Mass-to-flux ratio ( $M / Φ_{B}$ )

The mass-to-flux ratio is the matter carried per unit magnetic flux by a bundle of field lines. Ideal magnetohydrodynamics preserves it for a material flux tube.

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- Critical mass-to-flux ratio Mass-to-flux ratio

Critical mass-to-flux ratio ( $(M /Φ)_{crit} = λ / μ_{0} G$ )

For fixed cloud shape, gravitational energy scales as

- C_{g} G M^{2} / L

and magnetic energy as

C_{B} Φ^{2} / (μ_{0} L)

. The magnetic-criticality threshold for negligible pressure is

M /Φ > C_{B} / C_{g} / μ_{0} G

. Ideal flux freezing keeps this ratio fixed during homologous collapse; geometry determines the numerical coefficient.

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