Magnetized Singular Isothermal Toroids

Abstract

We consider the end states for a quasi-magnetostatic phase of evolution of molecular cloud cores by ambipolar diffusion. The models yield good initial states for fully dynamical collapse to isolated proto-stellar systems. These pivotal transition states are self-gravitating, magnetized, isothermal masses of gas in which the density scales with spherical radius r as r–2 and the magnetic field as r–1. The dependences of these quantities with angle θ satisfy the constraints of magnetostatic equilibrium. Under these circumstances, we find a linear sequence of possible pivotal states, each member characterized by a separate value of the differential mass-to-flux ratio in dimensionless form, λ≡ 2πG1/2dM/dΦ ≥ 1. In general, the pivotal states are toroids, with the density distribution on a circle of constant r in the meridional plane declining from a maximum value on the magnetic equator, θ = π/2, to zero over the magnetic poles, θ = 0 and θ = π. For λ ≫ 1, the pivotal configurations approach the unmagnetized singular isothermal sphere, with volume density ρ = (a2/2πG)r–2. For λ close to 1, the pivotal configurations flatten to a thin disk, with surface density Σ = [(1 + H0) a2/πG]r−1, where H0 is a number ≫1. We comment on the implications of these results for observations and other theoretical investigations.