Magnetic screening in accreting neutron stars

We investigate whether the magnetic field of an accreting neutron star may be diamagnetically screened by the accreted matter. We assume the freshly accumulated material is unmagnetized and calculate the rate at which the intrinsic stellar magnetic flux is transported into it via Ohmic diffusion from below. For very high accretion rates (M) over dot (larger than the Eddington rate (M) over dot(Edd)), Brown & Bildsten have shown that the liquid ocean and outer crust of the neutron star are built up on a timescale much shorter than the Ohmic, penetration time. We extend their work to lower accretion rates and calculate the resulting screening of the magnetic field. We find that the Ohmic diffusion and accretion timescales are equal for (M) over dot approximate to 0.1 (M) over dot(Edd). We calculate the one-dimensional steady state magnetic field profiles and show that the magnetic field strength decreases as one moves up through the outer crust and ocean by n orders of magnitude, where n approximate to (M) over dot/0.02 (M) over dot(Edd). We show that these profiles are unstable to buoyancy instabilities when B greater than or similar to 10(10)-10(11) G in the ocean, providing a new limit on the strength of the buried field. Our results have interesting implications for the weakly magnetic neutron stars in low-mass X-ray binaries. We find that magnetic screening is ineffective for (M) over dot < 10(-2) (M) over dot(Edd), so that, no matter how the accreted material joins onto the star, the underlying stellar field should always be evident. This is consistent with the fact that the only known persistently pulsing accreting X-ray millisecond pulsar, SAX J1808.4-3658, has an unusually low accretion rate of (M) over dot similar to 10(-3) (M) over dot(Edd). Although the simplified magnetic and accretion geometry we adopt here does not allow us to definitively say so, we are led to suggest that perhaps most of the weakly magnetic neutron stars in low-mass X-ray binaries have a screened magnetic field, explaining the lack of persistent pulsations from these sources. If screened, then the underlying field will emerge after accretion halts, on a timescale of only 100-1000 yr, set by the Ohmic diffusion time across the outer crust.