During Lent term 2018, I will be giving 16 lectures
on the dynamics of astrophysical discs, as part of Part III of the
Cambridge Mathematical Tripos.
Lectures take place at 10am on Tuesdays and
Thursdays in room MR9.
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, (old) lecture notes and slides on accretion disk dynamics (here and here.)
- Latter, Ogilvie & Rein., draft 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.)
- Netzer (2006), (pdf.) (Summary of main physical processes in AGN.)
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. DAD Exam 2014 (pdf)
Schedule:
Lecture 1 (19/01/2017): Introduction (pdf)
- 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
Those interested in learning more about turbulence could read `A first course in turbulence' by Tennekes and Lumley (first two chapters are relevant to today's lecture) and 'Turbulence' by Peter Davidson (chapter 1 and maybe 5). See the book by Frank et al. (2002) for a fuller discussion of the derivation and analysis of the diffusion equation. You can also refer to Section III in Balbus and Hawley (1998) (ADS link). The notes by Ogilvie (here and here) are also a good reference.
- Boundary conditions
- Steady accretion disks
- Spectrum of steady disks
- Complications and observed SEDs
- Time-dependent solutions
- Greens functions
- 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 in cataclysmic variables
- The shearing sheet
- Orbital motion in the shearing sheet
- Symmetries and boundary conditions
- Incompressible disk dynamics and equations
- Inertial shearing waves
- Centrifugal instability and Rayleigh's criterion
- Introduction to vortices
Lecture 11 (23/02/2017): Vortices in Disks II
- Enstrophy conservation
- Kida vortex solution and its stability
- Compressible disk dynamics and equations
Lecture 12 (28/02/2017): Density Waves and Gravitational Instability
- Density waves
- Axisymmetric gravitational instability
- Non-axisymmetric instability and `gravitoturbulence'
- Test particle orbits in the presence of an embedded satellite
- Excitation of epicyclic oscillations
- The impulse approximation
- Angular momentum transfer between embedded satellites and their disks
- Gap opening
- Planet migration
- Equations of MHD
- Derivation of the axisymmetric dispersion relation
- Analysis of dispersion relation
- Importance of disk thickness, magnetic diffusion, and magnetic field strength on stability criterion
- Physical interpretation of dispersion relation
- Survey of numerical simulations