Magnetized Singular Isothermal Toroids

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 ≡ 2 πG 1/2 dM / d Φ ≥ 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 = ( a 2 /2π G ) r –2 . For λ close to 1, the pivotal configurations flatten to a thin disk, with surface density Σ = [(1 + H 0 ) a 2 /πG] r −1 , where H 0 is a number ≫1. We comment on the implications of these results for observations and other theoretical investigations.