The life cycle of star cluster in a tidal field
  The evolution of globular clusters due to 2-body relaxation results in an
outward flow of energy and at some stage all clusters need a central energy
source to sustain their evolution. Henon provided the insight that we do not
need to know the details of the energy production in order to understand the
relaxation-driven evolution of the cluster, at least outside the core. He
provided two self-similar solutions for the evolution of clusters based on the
view that the cluster as a whole determines the amount of energy that is
produced in the core: steady expansion for isolated clusters, and homologous
contraction for clusters evaporating in a tidal field. We combine these models:
the half-mass radius increases during the first half of the evolution, and
decreases in the second half; while the escape rate approaches a constant value
set by the tidal field. We refer to these phases as `expansion dominated' and
`evaporation dominated'. These simple analytical solutions immediately allow us
to construct evolutionary tracks and isochrones in terms of cluster half-mass
density, cluster mass and galacto-centric radius. From a comparison to the
Milky Way globular clusters we find that roughly 1/3 of them are in the second,
evaporation-dominated phase and for these clusters the density inside the
half-mass radius varies with the galactocentric distance R as rho_h ~ 1/R^2.
The remaining 2/3 are still in the first, expansion-dominated phase and their
isochrones follow the environment-independent scaling rho_h ~ M^2; that is, a
constant relaxation time-scale. We find substantial agreement between Milky Way
globular cluster parameters and the isochrones, which suggests that there is,
as Henon suggested, a balance between the flow of energy and the central energy
production for almost all globular clusters.
