On the mass-radius relation of hot stellar systems
  Most globular clusters have half-mass radii of a few pc with no apparent
correlation with their masses. This is different from elliptical galaxies, for
which the Faber-Jackson relation suggests a strong positive correlation between
mass and radius. Objects that are somewhat in between globular clusters and
low-mass galaxies, such as ultra-compact dwarf galaxies, have a mass-radius
relation consistent with the extension of the relation for bright ellipticals.
Here we show that at an age of 10 Gyr a break in the mass-radius relation at
~10^6 Msun is established because objects below this mass, i.e. globular
clusters, have undergone expansion driven by stellar evolution and hard
binaries. From numerical simulations we find that the combined energy
production of these two effects in the core comes into balance with the flux of
energy that is conducted across the half-mass radius by relaxation. An
important property of this `balanced' evolution is that the cluster half-mass
radius is independent of its initial value and is a function of the number of
bound stars and the age only. It is therefore not possible to infer the initial
mass-radius relation of globular clusters and we can only conclude that the
present day properties are consistent with the hypothesis that all hot stellar
systems formed with the same mass-radius relation and that globular clusters
have moved away from this relation because of a Hubble time of stellar and
dynamical evolution.
