Physical Properties of Parasitic Modes in Non-ideal Mhd Accretion Disks

We investigate the stability of incompressible, exact, non-ideal magnetorotational (MRI) modes against parasitic instabilities for a broad range of dissipation coefficients, relevant to astrophysical and laboratory environments. This allows us to uncover the asymptotic behavior of the fastest parasites in terms of the Elsasser number, Λη, when viscous effects are not important. We calculate the fastest growing parasitic modes feeding off the MRI and show that they correspond to Kelvin-Helmholtz instabilities for Λη ≥ 1 and tearing mode instabilities for Λη < 1. We study in detail the regime Λη ≃ 1 where both types of modes present comparable growth rates. We conjecture about the asymptotic behavior of saturation based on the idea that the saturation level of the MRI can be estimated by comparing growth rates (or amplitudes) of primary and secondary modes. In the ideal magnetohydrodynamic (MHD) limit, Λη ≫ 1, where Kelvin-Helmholtz modes dominate, these estimates lead to saturation levels for the stresses that are in rough agreement with current numerical simulations. For resistive MHD, Λη . 1, the stresses produced by the MRI primary modes, at the time when the fastest tearing modes have growth rates similar to their own, decay proportionally to the Elsasser number. This behavior seems consistent with numerical simulations of resistive MHD shearing boxes. Subject headings: accretion, accretion disks — black hole physics — instabilities — MHD — turbulence