Internal forcing of Mercury’s long period free librations

Observations of Mercury’s spin rate do not rule out that, in addition to the forced 88-day mantle libration induced by solar torques, a decadal timescale libration may also be present. It has been proposed that this signal represents an amplified forced libration caused by the periodic 11.86 yr perturbation on Mercury’s orbit by Jupiter. Here, we investigate the possibility that a decadal libration may be produced by a forcing internal to the planet. Our mechanism is based on the presence of time-dependent zonal flows generated by turbulent convection in Mercury’s fluid core. Through electromagnetic coupling, these flows entrain longitudinal displacements of the inner core, which then entrain mantle librations by gravitational coupling. We construct a simple model to capture this exchange of angular momentum. Although core zonal flows are expected to have a broad frequency spectrum, we show that the resulting mantle libration is dominated by the amplification that occurs at the period of the free decadal libration of the combined mantle and inner core. Our results suggest that for plausible values of Mercury’s internal magnetic field, if the inner core of Mercury is large (⩾1000 km), decadal mantle libration amplitudes of the order of 1 arcsec can be generated by zonal flows of the order of 1 km yr−1. Conversely, if future observations can robustly determine an upper bound on the amplitude of Mercury’s decadal librations, our results can be used as constraints on the convective dynamics in Mercury’s core.