Location of the inner radius of a magnetically threaded accretion disk

In models for disk accretion onto magnetized objects, the inner radius R(0) of the Keplerian disk is conventionally expressed in the form R(0) = xi r(A), where r(A) is the Alfven radius for spherical accretion and the parameter xi is usually taken to be 0.5. We point out that the value of xi in fact depends on the fraction of the star's magnetic flux threading the disk, which is poorly known from theory: in general, xi similar or equal to 1.35 eta(4/7), where eta less than or equal to 1 denotes the threading coefficient. Application of the beat frequency model to binary X-ray pulsars showing quasi-periodic oscillations suggests strongly that eta similar to 1 for these objects: the stellar dipole field essentially fully threads the disk and xi similar or equal to 1. When combined with improved accretion torque models characterized by critical fastness parameters near unity, the corrected values of xi = R(0)/r(A) should allow more reliable determinations of the accreting star's dipole moment and mass-radius relationship.