Steady Keplerian accretion disk with an inner torque ($\bar{\nu }\Sigma =\frac{\dot{M}}{3\pi }[1+(\lambda -1)\sqrt{r_{\mathrm{in}}/r}]$)

For a positive inner magnetic torque $T_m$, define $\lambda =T_m/(\dot{M}{h}_{\mathrm{in}})$. Integrating steady conservation of angular momentum gives $\mathcal{G}=T_m+\dot{M}(h-h_{\mathrm{in}})$. With Keplerian rotation, this determines the surface density of a disk in the displayed formula.

When the applied inner torque dominates the advective angular-momentum flux, the constant-kinematic viscosity inner profile resembles a decretion disk. This resemblance does not alone imply outward mass transport.