Corotation radius ($r_{\mathrm{co}}=(GM/{\Omega }_{\ast }^2{)}^{1/3}$)

The corotation radius is where a central star's spin matches the local Keplerian rotation. Equating ${\Omega }_{\ast }=\sqrt{GM/r_{\mathrm{co}}^3}$ gives $r_{\mathrm{co}}=(GM/{\Omega }_{\ast }^2{)}^{1/3}$. For example, doubling the stellar spin moves this radius inward by $2^{-2/3}$. Its relevance is dynamical: magnetic coupling outside it tends to accelerate disk gas toward the faster stellar rotation, whereas coupling inside it can brake the gas. The propeller effect also depends on whether the magnetospheric truncation radius lies outside this reference radius.