Low magnetic-Prandtl number flow configurations for cold astrophysical disk models: speculation and analysis

Abstract

Simulations of astrophysical disks in the shearing box that are subject to the magnetorotational instability (MRI) show that activity appears to be reduced as the magnetic Prandtl number (Pm) is lowered. On the other hand, calculations for laboratory experiments show that saturation is achieved through modification of the background shear for Pm << 1. Guided by the results of calculations appropriate for laboratory experiments when Pm is very low, the axisymmetric stability of inviscid disturbances in a shearing box model immersed in a constant vertical background magnetic field is considered under a variety of shear profiles and boundary conditions in order to evaluate the hypothesis that modifications of the shear bring about saturation of the instability. It is found that the emergence and stability of the MRI is sensitive to the boundary conditions adopted. Channel modes do not appear to be stabilized through any modification of the background shear whose average remains Keplerian. However, systems that have non-penetrative boundaries can saturate the MRI through modification of the background shear. Conceptually equating the qualitative results from laboratory experiments to the conditions in a disk may therefore be misleading.