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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. 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. 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. 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 $\eta > 10^{7-8} \, cm^2/s$), even in the presence of radiative spreading. 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., Comment: 10 pages, 7 figures, accepted in A&A

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. We use the spectropolarimeters Narval and ESPaDOnS to detect circular polarization within the photospheric absorption lines of our targets and use the least-squares deconvolution (LSD) method. We also measure the classical S-index activity indicator, 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. 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.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. 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, eta Psc) are detected with magnetic field strength at the sub-gauss level., Comment: 34 pages, 22 Figures, accepted for publication in Astronomy & Astrophysics

Tidal dissipation, which is directly linked to internal structure, is one of the key physical mechanisms that drive systems evolution and govern their architecture. A robust evaluation of its amplitude is thus needed to predict evolution time for spins and orbits and their final states. The purpose of this paper is to refine recent model of the anelastic tidal dissipation in the central dense region of giant planets, commonly assumed to retain a large amount of heavy elements, which constitute an important source of dissipation. The previous paper evaluated the impact of the presence 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. 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, a factor 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. 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 an elastic core's tidal dissipation of a two-layer model and the observations., Comment: 5 pages, 2 figures, Accepted for publication in Astronomy & Astrophysics

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. Our aim is to obtain seismic constraints on the internal transport and surface loss of 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. 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 $1.3 M_{\odot}$ models. Rotation profiles were derived from our evolutionary models and eigenfunctions from linear adiabatic oscillation calculations. 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. 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., Comment: 15 pages, 13 figures, accepted for publication in A&A

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 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 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., Comment: 5 pages, 3 figures, proceeding of the SF2A-2012 conference: Semaine de l'Astrophysique Francaise, meeting held in Paris, France, June 20-23, 2012

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, and these are still not well understood. 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 by the quality factor Q, as 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. 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 decoupled from the dynamical tide. The tidal kinetic energy is dissipated into heat through 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; it is responsible for the imaginary part of the disturbing function, which is implemented in the dynamical evolution equations, from which one derives characteristic evolution times. The rate at which the system evolves depends on the physical properties of tidal dissipation, and specifically on how the eddy viscosity varies with tidal frequency and on the thickness of the convective envelope for the fluid equilibrium tide. At low frequency, this tide retards by a constant time delay, whereas it lags by a constant angle when the tidal frequency exceeds the convective turnover rate., Comment: 13 pages, 5 figures, Accepted for publication in Astronomy & Astrophysics

Earth-like planets have viscoelastic mantles, whereas giant planets may have viscoelastic cores. The tidal dissipation of such solid regions, gravitationally perturbed by a companion body, highly depends on their rheology and on the tidal frequency. Therefore, modelling tidal interactions presents a high interest to provide constraints on planets' properties and to understand their history and their evolution, in our Solar System or in exoplanetary systems. We examine the equilibrium tide in the anelastic parts of a planet whatever the rheology, taking into account the presence of a fluid envelope of constant density. We show how to obtain the different Love numbers that describe its tidal deformation. Thus, we discuss how the tidal dissipation in solid parts depends on the planet's internal structure and rheology. Finally, we show how the results may be implemented to describe the dynamical evolution of planetary systems. The first manifestation of the tide is to distort the shape of the planet adiabatically along the line of centers. Then, the response potential of the body to the tidal potential defines the complex Love numbers whose real part corresponds to the purely adiabatic elastic deformation, while its imaginary part accounts for dissipation. 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. The rate at which the system evolves depends on the physical properties of tidal dissipation, and specifically on how the shear modulus varies with tidal frequency, on the radius and also the rheological properties of the solid core. The quantification of the tidal dissipation in solid cores of giant planets reveals a possible high dissipation which may compete with dissipation in fluid layers., Comment: 17 pages, 11 figures, Accepted for publication in Astronomy & Astrophysics

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 k2/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 (k2/Q= (2.3 \pm 0.7) \times 10-4), which is about ten 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 k2/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 longer time scale at the outer edge of the main rings. In an attempt to take into account for possible significant torques exerted by the rings on Mimas, we fitted a constant rate da/dt on Mimas semi-major axis, also. We obtained an unexpected large acceleration related to a negative value of da/dt= -(15.7 \pm 4.4) \times 10-15 au/day.

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. We test here the validity of this magnetic scenario through 3D numerical MHD simulations that encompass both the radiation zone and the convection zone. The numerical simulations are performed with the anelastic spherical harmonics (ASH) code. The computational domain extends from $0.07\;R_\odot$ to $0.97\;R_\odot$. In the parameter regime we explored, a dipolar fossil field aligned with the rotation axis can not 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. 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., Comment: 16 pages, 18 figures, to appear in A&A

This paper provides a prescription for the turbulent viscosity in rotating shear flows for use e.g. in geophysical and astrophysical contexts. This prescription is the result of the 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 the analysis applies more naturally to 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 mean 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 given by measurements in the case where the outer cylinder is at rest, the other one being a universal function provided here from experimental fits. As a result, we obtain a general expression for the turbulent viscosity and compare it to existing prescription in the literature. Finally, throughout all the paper we discuss the influence of additional effects such as stratification or magnetic fields., Comment: RevTex, 21 pages, 20 figures

(Abridged) 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 only are included in the simulations. Our analysis is based on a 2-D representation of the secular hydrodynamics, which is treated using expansions in spherical harmonics. 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 Msun for which the hydrodynamics has been previously extensively studied in the literature. We obtain a clear visualization and a precise estimation of the different terms entering the angular momentum and heat transport equations in radiative zones. 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 readjustements. 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 very well balanced by the barotropic effects and the thermal relaxation during most of the main sequence evolution. This enables us to derive simplifications 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., Comment: 16 pages, 18 figures. Accepted for publication in A&A

Aims. 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 $g\Omega$ waves) by the vortex mode through linear mode coupling in shear flows. Methods. Non-modal analysis of linearized Boussinesq equations 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 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 in account the vertical stratification and consequent mode coupling in the high Reynolds number regime., Comment: A&A (accepted)

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. 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. According to Spruit, it could also drive a dynamo. 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 Alfven waves; they cause negligible eddy-diffusivity and contribute little to the net transport of angular momentum. 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., Comment: 11 pages, 6 figures, Accepted in Astronomy & Astrophysics

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., Comment: 4 pages, SF2A-2005: Semaine de l'Astrophysique Francaise, meeting held in Strasbourg, France, June 27 - July 1, 2005, Edited by F. Casoli, T. Contini, J.M. Hameury and L. Pagani. Published by EdP-Sciences, Conference Series, 2005, p. 319

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 next future to improve our description of stellar radiation zones., Comment: 14 pages, 3 figures, Proceeding of the Joint HELAS and CoRoT/ESTA Workshop (20-23 November 2006, CAUP, Porto - Portugal)

We study the physics of the solar tachocline and related MHD instabilities. We have performed 3-D MHD simulations of the solar radiative interior to check whether a fossil magnetic field is able to prevent the spread of the tachocline. 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 massive parallel supercomputers. 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 deg 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. 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., Comment: 12 pages, 8 color figures (low res), published in A&A, october 2006

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 which 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. 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. 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., Comment: 4 pages, 2 figures (to appear in Astronomy & Astrophysics)

The solar magnetism is no more considered as a purely superficial phenomenon. The SoHO community has shown that the length of the solar cycle depends on the transition region between radiation and convection. Nevertheless, the internal solar (stellar) magnetism stays poorly known. Starting in 2008, the American instrument HMI/SDO and the European microsatellite PICARD will enrich our view of the Sun-Earth relationship. Thus obtaining a complete MHD solar picture is a clear objective for the next decades and it requires complementary observations of the dynamics of the radiative zone. For that ambitious goal, space prototypes are being developed to improve gravity mode detection. The Sun is unique to progress on the topology of deep internal magnetic fields and to understand the complex mechanisms which provoke photospheric and coronal magnetic changes and possible longer cycles important for human life. We propose the following roadmap in Europe to contribute to this "impressive" revolution in Astronomy and in our Sun-Earth relationship: SoHO (1995-2007), PICARD (2008-2010), DynaMICS (2009-2017) in parallel to SDO (2008-2017) then a world-class mission located at the L1 orbit or above the solar poles., Comment: 10 pages, 8 figures, will appear in the proceedings of 2005 ESLAB symposium 19-21 April 2005

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., Comment: 28 pages, 1 figure, accepted for publication in Astronomy and Astrophysics

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 [5], 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., Comment: 8 pages, 9 figures, Comments added to discussion of energy flow and introductory section abbreviated

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 $\Omega$ decreases outwards with radius $r$. At not too small stratification, its growth rate is a fraction of $\Omega$. The influence of viscous dissipation and thermal diffusivity on the instability is studied numerically, with emphasis on the case when $d \ln \Omega / d \ln r =-3/2$ (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., Comment: 19 pages, 13 figures, to appear in A&A

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 (1992) and Maeder & Zahn (1998) 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., Comment: 16 pages, no figures, accepted for publication in A&A

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 `beta-viscosity' is drawn from torque measurements in the classical Couette-Taylor experiment (Richard & Zahn 1999). 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., Comment: 5 pages, 3 figures, accepted for publication in Astronomy and Astrophysics

This paper deals with the problem of hydrodynamic shear turbulence in non-magnetized Keplerian disks. We wish to draw attention to a 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 a transient growth, and 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 on the occurrence of hydrodynamic shear turbulence in such disks is not founded., Comment: 8 pages, 1 figure, accepted in A & A

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 $S_{11}$ and $S_{34}$ 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 $X_{\rm inv}=0.732\pm 0.001$ and that based on the $^9$Be 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 $S_{11}(0)=4.06\pm 0.07$ $10^{-25}$ 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., Comment: 16 pages, 12 figures, A&A in press (1) JILA, University of Colorado, Boulder, CO 80309-0440, USA, (2) LUTH, Observatoire de Paris-Meudon, 92195 Meudon, France, (3) Tata Institute of Fundamental Research, Homi Bhabha road, Mumbai 400005, India, (4) Department of Physics, University of Mumbai, Mumbai 400098, India

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., Comment: submitted to Astronomy & Astrophysics, on Oct 02, 2001

Helioseismic inversions of the Sun's internal angular velocity profile show that the rotation changes from differential in latitude in the convection zone to almost uniform in the radiative region below. The transition occurs in a thin layer, the tachocline, which is the seat of strong shear in the vertical direction. In this Note we examine whether this rotation profile can lead to shear turbulence at the top of the radiation zone. By using the standard solar model, we show that such turbulence can be generated only in a narrow region 0.695R_sun < r < 0.713R_sun at the equator and even in narrower layers at higher latitudes. We conclude that the turbulence generated by this vertical shear is unlikely to play a significant role in the transport of matter and angular momentum, and that other mechanisms must be invoked to achieve this., Comment: 3 pages, 2 figures, Research note accepted by A&A

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-Chi\`eze and Zahn, 1999, in Astrophys. J.)., Comment: to appear in Annals of the New York Academy of Sciences, vol 898. Postscript file, 9 pages and 5 figures New Email Address for A. S. Brun: sabrun@solarz.colorado.edu

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 (CZ) and fail to predict the Li7 depletion. In parallel, helioseismology has shown that the transition from differential rotation in the CZ to almost uniform rotation in the radiative solar interior occurs in a shallow layer called the tachocline. This layer is presumably the seat of large scale circulation and of turbulent motions. Here, we introduce a macroscopic transport term in the structure equations, which is based on a hydrodynamical description of the tachocline proposed by Spiegel and Zahn, and we calculate the mixing induced within this layer. We discuss the influence of different parameters that represent the tachocline thickness, the Brunt-Vaissala frequency at the base of the CZ, 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: a) a good agreement with the observed photospheric chemical abundance of light elements such as He3, He4, Li7 and Be9, b) a smooth composition gradient at the base of the CZ, and c) a significant improvement of the sound speed square difference between the seismic sun and the models in this transition region, when we allow the phostospheric heavy element abundance to adjust, within the observational incertitude, due to the action of this mixing process. The impact on neutrino predictions is also discussed., Comment: 15 pages, 7 figures, to be published in ApJ (used emulateapj style for latex2e). New email for A. S. Brun: sabrun@solarz.colorado.edu

With the recent results of helioseismology aboard SOHO, solar models are more and more constrained (Brun, Turck-Chieze and Morel 1998 (astro-ph/9806272)). New physical processes, mainly connected to macroscopic motions, must be introduced to understand these new observations. In this poster, we present solar models including a turbulent pressure in the outer layers and mixing due to the tachocline (Spiegel and Zahn 1992). Our results lead us to conclude that: - Turbulent pressure improves the absolute value of the acoustic mode frequencies (~ 10 microHz at 4mHz), - Mixing in a tachocline thickness of 0.05 +/- 0.03 Ro (Corbard et al. 1997) looks promising., Comment: 5 pages, 7 figures To appear in SOHO6/GONG98 Proceedings "Structure and Dynamics of the Interior of the Sun and Sun-like Stars", (email: sacha.brun@cea.fr, turck@discovery.saclay.cea.fr, zahn@mokus.obspm.fr)

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 ($\mu$). We find that the critical shear which is able to overcome the $\mu$-gradient is substantially reduced by this anisotropic turbulence, and we derive an estimate for the resulting turbulent diffusivity in the vertical direction., Comment: 4 pages, LaTeX, using l-aa.sty, 1 eps figure included, accepted by A&A June 7th, 1996