Shared periodicities between the length of day and the geomagnetic field at millennial timescales

The dynamics of Earth's outer core control the geomagnetic field and produce variations in the length of day (LOD). This phenomenon has been extensively studied at decadal and interannual scales but is still little known on the millennial timescale. Reconstructed variations in the length of day from ancient records of eclipses exhibit an oscillating component with a millennial period that cannot be explained by tidal effects, glacial isostatic adjustment or the ocean and atmospheric dynamics. In this work, frequency analysis and correlation techniques have been applied to LOD variations and to the dipole and quadrupole geomagnetic field provided by paleomagnetic reconstructions. We found that the non-tidal fluctuations of the LOD are correlated with the paleosecular variation of the Earth's magnetic field over the last three millennia. In particular, LOD maxima occur when the eccentric dipole shifts towards the Pacific region and the geocentric dipole becomes more axial, and LOD minima correspond to a more centred eccentric dipole and a more tilted geocentric dipole towards Atlantic region. These results provide new information about the coupling between the Earth's rotation and the paleosecular variation of the geomagnetic field on millennial time scales. • Millennial LOD oscillations share common periodicities with the energy terms of the dipolar and quadrupolar geomagnetic field. • LOD maxima correspond to a more axial geocentric dipole and a eccentric dipole shifted toward the Pacific. • At local LOD minima the eccentric dipole is closer to Earth's centre, and the geocentric dipole tilts toward Euro-Atlantic.