Mercury's annual and long-term librations from self-registration of MLA profiles

Mercury's annual longitudinal libration (88 days) and its mean rotation rate have been  determined based on independent observations from the ground-based radar (Margot et al., 2012), camera and/or laser altimetry (Stark et al., 2015; Bertone et al., 2021), and radio science (Mazarico et al., 2014; Genova et al., 2019; Konopliv et al., 2020). Although consistent, the precision of the libration measurements precludes identification of a large solid inner core (Van Hoolst et al., 2012). At the same time, the measured rotation rates are largely inconsistent. Deviation from the resonant rotation rate is caused by the planet-induced long-term librations which can be amplified if their periods are close to that of a free libration mode (Yseboodt et al., 2013).

We devise an alternative and innovative approach aimed at precisely tracking how the rotation angle varies with time so that various libration terms can be analyzed quantitatively. The approach involves two self-registration processes of the MESSENGER Mercury Laser Altimeter (MLA) profiles (Xiao et al., 2024). We focus on a small polar region from 81°N to 84°N. In the first step, we carry out the self-registration by shifting the individual profiles laterally and radially to get rid of the slow-varying orbit, pointing, and timing errors, which can be treated as near-constant. In contrast to the aforementioned near-constant shifts, offsets in the rotation angles can lead to non-linear rotation-like distortions of the profiles. Offsets in the orientation angles of the spin axis can shift the profiles as a whole, ensuring that our approach is insensitive to the a priori orientation state. Then in the second step, we update the inertial coordinates of the profiles and perform the second self-registration in which adjustments are made to the rotation angles at the acquisition times of each of the profiles. However, as the periapsis of the spacecraft has drifted throughout the mission, the ground track does not exactly cross the North Pole and an offset in the rotation angle can also shift the centroid of the profile. In the light of this, the above two-step process needs to be iterated till convergence. Finally, we obtain the updated rotation angle per profile uncontaminated by external error sources.

We have experimented with various a priori rotation and orientation values, i.e., Stark2015, IAU2015 (Archinal et al., 2018), Genova2019, and Bertone2021. An example of the obtained variation of the rotation with time is shown in Figure 1. The long-term libration most likely to be amplified and captured is that with a period of around 6 years, induced by Venus (5.66 y), or by Jupiter (5.93 y), or by the Earth (6.57 y). The superposition of multiple long-period terms is also possible. We will carry out close-loop simulations to assess uncertainty and consider interior and libration modelings to interpret the scientific implications.

Figure 1: Rotation variation with time using the IAU2015 model as a priori values. Correction is with respect to Mercury’s resonant rotation.

References:

Archinal et al., 2018. Celest. Mech. Dyn. Astron.. Bertone et al., 2021. JGR. Mazarico et al., 2014. JGR. Genova et al., 2019. GRL. Konopliv et al., 2020. Icarus.  Margot et al., 2012. JGR.  Stark et al., 2015. GRL.  Van Hoolst et al., 2012. EPSL. Xiao et al., 2024. Authorea Preprints. Yseboodt et al., 2013. Icarus.