Università Roma Tre

Stellar Observations
Magnitude of a star. Brightness intensity. Apparent and relative magnitude. Black body spectrum. Wien and Stefan-Boltzmann laws. The colors of stars. Optical Depth. Radiation transport equation. Eddington-Barbier approximation. Gray atmosphere. Definition of photosphere and effective temperature. Hertzprung-Russell and Color-Magnitude diagrams. Stellar spectra. Saha and Boltzman equations. Hydrogen lines. Balmer's discontinuity. Spectral Types.

Radiation and opacity transport.
Electromagnetic radiation. Relation between energy radial flux and temperature gradient. Opacity and free path of photons. Rosseland's average opacity coefficient. Photon absorption mechanisms: bound-bound, , bound-free, and free-free. Kramer's opacity. Thomson scattering. Electronic conduction. Relative importance of the various types of opacity in the density-temperature plan.

Convection in the stars.
Convective instability. Schwarzschild and Ledoux criteria for convective instability. Main causes for establishing convective instability. Convection efficiency. The "Mixing Length Theory" and the free parameter alpha. Convection-related uncertainties. Free parameter calibration. Problems related to turbulence and non-local nature of convection.

State equation
Equation of state for stellar interiors. Ideal gas and radiation pressures. Electron degeneracy. The role of the Pauli Principle. The Fermi momentum. Partial and complete degeneracy. Equation of state for degenerate gas in the relativistic and non-relativistic case. Crystallization. Neutronization. Relative importance of the various types of pressure in the density-temperature plane.

Generation of nuclear energy
Nuclear reactions. Mass defect. Tunnel effect. Resonances. Cross sections. Rate of nuclear reactions.
Nuclear energy generation coefficient. Gamow Peak. Functional dependence of the rate of nuclear reactions on the temperature. Electrons screening. The proton-proton chain. The CNO cycle and the relative equilibrium. The 3α reactions.

The equations of stellar structure
Equilibrium equations of the star. Mass Conservation. Expression and physical significance of the gravitational energy generation coefficient. Energy conservation. Hydrostatic balance. Energy transport. Neutrinos energy. Treatment of atmospheric layers. Stellar structure equations in adimensional form.

The birth of the stars and early evolutionary phases
The Virial theorem. Jeans criterion for collapse. The Jeans mass. Hierarchical fragmentation. Radiative cooling. Isothermal and adiabatic collapse. Accretion disks and disk structure. Energy balance during the accretion phase. Protostars. Hayashi theory for pre-main sequence stars. Hayashi lines and their physical meaning. Stratification of entropy into radiative and convective stars. Pre-main sequence evolutionary tracks in the HR diagram. The Kelvin-Helmotz time scale. The Palla &
Stahler model. Evolution of the core in hydrostatic equilibrium. The "birthline”. Pre main sequence lithium burning. Lithium in stars belonging to young associations. The mass limit for the ignition of hydrogen burning. Brown dwarfs and giant planets. The role of electronic degeneracy. "Disk-locking" and magnetic braking.

Core hydrogen burning
Main sequences (MS) of open and globular clusters. Mass-Luminosity relation for MS stars. The shape of the Zero Age Main Sequence (ZAMS). Lower and upper limit for the mass of MS stars. Structure of MS stars of different mass: the extension of convective and radiative zones. Mass limit for proton - proton and CNO burning. The role of the formation of molecular hydrogen in the external regions of the stars on the ZAMS Morphology. Main sequences observed in globular and open clusters: interpretation. Evolutionary tracks of main sequence stars. Theoretical uncertainties about the evolution of MS stars: overshooting from the core, temperature gradient in convective envelopes.

The red giant stage
Post-MS evolution. Giant expansion. The Schonberg-Chandrasekhar instability. Degeneracy of the helium core in low mass models. First dredge-up: causes and effects. Extension of the convective envelope of the stars according to the effective temperature. Luminosity functions. Bump of the luminosity function during the giant phase. Evolution of low-mass stars up to the red giant tip. The role of the CNO shell. Core mass - luminosity relationship for low-mass stars. The role of neutrinos for the determination of the temperature peak. Helium Flash. Flash thermodynamics. The role of electron degeneracy. Mini-flash episodes. Comparison of pre- and post-flash thermodynamic structures. Horizontal branch evolution: evolutionary tracks towards the blue and the red side of the HR diagram. The role of helium. Interpretation of the horizontal branches of globular clusters: the role of age and mass loss. Helium burning in non degenerate stars. "Blue loop" in the HR diagram.

Asymptotic branch evolution
Second dredge-up. Degeneracy of carbon and oxygen core. Double shell nuclear burning. Thermal instability of the thermal pulse. Asymptotic Giant branch evolution. Luminosity - core mass relationship for AGB Stars. "Hot Bottom Burning" and Third Dredge-up. Llithium-rich stars. Carbon stars. Changes in the surface chemistry of AGB stars of different mass. Super-AGB evolution: Convective flame and the formation of a core of Oxygen and Neon. Dust production during the asymptotic giant branch phase. Interpretation of the observational diagrams of evolved stellar populations in the Magellanic Clouds.

White dwarf
Late stages of evolution of stars of small or intermediate mass. The Planetary Nebula evolution. Chandrasekhar's theory for white dwarf stars. Structural properties of white dwarfs: mass-radius relationship. Energy balance of white dwarfs. Luminosity of White Dwarfs. Cooling theory.

Variable stars
Stellar variability: historical introduction. Radial oscillations. Period of propagation of an acoustic perturbation. The comparison between variable stars and thermal machines. Mechanisms ε and k for the production of the ‘driving’ mechanism of pulsations. Hydrogen and helium partial ionization zones as drivers of star variability. Distribution of variable stars in the HR diagram, and its interpretation. Strips of instability. Cepheid and RR Lyrae Variables: Evolutionary Stage, and Period-Luminosity relationships.


Stellar clusters
The spatial distribution of stellar clusters across the Milky Way. Distribution of stars in clusters in the color-magnitude plane. Differences between open and globular clusters. The isochrone fitting method: turn-off magnitude as distance and age indicator. Reddening and extinction. Impact of metallicity on the color of the main sequence of star clusters. Interpretation of the horizontal branches of globular clusters. Chemical anomalies in globular clusters stars. Oxygen-sodium and magnesium-aluminum anti-correlations. Photometric evidence of the presence of one or more stellar components enriched in helium. The AGB scenario for the formation of multiple populations in globular clusters.


Massive stars evolution
The final stages of the evolution of massive stars: LBV and Wolf-Rayet stars. Supernovae: Supernovae observations of types Ia, Ib, Ic and II. Post-carbon evolutionary phases: formation of a degenerate core. Collapse of the core. Core photo-disintegration .Explosive Mechanisms.

Title: Stellar structure and evolution
Authors: Kippenhahn, Weigert
Springer-Verlag 1990

Title: Introduction to stellar Astrophysics (vol. 2)
Author: E. Bohm-Vitense
Cambridge University Press 1992

Title: Introduction to stellar Astrophysics (vol. 3)
Author: E. Bohm-Vitense
Cambridge University Press 1992