Solution (source code)

= Solution

Let $\tau_*=P/|\dot P|=300$ yr. With constant moment of inertia, the observed positive spin-up <torque> is
$$
N_*=I\dot\Omega_* =\frac{I\Omega_*}{\tau_*}=4.84\times10^{28}\ \mathrm{N\,m}.
$$
Nearly Keplerian material at the inner disk carries specific <angular momentum> $\ell=\sqrt{GMr_{\rm Alf}}$. Equating its inflow rate to the observed <torque> gives
$$
\dot M_{\rm acc}=\frac{I(2\pi/P)}{\tau_*\sqrt{GMr_{\rm Alf}}}
=\frac{I(2\pi/P)}{\tau_*\sqrt{GMr_{\rm co}}}\left(\frac{r_{\rm Alf}}{r_{\rm co}}\right)^{-1/2}.
$$
In the <surface accretion Eddington rate> convention,
$$
\boxed{\dot M_{\rm acc}=2.23\left(\frac{r_{\rm Alf}}{r_{\rm co}}\right)^{-1/2}\dot M_{\rm Edd}
\simeq2\left(\frac{r_{\rm Alf}}{r_{\rm co}}\right)^{-1/2}\dot M_{\rm Edd}}.
$$
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.