First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SCM0014352, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2015/16

Information on the course unit
Degree course First cycle degree in
SC1160, Degree course structure A.Y. 2008/09, A.Y. 2017/18
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Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination ASTROPHYSICS 2
Website of the academic structure
Department of reference Department of Physics and Astronomy
Mandatory attendance
Language of instruction English

Teacher in charge PAOLA MARIGO FIS/05

Course unit code Course unit name Teacher in charge Degree course code

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses FIS/05 Astronomy and Astrophysics 6.0

Mode of delivery (when and how)
Period Second semester
Year 3rd Year
Teaching method frontal

Organisation of didactics
Type of hours Credits Hours of
Hours of
Individual study
Lecture 6.0 48 102.0 No turn

Start of activities 26/02/2018
End of activities 01/06/2018

Prerequisites: Elements of plane trigonometry, derivatives, integrals, basic knowledge of physics relating to previous courses.
Preparatory courses: Astronomy I (two years) and Astronomy II (model A, third year).
Target skills and knowledge: This course aims at providing the students with the fundamental elements of the structure and evolution of stars, from their birth to their final stages.
Examination methods: Oral/written examination on all topics covered during the course.
Assessment criteria: Assessment of understanding and mastery of the topics.
Course unit contents: 1. Introduction and overview.
Observational constraints, the H-R diagram, mass-luminosity and mass-radius relations, stellar populations and abundances.
2. Hydrostatics, energetics and timescales.
Derivation of three of the structure equations (mass, momentum and energy conservation). Hydrostatic and thermal equilibrium. Derivation of the virial theorem and its consequences for stellar evolution. Derivation of the characteristic timescales of stellar evolution.
3. Equation of state (EoS).
Local Thermodynamical equilibrium. General derivation of n, U, P from statistical mechanics. Limiting cases: ideal gas, degeneracy. Mixture of gas and radiation. Adiabatic processes. Ionization (Saha equation, consequences for thermodynamic properties).
4. Energy transport in stellar interiors.
The 4th equation of stellar structure: the energy transport equation.
Diffusion approximation for radiation transport. The radiative temperature gradient . Opacity. Eddington luminosity. Convection: Derivation of stability criteria (Schwarzschild, Ledoux) .Convective energy transport: order-of-magnitude derivation. Mixing-length theory.
5.Nuclear reactions.
Nuclear energy generation (binding energy). Derivation of thermonuclear reaction rates (cross sections, tunnel effect, Gamow peak). Temperature dependence of reaction rates .Nuclear burning cycles: H-burning by pp-chain and CNO-cycle. He burning by 3-alpha and alpha+C reactions. Advanced burning reactions.
6. Stellar evolution equations.
Overview, time/space derivatives, limiting cases. Boundary conditions and their effect on stellar structure. How to obtain solutions.
7. Simple stellar models.
Polytropic models.Homology relations: principles, derivations, application to contraction and the main sequence. Stability of stars: derivation of simplified criteria for dynamical and secular stability.
8. Schematic evolution from the virial theorem (VT).
Evolution of the stellar centre combining the VT and the EoS: evolution tracks in terms of (P,rho) and (T,rho). Evolution towards degeneracy or not. The Chandrasekhar mass, low-mass vs massive stars . Critical ignition masses, brown dwarfs, nuclear burning cycles.
9. Detailed evolution: towards and on the main sequence.
Simple derivation of Hayashi line, pre-MS evolution tracks properties of the ZAMS: M-L and M-R relations, occurrence of convection zones evolution across the MS band: structural changes, low-mass vs high-mass, effects of overshooting.
10. Post-MS evolution.
The Schoenberg-Chandrasekhar limit, the mirror principle. H-shell burning: Hertzsprung-gap, red giant branch, first dredge-up. He-burning: horizontal branch, loops, Cepheids. RGB mass loss.
11. Late evolution of low- and intermediate-mass stars.
The Asymptotic Giant Branch: thermal pulses, 2nd/3rd dredge-up, mass loss, nucleosynthesis. White dwarfs: structure, non-ideal effects, derivation of simple cooling theory.
12. Pre-SN evolution of massive stars.
Importance of mass loss across the HRD (O stars, RSG, LBV and WR stars). Modern evolution tracks. Advanced evolution of the core: nuclear burning cycles and neutrino losses, acceleration of core evolution. Pre-SN structure
13. Explosions and remnants of massive stars.
Evolution of the core towards collapse: Fe-disintegration, electron captures, role of neutrinos supernovae. Observed properties and relation to massive star evolution. Limiting masses for neutron star and black hole formation, dependence on mass loss and metallicity.
Planned learning activities and teaching methods: Lectures, with use of both classical methodology (lectures at the blackboard) that the media (slides, movies, applets, web-interfaces for the on-the-fly generation of stellar models).
Additional notes about suggested reading: Slides and other material available in electronic format to the students.
Textbooks (and optional supplementary readings)
  • M. Salaris & S. Cassisi, Evolution of Stars and Stellar Populations. --: John Wiley & Sons, 2005. Testo consigliato, non obbligatorio. Puo' essere consultato presso l'ufficio del docente. Cerca nel catalogo
  • C.J. Hansen, S.D. Kawaler & V. Trimble, Stellar Interiors. --: Springer-Verlag, 2004. Testo consigliato, non obbligatorio. Puo' essere consultato presso l'ufficio del docente. Cerca nel catalogo
  • R. Kippenhahn & A. Weigert, Stellar Structure and Evolution. --: Springer-Verlag, 1990. Testo consigliato, non obbligatorio. Puo' essere consultato presso l'ufficio del docente. Cerca nel catalogo
  • D. Prialnik, An Introduction to the Theory of Stellar Structure and Evolution. --: Cambridge University Press, 2009. Testo consigliato, non obbligatorio. Puo' essere consultato presso l'ufficio del docente. Cerca nel catalogo