#### Candidacy Topic - Astronomy and Astrophysics

**Introduction:** The following list of topical areas and subtopics covers the areas of astronomy and astrophysics which students are expected to have some mastery of. This is a very broad research area and examinees are not expected to be deeply knowledgeable in all topics. Typically they should be somewhat knowledgeable of topics well removed from their research area(s), and fairly knowledgeable about all topics of close relevance to their research area. The examining committee and student may, after consultation, refine and focus this list.

**Basic Observational Astronomy:** Celestial sphere, coordinates, photometric systems, magnitude equation, distance modulus, extinction, parallax, spectral types, telescopes, resolution, basic spectrometer properties, HR diagram

**Radiation Processes:** radiative transfer terms definition and usage, the fundamental equation of radiative transfer, definition of source function and optical depth, electromagnetic spectrum regions, blackbody radiation, Einstein A and B coefficients, Maxwell equations and electromagnetic waves, power emitted from accelerated charges (amount, angular pattern, and polarization), Four vectors, covariance, relativistic transformations involving E and B fields, free-free emission (bremstrahlung), bound-free (photo-electric effect) and free-bound processes and spectra, cyclotron and synchrotron radiation, Compton scattering (cross section and effect on spectrum), inverse compton scattering, pair creation and annihilation, plasma effects of rotation measure and dispersion measure, basic atomic structure of single-electron and multi-electron atoms spectroscopic notation, definitions of permitted and forbidden emission lines, line broadening (natural, thermal, and collisional), energy levels of diatomic molecules, symmetries, rotation-vibration spectra of molecules.

**Stellar Atmopheres:***Energy Transport:* Conductive, radiative and convective energy transport and conditions for each, basic thermodynamics

*Stellar Continua:* Sources of continuous opacity, Saha equation, shapes of stellar continua, changes with temperature, gravity, metallicity, limb darkening, line blanketing

*Model Photospheres:* Hydrostatic equilibrium, radiative equilibrium, plane parallel assumption, LTE, a schematic understanding the structure is calculated and what is needed to specify the structure

*Spectral Lines:* Boltzmann equation, Gaussian and Lorentz profiles, Voigt function, line broadening mechanisms and what they diagnose about a stellar atmosphere, equivalent width, Zeeman effect, contribution function, curve of growth, behavior of spectral lines with temperature, gravity, and metallicity, line blanketing

*Advanced Topics:* Determining fundamental stellar properties (temperature, radii, abundance, rotation), basics about NLTE (when it is important, first order effects), stellar winds and the formation of a PCygni profile

**Stellar Structure:***Equations of Stellar Structure:* Basic hydrodynamics, hydrostatic equilibrium, mass continuity, energy generation, radiative transport, convective transport, required constitutive relations

*Homologous Models & Polytropes:* Homologous relations, definition and examples of polytropes

*Nuclear Energy Generation:* P-P chain and its properties, triple-alpha reaction, CNO cycle and its properties, minimum mass for hydrogen fusion and brown dwarfs, He fusion and beyond, iron catastrophe

*Pre-Main Sequence Stellar Evolution:* Hertzsprung-Russell diagram, Jeans mass and Radius, Pre-main sequence evolutionary tracks, accretion disk diagnostics, feedback into the interstellar medium

*Post-Main Sequence Stellar Evolution:* Evolution of low mass stars including formation of planetary nebulae and white dwarfs, evolution of high mass stars to supernova and neutron star or black hole formation

**Compact Objects:***Special Relativity:* Relativistic kinematics, Lorentz transformations, Lorentz invariants and covariance

*General Relativity:* curvature, geodesics, classic experimental tests, black holes, Schwarzschild radius, redshift, gravitational waves

*Post-Main Sequence Stars:* quantum degeneracy pressure in white dwarfs and neutron stars, mass-radius relationship, Chandrasekhar and neutron star mass limits

*Accreting Systems:* Eddington luminosity and mass accretion limit, Bondi accretion, Shakura-Sunyaev alpha disks

**Nebular Astrophysics and the Interstellar Medium***Physical Processes:* Collisions, charge Exchange, photoexcitation, decay, fluorescence, photoionization, recombination, collisional ionization, energy levels, collisional excitation and deexcitation

*Forbidden Lines:* critical density and excitation, optical depth, examples

*HII Regions:* Stromgren sphere, inclusion of dust, overall spectrum, temperature, abundances, simple applications

*Planetary Nebulae:* Formation, excitation, spectrum

*Dynamics:* Kepler’s Laws, virial theorem, fluid equations, instabilities, shocks and ionization fronts, gravitational collapse, simple applications

*ISM:* Phase of the ISM, dispersion and rotation measures

*Supernova remnants:* dynamics, Sedov phase, line spectroscopy, cosmic ray production

**Normal and Active Galaxies:***Galaxy phenomenology:* Discovery of galaxies, Shapley-Curtis debate, Hubble’s classification scheme

*Spiral galaxies:* structure of the Milky Way, the Galactic center region, velocity dispersions, rotation curves, dark matter inferences, Tully-Fisher relation, spiral structure, density wave theory

*Elliptical Galaxies:* triaxiality, subclasses of ellipticals, Faber-Jackson relation, King’s model, gravitational relaxation, gas cooling

*Active Galaxies:* Seyfert galaxies, broad and narrow emission line regions, reverberation mapping, Lyman-alpha forest, radio galaxies, lobes and hot spots, VLBI, unification schemes

*Extragalactic Jet systems and Microquasars:* quasar and blazar phenomology, superluminal motion, Doppler boosting, shock acceleration

**Structure of the Universe and Cosmology:***Cosmic structures:* distance determination techniques, Hubble’s Law, galaxy distributions, galaxy clusters, supernova surveys, large scale structure, gravitational lensing

*Newtonian cosmology:* Olber’s paradox, the cosmological principle, cosmochronology – dating the universe, Friedmann’s equation and solutions, critical density, matter-dominated universes

*Relativistic cosmology:* Robertson-Walker metric, radiation and cosmological constant in Friedmann’s equation, global solution for our universe, particle horizons

*Observational cosmology:* deceleration parameter, angular diameter and luminosity distances, cosmological determinations using supernovae

*Early universe:* cosmic microwave background anticipation and discovery, COBE and WMAP results and implications, acoustic oscillations and gravitational seed perturbations, recombination, redshift of last scattering, primordial nucleosynthesis, inflation, GUT era.