Astronomy 825: Radiative Gas Dynamics
Syllabus, Winter 2007

David Weinberg, Dept. of Astronomy, 4041 McPherson Lab, 292-6543

Meetings: The course is scheduled for Tuesday, Thursday, 11:10-12:30, in McPherson 4054. There will be a couple of weeks in which I shift a class to a different day because of travel.

Course Objectives

This course is a graduate-level introduction to gas dynamical processes in astrophysics. It has three overlapping goals. The first is to teach you the basic concepts and equations of gas dynamics (a.k.a. fluid dynamics or hydrodynamics). The second is to illustrate the application of gas dynamics to astrophysics, by examining some of the ``classic'' problems that should be useful reference points when you attack research problems of your own. The third is to teach some more general lessons about ``methods in theoretical astrophysics.'' This goal is more nebulous than the other two, but it is significant nonetheless.

In light of this last goal, as the course proceeds you should pay attention to general issues: how we go from physical approximations to the equations that describe gas dynamics in various limits, how we develop a physical intuition for the meaning of these equations, the kinds of solutions that we can search for (static, steady-state, self-similar, fully dynamic), the questions we must ask to assess the applicability of these solutions to a given physical situation (validity of approximations, stability), and methods of obtaining solutions (approximate analytic, exact analytic, numerical). I am planning to make numerical solution methods an explicit sub-theme of the course, mainly through the assignments (see below).

Some of the topics that I hope to cover are listed below, but I am invariably overoptimistic about the amount of material I can cover in 10 weeks. Since we need to understand the fundamentals before we can apply them, the first 2-3 weeks are likely to be drier than the later parts of the course.

The fluid approximation
The Boltzmann equation, Euler equations, and Navier-Stokes equations
Hydrostatic equilibrium
Instabilities: Rayleigh-Taylor, Jeans, thermal, ...
Radiative cooling processes

Isothermal spheres, galaxy clusters
Spherical infall and galaxy formation
Accretion flows
Supernova blast waves
The diffuse intergalactic medium
Molecular cloud turbulence and star formation

Readings and Assignments

There is no textbook for the course, but there are two valuable reference sources, which will give you more depth and a different angle on material that we cover in class. First, and probably most useful, are the detailed and astoundingly clear lecture notes that Barbara Ryden wrote when she taught the course. These are available in a notebook binder in the reading room. You are welcome to make your own copies of these notes, but remember to give appropriate credit to Barbara if you make use of them in the future (e.g., when you get to teach a course on radiative gas dynamics) and to ask her permission before giving large chunks of them to others. The second source is Frank Shu's excellent book, The Physics of Astrophysics, specifically Volume II, Gas Dynamics. This book is on reserve in the reading room, and although it is not required for this course, you should think seriously about purchasing your own copy as a reference for the future. I will give pointers to the relevant sections of Barbara's notes and Shu's book as the course progresses. In general, you should be sure to read the indicated sections of Barbara's notes, and you should refer to Shu's book if you want greater depth and/or a more rigorous discussion.

On some occasions, I will assign review papers or journal articles on the astrophysical topics listed above.

Problem Sets and Workload

The other assignments will be a take-home final exam and problem sets. I think you will typically need to spend 1-2 hours a week on reading and review of class notes, though this will be variable. Most of the problem sets will have a numerical component, and some will be entirely numerical. As a rule of thumb, you should devote 5-7 hours to a problem set. After five hours, you should continue if you think that doing so will be valuable to your research training. However, if it is a better use of your time to go back to your own research, then that is what you should do; spend a little time tidying up your solution, write ``this is how far I got'' at the end, and turn it in.

For numerical solutions, you can use whatever programming language you like: fortran, C, pascal, basic, perl, ... I will provide my solutions in C, so if you don't know C but would like to learn it, this might be a good opportunity to do so. Numerical Recipes, by Press et al., will often be a useful reference for the numerical components of problem sets; we don't have a copy in the reading room, but there are many floating around the department, so you should be able to borrow one as needed. It is a book worth owning, not so much for the subroutines themselves (which are of mixed quality and should therefore be used with caution) but for the excellent introduction it provides to a wide variety of numerical and statistical algorithms.

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Updated: 2007 January 3[dhw]