Check chapter 1 if there is something there that is still new to you. First four pages of chapter 4.
Complete before class on April 1.

2. Potential theory. April 1, 6

Sections 2.1, 2.4, 2.5.
The rest of the sections in Chapter 2 are less important, you should look over sections 2.2, 2.3, 2.6, so that you know that there are these mathematical methods for computing potentials of ellipsoidal systems and disks, but don't worry about all the math in there (you'll just come back to consult this book if you ever need this). Section 2.7 is useful for the general method described, but somewhat outdated, much better information is found in Galactic Astronomy by Binney and Merrifield (see also the references below).

Problems to read and think about (not for homework): 2.1, 2.2, 2.3, 2.4, 2.6, 2.10
Complete before class on April 6.

Useful references (not assigned reading) for updates on the structure of the Milky Way:


Dwek, E., etal. 1995, ApJ, 445, 716: bulge structure from COBE.
Binney, J., Gerhard, O., Spergel, D. N. 1997, MNRAS, 288, 365: Photometric structure of the inner bar.
Binney, J., Evans, N. W. 2001, MNRAS 327-L27: Joint analysis of microlensing and dynamical data in bulge-bar.
Sackett, P. 1997, ApJ, 483, 103: nice review of disk structure.
Kochanek, C. S. 1996, ApJ, 457, 228; Wilkinson, M. I., Evans, N. W. 1999, MNRAS, 310, 645: the Milky Way halo.

3. Orbits . April 8, 9, 13, 15

Sections 3.1, 3.2: read by April 8.
Sections 3.3, 3.4: read by April 13.
Sections 3.5, 3.6: read by April 15.
You should read all sections of this chapter, they are all quite useful and important. You may find section 3.3 a bit difficult, but it is important that you understand what surfaces of section are and what the Lindblad resonance in a rotating potential is. Section 3.5 is the most difficult, and you may read this less carefully than the others although you should still have a basic idea of what angle-action variables are (you can skip the stuff on Floquet analysis).

Problems: 3.3, 3.4, 3.5, 3.7, 3.9, 3.18.

Additional useful reading (not required):
`The Galactic Center environment', by M. Morris, E. Serabyn (1996), ARAA, 34, 645: Sections 3.1 and 3.2 show an interesting application to the real world of the types of orbits discussed for rotating barred potentials. More details are found in Binney et al. 1991, MNRAS, 252, 210.
`Regular and Chaotic Dynamics of Triaxial Stellar Systems', by M. Valluri and D. Merritt (1998), ApJ, 506, 686. This is a long paper, but you'll find it useful to read the introduction and discussion and glance through the rest of it. There is an interesting idea on how stochastic orbits on triaxial potentials might provide an explanation for the correlation of nuclear black holes with bulge properties.

4. Equilibria of Collisionless Systems. April 19, 20, 22, 27, 29

Sections 4.1, 4.2, 4.3: read by April 19.
Sections 4.4, 4.5: read by April 22.
Sections 4.7: read by April 29.

Problems: 4.8, 4.9, 4.10, 4.12, 4.15, 4.18, 4.19, 4.22, 4.25.

Useful references:
`The distribution of nearby stars in phase space mapped by Hipparcos. I. The potential well and local dynamical mass', by M. Crézé et al., 1998, A&A, 329, 920. The value for the dynamical density they find is 0.076 +/- 0.015 Msun/pc^3, much lower than found before and leaving no room for disk dark matter.

Examples of Jeans' equations in spherical systems:
In clusters of galaxies: `The velocity and mass distribution of clusters of galaxies from the CNOC1 cluster redshift survey', van der Marel et al., 2000, AJ 119, 2038.
In galactic nuclei: Kormendy and Richstone 1995, ARAA 33-581, a general review of the search for black holes in galactic nuclei.
In the Milky Way nucleus: Genzel et al. 2000, MNRAS 317-348.

Rotation of elliptical galaxies:
After the B&T book was published it was found that not all dwarf ellipticals are flattened by rotation, some dwarfs are also flattened by anisotropic velocity dispersion tensors.
Bender & Nieto 1990, A&A, 239, 97.
Geha, Guhathakurta, & van der Marel 2003, AJ, 126, 1794.

`Statistical Mechanics of Violent Relaxation', by Spergel and Hernquist (1992), ApJ, 397, L75: an interesting idea of using entropy maximization to understand the state that a collisionless system tends to reach after violent relaxation, by restricting particles to orbits that are accessible, with an upper limit to the angular momentum.

5. Stability.

Section 5.1 and 5.4:
The Jeans analysis is generally most useful in the cosmological context, in an expanding medium (where you don't need to waive your hands about the Jeans swindle). You may try Sections 5.2 and 5.3, but they are rather dense. It may be easier to just take a brief look at the results of the theorems, and just read the summary at the end. We will probably skip this chapter.

6. Disks and Spiral Structure. May 4, 5