流体核和固体内核对水星卡西尼状态的影响
The influence of a fluid core and a solid inner core on the Cassini sate of Mercury
摘要：
我们提出了一个模型的卡西尼状态的水星，包括一个内核，流体核心和地幔。我们的模型包括内部区域之间的惯性和重力力矩，以及流体核心边界处的粘性和电磁（EM）耦合。我们表明，水星的内部区域之间的耦合是足够强的地幔自旋轴的磁致伸缩性偏离一个刚性的行星不超过0.01弧分。随着内核尺寸的增大，地幔的结晶度减小，但大的和没有内核的地幔结晶度之间的变化被限制在0.015弧分。EM耦合比内核边界处的粘性耦合强，并且如果内核磁场强度高于0.3 mT，则将流体和固体内核锁定为共同的进动运动。由于地幔和内核之间的强引力耦合，内核越大，这个共同旋进的内核就越与地幔对齐，极区的转动惯量越接近刚性行星的预期值。极转动惯量与地幔自转轴之间的偏差随内核尺寸的增大而增大，但不超过0.007弧分。我们的研究结果意味着，地幔自旋轴和极转动惯量的测量精度应该在目前的测量误差水平上一致，并且不能与刚性行星的精度区分开来。
英文摘要：
We present a model of the Cassini state of Mercury that comprises an inner core, a fluid core and a mantle. Our model includes inertial and gravitational torques between interior regions, and viscous and electromagnetic (EM) coupling at the boundaries of the fluid core. We show that the coupling between Mercury's interior regions is sufficiently strong that the obliquity of the mantle spin axis deviates from that of a rigid planet by no more than 0.01 arcmin. The mantle obliquity decreases with increasing inner core size, but the change between a large and no inner core is limited to 0.015 arcmin. EM coupling is stronger than viscous coupling at the inner core boundary and, if the core magnetic field strength is above 0.3 mT, locks the fluid and solid cores into a common precession motion. Because of the strong gravitational coupling between the mantle and inner core, the larger the inner core is, the more this co-precessing core is brought into an alignment with the mantle, and the more the obliquity of the polar moment of inertia approaches that expected for a rigid planet. The misalignment between the polar moment of inertia and mantle spin axis increases with inner core size, but is limited to 0.007 arcmin. Our results imply that the measured obliquities of the mantle spin axis and polar moment of inertia should coincide at the present-day level of measurement errors, and cannot be distinguished from the obliquity of a rigid planet.
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