ASTROPHYSICS 2

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.