  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.
