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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.

Magnetic subcriticality refers to a mass-to-flux ratio below its critical mass-to-flux ratio. For an idealized thin layer threaded by a uniform frozen-in perpendicular magnetic field, define in SI unitsHere $\Sigma$ is the surface density and $B_{z0}$ the perpendicular magnetic field. The magnetically subcritical case has $\lambda <1$, or $B_{z0}^2>\pi G{\mu }_0{\Sigma }^2$. In the specified ideal layer, magnetic support prevents the linear gravitational collapse studied by Takenori Nakano and Takashi Nakamura. Their original Gaussian-unit threshold is $\Sigma /|B_{z0}|<1/(2\pi \sqrt{G})$. The numerical coefficient is tied to geometry and field assumptions.^[ref]

A complementary sufficient-contraction result applies to an isolated cold initially resting razor-thin disk. If $B_{z0}^2<\pi G{\mu }_0{\Sigma }^2$ pointwise, the absolute gravity-equivalent magnetic surface density is smaller than the actual surface density. The positive-kernel comparison of thin-disk fields then makes the integrand in the horizontal virial balance of a cold magnetized fluid negative above and below the disk. Its radial second moment therefore begins to decrease. This weak-field inequality is on the magnetically supercritical disk side of the mass-to-flux convention.

The second-moment conclusion is global. It does not establish inward acceleration of every fluid element, and it does not prove unlimited subsequent collapse. Pressure, rotation, magnetic flux loss and different boundary-field configurations require their own analysis.