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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.

Takashi Nakamura, with Takenori Nakano, analyzed the gravitational instability of an isothermal gaseous disk threaded perpendicularly by a frozen-in magnetic field. Their 1978 linear stability analysis showed how magnetic support changes whether perturbations can collapse.^[ref]

The competition is scale dependent: gas pressure stabilizes sufficiently short wavelengths, while the mass-to-flux ratio determines whether gravity can overcome magnetic support at larger scales.

Takenori Nakano investigated magnetic support against gaseous-disk collapse with Takashi Nakamura. For their 1978 thin-disk configuration with perpendicular frozen-in magnetic field, the critical mass-to-flux ratio isin Gaussian units, with surface mass density $\Sigma$ and field magnitude $B$. Below the threshold, magnetic support prevents the modeled gravitational instability; gas pressure also suppresses short wavelengths.^[ref]

The coefficient belongs to this geometry and magnetic coupling, rather than being a universal number for every magnetized cloud.