Scale‐free Equilibria of Isopedic Polytropic Clouds

We investigate the equilibrium properties of self-gravitating magnetized clouds with polytropic equations of state with negative index n . In particular, we consider scale-free isopedic configurations that have constant dimensionless spherical mass-to-flux ratio λ r and that may constitute "pivotal" states for subsequent dynamical collapse to form groups or clusters of stars. For given Γ = 1 + 1/ n , equilibria with smaller values of λ r are more flattened, ranging from spherical configurations with λ r = ∞ to completely flattened states for λ r = 1. For a given amount of support provided by the magnetic field as measured by the dimensionless parameter H 0 , equilibria with smaller values of Γ are more flattened. However, logatropic (defined by Γ = 0) disks do not exist. The only possible scale-free isopedic equilibria with logatropic equation of state are spherical uniformly magnetized clouds.