Recycled pulsars with multipolar magnetospheres from accretion-induced magnetic burial

Many millisecond pulsars are thought to be old neutron stars spun up (`recycled') during an earlier accretion phase. They typically have relatively weak ($\lesssim 10^{9} \text{ G}$) dipole field strengths, consistent with accretion-induced magnetic burial. Recent data from the Neutron Star Interior Composition Explorer indicate that hot spots atop the recycled pulsar PSR J0030$+$0451 are not antipodal, so that the magnetic field cannot be that of a centered dipole. In this paper it is shown that multipolarity is naturally expected in the burial scenario because of equatorial field line compression. Grad-Shafranov equilibria are constructed to show how magnetic multipole moments can be calculated in terms of various properties, such as the amount of accreted mass and the crustal equation of state.