Burial of the polar magnetic field of an accreting neutron star – I. Self-consistent analytic and numerical equilibria

The hydromagnetic structure of a neutron star accreting symmetrically at both magnetic poles is calculated as a function of accreted mass, M_a, and polar cap radius,starting from a centered magnetic dipole and evolving through a quasistatic sequence of two-dimensional, Grad-Shafranov equilibria. The calculation is the first to track fully the growth of high-order magnetic multipoles, due to equatorward hydromagnetic spreading, while simultaneously preserving flux freezing and a self-consistent mass-flux distribution. Equilibria are constructed numerically by an iterative scheme and analytically by Green functions. Two key results are obtained, with implications for recycled pulsars. (i) The mass required to significantly reduce the magnetic dipole moment, 10^{-5} Msun, greatly exceeds previous estimates (~ 10^{-10} Msun), which ignored the confining stress exerted by the compressed equatorial magnetic field. (ii) Magnetic bubbles, disconnected from the stellar surface, form in the later stages of accretion (M_a > 10^{-4} Msun).