Gravitational wave emission from accreting neutron stars

We investigate whether gravitational radiation can balance the accretion-driven spinup of neutron stars in low-mass X-ray binaries at spin frequencies near 300 Hz inferred from recent observations. We consider two mechanisms for this equilibrium: mass quadrupole radiation from wavy electron capture layers in the crust, and current quadrupole radiation from unstable r-mode oscillations in the core.; Small nonaxisymmetric temperature variations in the crust deform electron capture layers, and the resulting horizontal density variations generate a mass quadrupole moment. We present a full calculation of the elastic response of the crust to these density perturbations. Capture layers in the deep inner crust can generate a quadrupole moment, 1037–10 38 g cm2, necessary to balance the accretion torque with gravitational waves, as long as there are approximately 5% lateral temperature variations, and as long as the crustal breaking strain is high enough. We find that temperature gradients this large are easily maintained by asymmetric heat sources or lateral composition gradients in the crust. A smooth 0.5% lateral composition gradient in the crust will also result in a quadrupole sufficient to halt spin-up from accretion even in the absence of a lateral temperature gradient. We also derive a general relation between the stresses and strains in the crust and the maximum quadrupole moment they can generate. We show, under quite general conditions, that maintaining a quadrupole large enough to balance the accretion torque requires a dimensionless strain of 10−2 at near-Eddington accretion rates.; Recent work has raised a possibility that r-modes in cores of rotating neutron stars might be strong gravitational wave sources. We estimate the effect of a solid crust on their viscous damping and show that the dissipation rate in the viscous boundary layer between the core and the crust is more than 105 times higher than that from the shear throughout the interior. This dissipation increases the minimum frequency for the onset of the r-mode instability to at least 700 Hz when the core temperature is less than 109 K and likely rules out gravitational radiation from unstable r-modes as the mechanism for balancing the accretion torque in low-mass X-ray binaries.