= Magnetic Jeans mass
{c}
{title2=$M_B=C\frac{B^3}{(\mu_0G)^{3/2}\rho^2}$}
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.
Back to article page
