Mercury's tidal Love number h2 from co-registration of reprocessed MLA profiles

Abstract

Due to its eccentric orbit, Mercury experiences varying gravitational pull from the Sun along its orbital course, leading to periodic tidal deformation, i.e, stretching and squeezing of the planet. Prectically speaking, Mercury’s surface will rise “up and down” periodically. The magnitude of these surface height variations, typically quantified by the tidal Love number h2, depends on properties of the deep interior.  A reliable measurement of the tidal h2 can thus shed crucial insights into Mercury’s interior structure, especially the size and physical state of its core.  The estimation of the tidal deformation requires laser or radar altimetric measurements. So far, the tidal h2 of Mercury has only been measured by Bertone et al. (2021) through minimizing height misfits at the intersection points, cross-overs, of the Mercury Laser Altimeter (MLA) profiles. However, only their lower bound is consistent with the existing modeling results (Steinbrügge et al., 2018; Goossens et al., 2022; Figure 1).In this study, we look into Mercury's tidal deformation by applying an alternative approach to reprocessed MLA profiles, which is based on the co-registration techniques. Previously, we have successfully applied these techniques to Mars Orbiter Laser Altimeter (MOLA) profiles to obtain the spatio-temporal thickness variations of the seasonal CO2 snow/ice at Martian polar regions (Xiao et al., 2022a, b). By employing the co-registration procedures to the MLA profiles, the interpolation errors associated with the usage of cross-overs are avoided. During the reprocessing to improve the profiles’ geolocation, we correct for a pointing aberration due to relativity effects (Xiao et al., 2021) and incorporate an updated spacecraft orbit model that has better accounted for the non-gravitational forces (Andolfo et al., 2024). We carry out the study at the very polar region of 77°N to 84°N where footprints are the densest and off-nadir pointing angles are generally the smallest. For verification of the proposed approach and quantification of its uncertainty, we generate realistic synthetic profiles and conduct extensive simulations. We obtain a tidal h2 of 0.92±0.51 (3-sigma), with a central value 0.63 smaller than that of Bertone et al. (2021, 1.55±0.65), but compatible with existing models (Figure 1). Combined with the most recent gravitational deformation measurements, our measured tidal h2 favors a small to medium-sized solid inner core (