A Dynamical Potential-Density Pair for Star Clusters With Nearly
  Isothermal Interiors
  We present a potential-density pair designed to model nearly isothermal star
clusters (and similar self-gravitating systems) with a central core and an
outer turnover radius, beyond which density falls off as $r^{-4}$. In the
intermediate zone, the profile is similar to that of an isothermal sphere
(density $\rho \propto r^{-2}$), somewhat less steep than the King 62 profile,
and with the advantage that many dynamical quantities can be written in a
simple closed form. We derive new analytic expressions for the cluster binding
energy and velocity dispersion, and apply these to create toy models for
cluster core collapse and evaporation. We fit our projected surface brightness
profiles to observed globular and open clusters, and find that the quality of
the fit is generally at least as good as that for the surface brightness
profiles of King 62. This model can be used for convenient computation of the
dynamics and evolution of globular and nuclear star clusters.
