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Titan's ice shell floats on top of a global ocean revealed by the large tidal Love number $k_2 = 0.616\pm0.067$ registered by Cassini. The Cassini observation exceeds the predicted $k_2$ by one order of magnitude in the absence of an ocean, and is 3-$\sigma$ away from the predicted $k_2$ if the ocean is pure water resting on top of a rigid ocean floor. Previous studies demonstrate that an ocean heavily enriched in salts (salinity $S\gtrsim200$ g/kg) can explain the 3-$\sigma$ signal in $k_2$. Here we revisit previous interpretations of Titan's large $k_2$ using simple physical arguments and propose a new interpretation based on the dynamic tidal response of a stably stratified ocean in resonance with eccentricity tides raised by Saturn. Our models include inertial effects from a full consideration of the Coriolis force and the radial stratification of the ocean, typically neglected or approximated elsewhere. The stratification of the ocean emerges from a salinity profile where salt concentration linearly increases with depth. We find multiple salinity profiles that lead to the $k_2$ required by Cassini. In contrast with previous interpretations that neglect stratification, resonant stratification reduces the bulk salinity required by observations by an order of magnitude, reaching a salinity for Titan's ocean that is compatible with that of Earth's oceans and close to Enceladus' plumes. Consequently, no special process is required to enrich Titan's ocean to a high salinity as previously suggested., Comment: 29 pages, 8 figures, accepted to PSJ

At mid-mission perijove 17, NASA's Juno mission has revealed a $7\sigma$ discrepancy between Jupiter's observed high-degree tidal response and the theoretical equilibrium tidal response, namely the Love number $k_{42}$. Here, we propose an interpretation for this puzzling disagreement based on an interior-orbital resonance between internal gravity waves trapped in Jupiter's dilute core and the orbital motion of Io. We use simple Jupiter models to calculate a fractional correction $\Delta k_{42}$ to the equilibrium tidal response that comes from the dynamical tidal response of a $g$-mode trapped in Jupiter's dilute core. Our results suggest that an extended dilute core ($r\gtrsim0.7R_J$) produces an interior-orbital resonance with Io that modifies Jupiter's tidal response in $\Delta k_{42}\sim-11\%$, allowing us to fit Juno's $k_{42}$. In our proposed self-consistent scenario, Jupiter's dilute core evolves in resonant locking with Io's orbital migration, which allows the interior-orbital resonance to persist over geological timescales. This scenario requires a dilute core that becomes smoother or shrinks over time, together with a $_4^2g_1$ mode ($\ell,m,n=4,2,1$) with resonant tidal dissipation reaching $Q_4\sim1000$. Jupiter's dilute core evolution path and the dissipation mechanism for the resonant $_4^2g_1$ mode are uncertain and motivate future analysis. No other alternative exists so far to explain the $7\sigma$ discrepancy in Juno $k_{42}$. Our proposed interior-orbital resonance can be tested by Juno observations of $k_{42}$ tides raised on Jupiter by Europa as obtained at the end of the extended mission (mid 2025), and by future seismological observations of Jupiter's $_4^2g_1$ mode oscillation frequency., Comment: 14 pages, 5 figures, accepted to PSJ

NASA's Juno mission recently reported Jupiter's high-degree (degree $\ell$, azimuthal order $m$ $=4,2$) Love number $k_{42}=1.289\pm0.063$ ($1\sigma$), an order of magnitude above the hydrostatic $k_{42}$ obtained in a nonrotating Jupiter model. After numerically modeling rotation, the hydrostatic $k_{42}=1.743\pm0.002$ is still $7\sigma$ away from the observation, raising doubts about our understanding of Jupiter's tidal response. Here, we use first-order perturbation theory to explain the hydrostatic $k_{42}$ result analytically. We use a simple Jupiter equation of state ($n=1$ polytrope) to obtain the fractional change in $k_{42}$ when comparing a rotating model with a nonrotating model. Our analytical result shows that the hydrostatic $k_{42}$ is dominated by the tidal response at $\ell=m=2$ coupled into the spherical harmonic $\ell,m=4,2$ by the planet's oblate figure. The $\ell=4$ normalization in $k_{42}$ introduces an orbital factor $(a/s)^2$ into $k_{42}$, where $a$ is the satellite semimajor axis and $s$ is Jupiter's average radius. As a result, different Galilean satellites produce a different $k_{42}$. We conclude that high-degree tesseral Love numbers ($\ell> m$, $m\geq2$) are dominated by lower-degree Love numbers and thus provide little additional information about interior structure, at least when they are primarily hydrostatic. Our results entail important implications for a future interpretation of the currently observed Juno $k_{42}$. After including the coupling from the well-understood $\ell=2$ dynamical tides ($\Delta k_2 \approx -4\%$), Jupiter's hydrostatic $k_{42}$ requires an unknown dynamical effect to produce a fractional correction $\Delta k_{42}\approx-11\%$ in order to fit Juno's observation within $3\sigma$. Future work is required to explain the required $\Delta k_{42}$., Comment: 8 pages, 2 tables, accepted to PSJ

The Juno orbiter continues to collect data on Jupiter's gravity field with unprecedented precision since 2016, recently reporting a non-hydrostatic component in the tidal response of the planet. At the mid-mission perijove 17, Juno registered a Love number $k_2=0.565\pm0.006$ that is $-4\pm1\%$ ($1\sigma$) from the theoretical hydrostatic $k_2^{(hs)}=0.590$. Here we assess whether the aforementioned departure of tides from hydrostatic equilibrium represents the neglected gravitational contribution of dynamical tides. We employ perturbation theory and simple tidal models to calculate a fractional dynamical correction $\Delta k_2$ to the well-known hydrostatic $k_2$. Exploiting the analytical simplicity of a toy uniform-density model, we show how the Coriolis acceleration motivates the negative sign in the $\Delta k_2$ observed by Juno. By simplifying Jupiter's interior into a core-less, fully-convective, and chemically-homogeneous body, we calculate $\Delta k_2$ in a model following an $n=1$ polytrope equation of state. Our numerical results for the $n=1$ polytrope qualitatively follow the behaviour of the uniform-density model, mostly because the main component of the tidal flow is similar in each case. Our results indicate that the gravitational effect of the Io-induced dynamical tide leads to $\Delta k_2=-4\pm1\%$, in agreement with the non-hydrostatic component reported by Juno. Consequently, our results suggest that Juno obtained the first unambiguous detection of the gravitational effect of dynamical tides in a gas giant planet. These results facilitate a future interpretation of Juno tidal gravity data with the purpose of elucidating the existence of a dilute core in Jupiter., Comment: 22 pages, 5 figures, accepted to PSJ