2023-2024 / SPAT0005-1

Stellar stability and asteroseismology


30h Th, 10h Pr

Number of credits

 Master in space sciences (120 ECTS)4 crédits 


Marc-Antoine Dupret

Language(s) of instruction

English language

Organisation and examination

Teaching in the second semester


Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

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 and interpretation of these oscillations is the golden path to probe the internal structure of stars. This method is called asteroseismology.
This course presents the basics of the theory of stellar oscillations. We begin by establishing the mathematical foundation of the corresponding eigenvalue problem. We begin by studying the adiabatic radial oscillations and next the non-radial oscillations (both hermitian problems) of stars. To present asteroseismology, we study the link between the internal characteristics of stars and their oscillation frequencies. In this framework we consider in detail 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, ...

Learning outcomes of the learning unit

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

Prerequisite knowledge and skills

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.
Co-required courses:
SPAT0044-1 Structure et évolution des étoiles I. SPAT0040-1 Fluid mechanics (P.C. Dauby)
Recommended complementary courses:
"Variable stars" and "Geophysical fluid dynamics - part 1."

Planned learning activities and teaching methods

Mode of delivery (face to face, distance learning, hybrid learning)

3h/week the 2nd semester.
From the academic year 2016-2017, the course is given in English, except if the students ask it to be in French.

Recommended or required readings

Lecture notes and powerpoint presentations will be made available to the students.

Any session :

- In-person

oral exam

- Remote

oral exam

- If evaluation in "hybrid"

preferred in-person

Additional information:

A list of possible questions covering the most important aspects of the course is provided (and commented) at the end of the semester. The student must answer one of them (drawn randomly) during the oral exam, he can choose to answer in English or French.
If the assessment is remote, the student chooses in advance the subject he will present.

Work placement(s)

Organisational remarks and main changes to the course


Marc-Antoine Dupret
email: MA.Dupret@ulg.ac.be
address: Institut d'Astrophysique et Géophysique, bât. B5c, +1
Tél: 04 366 97 32

Association of one or more MOOCs

Items online

Complément 1
Notes de l'ancien cours de Richard Scuflaire

Complément 2
Notes du cours de Jorgen Christensen-Dalsgaard (Aarhus - Danemark)

Notes du cours
Dias powerpoint