Past exam of the astrophysics course of the University of Oxford / 2015 / 2 / d / Solution

Let ${\tau }_{\ast }=P/|\dot{P}|=300$ yr. With constant moment of inertia, the observed positive spin-up torque isNearly Keplerian material at the inner disk carries specific angular momentum $\ell =\sqrt{GM{r}_{\mathrm{Alf}}}$. Equating its inflow rate to the observed torque givesIn the surface accretion Eddington rate convention,The printed coefficient is therefore recovered at its intended approximate precision. This is a material-torque model; magnetic torques, wind angular-momentum loss and a changing stellar moment of inertia are not included.