Summary: ASTR 5120: Problem Set 1
1. In practice, the collisionless Boltzmann equation and Fokker­Planck equations are
useful when the system under consideration is symmetric enough to cut down the
number of degrees of freedom to something more manageable. Consider a spherically
symmetric cluster (perhaps of galaxies) that is in a steady state and in which v r
and v # vanish. By expressing the collisionless Boltzmann equation in spherical co­
ordinates and taking moments (as we did to in the general case) show that the
system obeys,
d(#v 2
r )
dr
+
#
r # 2v 2
r - # v 2
# + v 2
# ## = -#
d#
dr
.

Source: Armitage, Phil - Department of Astrophysical and Planetary Sciences, University of Colorado at Boulder

Collections: Physics