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.
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机译：我们研究了引力辐射是否可以平衡自最近观测得出的自旋频率在300 Hz附近的低质量X射线双星中中子星的增生驱动旋转。我们考虑了实现这种平衡的两种机制：地壳中波浪形电子捕获层的质量四极辐射，以及铁心中不稳定r模振荡的电流四极辐射。地壳中小的非轴对称温度变化会使电子捕获层变形，并且所产生的水平密度变化会产生质量四极矩。我们对地壳对这些密度扰动的弹性响应进行了全面的计算。深内壳中的俘获层可以产生四极矩10 37 –10 38 g cm 2 ，这是平衡吸积扭矩与重力波，只要横向温度变化大约5％，并且地壳破裂应变足够高。我们发现，通过不对称的热源或地壳中的侧向成分梯度，可以轻松保持如此大的温度梯度。即使在没有横向温度梯度的情况下，地壳中光滑的0.5％横向成分梯度也将导致四极杆足以阻止自吸积物向上旋转。我们还得出了地壳中的应力和应变与它们可能产生的最大四极矩之间的一般关系。我们表明，在相当普遍的条件下，要保持足够大的四极杆平衡吸积扭矩，就需要在接近爱丁顿的吸积速率下产生10 -2 的无量纲应变。最近的工作提出了一种可能性，即旋转中子星的核心中的r模式可能是强大的引力波源。我们估计了固体壳对其粘性阻尼的影响，结果表明，在整个岩心和壳之间，粘性边界层的耗散率比整个剪切过程中的耗散率高出10 5 倍。内部。当核心温度低于10 9 K时，这种耗散将r模式不稳定性发作的最小频率提高到至少700 Hz，并可能排除不稳定r模式的重力辐射，因为平衡低质量X射线二进制文件中吸积扭矩的机制。
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