Magnetic Jeans mass ($M_B=C\frac{B^3}{({\mu }_{0}G{)}^{3/2}{\rho }^2}$)

Replacing the sound speed in a Jeans mass estimate by the Alfvén speed $B/\sqrt{{\mu }_0\rho }$ gives the displayed magnetic-support mass scale. A sphere whose diameter is the corresponding wavelength gives $C={\pi }^{5/2}/6$; the crossing-time cloud support mass instead gives $C=(4\pi /3)(3\pi /32{)}^{3/2}$. The coefficient is model dependent, and a real magnetic field supplies anisotropic stresses rather than isotropic gas pressure.

During isotropic magnetic flux freezing, $B\propto {\rho }^{2/3}$, so $M_B$ and the number of such masses in a fixed material cloud remain constant. This is another expression of a conserved mass-to-flux ratio. It contrasts with the decreasing thermal Jeans mass of isothermal fragmentation, and does not rule out motion or fragmentation along field lines.