During Lent term 2025, I will be giving 16 lectures
on the dynamics of astrophysical discs, as part of Part III of the
Cambridge Mathematical Tripos.
Lectures will be at 11am on Tuesdays and Thursday in MR12
There will be three examples classes and a revision class
in Easter term.
On this webpage I will post the course schedule, pictures, movies, and
other material that appear in
the lectures, as well as suggestions for additional reading, original
references, example sheets, etc.
Introductory references and general review articles
- Ogilvie, lecture notes and slides on accretion disk dynamics (here.)
- Latter, Ogilvie & Rein (2018), review chapter covering rings and disks (pdf.)
- Frank, King & Raine (2002). Accretion Power in Astrophysics, 3rd edn, CUP. (Textbook on classical disk theory.)
- Pringle (1981), ARA&A, 19, 137. (ADS link.) (Succinct review article on viscous disks.)
- Balbus (2003), ARA&A, 41, 555. (ADS link.) (Clear and concise account of instabilities and waves in disks.)
- Esposito (2010), AREPS, 38, 383. (ADS link.) (Gentle recent review of Saturn's rings.)
- Goldreich & Tremaine (1982), ARA&A, 20, 249. (ADS link.) (Detailed account of the physics of planetary rings.)
- Hellier (2001), Cataclysmic Variable Stars: how and why they vary, Springer-Verlag. (Very readable book on CVs.)
- Armitage (2011), ARA&A, 49, 195. (ADS link.) (Good reference on the dynamics of protoplanetary disks.)
- Ferrarese and Ford (2005), SSRv, 116, 523. (link.) (Well written and thorough account of AGN. The first 20 pages are worth reading for an overview on the subject.)
Example sheets & classes
- Example Class 1: TBC. First problem sheet (pdf)
- Example Class 2: TBC. Second problem sheet (pdf)
- Example Class 3: TBC. Third problem sheet (pdf)
- Revision Class: TBC. Two past exam questions TBC.
Schedule:
Lecture 1: Introduction
- Survey of astrophysical disk systems
- Basic physical and observational properties
- Equations of motion, circular orbits
- Characteristic frequencies
- Perturbed orbits: epicyclic oscillations
- Precession
- Elementary mechanics of accretion
- Equations of astrophysical fluid dynamics
- Viscosity as proxy for turbulent flow
- Derivation of the diffusion equation
- Boundary conditions
- Steady accretion disks
- Spectrum of steady disks
- Complications and observed SEDs
- Time-dependent solutions
- Greens functions
- Algebraic similarity solutions
- Vertical hydrostatic equilibrium
- Important length and time scales
- Isothermal and polytropic disk models
- Radiative disk models and opacity laws
- Approximate algebraic solution for an alpha disk
- Thermal instability and outbursts in dwarf novae
- The shearing sheet
- Orbital motion in the shearing sheet
- Symmetries and boundary conditions of the shearing sheet
- Incompressible disk dynamics and equations
- Inertial shearing waves
- Centrifugal instability and Rayleigh's criterion
- Introduction to vortices
- Enstrophy conservation
- Kida vortex solution and its stability
- Compressible disk dynamics and equations
- Density waves
- Axisymmetric gravitational instability
- Non-axisymmetric instability and `gravitoturbulence'
- Test particle orbits in the presence of an embedded satellite
- Excitation of epicyclic oscillations
- Angular momentum transfer between embedded satellites and their disks
- Gap opening
- Planet migration
- Equations of MHD
- Derivation of the axisymmetric MRI dispersion relation
- Analysis of the dispersion relation
- Importance of disk thickness, magnetic diffusion, and magnetic field strength on the stability criterion
- Physical interpretation of dispersion relation
- Survey of numerical simulations