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

We analyze an axisymmetric magnetohydrodynamics configuration, describing the morphology of a purely differentially rotating thin plasma disk, in which linear and nonlinear perturbations are triggered associated with microscopic magnetic structures. We study the evolution of the nonstationary correction in the limit in which the corotation 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 nonlinear 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 nonlinear 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 nonlinear regime is available and a very fast instability is triggered.

Figure 1

Plot of the dimensionless pressure of Eq. (39) for $\overline{t}=0, \mathrm{\Pi }=1, {\epsilon }_z=0.001, A=1$, and $\gamma =-0.5$ (top) and $\gamma =0.01$ (bottom).

Figure 2

Plot of $\tau {\omega }_K\left(\mathrm{Pm}\right)$ in Eq. (48). To illustrate the behavior of such a quantity, we set $H^2{\nu }_{ie}{\rho }_0/3{\eta }_V=1$. The dashed red line represents the asymptote for $\mathrm{Pm}=1$.