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Large scale magnetic field threading an accretion disk is a key ingredient inthe jet formation model. The most attractive scenario for the origin of such alarge scale field is the advection of the field by the gas in the accretiondisk from the interstellar medium or a companion star. However, it is realizedthat outward diffusion of the accreted field is fast compared to the inwardaccretion velocity in a geometrically thin accretion disk if the value of thePrandtl number Pm is around unity. In this work, we revisit this problemconsidering the angular momentum of the disk is removed predominantly by themagnetically driven outflows. The radial velocity of the disk is significantlyincreased due to the presence of the outflows. Using a simplified model for thevertical disk structure, we find that even moderately weak fields can causesufficient angular momentum loss via a magnetic wind to balance outwarddiffusion. There are two equilibrium points, one at low field strengthscorresponding to a plasma-beta at the midplane of order several hundred, andone for strong accreted fields, beta~1. We surmise that the first is relevantfor the accretion of weak, possibly external, fields through the outer parts ofthe disk, while the latter one could explain the tendency, observed in full 3Dnumerical simulations, of strong flux bundles at the centers of disk to stayconfined in spite of strong MRI turbulence surrounding them.

The large scale magnetic fields of thin accretion disks