Planetary interiors via Love numbers determined from radial velocities

Kurzfassung

We study the inner structure of exoplanets by determining the Love numbers k_n and h_n (Love 1911), which describe the susceptibility of their shape to change in response to a tidal and rotational potential. The second degree Love number k_2 is highly sensitive to the thickness of the interior layers and rheology of the planet and it is proportional to the concentration of mass towards the centre of the planet, therefore it is used to infer the internal structure of the body. In the present decade, with new RV-instruments, such as the Echelle SPectrograph for Rocky Exoplanets and Stable Spectroscopic Observations (ESPRESSO) and the Habitable Zone Planet Finder (HPF), we will be able to measure the periastron precession rates for many exoplanets, and thus the Love numbers can be determined. We will present the method to analyze the radial velocity curve in presence of apsidal motion caused by general relativity and by tidal interaction between the star and the planet. The latter can be linked to the Love number k2 (Kopal 1959) which constrains the planetary interior as a third measurable parameter beyond the mass and radius (Baumeister et al. 2020). We also study the effect of the rotationally and tidally distorted stellar shape on the radial velocity (RV) curves. This causes distortion in the shape of the RV curve as well, and leads to the presence of an apparent eccentric orbit in the RV curve. We show that the correct estimate of this effect must be taken into account and some earlier studies overestimated its amplitude and significance. Finally, we show our first results when we applied our method to real exoplanetary systems.