Location of the Inner Radius of a Magnetically Threaded Accretion Disk

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Abstract
In models for disk accretion onto magnetized objects, the inner radius R0 of the Keplerian disk is conventionally expressed in the form R0 = ξrA, where rA is the Alfvén radius for spherical accretion and the parameter ξ is usually taken to be 0.5. We point out that the value of ξ in fact depends on the fraction of the star's magnetic flux threading the disk, which is poorly known from theory: in general, ξ 1.35η4/7, where η ≤ 1 denotes the threading coefficient. Application of the beat frequency model to binary X-ray pulsars showing quasi-periodic oscillations suggests strongly that η ~ 1 for these objects: the stellar dipole field essentially fully threads the disk and ξ 1. When combined with improved accretion torque models characterized by critical fastness parameters near unity, the corrected values of ξ ≡ R0/rA should allow more reliable determinations of the accreting star's dipole moment and mass-radius relationship.