In magnetically channelled accretion, an outer accretion disk supplies nearly Keplerian material. Near the magnetospheric truncation radius, magnetic stresses disrupt the disk and guide matter along field lines onto polar accretion columns. Shocks and settling near the surface release gravitational binding energy, and an oblique magnetic geometry makes the rotating emission pattern pulsate.
The corotation radius satisfies , hence
The accretion Alfvén radius estimates where magnetic stress becomes comparable with the inflow's dynamical stress; it is the magnetic truncation scale in this application, not the Alfvén critical point of an outward stellar wind. The supplied seventh-root scaling follows from a dipole's rapidly decreasing magnetic pressure and an accretion-pressure estimate. Its coefficient depends on disk geometry. Ordinary inward surface accretion requires the magnetosphere to remain outside the star and usually inside or near corotation, . Beyond corotation, a rapidly moving magnetosphere can transfer angular momentum outward and inhibit inflow through the propeller effect.
Figure 1.
Magnetic channeling from a truncated accretion disk to neutron-star polar caps, with the corotation condition shown separately
. Details.
The corotation radius is where the stellar spin matches Keplerian rotation:
A parcel forced into corotation at has outward centrifugal acceleration . This exceeds the inward gravitational acceleration when
This 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 has nonnegative specific orbital energy only if
Additional magnetic work, radial motion or pressure can alter that escape condition.