Physics 431/531: Galactic Astrophysics
Fall 2019
Course Outline
[SG = Sparke & Gallagher, BT = Binney &
Tremaine]
- Introduction: The Milky Way and other galaxies
[SG Sections 1.1, 1.2, 1.3]
- distance measurement in astronomy
- early estimates of the size and shape of the Galaxy
- the Kapteyn universe
- Shapley and the size of the Milky Way
- spiral nebulae and galaxies
- distances to the spiral nebulae
- components of the Milky Way galaxy
- other types of galaxy
- properties of stars
- measurement of distance: trigonometric parallax
- flux, luminosity, and the inverse-square law
- Astronomical basics
[SG Sections 1.1, 2.1, 2.2; BT Section 1.1]
- properties of stars (continued)
- stellar temperatures and radii
- flux and filters
- the Hertzsprung-Russel diagram: the main sequence
- stellar spectra and spectral types
- stellar composition
- apparent and absolute magnitudes
- apparent magnitudes and colors: the color-magnitude
diagram
- stellar masses
- the mass-radius and mass-luminosity relations
- Stars in the Milky Way
[SG Sections 1.1, 2.1, 2.2; BT Sections 1.1, 3.2.3]
- stellar evolution and lifetimes
- basic reactions
- star cluster color-magnitude diagrams
- cluster ages
- multiple stellar populations
- the stellar luminosity and mass functions
- the luminosity function
- corrections for flux limits and evolution
- the initial mass function
- Galactic structure
[SG Sections 2.2, 2.3; BT Sections 1.1, 3.2.3]
- more distance-measurement techniques:
- proper motion
- spectroscopic parallax
- luminosity classes
- local structure of the Galactic disk
- scale heights and spectral types
- velocity dispersions
- dependence on age
- thin and thick disks
- measuring the local Galactic density
- weighing the local disk
- CMD fitting
- main-sequence turn-off
- isochrone fitting
- open and globular clusters
- disk, spheroid, and bulge
- the Galactic center
- observations of stellar motion
- the central black hole
- Galactic structure and kinematics
[SG Sections 2.3, 2.4]
- the Galactic center
- mass of the central black hole
- distance to the Galactic center
- distance measurement using standard candles
- variable stars
- supernovae
- Galactic rotation
- differential rotation
- local measurements: the Oort constants
- global gas kinematics
- Galactic structure and kinematics (continued)
[SG Sections 2.3, 2.4]
- Galactic rotation
- the Oort constants
- global gas kinematics
- mapping the Galactic rotation curve
- the mass of the Milky Way Galaxy
- dark matter
- cosmic composition
- gas in the Milky Way
- observations
- spatial distribution
- physical state
- heating and cooling processes
- Star formation
[SG Sections 2.4, 8.5.1; BT Sec. 5.2, Appendix F; handout]
- introduction to fluid mechanics
- the continuity and Euler equations
- equation of state
- linearized analysis: sound waves
- inclusion of gravity
- order of magnitude estimates
- the Jeans instability
- the Jeans length
- the Jeans mass
- Star formation (continued)
[SG Sections 2.4, 8.5.1; BT Sec. 5.2, Appendix F; handout]
- more rigorous rederivation of the Jeans criterion
- Poisson's equation
- the "Jeans swindle"
- linearization
- the dispersion relation
- the Jeans length and mass
- the dynamical (free-fall) time scale
- alternative restatements of the criterion
- comparison of potential and thermal energy
- comparison of time scales
- cooling and fragmentation
- Stellar dynamics
[SG Sections 3.1, 3.3; BT Section 3.1]
- virialization
- the virial theorem
- using the virial theorem to estimate cluster masses
- hot gas in galaxy clusters
- Stellar dynamics (continued)
[SG Sections 3.1, 3.2, 4.5; BT Sections 1.2, 7.1]
- the two-body problem (review)
- method of solution
- geometrical (a, e) and physical (E, L) quantities
- unbound motion
- strong and weak endounters
- 90-degree scattering distance
- cross sections
- strong encounter time scale
- Scattering and relaxation
[SG Section 3.2; BT Sections 1.2, 7.1]
- large-angle scattering
- close encounters and collisions
- gravitational focusing
- small-angle scattering
- deflection by repeated scatterings
- the relaxation time
- half-mass relaxation time and dynamical time
- collisional and collisionless systems
- MID-TERM EXAMINATION
- coverage: weeks 1-4 (homeworks 1-3)
- Collisional systems
[SG Section 3.2; BT Sections 1.2, 7.1]
- star cluster evolution
- thermalization and escape - evaporation
- the simple evaporative model
- negative specific heat
- core collapse
- core collapse observed in globular clusters
- post-collapse cluster evolution
- binary formation
- binary heating
- other energy sources
- black hole heating
- stellar mass loss
- Modeling the Galaxy
[SG Sections 3.1, 3.3; BT Sections 2.2, 2.3, 3.1]
- Newtonian gravity and Poisson's equation
- general solution in 1-D (spherical symmetry)
- potential-density pairs in 1-D
- point mass
- homogeneous sphere
- Plummer sphere
- power law
- non-spherical geometries
- Distribution functions and the Jeans equation
[SG Section 3.4; BT Sections 4.1, 4.2]
- definition of the distribution function
- moments ==> density, velocity, etc.
- collisionless Boltzmann equation
- Jeans equations: moments of the collisionless Boltzmann equation
- interpretation in terms of fluid flow
- application to mass distribution in the Galactic disk
- Jeans Theorem(s)
- conserved quantities (integrals)
- collisionless system: f(E, L)
- Self-consistent dynamical models
[SG Section 3.4; BT Sections 4.3]
- relative potential and energy - convention
- spherical symmetry
- isotropy
- general form of Poisson's equation
- polytropes
- the Lane-Emden equation
- the Plummer model
- the isothermal sphere
- lowered Maxwellians - King models
- ...but why a Maxwellian?
- stability of disks
- disk dispersion relation
- stability criteria - Toomre Q
- local stability near the Sun
- bar formation
- Disk galaxies
[SG Sections 5.3, 5.5; BT Section 5.3]
- spiral structure
- basic observations
- star formation
- the winding problem
- density waves
- motion in a disk
- epicyclic and vertical frequencies
- epicyclic motion
- Spiral structure
[SG Sections 5.3, 5.5; BT Sections 6.1, 6.2]
- kinematic density waves - pattern speed
- wave propagation - tightly wound approximation
- disk dynamics
- forced oscillations
- Lindblad resonances
- corotation resonance
- location of resonances
- numbers for our Galaxy
- dispersion relation
- group velocity
- still have a winding problem!
- density waves and observations
- gas response
- locations of gas, star formation, young, old stars, etc.
- need to sustain the wave by other means: bar,
external tides, ...
- Galaxy interactions and mergers
[SG Sections 3.2, 4.1, 7.1; BT Sections 8.1, 8.3]
- dynamical friction
- physical mechanism and the Chandrasekhar formula
- relevance to collisionless systems - galactic cannibalism
- sinking satellites
- the final parsec problem
- tidal limit
- tidal disruption
- Galaxy Interactions and Mergers (continued)
[SG Sections 3.2, 7.1; BT Section 8.5]
- accretion and mergers
- minor and major mergers
- merger simulations
- tidal streams
- tidal tails
- thick and thin disks
- detailed modeling