Hydromagnetic Structure of a Neutron Star Accreting at Its Polar Caps

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Abstract
The hydromagnetic structure of a neutron star accreting symmetrically at both magnetic poles is calculated as a function of accreted mass, M a, starting from a polytropic sphere plus central magnetic dipole (M a =0) and evolving the configuration through a quasistatic sequence of twodimensional, Grad–Shafranov equilibria as M a increases. It is found that the accreted material spreads equatorward under its own weight, compressing the magnetic field into a thin boundary layer and burying it everywhere except in a narrow, equatorial belt. The magnetic dipole moment of the star is given by µ=5.2×1024(B 0/1012.5G)1.3(M a/10−8 M ʘ yr−1)0.18(M a/Mʘ)−1.3Gcm3, and the fractional difference between its principal moments of inertia is given by Є=2.1×10−5(B 0/1012.5G)0.27(M a/10−8 Myr−1)0.18(M a/M ʘ)1.7, for M a in the range 10−5 M a/Mʘ10−1,where B 0 is the pre-accretion magnetic field strength, and M a is the accretion rate.