Binney and Tremaine, 4.4, 4.7.1
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 8.1.2 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
King,
I. 1966, AJ 71, 64 - King models
Gunn,
J. E., and Griffin, R. F. 1979, AJ 84, 752 - a classic study of the
dynamics of the globular cluster M3 using Michie models
A more detailed discussion of anisotropic models
(constant-anisotropy models and Osipkov-Merritt models) is given in
Section 4.3.2 of the second
edition of Binney & Tremaine
Tremaine, S., Henon, M., and Lynden-Bell, D. 1986, MNRAS 219, 285 - entropy in stellar systems
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