We examine the viscosity associated with the shear stress exerted by ions in the presence of a tangled magnetic field. As an application, we consider the effect of this mechanism on the structure of black hole accretion disks. We do not attempt to include a self-consistent description of the magnetic field. Instead, we assume the existence of a tangled field with coherence length λcob• which is the average distance between the magnetic "kinks" that scatter the particles. For simplicity, we assume that the field is self-similar, and take λcob to be a fixed fraction ξ of the local disk height H. Ion viscosity in the presence of magnetic fields is generally taken to be the cross-field viscosity, wherein the effective mean free path is the ion Larmor radius λL, which is much less than the ion-ion Coulomb mean free path λu in hot accretion disks. However, we arrive at a formulation for a "hybrid" viscosity in which the tangled magnetic field acts as an intermediary in the transfer of momentum between different layers in the shear flow. The hybrid viscosity greatly exceeds the standard cross-field viscosity when (λ/λL >> (λL/λu), where λ = (λu^-1 + λcob^-1) is the effective mean free path for the ions. This inequality is well satisfied in hot accretion disks, which suggests that the ions may play a much larger role in the momentum transfer process in the presence of magnetic fields than was previously thought. The effect of the hybrid viscosity on the structure of a steady-state, two-temperature, quasi-Keplerian accretion disk is analyzed. The hybrid viscosity is influenced by the degree to which the magnetic field is tangled (represented by ξ = λcob/H), and also by the relative accretion rate M/ME, where ME= Le/c^2 and Le is the Eddington luminosity. We find that ion viscosity in the presence of magnetic fields (hybrid viscosity) can dominate over conventional magnetic viscosity for fields that are tangled on sufficiently small scales.
Subramanian, P., Becker, P.A., Kafatos, M. (1996) Ion Viscosity Mediated by Tangled Magnetic Fields: An Application to Black Hole Accretion Disks, Astrophysical Journal, 469:784-793