Basics of Stellar Dynamics
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Consider a stellar system as a gas of mass points 
(i.e., stars), interacting gravitationally.  Note 
the connections with statistical mechanics and 
kinetic theory (--> gravothermodynamics), and both 
the similarities and dissimilarities with plasma 
physics.

The basic descriptor is the distribution function 
in the 6-dim. phase space:



Specification of         completely determines the 
system and its evolution.

Generally, the evolution of         is described 
by the Boltzmann eq., but often the problem is 
simpler.  If the number of stars is conserved,  
then         will follow a continuity equation 
in the phase space (i.e., the Liouville eq.)

The density distribution is the integral of
                over the velocities, and must 
satisfy the Poisson eq.

One of the basic goals of stellar dynamics is 
construction of consistent models of stellar 
systems, and studies of their stability and 
evolution, usually under some symmetry assumptions 
(e.g., spheres, ellipsoids, disks), or for 
assumed forms of the potentials.

Note that not all potentials have to lead to 
physically meaningfull models (e.g., with 
non-negative densities).