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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 $ρ\propto r^{-2}$), 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.