Influence of Bulk Compressibility on Tides in Rocky and Icy Worlds

Abstract

The tidal response of terrestrial planets or icy moons is a complex interplay between the interior and orbit of the world. A significant factor in this response comes from the thermal and viscoelastic state of the deep interior. Suggesting that if measurements of the tidal and mass-loading (if applicable) response are obtained with sufficient precision, then tides can provide a probe of these properties that are otherwise hidden from other measurement techniques. This has been utilized across the Solar System to constrain questions such as, does Mercury or Venus have a solid core? Does our Moon have significant partial melting in its mantle? Or do icy moons in the outer Solar System contain large, and astrobiologically relevant, liquid oceans? New missions like BepiColombo, VERITAS, Europa Clipper, and more will provide high-precision measurements of tidally-relevant properties such as the Love Number k₂ (and perhaps h₂ and their phase lags). However, linking these observations to the interior requires proper modeling of all the major factors that drive changes in these values.In this study, we look at an often-omitted concept in tidal modeling: Bulk Compressibility, which is the inclusion of bulk modulus in the viscoelastic-gravitational equations used to calculate planetary Love numbers. Including bulk modulus can be mathematically and computationally complex so it is not uncommon to ignore it. This is occasionally justified by the misnomer of “compressibility” being only relevant to large bodies. However, bulk compressibility is not directly dependent on the size or mass of a planet. Instead, it provides another degree of freedom for the world to respond to tidal or loading stresses.In this presentation, we will discuss the background and theory behind bulk compressibility and showcase that its addition can have a measurable impact on tidal and loading Love numbers. For example, work by this team has shown that it can lead to >20% difference in the tidal and loading Love number k₂ and up to 40% difference for h₂. Furthermore, it can significantly alter the phase lag of these numbers which is an important probe of thermal and rheological properties. Finally, we will discuss when bulk compressibility can be ignored and what sort of measurement precision is most affected.