On the degeneracy of the tidal Love number k₂ in multi-layer planetary models: application to Saturn and GJ 436b

Abstract

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 k₂.
Aims: In this paper we aim to study the capability of k₂ to reveal further information about the interior structure of a planet.
Methods: 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.
Results: 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 GJ 436b. As a result of the degeneracy, the planetary parameter k₂ 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 k₂. To significantly narrow the uncertainty about the core mass of GJ 436b the combined knowledge of k₂ and atmospheric metallicity and temperature profile is necessary.