Refining Mercury's tidal Love number h2 through self-registration of MESSENGER laser profiles

Mercury experiences periodic radial surface deformation, quantified by the Love number h₂, due to tidal forces exerted by the Sun. Existing measurements come from processing of the Mercury Laser Altimeter (MLA ) profiles using independent approaches: (1) the cross-over analysis (1.55±0.65; Bertone et al., 2021), the self-registration techniques (0.92±0.58; Xiao et al., 2025), and (3) the direct altimetry (1.05±0.29; Stenzel et al., 2025). Unfortunately, the associated uncertainties are still too large to offer meaningful insights into Mercury’s interior (Stenzel et al., this meeting).   

We base our study on Xiao et al. (2025a), but focus on a more polar region of 80°N to 84°N. We permit more reference profiles during the self-registration iterations, adopt higher spatial resolution for the reference terrain model, and minimize projection-induced distortions. To improve the geolocation of MLA footprints, we refine the MESSENGER orbits by carefully modeling non-conservative forces experienced by the spacecraft (Andolfo et al., 2024). Trajectory uncertainty stability is assessed using two independent precise orbit determination frameworks, based on the GEODYN II and MONTE software, respectively. 

The derived tidal deformation time series are shown in Figure 1 and their general trends resemble well that of the tidal signal. After removing the outliers, the inverted tidal h₂ converges to between 1.3 and 1.4. Bootstrappings by subsamplings and perturbations considering measurement errors indicate a 3-sigma uncertainty of around 0.1.   

Figure 1. Measured radial tidal deformation against Mercury's mean anomaly (black dots). Theoretical tidal deformation is shown for comparison (blue curves). 

We use the Markov Chain Monte Carlo (MCMC) to infer plausible Mercury interior structure that are consistent with the measured annual libration (Xiao et al., 2025b), tidal Love number k₂ (Konopliv et al., 2020), and polar Moment of Inertia (Bertone et al., 2021).  We assume a forsterite/enstatite mantle and a Fe-S-Si core, and consider pressure/temperature dependent properties of the materials. Besides, we take into account the gravitational-pressure couplings at the layer boundaries when estimating the annual libration (Rivoldini and Van Hoolst, 2013). The tidal h₂ prediction is around 0.9, which is much smaller than our measurement. 

Currently, we are examining factors that may possibly bias our estimate. We should also note that the study region is extremely limited to within the northern smooth plains which are caused by massive flood volcanism in the past. The large tidal h₂ may point to lingering interior heterogeneties, for example, a softer or warmer mantle beneath. 

These activities also stand as a preparation for the upcoming data collected by the BepiColombo Laser Altimeter (BELA) onboard ESA/JAXA’s BepiColombo mission to Mercury (Hussmann and Stark, 2020).  

Acknowledges

AG acknowledges the California Institute of Technology (Caltech) and the Jet Propulsion Laboratory (JPL) for the license of the software MONTE Project Edition. 

References 

Andolfo et al., 2024. JGCD, 47(3), 518-530. Bertone et al., 2021. JGR: Planets, 126(4), e2020JE006683. Hussmann and Stark, 2020. EPJ ST, 229(8), 1379-1389. Konopliv et al., 2020. Icarus, 335, 113386. Rivoldini and Van Hoolst, 2013. EPSL, 377, 62-72. Stenzel et al., 2025. Authorea Preprints. Xiao et al., 2025a. GRL, 52(7), e2024GL112266. Xiao et al., 2025b. EPSC-DPS2025-325.