Turbulence in the outer regions of protoplanetary disks. II. Strong accretion driven by a vertical magnetic field

Jacob B. Simon, Xue Ning Bai, Philip J. Armitage, James McLellan Stone, Kris Beckwith

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We carry out a series of local, vertically stratified shearing box simulations of protoplanetary disks that include ambipolar diffusion and a net vertical magnetic field. The ambipolar diffusion profiles we employ correspond to 30 AU and 100 AU in a minimum mass solar nebula (MMSN) disk model, which consists of a far-ultraviolet-ionized surface layer and low-ionization disk interior. These simulations serve as a follow-up to Simon et al., in which we found that without a net vertical field, the turbulent stresses that result from the magnetorotational instability (MRI) are too weak to account for observed accretion rates. The simulations in this work show a very strong dependence of the accretion stresses on the strength of the background vertical field; as the field strength increases, the stress amplitude increases. For a net vertical field strength (quantified by β0, the ratio of gas to magnetic pressure at the disk mid-plane) of β0 = 104 and β0 = 105, we find accretion rates -10-7 M yr-1. These accretion rates agree with observational constraints, suggesting a vertical magnetic field strength of ∼60-200 μG and 10-30 μG at 30 AU and 100 AU, respectively, in a MMSN disk. Furthermore, the stress has a non-negligible component due to a magnetic wind. For sufficiently strong vertical field strengths, MRI turbulence is quenched, and the flow becomes largely laminar, with accretion proceeding through large-scale correlations in the radial and toroidal field components as well as through the magnetic wind. In all simulations, the presence of a low-ionization region near the disk mid-plane, which we call the ambipolar damping zone, results in reduced stresses there.

Original languageEnglish (US)
Article number73
JournalAstrophysical Journal
Issue number1
StatePublished - Sep 20 2013

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • accretion, accretion disks
  • magnetohydrodynamics (MHD)
  • protoplanetary disks
  • turbulence


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