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arXiv 1105.6086astro-ph.EPphysics.geo-ph
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自旋轨道共振附近的体潮

Bodily tides near spin-orbit resonances

Michael Efroimsky

发表信息：
Celestial Mechanics and Dynamical Astronomy, Vol. 112, pp. 283 - 330 (March 2012)
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摘要：

自旋轨道耦合可以用两种方法来描述。称为“麦克唐纳转矩”的方法通常与品质因数Q与频率无关的假设相结合。这使得该方法不一致，因为麦克唐纳理论通过将Q标度作为潮汐频率的倒数来默认地固定流变学。自旋-轨道耦合也可以用一种称为“达尔文力矩”的方法来处理。虽然这一理论是一般性的，足以容纳一个任意的频率依赖性的Q，这个优点还没有被利用在文献中，其中Q被假定为常数或被设置为逆潮汐频率的比例，后者的断言，使达尔文扭矩相当于一个修正版本的麦克唐纳扭矩。然而，无论是常数还是逆频率Q都不能反映实际地幔和结壳的性质，因为实际的频率依赖性更为复杂。因此，有必要用正确的频率依赖性来丰富自旋轨道相互作用理论。我们完成了这个方案的达尔文扭矩为基础的模型附近的共振。我们从第一原理推导出潮汐力矩的频率依赖性，即，从时间域中的地幔顺应性的表达式。我们还解释了潮汐力矩不仅包括长期部分，而且还包括振荡部分。我们证明，当次级穿越lmpq共振时，潮汐扭矩的达尔文-考拉展开的lmpq项平滑地通过零（例如，当次级潮汐力矩穿过同步轨道时，主潮汐力矩平稳地通过n1）。我们还提供了一个可能的解释，意想不到的频率依赖性的潮汐耗散率在月球上，发现LLR。

英文摘要：

Spin-orbit coupling can be described in two approaches. The method known as "the MacDonald torque" is often combined with an assumption that the quality factor Q is frequency-independent. This makes the method inconsistent, because the MacDonald theory tacitly fixes the rheology by making Q scale as the inverse tidal frequency. Spin-orbit coupling can be treated also in an approach called "the Darwin torque". While this theory is general enough to accommodate an arbitrary frequency-dependence of Q, this advantage has not yet been exploited in the literature, where Q is assumed constant or is set to scale as inverse tidal frequency, the latter assertion making the Darwin torque equivalent to a corrected version of the MacDonald torque. However neither a constant nor an inverse-frequency Q reflect the properties of realistic mantles and crusts, because the actual frequency-dependence is more complex. Hence the necessity to enrich the theory of spin-orbit interaction with the right frequency-dependence. We accomplish this programme for the Darwin-torque-based model near resonances. We derive the frequency-dependence of the tidal torque from the first principles, i.e., from the expression for the mantle's compliance in the time domain. We also explain that the tidal torque includes not only the secular part, but also an oscillating part. We demonstrate that the lmpq term of the Darwin-Kaula expansion for the tidal torque smoothly goes through zero, when the secondary traverses the lmpq resonance (e.g., the principal tidal torque smoothly goes through nil as the secondary crosses the synchronous orbit). We also offer a possible explanation for the unexpected frequency-dependence of the tidal dissipation rate in the Moon, discovered by LLR.

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