Mass–Radius Spirals for Steady State Families of the Vlasov–Poisson System

We consider spherically symmetric steady states of the Vlasov–Poisson system, which describe equilibrium configurations of galaxies or globular clusters. If the microscopic equation of state, i.e., the dependence of the steady state on the particle energy (and angular momentum) is fixed, a one-parameter family of such states is obtained. In the polytropic case the mass of the state along such a one-parameter family is a monotone function of its radius. We prove that for the King, Woolley–Dickens, and related models this mass–radius relation takes the form of a spiral.