Self-gravitating systems, like globular clusters or elliptical galaxies, are
the prototypes of many-body systems with long-range interactions, and should be
the natural arena where to test theoretical predictions on the statistical
behaviour of long-range-interacting systems. Systems of classical
self-gravitating particles can be studied with the standard tools of
equilibrium statistical mechanics, provided the potential is regularized at
small length scales and the system is confined in a box. The confinement
condition looks rather unphysical in general, so that it is natural to ask
whether what we learn with these studies is relevant to real self-gravitating
systems. In order to provide a first answer to this question we consider a
basic, simple, yet effective model of globular clusters, the King model. This
model describes a self-consistently confined system, without the need of any
external box, but the stationary state is a non-thermal one. In particular, we
consider the King model with a short-distance cutoff on the interactions and we
discuss how such a cutoff affects the caloric curve, i.e. the relation between
temperature and energy. We find that the cutoff stabilizes a low-energy phase
which is absent in the King model without cutoff; the caloric curve of the
model with cutoff turns out to be very similar to that of previously studied
confined and regularized models, but for the absence of a high-energy gas-like
phase. We briefly discuss the possible phenomenological as well as theoretical
implications of these results.Comment: 21 pages, 13 figure
