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 _ { \mathrm { I } } \sim 10 ^ { 5 } -10 ^ { 8 } yr ( depending on the conductivity of the neutron star crust ) for an accreted mass of M _ { a } = 1.2 \times 10 ^ { -4 } M _ { \odot } .
The magnetic dipole moment simultaneously reemerges as the screening currents dissipate over \tau _ { \mathrm { I } } .
For nonaxisymmetric mountains , ohmic dissipation tends to restore axisymmetry by magnetic reconnection at a filamentary neutral sheet in the equatorial plane .
Ideal-MHD oscillations on the Alfvén time-scale , which can be excited by external influences , such as variations in the accretion torque , compress the magnetic field and hence decrease \tau _ { \mathrm { 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 .