Magnetically supercritical disk

A magnetically supercritical disk has a mass-to-magnetic-flux ratio above the critical value for magnetic support in a specified geometry. With surface mass density $\Sigma$ and perpendicular magnetic field $B_z$, a common idealized sheet convention in Gaussian units is $\lambda =2\pi \sqrt{G}\Sigma /|B_z|$, with supercriticality defined by $\lambda >1$.

The ratio compares self-gravity with magnetic support, not with every possible restoring mechanism. Rotation and gas pressure can still stabilize some disturbances, and thermal evolution controls nonlinear fragmentation. The numerical critical coefficient depends on the geometry and boundary assumptions, so a mass-to-flux criterion should not be transferred unchanged between a sheet, a sphere and a realistic disk.