Magnetic field evolution of accreting neutron stars

Abstract

The flow of a matter, accreting on to a magnetized neutron star, is accompanied by an electric current. The closing of the electric current occurs in the crust of a neutron stars in the polar region across the magnetic field. But the conductivity of the crust along the magnetic field greatly exceeds the conductivity across the field, so the current penetrates deep into the crust down up to the superconducting core. The magnetic field, generated by the accretion current, increases greatly with the depth of penetration due to the Hall conductivity of the crust is also much larger than the transverse conductivity. As a result, the current begins to flow mainly in the toroidal direction, creating a strong longitudinal magnetic field, far exceeding an initial dipole field. This field exists only in the narrow polar tube of r width, narrowing with the depth, i.e. with increasing of the crust density ρ, r α ρ -1/4. Accordingly, the magnetic field B in the tube increases with the depth, Bαρ1/2, and reaches the value of about 1017 Gauss in the core. It destroys superconducting vortices in the core of a star in the narrow region of the size of the order of 10 cm. Because of generated density gradient of vortices, they constantly flow into this dead zone and the number of vortices decreases, the magnetic field of a star decreases as well. The attenuation of the magnetic field is exponential, B = B0(1 + t/τ)-1. The characteristic time of decreasing of the magnetic field t is equal to τ ≃ 103 yr. Thus, the magnetic field of accreted neutron stars decreases to values of 108-109 Gauss during 107-106 yr.