ASTRON 449: Stellar Dynamics, Winter 2019

Syllabus. Regular office hour is Tuesday 2:30, on days before a problem set is due (note: this has been updated from the original office hour in the syllabus)

Announcements: – Heads up regarding computational problems: This year the course will include a large computational component, which will consist primarily of homework problems that will require the use of Python. I will not teach Python in the course, but rather assume that students have some prior programming experience and familiarity with Python. If this is not the case, then I encourage you learn the basics before the Winter quarter starts (there are many online tutorials).

You should also make sure to have a working installation of the following Python modules: Python, numpy, matplotlib, and (possibly) scipy. One easy way to install all these packages at once is through the Anaconda distribution ( As for the Python version, Python 2.7 is sufficient (this is what I use at the moment) though if you are already using Python 3.7, that should work as well.

The programs that we will develop in this course are ones that can be run on recent a laptop. If you are worried that your personal computer may not be adequate, you can obtain an allocation to use Northwestern’s Quest computing cluster ( Note that it takes some time for Quest a allocation to be created, so if you anticipate needing one please start the process of creating it now.

Reading: This includes parts that we have covered and that we plan to cover in upcoming lectures, for students who would like to read the textbook in advance (this will be updated as the term progresses):

– BT2 SS1.1, 1.2
– BT2 SS2.1, 2.2, 2.9
– Read S2.8 for a discussion of gravitational potential models for the Milky Way (we will not cover this section in detail, but useful to gain intuition regarding realistic potential models)
– BT2 S2.9 on numerical method for Poisson solvers
– BT2 S3.4 on numerical methods for orbit integration. This section is much more detailed than what we will cover in class; it is to be used primarily as a reference for the leapfrog and Runge-Kutta integration methods. The slides shown in class contain the essential information for this course.
– Our treatment of the Boltzmann and Jeans equations will closely follow Paul Schechter’s lecture notes. These topics are covered in BT2 SS4.1, 4.2, 4.3, 4.8, but again in much more detail than we will cover in this course.
– BT2 S4.8.3 discusses the viral theorem, but in the more general form that the scalar version that we covered in class.
– BT2 S5.2 discusses the Jeans instability
– BT2 S6.1 discusses the phenomenology of spiral structure in galaxies, as well as angular momentum transport by spiral arms
– BT2 S3.2.3 derives the epicyclic approximation
– BT2 S6.2 discusses the Toomre instability
– BT2 SS6.3-6.4 discuss swing amplification and the excitation of spiral structure
– BT2 S8.1 discusses dynamical friction
– BT2 S8.5 discusses galaxy mergers
– BT2 S9.4 discusses the “merger sequence” and AGN

Lecture materials:Slides on simple/useful potentials, and on properties of dark matter halos
Slides on numerical methods for N-body simulations
Slides on mass-velocity anisotropy degeneracy and black hole masses
Slides on phenomenology and origins of spiral structure
Slides on the epicyclic approximation
Slides on Toomre phenomenology and swing amplification
Slides on dynamical friction, galaxy mergers, and AGN

Problem sets:

Problem set 1, due Thu Jan. 17. Upload code files here (include all files in a .zip archive identified by your last name:
Discussion leaders: Monica Gallegos Garcia, Candice Stauffer, Dennis Lee

Problem set 2, due Thu Jan. 31. Upload code files here.
Discussion leaders: Kaushik Rao, Andra Maria Ionescu, Monica Rizzo

Problem set 3, due Thu Feb. 14. Upload code files here.
Discussion leaders: Anya Nugent, Danat Issa

Homogeneous sphere ICs: N=200, N=500, N=1000

Problem set 4, due Thu Feb. 28. Upload code files here.
Discussion leaders: Lindsey Byrne, Kyle Rocha

ICs for extreme-mass-ratio binary test problem (~Keplerian orbit of light particle)

Problem set 5, due Thu Mar. 14. Upload code files here.
Discussion leaders: Newlin Wheaterford, Michael Bueno