论文标题
月球内的粘弹性放松及其Cassini状态的相位铅
Viscoelastic relaxation within the Moon and the phase lead of its Cassini state
论文作者
论文摘要
对月球激光射程数据的分析表明，月球的自旋对称轴以$ ϕ_p $ = 0.27 arcsec的角度领先于其预期的Cassini状态。这表明存在作用于月球旋转的一种或多种耗散机制。在先前的研究中，已经提出了实体潮汐和粘性核心壳耦合的组合。在这里，我们研究了月球中心的固体内芯内的粘弹性变形是否也可以解释观察到的相位铅角$ ϕ_p $的一部分。我们构建了一个包含内核，流体芯和地幔的旋转动力学模型，并允许固体区域以响应施加的强迫而变形。我们表明，内核的存在不会改变月球的全球月度Q，因此，从实体潮汐到$ ϕ_p $的贡献很大程度上不受内心核心的影响。但是，我们还表明，内核内的粘弹性变形，作用于其数字轴与地幔的数字轴，可以通过内部核心 - 掩体重力耦合对$ ϕ_p $显着贡献。我们表明，当内部核心粘度在$ 10^{13} $之间，至$ 10^{14} $ pa s的范围内，对$ ϕ_p $的贡献是最大的，当内核半径较大并且自由内部核心营养频率与共振相连时，预进点频率为$2π/18.6 $ yr $ yr $^$^{-1} $。
Analyses of Lunar Laser Ranging data show that the spin-symmetry axis of the Moon is ahead of its expected Cassini state by an angle of $ϕ_p$ = 0.27 arcsec. This indicates the presence of one or more dissipation mechanisms acting on the lunar rotation. A combination of solid-body tides and viscous core-mantle coupling have been proposed in previous studies. Here, we investigate whether viscoelastic deformation within a solid inner core at the centre of the Moon can also account for a part of the observed phase lead angle $ϕ_p$. We build a rotational dynamic model of the Cassini state of the Moon that comprises an inner core, a fluid core and a mantle, and where solid regions are allowed to deform viscoelastically in response to an applied forcing. We show that the presence of an inner core does not change the global monthly Q of the Moon and hence, that the contribution from solid-body tides to $ϕ_p$ is largely unaffected by an inner core. However, we also show that viscoelastic deformation within the inner core, acting to realign its figure axis with that of the mantle, can contribute significantly to $ϕ_p$ through inner core-mantle gravitational coupling. We show that the contribution to $ϕ_p$ is largest when the inner core viscosity is in the range of $10^{13}$ to $10^{14}$ Pa s, when the inner core radius is large and when the free inner core nutation frequency approaches a resonance with the precession frequency of $2π/18.6$ yr$^{-1}$.
