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| SPAT0005-1 | Stellar stability and asteroseismology
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| Duration : | 30h Th, 10h Pr |
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| Lecturer : | Marc-Antoine Dupret |
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Language(s) of instruction :
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| French language |
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Organisation and examination :
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| Teaching in the second semester |
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Course contents :
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| During their evolution, stars undergo phases of instability, which can manifest themselves violently, by a simple acceleration of their evolution, or by inducing oscillations. The study of these oscillations leads to information about their internal structure. This is called asteroseismology.
This course presents the basics of the theory of stellar oscillations. We begin by establishing the mathematical foundations of the corresponding eigenvalue problem. We begin by studying the adiabatic radial oscillations and next the non-radial oscillations (both hermitian problems). To present asteroseismology, we study the link between the internal characteristics of stars and their oscillation frequencies. In this framework we consider in details the analogy with a simpler problem: acoustic modes in a pipe. And we generalize to the case of stellar oscillations. Next, we consider the 3 main types of pulsation: pressure (acoustic) modes, gravity modes and mixed modes; and we show how they appear in practice in different types of pulsating stars. We also consider the impact of stellar rotation on the frequency spectrum (analogy with the Zeeman effect).
In the second part, we study the problem of stellar stability. We begin by establishing the criterion of dynamical stability. Next, we put in equations the general problem of non-adiabatic stellar oscillations (inclusion of energetic aspects). A first limiting case allows us to briefly discuss the secular stability of stars. We consider next in more details the case of stellar oscillations, which leads us to the notion of vibrational stability. This allows us to explain the main energetic mechanisms at the origin of stellar oscillations: motor thermodynamical cycles due to opacity variations, ... |
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Learning outcomes of the course :
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| The general objective of this course is to present the foundations of the stellar oscillations theory. From a mathematical point of view, it is an eigenvalue problem analogous to other physical situations (quantum physics, acoustics, vibration modes, ...). The analysis presented here is thus useful in a broader context. The students are confronted here with a field at the front of current research. Indeed, asteroseismology is the most promising modern method for the probing of stellar internal physics.
Most of the following topics will be adressed and will have to be known.
* Position of a few types of variable stars in the HR diagram
* Stellar time scales
* Equations of hydrodynamics and thermodynamics
* Equilibrium configurations
* Small perturbations method
* Adiabatic perturbations
* Radial oscillations
* Adiabatic radial oscillations
* Asymptotic expression of radial frequencies
* Non radial oscillations
* Description of the non radial modes
* Influence of rotation
* Basic techniques of asteroseismology on the main sequence of the HR diagram.
* Modes in simple cavities
* Excitation mechanisms in stars
* Mode identification |
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Prerequisites and co-requisites/ Recommended optional programme components :
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| The student needs knowledge of mathematics and physics at the level of that taught at the level of bachelor in the physics section. Some knowledge of stellar structure and evolution will be useful. |
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Planned learning activities and teaching methods :
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Mode of delivery (face-to-face ; distance-learning) :
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| 30 hours of lectures and 10 hours of practical lectures. |
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Recommended or required readings :
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| Lecture notes and powerpoint presentations will be made available to the students. |
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Assessment methods and criteria :
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| During the oral exam each student presents, in about 20 minutes, a question of his/her choice considered during the course. He/she is also briefly questioned about other aspects of the course. |
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Work placement(s) :
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Organizational remarks :
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Contacts :
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| Marc-Antoine Dupret
email: MA.Dupret@ulg.ac.be
address: Institut d'Astrophysique et Géophysique, bât. B5c, +1
Tél: 04 366 97 32 |
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| Items online : |
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| Complément 1 |
| Notes de l'ancien cours de Richard Scuflaire |
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| Complément 2 |
| Notes du cours de Jorgen Christensen-Dalsgaard (Aarhus - Danemark) |
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| Notes du cours |
| Dias powerpoint |
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