Inner Cassini States of the Moon, and their Implications for a Mechanically Generated Dynamo

• Author / Creator

  Stys, Christopher

• We present a model of the precession dynamics of the Moon that comprises a fluid outer core and a solid inner core. We show that three Cassini states associated with the inner core exist. The tilt angle of the inner core in each of these states is determined by the ratio between the free inner core nutation frequency (ωficn) and the precession frequency Ωp = 2π/18.6 yr −1. All three Cassini states are possible if |ωficn| > 2π/16.4 yr −1, but only one is possible otherwise. Assuming that the lowest energy state is favoured, this transition marks a discontinuity in the tilt angle of the inner core, transiting from −33 degrees to 17 degrees as measured with respect to the mantle figure axis, where negative angles indicate a tilt towards the orbit normal. Possible Lunar interior density structures cover a range of ωficn, from approximately half to twice as large as Ωp, so the precise tilt angle of the inner core remains unknown, though it is likely large because Ωp is within the resonant band of ωficn. Adopting one specific density model, we suggest an inner core tilt of approximately −17 degrees. Viscoelastic deformations within the inner core and melt and growth at the surface of a tilted inner core, both neglected in our model, should reduce this amplitude. If the inner core is larger than approximately 200 km, it may contribute by as much as a few thousandths of a degree on the observed mantle precession angle of 1.543 degrees .A natural extension of our Cassini state model is to investigate the impact of the rotational dynamics of the Lunar interior on the generation of an ancient Lunar magnetic field. Purely thermally driven convective dynamo models have had a difficult time explaining the paleomagnetic intensities recorded in Lunar rocks. Mechanical stirring from differential rotation at the core mantle boundary (CMB) and inner core boundary(ICB) can generate large viscous dissipation, potentially sufficiently large in the Lunar past to have powered a dynamo. We present estimates of the paleomagnetic field intensities Bcmb and Bicb based on dynamos associated with viscous dissipation at the CMB and ICB, respectively. We show that Bcmb may have been larger than 25 μT early in Lunar history, although the dynamo would have shut off around 3.9 Gyr ago. We also show that the inner core radius must be larger than approximately 100 km for viscous dissipation at the ICB to be above the dynamo threshold. Bicb can be as large as approximately 8.5 μT, weaker than Bcmb, but a dynamo from dissipation at the ICB may have persisted until very recently.

• Subjects / Keywords

  • Cassini states, dynamo

• Graduation date

  Spring 2019

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-42xk-s733

• License

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