Models of self-gravitating systems with short-range cutoff on the interactions

A class of spherically symmetric mean-field models of self-gravitating systems is defined by introducing a short-distance regularization of the gravitational interactions as an effective description of the small-scale physics regardless of its precise physical origin, yet retaining the lowered-Maxwellian ansatz on the distribution function as in the classic King model. We show that with these models it is possible to precisely recover all the solutions of the standard King model as well as to consistently describe highly concentrated density profiles. Preliminary results indicate that the latter are in good agreement with observed density profiles of some globular clusters deviating from the King model prediction in the inner regions. We argue that this approach may be a first step towards a unified theoretical description of a wide class of self-gravitating systems.