2. Some observational characteristics
The characteristic shape of a globular cluster shows a
spatial distribution of stars such that the density
is highest at the centre and decreases to the outer parts
until it gradually turns into the low populated
halo field of the galaxy.
On short time scales the density function is well
balanced between the selfgraviting forces of the
total star assembly, pointing inwards to the cluster centre,
and the outward forces, resulting from the motion of the
members which are deflected out of the crowded areas.
This kind of balance is called a "virial equilibrium",
and the cluster is considered as "relaxed".
M 15, a Globular Cluster with the densest core.
The radial profiles of most of the clusters qualitatively
show a central region or "core radius" within which the
brightness does not change very much;
these systems are well fitted by conventional equilibrium
models.
But there are also exceptions, among them M 15.
The surface brightness of this cluster continues to rise
all the way to its centre rather than flattening out,
and it is apparent that it possesses a remarkably sharp
central "cusp" suggesting an infinite density.
The excess of brightness in M 15 has been recognized for
quite some time, but it was treated as something of an
oddity.
Various explanations were advanced, ranging from a massive
black hole harboured in the core to dynamical shrinking.
In fact, numerical studies of self-gravitating systems
showed that even clusters with an initially "flat" core
ultimately become instable at their centres.
This phenomenon was to become the most puzzling paradox
of self-gravitating systems and the "Holy Grail" of stellar
dynamics: the core collapse.
1. Secrets of stellar clusters
