Deviation of Mercury's spin axis from an exact Cassini state induced by
dissipation
Abstract
We compute predictions of the deviation of Mercury’s spin axis from an
exact Cassini state caused by tidal dissipation, and viscous and
electromagnetic (EM) friction at the core-mantle boundary (CMB) and
inner core boundary (ICB). Viscous friction at the CMB generates a phase
lead, viscous and EM friction at the ICB produce a phase lag; the
magnitude of the deviation depends on the inner core size, kinematic
viscosity and magnetic field strength, but cannot exceed an upper bound.
For a small inner core, viscous friction at the CMB results in a maximum
phase lead of 0.027 arcsec. For a large inner core (radius
>1000 km), EM friction at the ICB generates the largest
phase lag, but it does not exceed 0.1 arcsec. Elastic deformations
induced by the misaligned fluid and solid cores play a first order role
in the phase lead/lag caused by viscous and EM coupling, and contribute
to a perturbation in mantle obliquity on par with that caused by tidal
deformations. Tidal dissipation results in a phase lag and its magnitude
(in units of arcsec) is given by the empirical relation (80/Q), where Q
is the quality factor; Q=80 results in a phase lag of ~1
arcsec. A large inner core with a low viscosity of the order of
10^{17} Pa s or lower can significantly affect Q and thus the
resulting phase lag. The limited mantle phase lag suggested by
observations (<10 arcsec) implies a lower limit on the bulk
mantle viscosity of approximately 10^{17} Pa s.