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Context. Stellar oscillations are key to unravelling stellar properties, such as their mass, radius, and age. This in turn enables us to date and characterize their exoplanetary systems. The amplitudes of acoustic (p-) modes in solar-like stars are intrinsically linked to their convective turbulent excitation source, which in turn is influenced by magnetism. In the observations of the Sun and stars, the mode amplitudes are modulated following their magnetic activity cycles: the higher the magnetic field, the lower the mode amplitudes. When the magnetic field is strong, it can even inhibit acoustic modes, which are not detected in most of the solar-like stars that are strongly magnetically active. Magnetic fields are known to freeze convection when they stronger than a critical value: the so-called on-off approach is used in the literature. Aims. We investigate the impact of magnetic fields on the stochastic excitation of acoustic modes. Methods. First, we generalise the forced-wave equation formalism, including the effects of magnetic fields. Second, we assess how convection is affected by magnetic fields using results from the magnetic mixing-length theory. Results. We provide the source terms of the stochastic excitation, including a new magnetic source term and the Reynolds stresses. We derive scaling laws for the mode amplitudes that take both the driving and the damping into account. These scalings are based on the inverse Alfvén dimensionless parameter: The damping increases with the magnetic field and reaches a saturation threshold when the magnetic field is strong. The driving of the modes diminishes when the magnetic field becomes stronger and the turbulent convection is weaker. Conculsions. As expected from the observations, we find that a stronger magnetic field diminishes the resulting mode amplitudes. The evaluation of the inverse Alfvén number in stellar models provides a means for estimating the expected amplitudes of acoustic modes in magnetically active solar-type stars. [ABSTRACT FROM AUTHOR]

Context. As the observed occurrence for planets or stellar companions orbiting low- and intermediate-mass evolved stars is increasing, so is the importance of understanding and evaluating the strength of their interactions. This is important for the further evolution of both our own Earth-Sun system and most of the observed exoplanetary systems. One of the most fundamental mechanisms behind this interaction is the tidal dissipation in these stars, as it is one of the engines of the orbital and rotational evolution of star-planet and star-star systems. Aims. This article builds upon previous works that studied the evolution of the tidal dissipation along the pre-main sequence and the main sequence of low- and intermediate-mass stars and found a strong link between the structural and rotational evolution of stars and tidal dissipation. This article provides, for the first time, a complete picture of tidal dissipation along the entire evolution of low- and intermediate-mass stars, including the advanced phases of evolution. Methods. Using stellar evolutionary models, the internal structure of the star was computed from the pre-main sequence all the way up to the white dwarf phase for stars with initial masses between 1 and 4 M⊙. Using this internal structure, the tidal dissipation was computed along the entire stellar evolution. Tidal dissipation was separated into two components: the dissipation of the equilibrium (non-wave-like) tide and the dissipation of the dynamical (wave-like) tide. For evolved stars, the dynamical tide is constituted by progressive internal gravity waves. The evolution of the tidal dissipation was investigated for both the equilibrium and dynamical tides, and the results were compared. Results The significance of both the equilibrium and dynamical tide dissipation becomes apparent within distinct domains of the parameter space. The dissipation of the equilibrium tide is dominant when the star is large or the companion is far from the star. Conversely, the dissipation of the dynamical tide is important when the star is small or the companion is close to the star. The size and location of these domains depend on the masses of both the star and the companion, as well as on the evolutionary phase. Conclusions Both the equilibrium and the dynamical tides are important in evolved stars, and therefore both need to be taken into account when studying the tidal dissipation in evolved stars and the evolution of the planetary and/or stellar companions orbiting them. [ABSTRACT FROM AUTHOR]

Context. The Juno spacecraft has acquired exceptionally precise data on Jupiter's gravity field, offering invaluable insights into Jupiter's tidal response, interior structure, and dynamics, establishing crucial constraints. Aims. We aim to develop a new model for calculating Jupiter's tidal response based on its latest interior model, while also examining the significance of different dissipation processes for the evolution of its system. We studied the dissipation of dynamical tides in Jupiter by thermal, viscous, and molecular diffusivities acting on gravito-inertial waves in stably stratified zones and inertial waves in convection ones. Methods. We solved the linearised equations for the equilibrium tide. Next, we computed the dynamical tides using linear hydrodynamical simulations based on a spectral method. The Coriolis force is fully taken into account, but the centrifugal effect is neglected. We studied the dynamical tides occurring in Jupiter using internal structure models that respect Juno's constraints. We specifically looked at the dominant quadrupolar tidal components, and our focus is on the frequency range that corresponds to the tidal frequencies associated with Jupiter's Galilean satellites. Results. By incorporating the different dissipation mechanisms, we calculated the total dissipation and determined the imaginary part of the tidal Love number. We find a significant frequency dependence in dissipation spectra, indicating a strong relationship between dissipation and forcing frequency. Furthermore, our analysis reveals that, in the chosen parameter regime in which kinematic viscosity and thermal and molecular diffusivities are equal, the dominant mechanism contributing to dissipation is viscosity, exceeding both thermal and chemical dissipation in magnitude. We find that the presence of stably stratified zones plays an important role in explaining the high dissipation observed in Jupiter. [ABSTRACT FROM AUTHOR]

Context. Signatures of coupling between an inertial mode in the convective core and a gravito-inertial mode in the envelope have been found in four-year Kepler light curves of 16 rapidly rotating γ Doradus (γ Dor) stars. This makes it possible to obtain a measurement of the rotation frequency in their convective core. Despite their similar internal structure and available data, inertial modes have not yet been reported for slowly pulsating B (SPB) stars. Aims. We aim to provide a numerical counterpart of the recently published theoretical expressions for the mode-coupling coefficients, ε and ε̃ ε ∼ $ \tilde{\varepsilon} $. These coefficients represent the two cases of a continuous and a discontinuous Brunt-Väisälä frequency profile at the core-envelope interface, respectively. We consider γ Dor and SPB stars to shed light on the difference between these two classes of intermediate-mass gravito-inertial mode pulsators in terms of core and envelope mode coupling. Methods. We used asteroseismic forward models of two samples consisting of 26 SPB stars and 37 γ Dor stars to infer their numerical values of ε and ε̃ ε ∼ $ \tilde{\varepsilon} $. For both samples, we also computed: the linear correlation coefficients between ε or ε̃ ε ∼ $ \tilde{\varepsilon} $ and the near-core rotation frequency, the chemical gradient, the evolutionary stage, the convective core masses and radii, and the Schönberg-Chandrasekhar limiting mass representing the maximum mass of an inert helium core at central hydrogen exhaustion that can still withstand the pressure of the overlaying envelope. Results. The asteroseismically inferred values of ε and ε̃ ε ∼ $ \tilde{\varepsilon} $ for the two samples are between 0.0 and 0.34. While ε is most strongly correlated with the near-core rotation frequency for γ Dor stars, the fractional radius of the convective core instead provides the tightest correlation for SPB stars. We find ε to decrease mildly as the stars evolve. For the SPB stars, ε and ε̃ ε ∼ $ \tilde{\varepsilon} $ have similar moderate correlations with respect to the core properties. For the γ Dor stars, ε̃ ε ∼ $ \tilde{\varepsilon} $ reveals systematically lower and often no correlation to the core properties; their ε is mainly determined by the near-core rotation frequency. The Schönberg-Chandrasekar limit is already surpassed by the more massive SPB stars, while none of the γ Dor stars have reached it yet. Conclusions. Our asteroseismic results for the mode coupling support the theoretical interpretation and reveal that young, fast-rotating γ Dor stars are most suitable for undergoing couplings between inertial modes in the rotating convective core and gravito-inertial modes in the radiative envelope. The phenomenon has been found in 2.4% of such pulsators with detected period spacing patterns, whereas it has not been seen in any of the SPB stars so far. [ABSTRACT FROM AUTHOR]

Context. The arrival of powerful instruments will provide valuable data for the characterization of rocky exoplanets. Rocky planets are mostly found in close-in orbits. They are therefore usually close to the circular-coplanar orbital state and are thus considered to be in a tidally locked synchronous spin state. For planets with larger orbits, however, exoplanets should still have nonzero eccentricities and/or obliquities, and realistic models of tides for rocky planets can allow for higher spin states than the synchronization state in the presence of eccentricities or obliquities. Aims. This work explores the secular evolution of a star–planet system under tidal interactions, both gravitational and thermal, induced by the quadrupolar component of the gravitational potential and the irradiation of the planetary surface, respectively. We show the possible spin–orbit evolution and resonances for eccentric orbits and explore the possibility of spin-orbit resonances raised by the obliquity of the planet. Then, we focus on the additional effect of a thick atmosphere on the possible resulting spin equilibrium states and explore the effect of the evolution of the stellar luminosity. Methods. We implemented the general secular evolution equations of tidal interactions in the secular code called ESPEM. In particular, we focus here on the tides raised by a star on a rocky planet and consider the effect of the presence of an atmosphere, neglecting the contribution of the stellar tide. The solid part of the tides was modeled with an anelastic rheology (Andrade model), while the atmospheric tides were modeled with an analytical formulation that was fit using a global climate model simulation. We focused on a Sun-Venus-like system in terms of stellar parameters, orbital configuration and planet size and mass. The Sun-Venus system is a good laboratory for studying and comparing the possible effect of atmospheric tides, and thus to explore the possible spin state of potential Venus-like exoplanets. Results. The formalism of Kaula associated with an Andrade rheology allows spin orbit resonances on pure rocky worlds. Similarly to the high-order spin–orbit resonances induced by eccentricity, the spin obliquity allows the excitation of high-frequency Fourier modes that allow some spin-orbit resonances to be stable. If the planet has a dense atmosphere, like that of Venus, another mechanism, the thermal tides, can counterbalance the effect of the gravitational tides. We found that thermal tides change the evolution of the spin of the planet, including the capture in spin–orbit resonances. If the spin inclination is high enough, thermal tides can drive the spin toward an anti-synchronization state, that is, a the 1:1 spin–orbit resonance with an obliquity of 180 degrees. Conclusions. Through our improvement of the gravitational and thermal tidal models, we can determine the dynamical state of exo-planets better, especially if they hold a thick atmosphere. In particular, the contribution of the atmospheric tides allows us to reproduce the spin state of Venus at a constant stellar luminosity. Our simulations have shown that the secular evolution of the spin and obliquity can lead to a retrograde spin of the Venus-like planet if the system starts from a high spin obliquity, in agreement with previous studies. The perturbing effect of a third body is still needed to determine the current state of Venus starting from a low initial obliquity. When the luminosity evolution of the Sun is taken into account, the picture changes. We find that the planet never reaches equilibrium: the timescale of the rotation evolution is longer than the luminosity variation timescale, which suggests that Venus may never reach a spin equilibrium state, but may still evolve. [ABSTRACT FROM AUTHOR]

With the discovery of TRAPPIST-1 and its seven planets residing within 0.06 au, it is becoming increasingly necessary to carry out correct treatments of tidal interactions. The eccentricity, rotation, and obliquity of the planets of TRAPPIST-1 do indeed result from the tidal evolution over the lifetime of the system. Tidal interactions can also lead to tidal heating in the interior of the planets (as for Io), which may then be responsible for volcanism or surface deformation. In the majority of studies aimed at estimating the rotation of close-in planets or their tidal heating, the planets are considered as homogeneous bodies and their rheology is often taken to be a Maxwell rheology. Here, we investigate the impact of taking into account a multi-layer structure and an Andrade rheology in the way planets dissipate tidal energy as a function of the excitation frequency. We use an internal structure model, which provides the radial profile of structural and rheological quantities (such as density, shear modulus, and viscosity) to compute the tidal response of multi-layered bodies. We then compare the outcome to the dissipation of a homogeneous planet (which only take a uniform value for shear modulus and viscosity). We find that for purely rocky bodies, it is possible to approximate the response of a multi-layer planet by that of a homogeneous planet. However, using average profiles of shear modulus and viscosity to compute the homogeneous planet response leads to an overestimation of the averaged dissipation. We provide fitted values of shear modulus and viscosity that are capable of reproducing the response of various types of rocky planets. However, we find that if the planet has an icy layer, its tidal response can no longer be approximated by a homogeneous body because of the very different properties of the icy layers (in particular, their viscosity), which leads to a second dissipation peak at higher frequencies. We also compute the tidal heating profiles for the outer TRAPPIST-1 planets (e to h). [ABSTRACT FROM AUTHOR]

Context. HD 49330 is an early Be star that underwent an outburst during its five-month observation with the CoRoT satellite. An analysis of its light curve revealed several independent p and g pulsation modes, in addition to showing that the amplitude of the modes is directly correlated with the outburst. Aims. We modelled the results obtained with CoRoT to understand the link between pulsational parameters and the outburst of this Be star. Methods. We modelled the flattening of the structure of the star due to rapid rotation in two ways: Chandrasekhar-Milne's expansion and 2D structure computed with ROTORC. We then modelled κ-driven pulsations. We also adapted the formalism of the excitation and amplitude of stochastically excited gravito-inertial modes to rapidly rotating stars, and we modelled those pulsations as well. Results. We find that while pulsation p modes are indeed excited by the κ mechanism, the observed g modes are, rather, a result of stochastic excitation. In contrast, g and r waves are stochastically excited in the convective core and transport angular momentum to the surface, increasing its rotation rate. This destabilises the external layers of the star, which then emits transient stochastically excited g waves. These transient waves produce most of the low-frequency signal detected in the CoRoT data and ignite the outburst. During this unstable phase, p modes disappear at the surface because their cavity is broken. Following the outburst and ejection of the surface layer, relaxation occurs, making the transient g waves disappear and p modes reappear. Conclusions. This work includes the first coherent model of stochastically excited gravito-inertial pulsation modes in a rapidly rotating Be star. It provides an explanation for the correlation between the variation in the amplitude of frequencies detected in the CoRoT data and the occurrence of an outburst. This scenario could apply to other pulsating Be stars, providing an explanation to the long-standing questions surrounding Be outbursts and disks. [ABSTRACT FROM AUTHOR]

Context. Rotational mixing transports angular momentum and chemical elements in stellar radiative zones. It is one of the key processes for modern stellar evolution. In the past two decades, an emphasis has been placed on the turbulent transport induced by the vertical shear instability. However, instabilities arising from horizontal shear and the strength of the anisotropic turbulent transport that they may trigger remain relatively unexplored. The weakest point of this hydrodynamical theory of rotational mixing is the assumption that anisotropic turbulent transport is stronger in horizontal directions than in the vertical one. Aims. This paper investigates the combined effects of stable stratification, rotation, and thermal diffusion on the horizontal shear instabilities that are obtained and discussed in the context of stellar radiative zones. Methods. The eigenvalue problem describing linear instabilities of a flow with a hyperbolic-tangent horizontal shear profile was solved numerically for a wide range of parameters. When possible, the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximation was applied to provide analytical asymptotic dispersion relations in both the nondiffusive and highly diffusive limits. As a first step, we consider a polar f -plane where the gravity and rotation vector are aligned. Results. Two types of instabilities are identified: the inflectional and inertial instabilities. The inflectional instability that arises from the inflection point (i.e., the zero second derivative of the shear flow) is the most unstable when at a zero vertical wavenumber and a finite wavenumber in the streamwise direction along the imposed-flow direction. While the maximum two-dimensional growth rate is independent of the stratification, rotation rate, and thermal diffusivity, the three-dimensional inflectional instability is destabilized by stable stratification, while it is stabilized by thermal diffusion. The inertial instability is rotationally driven, and a WKBJ analysis reveals that its growth rate reaches the maximum value of √ (1-f) in the inviscid limit as the vertical wavenumber goes to infinity, where f is the dimensionless Coriolis parameter. The inertial instability for a finite vertical wavenumber is stabilized as the stratification increases, whereas it is destabilized by the thermal diffusion. Furthermore, we found a selfsimilarity in both the inflectional and inertial instabilities based on the rescaled parameter PeN2 with the Péclet number Pe and the Brunt-Väisälä frequency N. [ABSTRACT FROM AUTHOR]

Context. The traditional approximation of rotation (TAR) is a treatment of the dynamical equations of rotating and stably stratified fluids in which the action of the Coriolis acceleration along the direction of the entropy (and chemicals) stratification is neglected, while assuming that the fluid motions are mostly horizontal because of their inhibition in the vertical direction by the buoyancy force. This leads to the neglect of the horizontal projection of the rotation vector in the equations for the dynamics of gravito-inertial waves (GIWs) that become separable, such as in the non-rotating case, while they are not separable in the case in which the full Coriolis acceleration is taken into account. This approximation, first introduced in geophysical fluid dynamics for thin atmospheres and oceans, has been broadly applied in stellar (and planetary) astrophysics to study low-frequency GIWs that have short vertical wavelengths. The appoximation is now being tested thanks to direct 2D oscillation codes, which constrain its domain of validity. The mathematical flexibility of this treatment allows us to explore broad parameter spaces and to perform detailed seismic modelling of stars. Aims. The TAR treatment is built on the assumptions that the star is spherical (i.e. its centrifugal deformation is neglected) and uniformly rotating while an adiabatic treatment of the dynamics of the waves is adopted. In addition, their induced gravitational potential fluctuations is neglected. However, it has been recently generalised with including the effects of a differential rotation. We aim to carry out a new generalisation that takes into account the centrifugal acceleration in the case of deformed stars that are moderately and uniformly rotating. Methods. We construct an analytical expansion of the equations for the dynamics of GIWs in a spheroidal coordinates system by assuming the hierarchies of frequencies and amplitudes of the velocity components adopted within TAR in the spherical case. Results. We derive the complete set of equations that generalises TAR by taking the centrifugal acceleration into account. As in the case of a differentially rotating spherical star, the problem becomes 2D but can be treated analytically if we assume the anelastic and JWKB approximations, which are relevant for low-frequency GIWs. This allows us to derive a generalised Laplace tidal equation for the horizontal eigenfunctions and asymptotic wave periods, which can be used to probe the structure and dynamics of rotating deformed stars thanks to asteroseismology. A first numerical exploration of its eigenvalues and horizontal eigenfunctions shows their variation as a function of the pseudo-radius for different rotation rates and frequencies and the development of avoided crossings. [ABSTRACT FROM AUTHOR]

Context. Eccentricity tides generate a torque that can drive an ocean planet towards asynchronous rotation states of equilibrium when enhanced by resonances associated with the oceanic tidal modes. Aims. We investigate the impact of eccentricity tides on the rotation of rocky planets hosting a thin uniform ocean and orbiting cool dwarf stars such as TRAPPIST-1, with orbital periods ~1−10 days. Methods. Combining the linear theory of oceanic tides in the shallow water approximation with the Andrade model for the solid part of the planet, we developed a global model including the coupling effects of ocean loading, self-attraction, and deformation of the solid regions. From this model we derive analytic solutions for the tidal Love numbers and torque exerted on the planet. These solutions are used with realistic values of parameters provided by advanced models of the internal structure and tidal oscillations of solid bodies to explore the parameter space both analytically and numerically. Results. Our model allows us to fully characterise the frequency-resonant tidal response of the planet, and particularly the features of resonances associated with the oceanic tidal modes (eigenfrequencies, resulting maxima of the tidal torque, and Love numbers) as functions of the planet parameters (mass, radius, Andrade parameters, ocean depth, and Rayleigh drag frequency). Resonances associated with the oceanic tide decrease the critical eccentricity beyond which asynchronous rotation states distinct from the usual spin-orbit resonances can exist. We provide an estimation and scaling laws for this critical eccentricity, which is found to be lowered by roughly one order of magnitude, switching from ~0.3 to ~0.06 in typical cases and to ~0.01 in extremal ones. [ABSTRACT FROM AUTHOR]

Context. Stellar magnetic fields are often invoked to explain the missing transport of angular momentum observed in models of stellar interiors. However, the properties of an internal magnetic field and the consequences of its presence on stellar evolution are largely unknown. Aims. We study the effect of an axisymmetric internal magnetic field on the frequency of gravity modes in rapidly rotating stars to check whether gravity modes can be used to detect and probe such a field. Methods. Rotation is taken into account using the traditional approximation of rotation and the effect of the magnetic field is computed using a perturbative approach. As a proof of concept, we compute frequency shifts due to a mixed (i.e. with both poloidal and toroidal components) fossil magnetic field for a representative model of a known magnetic, rapidly rotating, slowly pulsating B-type star: HD 43317. Results. We find that frequency shifts induced by the magnetic field scale with the square of its amplitude. A magnetic field with a near-core strength of the order of 150 kG (which is consistent with the observed surface field strength of the order of 1 kG) leads to signatures that are detectable in period spacings for high-radial-order gravity modes. Conclusions. The predicted frequency shifts can be used to constrain internal magnetic fields and offer the potential for a significant step forward in our interpretation of the observed structure of gravity-mode period spacing patterns in rapidly rotating stars. [ABSTRACT FROM AUTHOR]

Context. Recent Juno observations have suggested that the heavy elements in Jupiter could be diluted throughout a large fraction of its gaseous envelope, providing a stabilising compositional gradient over an extended region of the planet. This could trigger layered semi-convection, which, in the context of giant planets more generally, may explain Saturn's luminosity excess and play a role in causing the abnormally large radii of some hot Jupiters. In giant planet interiors, it could take the form of density staircases, which are convective layers separated by thin stably stratified interfaces. In addition, the efficiency of tidal dissipation is known to depend strongly on the planetary internal structure. Aims. We aim to study the resulting tidal dissipation when internal waves are excited in a region of layered semi-convection by tidal gravitational forcing due to other bodies (such as moons in giant planet systems, or stars in hot Jupiter systems). Methods. We adopt a local Cartesian model with a background layered density profile subjected to an imposed tidal forcing, and we compute the viscous and thermal dissipation rates numerically. We consider two sets of boundary conditions in the vertical direction: periodic boundaries and impenetrable, stress-free boundaries, with periodic conditions in the horizontal directions in each case. These models are appropriate for studying the forcing of short-wavelength tidal waves in part of a region of layered semi-convection, and in an extended envelope containing layered semi-convection, respectively. Results. We find that the rates of tidal dissipation can be enhanced in a region of layered semi-convection compared to a uniformly convective medium, where the latter corresponds with the usual assumption adopted in giant planet interior models. In particular, a region of layered semi-convection possesses a richer set of resonances, allowing enhanced dissipation for a wider range of tidal frequencies. The details of these results significantly depend on the structural properties of the layered semi-convective regions. Conclusions. Layered semi-convection could contribute towards explaining the high tidal dissipation rates observed in Jupiter and Saturn, which have not yet been fully explained by theory. Further work is required to explore the efficiency of this mechanism in global models. [ABSTRACT FROM AUTHOR]

Context. With the discovery over the last two decades of a large diversity of exoplanetary systems, it is now of prime importance to characterize star–planet interactions and how such systems evolve. Aims. We address this question by studying systems formed by a solar-like star and a close-in planet. We focus on the stellar wind spinning down the star along its main-sequence phase and tidal interaction causing orbital evolution of the systems. Despite recent significant advances in these fields, all current models use parametric descriptions to study at least one of these effects. Our objective is to introduce ab initio prescriptions of the tidal and braking torques simultaneously, so as to improve our understanding of the underlying physics. Methods. We develop a one-dimensional (1D) numerical model of coplanar circular star–planet systems taking into account stellar structural changes, wind braking, and tidal interaction and implement it in a code called ESPEM. We follow the secular evolution of the stellar rotation and of the semi-major axis of the orbit, assuming a bilayer internal structure for the former. After comparing our predictions to recent observations and models, we perform tests to emphasize the contribution of ab initio prescriptions. Finally, we isolate four significant characteristics of star–planet systems: stellar mass, initial stellar rotation period, planetary mass and initial semi-major axis; and browse the parameter space to investigate the influence of each of them on the fate of the system. Results. Our secular model of stellar wind braking accurately reproduces the recent observations of stellar rotation in open clusters. Our results show that a planet can affect the rotation of its host star and that the resulting spin-up or spin-down depends on the orbital semi-major axis and on the joint influence of magnetic and tidal effects. The ab initio prescription for tidal dissipation that we used predicts fast outward migration of massive planets orbiting fast-rotating young stars. Finally, we provide the reader with a criterion based on the characteristics of the system that allows us to assess whether or not the planet will undergo orbital decay due to tidal interaction. [ABSTRACT FROM AUTHOR]

Context. The surface angular velocity evolution of low-mass stars is now globally understood and the main physical mechanisms involved in it are observationally quite constrained. However, while the general behaviour of these mechanisms is grasped, their theoretical description is still under ongoing work. This is the case, for instance, about the description of the physical process that extracts angular momentum from the radiative core, which could be described by several theoretical candidates. Additionally, recent observations showed anomalies in the rotation period distribution of open cluster, main sequence, early K-type stars that cannot be reproduced by current angular momentum evolution models. Aims. In this work, we study the parameter space of star-planet system's configurations to investigate if including the tidal star-planet interaction in angular momentum evolution models could reproduce the anomalies of this rotation period distribution. Methods. To study this effect, we use a parametric angular momentum evolution model that allows for core-envelope decoupling and angular momentum extraction by magnetized stellar wind that we coupled to an orbital evolution code where we take into account the torque due to the tides raised on the star by the planet. We explore different stellar and planetary configurations (stellar mass from 0.5 to 1.0 M⊙ and planetary mass from 10 M⊕ to 13 Mjup) to study their effect on the planetary orbital and stellar rotational evolution. Results. The stellar angular momentum is the most impacted by the star-planet interaction when the planet is engulfed during the early main sequence phase. Thus, if a close-in Jupiter-mass planet is initially located at around 50% of the stellar corotation radius, a kink in the rotational period distribution opens around late and early K-type stars during the early main sequence phase. Conclusions. Tidal star-planet interactions can create a kink in the rotation period distribution of low-mass stars, which could possibly account for unexpected scatter seen in the rotational period distribution of young stellar clusters. [ABSTRACT FROM AUTHOR]

Context. Oceanic tides are a major source of tidal dissipation. They drive the evolution of planetary systems and the rotational dynamics of planets. However, two-dimensional (2D) models commonly used for the Earth cannot be applied to extrasolar telluric planets hosting potentially deep oceans because they ignore the three-dimensional (3D) effects related to the ocean’s vertical structure. Aims. Our goal is to investigate, in a consistant way, the importance of the contribution of internal gravity waves in the oceanic tidal response and to propose a modelling that allows one to treat a wide range of cases from shallow to deep oceans. Methods. A 3D ab initio model is developed to study the dynamics of a global planetary ocean. This model takes into account compressibility, stratification, and sphericity terms, which are usually ignored in 2D approaches. An analytic solution is computed and used to study the dependence of the tidal response on the tidal frequency and on the ocean depth and stratification. Results. In the 2D asymptotic limit, we recover the frequency-resonant behaviour due to surface inertial-gravity waves identified by early studies. As the ocean depth and Brunt–Väisälä frequency increase, the contribution of internal gravity waves grows in importance and the tidal response becomes 3D. In the case of deep oceans, the stable stratification induces resonances that can increase the tidal dissipation rate by several orders of magnitude. It is thus able to significantly affect the evolution time scale of the planetary rotation. [ABSTRACT FROM AUTHOR]

Context. Thermal atmospheric tides can torque telluric planets away from spin-orbit synchronous rotation, as observed in the case of Venus. They thus participate in determining the possible climates and general circulations of the atmospheres of these planets. Aims. The thermal tidal torque exerted on an atmosphere depends on its internal structure and rotation and on the tidal frequency. Particularly, it strongly varies with the convective stability of the entropy stratification. This dependence has to be characterized to constrain and predict the rotational properties of observed telluric exoplanets. Moreover, it is necessary to validate the approximations used in global modelings such as the traditional approximation, which is used to obtain separable solutions for tidal waves. Methods.We wrote the equations governing the dynamics of thermal tides in a local vertically stratified section of a rotating planetary atmosphere by taking into account the effects of the complete Coriolis acceleration on tidal waves. This allowed us to analytically derive the tidal torque and the tidally dissipated energy, which we used to discuss the possible regimes of tidal dissipation and to examine the key role played by stratification. Results. In agreement with early studies, we find that the frequency dependence of the thermal atmospheric tidal torque in the vicinity of synchronization can be approximated by a Maxwell model. This behavior corresponds to weakly stably stratified or convective fluid layers, as observed previously. A strong stable stratification allows gravity waves to propagate, and makes the tidal torque negligible. The transition is continuous between these two regimes. The traditional approximation appears to be valid in thin atmospheres and in regimes where the rotation frequency is dominated by the forcing or the buoyancy frequencies. Conclusions. Depending on the stability of their atmospheres with respect to convection, observed exoplanets can be tidally driven toward synchronous or asynchronous final rotation rates. The domain of applicability of the traditional approximation is rigorously constrained by calculations. [ABSTRACT FROM AUTHOR]

Context. Layered semi-convection is a possible candidate to explain Saturn's luminosity excess and the abnormally large radius of some hot Jupiters. In giant planet interiors, it could lead to the creation of density staircases, which are convective layers separated by thin stably stratified interfaces. These are also observed on Earth in some lakes and in the Arctic Ocean. Aims. We aim to study the propagation of internal waves in a region of layered semi-convection, with the aim to predict energy transport by internal waves incident upon a density staircase. The goal is then to understand the resulting tidal dissipation when these waves are excited by other bodies such as moons in giant planets systems. Methods. We used a local Cartesian analytical model, taking into account the complete Coriolis acceleration at any latitude, thus generalising previous works. We used a model in which stably stratified interfaces are infinitesimally thin, before relaxing this assumption with a second model that assumes a piecewise linear stratification. Results. We find transmission of incident internal waves to be strongly affected by the presence of a density staircase, even if these waves are initially pure inertial waves (which are restored by the Coriolis acceleration). In particular, low-frequency waves of all wavelengths are perfectly transmitted near the critical latitude, defined by θc = sin-1(ω/ 2Ω), where ω is the wave's frequency and Ω is the rotation rate of the planet. Otherwise, short-wavelength waves are only efficiently transmitted if they are resonant with a free mode (interfacial gravity wave or short-wavelength inertial mode) of the staircase. In all other cases, waves are primarily reflected unless their wavelengths are longer than the vertical extent of the entire staircase (not just a single step). Conclusions. We expect incident internal waves to be strongly affected by the presence of a density staircase in a frequency-, latitude- and wavelength-dependent manner. First, this could lead to new criteria to probe the interior of giant planets by seismology; and second, this may have important consequences for tidal dissipation and our understanding of the evolution of giant planet systems. [ABSTRACT FROM AUTHOR]

Recent spectropolarimetric observations of otherwise ordinary G, K, and M giants revealed localized magnetic strips in the HRD coincident with the regions where the first dredge-up and core He-burning occur. We seek to understand the origin of magnetic fields in such late-type giant stars. In analogy with late-type dwarf stars, we focus primarily on parameters known to influence the generation of magnetic fields in the outer convective envelope. We compute the classical dynamo parameters along the evolutionary tracks of low- and intermediate-mass stars at various metallicities using stellar models that have been extensively tested by spectroscopic and asteroseismic observations. These include convective turnover timescales and convective Rossby numbers, computed from the PMS to the tip of the RGB or the early AGB. To investigate the effects of the very extended outer convective envelope, we compute these parameters both for the entire convective envelope and locally, that is, at different depths within the envelope. We also compute the turnover timescales and corresponding Rossby numbers for the convective cores of intermediate-mass stars on the main sequence. Our models show that the Rossby number of the convective envelope becomes lower than unity in the well-delimited locations of the Hertzsprung-Russell diagram where magnetic fields have indeed been detected. We show that α-Ω dynamo processes might not be continuously operating, but that they are favored in the stellar convective envelope at two specific moments along the evolution tracks, that is, during the first dredge-up at the base of the RGB and during central helium burning in the helium-burning phase and early-AGB. This general behavior can explain the so-called magnetic strips recently discovered by dedicated spectropolarimetric surveys of evolved stars. [ABSTRACT FROM AUTHOR]

Context. Lithium abundance A(Li) and surface rotation are good diagnostic tools to probe the internal mixing and angular momentum transfer in stars. Aims. We explore the relation between surface rotation, A(Li), and age in a sample of seismic solar-analogue stars, and we study their possible binary nature. Methods. We selected a sample of 18 solar-analogue stars observed by the NASA Kepler satellite for an in-depth analysis. Their seismic properties and surface rotation rates are well constrained from previous studies. About 53 h of high-resolution spectroscopy were obtained to derive fundamental parameters from spectroscopy and A(Li). These values were combined and compared with seismic masses, radii, and ages, as well as with surface rotation periods measured from Kepler photometry. Results. Based on radial velocities, we identify and confirm a total of six binary star systems. For each star, a signal-to-noise ratio of 80 ≲ S=N ≲ 210 was typically achieved in the final spectrum around the lithium line. We report fundamental parameters and A(Li). Using the surface rotation period derived from Kepler photometry, we obtained a well-defined relation between A(Li) and rotation. The seismic radius translates the surface rotation period into surface velocity. With models constrained by the characterisation of the individual mode frequencies for single stars, we identify a sequence of three solar analogues with similar mass (~1.1 M⊙) and stellar ages ranging between 1 to 9 Gyr. Within the realistic estimate of ~7% for the mass uncertainty, we find a good agreement between the measured A(Li) and the predicted A(Li) evolution from a grid of models calculated with the Toulouse-Geneva stellar evolution code, which includes rotational internal mixing, calibrated to reproduce solar chemical properties. We found a scatter in ages inferred from the global seismic parameters that is too large when compared with A(Li). Conclusions. We present the Li-abundance for a consistent spectroscopic survey of solar-analogue stars with a mass of 1:00 ± 0:15 M⊙ that are characterised through asteroseismology and surface rotation rates based on Kepler observations. The correlation between A(Li) and Prot supports the gyrochronological concept for stars younger than the Sun and becomes clearer when the confirmed binaries are excluded. The consensus between measured A(Li) for solar analogues with model grids, calibrated on the Sun's chemical properties, suggests that these targets share the same internal physics. In this light, the solar Li and rotation rate appear to be normal for a star like the Sun. [ABSTRACT FROM AUTHOR]

Context: Until recently almost nothing was known about the evolution of magnetic fields found in upper main sequence Ap/Bp stars during their long main sequence lifetime. We are thus studying magnetic Ap/Bp stars in open clusters in order to obtain observational evidence of how the properties of Ap/Bp magnetic stars, such as field strength and structure, evolve with age during the main sequence. One important aspect of this study is to search for the very rare examples of hot magnetic stars in short-period binary systems among magnetic cluster members. Aims: In this paper we characterise the object BD-19 5044L, which is both a member of the open cluster IC 4725 = M 25, and a short-period SB2 system containing a magnetic primary star. Methods: We have obtained a series of intensity and circular polarisation spectra distributed through the orbital and rotation cycles of BD-19 5044L with the ESPaDOnS spectropolarimeter at CFHT. From these data we determine the orbital and stellar properties of each component. Results: We find that the orbit of BD-19 5044LAB is quite eccentric (e = 0.477), with a period of 17.63 d. The primary is a magnetic Bp star with a variable longitudinal magnetic field, a polar field strength of ~1400 G and a low obliquity, while the secondary is probably a hot Am star and does not appear to be magnetic. The rotation period of the primary (5.04 d) is not synchronised with the orbit, but the rotation angular velocity is close to being synchronised with the orbital angular velocity of the secondary at periastron, perhaps as a result of tidal interactions. Because this system is a member of IC 4725, the two stars have a common age of logt = 8.02 ± 0.05 dex. Conclusions: The periastron separation is small enough (about 12 times the radius of the primary star) that BD-195044L may be one of the very rare known cases of a tidally interacting SB2 binary system containing a magnetic Ap/Bp star. [ABSTRACT FROM AUTHOR]

Context. With the ever growing number of detected and confirmed exoplanets, the probability of finding a planet that looks like the Earth increases continuously. While it is clear that the presence of a planet in the habitable zone does not imply the planet is habitable, a systematic study of the evolution of the habitable zone is required to account for its dependence on stellar parameters. Aims. In this article, we aim to provide the community with the dependence of the habitable zone upon the stellar mass, metallicity, rotation, and for various prescriptions of the limits of the habitable zone. Methods. We use stellar evolution models computed with the code STAREVOL, which includes the most current physical mechanisms of internal transport of angular momentum and external wind braking, to study the evolution of the habitable zone and the continuously habitable zone limits. Results. The stellar parameters mass and metallicity affect the habitable zone limits most dramatically. Conversely, for a given stellar mass and metallicity, stellar rotation has only a marginal effect on these limits and does not modify the width of the habitable zone. Moreover, and as expected in the main-sequence phase and for a given stellar mass and metallicity, the habitable zone limits remain almost constant, and this confirms the usual assumptions of a relative constancy of these limits during that phase. The evolution of the habitable zone limits is also correlated to the evolution of the stellar activity (through the Rossby number), which depends on the stellar mass considered. While the magnetic activity has negligible consequence in the case of more massive stars, these effects may have a strong impact on the habitability of a planet around M-dwarf stars. Thus, stellar activity cannot be neglected and may have a strong impact on the development of life during the early stage of the continuously habitable zone phase of low-mass stars. Using observed trends of stellar magnetic field strength, we also constrain the planetary magnetic field (at the zero order) required for a suffcient magnetospheric protection during the whole stellar evolution. Conclusions. We explain for the first time the systematic dependence of planet habitability on stellar parameters along the full evolution of low- and intermediate-mass stars. These results can be used as physical inputs for a first order estimation of exoplanetary habitability. [ABSTRACT FROM AUTHOR]

Context. Tidal dissipation in planets and stars is one of the key physical mechanisms driving the evolution of star-planet and planetmoon systems. Several signatures of its action are observed in planetary systems thanks to their orbital architecture and the rotational state of their components. Aims. Tidal dissipation inside the fluid layers of celestial bodies is intrinsically linked to the dynamics and physical properties of those bodies. This complex dependence must be characterized. Methods. We compute the tidal kinetic energy dissipated by viscous friction and thermal diffusion in a rotating local fluid Cartesian section of a star, planet, or moon submitted to a periodic tidal forcing. The properties of tidal gravito-inertial waves excited by the perturbation are derived analytically as explicit functions of the tidal frequency and local fluid parameters (i.e. the rotation, the buoyancy frequency characterizing the entropy stratification, viscous and thermal diffusivities) for periodic normal modes. Results. The sensitivity of the resulting dissipation frequency-spectra, which could be highly resonant, to a control parameter of the system is either important or negligible depending on the position in the regime diagram relevant for planetary and stellar interiors. For corresponding asymptotic behaviours of tidal gravito-inertial waves dissipated by viscous friction and thermal diffusion, scaling laws for the frequencies, number, width, height, and contrast with the non-resonant background of resonances are derived to quantify these variations. Conclusions. We characterize the strong impact of the internal physics and dynamics of fluid planetary layers and stars on the dissipation of tidal kinetic energy in their bulk. We point out the key control parameters that really play a role in tidal dissipation and demonstrate how it is now necessary to develop ab initio modelling for tidal dissipation in celestial bodies [ABSTRACT FROM AUTHOR]

Context. The revolution of helio- and asteroseismology provides access to the detailed properties of stellar interiors by studying the star's oscillation modes. Among them, gravity (g) modes are formed by constructive interferences between progressive internal gravity waves (IGWs), propagating in stellar radiative zones. Our new 3D nonlinear simulations of the interior of a solar-like star allows us to study the excitation, propagation, and dissipation of these waves. Aims. The aim of this article is to clarify our understanding of the behavior of IGWs in a 3D radiative zone and to provide a clear overview of their properties. Methods. We use a method of frequency filtering that reveals the path of individual gravity waves of different frequencies in the radiative zone. Results. We are able to identify the region of propagation of different waves in 2D and 3D, to compare them to the linear raytracing theory and to distinguish between propagative and standing waves (g-modes). We also show that the energy carried by waves is distributed in different planes in the sphere, depending on their azimuthal wave number. Conclusions. We are able to isolate individual IGWs from a complex spectrum and to study their propagation in space and time. In particular, we highlight in this paper the necessity of studying the propagation of waves in 3D spherical geometry, since the distribution of their energy is not equipartitioned in the sphere. [ABSTRACT FROM AUTHOR]

Context. Since 1995, more than 1500 exoplanets have been discovered around a wide variety of host stars (from M- to A-type stars). Tidal dissipation in stellar convective envelopes is an important factor that shapes the orbital architecture of short-period systems. Aims. Our objective is to understand and evaluate how tidal dissipation in the convective envelope of low-mass stars (from M to F types) depends on their mass, evolutionary stage, and rotation. Methods. Using a simplified two-layer assumption, we analytically compute the frequency-averaged tidal dissipation in the convective envelope. This dissipation is due to the conversion into heat of the kinetic energy of tidal non-wavelike/equilibrium flow and inertial waves because of the viscous friction applied by turbulent convection. Using grids of stellar models allows us to study the variation of the dissipation as a function of stellar mass and age on the pre-main sequence and on the main sequence for stars with masses ranging from 0:4 to 1:4 M☉Results. During their pre-main sequence, all low-mass stars have an increase in the frequency-averaged tidal dissipation for a fixed angular velocity in their convective envelope until they reach a critical aspect and mass ratios (respectivelyα= Rc=Rs and β= Mc=Ms, where Rs; Ms; Rc, and Mc are the star's radius and mass and its radiative core's radius and mass). Next, the dissipation evolves on the main sequence to an asymptotic value that is highest for 0:6 M☉ K-type stars and that then decreases by several orders of magnitude with increasing stellar mass. Finally, the rotational evolution of low-mass stars strengthens the importance of tidal dissipation during the pre-main sequence for star-planet and multiple star systems. Conclusions. As shown by observations, tidal dissipation in stars' convection zones varies over several orders of magnitude as a function of stellar mass, age, and rotation. We demonstrate that i) it reaches a maximum value on the pre-main sequence for all stellar masses and ii) on the main sequence and at fixed angular velocity, it is at a maximum for 0:6 M☉K-type stars and decreases with increasing mass. [ABSTRACT FROM AUTHOR]

The detection of mixed modes in subgiants and red giants by the CoRoT and Kepler space-borne missions allows us to investigate the internal structure of evolved low-mass stars, from the end of the main sequence to the central helium-burning phase. In particular, the measurement of the mean core rotation rate as a function of the evolution places stringent constraints on the physical mechanisms responsible for the angular momentum redistribution in stars. It showed that the current stellar evolution codes including the modelling of rotation fail to reproduce the observations. An additional physical process that efficiently extracts angular momentum from the core is thus necessary. Our aim is to assess the ability of mixed modes to do this. To this end, we developed a formalism that provides a modelling of the wave fluxes in both the mean angular momentum and the mean energy equations in a companion paper. In this article, mode amplitudes are modelled based on recent asteroseismic observations, and a quantitative estimate of the angular momentum transfer is obtained. This is performed for a benchmark model of 1.3 M at three evolutionary stages, representative of the evolved pulsating stars observed by CoRoT and Kepler. We show that mixed modes extract angular momentum from the innermost regions of subgiants and red giants. However, this transport of angular momentum from the core is unlikely to counterbalance the effect of the core contraction in subgiants and early red giants. In contrast, for more evolved red giants, mixed modes are found efficient enough to balance and exceed the effect of the core contraction, in particular in the hydrogen-burning shell. Our results thus indicate that mixed modes are a promising candidate to explain the observed spin-down of the core of evolved red giants, but that an other mechanism is to be invoked for subgiants and early red giants. [ABSTRACT FROM AUTHOR]

Context. Tidal dissipation in planetary interiors is one of the key physical mechanisms that drive the evolution of star-planet and planet-moon systems. New constraints on this dissipation are now obtained both in the solar and exo-planetary systems. Aims. Tidal dissipation in planets is intrinsically related to their internal structure. Indeed, the dissipation behaves very differently when we compare its properties in solid and fluid planetary layers. Since planetary interiors consist of both types of regions, it is necessary to be able to assess and compare the respective intensity of the reservoir of dissipation in each type of layers. Therefore, in the case of giant planets, the respective contribution of the potential central dense rocky/icy core and of the deep convective fluid envelope must be computed as a function of the mass and the radius of the core. This will allow us to obtain their respective strengths. Methods. Using a method that evaluates the reservoir of dissipation associated to each region, which is a frequency-average of complex tidal Love numbers, we compared the respective contributions of the central core and of the fluid envelope. Results. For Jupiter- and Saturn-like planets, we show that the viscoelastic dissipation in the core could dominate the turbulent friction acting on tidal inertial waves in the envelope. However, the fluid dissipation would not be negligible. This demonstrates that it is necessary to build complete models of tidal dissipation in planetary interiors from their deep interior to their surface without any arbitrary assumptions. Conclusions. We demonstrate how important it is to carefully evaluate the respective strength of each type of dissipation mechanism in planetary interiors and to go beyond the usually adopted ad-hoc models. We confirm the significance of tidal dissipation in the potential dense core of gaseous giant planets. [ABSTRACT FROM AUTHOR]

Context. Gravity waves (or their signatures) are detected in stars thanks to helio- and asteroseismology, and they may play an important role in the evolution of stellar angular momentum. Moreover, a previous observational study of the CoRoT target HD51452 demonstrated the potential strong impact of rotation on the stochastic excitation of gravito-inertial waves in stellar interiors. Aims. Our goal is to explore and unravel the action of rotation on the stochastic excitation of gravity and gravito-inertial waves in stars. Methods. The dynamics of gravito-inertial waves in stellar interiors in both radiation and in convection zones is described with a local non-traditional f -plane model. The coupling of these waves with convective turbulent flows, which leads to their stochastic excitation, is studied in this framework. Results. First, we find that in the super-inertial regime in which the wave frequency is twice as high as the rotation frequency (σ > 2Ω), the evanescence of gravito-inertial waves in convective regions decreases with decreasing wave frequency. Next, in the sub-inertial regime (σ < 2Ω), gravito-inertial waves become purely propagative inertial waves in convection zones. Simultaneously, turbulence in convective regions is modified by rotation. Indeed, the turbulent energy cascade towards small scales is slowed down, and in the case of rapid rotation, strongly anisotropic turbulent flows are obtained that can be understood as complex non-linear triadic interactions of propagative inertial waves. These different behaviours, due to the action of the Coriolis acceleration, strongly modify the wave coupling with turbulent flows. On one hand, turbulence weakly influenced by rotation is coupled with evanescent gravitoinertial waves. On the other hand, rapidly rotating turbulence is intrinsically and strongly coupled with sub-inertial waves. Finally, to study these mechanisms, the traditional approximation cannot be assumed because it does not properly treat the coupling between gravity and inertial waves in the sub-inertial regime. Conclusions. Our results demonstrate the action of rotation on stochastic excitation of gravity waves thanks to the Coriolis acceleration, which modifies their dynamics in rapidly rotating stars and turbulent flows. As the ratio 2Ω/σ increases, the couplings and thus the amplitude of stochastic gravity waves are amplified. [ABSTRACT FROM AUTHOR]

Context. Internal gravity waves (IGWs) are studied for their impact on the angular momentum transport in stellar radiation zones and the information they provide about the structure and dynamics of deep stellar interiors. We present the first 3D nonlinear numerical simulations of IGWs excitation and propagation in a solar-like star. Aims. The aim is to study the behavior of waves in a realistic 3D nonlinear time-dependent model of the Sun and to characterize their properties. Methods. We compare our results with theoretical and 1D predictions. It allows us to point out the complementarity between theory and simulation and to highlight the convenience, but also the limits, of the asymptotic and linear theories. Results. We show that a rich spectrum of IGWs is excited by the convection, representing about 0.4% of the total solar luminosity.We study the spatial and temporal properties of this spectrum, the effect of thermal damping, and nonlinear interactions between waves. We give quantitative results for the modes' frequencies, evolution with time and rotational splitting, and we discuss the amplitude of IGWs considering different regimes of parameters. Conclusions. This work points out the importance of high-performance simulation for its complementarity with observation and theory. It opens a large field of investigation concerning IGWs propagating nonlinearly in 3D spherical structures. The extension of this work to other types of stars, with different masses, structures, and rotation rates will lead to a deeper and more accurate comprehension of IGWs in stars. [ABSTRACT FROM AUTHOR]

Context. The continuous high-precision photometric observations provided by the CoRoT and Kepler space missions have allowed us to understand the structure and dynamics of red giants better using asteroseismic techniques. A small fraction of these stars show dipole modes with unexpectedly low amplitudes. The reduction in amplitude is more pronounced for stars with a higher frequency of maximum power, Vmax. Aims. In this work we want to characterise KIC 8561221 in order to confirm that it is currently the least evolved star among this peculiar subset and to discuss several hypotheses that could help explain the reduction of the dipole mode amplitudes. Methods. We used Kepler short- and long-cadence data combined with spectroscopic observations to infer the stellar structure and dynamics of KIC 8561221. We then discussed different scenarios that could contribute to reducing the dipole amplitudes, such as a fast-rotating interior or the effect of a magnetic field on the properties of the modes. We also performed a detailed study of the inertia and damping of the modes. Results. We have been able to characterise 36 oscillations modes, in particular, a few dipole modes above Vmax that exhibit nearly normal amplitudes. The frequencies of all the measured modes were used to determine the overall properties and the internal structure of the star.We have inferred a surface rotation period of ~91 days and uncovered a variation in the surface magnetic activity during the last 4 years. The analysis of the convective background did not reveal any difference compared to "normal" red giants. As expected, the internal regions of the star probed by the ⨏ = 2 and 3 modes spin 4 to 8 times faster than the surface. Conclusions. With our grid of standard models we are able to properly fit the observed frequencies. Our model calculation of mode inertia and damping give no explanation for the depressed dipole modes. A fast-rotating core is also ruled out as a possible explanation. Finally, we do not have any observational evidence of a strong deep magnetic field inside the star. [ABSTRACT FROM AUTHOR]

Context. The bright B pulsator γ Peg shows both p and g modes of β Cep and SPB types. It has also been claimed that it is a magnetic star, while others do not detect any magnetic field. Aims. We check for the presence of a magnetic field, with the aim to characterise it if it exists, or else provide a firm upper limit of its strength if it is not detected. If γ Peg is magnetic as claimed, it would make an ideal asteroseismic target for testing various theoretical scenarios. If it is very weakly magnetic, it would be the first observation of an extension of Vega-like fields to early B stars. Finally, if it is not magnetic and we can provide a very low upper limit on its non-detected field, it would make an important result for stellar evolution models. Methods. We acquired high resolution, high signal-to-noise spectropolarimetric Narval data at Telescope Bernard Lyot (TBL).We also gathered existing dimaPol spectropolarimetric data from the Dominion Astrophysical Observatory (DAO) and Musicos spectropolarimetric data from TBL. We analysed the Narval and Musicos observations using the least-squares deconvolution (LSD) technique to derive the longitudinal magnetic field and Zeeman signatures in lines. The longitudinal field strength was also extracted from the Hβ line observed with the DAO. With a Monte Carlo simulation we derived the maximum strength of the field possibly hosted by γ Peg. Results. We find that no magnetic signatures are visible in the very high quality spectropolarimetric data. The average longitudinal field measured in the Narval data is Bl = -0.1 ± 0.4 G. We derive a very strict upper limit of the dipolar field strength of Bpol ~ 40 G. Conclusions. We conclude that γ Peg is not magnetic: it hosts neither a strong stable fossil field as observed in a fraction of massive stars nor a very weak Vega-like field. There is therefore no evidence that Vega-like fields exist in B stars, contrary to the predictions by fossil field dichotomy scenarios. These scenarios should thus be revised. Our results also provide strong constraints for stellar evolution models. [ABSTRACT FROM AUTHOR]

Context. Tidal dissipation in planets and in stars is one of the key physical mechanisms that drive the evolution of planetary systems. Aims. Tidal dissipation properties are intrinsically linked to the internal structure and the rheology of the studied celestial bodies. The resulting dependence of the dissipation upon the tidal frequency is strongly different in the cases of solids and fluids. Methods. We computed the tidal evolution of a two-body coplanar system, using the tidal-quality factor frequency-dependencies appropriate to rocks and to convective fluids. Results. The ensuing orbital dynamics is smooth or strongly erratic, depending on the way the tidal dissipation depends upon frequency. Conclusions. We demonstrate the strong impact of the internal structure and of the rheology of the central body on the orbital evolution of the tidal perturber. A smooth frequency-dependence of the tidal dissipation causes a smooth orbital evolution, while a peaked dissipation can produce erratic orbital behaviour. [ABSTRACT FROM AUTHOR]

Context. With the progress of observational constraints on stellar rotation and on the angular velocity profile in stars, it is necessary to understand how angular momentum is transported in stellar interiors during their whole evolution. In this context, more highly refined dynamical stellar evolution models have been built that take into account transport mechanisms. Aims. Internal gravity waves (IGWs) excited by convective regions constitute an efficient transport mechanism over long distances in stellar radiation zones. They are one of the mechanisms that are suspected of being responsible for the quasi-flat rotation profile of the solar radiative region up to 0.2 R☉. Therefore, we include them in our detailed analysis started in Paper I of the main physical processes responsible for the transport of angular momentum and chemical species in stellar radiation zones. Here, we focus on the complete interaction between differential rotation, meridional circulation, shear-induced turbulence, and IGWs during the main sequence. Methods. We improved the diagnosis tools designed in Paper I to unravel angular momentum transport and chemical mixing in rotating stars by taking into account IGWs. The star's secular hydrodynamics is treated using projection on axisymmetric spherical harmonics and appropriate horizontal averages that allow the problem to be reduced to one dimension while preserving the nondiffusive character of angular momentum transport by the meridional circulation and IGWs. Wave excitation by convective zones is computed at each time-step of the evolution track. We choose here to analyse the evolution of a 1.1 M☉, Z☉ star in which IGWs are known to be efficient. Results. We quantify the relative importance of the physical mechanisms that sustain meridional currents and that drive the transport of angular momentum, heat, and chemicals when IGWs are taken into account. First, angular momentum extraction, Reynolds stresses caused by IGWs, and viscous stresses sustain a large-scale multi-cellular meridional circulation. This circulation in turn advects entropy, which generates temperature fluctuations and a new rotation profile because of thermal wind. Conclusions. We have refined our diagnosis of secular transport processes in stellar interiors. We confirm that meridional circulation is sustained by applied torques, internal stresses, and structural readjustments, rather than by thermal imbalance, and we detail the impact of IGWs. These large-scale flows then modify the thermal structure of stars, their internal rotation profile, and their chemical stratification. The tools we developed in Paper I and generalised for the present analysis will be used in the near future to study secular hydrodynamics of rotating stars taking into account IGWs in the whole Hertzsprung-Russell diagram. [ABSTRACT FROM AUTHOR]

In the context of the ESPaDOnS and Narval spectropolarimetric surveys of Herbig Ae/Be stars, we discovered and then monitored the magnetic field of HD 190073 over more than four years, from 2004 to 2009. Our observations all displayed similar Zeeman signatures in the Stokes V spectra, indicating that HD 190073 hosted an aligned dipole, stable over many years, consistent with a fossil origin. We obtained new observations of the star in 2011 and 2012 and detected clear variations of the Zeeman signature on timescales of days to weeks, indicating that the configuration of its field has changed between 2009 and 2011. Such a sudden change of external structure of a fossil field has never previously been observed in any intermediate or high-mass star. HD 190073 is an almost entirely radiative pre-main sequence star, probably hosting a growing convective core. We propose that this dramatic change is the result of the interaction between the fossil field and the ignition of a dynamo field generated in the newly-born convective core. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Context. HD181231 and HD175869 are two late rapidly rotating Be stars, which have been observed using high-precision photometry with the CoRoT satellite during about five consecutive months and 27 consecutive days, respectively. An analysis of their light curves, by Neiner and collaborators and Gutiérrez-Soto and collaborators respectively, showed that several independent pulsation g-modes are present in these stars. Fundamental parameters have also been determined by these authors using spectroscopy. Aims. We aim to model these results to infer seismic properties of HD181231 and HD175869, and constrain internal transport processes of rapidly rotating massive stars. Methods. We used an adiabatic (NRO) and a non-adiabatic (Tohoku) oscillation code that accounts for the combined action of Coriolis and centrifugal accelerations on stellar pulsations as needed for rapid rotator modelling. We coupled these codes with a 2D (ROTORC) stellar structure model to take the rotational deformation of the star into account. The action of transport processes was parametrised with the mixing parameter αov, which represents the "non-standard" extension of the convective core, and determined by matching observed pulsation frequencies assuming a single star evolution scenario. In a second step, we used (Geneva) evolution models to evaluate the contribution of the secular rotational transport and mixing processes in the radiative envelope. A Monte Carlo analysis of spectropolarimetric data was also performed to examine the role of a potential fossil magnetic field. Finally, based on state-of-the-art modelling of penetrative convection and internal waves, we unravelled their respective contribution to the needed "non-standard" mixing. Results. We find that extra mixing of αov = 0.3-0.35Hp is needed in HD181231 and HD175869 to match the observed frequencies with those of prograde sectoral g-modes. We also detect the possible presence of r-modes. We investigated the respective contributions of several transport processes to this mixing: the hydrodynamical processes in particular the meridional circulation and shear-induced turbulence caused by the radiative envelope differential rotation, the possible magnetic field, the penetrative convection at the top of the convective core, and the transport by internal waves. Conclusions. We showed that the extension of the convective core needed to match observations and models may be explained by mixing induced by the penetrative movements at the bottom of the radiative envelope and by the secular hydrodynamical transport processes induced by the rotation in the envelope. We showed how asteroseismology opens a new door to probe transport processes in stellar interiors. [ABSTRACT FROM AUTHOR]