We examine the hydromagnetic stability of magnetically confined mountains, which arise when material accumulates at the magnetic poles of an accreting neutron star. We extend a previous axisymmetric stability analysis by performing three-dimensional simulations using the ideal-magnetohydrodynamic (ideal-MHD) code ZEUS-MP, investigating the role played by boundary conditions, accreted mass, stellar curvature and (briefly) toroidal magnetic field strength. We find that axisymmetric equilibria are susceptible to the undular submode of the Parker instability but are not disrupted. The line-tying boundary condition at the stellar surface is crucial in stabilizing the mountain. The non-linear three-dimensional saturation state of the instability is characterized by a small degree of non-axisymmetry ( 0.1 per cent) and a mass ellipticity of ∼ 10 −5 for an accreted mass of M a = 10 −5 M . Hence, there is a good prospect of detecting gravitational waves from accreting millisecond pulsars with long-baseline interferometers such as Advanced Laser Interferometer Gravitational-Wave Observatory. We also investigate the ideal-MHD spectrum of the system, finding that long-wavelength poloidal modes are suppressed in favour of toroidal modes in the non-axisymmetric saturation state.

We present three‐dimensional, non‐relativistic, hydrodynamic simulations of bow shocks in pulsar wind nebulae. The simulations are performed for a range of initial and boundary conditions to quantify the degree of asymmetry produced by latitudinal variations in the momentum flux of the pulsar wind, radiative cooling in the post‐shock flow and density gradients in the interstellar medium (ISM). We find that the bow shock is stable even when travelling through a strong ISM gradient. We demonstrate how the shape of the bow shock changes when the pulsar encounters density variations in the ISM. We show that a density wall can account for the peculiar bow shock shapes of the nebulae around PSR J2124−3358 and PSR B0740−28. A wall produces kinks in the shock, whereas a smooth ISM density gradient tilts the shock. We conclude that the anisotropy of the wind momentum flux alone cannot explain the observed bow shock morphologies but it is instead necessary to take into account external effects. We show that the analytic (single layer, thin shell) solution is a good approximation when the momentum flux is anisotropic, fails for a steep ISM density gradient and approaches the numerical solution for efficient cooling. We provide analytic expressions for the latitudinal dependence of a vacuum‐dipole wind and the associated shock shape, and compare the results to a split‐monopole wind. We find that we are unable to distinguish between these two wind models purely from the bow shock morphology.

We give an improved estimate of the detectability of gravitational waves from magnetically confined mountains on accreting neutron stars. The improved estimate includes the following effects for the first time: three-dimensional hydromagnetic ('fast') relaxation, threedimensional resistive ('slow') relaxation, realistic accreted masses M a 2 × 10 −3 M (where the mountain is grown ab initio by injection) and verification of the curvature rescaling transformation employed in previous work. Typically, a mountain does not relax appreciably over the lifetime of a low-mass X-ray binary. The ellipticity reaches ≈ 2 × 10 −5 for M a = 2 × 10 −3 M . The gravitational wave spectrum for triaxial equilibria contains an additional line, which, although weak, provides valuable information about the mountain shape. We evaluate the detectability of magnetic mountains with initial and advanced Laser Interferometer Gravitational Wave Observatory (LIGO). For a standard, coherent matched filter search, we find a signal-to-noise ratio of d = 28(M a /10 −4 M ) (1 + 5.5M a /10 −4 M ) −1 (D/10 kpc) −1 (T 0 /14 d) 1/2 for initial LIGO, where D is the distance and T 0 is the observation time. From the non-detection of gravitational waves from low-mass X-ray binaries to date, and the wave strain limits implied by the spin frequency distribution of these objects (due to gravitational wave braking), we conclude that there are other, as yet unmodelled, physical effects that further reduce the quadrupole moment of a magnetic mountain, most notably sinking into the crust.

The software is freely available at http://www.csse.monash.edu.au/~berndm/inchman/.

We perform ideal-magnetohydrodynamic axisymmetric simulations of magnetically confined mountains on an accreting neutron star, with masses less than ~0.12 solar masses. We consider two scenarios, in which the mountain sits atop a hard surface or sinks into a soft, fluid base. We find that the ellipticity of the star, due to a mountain grown on a hard surface, approaches ~2e-4 for accreted masses greater than ~1.2e-3 solar masses, and that sinking reduces the ellipticity by between 25% and 60%. The consequences for gravitational radiation from low-mass x-ray binaries are discussed.Comment: 13 pages, 12 figures, and 3 tables; accepted for publication in MNRA