Scale-free equilibria of isopedic polytropic clouds

We investigate the equilibrium properties of self-gravitating magnetized cl ouds with polytropic equations of state with negative index n. In particula r, we consider scale-free isopedic configurations that have constant dimens ionless spherical mass-to-flux ratio lambda(r) and that may constitute "piv otal" states for subsequent dynamical collapse to form groups or clusters o f stars. For given Gamma = 1 + 1/n, equilibria with smaller values of lambd a(r) are more flattened, ranging from spherical configurations with lambda( r) = infinity to completely flattened states for lambda(r) = 1. For a given amount of support provided by the magnetic field as measured by the dimens ionless parameter H-0, equilibria with smaller values of Gamma are more fla ttened. However, logatropic (defined by Gamma = 0) disks do not exist. The only possible scale-free isopedic equilibria with logatropic equation of st ate are spherical uniformly magnetized clouds.