II Astrophysics

In Part II (3rd year undergraduate), I chose to study Astrophysics rather than Physics. Cambridge Astrophysics consists of 8 compulsory lecture courses and the CATAM (computational coursework shared with maths students).

For all of the courses except Cosmology and Topics in Astrophysics, I made handwritten notes based on the lectures. Closer to the exams, I typed up the notes into RemNote, which automatically generates spaced-repetition flashcards.

The RemNote documents (which can be viewed as flashcards by clicking “Test yourself on these rem”) are linked here.

• Stellar Structure and Evolution
  • Stellar measurements: distances, spectra, binary systems
  • Stellar atmospheres: temperature, opacity, curve of growth
  • Stellar radiation: virial theorem, nuclear energy generation, nucleosynthesis
  • Energy transport: Eddington equation for radiative equilibrium, Schwarzschild criterion
  • Stellar models: structure equations and homology
  • Star formation: protostars, pre-main sequence
  • Evolution on the main sequence
  • Post-MS evolution of solar-mass stars
  • White Dwarfs: degeneracy pressure, ageing
  • Post-MS evolution of Massive Stars: winds, supernovae
  • Close binary systems
• Principles of Quantum Mechanics
  • Hilbert space: properties, continuum states, operators, postulates of QM
  • Transformations: generators, translations, rotations, parity, time evolution
  • Angular momentum: ladders, spin, orbital angular momentum, addition
  • Harmonic oscillator: ladders, time evolution, radial Hamiltonian
  • Identical particles
  • Time-independent perturbation theory: degenerate case, fine structure of hydrogen/helium, Stark effect
  • Time-dependent perturbation theory: interaction picture, ionisation
  • Interpreting QM: density operator, Von Neumann entropy, entanglement, Bell’s inequalities
• Statistical Physics
  • Fundamentals of statistical physics: partition functions etc
  • Classical gases: Maxwell distribution, interacting gases
  • Quantum gases: photon and phonon gas
  • Bose-Einstein distribution
  • Fermi-Dirac distribution
  • Classical thermodynamics: laws of thermodynamics, Carnot engines
  • Phase transitions: van der Waals liquids, Clausius-Clapeyron, critical exponents
  • Ising model: mean field theory, Landau theory
• Topics in Astrophysics
  • Timescales and distributions
  • Tides: tidal capture, tidal disruption, the origin of the moon, evolution of clusters.
  • Planets: the solar system, exoplanets, exoplanet detection,
  • Protoplanetary disks: disk dynamics, disk heating, disk evolution
  • Planet formation: planetesimals from dust, planets from planetesimals
• Stellar Dynamics and the Structure of Galaxies
  • Orbits: dynamics, Keplerian orbits, general radial orbits,
  • Poisson’s equation: Gauss’ theorem, galaxy profiles, near-circular orbits
  • Axisymmetric potentials: near-circular orbits, spherical coordinates (Legendre polynomials), cylindrical coordinates (Bessel functions), Oort constants, rotation curves.
  • Collisionless systems: gravitational drag, the collisionless Boltzmann equation, Jeans equations, virial theorem
  • Jeans theorem and self-consistent models
  • Clusters: isothermal sphere, anisotropic velocity distributions, cluster evolution
• Relativity
  • Special relativity: Lorentz boosts, spacetime diagrams, velocity and acceleration
  • Manifolds and coordinates: Riemannian manifolds, local Cartesian coordinates, vector algebra
  • Tensor calculus: metric tensor, covariant derivatives, intrinsic derivatives
  • Minkowski spacetime: 4-vectors, dynamics
  • Electromagnetism: Maxwell tensor, coordinate-free Maxwell equations
  • Spacetime curvature: weak-field limit, intrinsic curvature, Riemann curvature tensor, geodesics
  • Einstein field equations: energy-momentum tensor, weak-field limit, Schwarzschild solution, geodesics in Schwarzschild spacetime
  • Orbits: Lagrangian, orbit equation under the Schwarzschild metric, deflection of light
  • Schwarzschild black holes: causal structure, Eddington-Finkelstein coordinates
  • Cosmology
• Astrophysical fluid dynamics
  • Fluid equations: fluid element, Eulerian vs Lagrangian pictures, conservation laws, gravitation
  • Equations of state: barotropic fluid, adiabatic fluid, the energy equation, astrophysical heating/cooling
  • Stellar fluids: hydrostatic equilibrium, polytropes, scaling relations
  • Sound waves: linear perturbation analysis, shocks, Rankine-Hugoniot conditions, supernova blastwaves
  • Bernoulli’s equation: Bernoulli’s principle, Helmholtz equation, Kelvin vorticity, De Laval nozzle, spherical accretion
  • Fluid instability: convective instability, Jeans instability, interface instability (Rayleigh-Taylor and Kelvin-Helmholtz), Thermal instability
  • Viscous flows: shear viscosity, Navier-Stokes equation, energy dissipation
  • Accretion disks: rotating frames, evolution, steady-state
  • Plasmas: ideal MHD, magnetorotational instability
• Cosmology
  • FRW cosmology: Friedman equations, particular cosmologies, the CMB
  • Age and size of the universe: redshift, distances, horizons
  • Thermal history: statistical weight, neutrino temperature, Big Bang nucleosynthesis, recombination
  • Dark matter: evidence for dark matter, MACHOs
  • Dark energy
  • Fluctuations: power spectra, sound horizon, baryon acoustic oscillations
  • Inflation: horizon problem, scalar fields, e-foldings, slow-roll
  • Testing cosmological models: lensing, BAOs, Lyman alpha forest
  • Nonlinear evolution