On the degeneracy of the tidal Love number k2 in multi-layer planetary models: application to Saturn and GJ436b

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 k2. In this paper we aim to study the capability of k2 to reveal further information about the interior structure of a planet. With theoretical planetary models we investigate how the tidal Love number k2 responds to the internal density distribution of a planet. In particular, we demonstrate the effect of the degeneracy of k2 due to a density discontinuity in the envelope of a three-layer planetary model. The effect of a possible outer density discontinuity masks the effect of the core mass on the Love number k2. Hence, there is no unique relationship between the Love number k2 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 GJ436b. As a result of the degeneracy, the planetary parameter k2 cannot be used to further constrain Saturnian models and for GJ436b only a maximum possible core mass can be derived from a given k2. To significantly narrow the uncertainty about the core mass of GJ436b the combined knowledge of k2 and atmospheric metallicity and temperature profile is necessary.