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Energetic Study of Solar-Like Oscillations in Red Giants

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Energetic Study of Solar-Like Oscillations in Red Giants Université de Liège Faculté des Sciences Département d’Astrophysique, de Géophysique et d’Océanographie Energetic study of solar-like oscillations in red giants Mathieu Grosjean PhD Thesis October 2015 Jury members : Pr. Pierre Magain (President) Pr. Marc-Antoine Dupret (Supervisor) Dr. Kevin Belkacem (Supervisor) Dr. Valérie Van Grootel Pr. Arlette Noels Pr. Benoit Mosser Dr. Andréa Miglio Abstract Observations of solar-like oscillations by CoRoT and Kepler space-borne telescopes, have opened new opportunities for the energetic modelling of these oscillations. In particular, oscillations propagating in both the convective envelope and the radiative core of evolved low-mass stars, called mixed-modes, have been detected, allowing us to investigate various physical processes acting on oscillations in these two regions. Theoretical predictions for the linewidths and the amplitudes of solar-like oscillations, as obtained and discussed in this thesis, strongly depend on the treatment of the interaction between convection and oscillations. Observed properties of solar-like oscillations thus gives us the opportunity to test and constrain this treatment. The comparisons between observed and theoretical linewidths of main-sequence stars allow us to constrain the parameters of the time-dependent treatment of convection and to produce more accurate results. The remaining discrepancies will give us new clues for the improvement of the treatment of the interaction between convection and oscillations. The modelling of the energetic aspects of solar-like oscillations in red giants allows us to derive a detectability limit for mixed-modes. These results are in overall good agreement with typical red-giant observed power spectra. A detailed comparison between an observed subgiant and the corresponding theoretical predic- tions confirms that the main aspects of the observed energetic properties of solar-like oscillations are well reproduced by the theoretical modelling. Discrepancies between observed and theoret- ical linewidths of quadrupole mixed-modes lead us to invoke the existence of a new damping mechanism in the core of this star. Resumé L’observation d’oscillations de type solaire, dans de nombreuses étoiles de faible masse, par les satellites CoRoT et Kepler a ouvert de nouvelles possibilités pour la modélisation des aspects énergétiques de ces oscillations. En particulier, la détection de modes mixtes, se propageant dans l’enveloppe convective et dans le coeur radiatif des géantes rouges, nous permet d’étudier les processus physiques à l’origine des propriétés énergétiques des modes dans ces deux régions. Les prédictions théoriques pour les largeurs et les amplitudes des oscillations de type solaire, telles qu’obtenues et discutées dans cette thèse, dépendent fortement du traitement des processus d’interaction entre la convection et les oscillations. La détermination observationnelle des largeurs et amplitudes des modes nous donne donc l’opportunité de tester et contraindre un tel traitement. Les comparaisons des largeurs observées et théoriques pour des étoiles de séquence principale nous permet de contraindre précisément les paramètres du traitement de la convection dépendante du temps et ainsi de produire des résultats bien plus réalistes. Les différences restantes entre largeurs observées et théoriques apportent de nouvelles pistes pour une amélioration du traitement de l’interaction entre la convection et les oscillations. La modélisation des aspects énergétiques des oscillations de type solaire dans les géantes rouges nous permet d’établir une limite de détectabilité des modes mixtes. Il apparait que les résultats de cette modélisation sont globalement en accord avec les observations. Une comparaison détaillée des propriétés énergétiques des modes observés dans une sous-géante et prédites par une modélisation théorique de cette étoile, montre que la plupart des aspects én- ergétiques des oscillations de type solaire sont bien reproduits par les modèles théoriques. Les dif- férences entre les observations et les prédictions théoriques des largeurs et amplitudes des modes mixtes quadripolaires nous amènent à l’hypothèse qu’un nouveau mécanisme d’amortissement est à l’oeuvre dans le coeur de cette étoile. Merci !! Au moment de finir cette thèse, je souhaite remercier celles et ceux qui ont contribué à cette aventure. Tout d’abord, un grand merci à Marc-Antoine et Kevin pour m’avoir guidé dans ce parcours scientifique. Leur aide, leurs conseils et leurs avis dans mes recherches et dans la rédaction de cette thèse, m’ont été très précieux. Merci également à Réza, Richard, Josefina, Arlette, Benoit, Othman et Sébastien pour leurs conseils, leur disponibilité, leur aide et pour les outils qu’ils ont mis à ma disposition. Merci aux membres du jury, d’avoir accepté de prendre le temps de lire cette thèse. Je remercie aussi le F.R.I.A. pour m’avoir permis d’effectuer ce doctorat. Un merci tout particulier à Angela, pour son aide dans la production de cette thèse ainsi que tout au long de mon doctorat. Je remercie toutes les personnes du département d’astrophysique et plus particulièrement celles du B5c +1 pour leur accueil. Un tout grand merci à tous mes amis, qui m’ont soutenu, encouragé, parfois supporté tout au long de ces 4 années de thèse. Un merci tout particulier à Lionel avec lequel j’ai découvert beaucoup de choses. Merci également pour m’avoir aidé à garder toute la forme et l’énergie nécessaires pour avancer dans cette thèse. A Xavier, pour son grand soutien et pour les recharges en énergie autour d’un thé toujours très constructif. Un big merci à Vivien et à Quentin, partenaires indéfectibles de mon doctorat et de toutes les activités gravitant autour. Merci à Gregory, Jérémy, Ludo pour avoir joué les parfaits supports. Aux étudiants du bachelier en sciences physiques pour l’enthousiasme qu’ils ont manifesté pour mes recherches ainsi que pour l’animation qu’ils apportent. Enfin, je souhaite remercier ma famille qui m’a toujours soutenu et encouragé durant tout mon parcours universitaire. 6 Contents 1 Introduction 11 1.1 Historical context of solar-like oscillations . 13 1.1.1 Oscillations of the Sun . 13 1.1.2 From the Sun to solar-like oscillators . 15 1.2 Problematic and organisation of the manuscript . 21 I Theoretical background on low-mass stars and solar-like oscilla- tions 23 2 Structure and evolution of low-mass stars 25 2.1 Time scales of stellar dynamics . 25 2.2 Basic equations of stellar structure and evolution . 26 2.2.1 General equations of hydrodynamics . 27 2.2.2 The four equilibrium equations . 28 2.3 Energy transport mechanisms . 30 2.3.1 Radiation and conduction . 30 2.3.2 Convection . 31 2.4 The convective treatment in stellar interior. 32 2.4.1 The approximations of the MLT . 33 2.4.2 Derivation of the convective flux . 34 2.4.3 The temperature gradient . 36 2.4.4 The cubic MLT equation . 38 2.5 The evolution path of low-mass stars . 39 2.6 Beyond the standard model : problems and prospects . 44 2.6.1 Convection . 44 2.6.2 Main transport mechanisms . 45 2.6.3 Other Physical mechanisms . 45 3 Solar-like oscillations 47 3.1 Theory of stellar oscillations . 47 3.1.1 Small perturbations approach . 48 3.1.2 Non-adiabatic non-radial oscillations . 49 3.1.3 Physical nature of modes . 52 3.1.4 Driving and damping of oscillations. 62 3.2 Time-dependent treatment of convection . 63 3.2.1 General hydrodynamic equations . 65 3.2.2 Equations of the average medium . 65 7 CONTENTS 3.2.3 Equations for convective fluctuations . 66 3.2.4 Stationary case . 68 3.2.5 Perturbation of the average structure . 69 3.2.6 Perturbation of the convection . 70 3.2.7 Damping rates of oscillations . 72 3.3 Non-local treatment of convection . 73 3.4 Stochastic excitation . 74 3.4.1 The problematic of mode amplitude . 74 3.4.2 The stochastic excitation mechanism . 75 3.4.3 Physical key quantities for stochastic excitation . 80 3.5 Asteroseismic techniques for solar-like oscillations. 82 3.5.1 Global asteroseismic quantities and scaling relations . 82 3.5.2 Individual mode frequencies . 84 3.5.3 Perspectives . 85 II New results on the energetic properties of solar-like oscillations 87 4 Models and methods for computing theoretical power spectra 89 4.1 Equilibrium models . 91 4.1.1 The stellar evolutionary codes . 91 4.1.2 Specificities of red-giant equilibrium models . 91 4.2 Non-adiabatic computations . 93 4.2.1 Non-local, time-dependent treatment of convection . 93 4.2.2 Specificities of mixed-modes in red giants . 93 4.3 Constraining the main TDC parameter β ...................... 94 4.4 Stochastic excitation and peak properties in a power spectrum . 100 4.4.1 Mode amplitudes . 100 4.4.2 The shape of a mode peak . 101 5 Impact of the TDC treatment on main sequence linewidths 105 5.1 Constraints on the TDC β parameter . 105 5.1.1 Local behavior of the damping rates around the optimized value of β ... 105 5.1.2 The Γmax - Teff scaling relation . 107 5.1.3 Fit of four Kepler main-sequence star linewidths . 109 5.2 Additional changes in the TDC parameters and hypothesis . 111 5.2.1 Non-local parameters . 111 5.2.2 Perturbation of the mixing-length . 114 5.2.3 The anisotropy factor . 114 6 Theoretical power spectra of mixed-modes in low-mass red-giant stars 117 6.1 Power spectrum evolution from the bottom of the RGB to the horizontal branch 117 6.1.1 Non-adiabatic effects on mixed-mode heights . 118 6.1.2 Red-giant models and general tendencies . 119 6.1.3 Detailed description of the evolution of a theoretical power spectrum . 125 6.2 Generalisation of the results on mixed-modes detectability .
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