Spring 2017 Astronomy 735 Wed 14:30 — 15:30

A galaxy can be modeled as a system of stars confined by their mutual self-gravity. Such a model is easily extended to include particulate forms of dark matter. This ASTR 735 seminar is a 1-credit course on the dynamics of self-gravitating stellar systems. it is designed for students who have had a general introduction to galactic astronomy and have studied some classical mechanics. The objective is to introduce the key ideas of Stellar Dynamics and explore some applications to galactic astronomy. One lecture or presentation session will be given each week.

Time & Place:  Wednesday, 15:00 — 16:00 in IfA C221
Professor:  Joshua E. Barnes (barnes at
Office: Institute for Astronomy, Room C-219 (956-8138)
Office hours: by appointment at the IfA
Useful Books:  Galactic Dynamics (GD), by James Binney & Scott Tremaine
Galaxy Formation and Evolution (GFE), by Houjun Mo, Frank van den Bosch, & Simon White

Course Outline & Schedule

The schedule outlined here is provisional. The twelve class meetings listed below may be extended if additional time is needed to properly cover the key ideas.

Date Topic   Reading
1/25 Classical Mechanics: Review Gravitational N-body systems. Conservation laws: Noether's theorem. Lagrangian & Hamiltonian mechanics. GD Appendix D.1–D4.1
2/01 Two-Body Relaxation Random walks. Impulse approximation. Coulomb integral. Relaxation time. GD Ch. 1.2
GFE Ch. 5.4.1
2/08 Gravitational Potentials Conservative force fields. Poisson's equation. Gauss's theorem. Spherical systems. Disk potentials. Flattened systems. Triaxial systems. GD Ch. 2.1-2.3,2.5,2.6
2/15 Regular Orbits Constants & integrals of motion. Orbits in spherical potentials. Action-angle variables. Orbits in axisymmetric potentials. Non-classical integrals. Orbits in separable potentials. GD Ch. 3.1-3.3,3.5
GFE Ch. 5.4.5
2/22 Chaotic Orbits Boxlet orbits. Resonances. Surface of section. Irregular orbits. Arnold diffusion. GD Ch. 3.7,3.8
3/08 Collisionless Dynamics Distribution functions. Continuity equation in phase space. Collisionless Boltzmann equation. Conservation of phase-space density. GD Ch. 4.1
GFE Ch. 5.4.2
3/15 Equilibrium Systems Jeans theorem. Spherical models. Axisymmetric & triaxial models. Schwarzschild's method. GD Ch. 4.2-4.5,4.7.2
GFE Ch. 5.4.6-5.4.9
3/22 Moment Equations Jeans equations. Virial theorem. Applications. GD Ch. 4.8
GFE Ch. 5.4.3,5.4.4
4/05 Simulations
4/12 Presentations
4/19 Presentations
4/26 Summary

Learning Objectives

This course aligns with a number of UH Manoa's Institutional Learning Objectives, including: objective 1a (general understanding of the Universe), objectives 2a (critical and creative thinking, problem solving, mathematical reasoning) and 2c (collaborative work with peers), and objective 3a (intellectual curiosity).

Grading Policy

Students are strongly encouraged to take this course for a letter grade. Final grades will be based on in-class participation (15%); two problem sets, each covering several weeks of material (50%), and an in-class presentation describing an application of stellar dynamics to astronomy (35%).

Joshua E. Barnes      (barnes at
Updated: 12 March 2017
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