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 protostellar 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≡2πG½dM/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 p = (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-2, where H0 is a number ≫ 1. We comment on the implications of these results for observations and other theoretical investigations.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- November 1996
- DOI:
- 10.1086/178056
- Bibcode:
- 1996ApJ...472..211L
- Keywords:
-
- DIFFUSION;
- ISM: CLOUDS;
- STARS: FORMATION