On the degeneracy of the tidal Love number k_2 in multi-layer planetary models: application to Saturn and GJ 436b

Context. In order to accurately model giant planets, a whole set of observational constraints is needed. As the conventional constraints for extrasolar planets like mass, radius, and temperature allow for a large number of acceptable models, a new planetary parameter is desirable in order to further constrain planetary models. Such a parameter may be the tidal Love number k_2. Aims. In this paper we aim to study the capability of k_2 to reveal further information about the interior structure of a planet. Methods. With theoretical planetary models we investigate how the tidal Love number k_2 responds to the internal density distribution of a planet. In particular, we demonstrate the effect of the degeneracy of k_2 due to a density discontinuity in the envelope of a three-layer planetary model. Results. The effect of a possible outer density discontinuity masks the effect of the core mass on the Love number k_2. Hence, there is no unique relationship between the Love number k_2 and the core mass of a planet. We show that the degeneracy of k2 with respect to a layer boundary in the envelope also occurs in existing planets, e.g. Saturn and the Hot Neptune GJ 436b. As a result of the degeneracy, the planetary parameter k_2 cannot be used to further constrain the core mass of state-of-the-art Saturn models and for GJ 436b only a maximum possible core mass can be derived from a given k_2. To significantly narrow the uncertainty about the core mass of GJ 436b the combined knowledge of k_2 and atmospheric metallicity and temperature profile is necessary