General steady viscous flux in a Keplerian disk ($\bar{\nu }\Sigma =A+B{r}^{-1/2},\dot{M}=3\pi A$)

Two integrations of the steady Keplerian viscous diffusion equation give this general transported quantity. $A$ fixes the mass accretion rate, while $B$ fixes the additive angular-momentum flux or inner torque. A zero-torque inner boundary condition gives $B=-A\sqrt{r_{\mathrm{in}}}$; a nonaccreting constant-torque disk has $A=0$.