Gravitational Radiation from an Accreting Millisecond Pulsar with a Magnetically Confined Mountain

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 generally misaligned with the rotation axis, 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 orientation- and polarization-averaged gravitational wave strain at Earth is found to be h_c = 6 × 10^-24(M_a/M_c)(1 + M_ab²/8M_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 cutoff 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.