Tidal constraints on the radial extension and static stability of Jupiters dilute core

NASA's Juno mission recently proposed that Jupiter hosts a dilute core with a compositional gradient that could be present as far out as ~0.6RJ, contrary to the traditional view of a compact core. Here we use simple models to evaluate the response of Jupiter's dilute core to tidal excitation. We model Jupiter's interior as a mixture of H-He fluid and heavy elements, including a He gradient at ~0.8RJ promoted by the immiscibility of He in H. Idini & Stevenson (2021) previously determined a dynamical effect on k2 (the l=m=2 Love number) equal to -4% in the case of Io's tidal excitation of a homogeneous, adiabatic Jupiter model. Our results reported here suggest that a dilute core introduces an additional non-resonant effect close to +2% for a compositional gradient present at ~0.6RJ and the He gradient an additional +2% effect, leading to a close to zero net effect. Our prediction neglects the dynamical contribution from g-modes trapped in the dilute core, excluding near-resonant effects from our results. The most recent Juno observation (perijove 17) disagrees with our ~0.6RJ dilute core model, suggesting that Jupiter hosts a dilute core that only extends as far out as ~0.4RJ. The uncertainty in the k2 Juno observation is expected to diminish by an order of magnitude at the end of Juno's extended mission (mid 2025), allowing us to set tighter constraints on the existence or extension of Jupiter's dilute core. Our prediction provides the first direct estimate of the static stability in the proposed dilute core in Jupiter.