Motivated by the narrow range of spin frequencies of nearly 20 accreting neutron stars, Bildsten (1998) conjectured that their spin-up had been halted by the emission of gravitational waves. He also pointed out that small nonaxisymmetric temperature variations in the accreted crust will lead to wavy electron capture layers, whose horizontal density variations naturally create a mass quadrupole moment. We present a full calculation of the crusts elastic adjustment to these density perturbations and find that the elastic response of the crust reduces Bildstens original estimate of the quadrupole moment in the thin outer crust by a factor of 20-50. However, this basic picture, when applied to capture layers in the deep inner crust, can generate quadrupoles in the necessary range as long as there are ~5% lateral temperature variations in the inner crust. By calculating the thermal flow throughout the core and the crust, we find that temperature gradients this large are easily maintained by asymmetric heat sources or lateral composition gradients in the crust. 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 of the magnitude necessary to balance the accretion torque requires dimensionless strains close to 0.01 at near-Eddington accretion rates, of order the breaking strain of conventional materials.
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