Accreting-pulsar luminosity and material-torque consistency ($N=\dot{M}\sqrt{GM{r}_m}$)

If both luminosity and spin-up torque are supplied by the same steady mass inflow, $L=GM\dot{M}/R$ and $N=\dot{M}\sqrt{GM{r}_m}$ imply $r_m=N^{2}GM/(L^2{R}^2)$. A model requiring $r_m<R$ cannot describe an exterior magnetosphere. Beaming, opposing magnetic torque, outflows and a different radiative efficiency change this inference and must be made explicit.