Behavior of thin disk crystalline morphology in the presence of corrections to ideal magnetohydrodynamics

TL;DR

This paper investigates how microscopic magnetic structures and non-ideal effects like resistivity and viscosity influence the morphology and stability of thin, differentially rotating plasma disks in astrophysical contexts.

Contribution

It provides a detailed analysis of the impact of resistivity and viscosity on flux perturbations and disk morphology, highlighting the emergence of crystalline structures and instabilities.

Findings

Resistivity leads to damped, oscillating crystalline structures in the disk.

Viscosity dominance causes rapid non-linear instabilities.

Transient behaviors can inform models of jet formation and cataclysmic variables.

Abstract

We analyze an axisymmetric magnetohydrodynamics configuration, describing the morphology of a purely differentially rotating thin plasma disk, in which linear and non-linear perturbations are triggered associated with microscopic magnetic structures. We study the evolution of the non-stationary correction in the limit in which the co-rotation condition (i.e., the dependence of the disk angular velocity on the magnetic flux function) is preserved and the poloidal velocity components are neglected. The main feature we address here is the influence of ideal (finite electron inertia) and collisional (resistivity, viscosity, and thermal conductivity) effects on the behavior of the flux function perturbation and of the associated small-scale modifications in the disk. We analyze two different regimes in which resistivity or viscosity dominates and study the corresponding linear and non-linear behaviors of the perturbation evolution, i.e., when the backreaction magnetic field is negligible or comparable to the background one, respectively. We demonstrate that when resistivity dominates, a radial oscillating morphology (crystalline structure) emerges and it turns out to be damped in time, in both the linear and non-linear regimes, but in such a way that the resulting transient can be implemented in the description of relevant astrophysical processes, for instance, associated with jet formation or cataclysmic variables. When the viscosity effect dominates the dynamics, only the non-linear regime is available and a very fast instability is triggered.