Instability of Non-uniform Toroidal Magnetic Fields in Accretion Disks

Abstract

A new type of instability that is expected to drive magnetohydrodynamic (MHD) turbulence from a purely toroidal magnetic field in an accretion disk is presented. It is already known that in a differentially rotating system, the uniform toroidal magnetic field is unstable due to a magnetorotational instability (MRI) under a non-axisymmetric and vertical perturbation, while it is stable under a purely vertical perturbation. Contrary to the previous study, this paper proposes an unstable mode completely confined to the equatorial plane, driven by the expansive nature of the magnetic pressure gradient force under a non-uniform toroidal field. The basic nature of this growing eigenmode, to which we give a name "magneto-gradient driven instability", is studied using linear analysis, and the corresponding nonlinear evolution is then investigated using two-dimensional ideal MHD simulations. Although a single localized magnetic field channel alone cannot provide sufficient Maxwell stress to contribute significantly to the angular momentum transport, we find that the mode coupling between neighboring toroidal fields under multiple localized magnetic field channels drastically generates a highly turbulent state and leads to the enhanced transport of angular momentum, comparable to the efficiency seen in previous studies on MRIs. This horizontally confined mode may play an important role in the saturation of an MRI through complementray growth with the toroidal MHDs and coupling with magnetic reconnection.