Detection of a gravitational oscillation in length-of-day

A high resolution length-of-day data set spanning approximately the last 42 years is found to contain an oscillation with a period of 5.8 ± 0.8 years. This oscillation is interpreted to represent a normal mode of the Earth that arises due to gravitational coupling between the mantle and inner core. In order to match the observed period of the oscillation, the strength of the gravitational coupling between the mantle and inner core must be ∼ 3.0 × 10 20 N m. This coupling constant depends on the heterogeneous density distribution of the mantle, including flow-induced deformation of the core–mantle boundary. The existence of this normal mode requires that the relaxation time of the inner core be sufficiently long (on the order of a few years or more) that a perturbation from equilibrium results predominantly in solid-body rotation, not viscous deformation, of the inner core. The inferred lower bound for the viscosity of the inner core is of the order of 10 17 Pa s.