Viscoelastic Tides of Mercury and the Determination of its Inner Core Size

Plain Language Summary We computed interior structure models of Mercury and analyzed their viscoelastic tidal response. The models are consistent with MErcury Surface, Space Environment, GEochemistry, and Ranging mission inferences of mean density, mean moment of inertia, moment of inertia of mantle and crust, and tidal Love number k(2). Based on these constraints we predict the tidal Love number h(2) to be in the range from 0.77 to 0.93. Using an Andrade rheology for the mantle the tidal phase-lag is predicted to be 4 degrees at maximum. The corresponding tidal dissipation in Mercury's silicate mantle induces a surface heat flux smaller than 0.16mW/m(2). We show that, independent of the adopted mantle rheological model, the ratio of the tidal Love numbers h(2) and k(2) provides a better constraint on the maximum inner core size with respect to other geodetic parameters (e.g., libration amplitude or a single Love number), provided it responds elastically to the solar tide. For inner cores larger than 700km, and with the expected determination of h(2) from the upcoming BepiColombo mission, it may be possible to constrain the size of the inner core. The measurement of the tidal phase-lag with an accuracy better than approximate to 0.5 degrees would further allow constraining the temperature at the core-mantle boundary for a given grain size and therefore improve our understanding of the physical structure of Mercury's core. Due to the proximity to the Sun, tides are raised on Mercury in a similar way the Moon causes ocean tides on Earth. Although Mercury's surface is rigid, a large fluid core causes a tidal wave propagating around the planet. Using results from NASA's MESSENGER mission, we calculate that the surface should also deform by around 20cm to 2.40m during each Mercury orbit around the Sun. This is an amplitude that could be detected with a laser altimeter, one of the instruments onboard the upcoming BepiColombo mission. We show how the interior structure of the planet, in particular the size of an inner solid core, can be constrained by the tidal measurement. This result will help us to better understand Mercury's evolution and to constrain models explaining the magnetic field generation in Mercury's iron core.