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, 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 =5.2×10 24 ( B 0 /10 12.5 G) 1.3 ( M a /10 −8 M ʘ yr −1 ) 0.18 ( M a /M ʘ ) −1.3 Gcm 3 , and the fractional difference between its principal moments of inertia is given by Є=2.1×10 −5 ( B 0 /10 12.5 G) 0.27 ( M a /10 −8 M yr −1 ) 0.18 ( M a / M ʘ ) 1.7 , for M a in the range 10 −5 M a /M ʘ 10 −1, where B 0 is the pre-accretion magnetic field strength, and M a is the accretion rate.