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 ≡ 2πG~(1/2)dM/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 = (a~2/2πG)r~(-2). For λ close to 1, the pivotal configurations flatten to a thin disk, with surface density ∑ = [(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.
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