TRANSPORT OF LARGE-SCALE MAGNETIC FIELDS IN ACCRETION DISKS. I. STEADY SOLUTIONS AND AN UPPER LIMIT ON THE VERTICAL FIELD STRENGTH

Large-scale magnetic fields are key ingredients of magnetically driven disk accretion. We study how large-scale poloidal fields evolve in accretion disks, with the primary aim of quantifying the viability of magnetic accretion mechanisms in protoplanetary disks. We employ a kinematic mean-fieldmodel for poloidal field transport and focus on steady states where inward advection of a field balances with outward diffusion due to effective resistivities. We analytically derive the steady-state radial distribution of poloidal fields in highly conducting accretion disks. The analytic solution reveals an upper limit on the strength of large-scale vertical fields attainable in steady states. Any excess poloidal field will diffuse away within a finite time, and we demonstrate this with time-dependent numerical calculations of the mean-field equations. We apply this upper limit to large-scale vertical fields threading protoplanetary disks. We find that the maximum attainable strength is about 0.1G at 1AU, and about 1mG at 10AU from the central star. When combined with recent magnetic accretion models, the maximum field strength translates into the maximum steady-state accretion rate of similar to 10(-7)M(circle dot) yr(-1), in agreement with observations. We also find that the maximum field strength is similar to 1 kG at the surface of the central star provided that the disk extends down to the stellar surface. This implies that any excess stellar poloidal field of strength greater than or similar to kG can be transported to the surrounding disk. This might in part resolve the magnetic flux problem in star formation.