convection, and puts his emphasis on those which occur in the radiative envelope. There the main transport mechanisms are a thermally driven meridian circulation, which departs significantly from the classical Eddington-Sweet description, together with turbulent motions generated by the differential rotation. This rotation-induced mixing will surround the convective core of such stars with a region of decreasing helium content, which may prevent semi-convection from ever appearing; the extent of this region depends sensitively on the rotation rate. The results are compared with those obtained earlier by Mestel (1953). Work is in progress to verify whether stars which rotate sufficiently fast may be thoroughly mixed. Title: Structure and evolution of massive stars: mixing processes and stellar evolution Authors: Zahn, J. -P. Bibcode: 1993SSRv...66..285Z Altcode: We review some of the mixing processes that may influence the evolution of massive stars, such as penetrative convection, and put our emphasis on those which occur in the radiative envelope. There the main transport mechanisms are a thermally driven meridian circulation, which departs significantly from the classical Eddington-Sweet description, together with turbulent motions generated by the differential rotation. This rotation-induced mixing will surround the convective core of such stars with a region of decreasing helium content, which may prevent semi-convection from ever appearing; the extent of this region depends sensitively on the rotation rate. The results are compared with those obtained earlier by Mestel (1953). Work is in progress to verify whether stars which rotate sufficiently fast may be thoroughly mixed. Title: Turbulence in stellar interiors. Authors: Zahn, Jean-Paul Bibcode: 1993ASPC...40..236Z Altcode: 1993ist..proc..236Z; 1993IAUCo.137..236Z This review focusses on the most recent work which has been achieved concerning turbulence in stellar interiors. Among all possible causes for such turbulence, the most powerful is certainly the convective instability in unstably stratified regions, but little was known until now beyond the fact that thermal convection is capable of establishing an almost adiabatic stratification. Title: Astrophysical Fluid Dynamics. Les Houches Session LXVII Authors: Zahn, J. -P.; Zinn-Justin, J. Bibcode: 1993asfd.conf.....Z Altcode: No abstract at ADS Title: Astrophysical fluid dynamics. Authors: Zahn, J. -P.; Zinn-Justin, J. Bibcode: 1993afd..conf.....Z Altcode: No abstract at ADS Title: Instabilities and turbulence in rotating stars. Authors: Zahn, J. -P. Bibcode: 1993afd..conf..561Z Altcode: Contents: 1. Rotating objects. 2. Baroclinic instabilities. 3. Shear instabilities. 4. Thermal imbalance and meridional circulation in rotating stars. 5. Turbulence in rotating stars. Title: Seismological constraints on convective penetration in the Sun. Authors: Berthomieu, G.; Morel, P.; Provost, J.; Zahn, J. -P. Bibcode: 1993ASPC...40...60B Altcode: 1993IAUCo.137...60B; 1993ist..proc...60B Penetrative convection is expected below stellar convection zones, where it should achieve a nearly adiabatic stratification. A theoretical prediction of the penetration depth has been recently made by Zahn (1991) which includes an arbitrary parameter ζ depending on the properties of the convective motions. The authors use the helioseismological constraints to calibrate the value of this parameter. Title: The solar tachocline. Authors: Spiegel, E. A.; Zahn, J. -P. Bibcode: 1992A&A...265..106S Altcode: Acoustic sounding of the Sun reveals that the variation of angular velocity with latitude is independent of depth in the convection zone. By contrast, deep within the radiative zone, the rotation appears to be rigid. The transition between the two rotation laws occurs in a thin, unresolved layer that the authors here call the tachocline. This paper is an examination of the structure and previous evolution of this layer. It is assumed that the stress exerted by the convection zone is prescribed, much as oceanographers take the wind stress on the sea surface as given. It is concluded that the helioseismic observations are best rationalized by a scenario in which, after an initial adjustment or spindown period, the subconvective rotation settles into a quasisteady state with a turbulent boundary layer. In the tachocline, the advection of angular momentum is controlled by horizontal turbulence. If this turbulence is intense enough, the tachocline is thin and is unresolved. Title: Circulation and turbulence in rotating stars. Authors: Zahn, J. -P. Bibcode: 1992A&A...265..115Z Altcode: The author examines the interaction between meridian circulation and turbulence in rotating, non-magnetic stars. The turbulence is assumed to be anisotropic, with stronger transport in the horizontal directions than in the vertical, thereby enforcing a rotation rate which depends only on depth, to first approximation. This conjecture is supported by the interior rotation of the Sun, which is now being revealed through acoustic sounding. The main result is that both the meridian circulation and the turbulence are determined by the loss of angular momentum, which the author ascribes here solely to a stellar wind. When there is no wind, the meridian flow is very weak, and it can even vanish in slow rotators. When the wind is active, it drives the circulation in order to transport angular momentum to the surface, but the advection of chemical species by this flow is partly inhibited because of the horizontal turbulence. Title: Rotation-induced mixing and lithium depletion in galactic clusters. Authors: Charbonnel, C.; Vauclair, S.; Zahn, J. -P. Bibcode: 1992A&A...255..191C Altcode: Results are presented of computations of lithium depletion in a rotating star due to turbulence induced by nuclear burning and by rotation-induced mixing, taking into account the deceleration of the rotation as the star evolves on the main sequence (but treating the interior as if it were rotating uniformly). Numerical simulations are performed for a range of stellar masses, and their results are compared with the Li and Be abundances observed in the Hyades. It is found that the theoretical predictions agree reasonably well with the observations. However, some discrepancies remain, leading to a conclusion that it is necessary to take into account the mixing associated with the differential rotation which builds up inside the star while it is spinning down on the main sequence. Title: Convective Penetration in the Sun Authors: Berthomieu, G.; Morel, P.; Provost, J.; Zahn, J. -P. Bibcode: 1992ASPC...26..158B Altcode: 1992csss....7..158B No abstract at ADS Title: Effect of horizontal turbulent diffusion on transport by meridional circulation. Authors: Chaboyer, B.; Zahn, J. -P. Bibcode: 1992A&A...253..173C Altcode: The present examination of horizontal turbulent motion effects of chemical transport by a stellar radiation zone's meridional circulation notes that such diffusion, when sufficiently strong, inhibits the advection of a chemical element through homogenization of horizontal layers; the vertical transport then reduces to a diffusion process, and the differential rotation is smoother out in latitude. The presence of horizontal turbulence may explain the discrepancy between chemical transport and angular momentum transport as observed in the sun. The advection of angular momentum is formulated as a one-dimensional problem. Title: The Turbulent Tachycline Authors: Spiegel, E. A.; Zahn, J. -P. Bibcode: 1992ASPC...26..188S Altcode: 1992csss....7..188S No abstract at ADS Title: Present state of the tidal theory. Authors: Zahn, J. -P. Bibcode: 1992btsf.work..253Z Altcode: 1992bats.proc..253Z Contents: 1. Introduction. 2. The mechanism of tidal breaking. 3. The physical causes of tidal friction. 4. Refining the theory to meet the observations. 5. Concluding remarks. Title: Book-Review - Rotation and Mixing in Stellar Interiors Authors: Goupil, M. J.; Zahn, J. P.; de Jager, C. Bibcode: 1992SSRv...59..410G Altcode: No abstract at ADS Title: Convective penetration in stellar interiors. Authors: Zahn, J. -P. Bibcode: 1991A&A...252..179Z Altcode: Evidence for convective penetration from a variety of sources is used to deduce a simple model which establishes a relation between the subadiabatic extent of a convective region and the velocity of the penetrating motions. It is found that the subadiabatic penetration at the bottom of a convective envelope is of the order of a pressure scale height, and that above a convective core it amounts to a substantial fraction of the core radius. It is shown that the requirements for nearly adiabatic penetration are met deep enough in a stellar interior and that the departures from adiabaticity are confined to a thin boundary layer. This allows the use of Roxburgh's integral constraint to predict the actual size of a convective core. Title: Convection and Turbulence in Stars Authors: Zahn, Jean-Paul Bibcode: 1991LNP...373..355Z Altcode: 1991lsse.conf..355Z No abstract at ADS Title: Large scale convection in stars : Towards a model for the action of coherent structures Authors: Rieutord, Michel; Zahn, Jean-Paul Bibcode: 1991LNP...380...33R Altcode: 1991sacs.coll...33R; 1991IAUCo.130...33R We show that, representing the descending fluid in a convection zone by a porous medium, the differential rotation of the (rising) fluid is very close to that in an axisymmetric model of the convection zone with anisotropic viscosity Title: On the Nature of Disk Viscosity. Authors: Zahn, J. P. Bibcode: 1991sepa.conf...87Z Altcode: 1991IAUCo.129...87Z No abstract at ADS Title: Convective Penetration into Stellar Radiation Zones Authors: Zahn, Jean-Paul Bibcode: 1991LNP...388..225Z Altcode: 1991ctsm.conf..225Z We recall the evidence for convective penetration exhibited by geophysical fluids, laboratory experiments and computer simulations. A simple model is deduced from these observations, which serves to establish a relation between the subadiabatic extent of a convective region and the velocity of the penetrating motions. Assuming that this velocity obeys the usual scaling of thermal convection, we find that the subadiabatic penetration at the bottom of a convective envelope is of the order of a pressure scale-height, and that above a convective core it amounts to a substantial fraction of the core radius. We show that the requirements for nearly adiabatic penetration are met deep enough in a stellar interior, and that the departures from adiabaticity are confined to a thin boundary layer. This allows the use of Roxburgh's integral constraint to predict the actual size of a convective core. Title: Theory of Transport Processes Authors: Zahn, Jean-Paul Bibcode: 1990ASSL..159..425Z Altcode: 1990insu.conf..425Z; 1990IAUCo.121..425Z No abstract at ADS Title: Turbulent shear flow and rotation Authors: Zahn, J. P. Bibcode: 1990nwus.book..291Z Altcode: No abstract at ADS Title: Conclusion Authors: Zahn, Jean-Paul Bibcode: 1990LNP...366..183Z Altcode: 1990rmsi.conf..183Z No abstract at ADS Title: Turbulent Transport in Stellar Radiation Zones: Causes and Effects Authors: Zahn, Jean-Paul Bibcode: 1990LNP...366..141Z Altcode: 1990rmsi.conf..141Z We briefly review the instabilities which are the most likely to generate turbulent transport of chemicals and of angular momentum in radiative stellar interiors, namely the shear instabilities due to differential rotation. Estimates are given for the turbulent diffusivity, and it is examined how a meridional circulation can cause such differential rotation. Title: Rotation and Mixing in Stellar Interiors Authors: Goupil, Marie-Jo; Zahn, Jean-Paul Bibcode: 1990LNP...366.....G Altcode: 1990rmsi.conf.....G No abstract at ADS Title: Tidal evolution of close binary stars. II. Orbital circularization oflate-type binaries. Authors: Zahn, J. -P.; Bouchet, L. Bibcode: 1989A&A...223..112Z Altcode: The premain-sequence evolution of close binary systems with masses ranging from 0.5 to 1.25 solar masses is described. It is demonstrated that most of the orbital circularization occurs during the Hayashi phase, and that the subsequent decrease in eccentricity on the main-sequence is negligible. The theoretical cutoff period, which separates the circular from the eccentric systems, lies between 7.2 and 8.5 days, depending on the masses and on the assumptions made about the initial conditions; it agrees well with the observed period of about 8 days. This cutoff period is a function of the initial radius of the stars on the Hayashi track. In these calculations, the values predicted by the star formation theory of Stahler et al. (1980) are used; hence the good agreement mentioned above provides a new validation of that theory. It is also shown that systems around that cutoff period reach the zero-age main-sequence with their components rotating faster than the orbital rate. Title: Tidal evolution of close binary stars. I - Revisiting the theory of the equilibrium tide Authors: Zahn, J. -P. Bibcode: 1989A&A...220..112Z Altcode: The theory of the equilibrium tide in stars that possess a convective envelope is reexamined critically, taking recent developments into account and treating thermal convection in the most consistent way within the mixing-length approach. The weak points are identified and discussed, in particular, the reduction of the turbulent viscosity when the tidal period becomes shorter than the convective turnover time. An improved version is derived for the secular equations governing the dynamical evolution of close binaries of such type. Title: Open problems in modeling the solar and stellar environment. Authors: Zahn, Jean-Paul Bibcode: 1989mse..proc..119Z Altcode: Contents: 1. Basic physical properties of the stellar environment. 2. Instabilities. 3. Accretion disks and collimated flows. 4. The stars. 5. Conclusion. Title: Turbulent transport in the radiative zone of a rotating star Authors: Zahn, J. -P. Bibcode: 1987ASSL..137..201Z Altcode: 1987isav.symp..201Z Hydrodynamical instabilities that occur in the radiation zone of a differentially rotating star may produce the mild turbulent mixing which is required to explain various observations. The author discusses a consistent scheme in which the energy which sustains the turbulent motions originates in the thermal imbalance caused by the rotation. An approximate expression is derived for the vertical diffusion coefficient and the consequences of this process are compared with those of the classical meridional circulation. Title: Solar and Stellar Convection Authors: Zahn, J. -P. Bibcode: 1987LNP...292...55Z Altcode: 1987ssp..conf...55Z The author examines the progress made during the last decade in our knownledge of stellar convection, first in the theory and using numerical simulation, and second through observations, from ground and space. Special emphasis is put on those results which allow to tackle the basic questions: (1) Is the same mechanism responsible for the different types and scales of motions that are currently identified in the solar convection zone: granulation, mesogranulation, supergranulation, large eddies? (2) On which scale(s) is energy injected into the convective motions? For what reason? Title: Instabilities due to convection and rotation Authors: Zahn, J. -P. Bibcode: 1987ASSL..136..143Z Altcode: 1987ilet.work..143Z This paper examines whether some of the instabilities observed in early-type luminous stars can be caused by thermal convection or are due to the rotation of those stars. The effects of instabilities associated with convection on the behavior of the stellar surface layers are reviewed. The usefulness of numerical simulations in studying such effects is addressed. Baroclinic instabilities and shear instabilities caused by rotation are discussed, and the possible mechanisms for maintaining differential rotation are considered. Title: Hydrodynamics in Stars Authors: Zahn, J. -P. Bibcode: 1986MitAG..67..163Z Altcode: Fluid dynamics plays a central role in astrophysics, even though it has been given, until now, insufficient recognition. The purpose of this paper is to contribute a little to remedy this situation by presenting some of the hydrodynamical problems occurring in an important class of objects, the stars. Title: Astronomie Flammarion, Vols. 1+2. Authors: Rösch, J.; Wlérick, G.; Guibert, J.; Bonnet, R.; Vedrenne, G.; Celnikier, L.; Morando, B.; Boischot, A.; Brahic, A.; Kandel, R.; Dumont, S.; Praderie, F.; Magnan, C.; Gerbaldi, M.; Zahn, J. -P.; Gouguenheim, L.; Bottinelli, L.; Heidmann, N.; Heidmann, J.; Véron, P.; Nottale, L.; Pecker, J. -C.; Golay, M. Bibcode: 1985afv..book.....R Altcode: Contents: L'astronomie à l'œil nu (J. Rösch). L'astronomie optique; de Galilée à la fin du XXe siècle (G. Wlérick). Télescopes et lunettes du XXe siècle (G. Wlérick). La radioastronomie (J. Guibert). L'astronomie spatiale (R. Bonnet). L'astronomie des hautes énergies (G. Vedrenne). L'exploration in situ dumilieu astronomique (L. Celnikier). Le système solaire: généralités (B. Morando). Les planètes telluriques (L. Celnikier). Astéroïdes, comètes et météorites (L. Celnikier). Jupiter (A. Boischot). Le monde de Saturne (A. Brahic). Les confins du système solaire (Uranus, Neptune et Pluton) (A. Brahic). Le Soleil, les planètes, la Terre (R. Kandel). Le Soleil, étoile typique (S. Dumont). Les spectres stellaires: la connaissance des étoiles (F. Praderie). L'interaction des étoiles et du milieu environnant (C. Magnan). La Galaxie: étoiles et matière interstellaire (M. Gerbaldi). L'évolution des étoiles (J.-P. Zahn). Les facteurs de l'évolution galactique (L. Gouguenheim). Forme et classification des galaxies (L. Bottinelli, N. Heidmann). Amas et superamas de galaxies (J. Heidmann). Les quasars (P. Véron). Évolution des galaxies (L. Gouguenheim). Les faits cosmologiques (L. Bottinelli). La cosmologie de la grandeexplosion (L. Nottale). Le débat cosmologique (L. Nottale). Title: Penetrative cellular convection in a stratified atmosphere Authors: Massaguer, J. M.; Latour, J.; Toomre, J.; Zahn, J. -P. Bibcode: 1984A&A...140....1M Altcode: In the present investigation of penetrative convection within a simple compressible model, the middle one of the three layers of differing stratification prior to the onset of convection is a convectively unstable polytrope bounded above and below by two stably stratified polytropes. One- and two-mode steady solutions with hexagonal planforms have been studied for Rayleigh numbers up to aobut 1000 times critical, and for a range of Prandtl numbers, horizontal wavenumbers, and stratifications. These indicate that the penetration into the lower stable layer by downward plumes is substantially larger in a stratified medium than in a Boussinesq fluid, and produces an extended region of adiabatic stratification. The strong asymmetry between upward and downward penetration in compressible media has major implications for the mixing of stable regions above and below stellar convection zones. Title: Introductory report : Stability of Rotation Laws Authors: Zahn, J. P. Bibcode: 1984LIACo..25..407Z Altcode: 1984tpss.conf..407Z; 1984trss.conf..407Z No abstract at ADS Title: Book-Review - Astrophysical Processes in Upper Main Sequence Stars Authors: Cox, A. N.; Vauclair, S.; Zahn, J. P. Bibcode: 1984S&T....67Q.526C Altcode: No abstract at ADS Title: Book-Review - Astrophysical Processes in Upper Main Sequence Stars - Saas-Fee 13TH - 1983MAR Authors: Cox, A.; Vauclair, S.; Zahn, J. P. Bibcode: 1984Mercu..13...93C Altcode: No abstract at ADS Title: Tidal Effects in Close Binary Stars Authors: Zahn, J. P. Bibcode: 1984IAUS..105..379Z Altcode: This review addresses the question of what can be learned about the stellar interiors from the study of the tidal effects in close binary stars. Title: Un télescope pour les amateurs au Pic-du-Midi. Authors: Zahn, J. -P. Bibcode: 1983LAstr..97...27Z Altcode: No abstract at ADS Title: Les instabilités dues à la rotation. Authors: Zahn, J. -P. Bibcode: 1983ihaa.conf..389Z Altcode: Contents: Instabilité de cisaillement. Instabilité barocline. Instabilités multidiffusives. Comparaison des différentes instabilités. Esquisse d'une solution. Title: Nonlinear Anelastic Modal Theory for Solar Convection Authors: Latour, J.; Toomre, J.; Zahn, J. -P. Bibcode: 1983SoPh...82..387L Altcode: 1983IAUCo..66..387L Preliminary solar envelope models have been computed using the single-mode anelastic equations as a description of turbulent convection. This approach provides estimates for the variation with depth of the largest convective cellular flows, akin to giant cells, with horizontal sizes comparable to the total depth of the convection zone. These modal nonlinear treatments are capable of describing compressible motions occurring over many density scale heights. Single-mode anelastic solutions have been constructed for a solar envelope whose mean stratification is nearly adiabatic over most of its vertical extent because of the enthalpy (or convective) flux explicitly carried by the big cell; a sub-grid scale representation of turbulent heat transport is incorporated into the treatment near the surface. The single-mode equations admit two solutions for the same horizontal wavelength, and these are distinguished by the sense of the vertical velocity at the center of the three-dimensional cell. It is striking that the upward directed flows experience large pressure effects when they penetrate into regions where the vertical scale height has become small compared to their horizontal scale. The fluctuating pressure can modify the density fluctuations so that the sense of the buoyancy force is changed, with buoyancy braking actually achieved near the top of the convection zone. The pressure and buoyancy work in the shallow but unstable H+ and He+ ionization regions can serve to decelerate the vertical motions and deflect them laterally, leading to strong horizontal shearing motions. It appears that such dynamical processes may explain why the amplitudes of flows related to the largest scales of convection are so feeble in the solar atmosphere. Title: Circulation méridienne dans les étoiles. Authors: Zahn, J. -P. Bibcode: 1983ihaa.conf..409Z Altcode: Contents: Le déséquilibre radiatif dans une étoile en rotation. Les premiers travaux. La solution des Tassoul. Title: Astrophysical process in upper main sequence stars Authors: Cox, A. N.; Vauclair, S.; Zahn, J. P. Bibcode: 1983apum.conf.....C Altcode: 1983SAAS...13.....C; 1983QB799.C69...... No abstract at ADS Title: Instability and Mixing Processes in Upper Main Sequence Stars Authors: Zahn, J. -P. Bibcode: 1983apum.conf..253Z Altcode: 1983SAAS...13..253Z Introduction Generalities The basic equations Global time scales The Brunt-Väisälä frequency The Rayleigh frequency Application to rotating stars The Eddington-Sweet Circulation The early investigations The Tassoul's solution Ekman Pumping, Spin-Down The Ekman layer Ekman pumping and spin-down time Penetrative Convection Mixing length treatment Hydrodynamical calculations Double Diffusive Instabilities. Semi-Convection Shear Flow Instability Generalities Startified shear flows Effect of rotation The Taylor experiment Baroclinic Instability The basic mechanism The instability condition Application to stars Multidiffusive Instabilities Involving Angular Momentum Goldreich-Schubert-Fricke instability Triply diffusive instabilities Trubulence and Mixing Comparison of the instabilities Three-dimensional turbulence Two-dimensional turbulence Turbulent mixing Sketch of a Possible Solution General outline Quantitative requirements Efficiency of the turbulence generation Vertical diffusivity and mixing References Title: Nonlinear modal analysis of penetrative convection Authors: Zahn, J. -P.; Toomre, J.; Latour, J. Bibcode: 1982GApFD..22..159Z Altcode: It is pointed out that thermal convection in many astrophysical and geophysical settings occurs in an unstable layer bounded above and below by regions which are stably stratified. The convective motions may extend a substantial distance into the adjacent stable zones. If the motions have little direct effect upon the mean stratification of the stable zone, then they are usually referred to as convective overshooting. The primary objective of the present investigation is to study the dynamics of overshooting at very large Rayleigh numbers, mainly with stellar applications in mind. Numerically this is only feasible if severe simplifications are made in the description of what are likely to be turbulent motions. The approach employed in the investigation utilizes nonlinear modal equations in which the vertical and temporal structure of the convection is described accurately at the expense of the horizontal structure. A summary of the salient properties of penetrative convection is provided on the basis of the results of the conducted studies. Title: Book reviews Authors: Ne'Eman, Y.; Zahn, J. -P.; Habing, H. J.; Wittenberg, H.; Zwaan, C.; Murray, C. A.; de Jager, Cornelis; Kresák, L. Bibcode: 1982SSRv...33..459N Altcode: No abstract at ADS Title: Book-Review - Hydrodynamic Instabilities and the Transition to Turbulence Authors: Swinney, H. L.; Gollub, J. P.; Zahn, J. P. Bibcode: 1982SSRv...33R.459S Altcode: No abstract at ADS Title: Stellar convection theory. III - Dynamical coupling of the two convection zones in A-type stars by penetrative motions Authors: Latour, J.; Toomre, J.; Zahn, J. -P. Bibcode: 1981ApJ...248.1081L Altcode: The thermal convection occurring over many density scale heights in an A-type star outer envelope, encompassing both the hydrogen and helium convectively unstable zones, is examined by means of anelastic modal equations. The single-mode anelastic equations for such compressible convection display strong overshooting of the motions into adjacent radiative zones, which would preclude diffusive separation of elements in the supposedly quiescent region between the two unstable zones. In addition, the anelastic solutions reveal that the two zones of convective instability are dynamically coupled by the overshooting motions. The two solutions that the nonlinear single-mode equations admit for the same horizontal wavelength are distinguished by the sense of the vertical velocity at the center of the three-dimensional cell. It is suggested that strong horizontal shear flows should be present just below the surface of the star, and that the large-scale motions extending into the stable atmosphere would appear mainly as horizontal flows. Title: Nonlinear Anelastic Models of Solar Convection Authors: Toomre, J.; Latour, J.; Zahn, J. -P. Bibcode: 1981BAAS...13Q.907T Altcode: No abstract at ADS Title: Workshop on pulsating B stars. Proceedings of a workshop held at Nice Observatory, June 1 - 5, 1981. (Centenaire de l'Observatoire de Nice 1881 - 1981). Authors: Auvergne, M.; Baglin, A.; Ducatel, D.; Le Contel, J. -M.; Morel, P. J.; Sareyan, J. -P.; Valtier, J. -C.; Sterken, C.; Zahn, J. -P. Bibcode: 1981wopb.book.....A Altcode: No abstract at ADS Title: Cent ans d'astronomie à l'Observatoire de Nice 1881 - 1981. Authors: Clorennec, A.; Feldman, R.; Zahn, J. -P.; Willemse, H. Bibcode: 1981cad..book.....C Altcode: No abstract at ADS Title: Convection zones in sun and stars. Authors: Zahn, J. P. Bibcode: 1981ASIC...68..123Z Altcode: 1981spss.conf..123Z Aspects of the current understanding of the nature, description and observational properties of solar and stellar convection zones are discussed. The origin of a convective zone as a result of the increase in the luminosity/mass ratio of a star in its center and increases in the opacity in the outer layers of a star is discussed, and the standard mixing length treatment of the ensuing envelope convection is presented. The expected effects of convective motions are examined in order to demonstrate the inadequacy of the standard approach in accounting for the generation of kinetic energy and the transport of angular momentum and magnetic field, and alternative hydrodynamic approaches are described. Observations of solar oscillations and supergranulation and stellar atmospheres, rotation rates and orbital eccentricities which have a bearing on the properties and existence of convection zones are also noted. Title: Pulsating Stars. (Book Reviews: Theory of Stellar Pulsation) Authors: Zahn, Jean-Paul Bibcode: 1980Sci...210.1119Z Altcode: 1980Sci...210.1119C No abstract at ADS Title: Anelastic Modal Theory Applied to the Solar Convection Zone Authors: Toomre, J.; Latour, J.; Zahn, J. P. Bibcode: 1980BAAS...12..895T Altcode: No abstract at ADS Title: Cellular convection in a stratified atmosphere Authors: Massaguer, J. M.; Zahn, J. -P. Bibcode: 1980A&A....87..315M Altcode: The properties of thermal convection in an atmosphere spanning several density scale heights are examined. Both the conductivity and the shear viscosity are assumed to be constant. The anelastic approximation is used, together with a modal expansion procedure in the horizontal directions; this expansion is severely truncated, keeping one or two modes. Only steady solutions are built, for Rayleigh numbers up to 100,000 times critical and Prandtl numbers of 1, 0.01 and 0.0001. The most striking properties of the solutions is that they display an inversion of the buoyancy force in the upper part of the domain, and that the pressure fluctuations play an essential role in controlling the dynamics. Both the effects are ignored in the current mixing-length approach. Title: Stellar convection theory Authors: Zahn, J. -P. Bibcode: 1980LNP...114....1Z Altcode: 1980sttu.coll....1Z; 1980IAUCo..51....1Z Stellar turbulence due to thermal convection is considered, as well as the modelling of convective transport and specifically, the study of the advection of a passive scalar, ignoring molecular diffusion. Attention is given to the introduction of the diffusion approximation in applying the mixing length approach to stellar convection. Solving the original fluid dynamical equations is discussed in terms of hydrodynamical approaches, which include working either in the Fourier space or the physical space or utilizing the modal expansion procedure. In addition, considering the effect of strong density stratification, the anelastic approximation is discussed, with attention given to pressure and buoyancy forces, and pressure and temperature fluctuations. Title: Compressible Convection in the Outer Envelope of A-type Stars Authors: Toomre, J.; Latour, J.; Zahn, J. -P. Bibcode: 1978BAAS...10..677T Altcode: No abstract at ADS Title: On the boundary conditions imposed by a stratified fluid Authors: Latour, J.; Zahn, J. -P. Bibcode: 1978GApFD..10..311L Altcode: Through generalization of the results obtained by Stix (1970) and by Whitehead (1971), the paper presents the homogeneous boundary conditions that are imposed by a fluid of stable but otherwise arbitrary stratification. These penetrating conditions are strictly valid only in the limit of steady linearized flow. However, under some conditions they can also be applied to nonlinear problems. An example of linear penetrative convection is treated in order to illustrate the use of these boundary conditions. Title: Défense du site de l'observatoire. Authors: Zahn, J. -P.; Baglin, A. Bibcode: 1978BONic..13...25Z Altcode: No abstract at ADS Title: Tidal friction in close binary systems. Authors: Zahn, J. -P. Bibcode: 1977A&A....57..383Z Altcode: 2009A&A...500..121Z We examine various physical mechanisms which may produce tidal friction in close binary stars. We find that the most efficient in stars with convective envelopes is turbulent viscosity retarding the equilibrium tide, and in stars with radiative envelopes the action of radiative damping on the dynamical tide. Theoretical predictions based on these dissipative processes are in good agreement with the rotational velocities and orbital eccentricities observed in close binaries. The results are applied to the X-ray binaries Her X-1 and Cen X-3. Title: Anelastic Stellar Convection Theory Applied to A-type Stars. Authors: Toomre, J.; Latour, J.; Zahn, J. -P. Bibcode: 1977BAAS....9..337T Altcode: No abstract at ADS Title: Penetrative convection in stars Authors: Zahn, J. -P. Bibcode: 1977LNP....71..225Z Altcode: 1977IAUCo..38..225Z; 1977stco.coll..225Z; 1977psc..conf..225Z Methods developed to describe stellar convection are reviewed, and their suitability for describing the penetration of convective motions into stable surroundings is considered. Phenomenological approaches based on local and nonlocal mixing-length treatments are examined along with procedures based on the concept of thermals and direct approaches for treating Boussinesq convection as well as convection in a stratified medium. Possible observational tests of the various methods are outlined. Title: Problems of stellar convection Authors: Spiegel, E. A.; Zahn, J. -P. Bibcode: 1977LNP....71.....S Altcode: 1977IAUCo..38.....S; 1977stco.coll.....S The papers deal with various aspects of stellar convection theory ranging from mixing-length formalisms to computations based on full equations. The major subjects encompass mixing-length theory, linear theory, observational aspects of convection, numerical solutions to stellar-convection problems, effects of rotation and magnetic fields, penetration of convection, special types of convection, waves, and turbulence. Specific topics include the current state of mixing-length theory, dynamical instabilities in stars, observations bearing on convection, the evolutionary pattern of exploding granules, numerical methods in convection theory, convection in rotating stars, and convective dynamos. Other contributions examine penetrative convection in stars, convective overshooting in the solar photosphere, thermosolutal convection, Urca convection, photoconvection, convection in the helium flash, and the roles of determinism and chaos in turbulence. Title: Stellar convection theory. II. Single-mode study of the second convection zone in an A-type star. Authors: Toomre, J.; Zahn, J. -P.; Latour, J.; Spiegel, E. A. Bibcode: 1976ApJ...207..545T Altcode: The anelastic modal equations presented in Paper I are considered in their simplest version: only one mode is retained in the representation of the fluctuating dynamic and thermodynamic variables of convection theory. These single-mode equations are used to examine the structure of the second convection zone of an A-type star. Two- and three-dimensional numerical solutions are obtained for a range of parameters in the theory, and a simple analysis is provided for their interpretation. The principal results are for three-dimensional motions, since these are most likely to be relevant to stellar convection. Such motions produce a convective heat flux several orders of magnitude greater than predicted by standard mixing-length theory for the same situation; we find that convection carries up to 6 percent of the total flux. The most significant astrophysical implication of our results is that they suggest strong overshooting into the adjacent radiative zones. We anticipate that mixing will extend to the overlying hydrogen convection zone. This would rule out some interpretations of metallic-line stars which invoke diffusive element separation between the two convection zones. Subject headings: convection - stars: interiors - stars: metallic-line Title: Stellar convection theory. I. The anelastic modal equations. Authors: Latour, J.; Spiegel, E. A.; Toomre, J.; Zahn, J. -P. Bibcode: 1976ApJ...207..233L Altcode: Methods are developed for dealing with the various dynamical problems that arise because of convective zones in stars. A system of equations for stellar convection is derived from the full equations of compressible fluid dynamics with the aid of two major approximations. The first of these is the anelastic approximation, which involves both the filtering out of acoustic waves and a suitable linearization of the fluctuating thermodynamic variables. The second one approximates the horizontal structure of convection by expanding the motion in a set of horizontal cellular platforms and severely truncating the expansion. The resulting system of partial differential equations, referred to as the anelastic modal equations, is outlined along with suggested boundary conditions and techniques for solving the equations. Ways of assessing the overall validity of the present treatment are discussed. Title: The Second Convection Zone in an A-type Star Authors: Latour, J.; Spiegel, E. A.; Toomre, J.; Zahn, J. P. Bibcode: 1975BAAS....7..526L Altcode: No abstract at ADS Title: The dynamical tide in close binaries. Authors: Zahn, J. -P. Bibcode: 1975A&A....41..329Z Altcode: The non-adiabatic oscillations of a star, driven by an outer rotating gravitational field, have been studied by the use of matched asymptotic expansions. The interior and envelope solutions in this procedure are derived in Sections 2 and 3. The results apply to stars which have a convective core and a radiative envelope, and they are discussed in Section 4. We find that the resonances of the free gravity modes are damped by radiative dissipation, which operates in a relatively thin region below the surface of the star. Due to that dissipation, some properties of the dynamical tide have observable consequences in close binary systems: (1) A torque is applied to a binary component; this serves to make it corotate with its companion in a time which can be short compared to its nuclear life. (2) Before that synchronization is achieved, the brightness distribution over the surface of the star is in general phase shifted relative to the external driving potential. Title: Differential Rotation and Turbulence in Stars Authors: Zahn, J. P. Bibcode: 1975MSRSL...8...31Z Altcode: 1975phs..conf...31Z No abstract at ADS Title: Rotational Instabilities and Stellar Evolution Authors: Zahn, J. -P. Bibcode: 1974IAUS...59..185Z Altcode: This review deals with the local instabilities arising when the effects of rotation are taken into account in the evolution of a nonmagnetic star. The Rayleigh and shear instabilities will be examined under the conditions prevailing in radiative zones where the effect of density stratification, thermal diffusion, viscosity and varying chemical composition must be taken into account. The possible consequences on the evolution of a star are finally outlined. Title: Pleading for Hydrodynamics Authors: Zahn, J. P. Bibcode: 1972oss..conf..371Z Altcode: No abstract at ADS Title: Sur la rotation des étoiles doubles serées. Authors: Zahn, J. -P. Bibcode: 1972CRASB.274.1443Z Altcode: No abstract at ADS Title: Instabilities of Differential Rotation Authors: Spiegel, E. A.; Zahn, J. -P. Bibcode: 1970CoASP...2..178S Altcode: 1970ComAp...2..178S No abstract at ADS Title: Forced Oscillations in Close Binaries. The Adiabatic Approximation Authors: Zahn, J. P. Bibcode: 1970A&A.....4..452Z Altcode: The forced oscfflations of a star are discussed, due to a periodic varying gravitational field. The following approximations are made: the star is not rotating, the oscfflations are adiabatic and small enough to allow linearization. Olver's method is employed to derive a second-order asymptotic expression for the eigenfunctions. The results predict large amplitudes for the tides near the surface, where however adiabacy is a pcor approximation. Title: Appel aux observateurs Authors: Zahn, J. -P. Bibcode: 1969LAstr..83..114Z Altcode: No abstract at ADS Title: Possible Effects of the Resonance in Close Binaries on their Mass Exchanges Authors: Zahn, J. -P. Bibcode: 1969ASSL...13..267Z Altcode: 1969mlfs.conf..267Z No abstract at ADS Title: On Possible Non-Radial Pulsations of Baker's One-Zone Model Authors: Zahn, J. P. Bibcode: 1968ApL.....1..209Z Altcode: No abstract at ADS Title: Internal structure and evolutionary changes in binaries: Variation des éléments orbitaux sous l'influence des marées Authors: Zahn, J. P. Bibcode: 1967oeds.conf..108Z Altcode: No abstract at ADS Title: Internal structure and evolutionary changes in binaries: Causes possibles d'évolution homogène des binaires serrées Authors: Zahn, J. P. Bibcode: 1967oeds.conf..124Z Altcode: No abstract at ADS Title: Les éruptions solaires Authors: Zahn, J. -P. Bibcode: 1966LAstr..80..359Z Altcode: No abstract at ADS Title: Les marées dans une étoile double serrée (suite) Authors: Zahn, J. P. Bibcode: 1966AnAp...29..489Z Altcode: No abstract at ADS Title: Les marées dans une étoile double serrée (suite et fin) Authors: Zahn, J. P. Bibcode: 1966AnAp...29..565Z Altcode: No abstract at ADS Title: Les marées dans une étoile double serrée Authors: Zahn, J. P. Bibcode: 1966AnAp...29..313Z Altcode: No abstract at ADS Title: Éclipse de Lune du 19 décembre 1964 Authors: Marin, M.; Zahn, J. -P. Bibcode: 1965LAstr..79..326M Altcode: No abstract at ADS Title: L'éclipse de Lune des 24 et 25 juin 1964 Authors: Marin, M.; Zahn, J. -P. Bibcode: 1965LAstr..79...14M Altcode: No abstract at ADS Title: L'âge des étoiles Authors: Zahn, J. -P. Bibcode: 1964LAstr..78..457Z Altcode: No abstract at ADS Title: Préparons-nous à observer la prochaine éclipse de Lune Authors: Coupinot, G.; Zahn, J. -P. Bibcode: 1964LAstr..78..148C Altcode: No abstract at ADS Title: Cinq jeunes suivent un stage à l'Observatoire de Nice Authors: Zahn, J. -P. Bibcode: 1964LAstr..78...96Z Altcode: No abstract at ADS Title: Préparons-nous à observer la prochaine éclipse de Lune Authors: Coupinot, G.; Zahn, J. -P. Bibcode: 1964LAstr..78...97C Altcode: No abstract at ADS Title: Appel aux Jeunes Authors: Zahn, J. -P. Bibcode: 1964LAstr..78...64Z Altcode: No abstract at ADS Title: Le magnétisme stellaire Authors: Zahn, J. P. Bibcode: 1963LAstr..77..313Z Altcode: No abstract at ADS Title: Autres observations de l'éclipse partielle de Lune des 15-16 juillet 1954 Authors: Hannorat, M.; Zahn, J. -P. Bibcode: 1954LAstr..68..384H Altcode: No abstract at ADS Title: L'éclipse partielle de Soleil du 30 juin 1954 Authors: Pollachi, L. G.; Porret, R.; Weber, R.; Dumser, L.; Kern, H.; Zahn, J. -P.; Badina, V. -E. Bibcode: 1954LAstr..68..372P Altcode: No abstract at ADS