This roadmap presents the state-of-the-art, current challenges and near future developments anticipated in the thriving field of warm dense matter physics. Originating from strongly coupled plasma physics, high pressure physics and high energy density science, the warm dense matter physics community has recently taken a giant leap forward. This is due to spectacular developments in laser technology, diagnostic capabilities, and computer simulation techniques. Only in the last decade has it become possible to perform accurate enough simulations & experiments to truly verify theoretical results as well as to reliably design experiments based on predictions. Consequently, this roadmap discusses recent developments and contemporary challenges that are faced by theoretical methods, and experimental techniques needed to create and diagnose warm dense matter. A large part of this roadmap is dedicated to specific warm dense matter systems and applications in astrophysics, inertial confinement fusion and novel material synthesis.

Jupiter’s gravity field observed by NASA’s Juno spacecraft indicates that the density in the 10–100 GPa region is lower than one would expect from a H/He adiabat with 0.5–5× solar water abundance, as has been observationally inferred in Jupiter’s atmosphere, supported by the 2–4× solar enrichment in the heavy noble gases and other volatiles observed by the Galileo entry probe. Here, we assume that Jupiter’s envelope harbors a radiative window at ∼0.975–0.99 R _J . This outer stable layer (OSL) delays particle exchange and accelerates the cooling of the deep interior. Consequently, the He depletion at the Mbar level, where H/He phase separation occurs, would be stronger than seen in the atmosphere. We find that the inverted He gradient across the OSL leads to atmospheric heavy element abundances that are up to Δ Z _atm = 0.03(+2× solar) higher than for adiabatic models. With an additional inverted Z gradient, Z _atm up to 3× solar is possible. Models with 1× solar Z _atm have a dilute core confined to the inner 0.2–0.3 M _J (0.4–0.5 R _J ), smaller than in adiabatic models. Models with 3× solar Z _atm have a largely homogeneous Z interior at 1× solar. The low observed atmospheric Ne/He ratio suggests that Ne is transported through the OSL as efficiently as He is, and at an enhanced diffusivity, as is characteristic of double-diffusive convection. Better knowledge of the H/He equation of state in the 10–100 GPa region and of the H/He phase diagram is needed to understand Jupiter’s interior structure.

Sub-Neptunes occupy an intriguing region of planetary mass–radius space, where theoretical models of interior structure predict that they could be water-rich, where water is in steam and supercritical state. Such planets are expected to evolve according to the same principles as canonical H _2 –He rich planets, but models that assume a water-dominated atmosphere consistent with the interior have not been developed yet. Here, we present a state-of-the-art structure and evolution model for water-rich sub-Neptunes. Our setup combines an existing atmospheric model that controls the heat loss from the planet, and an interior model that acts as the reservoir of energy. We compute evolutionary tracks of planetary radius over time. We find that planets with pure water envelopes have smaller radii than predicted by previous models, and the change in radius is much slower (within ∼10%). We also find that water in the deep interior is colder than previously suggested, and can transition from plasma state to superionic ice, which can have additional implications for their evolution. We provide a grid of evolutionary tracks that can be used to infer the bulk water content of sub-Neptunes. We compare the bulk water content inferred by this model and other models available in the literature, and find statistically significant differences between models when the uncertainties on measured mass and radius are both smaller than 10%. This study shows the importance of pursuing efforts in the modeling of volatile-rich planets, and how to connect them to observations.

Demixing properties of planetary major constituents influence the interior structure and evolution of planets. Comparing experimental and computational data on the miscibility of hydrogen and water to adiabatic profiles suggests phase separation between these components occurs in the ice giants Uranus and Neptune. We aim to predict the atmospheric water abundance and transition pressure between the water-poor outer envelope and the water-rich deep interior in Uranus and Neptune. We construct seven H2-H2O phase diagrams from the available experimental and computational data. We compute interior adiabatic structure models and compare these to the phase diagrams to infer whether demixing is occurring. We obtain a strong water depletion in the top layer due to rain-out of water and find upper limits on the atmospheric water mass fraction Z_atm of 0.21 for Uranus and 0.16 for Neptune. The transition from the water-poor to the water-rich layer is sharp and occurs at pressures P_Z between 4 and 11 GPa. Using these constraints on Z_atm and P_Z, we find that the observed gravitational harmonics J2 and J4 can be reproduced if P_Z > 10 GPa in Uranus and > 5 GPa in Neptune, and if the deep interior has a high primordial water mass fraction of 0.8, unless rocks are also present. The agreement with J4 is improved if rocks are confined deeper than P_Z, for instance below a rock cloud level at 2000 K (20-30 GPa). These findings confirm classical few-layer models and suggest that a layered structure may result from a combination of primordial mass accretion and subsequent phase separation. Reduced observational uncertainty in J4 and its dynamic contribution, atmospheric water abundance measurements from an Orbiter with a Probe mission to Uranus (UOP) or Neptune, and better understanding of the mixing behaviour of constituents are needed to constrain the interiors of ice giants.

. Introduction. Hydrogen (H), helium (He) and oxygen (O) are the most abundant elements in the Sun, as they were in the protosolar nebula. By analyzing the bulk composition of Jupiter, in which a large fraction of the nebula material is confined today, information on the conditions in the disk at the time of planet formation can be obtained. Here, we use the water abundance observed by Juno to infer Jupiter's heavy element mass fraction Z from interior modeling. The Galileo entry Probe measured a depletion in He, Ne, and water with respect to protosolar values [1]. While the He-Ne depletion is generally considered evidence of H/He phase separation and He-rain at Mbar pressures, the water abundance at depth where the atmosphere is supposed to be quiet and homogeneous remained obscure. Juno measurements of convective storms, lightning, the cloud height, the upper tropospheric CO abundance, as well as ongoing analysis of the microwave absorption, finally constrained the deep water abundance to be within 0.1x and 7x solar [2]. A 0.1x (1x/2x/3x) solar water (or O/H) abundance corresponds to Z of ~0.5x (1.2x/2x/2.8x) solar for Zsol=0.015. The temperature at a reference level of 1-bar is observed to be T1bar=166-174 K [3].Jupiter interior models are in addition constrained by the gravitational harmonics J2 and J4. However, current models that fit the Juno gravity measurements struggle to reach 1x solar Z in the atmosphere. Higher values like 2x solar are out of reach. In practise, H/He adiabats tend to be too dense to permit adding heavy elements in the amount of 1x solar or more, where the J2 and J4 are most sensitive. Possibilities to reconcile the Jupiter models with the Juno measurements include substantial over-estimation of density along the Jupiter adiabat by current H/He-EOSs [4] or that Jupiter's adiabat is on a higher entropy, corresponding to T1bar ~180 K, than seen in the atmosphere [5]. Here, we insert an outer stable layer (OSL) with inverted He-gradient and investigate to what extent the low atmospheric-Z issue can be mitigated. Strong He-depletion at the bottom of the OSL is assumed to result from H/He phase separation at Mbar pressures. We validate this model against the (shifted) LHR0911 H/He phase diagram. 2. Method. We place the OSL between 0.1 and 2 GPa. The temperature-gradient is adjusted to satisfy Ledoux-stability at Rρ-1=0.9. This places the OSL in the regime of fingering double diffusive convection [6]. We compute Jupiter models in sufficient agreement with the observed gravitational harmonics. We vary (i) the He-gradient dY across the OSL, (ii) the transition pressure PHe between the He-depleted and He-rich layer at Mbar pressures, (iii) the deeper transition pressure PZ between Zatm and Zdeep, which are adjusted to fit J2 and J4, and (iv) T1bar between 166 and 174 K. For H/He we use the CD21-EOS [7], while for Z we use water-Equations of State (EOS). 3. Results for ZFigure 1: Resulting Zatm (open symbols) and Zdeep (filled) over the assumed He-gradient -dY across the Outer Stable Layer. The color scale shows PHe, and different symbols indicate T1bar. With the removal of He (larger -dY) and its deposition deeper down, Zatm increases. A threshold of 1x atmospheric-Z can easily be reached and passed. For stronger He-depletion, up to 2x solar Zatm is possible if He rain extends to deep levels of 3-4 Mbars, see Figure 1. Simultaneously, the dilute core, which is clearly seen at dY=0, becomes more dilute (Zdeep decreases). Eventually, Zatm ~ Zdeep: a homogeneous-Z interior has emerged with a Z of 1.5-2x solar and a few ME rock core mass. The dilute core has disappeared. 4. Comparison to H/He phase diagram. We compare the deep He-depletion at Mbar levels of our Jupiter models with the He-depletion predicted by the (shifted) LHR0911 H/He-phase diagram [8]. For adiabatic standard models (dY=0) based on CD21-EOS, a fine-tuned shift of this H/He phase diagram by -1100 K is needed to yield the observed atmospheric value YGal ~ 0.238. For our models with variable dY, consistency occurs where the region spanned by the points (Jupiter models) and the lines (H/He phase diagram) overlap. The overlap region is wide and relaxes the required shift to be within 1000-1200 K, see Figure 2. Figure 2: Lines: He depletion along adiabats defined by T1bar (color code along the lines) according to the LHR0911 H/He-phase diagram [8] for different shifts thereof. Points: He depletion at the 1 Mbar level of P-T profiles with OSL. 5. Conclusions. Insertion of an Outer Stable Layer with inverted He-gradient lifts Zatm up to 2x solar (O/H = 2x solar). Such Jupiter models have a homogeneous-Z interior and a small compact core. The dilute core has disappeared in favor of an enhanced He abundance. We furthermore find that a H/He phase diagram than can explain the observed atmospheric He-abundance will as well be consistent with strong depletion at Mbar depths, in which case the deep adiabats are cold. This may point to an actually super-adiabatic, stable He-rain region. Indeed, an extended deep stable region is suggested by Jupiter's gravitational response to tides observed by Juno [9]. 6. References. [1] Atreya, Mahaffy, Niemann et al Pl.Sp.Sci 51:105 (2003) [2] Cavalie, Lunine, Mousis SSRv. 220:8 (2024) [3] Gupta, Atreya, Steffes, et al PSJ 3:159 (2022) [4] Howard, Guillot, Bazot et al AA 672:A33 (2023) [5] Miguel, Bazot, Guillot et al AA 662:A18 (2022) [6] Brown, Garaud, Stellmach ApJ 768:34 (2014) [7] Chabrier & Debras ApJ 917:4 (2021) [8] Lorenzen, Holst, Redmer PRB 84:235109 (2011) [9] Idini & Stevenson 3:89 PSJ (2022)

Context. Demixing properties of major planetary constituents influence the interior structure and evolution of planets. Comparing experimental and computational data on the miscibility of hydrogen and water to adiabatic profiles suggests that phase separation between these two components occurs in the ice giants Uranus and Neptune. Aims. We aim to predict the atmospheric water abundance and transition pressure between the water-poor outer envelope and the water-rich deep interior in Uranus and Neptune. Methods. We constructed seven H-2-H2O phase diagrams from the available experimental and computational data. We computed interior adiabatic structure models and compared these to the phase diagrams to infer whether demixing occurred. Results. We obtain a strong water depletion in the top layer due to the rain-out of water and find upper limits on the atmospheric water-mass fraction Z(atm) of 0.21 for Uranus and 0.16 for Neptune. The transition from the water-poor to the water-rich layer is sharp and occurs at pressures P-Z between 4 and 11 GPa. Using these constraints on Z(atm) and P-Z, we find that the observed gravitational harmonics J(2) and J(4) can be reproduced if P-Z greater than or similar to 10 GPa in Uranus and greater than or similar to 5 GPa in Neptune, and if the deep interior has a high primordial water-mass fraction of 0.8, unless rocks are also present. The agreement with J(4) is improved if rocks are confined deeper than P-Z, for instance, below a rock cloud level at 2000 K (20-30 GPa). Conclusions. These findings confirm classical few-layer models and suggest that a layered structure may result from a combination of primordial mass accretion and subsequent phase separation. Reduced observational uncertainty in J(4) and its dynamic contribution, atmospheric water abundance measurements from the Uranus Orbiter and Probe (UOP) or a Neptune mission, and better understanding of the mixing behaviour of constituents are needed to constrain the interiors of ice giants.

Linking the interior and atmospheric abundances of giant planets is a crucial step in understanding their formation, interior structure, and evolution [1]. In the case of Uranus and Neptune, there are still major uncertainties regarding their bulk composition and distribution of elements. In this work, we present predictions of the atmospheric water abundance of the ice giants, which can reveal important insights into their internal structures. Interior models constrained by the observed gravitational harmonics J2 and J4 indicate that the interiors are composed of a H/He-rich envelope atop an ice/rock-rich interior [2]. To explain such a structure, the phase separation of the two major constituents, water and molecular hydrogen, has been proposed as a possible explanation for this structure [3]. In this scenario, the demixing of hydrogen and water would lead to rain-out of water, leaving the atmosphere depleted of water over time. Here, we employ H2-H2O phase diagrams constrained by experimental data up to 4 GPa [4,5,6] (Figure 1) to predict the atmospheric water abundance over the planets’ evolution (Figure 2). We simulate the process of demixing by applying mass conservation and show that phase separation can occur over a wide range of assumed initial bulk water abundances and may have started already billions of years ago, with higher initial water abundances leading to colder interiors and earlier onsets of demixing. We find that water rain-out can substantially reduce the atmospheric water abundance down to levels between 0.05-0.15wt% whilst the deep water abundance remains essentially primordial.We also compare the gravity field of our ice giant models to the observed J2 and J4 values [7], noting that the latter also include a contribution from the winds. We compute J2, and J4 both for the models constrained by the H2-H2O phase diagrams and for unconstrained models where the Z-poor/Z-rich transition is variable. We find a preference for models with a water-poor/water-rich transition at 5-15 GPa. For the constrained model, this could imply that the water-poor/water-rich transition could be gradual, or that further transitions perhaps in the C-H system play a role, or that J4 is substantially reduced by zonal winds.This work connects volatile abundances to gravity field and interior structure of the ice giants, and in light of the exciting Uranus Flagship mission, we stress the importance of obtaining gravity field data as well as in-situ abundance measurements from an atmospheric probe coupled with remote sensing. Such measurements could provide important constraints for the deep water abundance.Figure 1: (Left): Experimental and computational data points for H2-H2O miscibility from [4] (purple), [5] (yellow), [6] (green) and [8] (blue). Filled symbols correspond to the coexistence of two phases and empty squares to complete mixing of H2 and H2O. The lines indicate different fits to the data points. A linear extrapolation of the data by [5] to 4 and 5 GPa is shown by the dashed yellow line. Three different extensions above 3.5 GPa for the [6] data (flat, convergence to 1800 K and 2000 K) are shown by green dotted, solid and dashed lines, respectively. (Right): Phase diagram based on the shape of the 0.2 GPa curve from [4] (original data: purple dots). Higher isobars are obtained by shifting the 0.2 GPa curve to match the respective 1:1 critical curves in T-P space.Figure 2: Predicted atmospheric water abundance as a function of the atmospheric temperature at 1 bar for the different phase diagrams used. The older the planet, the colder the adiabat as specified by T1bar, and the more water rains down, depleting the atmosphere. In our simulation, the planet starts completely mixed with homogeneous envelopes and ends with a water-depleted top envelope. For comparison, the atmospheric water abundances determined from structure models are included together with standard Neptune evolution curves from [2] on the top x-axis. [1] National Academies of Sciences, Origins, Worlds, and Life: A Decadal Strategy for Planetary Science and Astrobiology 2023-2032. (2023), The National Academies Press [2] Nettelmann N., Helled R., Fortney J., Redmer R., (2013), Planet. Space Sci., 77, 143[3] Bailey E., Stevenson D. J., (2021), Planet. Sci. J., 2, 64[4] Seward T., Franck E., (1981), Berichte der Bunsengesellschaft für physikalische Chemie, 85, 2[5] Bali E., Audétat A., Keppler H., (2013), Nature, 495, 220[6] Vlasov K., Audétat A., Keppler H., (2023), Contrib. Mineral. Petrol., 178, 36[7] Helled R., Fortney J.J., (2020), Philos. Trans. R. Soc. Lond. Ser. A, 378, 20190474[8] Bergermann A., French M., & Redmer R. (2021), Phys. Chem. Chem. Phys., 23, 12637, 23, 12637

Determining the internal structure of Uranus is a key objective for planetary science. Knowledge of Uranus's bulk composition and the distribution of elements is crucial to understanding its origin and evolutionary path. In addition, Uranus represents a poorly understood class of intermediate-mass planets (intermediate in size between the relatively well studied terrestrial and gas giant planets), which appear to be very common in the Galaxy. As a result, a better characterization of Uranus will also help us to better understand exoplanets in this mass and size regime. Recognizing the importance of Uranus, a Keck Institute for Space Studies (KISS) workshop was held in September 2023 to investigate how we can improve our knowledge of Uranus's internal structure in the context of a future Uranus mission that includes an orbiter and a probe. The scientific goals and objectives of the recently released Planetary Science and Astrobiology Decadal Survey were taken as our starting point. We reviewed our current knowledge of Uranus's interior and identified measurement and other mission requirements for a future Uranus spacecraft, providing more detail than was possible in the Decadal Survey's mission study and including new insights into the measurements to be made. We also identified important knowledge gaps to be closed with Earth-based efforts in the near term that will help guide the design of the mission and interpret the data returned.

Noble gases are accreted to the giant planets as part of the gas component of the planet-forming disk. While heavier noble gases can separate from the evolution of the hydrogen-rich gas, helium is thought to remain at the protosolar H/He ratio Y_proto∼ 0.27 –0.28. However, spacecraft observations revealed a depletion in helium in the atmospheres of Jupiter, Saturn, and Uranus. For the gas giants, this is commonly seen as indication of H/He phase separation at greater depths. Here, we apply predictions of the H/He phase diagram and three H/He-EOS to compute the atmospheric helium mass abundance Y_atm as a result of H/He phase separation. We obtain a strong depletion Y_atm<0.1 for the ice giants if they are adiabatic. Introducing a thermal boundary layer at the Z-poor/Z-rich compositional transition with a temperature increase of up to a few 1000 K, we obtain a weak depletion in Uranus as observed. Our results suggest dissimilar internal structures between Uranus and Neptune. An accurate in-situ determination of their atmospheric He/H ratio would help to constrain their internal structures. This is even more true for Saturn, where we find that any considered H/He phase diagram and H/He-EOS would be consistent with any observed value. However, some H/He-EOS and phase diagram combinations applied to both Jupiter and Saturn require an outer stably-stratified layer at least in one of them.

The PLATO mission is scheduled for launch in 2026. This study aims to estimate the number of exoplanets that PLATO can detect as a function of planetary size and period, stellar brightness, and observing strategy options. Deviations from these estimates will be informative of the true occurrence rates of planets, which helps constraining planet formation models. For this purpose, we developed the Planet Yield for PLATO estimator (PYPE), which adopts a statistical approach. We apply given occurrence rates from planet formation models and from different search and vetting pipelines for the Kepler data. We estimate the stellar sample to be observed by PLATO using a fraction of the all-sky PLATO stellar input catalog (PIC). PLATO detection efficiencies are calculated under different assumptions that are presented in detail in the text. The results presented here primarily consider the current baseline observing duration of four years. We find that the expected PLATO planet yield increases rapidly over the first year and begins to saturate after two years. A nominal (2+2) four-year mission could yield about several thousand to several tens of thousands of planets, depending on the assumed planet occurrence rates. We estimate a minimum of 500 Earth-size (0.8-1.25 RE) planets, about a dozen of which would reside in a 250-500d period bin around G stars. We find that one-third of the detected planets are around stars bright enough (V $\leq 11$) for RV-follow-up observations. We find that a three-year-long observation followed by 6 two-month short observations (3+1 years) yield roughly twice as many planets as two long observations of two years (2+2 years). The former strategy is dominated by short-period planets, while the latter is more beneficial for detecting earths in the habitable zone.

We present a review of Saturn's interior structure and thermal evolution, with a particular focus on work in the past 5 years. Data from the Cassini mission, including a precise determination of the gravity field from the Grand Finale orbits, and the still ongoing identification of ring wave features in Saturn's C-ring tied to seismic modes in the planet, have led to dramatic advances in our understanding of Saturn's structure. Models that match the gravity field suggest that differential rotation, as seen in the visible atmosphere, extends down to at least a depth of 10,000 km (1/6$^{\rm th}$ the planet's radius). At greater depths, a variety of different investigations all now point to a deep Saturn rotation rate of 10 hours and 33 minutes. There is very compelling evidence for a central heavy element concentration (``core''), that in most recent models is 12-20 Earth masses. Ring seismology strongly suggests that the core is not entirely compact, but is dilute (mixed in with the overlying H/He), and has a substantial radial extent, perhaps out to around one-half of the planet's radius. A wide range of thermal evolution scenarios can match the planet's current luminosity, with progress on better quantifying the helium rain scenario hampered by Saturn's poorly known atmospheric helium abundance. We discuss the relevance of magnetic field data on understanding the planet's current interior structure. We point towards additional future work that combines seismology and gravity within a framework that includes differential rotation, and the utility of a Saturn entry probe.

Revealing the true nature of the gas giant planets in our Solar System is challenging. The masses of Jupiter and Saturn are about 318 and 95 Earth masses, respectively. While they mostly consist of hydrogen and helium, the total mass and distribution of the heavier elements, which reveal information on their origin, are still unknown. Recent accurate measurements of the gravitational fields of Jupiter and Saturn together with knowledge of the behavior of planetary materials at high pressures allow us to better constrain their interiors. Updated structure models of Jupiter and Saturn suggest that both planets have complex interiors that include composition inhomogeneities, non-convective regions, and fuzzy cores. In addition, it is clear that there are significant differences between Jupiter and Saturn and that each giant planet is unique. This has direct implications for giant exoplanet characterization and for our understanding of gaseous planets as a class of astronomical objects. In this review we summarize the methods used to model giant planet interiors and recent developments in giant planet structure models.

Models of Jupiter s interior struggle to agree with measurements of the atmospheric composition. Interior models favour a subsolar or solar abundance of heavy elements Z while atmospheric measurements suggest a supersolar abundance. One potential solution may be the presence of an inverted Z-gradient, namely an inward decrease of Z, which implies a larger heavy element abundance in the atmosphere than in the outer envelope. We investigate two scenarios in which the inverted Z gradient is located either where helium rain occurs (Mbar level) or at upper levels (kbar level) where a radiative region could exist. We aim to assess how plausible these scenarios are. We calculate interior and evolution models of Jupiter with such inverted Z-gradient and use constraints on the stability and the formation of an inverted Z-gradient. We find that an inverted Z-gradient at the location of helium rain cannot work as it requires a late accretion and of too much material. We find interior models with an inverted Z-gradient at upper levels, due to a radiative zone preventing downward mixing, that could satisfy the present gravity field of the planet. However, our evolution models suggest that this second scenario might not be in place. An inverted Z-gradient in Jupiter could be stable. Yet, its presence either at the Mbar level or kbar level is rather unlikely.

Context. The Juno mission has provided measurements of Jupiter’s gravity field with an outstanding level of accuracy, leading to better constraints on the interior of the planet. Improving our knowledge of the internal structure of Jupiter is key to understanding its formation and evolution but is also important in the framework of exoplanet exploration. Aims. In this study, we investigated the differences between the state-of-the-art equations of state and their impact on the properties of interior models. Accounting for uncertainty on the hydrogen and helium equation of state, we assessed the span of the interior features of Jupiter. Methods. We carried out an extensive exploration of the parameter space and studied a wide range of interior models using Markov chain Monte Carlo simulations. To consider the uncertainty on the equation of state, we allowed for modifications of the equation of state in our calculations. Results. Our models harbour a dilute core and indicate that Jupiter’s internal entropy is higher than what is usually assumed from the Galileo probe measurements. We obtain solutions with extended dilute cores, but contrary to other recent interior models of Jupiter, we also obtain models with small dilute cores. The dilute cores in such solutions extend to ~20% of Jupiter’s mass, leading to better agreement with formation–evolution models. Conclusions. We conclude that the equations of state used in Jupiter models have a crucial effect on the inferred structure and composition. Further explorations of the behaviour of hydrogen–helium mixtures at the pressure and temperature conditions in Jupiter will help to constrain the interior of the planet, and therefore its origin.

The Juno mission has revolutionized and challenged our understanding of Jupiter. As Juno transitioned into its extended mission, we review the major findings of Jupiter's internal structure relevant to understanding Jupiter's formation and evolution. Results from Juno's investigation of Jupiter's interior structure imply that the planet has compositional gradients and is accordingly non-adiabatic, with a complex internal structure. These new results imply that current models of Jupiter's formation and evolution require a revision. In this paper, we discuss potential formation and evolution paths that can lead to an internal structure model consistent with Juno data, and the constraints they provide. We note that standard core accretion formation models, including the heavy-element enrichment during planetary growth is consistent with an interior that is inhomogeneous with composition gradients in its deep interior. However, such formation models typically predict that this region, which could be interpreted as a primordial dilute core, is confined to ∼10% of Jupiter's total mass. In contrast, structure models that fit Juno data imply that this region contains 30% of the mass or more. One way to explain the origin of this extended region is by invoking a relatively long (~2 Myrs) formation phase where the growing planet accretes gas and planetesimals delaying the runaway gas accretion. This is not the same as the delay that appears in standard giant planet formation models because it involves additional accretion of solids in that period. However, both the possible new picture and the old picture are compatible with the formation scenario recently proposed to explain the separation of two meteoritic populations in the solar system. Alternatively, Jupiter's fuzzy core could be a result of a giant impact or convection post-formation. These novel scenarios require somewhat special and specific conditions. Clarity on the plausibility of such conditions could come from future high-resolution observations of planet-forming regions around other stars, from the observed and modeled architectures of extrasolar systems with giant planets, and future Juno data obtained during its extended mission.

Background: Some fundamental properties of the interiors of the Ice giants Uranus and Neptune are far from being understood. According to structure models which follow observed gravitational harmonics J2 and J4, the interiors are composed of a H/He-rich envelope transitioning into an ice-rock interior. Formation theories can explain their current structure given certain conditions related to the formation location within the protoplanetary disk nebula and the degree of gas depletion during said formation are met, conditions which themselves seek an explanation [1]. A rather sharp boundary yields the simplest solution to the gravity field [2] and the luminosity of the planets [3]. Recently, the phase separation of two major constituents (water and molecular hydrogen) in the evolved and cooled planets Uranus and Neptune has been proposed as an explanation for the presence of this sharp interface. Furthermore, different H2O/H2 demixing states may offer an explanation for the paradox between intrinsic heat flux of both planets [2]. On the other hand, evolution models guided by the observed luminosities suggest the existence of a compositional barrier inhibiting or slowing down convection. Assuming small differences in the structure of both planets, this mechanism can account for the faintness of Uranus and the brightness of Neptune [3]. However, their evolution could be affected by possible complementary processes such as phase separation [2] or condensation in their atmospheres. In this work, we follow up on the possibility of demixing between the major constituents in the H-He-H2O system. First, we show that interior models which adjust to the luminosity [3] lead to temperatures above the critical temperature for H2O/H2 demixing to occur, and thus would predict a protosolar atmospheric helium abundance. Second, we adopt the assumption of an initially more homogeneous interior which did cool sufficiently to allow for H2O/H2 demixing [2]. We find that for deep interior H/He phase separation, which occurs at higher temperatures, favourable interior conditions were met much earlier in the evolution [4]. Figure 1: Helium particle fraction as a function of assumed water mass fraction in the deep interior of Uranus. Error bars placed at ZH2O= 0 show the observed atmospheric He abundances of Jupiter, Saturn, Uranus, and Neptune, while also a value for Jupiter's deep interior. The grey area delimits the uncertainty region marking the lower limit of He/H ratio necessary for phase separation to occur in Uranus. This figure shows how the He/H ratio relevant to H/He demixing behaves with the water abundance. In Figure 1, we plot the He particle fraction as a function of the assumed water mass fraction in the deep interior assuming full dissociation of water and hydrogen. Protosolar values for the atmospheric helium abundance Y were adopted for Uranus (0.26-0.28). The grey region shows the uncertainty region above which H/He demixing can occur, inferred from the H/He non-ideal entropy phase diagram of [4]. Figure 1 shows H/He phase separation cannot take place in a highly ice-rich interior ZH2O greater ~0.85. However, moving towards lower water contents, demixing can occur at pressure levels between 1.5 to 4 Mbar [4]. The atmospheric helium abundance prediction we aim for could be compared to probed in-situ measurements in the future. Acknowledgements: The authors acknowledge support from the Research Unit 2440/2 funded by the DFG (Deutsche Forschungsgemeinschaft). [1] Frelikh R. and Murray-Clay R.A., AJ 154:98 (2017). [2] Bailey E. and Stevenson D.S., PSJ 2:64 (2021). [3] Scheibe L. et al., A&A 650:A200 (2021). [4] Schöttler M. and Redmer R., PRL 120:115703 (2018).

Understanding Jupiter's present-day interior structure and dynamics is key to constraining planetary accretion models. In particular, the extent of stable stratification (i.e., non-convective regions) in the planet strongly influences long-term cooling processes, and may record primordial heavy element gradients from early in a planet's formation. Because the Galileo entry probe measured a subsolar helium abundance, Jupiter interior models often invoke an outer stably stratified region due to helium rain. Additionally, Juno gravity data suggest a deeper, potentially stratified dilute core extending halfway through the planet. However, fits to Jupiter's gravitational data are non-unique, and outstanding uncertainty over the equations of state for hydrogen and helium remain. Here, we use high-resolution numerical magnetohydrodynamic simulations of Jupiter's magnetic field to place constraints on the extent of stable stratification within the planet. We find that compared to traditional interior models, an upper stably stratified layer between 0.9 and 0.95 Jupiter radii (R-J) helps to explain both Jupiter's dipolar magnetic field and zonal winds. In contrast, an extended dilute core that is entirely stably stratified (no convective layers) yields significantly worse fits to both. However, our models with extended deep stratification still generate dipolar magnetic fields if an upper stratified region is also present. Overall, we find that a planet with a dilute core i.e., strongly stably stratified is increasingly challenging to reconcile with Jupiter's magnetic field and winds. Thus if a dilute core is present, alternative modalities such as a fully convective dilute core, a complex multilayered interior structure, or double diffusive convection may be required.

The small semi-major axes of Hot Jupiters lead to high atmospheric temperatures of up to several thousand Kelvin. Under these conditions, thermally ionised metals provide a rich source of charged particles and thus build up a sizeable electrical conductivity. Subsequent electromagnetic effects, such as the induction of electric currents, Ohmic heating, magnetic drag, or the weakening of zonal winds have thus far been considered mainly in the framework of a linear, steady-state model of induction. For Hot Jupiters with an equilibrium temperature T_eq > 1500 K, the induction of atmospheric magnetic fields is a runaway process that can only be stopped by non-linear feedback. For example, the back-reaction of the magnetic field onto the flow via the Lorentz force or the occurrence of magnetic instabilities. Moreover, we discuss the possibility of self-excited atmospheric dynamos. Our results suggest that the induced atmospheric magnetic fields and electric currents become independent of the electrical conductivity and the internal field, but instead are limited by the planetary rotation rate and wind speed. As an explicit example, we characterise the induction process for the hottest exoplanet, KELT-9b by calculating the electrical conductivity along atmospheric P-T-profiles for the day- and nightside. Despite the temperature varying between 3000 K and 4500 K, the resulting electrical conductivity attains an elevated value of roughly 1 S/m throughout the atmosphere. The induced magnetic fields are predominately horizontal and might reach up to a saturation field strength of 400 mT, exceeding the internal field by two orders of magnitude.

The rotation rate of the outer planet Saturn is not well constrained by classical measurements of periodic signals [1]. Recent and diverse approaches using a broad spectrum of Cassini and other observational data related to shape, winds, and oscillations are converging toward a value about 6 to 7 minutes faster than the Voyager rotation period.Here we present our method of using zonal wind data and the even harmonics J2 to J10 measured during the Cassini Grand Finale tour [2] to infer the deep rotation rate of Saturn. We assume differential rotation on cylinders and generate adiabatic density profiles that match the low-order J2 and J4values. Theory of Figures to 7th order is applied to estimate the differences in the high-order moments J6 to J10 that may result from the winds and the assumed reference rotation rate. Presented results are preliminary as the method is under construction [3].[1] Fortney, Helled, Nettelmann et al, in: 'Saturn in the 21st century', Cambridge U Press (2018)[2] Iess, Militzer, Kaspi, Science 364:2965 (2019)[3] Nettelmann, AGU Fall Meeting, P066-0007 (2020)

14 Interior modeling of Jupiter and Saturn has advanced to a state where thousands 15 of models are generated that cover the uncertainty space of many parameters. This 16 approach demands a fast method of computing their gravity field and shape. Moreover, 17 the Cassini mission at Saturn and the ongoing Juno mission delivered gravitational 18 harmonics up to J12. Here, we report the expansion of the Theory of Figures, which is 19 a fast method for gravity field and shape computation, to the 7th-order (ToF7), which 20 allows for computation of up to J14. We apply three different codes to compare the 21 accuracy using polytropic models. We apply ToF7 to Jupiter and Saturn interior models 22 in conjunction with CMS-19 H/He-EOS. For Jupiter, we find that J6 is best matched 23 by a transition from He-depleted to He-enriched envelope at 2–2.5 Mbar. However, the 24 atmospheric metallicity reaches 1× solar only if the adiabat is perturbed toward lower 25 densities, or if the surface temperature is enhanced by ∼ 14K from the Galileo value. 26 Our Saturn models imply a largely homogeneous-in-Z envelope at 1.5–4× solar atop 27 a small core. Perturbing the adiabat yields metallicity profiles with extended, heavy28 element enriched deep interior (diffuse core) out to 0.4 RSat, as for Jupiter. Classical 29 models with compact, dilute, or no core are possible as long as the deep interior is 30 enriched in heavy-elements. Including a thermal wind fitted to the observed wind 31 speeds, representative Jupiter and Saturn models are consistent with all observed Jn 32 values. 33