Magnetic field diffusion in self-consistently turbulent accretion disks

J. Heyvaerts*, E. R. Priest, A. Bardou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We show how the level of turbulence in accretion disks can be derived from a self-consistency requirement that the associated effective viscosity should match the instantaneous accretion rate. This method is applicable when turbulence has a direct energy cascade. Only limited information on the origin and properties of the turbulence, such as its injection scale and anisotropy, is needed. The method is illustrated by considering the case of turbulence originating from the magnetic shearing instability. The corresponding effective kinematic viscosity coefficient is shown to scale as the 1/3 power of surface mass density at a given radius in optically thick disks, and to be describable by a Shakura-Sunyaev law with α ≈ 0.04. Mass flow in disks fed at a localized hot spot is calculated for accretion regimes driven by such turbulence, as well as passive magnetic field diffusion and dragging. An important result of this analysis is that thin disks supported by turbulence driven by the magnetic shearing instability, and more generally any turbulence with injection scale of order of the disk thickness, are very low magnetic Reynolds number systems. Turbulent viscosity-driven solutions with negligible field dragging and no emission of cold winds or jets are natural consequences of such regimes. Disks of accreting objects that are magnetized enough to be shielded by a magnetopause, however, may not operate in their innermost regions in the magnetic shearing instability regime. The possibility therefore remains to be explored of centrifugally driven winds emanating from such regions.

Original languageEnglish
Pages (from-to)403-421
Number of pages19
JournalAstrophysical Journal
Issue number1 PART I
Publication statusPublished - 1996


  • Accretion, accretion disks
  • Diffusion
  • MHD
  • Stars: Mass loss
  • Turbulence


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