The large scale magnetic fields of thin accretion disks

Large scale magnetic field threading an accretion disk is a key ingredient in the jet formation model. The most attractive scenario for the origin of such a large scale field is the advection of the field by the gas in the accretion disk from the interstellar medium or a companion star. However, it is realized that outward diffusion of the accreted field is fast compared to the inward accretion velocity in a geometrically thin accretion disk if the value of the Prandtl number Pm is around unity. In this work, we revisit this problem considering the angular momentum of the disk is removed predominantly by the magnetically driven outflows. The radial velocity of the disk is significantly increased due to the presence of the outflows. Using a simplified model for the vertical disk structure, we find that even moderately weak fields can cause sufficient angular momentum loss via a magnetic wind to balance outward diffusion. There are two equilibrium points, one at low field strengths corresponding to a plasma-beta at the midplane of order several hundred, and one for strong accreted fields, beta~1. We surmise that the first is relevant for the accretion of weak, possibly external, fields through the outer parts of the disk, while the latter one could explain the tendency, observed in full 3D numerical simulations, of strong flux bundles at the centers of disk to stay confined in spite of strong MRI turbulence surrounding them.