Accretion by rotating magnetic neutron stars. III - Accretion torques and period changes in pulsating X-ray sources

The solutions of the two-dimensional hydromagnetic equations are used to calculate the torque on a magnetic neutron star accreting from a Keplerian disk. It is found that the magnetic coupling between the star and the plasma in the outer transition zone is appreciable; that as a result, the spin-up torque on fast rotators is substantially less than that on slow rotators, and that for sufficiently high stellar angular velocities or sufficiently low mass accretion rates, the rotation of the star can be braked while accretion continues. These results are applied to pulsating X-ray sources, revealing that at high luminosities a star of given spin period rotating in the same direction as the disk can experience either spin-up or spin-down, depending on its luminosity. Also considered are the general problem of interpreting period changes in pulsating X-ray sources, and the dipole magnetic moments of nine pulsating X-ray sources are estimated by fitting the theoretical spin-up equation to estimates of the average luminosity and spin-up rate of each source.