The disk-magnetosphere interaction in the accretion-powered millisecond pulsar SAX J1808.4-3658

The recent discovery of the first known accretion-powered millisecond pulsar with the Rossi X-Ray Timing Explorer provides the first direct probe of the interaction of an accretion disk with the magnetic field of a weakly magnetic (B ≲ 10¹⁰ G) neutron star. We demonstrate that the presence of coherent pulsations from a weakly magnetic neutron star over a wide range of accretion rates places strong constraints on models of the disk-magnetosphere interaction. We argue that the simple Ṁ^3/7 scaling law for the Keplerian frequency at the magnetic interaction radius, widely used to model disk accretion onto magnetic stars, is not consistent with observations of SAX J1808.4 - 3658 for most proposed equations of state for stable neutron stars. We show that the usually neglected effects of multipole magnetic moments, radiation drag forces, and general relativity must be considered when modeling such weakly magnetic systems. Using only very general assumptions, we obtain a robust estimate of μ ≃ (1-10) × 10²⁶ G cm³ for the dipole magnetic moment of SAX J1808.4-3658, implying a surface dipole field of ∼ 10⁸-10⁹ G at the stellar equator. We therefore infer that after the end of its accretion phase, this source will become a normal millisecond radio pulsar. Finally, we compare the physical properties of this pulsar with those of the nonpulsing, weakly magnetic neutron stars in low-mass X-ray binaries and argue that the absence of coherent pulsations from the latter does not necessarily imply that these neutron stars have significantly different magnetic field strengths from SAX J1808.4-3658.