Intro to Modern Astrophysics

Light, stars, galaxies and the large-scale universe

About this course

How light carries information about the sky, the structure and evolution of stars and their remnants, the solar system, and the Milky Way, galaxies and the cosmic web.

What you will be able to do

  • Use blackbody radiation and spectral lines to infer stellar temperatures and compositions
  • Derive stellar masses and radii from binary systems and place stars on the H–R diagram
  • Explain stellar structure, nuclear burning and energy transport in stellar interiors
  • Trace stellar evolution from star formation to white dwarfs, neutron stars and black holes
  • Explain the extragalactic distance scale and how it measures cosmic expansion

What this course covers

  • Tidal force as derivative of gravity
  • Roche limit from tidal disruption
  • Tidal torque, lag angle, and spin-orbit evolution
  • Io's tidal heating and orbital resonance
  • Atmospheric lapse rate and the greenhouse effect as height
  • Atmospheric escape and the lambda criterion
  • Maximum size of a cold hydrogen planet
  • Why mass cannot be measured from starlight
  • Classification of binary systems
  • Center of mass and the mass ratio
  • Kepler's harmonic law and the mass sum
  • Orbital inclination and the sine³ degeneracy
  • Eclipsing binaries and full system characterisation
  • The mass–luminosity relation and stellar lifetimes
  • The dust problem: extinction and reddening
  • Dust-corrected distance: Lambert W closed form
  • Star counts, survey yield, and Olbers' paradox
  • Galactic anatomy: disks, bulge, and stellar halo
  • Oort constants and local galactic rotation
  • Tangent-point method for the inner rotation curve
  • Flat rotation curve and dark matter
  • Weighing the central black hole with stellar orbits
  • Hydrostatic Equilibrium and the Pressure Gradient Equation
  • Minimum Central Pressure: A Model-Independent Lower Bound
  • The Virial Theorem and Negative Heat Capacity
  • Kelvin–Helmholtz Timescale and Its Failure
  • Mean Molecular Weight and Thermal Gas Pressure
  • Radiation Pressure and When It Dominates
  • Electron Degeneracy Pressure and How Stars End
  • Stellar Structure Equations: Counting and Closure
  • Celestial Coordinate Frame and Altitude Formula
  • Seasons: Tilt vs. Distance
  • Precession of the Celestial Frame
  • Kepler's Three Laws as Empirical Descriptions
  • Two-Body Reduction to One-Body Problem
  • Inverse-Square Law Derivation of Orbital Conics
  • Derived Third Law and Weighing Stars
  • Virial Theorem for Unresolved Systems
  • The Classical Barrier and Why It Fails
  • Quantum Tunneling Through the Coulomb Barrier
  • The Gamow Peak: A Window Neither Factor Would Choose
  • Two Fusion Chains and Their Temperature Exponents
  • The Crossover Temperature Between pp and CNO
  • Radiative vs. Convective Energy Transport and the Schwarzschild Criterion
  • Closing the Stellar Structure Equations
  • Isochron method: eliminating the unknown initial ratio
  • Lead-lead dating and the age of the Solar System
  • Asteroid belt mass deficit and Kirkwood gaps
  • Disc temperature profile and the water ice line
  • Collision outcome inequality: sticking vs. shattering
  • Hill radius and planetary isolation mass
  • Hot Jupiters, disc migration, and the stopping problem
  • Galaxy morphological classification and its limits
  • What morphological sequence actually tracks
  • Sérsic brightness profile family and its constants
  • The winding problem and density-wave resolution
  • Virial theorem as a mass estimator for non-rotating systems
  • Flat rotation curves and the dark matter conclusion
  • Tully-Fisher and Faber-Jackson scaling laws
  • The Fundamental Plane and measured tilt as physics
  • Radiant flux and the inverse square law
  • The magnitude scale
  • Stellar parallax and the parsec
  • Absolute magnitude and the distance modulus
  • Blackbody radiation and the Planck curve
  • Wien's law and the Stefan–Boltzmann law derived
  • Colour index as a distance-independent temperature
  • Stellar radius from two brightnesses and one angle
  • Why the original spectral alphabet failed
  • Spectral sequence as a temperature thermometer
  • Luminosity, radius, and the second spectral number
  • The Hertzsprung–Russell diagram and its reversed axes
  • Main sequence as a mass sequence and stellar lifetimes
  • Spectroscopic parallax: distance from a single spectrum
  • Error analysis and the asymmetric failure modes
  • Kirchhoff's Three Spectral Rules and Line Identity
  • The Central Question: Line Strength vs. Composition
  • The Bohr Energy Ladder: Quantized Orbits and the Rydberg Constant
  • Failure of the Orbit Picture and the Quantum State with Four Numbers
  • Selection Rules and Forbidden Lines as a Density Probe
  • Two-Factor Population Count: Excitation and Ionization
  • The Peak Temperature: Differentiating the Product
  • The stellar photosphere as an illusion
  • Specific intensity and its three moments
  • Optical depth as the natural coordinate
  • Radiative transfer and the Eddington–Barbier relation
  • Gray-atmosphere temperature structure
  • Limb darkening and opacity sources
  • Spectral line shapes and the curve of growth
  • Phases of the interstellar medium
  • Interstellar dust and the reddening law
  • The Jeans mass from the virial theorem
  • Turbulence and magnetic support of dense cores
  • Free-fall time and its density dependence
  • Hierarchical fragmentation as a cascade
  • End of fragmentation and the opacity limit
  • Protostellar contraction and the Hayashi track
  • Termination of star formation by massive stars
  • Galaxies as colliding systems
  • Tidal forces and the radius of survival
  • Dynamical friction and the role of dark matter
  • Satellite sinking timescale
  • Impulsive encounters and the virial response
  • Ram-pressure stripping
  • Hierarchical assembly versus monolithic collapse
  • Negative heat capacity of self-gravitating gas
  • Stellar thermostat: nuclear burning stability
  • Main-sequence brightening and the faint young Sun
  • Schönberg–Chandrasekhar-type limit on an inert core
  • Thermal versus nuclear timescale and the Hertzsprung gap
  • Giant-branch structure: radius, luminosity and temperature
  • Helium flash: thermostat failure in a degenerate core
  • Mass loss, thermal pulses and the full evolutionary track
  • The magnitude–distance exchange rate
  • Geometry-only distance methods and their limits
  • The cosmic distance ladder: inherited distances and the first rung
  • Dust removal via the Wesenheit combination
  • Malmquist bias in flux-limited samples
  • Systematic (common) errors and the floor on ladder precision
  • Hubble's law, the Hubble tension, and localising the disagreement
  • The sealed solar interior and the testing problem
  • Nuclear energy source and the 0.712% mass defect
  • Photon random walk and the escape-time theorem
  • Radiative vs. convective transport and the 0.71 solar-radius boundary
  • The solar surface: granulation, spectral lines, and the corona
  • Magnetic field ratio and the sunspot cycle
  • Helioseismology and the neutrino flavor-oscillation result
  • Two jobs of a telescope: collection and conversion
  • Diffraction limit and the 1.22 factor
  • Aperture buys sharpness and light at different rates
  • Focal ratio, surface brightness, and the brightness theorem
  • Atmospheric seeing and the crossover aperture
  • Photon counting, quantum efficiency, and the square-root law
  • Resolution limits at radio and X-ray wavelengths
  • Observed classes of pulsating stars
  • Period–density relation: two independent derivations
  • Period–luminosity relation and the distance ladder
  • The population-confusion error and its distance consequence
  • Thermodynamic engine condition: the phase and opacity criterion
  • Half-ionisation zones as the valve
  • The instability strip: width, edges, and the Sun's contrast
  • The Missing Mass Problem in Galaxy Clusters
  • The Virial Theorem and Dynamical Mass
  • Intracluster Gas: Temperature, X-ray Emission, and Hydrostatic Mass
  • Gravitational Lensing Mass and Component Budget
  • Colliding Clusters and the Nature of Dark Matter
  • Large-Scale Structure and the Galaxy Correlation Function
  • Tidal Eigenvalue Statistics and the Cosmic Web
  • Stellar burning timescales and the neutrino punchline
  • Nuclear binding energy peak and the semi-empirical mass formula
  • Fuel pricing and the invisible luminosity inversion
  • Photodisintegration removing thermal pressure
  • Electron capture removing degenerate pressure
  • Core collapse, neutron star size, and the stalled shock
  • Radioactive nickel-56 powering the light curve
  • Supernova classification, remnants, and heavy-element origin
  • SN 1987A neutrino detection and energy budget
  • Degeneracy pressure: temperature-independent support
  • Deriving the P ∝ ρ^(5/3) pressure law
  • Mass–radius relation: heavier white dwarfs are smaller
  • Relativistic correction and verification
  • Chandrasekhar mass: the central result
  • Neutron stars: same argument, different particle
  • Pulsars as rotating neutron stars: spin-down and field measurement
  • The Schwarzschild radius: one length per mass
  • The horizon: crossing time and observable fading
  • Innermost stable circular orbit and accretion efficiency
  • Gravitational redshift and the iron-line diagnostic
  • Tidal forces at the horizon: inverse-square mass dependence
  • The no-hair result: three numbers describe a black hole
  • Observational evidence: mass function, stellar orbits, and the shadow
  • Hawking temperature, evaporation timescale, and entropy
  • Effective potential in a rotating frame
  • Inner Lagrange point as a saddle, not a summit
  • Roche lobe size and the volume-radius correction
  • Angular momentum conservation and orbital response to mass transfer
  • Roche lobe elasticity and the Q = 5/6 stability threshold
  • Accretion disk formation and disk luminosity
  • Gravitational-to-nuclear energy ratio and its consequences

Syllabus

  1. Light and Observation

    1. L1 · The Celestial Sphere and Celestial Mechanics
    2. L2 · The Continuous Spectrum of Light
    3. L3 · The Interaction of Light and Matter
    4. L4 · Telescopes and Detectors

  2. The Properties of Stars

    1. L5 · Binary Systems and Stellar Parameters
    2. L6 · Classifying Stellar Spectra and the H–R Diagram
    3. L7 · Stellar Atmospheres
    4. L8 · The Sun

  3. Stellar Interiors and Evolution

    1. L9 · The Interiors of Stars I — Structure and Pressure
    2. L10 · The Interiors of Stars II — Nuclear Burning and Transport
    3. L11 · The Interstellar Medium and Star Formation
    4. L12 · Main Sequence and Post-Main-Sequence Evolution
    5. L13 · Stellar Pulsation
    6. L14 · The Fate of Massive Stars
    7. L15 · The Degenerate Remnants of Stars
    8. L16 · Black Holes
    9. L17 · Close Binary Star Systems

  4. The Solar System

    1. L18 · The Solar System I — Physical Processes and the Planets
    2. L19 · The Solar System II — Minor Bodies and Planet Formation

  5. Galaxies and the Universe

    1. L20 · The Milky Way
    2. L21 · The Nature of Galaxies
    3. L22 · Galactic Evolution
    4. L23 · The Extragalactic Distance Scale and the Expansion
    5. L24 · Clusters, Superclusters and the Cosmic Web