On the Mantle-Inner Core Gravitational Oscillation Under the Action of the Electromagnetic Coupling Effects

Abstract

Previous works indicated that the eigenperiod of the mantle-inner core gravitational coupling mode can match the observed 6-year period in length-of-day. However, this mode is only an ideal model, since it does not involve the electromagnetic (EM) coupling effects. Here, we further study the mantle-inner core gravitational mode and its mathematical equation under the action of the EM coupling effects, while the relevant damping oscillation analytical solution is also given. According to this theoretical model, we can constrain the core-mantle gravitational coupling strength Γ (>6.5 × 1019 Nm) and infer the EM coupling information at the core-mantle boundary (CMB) and the inner core boundary. This work indicates that a partial liquid core is necessarily required to be coupled to the inner core (IC) and axially rotates with the IC as a single body, which supports the recent assumption that only a part fluid core within the so-called tangent cylinder is locked to the IC. This explanation can greatly weaken the perturbation magnetic field due to the shear oscillation at the inner core boundary and eliminate the relevant EM damping dissipation, otherwise, the predicted 6-year oscillation will be rapidly decayed with a relaxation time ~9.8 days. In addition, we give the physical expression of the theoretical quality factor Q value of the 6-year oscillation, which is mainly related to the EM coupling at the CMB. According to the typical EM coupling parameters at the CMB, the theoretical Q value is predicted in the range of 40–75, which coincides with the current observed result (~51.6).