Numerical calculations of neutron star mountains supported by crustal lattice pressure

Abstract Gravitational waves may set the spin frequencies of neutron stars in low-mass X-ray binaries (LMXBs). One mechanism for facilitating such emission is the formation of a mass asymmetry - or ‘mountain’ - supported by elastic strains driven by thermal gradients. Most studies have focused either on the origin of the elastic strains or the temperature asymmetry in isolation, and have not considered the entire formation process. In previous work, we showed that anisotropic heat transport in magnetised accreting neutron stars can source a significant temperature asymmetry, and made rough estimates that suggested temperature-induced perturbations in the pressure supplied by the crustal lattice may be competitive with the widely known model of temperature-induced capture-layer shifts. In this paper we carry out detailed calculations to properly explore this scenario. We self-consistently calculate the temperature asymmetries, the perturbations in crustal lattice pressure, and the mass asymmetries within a single framework. For the first time, we make use of the set of realistic equations of state from the Brussels–Montreal nuclear energy-density functionals BSk19, BSk20, and BSk21 which describe all regions of accreting neutron stars in a thermodynamically consistent, unified way. We find these mountains are too small to dictate the spin-equilibrium of LMXBs, and estimate the level of gravitational wave emission they produce.