Local and global aspects of the linear MRI in accretion discs

Abstract

We revisit the linear MRI in a cylindrical model of an accretion disk and uncover a number of attractive results overlooked in previous treatments. In particular, we elucidate the connection between local axisymmetric modes and global modes, and show that a local channel flow corresponds to the evanescent part of a global mode. In addition, we find that the global problem reproduces the local dispersion relation without approximation, a result that helps explain the success the local analysis enjoys in predicting global growth rates. MRI channel flows are nonlinear solutions to the governing equations in the local shearing box. However, only a small subset of MRI modes share the same property in global disk models, providing further evidence that the prominence of channels in local boxes is artificial. Finally, we verify our results via direct numerical simulations with the Godunov code RAMSES.