We review the key observations and theories relevant to the origin and evolution of the Galilean satellites. Key observations include: the potentially undifferentiated nature of Callisto; the increasing ice fraction with semi-major axis; the present-day existence of the Laplace resonance; the potential resurfacing of Ganymede mid-way through its evolution; and the metal-enriched nature of Jupiter’s envelope. The most widely accepted theory for the formation of the satellites is the so-called “starved disk” model, although newer alternatives including decretion disks and pebble accretion have also been proposed. Models that allow slow satellite formation in a cold disk are preferred, based on the density progression and Callisto’s apparent differentiation state. Major model uncertainties include the angular momentum distribution of the material infalling to the circumplanetary disk, the source of the solids, and the thermal and viscosity structure of the disk. We identify six outstanding questions, some of which will be answered by JUICE, Europa Clipper and Tianwen-4. A major difficulty in answering some questions is overprinting of primordial characteristics by later events.

During the Juno extended mission, the spacecraft passed Jupiter’s Galilean moon Ganymede. The flyby of Ganymede was in June 2021, at a distance of ~1000 km, providing an opportunity to probe Ganymede’s icy subsurface at multiple microwave frequencies using Juno’s Microwave Radiometer (MWR). The observations provided several swaths across the moons at six frequencies, ranging from 600 MHz to 22 GHz.Early radar results of Jupiter’s icy moons dating back several decades identified the moons as extremely bright objects with significant radar scattering (Ostro et al., 1980). Comparisons of the radar properties of Europa & Ganymede indicated important differences in the radar signatures from each other and our Moon (Ostro et al., 1992). Possible explanations included modulations in porosity (Ostro and Shoemaker, 1990), random facets, larger than the observed wavelengths (Goldstein and Green, 1980), and the idea that the top meters of ice covering their surfaces may be crazed, fissured, and/or filled with jagged ice boulders (Goldstein and Green 1980).The Juno MWR observations represent the first resolved interrogation of Ganymede’s subsurface structure. For icy bodies such as Ganymede and Europa, the MWR observed brightness temperature, TB, is dependent on such ice shell parameters as ice purity, the thermal structure of the icy shell (providing a constraint on the global heat flux) as well as the distribution of internal microwave scattering, thus allowing MWR to provide integral constraints on these shell properties. The MWR observations of Ganymede showed TB generally increases with depth, has a significant reflected synchrotron radiation component at the lowest MWR frequency, 600 MHz, and was well correlated with terrain type. The TB was generally anticorrelated with visible reflectivity (albedo). hermal gradient from deepest channels constrains heat flux (and thickness of conductive ice shell). Analysis of the MWR results at Ganymede provided a new constraint on Ganymede’s heat flux and shell thickness (conductive and total). Using a thermal model based on modified Mixing Length Theory from Kamata et al. (2018) and a Radiative transfer model, the microwave radiation propagation through the ice shell constrains the properties of the subsurface shell including heat flux and thickness of conductive ice shell. The unprecedented MWR measurements of Ganymede, Europa and Io by Juno allow comparative studies of their surfaces and subsurface structures. The Juno MWR measurements complement previous ground-based radar and microwave radiometry observations, which provided early characterization of these surfaces. A comparison of the microwave spectra for all three satellites will be presented, as well as a detailed analysis and interpretation of the Ganymede MWR data that provide new constraints on ice subsurface properties.

Juno flew less than 360 km from the surface of Jupiter’s moon Europa on 29 September, 2022, and mapped part of the ice shell with the Microwave Radiometer (MWR) at frequencies of 0.6, 1.2, 2.5, 4.8, 9.6, and 22 GHz. The partial map covers a latitude range from ~20oS to ~50oN and a longitude range from 70oW to 50oE. At these frequencies, the emission originates well beneath the nearly-transparent surface, probing from as deep as 28 km (at 0.6 GHz) and less than 20 m (at 22 GHz), depending on the purity of the ice. Microwave reflection plays an important role, and MWR data suggest the presence of small (radius a few cm) scatterers at depths of many meters. Spatial variation is dominated by reflection, especially for the higher-frequency channels, and correlates with terrain type. We present analysis of the data and discuss the implications.

In this paper, the formation of Saturn is modeled by detailed numerical simulations according to the core-nucleated accretion scenario. Previous models are enhanced to include the dissolution of accreting planetesimals, composed of water ice, rock, and iron, in the gaseous envelope of the planet, leading to a nonuniform composition with depth. The immiscibility of helium in metallic hydrogen layers is also considered. The calculations start at a mass of 0.5 Earth masses and are extended to the present day. At 4.57 Gyr, the model, proceeding outward, has the following structure: (i) a central core composed of 100% heavy elements and molecules, (ii) a region with a decreasing heavy-element mass fraction, down to a value of 0.1, (iii) a layer of uniform composition with the helium mass fraction Y enhanced over the primordial value, (iv) a helium rain region with a gradient in Y , (v) an outer convective, adiabatic region with uniform composition in which Y is reduced from the primordial value, and (vi) the very outer layers where cloud condensation of the heavy elements occurs. Models of the distribution of heavy elements as a function of radius are compared with those derived to fit the observations of the Cassini mission, with rough qualitative agreement. The helium mass fraction in Saturn’s outer layers is estimated to be around 20%. Models are found that provide good agreement with Saturn’s intrinsic luminosity and radius.

On June 7, 2021, and September 29, 2022, the NASA Juno spacecraft flew by Jupiter’s Galilean moons, Ganymede, and Europa, respectively. The closest approach distance was only ~1000 km above Ganymede, and only ~350 km above Europa. More recently, on December 30, 2023, Juno passed by Io at a distance of 1500 km and is planned do so a second Io flyby on February 3, 2024 at a similar distance. The close flybys were the first encounters with the moons in over two decades and provided the first opportunity to map the subsurface of the their shells at multiple microwave frequencies using Juno’s Microwave Radiometer (MWR). The observations provided several swaths across the moons at six frequencies, ranging from 600 MHz to 22 GHz. The ice transparency at microwave frequencies is dependent on its purity; assuming pure ice, the observations probe depths ranging from meters to kilometers. The MWR observations represent the first resolved interrogation of Ganymede and Europa’s subsurface ice shell revealing new constraints on porosity, fracturing, differences in terrain type and possibly the thickness of the ice shell. These unprecedented measurements of Io, Europa and Ganymede will allow comparative studies of the surfaces and subsurface structures of the Jovian satellites. The Juno MWR measurements complement previous ground-based radar and microwave radiometry observations, which provided early characterization of these surfaces. A comparison of the microwave spectra for all three satellites will be presented, as well as a detailed analysis and interpretation of the Ganymede MWR data that provide new constraints on ice subsurface properties.

Small planetary bodies in the solar system, including Io, Ganymede, and Callisto, may have a crust denser than their underlying mantle. Despite the inherent gravitational instability of such structures, we show that the growth timescale of the Rayleigh–Taylor (RT) instability can be as long as the age of the solar system, owing to the strong temperature dependence of viscosity. Even in cases where the instability timescale is shorter, the instability is confined to a thin layer at the base of the crust, making the foundering of the entire crust improbable in many scenarios. This study delineates the onset and aftermath of the RT instability, applying a quantitative framework to assess the stability of (i) rock-contaminated crust on icy satellites, and (ii) silicate crust floating on top of a subsurface magma ocean on Io. Notably, for Io the RT instability peels off only 10–100 m from the crust’s base, and thermal diffusion rapidly recovers the crustal thickness through solidification of a magma ocean. Despite recurrent delamination of the crustal base, the initial crustal thickness is maintained by thermal diffusion, virtually stabilizing a floating dense crust. Cracking of the crust also is unlikely to result in the foundering of the crust. A dense crust on a small body is therefore difficult to be overturned, suggesting the potential ubiquity of dense surface layers throughout the solar system.

New interior models of Jupiter and Saturn suggest that both planets have "fuzzy cores". These cores should be viewed as central regions that are enriched with heavy elements but are not distinct from the rest of the deep interior. These cores may contain large amounts of hydrogen and helium though small pure-heavy element cores may also exist. New measurements along with advanced planetary modeling have revolutionized the way we think about the interiors of giant planets and provide important constraints for planet formation and evolution theories. These developments are also relevant for the characterization of giant exoplanets.

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.

We present results of simulations of the growth of giant planets that incorporate the mixing of light gases with denser material that enters the planet as solids. We find that heavy compounds and gas begin to intimately mix when the planet is quite small, and substantial mixing occurs when the planet becomes roughly as massive as Earth, because even incoming silicates can then fully vaporize if they arrive in the form of planetesimals or smaller bodies. Nonetheless, most of the icy and rocky material accreted by a giant planet settles to a region in which vaporized ice and rock are well-mixed until the growing planet is several times as massive as Earth. Subsequently, planetesimals break up in a region that is too cool for all the silicates to vaporize, so the silicates continue to sink, but the water remains at higher altitudes. As the planet continues to grow, silicates vaporize farther out. Because the mean molecular weight decreases rapidly outward at many radii, some of the radially inhomogeneities in composition produced during the accretion era are able to survive for billions of years. After 4.57 Gyr, our model Jupiter retains compositional gradients; from the inside outwards one finds: (i) an inner core, dominantly composed of heavy elements; (ii) a density-gradient region, containing the majority of the planet's heavy elements, where H and He increase in abundance with height, reaching ~90% mass fraction at 30% of Jupiter's radius, with rocky materials enhanced relative to ices in the lower part of this gradient region and the composition transitioning to ices enhanced relative to rock at higher altitudes; (iv) a large, uniform-composition region (we do not account for He immiscibility), enriched relative to protosolar in heavy elements, especially ices, that contains the bulk of the planet's mass; and (v) an outer region where condensation of many constituents occurs. This radial compositional profile has heavy elements more broadly distributed within the planet than predicted by classical Jupiter-formation models. NASA’s Juno spacecraft's measurements of Jupiter's gravity field also implies less concentration of heavy elements near the center of the planet than classical theoretical models. However, the preferred dilution of the core found in Juno-constrained gravity models is substantially larger than what is suggested by our accretion models, requiring some modification in the heavy element distribution. The compositional gradients in the region containing the bulk of the planet’s heavy elements prevent convection, both in our models and the models that fit current gravity, probably resulting in a hot deep interior where much of the energy from the early stages of the planet's accretion remains trapped.

Io experiences tidal deformation as a result of its eccentric orbit around Jupiter, which provides a primary energy source for Io's continuing volcanic activity and infrared emission1. The amount of tidal energy dissipated within Io is enormous and has been suggested to support the large-scale melting of its interior and the formation of a global subsurface magma ocean. If Io has a shallow global magma ocean, its tidal deformation would be much larger than in the case of a more rigid, mostly solid interior2. Here we report the measurement of Io's tidal deformation, quantified by the gravitational tidal Love number k2, enabled by two recent flybys of the Juno spacecraft. By combining Juno3,4 and Galileo5, 6-7 Doppler data from the NASA Deep Space Network and astrometric observations, we recover Re(k2) of 0.125 +/- 0.047 (1 sigma) and the tidal dissipation parameter Q of 11.4 +/- 3.6 (1 sigma). These measurements confirm that a shallow global magma ocean in Io does not exist and are consistent with Io having a mostly solid mantle2. Our results indicate that tidal forces do not universally create global magma oceans, which may be prevented from forming owing to rapid melt ascent, intrusion and eruption8,9, so even strong tidal heating-such as that expected on several known exoplanets and super-Earths10-may not guarantee the formation of magma oceans on moons or planetary bodies.

Planetary magnetic fields provide a window into the otherwise largely inaccessible dynamics of a planet’s deep interior. In particular, interaction between fluid flow in electrically conducting interior regions and the magnetic field there gives rise to observable secular variation (time dependency) of the externally observed magnetic field. Secular variation of Jupiter’s field has recently been revealed 1–3 and been shown to arise, in part, from an axisymmetric, equatorial jet 2 . Whether this jet is time dependent has not previously been addressed, yet it is of critical importance for understanding the dynamics of the planet’s interior. If steady, it would probably be a manifestation of deep dynamo convective flow (and jets are anticipated as part of that flow 4–9 ) but if time dependent on a timescale much shorter than the convective turnover timescale of several hundred years, it would probably have a different origin. Here we show that the jet has a wavelike fluctuation with a period of roughly 4 years, strongly suggestive of the presence of a torsional oscillation 10 (a cylindrically symmetric oscillating flow about the rotation axis) or a localized Alfvén wave in Jupiter’s metallic hydrogen interior. This opens a pathway towards revealing otherwise hidden aspects of the magnetic field within the metallic hydrogen region and hence constraining the dynamo that generates Jupiter’s magnetic field.

Recently, the Juno and Cassini spacecraft shed light on the interior of both Jupiter and Saturn, the two gas giants of the Solar System. Juno is currently orbiting Jupiter in a highly elliptical 53.5-day orbit, with a perijove altitude of about 4000 km. After the 33rd passage in April 2021 (labeled PJ33), the mission ended its nominal mission and entered its extended mission. On the contrary, the Cassini spacecraft ended its mission on September 15th, 2017 with a deliberate plunge into Saturn’s atmosphere. In its final phase, the Grand Finale, Cassini provided insights on Saturn’s rings, atmosphere, and interior. Out of the 22 proximal orbits, six pericenter passes have been devoted to the determination of the gravity field of the planet.The gravity science experiments on board Juno and Cassini precisely measured, respectively, Jupiter and Saturn zonal gravitational fields. The measured gravity harmonics have been used to constrain the interior structure and atmospheric zonal flow on both planets.The Cassini data analysis have shown the need to include unknown accelerations to properly fit the data to the expected noise (Iess, 2019). Similar unexplained accelerations have been observed also on Juno gravity data (Durante, 2020). Since Jupiter and Saturn are gas giants, unconventional phenomena can be at play, including normal modes, non-zonal atmospheric dynamics, or flows in the dynamo region.The analysis of the accelerations acting on Cassini provided evidence for p-modes on the planet (Markham, 2020), while the analysis of Juno gravity data revealed p-modes on Jupiter and provided upper bounds on lower frequency f-modes. Here, we show the results for normal modes on both Jupiter and Saturn obtained with the analysis of gravity data of both Juno and Cassini.

On 7 June 2021, Juno flew within 1,000 km of Ganymede's surface, partially mapping its ice shell at six frequencies ranging from 0.6 to 22 GHz. The radiance at these frequencies originates from successively deeper layers of the sub‐surface and may reach depths of 24 km at 0.6 GHz. The MWR observations cover a latitude range from 20°S to 60°N and a longitude range from 120°W to 60°E. We present brightness temperature and derived reflectivity maps of Ganymede with a spatial resolution of up to ∼140 km. The microwave brightness temperature at all MWR wavelengths is anti‐correlated with the visible brightness of the terrain. Normalizing the MWR brightness temperatures using a thermal model for the ice shell reveals that the brightest regions are significantly more reflective in the microwave than the dark regions and that all terrain types are more reflective than is expected from a solid ice surface. We suggest that multiple reflections of the colder sky background at sub‐surface interfaces (e.g., fractures) explain the depressed brightness temperatures observed in brighter terrain types. A thin silicate or salt contaminant surface layer, which is significantly more reflective than ice in the microwave, could explain the microwave reflectivity in the dark regions with little to no contribution from sub‐surface fractures. The observed 0.6–1.2 GHz brightness temperature difference suggests an upper bound on the ice shell conducting layer depth of 150 km in the observation area.

Striking exposures of Na‐carbonate‐bearing bright materials are found in Ahuna Mons and the central landforms of Occator and other impact craters on Ceres; however, most bright materials on its surface occur as excavated material on the rims and walls of impact craters. The source of the widespread excavated Na‐carbonate is uncertain. We map the distribution and extent of rim/wall Na‐carbonate with Dawn's Visible and Infrared Imaging Spectrometer and Dawn Framing Camera. We find a strong spatial correlation between domes and shallow subsurface Na‐carbonate deposits, suggesting that they form by the same or related processes. Using Monte Carlo impact models, we constrain the timing of emplacement of the shallow subsurface Na‐carbonate to be within the last ∼1 Ga and probably within the last few hundred Ma. We examine the likelihood that the Na‐carbonate was mobilized from Ceres' deep interior and the plausibility of brine upwelling or solid‐state processes. We demonstrate that a combination of processes, including diapirism driven by Rayleigh‐Taylor instabilities and solid‐state deformation due to differential loading, could mobilize Na‐carbonate‐bearing ices to the shallow subsurface without requiring the recent presence of brines.

We use the magnetic and gravity field data jointly to place constraints on the internal structure of Ganymede. The magnetic induction constraint comes mostly from the Galileo data, as the Juno flyby occurred when Ganymede was near the center of the magnetodisk, thus leading to low sensitivity to magnetic induction. The gravity field model of Ganymede jointly derived from the Galileo and Juno data to place constraints on Ganymede’s internal structure. Unlike in the previous works, the hydrostaticity was not imposed on the degree-2 gravity coefficients. Thus, despite including additional data from Juno, the uncertainties on the degree-2 coefficients increased. In addition, we explicitly treat the effect of non-hydrostaticity on the derived moment of inertia and find significantly wider confidence intervals on the moment of inertia. This leads to a larger allowed parameter space for the internal structure model.The new gravity solution confirms the past detection of non-hydrostatic anomalies. In our analysis, localized non-hydrostatic features with amplitudes higher than those found on Titan by the Cassini mission are identified. Titan is a useful comparison case as it shares with Ganymede nearly the same mean radius, mean density, and therefore, surface gravity. Thus, the non-hydrostatic deviations of the same amplitude either in shape or in gravity would correspond to approximately the same level of non-hydrostatic stress. On Titan, the gravity field for degree l > 2 reaches at most 5 mGal (Durante et al., 2019), which is a factor of 5 smaller than the largest anomalies found on Ganymede. One key difference between the two bodies is the lack of atmosphere-based erosion processes on Ganymede. Such erosional processes could have led to faster removal of non-hydrostatic signals at Titan reducing the amplitude of its gravity anomalies. In addition, Titan’s outer shell could be thinner and, therefore, less rigid than that of Ganymede, thus not being able to support as much non-hydrostaticity.Further insights on Ganymede’s interior will be coming from the JUICE mission in the next decade. Currently, the lack of an accurate shape model prevents separating degree-2 hydrostatic and non-hydrostatic contributions. Combined gravity, topography and rotation data acquired by JUICE will be crucial in determining the non-hydrostatic contribution to the degree-2 field to constrain Ganymede’s internal structure.

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.

On 7 June 2021, Juno had a close flyby of Jupiter’s moon Ganymede, flying within 1000 km of the surface. During the flyby, Juno’s Microwave Radiometer (MWR) observed Ganymede obtaining several swaths across Ganymede using Juno’s spin to partially map Ganymede’s ice shell in six channels ranging from 600 MHz to 22 GHz. The radiance at these frequencies originates from successively deeper layers of the sub-surface and may reach to depths of 20km at 0.6 GHz. The MWR observations cover a latitude range from 20S to 60N and an east longitude range from -120 to 60 degrees, roughly centered on the Perrine region. The local solar time varies from around noon to mid-night over the longitude range. We present resolved brightness temperature maps and associated microwave spectra of Ganymede with a spatial resolution of up to ~140 km (approximately 1/40th of Ganymede’s diameter). The microwave brightness temperature at all MWR wavelengths is anti-correlated with the visible brightness of the terrain, but is too large to be explained by albedo variations alone, suggesting sub-surface ice properties are not uniform with location. The dark regions tend to exhibit the warmest microwave spectra and brighter regions are observed to have a lower brightness temperature (up to half the blackbody temperature).The coldest microwave feature observed by MWR is the Tros crater and the immediate surrounding region. A radiative transfer algorithm, coupled with a thermal model for the conductive layer of Ganymede’s ice shell are fit to the MWR spectra providing an estimate of the conductive shell thickness. The microwave observations are globally colder than would be expected for pure water ice alone, suggesting thin highly reflective layer, possibly silicate dust, on the surface, although other interpretations remain possible. We suggest that scattering at sub-surface interfaces (e.g. fractures) explains the depressed brightness temperatures observed in brighter terrain types. Juno performed a close fly-by of Europa in September 2022, enabling a comparison of the sub-surface properties of these two icy satellites.

The atmospheric dynamics of Jupiter are dominated by strong zonal winds engulfing the planet. Since the first gravity measurements taken by Juno at Jupiter, the low-degree gravity harmonics ( J 3 – J 10 ) have been used to determine the depth and structure of the zonal winds observed at the cloud level, limiting inferences on the deep flows to the wide latitudinal structure of these harmonics. Here, using constraints on the dynamical contribution to gravity at high latitude, we present the gravity harmonics up to J 40. We find an excellent correlation between these measurements and the gravity harmonics resulting from the observed cloud-level winds extending inwards cylindrically to depths of ~10 5 bar (3,000 km). These measurements provide direct evidence that the flows penetrate inwards along the direction of the spin axis, confirming the cylindrical nature of the flow, which has been postulated theoretically since the 1970s. Furthermore, this detailed new gravity spectrum allows us to quantify the contribution of the various jets to the gravity signal, showing the dominance of the strong zonal flows around 20° latitude in both hemispheres.

A compelling question at the intersection of physics, neuroscience, and evolutionary biology concerns the extent to which the brains of various species evolved to encode regularities of the physical world. It would be parsimonious and adaptive, for example, for brains to evolve an innate understanding of gravity and the laws of motion, and to be able to detect, auditorily, those patterns of noises that ambulatory creatures make when moving about the world. One such physical regularity of the world is fractal structure, generally characterized by power-law correlations or 1/f β spectral distributions. Such laws are found broadly in nature and human artifacts, from noise in physical systems, to coastline topography (e.g., the Richardson effect), to neuronal spike patterns. These distributions have also been found to hold for the rhythm and power spectral density of a wide array of human music, suggesting that human music incorporates regularities of the physical world that our species evolved to recognize and produce. Here we show for the first time that 1/fβ laws also govern the spectral density of a wide range of animal vocalizations (music), from songbirds, to whales, to howling wolves. We discovered this 1/fβ power-law distribution in the vocalizations within all of the 17 diverse species examined. Our results demonstrate that such power laws are prevalent in the animal kingdom, evidence that their brains have evolved a sensitivity to them as an aid in processing sensory features of the natural world.

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.