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

TL;DR

This paper investigates how different shear profiles and boundary conditions affect the stability and saturation of the magnetorotational instability in astrophysical disk models with low magnetic Prandtl numbers, highlighting the importance of boundary conditions.

Contribution

It provides a theoretical analysis of MRI stability under various shear and boundary conditions, emphasizing the role of non-penetrative boundaries in MRI saturation at low Pm.

Findings

Boundary conditions significantly influence MRI stability.

Non-penetrative boundaries allow MRI saturation through shear modification.

Channel modes are not stabilized by shear modifications in Keplerian systems.

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.