Hydromagnetic Structure of a Neutron Star Accreting at Its Polar Caps

The hydromagnetic structure of a neutron star accreting symmetrically at both magnetic poles is calculated as a function of accreted mass, Ma, starting from a polytropic sphere plus central magnetic dipole (Ma = 0) and evolving the configuration through a quasistatic sequence of twodimensional, Grad–Shafranov equilibria as Ma 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× 10(B0/10 G)1.3(Ṁa/10−8 M yr−1)0.18(Ma/M )−1.3 G cm3, and the fractional difference between its principal moments of inertia is given by = 2.1× 10−5 (B0/10 G)0.27(Ṁa/10−8 M yr−1)0.18(Ma/M )1.7, forMa in the range 10−5 Ma/M 10−1, where B0 is the pre-accretion magnetic field strength, and Ṁa is the accretion rate.