Radial Transport of Large-scale Magnetic Fields in Accretion Disks. I. Steady Solutions and an Upper Limit on the Vertical Field Strength
Abstract
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-field model 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 0.1 G at 1 AU, and about 1 mG at 10 AU from the central star. When combined with recent magnetic accretion models, the maximum field strength translates into the maximum steady-state accretion rate of ~10-7 M ⊙ yr-1, in agreement with observations. We also find that the maximum field strength is ~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 >~ kG can be transported to the surrounding disk. This might in part resolve the magnetic flux problem in star formation.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- April 2014
- DOI:
- 10.1088/0004-637X/785/2/127
- arXiv:
- arXiv:1310.7446
- Bibcode:
- 2014ApJ...785..127O
- Keywords:
-
- accretion;
- accretion disks;
- magnetic fields;
- magnetohydrodynamics: MHD;
- planets and satellites: formation;
- protoplanetary disks;
- stars: formation;
- Astrophysics - Earth and Planetary Astrophysics;
- Astrophysics - Solar and Stellar Astrophysics
- E-Print:
- 16 pages, 9 figures, to appear in ApJ. v3: typos corrected, Figure 7 updated, some references added, a note added in proof