Welcome to the Astronomy 870 course! The objective of this course is to provide the student with a working knowledge of gravitational dynamical processes in stellar clusters, galaxies and galaxy clusters, sufficient to understand publications and embark on current research.
J. Binney & S. Tremaine, Galactic Dynamics (Princeton University Press, 1987).
The final grade of the course will be determined as:
Assigned reading will be announced in class. You should complete the reading by the due time so that you can come prepared with any questions you want to ask.
You are encouraged to ask questions in and out of class. If you feel lost on the homework I'll help you with some hints. Students are allowed to discuss the homework among them, although when you write your homework that should be your individual work.
For each chapter I will list the sections you should read, as well as any other assigned readings from other books or papers. Please complete the reading by the date indicated. I will write these dates as the course proceeds, allowing flexibility for the pace of the course. The most important thing is that we cover the material sufficiently well so that everybody understands it; we can slow down if we must even if that means that we will not have covered every topic by the end of the course. I will also list the problems in the book that seem most useful, which you should read and think about how to solve them. These problems are not required homework, although we may discuss them in class. You are encouraged to ask questions about these problems whenever you realise that you don't know how to solve them. The required homework problems will be posted separately below.
2. Potential theory. April 1, 6
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:
3. Orbits . April 8, 9, 13, 15
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
Problems: 4.8, 4.9, 4.10, 4.12, 4.15, 4.18, 4.19, 4.22, 4.25.
`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.
6. Disks and Spiral Structure. May 4, 5
Section 6.3 : read section 6.3.1 by May 5.
Sections 6.3.2, and the related one 6.2.4, are very hard to understand (good luck if you want to try).
A counterexample to the general rule of trailing spiral arms: The galaxy NGC 4622 has leading spiral arms in the outer parts of the disk, it seems due to a recent interaction.
7. Dynamical Friction and Galaxy Collisions. May 6, 11
Section 7.5: read by May 11.
Additional interesting (optional) reading: Sellwood and Binney, ``Radial Mixing in Galactic Disks'', astro-ph/0203510. A new mechanism connected to spiral structure near the corotation resonance is identified that can transport stars to orbits of very different radii in a galactic disk, while introducing a much smaller increase in the dispersion of eccentricities and orbital inclinations (or in the velocity dispersion).
8. Two-Body Relaxation and Globular Cluster Evolution. May 13, June 1.
Sections 8.4, 8.5: read by June 1.
Additional optional reading: Rauch and Tremaine, ``Resonant Relaxation in
Stellar Systems'', 1996, New Astronomy, 1, 149.
The calculation of the relaxation rate assumes that the velocity of a star changes due to random encounters with other stars. However, in certain systems repeated encounters with the same stars will cause changes in the orbits that are correlated among various encounters, leading to faster relaxation. One example is a cluster of stars around a black hole, in the Keplerian region of the potential, where orbits are nearly closed and pairs of stars may have repeated encounters.
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