# Lecture 7: Spherical stellar systems

**Reading:**

Binney and Tremaine 4.3 (new), 4.4 old)

**Optional reading:**

Derivations of the collisionless Boltzmann equation (called by other names) are given by:

Chandrasekhar, S. 1942, *Principles of stellar dynamics* (Chicago: University of Chicago Press)

Ogorodnikov, K. F. 1965, *Dynamics of stellar systems *(Oxford: Pergamon)

You can also look in almost any statistical mechanics book for **Liouville's equation** or **Liouville's theorem**,

although this normally is derived for a 6N-dimensional phase space (compare 7.2.2 in Binney and Tremaine)

Richstone, D. O., and Tremaine, S. 1986, AJ 92, 72 - determining mass-to-light ratios by core fitting (King's method)

Chandrasekhar, S. 1939, *An introduction to the study of stellar structure *(Chicago: University of Chicago Press) - a comprehensive analytic treatment of the isothermal sphere and ploytropes

King, I. 1966, AJ 71, 64 - King models

The fact that only spherical systems can have distribution functions that depend only on energy follows

from Lichtenstein's theorem (non-rotating barotropic stars must be spherical). See:

Tassoul, J.-L. 1978, Theory of rotating stars (Princeton: Princeton University Press)

Lindblom, L. 1977, J. Math. Phys. 18, 2352

Box 4.1 of Binney & Tremaine

Entropy:

Section 4.10.1 of Binney & Tremaine

Tremaine, S., Henon, M., and Lynden-Bell, D. 1986, MNRAS 219, 285 - entropy in stellar systems