Prof. G. Bono
Stellar Structure and Evolution
(S3, elective, 6 ECTS)
Learning Outcomes:The master is aimed at providing an advanced preparation on Physics, with a detailed knowledge of the key topics in the recent research in Astrophysics. The learning outcomes rely on a detailed knowledge of quantum mechanics and solid state physics. The main objective of the course in Stellar Astrophysics is to provide to the student the knowledge of the basic physics required to understand the formation and evolution of stellar structures. This knowledge is fundamental to understand not only the evolution of the baryonic content of the Universe, but also to trace its chemical evolution. These concepts are a stepping stone not only for the students interested in understanding the local Universe, but also for those interested in the large scale structure of the Universe in cosmological models and in compact objects (stellar mass black holes, neutron stars, white dwarfs).
Knowledge and Understanding:
The student at the end of the semester will acquire a detailed knowledge on the energy conservation equations (momentum, mass, energy) of stellar interiors and of the transport equation (radiation, conduction, convection). Moreover, the student will acquire solid knowledge on micro (equation of state, opacity, electron degeneracy, nuclear reactions) and macro (rotation, mass loss, convective transport, chemical evolution) physics driving the formation and the evolution of stellar structures. This knowledge will allow the students to fully understand the hydrogen-, helium-burning and advanced evolutionary phases for low-, intermediate- and massive stars. The student will be able to fully exploit the fundamental plane for stars (Hertzsprung Russell diagram) to trace the different evolutionary phases and its use to understand resolved stellar populations.
Applying Knowledge and Understanding:The student at the end of the semester will acquire the knowledge of stellar evolution physics to attack and solve a broad range of stellar astrophysical problems. To be more specific, the student will be able to estimate the absolute and relative age of globular clusters, to estimate the chemical abundances (primordial helium, metallicity) and to measure cosmic distances by using primary distance indicators. Moreover, the student will have a detailed knowledge of the impact that intrinsic and systematic errors affect the estimate of astrophysical and cosmological parameters.
PrerequisitesIt is mandatory that the student has a solid knowledge of quantum mechanics (interaction between matter and radiation, cross sections, nuclear reactions, Boltzmann and Saha equations) and of solid state physics (electron degeneracy, Debye radius, Coulomb effect, crystallization). It is important that the student has already acquired some knowledge of the numerical methods adopted to solve differential equations. It would be also quite useful that the student has already been exposed to a course of radiative transfer focussed on the formation of stellar spectra.
Program1. Stellar Structures: empirical scenario 1.1 Galactic spheroid 1.2 Stellar Populations 1.3 Stellar systems 1.4 Metallicity distributions 1.5 Kinematic properties 2. Stellar Structures: theoretical framework 2.1 Momentum conservation 2.2 Mass conservation 2.3 Radiative and conductive transport equations 2.4 convective trasport equation: Schwarzschild and Ledoux criteria 2.5 Mixing length theory 2.6 Energy Conservation 2.7 Stellar envelopes and atmospheres 3. Physical conditions in stellar interiors 3.1 Equation of state 3.2 Radiative and molecular opacities 3.3 Energy generation 3.4 Nuclear reactions 4. Solutions of the equations for stellar interiors 4.1 Analytical solutions 4.2 Virial theorem and electron degeneracy 4.3 Initial conditions and boundary conditions 4.4 Saha equation and evolution of chemical elements 5. Star formation 5.1 Jeans mass and star formation 5.2 Strutture stellari completamente convettive: Hayashi track 5.3 Approch to the central hydrogen burning phase 6. Hydrogen burning phases 6.1 The p-p chain 6.2 The bi-cycle CN-NO 6.3 The Main Sequence (MS) in low-, intermediate- and massive stars 6.4 Standard solar model 6.5 The Mass-Luminosity relation 6.6 The SchoËžnberg-Chandrasekhar limit 6.7 The sub giant branch and the red giant branch (RGB) 6.8 The RGB bump 6.9 The Tip of the RGB and the central Helium flash 7. Helium burning phases 7.1 Nuclear reactions 7.2 The Zero Age Horizonthal Branch (ZAHB) 7.3 Central Helium burning phase in low-, intermediate- and massive stars 8. Advansed evolutionary phases 8.1 Asymptotic giant Branch (AGB) 8.2 Chandrasekhar limit 8.3 Carbon/Oxygen and helium core white dwarfs 8.4 Advansed evolutionary phases in massive stars: Supernovae 9. Stellar observables of cosmological interest 9.1 Primordial helium content 9.2 Absolute and relative ages of globular clusters 9.3 The Cepheid instability strip 9.3 Primary and secondary distance indicators 9.4 The Hubble constant
Description of how the course is conductedThe two main modules of the course (basic physics of stellar interiors, different stellar evolutionary phases) rely on frontal teaching. The course requires the knowledge of a broad range of basic physical principles. To help the students in understanding the physical assumptions adopted to construct a stellar evolution model the course is entirely given to the blackboard, i.e. without the support of powerpoint presentations. The students, concerning the written report are requested to attend a few tutorials to introduce them to the web sites from which they can download either data (space, ground based) or evolutionary prescriptions. Moreover, they are introduced to the different methods adopted to propagate the errors (intrinsic systematic) affecting the estimate of astrophysical/cosmological parameters.
Description of the didactic methodsSee point above. Students are requested to attend the lectures given during the semester. Moreover, they are also requested to attend the lectures focussed on the project they have to prepare for the final exam.
Description of the evaluation methodsThe final exam is based on two independent types of learning assessment. a) An oral exam aimed to verify the knowledge of stellar evolution physics that the student accomplished during the semester. In particular, it is requested a detailed knowledge of micro (equation of state, opacity, electron degeneracy, nuclear reactions) and macro (rotation, mass loss, convective transport, chemical evolution) physics driving the formation and evolution of stellar structures. Moreover, it is also requested to know how and when these physical mechanisms affects hydrogen, helium and advanced evolutionary phases of low-, intermediate and massive stars. The student is also requested to master the mapping of the different evolutionary phases in the fundamental plane of stellar structures (Hertzsprung Russell diagram, color-magnitude diagram). b) Report of a project written either alone or in a small group aimed at verifying that the student understood stellar evolution physics and that he is able to attack and to solve stellar astrophysics problems. The proposed projects range from the estimate of absolute and relative globular cluster ages, to the estimate of primordial helium abundance and/or metallicity, to the determination of cosmic distances using primary distance indicators. A key issue in the evaluation of the project is the knowledge that the student accomplished in the estimate of astrophysical/cosmological parameters and the impact that intrinsic and systematic errors have on their determination. The final evaluation of the exam is based on tests a) and b) together with the participation to the lectures and to the project.
Adopted TextbooksEvolution of Stars and Stellar Populations by Salaris & Cassisi Old Stellar Populations by S. Cassisi & M. Salaris, Wiley-VCH Stellar Interiors, by C.J. Hansen, S.D. Kawaler & V. Trimble, Springer
Recommended readingsPhysics, Formation and Evolution of Rotating Stars by A. Maeder, Springer Stellar Structure and Evolution by R. Kippenhahn, A. Weigert, A. Weiss, Springer Stellar Evolution Physics: Physical processes in stellar interiors (vol. 1); Advanced evolution of single stars (vol. 2) by I. Iben, Cambridge University Press