Shear mixing in stellar radiative zones I. Effect of thermal diffusion and chemical stratification

Turbulent transport of chemical elements in radiative zones of stars is considered in current stellar evolution codes thanks to phenomenologically derived diffusion coefficients. Recent local numerical simulations (Prat & Ligni\`eres 2013, A&A, 551, L3) suggest that the coefficient for radial turbulent diffusion due to radial differential rotation satisfies $D_{\rm t}\simeq0.058\kappa/Ri$, in qualitative agreement with Zahn's model. However, this model does not apply when differential rotation is strong with respect to stable thermal stratification or when chemical stratification has a significant dynamical effect, a situation encountered at the outer boundary of nuclear-burning convective cores. We extend our numerical study to consider the effects of chemical stratification and of strong shear, and compare the results with prescriptions used in stellar evolution codes. We performed local, direct numerical simulations of stably stratified, homogeneous, sheared turbulence in the Boussinesq approximation. The regime of high thermal diffusivities, typical of stellar radiative zones, is reached thanks to the so-called small-P\'eclet-number approximation, which is an asymptotic development of the Boussinesq equations in this regime. The dependence of the diffusion coefficient on chemical stratification was explored in this approximation. Maeder's extension of Zahn's model in the strong-shear regime is not supported by our results, which are better described by a model found in the geophysical literature. As regards the effect of chemical stratification, our quantitative estimate of the diffusion coefficient as a function of the mean gradient of mean molecular weight leads to the formula $D_{\rm t}\simeq 0.45\kappa(0.12-Ri_\mu)/Ri$, which is compatible in the weak-shear regime with the model of Maeder & Meynet (1996, A&A, 313, 140).Comment: 10 pages, 9 figures, accepted in A&

Seismic diagnosis from gravity modes strongly affected by rotation

Most of the information we have about the internal rotation of stars comes from modes that are weakly affected by rotation, for example by using rotational splittings. In contrast, we present here a method, based on the asymptotic theory of Prat et al. (2016), which allows us to analyse the signature of rotation where its effect is the most important, that is in low-frequency gravity modes that are strongly affected by rotation. For such modes, we predict two spectral patterns that could be confronted to observed spectra and those computed using fully two-dimensional oscillation codes.Comment: 3 pages, 1 figure, to appear in the proceedings of the Joint TASC2 & KASC9 Workshop SPACEINN & HELAS8 Conference "Seismology of the Sun and the Distant Stars 2016

Internal magnetic fields in 13 red giants detected by asteroseismology

While surface fields have been measured for stars across the HR diagram, internal magnetic fields remain largely unknown. The recent seismic detection of magnetic fields in the cores of several Kepler red giants has opened a new avenue to understand better the origin of magnetic fields and their impact on stellar structure and evolution. We aim to use asteroseismology to systematically search for internal magnetic fields in red giant stars and to determine the strengths and geometries of these fields. Magnetic fields are known to break the symmetry of rotational multiplets. In red giants, oscillation modes are mixed, behaving as pressure modes in the envelope and as gravity modes in the core. Magnetism-induced asymmetries are expected to be stronger for g-dominated modes than for p-dominated modes and to decrease with frequency. After collecting a sample of 2500 Kepler red giant stars with clear mixed-mode patterns, we specifically searched for targets among 1200 stars with dipole triplets. We identified 13 stars exhibiting clear asymmetric multiplets and measured their parameters, especially the asymmetry parameter and the magnetic frequency shift. By combining these estimates with best-fitting stellar models, we measured average core magnetic fields ranging from 20 to 150kG, corresponding to 5% to 30% of the critical field strengths. We showed that the detected core fields have various horizontal geometries, some of which significantly differ from a dipolar configuration. We found that the field strengths decrease with stellar evolution, despite the fact that the cores of these stars are contracting. Even though these stars have strong internal magnetic fields, they display normal core rotation rates, suggesting no significantly different histories of angular momentum transport compared to other red giant stars. We also discuss the possible origin of the detected fields.Comment: Accepted for publication in A&A. Long appendi

Wave chaos in rapidly rotating stars

Effects of rapid stellar rotation on acoustic oscillation modes are poorly understood. We study the dynamics of acoustic rays in rotating polytropic stars and show using quantum chaos concepts that the eigenfrequency spectrum is a superposition of regular frequency patterns and an irregular frequency subset respectively associated with near-integrable and chaotic phase space regions. This opens new perspectives for rapidly rotating star seismology and also provides a new and potentially observable manifestation of wave chaos in a large scale natural system.Comment: 5 pages, 3 figures; accepted for publication in Phys. Rev.

Regular modes in rotating stars

Despite more and more observational data, stellar acoustic oscillation modes are not well understood as soon as rotation cannot be treated perturbatively. In a way similar to semiclassical theory in quantum physics, we use acoustic ray dynamics to build an asymptotic theory for the subset of regular modes which are the easiest to observe and identify. Comparisons with 2D numerical simulations of oscillations in polytropic stars show that both the frequency and amplitude distributions of these modes can accurately be described by an asymptotic theory for almost all rotation rates. The spectra are mainly characterized by two quantum numbers; their extraction from observed spectra should enable one to obtain information about stellar interiors.Comment: 5 pages, 4 figures, discussion adde

Rotation, magnétisme et turbulence dans les étoiles

Ce travail de thèse concerne à la fois la modélisation des processus magnétohydrodynamiques dans les étoiles et l'obtention de contraintes observationnelles sur ces processus. Une partie importante du mémoire est consacrée à l'étude des effets de la rotation sur les modes propres d'oscillation des étoiles. La méconnaissance de ces effets est depuis longtemps identifiée comme l'un des principaux obstacles à l'interprétation des fréquences d'oscillations observées dans les étoiles massives et de masse intermédiaire. Je décris ici la mise au point d'un code d'oscillation tenant compte des effets de la rotation, l'exploration des nouvelles propriétés des modes au moyen de ce code, l'interprétation de ces propriétés dans le cadre d'une théorie asymptotique et comment elles peuvent être utilisées pour interpréter les spectres de fréquences observés. Pour construire la théorie asymptotique, j'ai été amené à m'intéresser au chaos quantique (ou chaos d'onde), une thématique qui est issue de l'étude des propriétés semi-classiques des systèmes quantiques mais qui concerne en fait la physique des ondes en général. La deuxième thématique concerne le magnétisme des étoiles de masse intermédiaire (de type B tardif et de type A) de la séquence principale. C'est un sujet relié mais distinct de celui de ma thèse de doctorat qui était consacré à la modélisation de l'évolution du moment cinétique de ces étoiles dans leur phase pré-séquence-principale. Il s'agit ici d'observations spectropolarimétriques qui renouvellent assez largement notre vision du magnétisme de ces étoiles. D'abord, la mise en évidence d'une limite inférieure à l'intensité du champ des étoiles Ap/Bp a permis de proposer un nouveau scénario pour expliquer l'origine de cette classe d'étoiles, la seule classe d'étoiles magnétiques connue jusqu'alors dans ce domaine du diagramme HR. Puis, la découverte d'un champ magnétique de très faible amplitude à la surface de Véga a montré l'existence d'un nouveau type de magnétisme dans ce domaine. La troisième thématique concerne l'étude des mouvements turbulents dans les intérieurs stellaires, d'une part la modélisation de leur contribution au transport des éléments chimiques dans les zones radiatives d'étoile et d'autre part l'origine des structures cohérentes de la convection turbulente observées à la surface du Soleil

Numerical Exploration of Oscillation Modes in Rapidly Rotating Stars

peer reviewedIn this chapter, we show that two-dimensional oscillation codes help us to improve our knowledge of the effects of rapid rotation on acoustic (p) and gravity (g) modes. We first discuss how to solve the full problem of stellar oscillations in rapidly rotating stars by including the effects of the Coriolis force as well as those of the centrifugal distortion. We illustrate the development and the validation of a 2-D code using the Two-dimensional Oscillation Program (TOP) as an example. We then describe what strategies are being developed to explore the p- and g-mode spectra, how effective these methods are, and what intrinsic difficulties they face. In the last part of this chapter, we present results obtained with these techniques

Reduction of vertical transport in two-dimensional stably stratified forced shear flows

International audienceThe effect of stable stratification on the vertical transport of passive contaminants in forced, stationary, two-dimensional (2D) and inhomogeneous shear turbulence is investigated numerically. The mean flow consists of several superimposed parallel sheared layers in a stably stratified medium. We find that, as stratification increases, the vertical transport decreases much faster than predicted by mixing length estimates. For the highest stratification, particles vertical dispersion nearly vanishes. The proposed interpretation emphasizes the role of weakly sheared layers where the relative increase of the mean horizontal velocity with respect to the root-mean-square (rms) vertical velocity causes the decrease of the Lagrangian correlation timescale