Stable and unstable equilibria of uniformly rotating self-gravitating cylinders

The equilibrium configurations of self-gravitating uniformly rotating isothermal cylinders in contact with a heat bath and their stability is studied by recently derived analytical techniques. The known critical temperature T c obtained by Katz and Lynden-Bell is found to be a stability threshold with respect to axially symmetric perturbations. We provide the almost explicit expression of negative specific heat solutions whose densities are sharply concentrated either near the symmetry axis or near some off-axis filaments as T → T c − . The critical angular frequency observed numerically in literature is found to be the threshold value for the existence of these off-axis filaments. This is in strik- ing contrast with the static case analyzed by Katz and Lynden-Bell where equilibrium configurations are found only if T > T c and no negative specific heat equilibria exists at all. Metastability of the free energy’s relative maximizers for T ≤ T c is also discussed. Those off-axis configurations were predicted in the study of negative temperature states for guiding-centre plasmas and vortex systems.