The free librations of Mercury and the size of its inner core

The predicted period of the free libration of Mercury's mantle, if fully decoupled from the core, is approximately 12 yr. If the innermost part of the core is solid, this period is altered and a second free mode is possible. The period of these two modes depend on the mean solar torque acting on the elliptical figures of the mantle and inner core, and also on the gravitational torque they exert on one another. We show that one mode is well approximated by the free gravitational oscillation between the mantle and inner core that would occur in the absence of a solar torque; its period is as small as 4 yr depending on inner core size and other model parameters. The second free mode consists of an in-phase libration of the mantle and inner core. When the inner core is small, the period of this mode coincides with that of the decoupled free mantle libration of 12 yr. However, the period lengthens considerably when the inner core radius is larger than 1000 km, and can be as high as approximately 19 yr if Mercury's core is almost fully solidified. These modes should affect Mercury's libration dynamics at decadal timescale. This suggests that, in principle, constraints on the size of Mercury's inner core may be extracted from its long term libration motion, though in practice this may be difficult given data limitations. Citation: Dumberry, M. (2011), The free librations of Mercury and the size of its inner core, Geophys. Res. Lett., 38, L16202, doi:10.1029/2011GL048277.