Planetary interiors via Love numbers determined from radial velocities

We study the inner structure of exoplanets by determining the Love numbers kn and hn, which describe the susceptibility of their shape to change in response to a tidal and rotational potential. The second degree Love number k2 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. We will present the method how to analyze the radial velocity curve in presence of apsidal motion caused by tidal interaction between the star and the planet, and by general relativity. The former one can be linked to the Love number k2 which constrains the planetary interior as a third measurable parameter beyond the mass and radius. We also study the effect of the rotationally and tidally distorted stellar shape on the radial velocity (RV) curves. This causes distortion on the RV shape 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 system