The hydromagnetic structure of a neutron star accreting symmetrically at both magnetic poles is calculated as a function of accreted mass, M a , and polar cap radius, starting from a centred magnetic dipole and evolving through a quasi-static sequence of two-dimensional, Grad-Shafranov equilibria. The calculation is the first to track fully the growth of high-order magnetic multipoles, due to equatorward hydromagnetic spreading, while simultaneously preserving flux-freezing and a self-consistent mass-flux distribution. Equilibria are constructed numerically by an iterative scheme and analytically by Green functions. Two key results are obtained, with implications for recycled pulsars. (i) The mass required to reduce significantly the magnetic dipole moment, 10 −5 M , greatly exceeds previous estimates (∼10 −10 M ), which ignored the confining stress exerted by the compressed equatorial magnetic field. (ii) Magnetic bubbles, disconnected from the stellar surface, form in the later stages of accretion (M a 10 −4 M ).

The amplitude of the gravitational radiation from an accreting neutron star undergoing polar magnetic burial is calculated. During accretion, the magnetic field of a neutron star is compressed into a narrow belt at the magnetic equator by material spreading equatorward from the polar cap. In turn, the compressed field confines the accreted material in a polar mountain which is misaligned with the rotation axis in general, producing gravitational waves. The equilibrium hydromagnetic structure of the polar mountain, and its associated mass quadrupole moment, are computed as functions of the accreted mass, M a , by solving a Grad-Shafranov boundary value problem. The orientationand polarization-averaged gravitational wave strain at Earth is found to be h c = 6 × 10 −24 (M a /M c )(1 + M a b 2 /8M c ) −1 (f /0.6 kHz) 2 (d/1 kpc) −1 , where f is the wave frequency, d is the distance to the source, b is the ratio of the hemispheric to polar magnetic flux, and the cut-off mass M c ∼ 10 −5 M ⊙ is a function of the natal magnetic field, temperature, and electrical conductivity of the crust. This value of h c exceeds previous estimates that failed to treat equatorward spreading and flux freezing self-consistently. It is concluded that an accreting millisecond pulsar emits a persistent, sinusoidal gravitational wave signal at levels detectable, in principle, by long baseline interferometers after phase-coherent integration, provided that the polar mountain is hydromagnetically stable. Magnetic burial also reduces the magnetic dipole moment µ monotonically as µ ∝ (1 + 3M a /4M c ) −1 , implying a novel, observationally testable scaling h c (µ). The implications for the rotational evolution of (accreting) X-ray and (isolated) radio millisecond pulsars are explored.

Magnetically confined mountains on accreting neutron stars are promising sources of continuous‐wave gravitational radiation and are currently the targets of directed searches with long‐baseline detectors like the Laser Interferometer Gravitational Wave Observatory (LIGO). In this paper, previous ideal‐magnetohydrodynamic models of isothermal mountains are generalized to a range of physically motivated, adiabatic equations of state. It is found that the mass ellipticity ε drops substantially, from ε≈ 3 × 10−4 (isothermal) to ε≈ 9 × 10−7 (non‐relativistic degenerate neutrons), 6 × 10−8 (relativistic degenerate electrons) and 1 × 10−8 (non‐relativistic degenerate electrons) (assuming a magnetic field of 1012.5 G at birth). The characteristic mass Mc at which the magnetic dipole moment halves from its initial value is also modified, from Mc/M⊙≈ 5 × 10−4 (isothermal) to Mc/M⊙≈ 2 × 10−6, 1 × 10−7, and 3 × 10−8 for the above three equations of state, respectively. Similar results are obtained for a realistic, piecewise‐polytropic nuclear equation of state. The adiabatic models are consistent with current LIGO upper limits, unlike the isothermal models. Updated estimates of gravitational‐wave detectability are made. Monte Carlo simulations of the spin distribution of accreting millisecond pulsars including gravitational‐wave stalling agree better with observations for certain adiabatic equations of state, implying that X‐ray spin measurements can probe the equation of state when coupled with magnetic mountain models.

The theory of polar magnetic burial in accreting neutron stars predicts that a mountain of accreted material accumulates at the magnetic poles of the star, and that, as the mountain spreads equatorward, it is confined by, and compresses, the equatorial magnetic field. Here, we extend previous, axisymmetric, Grad-Shafranov calculations of the hydromagnetic structure of a magnetic mountain up to accreted masses as high as M a = 6 × 10 −4 M , by importing the output from previous calculations (which were limited by numerical problems and the formation of closed bubbles to M a < 10 −4 M ) into the time-dependent, ideal-magnetohydrodynamic code ZEUS-3D and loading additional mass on to the star dynamically. The rise of buoyant magnetic bubbles through the accreted layer is observed in these experiments. We also investigate the stability of the resulting hydromagnetic equilibria by perturbing them in ZEUS-3D. Surprisingly, it is observed that the equilibria are marginally stable for all M a 6 × 10 −4 M ; the mountain oscillates persistently when perturbed, in a combination of Alfvén and acoustic modes, without appreciable damping or growth, and is therefore not disrupted (apart from a transient Parker instability initially, which expels <1 per cent of the mass and magnetic flux).

Matter accreting onto the magnetic poles of a neutron star spreads under gravity towards the magnetic equator, burying the polar magnetic field and compressing it into a narrow equatorial belt. Steady-state, Grad-Shafranov calculations with a self-consistent mass-flux distribution (and a semiquantitative treatment of Ohmic diffusion) show that, for M a 10 −5 M ⊙ , the maximum field strength and latitudinal half-width of the equatorial magnetic belt arewhere M a is the total accreted mass andṀ a is the accretion rate. It is shown that the belt prevents north-south heat transport by conduction, convection, radiation, and ageostrophic shear. This may explain why millisecond oscillations observed in the tails of thermonuclear (type I) X-ray bursts in low-mass X-ray binaries are highly sinusoidal: the thermonuclear flame is sequestered in the magnetic hemisphere which ignites first. The model is also consistent with the occasional occurrence of closely spaced pairs of bursts. Time-dependent, ideal-magnetohydrodynamic simulations confirm that the equatorial belt is not disrupted by Parker and interchange instabilities.