We present the first three-dimensional (3D), hydrodynamic simulations of the core convection zone (CZ) and extended radiative zone spanning from 1% to 90% of the stellar radius of an intermediate mass (3 M ) star. This allows us to selfconsistently follow the generation of internal gravity waves (IGWs) at the convective boundary and their propagation to the surface. We find that convection in the core is dominated by plumes. The frequency spectrum in the CZ and that of IGW generation is a double power law as seen in previous two-dimensional (2D) simulations. The spectrum is significantly flatter than theoretical predictions using excitation through Reynolds stresses induced by convective eddies alone. It is compatible with excitation through plume penetration. An empirically determined distribution of plume frequencies generally matches the one necessary to explain a large part of the observed spectrum. We observe waves propagating in the radiation zone and excited standing modes, which can be identified as gravity and fundamental modes. They show similar frequencies and node patterns to those predicted by the stellar oscillation code GYRE. The continuous part of the spectrum fulfills the IGW dispersion relation. A spectrum of tangential velocity and temperature fluctuations close to the surface is extracted, which are directly related to observable brightness variations in stars. Unlike 2D simulations we do not see the high frequencies associated with wave breaking, likely because these 3D simulations are more heavily damped.

Several parametrizations for overshooting in 1D stellar evolution calculations coexist in the literature. These parametrizations are used somewhat arbitrarily in stellar evolution codes, based on what works best for a given problem or even for the historical reasons related to the development of each code. We point out that these different parametrizations correspond to different physical regimes of overshooting, depending on whether the effects of radiation are dominant, marginal, or negligible. Our analysis is based on previously published theoretical results, as well as on multidimensional hydrodynamical simulations of stellar convection where the interaction between the convective region and a stably stratified region is observed. Although the underlying hydrodynamical processes are the same, the outcome of the overshooting process is profoundly affected by radiative effects. Using a simple picture of the scales involved in the overshooting process, we show how three regimes are obtained, depending on the importance of radiative effects. These three regimes correspond to the different behaviors observed in hydrodynamical simulations so far and to the three types of parametrizations used in 1D codes. We suggest that the existing parametrizations for overshooting should coexist in 1D stellar evolution codes and should be applied consistently at convective boundaries depending on the local physical conditions.

Context. Rotation is one of the key physical mechanisms that deeply impact the evolution of stars. Helio-and asteroseismology reveal a strong extraction of angular momentum from stellar radiation zones over the whole Hertzsprung-Russell diagram. Aims. Turbulent transport in differentially rotating stably stratified stellar radiation zones should be carefully modeled and its strength evaluated. Stratification and rotation imply that this turbulent transport is anisotropic. Only phenomenological prescriptions have been proposed for the transport in the horizontal direction, which however constitutes a cornerstone in current theoretical formalisms for stellar hydrodynamics in evolution codes. We aim at improving its modeling. Methods. We derive a new theoretical prescription for the anisotropy of the turbulent transport in radiation zones using a spectral formalism for turbulence that takes simultaneously stable stratification, rotation, and a radial shear into account. Then, the horizontal turbulent transport resulting from 3D turbulent motions sustained by the instability of the radial differential rotation is derived. We implement this framework in the stellar evolution code STAREVOL and quantify its impact on the rotational and structural evolution of solar metallicity low-mass stars from the pre-main-sequence to the red giant branch. Results. The anisotropy of the turbulent transport scales as N 4 τ 2 / 2Ω 2 , N and Ω being the buoyancy and rotation frequencies respectively and τ a time characterizing the source of turbulence. This leads to a horizontal turbulent transport of similar strength in average that those obtained with previously proposed prescriptions even if it can be locally larger below the convective envelope. Hence the models computed with the new formalism still build up too steep internal rotation gradients compared to helioseismic and asteroseismic constraints. As a consequence, a complementary transport mechanism like internal gravity waves or magnetic fields is still needed to explain the observed strong transport of angular momentum along stellar evolution. Conclusions. The new prescription links for the first time the anisotropy of the turbulent transport in radiation zones to their stratification and rotation. This constitutes an important theoretical progress and demonstrates how turbulent closure models should be improved to get firm conclusions on the potential importance of other processes that transport angular momentum and chemicals inside stars along their evolution.

Context. Recent numerical simulations suggest that the model by Zahn (1992, A&A, 265, 115) for the turbulent mixing of chemical elements due to differential rotation in stellar radiative zones is valid. Aims. We investigate the robustness of this result with respect to the numerical configuration and Reynolds number of the flow. Methods. We compare results from simulations performed with two different numerical codes, including one that uses the shearingbox formalism. We also extensively study the dependence of the turbulent diffusion coefficient on the turbulent Reynolds number. Results. The two numerical codes used in this study give consistent results. The turbulent diffusion coefficient is independent of the size of the numerical domain if at least three large turbulent structures fit in the box. Generally, the turbulent diffusion coefficient depends on the turbulent Reynolds number. However, our simulations suggest that an asymptotic regime is obtained when the turbulent Reynolds number is larger than 10 3 . Conclusions. Shear mixing in the regime of small Péclet numbers can be investigated numerically both with shearing-box simulations and simulations using explicit forcing. Our results suggest that Zahn's model is valid at large turbulent Reynolds numbers.

Context. In stellar interiors, rotation is able to drive turbulent motions, and the related transport processes have a significant influence on the evolution of stars. Turbulent mixing in the radiative zones is currently taken into account in stellar evolution models through a set of diffusion coefficients that are generally poorly constrained. Aims. We want to constrain the form of one of them, the radial diffusion coefficient of chemical elements due to the turbulence driven by radial differential rotation, derived by Zahn (1974, IAU Symp., 59, 185 and 1992, A&A, 265, 115) on phenomenological grounds and largely used since. Methods. We performed local, direct numerical simulations of stably stratified homogeneous sheared turbulence using the Boussinesq approximation. The domain of low Péclet numbers found in stellar interiors is currently inaccessible to numerical simulations without approximation. It is explored here thanks to a suitable asymptotic form of the Boussinesq equations. The turbulent transport of a passive scalar is determined in statistical steady states. Results. We provide a first quantitative determination of the turbulent diffusion coefficient and find that the form proposed by Zahn is in good agreement with the results of the numerical simulations.

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.

Context. Mode identification is a crucial step to comparing observed frequencies with theoretical ones. However, it has proven to be particularly difficult in rapidly rotating stars. An important reason for this is the lack of simple frequency patterns such as those present in solar-type pulsators. This problem is further aggravated in δ Scuti stars by their particularly rich frequency spectra. Aims. As a first step to obtaining further observational constraints towards mode identification in rapid rotators, we aim to accurately calculate mode visibilities and amplitude ratios while fully taking into account the effects of rotation. Methods. We derive the relevant equations for calculating mode visibilities in different photometric bands while fully taking into account the geometric distortion from both the centrifugal deformation and the pulsation modes, the variations in effective gravity, and an approximate treatment of the temperature variations, given the adiabatic nature of the pulsation modes. These equations are then applied to 2D oscillation modes, calculated using the TOP code (Two-dimension Oscillation Program), in fully distorted 2D models based on the self-consistent field (SCF) method. The specific intensities come from a grid of Kurucz atmospheres, thereby taking into account limb and gravity darkening. Results. We obtain mode visibilities and amplitude ratios for 2 M models with rotation rates ranging from 0 to 80% of the critical rotation rate. Based on these calculations, we confirm a number of results from earlier studies, such as the increased visibility of numerous chaotic modes at sufficient rotation rates, the simpler frequency spectra with dominant island modes for pole-on configurations, or the dependence of amplitude ratios on inclination and azimuthal order in rotating stars. In addition, we explain how the geometric shape of the star leads to a smaller contrast between pole-on and equator-on visibilities of equatorially-focused island modes. We also show that modes with similar ( , |m|) values frequently have similar amplitude ratios, even in the most rapidly rotating models.

Aims. For the first time, the motion of granules (solar plasma on the surface on scales larger than 2.5 Mm) has been followed over the entire visible surface of the Sun, using SDO/HMI white-light data. Methods. Horizontal velocity fields are derived from image correlation tracking using a new version of the coherent structure tracking algorithm. The spatial and temporal resolutions of the horizontal velocity map are 2.5 Mm and 30 min, respectively. Results. From this reconstruction, using the multi-resolution analysis, one can obtain to the velocity field at different scales with its derivatives such as the horizontal divergence or the vertical component of the vorticity. The intrinsic error on the velocity is ∼0.25 km s −1 for a time sequence of 30 min and a mesh size of 2.5 Mm. This is acceptable compared to the granule velocities, which range between 0.3 km s −1 and 1.8 km s −1 . A high correlation between velocities computed from Hinode and SDO/HMI has been found (85%). From the data we derive the power spectrum of the supergranulation horizontal velocity field, the solar differential rotation, and the meridional velocity.