Magnetized Singular Isothermal Toroids

Abstract

We consider the end states for a quasi-magnetostatic phase of evolution of molecular cloud cores by ambipolar di†usion. 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 Ðeld as r~1. The dependences of these quantities with angle h satisfy the constraints of magnetostatic equilibrium. Under these circum- stances, we Ðnd a linear sequence of possible pivotal states, each member characterized by a separate value of the di†erential mass-to-Ñux ratio in dimensionless form, j42nG1@2dM/d'º1. 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, h/2, to zero over the magnetic poles, h\0 and h. For j?1, the pivotal conÐgurations approach the unmagnetized singular isothermal sphere, with volume density o\(a2/2nG)r~2. For j close to 1, the pivotal conÐgurations Ñatten to a thin disk, with surface density implications