Screening of the magnetic field of disk accreting stars

An analytical model is developed for the screening of the external magnetic field of a rotating, axisymmetric neutron star due to the accretion of plasma from a disk. The decrease of the field occurs as a result of the electric current in the infalling plasma. The deposition of this current-carrying plasma on the star's surface creates an induced magnetic moment with a sign opposite to that of the original magnetic dipole. The field decreases independent of whether the star spins up or spins down. The timescale for an appreciable decrease ( factor of > 100) of the field is found to be similar to 1.6 x 10(7) yr, for a mass accretion rate. M = 10(-9) M-circle dot yr(-1) and an initial magnetic moment mu(i) = 10(30) G cm(3), which corresponds to a surface field of 10(12) G if the star's radius is 10(6) cm. The timescale varies approximately as mu(i)(3.8)/M-1.9. The decrease of the magnetic field does not have a simple relation to the accreted mass. Once the accretion stops the field leaks out on an Ohmic diffusion timescale that is estimated to be > 10(9) yr.