Relaxation of magnetically-confined mountains on accreting neutron stars through cross-field mass transport

Hydromagnetic instabilities modify the structure of a magnetically confined mountain on an accreting neutron star, once the accreted mass exceeds a critical value. Ideal magnetohydrodynamics and flux freezing break down, and mass diffuses across magnetic field lines locally, wherever instabilities are excited. Here a self-consistent, iterative, numerical scheme is used to evolve an axisymmetric magnetic mountain through a quasistatic sequence of Grad-Shafranov equilibria as a function of the accreted mass, Ma, modified by instability-driven cross-field mass transport obeying the semi-analytic, Kulsrud-Sunyaev recipe. The results are compared to an artificially stabilised mountain, in which flux freezing does not break down, and there is no cross-field mass transport. It is shown that cross-field mass transport prevents instabilities from demolishing the mountain. Instead, the mass-flux distribution adjusts locally to nullify the instabilities and preserve a nonzero mass quadrupole moment indefinitely in the absence of ohmic dissipation.