Resistive relaxation of a magnetically confined mountain on an accreting neutron star

Three-dimensional numerical magnetohydrodynamic (MHD) simulations are performed to investigate how a magnetically confined mountain on an accreting neutron star relaxes resistively. No evidence is found for non-ideal MHD instabilities on a short time-scale, such as the resistive ballooning mode or the tearing mode. Instead, the mountain relaxes gradually as matter is transported across magnetic surfaces on the diffusion time-scale, which evaluates to tau(I) similar to 10(5)-10(8) yr (depending on the conductivity of the neutron star crust) for an accreted mass of M-a = 1.2 x 10(-4) M-circle dot. The magnetic dipole moment simultaneously re-emerges as the screening currents dissipate over tau(I). For non-axisymmetric mountains, ohmic dissipation tends to restore axisymmetry by magnetic reconnection at a filamentary neutral sheet in the equatorial plane. Ideal-MHD oscillations on the Alfven time-scale, which can be excited by external influences, such as variations in the accretion torque, compress the magnetic field and hence decrease t(I) by one order of magnitude relative to its standard value (as computed for the static configuration). The implications of long-lived mountains for gravitational wave emission from low-mass X-ray binaries are briefly explored.