Title: Interannual Magneto-Coriolis modes and their sensitivity on the magnetic field within the Earth's core

Abstract: Linear modes for which the Coriolis acceleration is almost entirely in balance with the Lorentz force are called Magneto-Coriolis (MC) modes. These MC modes are thought to exist in Earth's liquid outer core and could therefore contribute to the variations observed in Earth's magnetic field. The background state on which these waves ride is assumed here to be static and defined by a prescribed magnetic field and zero flow. We introduce a new computational tool to efficiently compute solutions to the related eigenvalue problem, and study the effect of a range of both axisymmetric and non-axisymmetric background magnetic fields on the MC modes. We focus on a hierarchy of conditions that sequentially partition the numerous computed modes into those which are (i) in principle observable, (ii) those which match a proxy for interannual geomagnetic signal over 1999-2023, and (iii) those which align with core-flows based on recent geomagnetic data. We found that the background field plays a crucial role in determining the structure of the modes. In particular, we found no examples of axisymmetric background fields that support modes consistent with recent geomagnetic changes, but that some non-axisymmetric background fields do support geomagnetically consistent modes.