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The recent discovery of the first known accretion-powered millisecond pulsarwith the Rossi X-Ray Timing Explorer provides the first direct probe of theinteraction of an accretion disk with the magnetic field of a weakly magnetic(B<10^10 G) neutron star. We demonstrate that the presence of coherentpulsations from a weakly magnetic neutron star over a wide range of accretionrates places strong constraints on models of the disk-magnetosphereinteraction. We argue that the simple Mdot^(3/7) scaling law for the Keplerianfrequency at the magnetic interaction radius, widely used to model diskaccretion onto magnetic stars, is not consistent with observations of SAXJ1808.4-3658 for most proposed equations of state for stable neutron stars. Weshow that the usually neglected effects of multipole magnetic moments,radiation drag forces, and general relativity must be considered when modelingsuch weakly magnetic systems. Using only very general assumptions, we obtain arobust estimate of mu~(1-10)x10^26 G cm^3 for the dipole magnetic moment of SAXJ1808.4-3658, implying a surface dipole field of ~10^8-10^9 G at the stellarequator. We therefore infer that after the end of its accretion phase, thissource will become a normal millisecond radio pulsar. Finally, we compare thephysical properties of this pulsar to those of the non-pulsing, weakly magneticneutron stars in low-mass X-ray binaries and argue that the absence of coherentpulsations from the latter does not necessarily imply that these neutron starshave significantly different magnetic field strengths from SAX J1808.4-3658.Comment: 20 pages, 4 figures. Accepted version (minor revisions and 1 new  figure). To appear in the Astrophysical Journa

The Disk‐Magnetosphere Interaction in the Accretion‐powered Millisecond Pulsar SAX J1808.4−3658