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

Abstract

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 orientation- and polarization-averaged gravitational wave strain, h_c ~ 6e-24 for a 0.6 kHz source at 1 kpc with M_a > 10^-5 M_Sun, 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, mu, monotonically, implying a novel, observationally testable scaling h_c(mu). The implications for the rotational evolution of (accreting) X-ray and (isolated) radio millisecond pulsars are explored.