Minimum magnetic-equilibrium spin period ($T_{\min }\propto B_{\ast }^{6/7}{R}_{\ast }^{15/7}$)

With magnetic spin equilibrium at the magnetospheric truncation radius, $T\propto R_M^{3/2}{M}^{-1/2}\propto B_{\ast }^{6/7}{R}_{\ast }^{18/7}{\dot{M}}^{-3/7}$ at fixed mass. Inserting the surface accretion Eddington rate changes the radius power to $15/7$. The relation assumes the boundary remains outside the star; very weak fields instead encounter surface-accretion and mass-shedding limits.