Prof. M. Faurobert, G. Nicollini
|Stellar Atmospheres for Helio & Asteroseismology, Modelisation
(S2, compulsory, 4 ECTS)
|Most of the information astronomers obtain from their telescopes is under the form of light spectra, i.e. the radiative energy emitted by the astrophysical objects as a function of the wavelength. More and more relevant physical information may be obtained by increasing the spatial and spectral resolutions. So one of the most fundamental tool for astrophysicists is spectra modeling which allows them to interpret the observations. To achieve this, one needs both to describe the physical phenomena taking place in the object and how the photons are created, absorbed or scattered and finally can escape the object and be detected by our instruments. In this course we shall focus on light emitted by stellar atmospheres.
|Knowledge and Understanding:
|In first basic models the atmosphere of the star is supposed to be in hydrostatic and radiative equilibrium (i.e. the energy created at the center of the star is transported through the atmosphere by the radiation without any net loss nor creation). We shall study how the atmosphere radiates and show that it emits a continuum spectrum quite close to a black body spectrum, allowing to define the so-called “effective temperature” of the star surface. Increasing the spectral resolution, we can observe absorption lines in the spectrum, i. e. a decrease of the radiative energy on narrow wavelength bands (a few hundredths of nanometers typically). These lines are due to the absorption of photons by chemical elements in the stellar atmosphere. If we increase the spatial resolution we see that the shape of the lines varies along the stellar surface. One of the challenges of the interpretation of stellar spectra is to be able to explain both the wavelength positions and the shapes of the spectral lines. If we can achieve that we get a wealth of information on the physics of the star, such as the abundances of the chemical elements, the acceleration of gravity at the surface, rotation velocity, turbulence, convection, pulsations, etc …To achieve this goal we need to know how both the continuum spectrum and spectral lines are formed.
|Applying Knowledge and Understanding:
|The course consists of a theoretical part illustrated by small exercices. Some real data acquired on various astronomical instruments, ground or space-based will be presented and analyzed. Also, ability to interpret asteroseismic data in a rigorous statistical framework. Ability to apply the data analysis concepts learned (Spectral analysis, Bayesian inference, inverse methods) in various fields of astrophysics.
|Fundamental physics, atomic physics. Basic knowledge of stellar structure and evolution, statistics and numerical methods. Helio and Asteroseismology fundamental courses.
|Course 1 : basic notions- Radiation processes, an overview – Recall on the laws of thermodynamic equilibrium Course 2 : Radiation field and radiative transfer equation- Specific intensity, and its angular moments- Absorption coefficient, emissivity and radiative transfer equation- Formal solution of the stationnary radiative transfer equation. Course 3 : Radiative transfer in dense stellar regions- Asymptotic expansion of the radiative transfer equation- Calculation of the radiative flux. Rosseland means of the opacity, diffusion approximation. Course 4 : Stellar atmospheres (stationary and in radiative equilibrium)-The physical model and the related equations (Stellar parameters)- One-dimensional approximation -Formal solution and Eddington-Barbier approximation for the emergent specific intensity and for the radiative flux.- Integral equation for the source function, the Lambda operator.- First applications, center-to-limb variations of the continuum radiation Course 5 : Grey atmosphere in radiative equilibrium- The Milne equation, boundary condition- Eddington approximation versus exact solution. The Hopf function.-Temperature variations in a grey atmosphere in Local Thermodynamic Equilibrium. Center-to-limb variation of the emergent intensity. Course 6 : Continuum spectrum emitted by a stellar atmosphere in LTE. -Computation of the absorption coefficient, example of the photo-ionisation of H- Algorithm for atmospheric modeling. Temperature-correction procedure- Examples of stellar atmosphere models. Course 7 : Formation of spectral lines. Basic notions- A brief overview of spectroscopy, Oscillator strength. Selection rules.- Einstein coefficients- Line absorption profiles-Opacity, emissivity and source function in a spectral line- Expression of the source function for a two-level atom. LTE versus non-LTE. Course 8 : Formation of spectral lines in LTE- Radiative transfer equation- Milne approximation- Curve of growth and the determination of abundances. Course 9: Formation of spectral lines under non-LTE conditions-Coupling of the line radiation with the statistical equilibrium of the atomic-level populations. – Two-level atom and the integral equation for the source function.- Properties of the Lambda operator. Scaling laws for the source function.- Numerical solutions : Lambda Iteration versus Accelerated Lambda Iteration. Course 10: Introduction to 3D atmospheres Hands-on exercises
|Description of how the course is conducted
|The course consists of theory lectures presented on both slide presentations and blackboard. The class is accompanied by exercises and examples so that the student can practice with the tools that have been presented. Exercices may be prepared by the students and presented to the class orally.
|Description of the didactic methods
|Active learning is expected through reading assignments, homework and classwork assignments, experimental hands-on, and mini-projects. Understanding will be evaluated by written/oral questions or oral presentations to their classmates. The second part of lectures is 40% theoretical and 60% application (modelization).
|Description of the evaluation methods
|Students need to pass a written test aimed at verifying their ability in applying the methods and tools given in the course for performing some standard analysis of stellar data. An oral exam is then meant to verify that the students have developed a critical understanding of the subject.
|Hubeny, I., Mihalas, D., 2015, Theory of stellar atmospheres, Princeton University Press
|Rob Rutten’s course notes : http://www.staff.science.uu.nl/~rutte101/Course_notes.html