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

Due to its eccentricorbit, Mercury experiences varying gravitational pullfrom the Sun along its orbital course, leading to periodic tidal deformation, i.e, stretchingandsqueezing of the planet. Prectically speaking, Mercurys surface willrise up and downperiodically. The magnitude of thesesurface heightvariations, typicallyquantified by the tidal Love number h2, depends onproperties ofthedeep interior. A reliable measurement ofthe tidal h2can thus shedcrucialinsights into Mercurys 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 h2of Mercury has only been measured by Bertone et al. (2021) through minimizing height misfits atthe intersection points, cross-overs,of the Mercury Laser Altimeter (MLA)profiles. However,only their lower boundis consistent with the existing modelingresults (Steinbrgge et al., 2018; Goossens et al., 2022; Figure 1).In this study, we look intoMercury's tidal deformation by applying an alternative approachto 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 CO2snow/ice at Martian polar regions (Xiao et al., 2022a, b). By employing the co-registration proceduresto the MLA profiles,the interpolationerrorsassociated with the usage of cross-overs are avoided.During the reprocessing to improve the profilesgeolocation, we correct for apointing aberration due to relativity effects(Xiao et al., 2021)and incorporatean updated spacecraftorbit modelthat has better accounted forthe non-gravitationalforces(Andolfoet al., 2024).We carry out the studyat the very polar region of 77N to 84Nwhere footprints are the densest and off-nadir pointing angles aregenerallythe smallest.For verification of the proposed approach and quantification of its uncertainty, we generate realistic synthetic profiles and conductextensive simulations.We obtain a tidal h2of 0.920.51 (3-sigma), with a central value 0.63smaller than that of Bertone et al. (2021, 1.550.65), 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 (