Hydromagnetic Structure of a Neutron Star Accreting at Its Polar Caps

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 =5.2×10²⁴(B₀/10^12.5G)^1.3( M_a/10^-8M yr^-1)^0.18(M_a/M)^-1.3Gcm³, and the fractional difference between its principal moments of inertia is given by =2.110^-5 (B₀/10^12.5G)^0.27 (M_a/10^-8M yr^-1)^0.18(M_a/M)^1.7, for M_a in the range 10^-5 M_a/M 10^-1,where B₀ is the pre-accretion magnetic field strength, and M_a is the accretion rate.