Tidal response of rocky and ice-rich exoplanets

Abstract

The amount of detected planets with sizes comparable to that of the Earth is increasing drastically. Most of the Earth-size planet candidates orbit at close distances from their central star, and therefore are subjected to large tidal forces. Accurate determination of the tidal parameters of exoplanets taking into account their interior structure and rheology is essential to better constrain their rotational and orbital history, and hence their impact on climate stability and planetary habitability. In the present study, we compute the tidal response of rocky and ice-rich solid exoplanets for masses ranging between 0.1 and 10 Earth masses using a multilayer approach and an Andrade rheology. We show that the amplitude of tidal response, characterized by the gravitational Love number, k2, is mostly controlled by self-gravitation and increases as a function of planet mass. For rocky planets, k2 depends mostly on the relative size of the iron core, and hence on the bulk iron fraction. For ice-rich planets, the presence of outer ice layers reduces the amplitude of tidal response compared to ice-free rocky planets of similar masses. For both types of planet (rocky and ice-rich), we propose relatively simple scaling laws to predict the potential Love number value as a function of radius, planet mass and composition. For the dissipation rate, characterized by the Q−1 factor, we did not find any direct control by the planet mass. The dissipation rate is mostly sensitive to the forcing frequency and to the internal viscosity, which depends on the thermal evolution of the planet, which is in turn controlled by the planet mass and composition. The methodology described in the present study can be applied to any kind of solid planet and can be easily implemented into any thermal and orbital evolution code.

Solid tides in Io’s partially molten interior

“…The viscoelastic deformation of Io under the action of periodic tidal forces is computed following the method of Tobie et al (2005Tobie et al ( , 2019. A novel step is taken with the inclusion of bulk dissipation in addition to shear dissipation in the calculation (Sect.…”

Solid tidal friction in multi-layer planets: Application to Earth, Venus, a Super Earth and the TRAPPIST-1 planets

“…Compared to the classically used Maxwell rheology, the Andrade rheology provides a more accurate description of the frequency dependency of both elastic and dissipative responses across a wide range of forcing frequencies and periods. The Maxwell rheological model provides a reasonable description of viscoelastic behavior for forcing periods near and larger than that of the Maxwell time, but it strongly underestimates viscous dissipation (or overestimates the Q factor) for forcing periods that are much smaller than the Maxwell time (e.g., Efroimsky 2012b; Tobie et al 2019).…”

“…In this particular example, a combined rheological model was used (Andrade 1910 at higher frequencies and Maxwell at lower frequencies) to show that the planets are trapped in spin-orbit resonances, whose order depends on the eccentricity (e.g., Mercury, Noyelles et al 2014). The rheology of Maxwell and Andrade is widely used, for instance, to estimate rotation states (e.g., Correia et al 2014) or tidal heating in planets (e.g., Renaud & Henning 2018;Tobie et al 2019). Maxwell's rheology describes a viscoelastic material, whereas Andrade's rheology describes an anelastic material.…”

“…It is necessary to take into account a better description of the tidal deformation in order to estimate the rotation states of planets (e.g., Noyelles et al 2014), their rotational and orbital evolution (e.g., Correia et al 2014;Boué et al 2016;Frouard et al 2016), or to estimate the tidal heating in rocky planets (e.g., Henning et al 2009;Henning & Hurford 2014;Tobie et al 2019 for generic planets;and Barr et al 2018 for TRAPPIST-1). Most of these different studies consider a homogeneous body (except for Henning & Hurford 2014;Tobie et al 2019) and most of them assume a Maxwell rheology (except for Noyelles et al 2014;Tobie et al 2019). We note that Walterová & Běhounková (2017) revisited the work of Correia et al (2014) using a multi-layer model for the planets, and investigated the tidal dissipation and tidal torques for the Maxwell and the Andrade rheology.…”

Possible Deep Structure and Composition of Venus With Respect to the Current Knowledge From Geodetic Data

“…Unfortunately, the tidal dissipation factor Q of Venus’s tide is still unknown. As a reference, the Q of Earth extrapolated to Venus’s tidal period (58.4 days) is considered to be approximately 100 (Tobie et al., 2019).…”