2001ApJ...550..314D

We present the results of the first numerical calculations to model magnetic decoupling in a collapsing molecular cloud core. Magnetic decoupling is the stage during which the motion of the neutrals ceases to significantly affect the magnetic field strength and the magnetic field ceases to significantly affect this motion. We have analyzed the resistivity of a weakly ionized, magnetic gas, and we have separated the contributions of ohmic dissipation and ambipolar diffusion. The chemical model used to determine the abundances of ionized particles accounts for, among other things, a distribution of grain radii. The evolution of an axisymmetric, magnetic molecular cloud core is followed from central densities of 300 to 2x10¹² cm^–3. Typically, magnetic decoupling begins at a central density of 3x10¹⁰ cm^–3 and is complete by a density of 2x10¹² cm^–3. We find that the mechanism responsible for magnetic decoupling is ambipolar diffusion, not ohmic dissipation, and that decoupling precedes the formation of a central stellar object. When the central density is a few times 10¹² cm^–3, a nearly uniform magnetic field of B_dec~0.1 G extends over a region ~20 AU in radius that contains a mass ~0.01 M_☉. This value of B_dec is consistent with measurements of remanent magnetization in meteorites. Magnetic decoupling at this stage is not accompanied by hydromagnetic shocks. We estimate that the ``magnetic flux problem'' of star formation is resolved by ambipolar diffusion before the magnetic field is refrozen in the matter because of thermal ionization.