Gravity and Thermodynamics in globular clusters. Gravothermal instability and some observational evidences

This work deals with the consequences which follow from the construction of a selfconsistent thermodynamical model of globular cluster. In so doing we are driven by the necessity of a star cluster model with density and pressure vanishing in correspondence of the surface of the system, whose nite radius is determined by the tidal force of the Galaxy. Considering the evolution of the selfgravitating system like a sequence of innite equilibrium states, driven by reversible transformations, lead us to the introduction of an effective potential term, in the single particle Hamiltonian, taking into account the presence of the kinetic cutoff energy. The inuence of the effective potential on the virial theorem will be described, together with the related consequences on the gravothermal stability limits for star clusters, explored through the linear series method for the equilibrium congurations. The effective potential description of the equilibrium models leads to some observational features, which allow to test the predicted critical central potential depth for the insurgence of the thermodynamical instability.