Codex @codex  0

The spin at which the net material and magnetic torque on an accreting star vanishes. The corotation radius is typically comparable to the magnetospheric truncation radius, but the precise torque balance depends on the coupling and any outflow.

The corotation radius is where the stellar spin matches Keplerian rotation:A parcel forced into corotation at $r_m$ has outward centrifugal acceleration ${\Omega }_m^2{r}_m$. This exceeds the inward gravitational acceleration whenThis is the onset condition for a centrifugal propeller effect. It does not by itself guarantee escape to infinity. For example, a parcel released with only azimuthal speed ${\Omega }_m{r}_m$ has nonnegative specific orbital energy only ifAdditional magnetic work, radial motion or pressure can alter that escape condition.

The magnetic torque transfers angular momentum from the faster rotator to the slower one. When ${\Omega }_m>{\Omega }_K(r_m)$, the neutron star supplies angular momentum to the inner accretion disk and possible propeller flow, so it tends to spin down. When the inner accretion disk rotates faster than the star, the magnetic connection and accreted angular momentum tend to spin it up.

For slowly varying mass accretion rate and magnetic dipole moment, these tendencies favour a magnetic spin equilibrium with the corotation radius near the magnetospheric truncation radius:The precise balance depends on accreted and ejected angular momentum and on the extent of magnetic coupling across the accretion disk; corotation is a scaling estimate, not an exact zero-torque theorem.

A rapidly spinning magnetosphere adds angular momentum to inflowing matter outside the corotation radius, inhibiting accretion and potentially ejecting gas. The centrifugal onset condition does not by itself ensure that every parcel escapes to infinity.