Univ. NICE
Lionel Bigot, Orlagh Creevey, Thierry Corbard
Helio and Asteroseismology
(S2, compulsory, 6 ECTS)
Learning Outcomes:Helio and asteroseismology have revolutionized our understanding of the Sun and stars in the past 40 years. Seismology is indeed the only technique that can infer the interiors of stars and is by far more accurate than any other methods. Asteroseismology is now demanded by many research fields in astrophysics, like Galactic Archaeology or exoplanet systems to obtain accurate fundamental parameters of stars. In this respect, lots of space missions have been dedicated to the seismology of stars : CoRoT (ESA), KEPLER, K2 (NASA), now TESS (NASA), and in the future PLATO (ESA, 2026), and HAYDN (ESA, 2037).
The student will become very familiar with all of the theoretical concepts concerning the internal structure of stars and stellar oscillations. The student will learn the relevant tools in order to interpret seismic data, We shall introduce the technique of internal structure modelization. We shall show the capacity to analyze and interpret solar-like seismic data collected from space or ground based instruments in order to extract global characterisation of the stars and their interiors or the age of stars.
Knowledge and Understanding:
At the end of the course, students will have the theoretical background to understand and analyze frequency spectra of datasets obtained in helio and asteroseismology. They will also have hands-on experience with interpreting stellar oscillation data
Applying Knowledge and Understanding:The lecture will be directly connected to other lectures of the Master: stellar evolution
Prerequisitessolar/stellar structure Fluid dynamics Thermodynamics Basic knowledge in mathematics (the formalism of quantum mechanics will be used)
ProgramTheory of stellar oscillations (16H)
The place of seismology in Milky Way, Stellar and Exoplanet science Stellar oscillation fundamentals Equations of hydrostatic structure Eulerian and Lagrangian perturbations Radial and non-radial oscillations. Nature and properties of the modes. Impact of stellar age onto the frequencies. Variational methods. Rotation and magnetic field effects. Stellar magnetic cycles. Surface effects and impacts convection of mode properties. Hands on Modelisation of Asteroseismology (16H)
Global Stellar Properties and scaling relations density, surface gravity, radius, mass, lift-times Mode identification Stellar evolution models and oscillation codes From frequencies to stellar global and structure properties and their uncertainties Forward Techniques local optimization, monte carlo, bayesian Glitch Seismology outer convective envelope properties, sound travel times Uncertainties and systematic errors sources of errors, methodology errors, model errors Hands-on
Helio seismology and Local inversion techniques of the Sun (16H)
Observational data: photometric and Doppler velocities From time-series to frequencies Spectral analysis: Nyquist sampling-Aliasing-temporal filtering Fourrier and Lomb-scargle periodogram– statistic of the power spectrum Statistical Inference : Frequentist / Bayesian parameter estimation Hypothesis testing Extraction of individual mode parameters (peak-bagging): Maximum Likelihood Estimation, Maximum a posteriori, sampling algorithms and the Markov Chain Monte Carlo method. From Frequencies to model parameters Monte Carlo simulations and Optimization methods Inverse Methods The relationship between sound-speed (density, etc..) and frequencies The relationship between rotation and frequency splittings Linear inverse methods: Regularized Least Squares, Generalized Singular Value Decomposition, Optimally Localized Averages. Non-linear methods.

Description of how the course is conductedLectures to acquire theoretical background on stellar oscillations: main properties of the different mode physics, the mathematical properties of the oscillation equations, and understanding the basic concepts to analyze real data obtained from space.
Active participation in the lectures will be asked. The course will be interactive: the student will have to derive themselves some analytical results, as exercises.
Hands-on: The student will use an open-source stellar oscillation code to understand the basic concepts and to analyze real data.
Description of the didactic methods
Description of the evaluation methodsThe examination will be based on 3 marks: a first one dedicated to the participation during the lecture and exercises, a second one dedicated to the analysis of real space data using an open source oscillation code, a third one dedicated to a final written exam. The three marks represent 20, 40, and 40% respectively of the final mark..
Adopted TextbooksNonradial oscillations of stars, Unno, Wasaburo; Osaki, Yoji, Ando, Hiroyasu, Saio, H., Shibahashi, H., Nonradial oscillations of stars, Tokyo: University of Tokyo Press, 1989, 2nd ed. ISBN: 9780860084396 Asteroseismology, Aerts, Conny, Christensen-Dalsgaard, Jørgen, Kurtz, Donald W., Asteroseismology, Astronomy and Astrophysics Library. ISBN 978-1-4020-5178-4., Springer Science+Business Media B.V., 2010, p.
Recommended readingsAsteroseismic data analysis, foundations and techniques, S. Basu & W.J. Chaplin, Princeton University Press, 2017 ISBN: 978-0-691-16292-8
Methods in helio- and asteroseismology, F. P. Pijpers, Imperial College Press, 2006 ISBN 1-86094-755-7