Dynamics of Astrophysical Discs

Lecture course on Dynamics of Astrophysical Discs
Mathematical Tripos, Part III
Lent Term 2020

16 lectures
Tuesdays and Thursdays at 12 noon, starting 16 January
Room MR9, Centre for Mathematical Sciences, Wilberforce Road

3 example classes
Wednesday 12 February, 2:00-3:30 pm, room MR5
Wednesday 26 February, 2:00-3:30 pm, room MR5
Wednesday 11 March, 2:00-3:30 pm, room MR5

Revision class
Thursday 14 May, 11:00 am-12:30 pm, via Zoom (please contact lecturer for details)
Questions to be covered: 2019 exam (Paper 321, available here)

Introductory lecture (PDF)

Lecture 2: Orbital dynamics (PDF)
Two excellent textbooks covering orbital dynamics are Binney & Tremaine and Murray & Dermott. The mechanics of accretion is discussed in Lynden-Bell & Pringle (1974). The relevance of period orbits of the restricted three-body problem for discs in binary stars is discussed in Paczyński (1977).
Lecture 3: Global and local views (PDF)
The shearing sheet was introduced in the context of galactic dynamics by Goldreich & Lynden-Bell (1965) and used for local simulations of planetary rings by Wisdom & Tremaine (1988).
Lecture 4: Evolution of an accretion disc (PDF)
Lecture 5: Boundary conditions and steady accretion (PDF)
Lecture 6: Time-dependent accretion (PDF)
The evolution of viscous discs is discussed in Lynden-Bell & Pringle (1974). A lot of the theory was worked out in the Cambridge PhD theses of these two authors.
Lecture 7: Vertical structure (PDF)
The alpha prescription for the viscosity (or stress) in a disc was proposed, and applied to the structure of steady accretion discs, by Shakura & Sunyaev (1973), the most famous paper in our subject.
Lecture 8: Radiative models (PDF)
Lecture 9: Thermal instability / Hydrodynamics of the shearing sheet (PDF)
Lecture 10: Vortices in discs (PDF)
Lecture 11: Density waves and gravitational instability (PDF)
Lecture 12: Outcome of gravitational instability (PDF)
Lecture 13: Magnetic fields in discs (PDF)
Lecture 14: The magnetorotational instability (PDF)
Lecture 15: Satellite-disc interaction (PDF)
Lecture 16: Satellite-disc / Particle-disc interaction (PDF)

Notes on AFD and MHD (PDF)
Note on the polytropic model and the gamma function (PDF)

Example sheet 1 (PDF)
Example sheet 2 (PDF)
Example sheet 3 (PDF)


Published by Gordon Ogilvie, May 2020