Detailed Outline of Graduate Program Core Curriculum

Astronomy 30100: Astrophysics I

1. Introduction to Stars (Physical)

Hydrostatic equilibrium. Estimates for stellar pressures and temperatures.
Photon diffusion, scattering, and stellar luminosities.
Stellar timescales: nuclear, Kelvin-Helmholtz, free-fall.
Virial theorem and its consequences.
Theoretical Hertzsprung-Russell diagram. Upper and lower main sequence.

2. Introduction to Stars (Observational)

Determinations of stellar properties: d, L, M, R, g, T_e, abundances.
Magnitudes and bolometric corrections; colors; spectral classification; color-magnitude diagram. Stellar populations.

3. Hydrodynamics of Self-Gravitating Fluids

Kinetic theory of dilute gases: Boltzmann equation.
Ideal hydrodynamics: Euler equation. Sound waves. Jeans instability and gravitational contraction.
Viscous hydrodynamics: Navier-Stokes equation.

4. Statistical Mechanics and Equations of State

Quantum statistics: distribution functions. Ideal gases, radiation.
Degenerate fermions: white dwarfs; Chandrasekhar limit. Neutron stars.
Ionization equilibrium: Saha equation. Debye screening.

5. Energy Transport in Stars

Radiative transfer; interiors vs. atmospheres.
Opacity: scattering and absorption processes. Rosseland mean.
Conduction.
Convection: Schwarzschild criterion. Mixing length theory. Turbulence and dissipation.

6. Nuclear Reactions in Astrophysics

Binding energy per nucleon. Isotopic abundances. H and He burning.
Cross sections. Coulomb barrier penetration. Non-resonant and resonant reactions.
Nuclear reaction rates: pp, CNO cycles. Advanced burning stages.

7. Stellar Models

Polytropes. The standard model. Convective equilibrium. Homology.
Numerical methods: computation of ZAMS structure.
The Sun: solar neutrino problem. Stellar pulsations: helioseismology.

8. Advanced Topics

Stellar Rotation.
Magnetic Fields: MHD. Stellar dynamos.

Astronomy 30200: Astrophysics II

1. Star Formation

Virial equations and dynamical collapse.
Jeans length and mass, collapse solutions for rotation, magnetic fields, external pressure.
Angular momentum problem, angular momentum transport, magnetic braking.
Evolution of protostars.

2. Main Sequence Evolution

Summarize equations of stellar structure. Include internal and gravitational energy.
PP chains. CNO cycles: solar neutrinos.
Convection. Hydrogen-ionization zone. Surface boundary conditions. Surface Li abundances.
Results of numerical solutions for homogeneous stars, with emphasis on physical properties.

3. Post-Main Sequence Evolution

Shell hydrogen burning, properties of giant stars.
Core helium burning, hydrogen shell burning. Properties of horizontal branch stars.
Adiabatic pulsations of a spherical star. Pulsational properties of RR Lyra and Cepheid variables.
Shell helium burning, helium flashes.
Dynamical instabilities of luminous, massive stars.
Late nuclear burning stages of massive stars. Nucleosynthesis.

4. Degenerate Stars, Supernovae

Compact stars, onset of degeneracy, relativity parameter, limiting mass.
Dynamical stability of white dwarfs and neutron stars, general relativistic effects, equation of state.
Neutronization, pion condensation, neutron drip, neutron star structure.
Evidence for M and R from pulsars and X-ray sources.
Supernovae of Types I and II.
Shock waves, evolution of SNR in a homogeneous medium.

Astronomy 30300: Astrophysics III

1. Interstellar Medium

Cold, dense gas: 21-cm and molecular observations, optical and UV absorption lines, depletion.
Dust: physical properties of grains, grain growth and destruction in the ISM, grain rotation and alignment. Dust opacity and the extinction curve. Infrared emission from dust. Scattered light from dust. Dust polarization by scattering and by dichroic emission/absorption.
Stromgren spheres. H II regions: ionization structure with and without dust, thermal structure.
Two-phase ISM, energy balance, thermal stability.
Evaporation, expansion of SNR in three-phase ISM.
Cosmic rays, Fermi acceleration.
Cosmic dynamos.

2. Collisionless Systems

Relaxation time.
Vlasov equation. Continuity equation. Jeans equation. Oort limit.
Tensor and scalar virial equation. Expansion of the universe.
Jeans mass. Galaxy formation. Fragmentation.

3. Distribution of Stars in the Solar Neighborhood

Fundamental equation of stellar statistics: luminosity function, density function.
Density perpendicular to the plane - Oort limit.
Initial luminosity/mass function.

4. Stellar Kinematics/Dynamics

Solar motion
Peculiar velocities: velocity ellipsoid, high velocity stars, statistical parallax.
Stellar populations as summary of much of above - chemical abundances - ages of clusters.
Galactic rotation: optical. Oort's A and B, radio rotation curves.
Evidence for dark matter in our galaxy and others.
Perturbations from galactic rotation.

5. Perturbations from galactic rotation.

Morphological classifications: Hubble, Morgan.
Determination of Ro.
Spiral structure: optical, radio, reasons for disagreement, density waves.
Gas in the halo - high velocity clouds - Magellanic stream - infall.
Chemical abundance gradients in disk and halo.
Chemical abundances in stars and gas.

6. Galactic Structure and Evolution: Theory

Models such as Bahcall and Soneira.
Dynamical models of galactic evolution.
Chemodynamic models of galactic evolution.

Astronomy 30400: Astrophysics IV

1. The observed universe

The cosmological distance scale
The cosmological principle
The expansion of the universe, Hubble's law, the deceleration parameter, the cosmological constant
The large-scale distribution of matter, clustering properties
The age of the universe, relationship to the Hubble constant, nucleocosmochronology, stellar evolution
Cosmic background radiations: diffuse x-ray background, cosmic microwave background
Light element abundances
The mass density of the universe

2. The universe at high redshift: quasars, lyman-alpha systems, early stages of galaxy evolution

3. The microwave background radiation as a probe of the early universe: isotropy, spectrum, decoupling, re-ionization.

4. Relativistic homogeneous isotropic cosmologies

A Newtonian picture of expansion.
The Friedmann--Robertson--Walker metric, the scale factor, co-moving coordinates
The Friedmann equation, the expansion rate
Solutions to the Friedmann equation for a radiation-dominated and matter-dominated universe: age-redshift relations, horizons

5. Evolution of structure in the universe

The power spectrum and the autocorrelation function
The Jeans instability in an expanding universe
Departures from the perfect-fluid approximation: recombination, Silk damping, free streaming
Growth in the non-linear regime

6. Primordial nucleosynthesis

Astronomy 30500: Radiative Processes in Astrophysics

1. Fundamentals of Radiative Transfer

E & M spectrum, radiative flux, specific intensity.
Principles of radiative transfer. Radiation field. Equation of transfer. Formal solution.
Emission and absorption of radiation. Einstein coefficients. Maser emission. Thermodynamic equilibrium. Blackbody radiation. Kirchhoff's law.
Scattering effects. Radiative diffusion.

2. Theory of Stellar Atmospheres

Model stellar atmospheres: the structure, radiative transfer, and radiative equilibrium calculations for a trial (R)$ relation.
Moments of the transfer equation. The Eddington approximation. Lambda iteration.
The gray atmosphere.
Results of numerical LTE solutions for non-gray cases.
Transfer with spectral-line opacity. Abundances.

3. Basic Theory of Radiation Fields

Maxwell's equations. Plane waves. Spectral synthesis.
Polarization and Stokes parameters.
Geometrical optics limit.
Radiation from moving charges: Lienard-Wiechert potentials, non-relativistic radiation limit, radiation reaction.
Thomson scattering.
Relativistic covariance and kinamatics: Lorentz transformations, covariance, fields of uniformly moving charges, emission from accelerated relativistic particles.

4. Continuum Emission Processes

Bremsstrahlung: single-speed electrons, thermal free-free emission, relativistic electrons, free-free absorption.
Synchrotron radiation: total power, spectra, polarization, self-absorption.
Compton Scattering: fundamental processes, inverse-Compton spectra, the Compton Y parameter, the Kompaneets equation, repeated scattering

5. Atomic and Molecular Emission

Atomic Structure: energy levels, spin-orbit coupling, Zeeman splitting, the Saha equation.
Radiative transitions: semi-classical theory, the dipole approximation, selection rules, bound-free transitions, radiative recombination, line broadening.
Molecular structure. The Born-Oppenheimer approximation. Electronic-rotational-vibrational spectra.

6. Plasma Effects

Model of a cold electron plasma. The plasma frequency. Index of Refraction. Pulsar dispersion measure.
Wave propagation in a magnetized plama. Faraday rotation and depolarization.
Plasma effects in high-energy emission processes: Cherenkov radiation and the Razin effect.

Astronomy 30600: Radiation Measurements in Astrophysics

1. Radiation Theory

EM Waves and photons
Blackbody radiation
Atomic Interactions

2. Light and Image Formation

How images are formed
Fresnel diffraction theory
Near field, far field regions
Fraunhoffer diffraction

3. Signal Processing Theory

Random fields
Correlation functions
Orthonomal functions
Fourier functions
Probability theory/Bayesian statistics/Jaynes
Convolution and deconvolution

4. Collecting Photons

Basic optics
Aberration theory
Telescope design
Atmospheric turbulence and adaptive optics

5. Analyzing Light

Design of spectrographs
Photon detectors
How CCDs work

6. Photometry

Stellar magnitudes
Atmospheric absorption
Background radiation

7. Radio Astronomy

Van Cittert equation
Radio Interferometry