Low- and high-order gravitational harmonics of rigidly rotating Jupiter

The Juno Orbiter has provided improved estimates of the even gravitational harmonics J2 to J8 of Jupiter. To compute higher-order moments, new methods such as the Concentric Maclaurin Spheroids (CMS) method have been developed which surpass the so far commonly used Theory of Figures (ToF) method in accuracy. This progress rises the question whether ToF can still provide a useful service for deriving the internal structure of giant planets in the Solar system. In this paper, I apply both the ToF and the CMS method to compare results for polytropic Jupiter and for the physical equation of state H/He-REOS.3 based models. An accuracy in the computed values of J2 and J4 of 0.1% is found to be sufficient in order to obtain the core mass safely within 0.5 Mearth numerical accuracy and the atmospheric metallicity within about 0.0004. ToF to 4th order provides that accuracy, while ToF to 3rd order does not for J4. Furthermore, I find that the assumption of rigid rotation yields J6 and J8 values in agreement with the current Juno estimates, and that higher order terms (J10 to J18) deviate by about 10% from predictions by polytropic models. This work suggests that ToF4 can still be applied to infer the deep internal structure, and that the zonal winds on Jupiter reach less deep than 0.9 RJup.Comment: 8 pages, accepted to A&

Tesseral harmonics of Jupiter from static tidal response

The Juno Orbiter is measuring the three-dimensional gravity field perturbation of Jupiter induced by its rapid rotation, zonal flows, and tidal response to its major natural satellites. This paper aims to provide the contributions to the tesseral harmonics coefficients Cnm, Snm, and the Love numbers knm to be expected from static tidal response in the gravity field of rotating Jupiter. For that purpose, we apply the method of Concentric Maclaurin Ellipsoids (CMS). As we are interested in the variation of the tidal potential with the longitudes of the moons, we take into account the simultaneous presence of the satellites Io, Europa, and Ganymede. We assume co-planar, circular orbits with normals parallel to Jupiter's spin axis. The planet-centered longitude of Io in the three-moon case is arbitrarily assumed varphi = 0. Under these assumptions we find maximum amplitudes and fluctuations of 3.5 times 10^-8 +- 15% for C22. For the Love numbers, largest variation of 10% to 20% is seen in k42 and k62, whereas the values k2, k33, and k44 fall into narrow ranges of 0.1% uncertainty or less. In particular, we find k2=k2,Io(1 +- 0.02%) where k2,Io=0.5897 is the static tidal response to lone Io. Our obtained gravity field perturbation leads to a maximum equatorial shape deformation of up to 28m. We suggest that should Juno measurements of the knm deviate from those values, it may be due to dynamic or dissipative effects on Jupiter's tidal response. Finally, an analytic expression is provided to calculate the tesseral harmonics contribution from static tidal response for any configuration of the satellites.Comment: Accepted to Ap

Matter under extreme conditions: modelling giant planets

We calculate the core mass, metallicity and cooling curves of Jupiter, Saturn, Uranus, and Neptune and evaluate the results with respect to the hydrogen equation of state, the phase diagram of water, and immiscibility of helium in hydrogen. We conclude a likely occurrence of He sedimentation, core erosion, and inhibited convection in these planets and propose alternative structure models as improved representations of these planets

Structure and evolution of the tidally heated hot-Jupiter KELT-9b

The hot Jupiter KELT-9b is observed to have a strong intrinsic heat flux T_int ~ 2400 +/- 800 K. However, requesting a bulk metallicity Z<20% requires significantly lower T_int. To resolve this discrepancy, we suggest (obliquity) tidal heating in a shell and a static k2 < 0.1

Thermal evolution of Uranus and Neptune I: adiabatic models

The brightness of Neptune is often found to be in accordance with an adiabatic interior, while the low luminosity of Uranus challenges this assumption. Here we apply revised equation of state data of hydrogen, helium, and water and compute the thermal evolution of Uranus and Neptune assuming an adiabatic interior. For this purpose, we have developed a new planetary model and evolution code. We investigate the influence of albedo, solar energy influx, and equations of state of H and He, and water on the cooling time. Our cooling times of about $\tau_\text{U}=5.1\times 10^9\text{ years}$ for Uranus and $\tau_\text{N}=3.7\times 10^9\text{ years}$ for Neptune bracket the known age of the planets of $4.56\times 10^9\text{ years}$ implying that neither planet's present-day luminosity can be explained by adiabatic cooling. We also find that uncertainties on input parameters such as the level of irradiation matter generally more for Uranus than for Neptune. Our results suggest that in contrast to common assumptions, neither planet is fully adiabatic in the deeper interior.Comment: Accepted for publication in A&A. Reproduced with permission from Astronomy & Astrophysics, \copyright ES

Exoplanetary Interiors

The discovered exoplanet population spans a wide range in planetary bulk properties, from large gas giants to low-mass sub-Neptunes and rocky planets. These discoveries open numerous questions regarding the internal structures, compositions, and formation mechanisms of these diverse planet types. This chapter discusses the state of the art and important science questions on exoplanetary interiors along with the challenges and opportunities on this frontier

Characterizing Uranus with an Ice giant Planetary Origins Probe (Ice-POP)

We now know from studies of planetary transits and microlensing that Neptune-mass planets are ubitquitous and may be the most common class of planets in the Galaxy. As such it is crucial that we understand the formation and evolution of the ice giant planets in our own solar system so that we can better understand planet formation throughout the galaxy. An entry probe mission to Uranus would help accomplish this goal. In fact the Planetary Decadal Survey recommended a Uranus orbiter with entry probe but did not explore in detail the specifications for the entry probe. NASA Ames is currently studying thermal protection system requirements for such a mission and this has led to questions regarding the minimum interesting science payload of such an entry probe. The single most important in-situ measurement for an ice giant entry probe is a measurement of atmospheric composition. For Uranus this would specifically include the methane and noble gas abundances. An in situ measurement of the methane abundance, from below the methane cloud, would constrain the atmospheric carbon abundance, which is believed to be roughly 30 to 50 times solar. There are hints from the transiting planets that extrasolar ice giants show comparable or even greater enhancements of heavy elements compared to their primary stars. However the origin of this carbon enhancement is controversial. Is Uranus a "failed core" of a larger gas giant or was the atmosphere enhanced by accretion of icy planetesimals' Constraining atmospheric abundances of C and perhaps S or even N from below 5 bars would provide badly needed data to address such issues. A measurement of the N abundance would provide clues on the origin of the planetesimals that formed Uranus. Low N-abundance indicates planetesimals from 'warmer' regions where N was mainly in form of NH3, whereas a strong enrichment could indicate planetesimals / cometary material from the colder outer regions of the nebula. Furthermore CO and HCN have been detected in Neptune but not in Uranus. A measurement of the abundance of either would constrain the source mechanisms for these molecules (exogenic or internal). A major surprise from the Galileo Entry Probe was that the heavier noble gases Ar, Kr, and Xe are enhanced in Jupiter's atmosphere at a level comparable to what was seen for the chemically active volatiles N, C, and S. It had been generally expected that Ar, Kr, and Xe would be present in solar abundances, as all were expected to accrete with hydrogen during the gravitational capture of nebular gases. Enhanced abundances of Ar, Kr, and Xe is equivalent to saying that these noble gases have been separated from hydrogen. There are several mechanisms that could accomplish this but these hypotheses require further testing. Measurement of noble gas abundances in an ice giant would constrain the planetary formation and nebular mechanisms responsible for this enhancement. Standard three-layer models of Uranus find that the outer, predominantly H/He layer of Uranus does not reach pressures high enough (approximately 1 Mbar) for H2 to transition to liquid metallic hydrogen. However, valid models can also be constructed with a smaller intermediate water-rich layer, with hydrogen then reaching the metallic hydrogen phase. If this occurs, He should phase separate from the hydrogen and ``rain out," taking along a substantial abundance of Ne, as suggested for Jupiter (and likely also for Saturn). Hence He and Ne depletions could be probes of the planet's structure in the much deeper interior. A determination of Uranus' atmospheric abundances, particularly of the noble gasses, is thus critical to understanding the formation of Uranus, and giant planets in general. These measurements can only be performed with an entry probe. The second key measurement would be a temperature-pressure sounding to provide ground truth for remote measurements of atmospheric temperature and composition and to constrain the internal heat flow. This would also establish that the methane abundance measurements have indeed been made below any possible methane cloud. Finally an ultra stable oscillator would measure wind speeds and constrain atmospheric dynamics. In our presentation we will discuss the importance of all of these measurements and argue that an entry probe is a crucial component of any ice giant mission

Forward and Inverse Modeling for Jovian Seismology

Jupiter is expected to pulsate in a spectrum of acoustic modes and recent re-analysis of a spectroscopic time series has identified a regular pattern in the spacing of the frequencies \citep{gaulme2011}. This exciting result can provide constraints on gross Jovian properties and warrants a more in-depth theoretical study of the seismic structure of Jupiter. With current instrumentation, such as the SYMPA instrument \citep{schmider2007} used for the \citet{gaulme2011} analysis, we assume that, at minimum, a set of global frequencies extending up to angular degree $\ell=25$ could be observed. In order to identify which modes would best constrain models of Jupiter's interior and thus help motivate the next generation of observations, we explore the sensitivity of derived parameters to this mode set. Three different models of the Jovian interior are computed and the theoretical pulsation spectrum from these models for $\ell\leq 25$ is obtained. We compute sensitivity kernels and perform linear inversions to infer details of the expected discontinuities in the profiles in the Jovian interior. We find that the amplitude of the sound-speed jump of a few percent in the inner/outer envelope boundary seen in two of the applied models should be reasonably inferred with these particular modes. Near the core boundary where models predict large density discontinuities, the location of such features can be accurately measured, while their amplitudes have more uncertainty. These results suggest that this mode set would be sufficient to infer the radial location and strength of expected discontinuities in Jupiter's interior, and place strong constraints on the core size and mass. We encourage new observations to detect these Jovian oscillations.Comment: 31 pages, 12 figures, accepted to Icaru