Models Of Jupiter Research Articles

The formation of Jupiter’s diluted core by a giant impact

The Juno mission1 has provided an accurate determination ofJupiter's gravitational field2, which hasbeenusedto obtain information about the planet's compositionand internal structure. Severalmodels of Jupiter's structure that fit the probe's data suggest that the planet has a diluted core, with a total heavy-element mass ranging from ten to a few tens of Earth masses(about5 to 15 per cent of the Jovian mass), and that heavy elements(elements otherthan hydrogen and helium)are distributed within a region extending to nearly half of Jupiter's radius3,4. Planet-formation models indicate that most heavy elements are accreted during the earlystages ofa planet's formation to create a relativelycompact core5-7 and that almost no solids are accreted duringsubsequent runaway gas accretion8-10. Jupiter's diluted core, combined with its possible high heavy-element enrichment, thus challenges standard planet-formation theory. A possible explanation is erosion of the initially compact heavy-element core, but the efficiency of such erosion is uncertain and depends on both the immiscibility of heavy materials in metallic hydrogen and on convective mixing as the planet evolves11,12. Another mechanism that canexplain this structure is planetesimal enrichment and vaporization13-15 during the formation process, although relevant modelstypically cannotproduce an extended diluted core. Here we show that a sufficiently energetic head-on collision (giant impact) between a large planetary embryo and the proto-Jupiter could have shattered its primordial compact core and mixed the heavy elements with the inner envelope. Models of such a scenario lead to an internal structure that is consistent with a diluted core, persisting over billions of years. We suggest that collisions were common in the young Solar system and thata similar event may have also occurred for Saturn, contributing to the structural differences between Jupiter and Saturn16-18.

The visual spectrum of Jupiter's Great Red Spot accurately modeled with aerosols produced by photolyzed ammonia reacting with acetylene

We report results incorporating the optical properties of the red-tinted photochemically-generated aerosols of Carlson et al. (2016, Icarus 274, 106–115) in spectral models of Jupiter's Great Red Spot (GRS). This material - created in laboratory GRS simulations from acetylene reacting with photolytic products of ammonia produced by ~0.2-μm radiation, similar to solar radiation on Jupiter within and above the upper troposphere, provides an excellent match to 0.35–1.05-μm spectra of the core of the Great Red Spot obtained by the Visual Infrared Mapping Spectrometer (VIMS) during the 2000–2001 Cassini-Huygens flyby. Radiative transfer models of GRS spectra acquired near the central-meridian (CM) and limb by the visual channel of the Cassini/VIMS near closest approach on December 31, 2000 and January 2, 2001, respectively, show remarkable agreement for model morphologies where the following conditions all exist: (1) most of the optical depth of the Carlson et al. (2016) chromophore resides near the top or above the main cloud layer, rather than being uniformly distributed within it, (2) the chromophore consists of relatively small particles in the 0.1–0.2 μm range, and (3) the 1-μm optical depth of the chromophore layer is small, of the order of 0.1–0.2. For such models, the chromophore layer mass abundance is 32–40 μgm cm−2. Consideration of the availability of the acetylene and ammonia parent gas material near the observed chromophore layers gives powerful support for the chromophore residing at the top of the main cloud in the upper troposphere rather than residing as a detached layer in the stratosphere. Under steady-state formation/loss conditions, consideration of plausible eddy diffusion coefficients pertaining to the relatively quiescent Jovian upper atmosphere yield untenable vertical transport times of more than several centuries required to supply the acetylene needed to form the chromophore layer, with stratospheric chromophore models requiring more than half a millennium. Consideration of the convective nature of the GRS and possible presence of acetylene-generating thunderstorms yields upper-troposphere chromophore layer formation times ranging from 11 years to 1.5 months for (1) plausible eddy diffusion coefficients ranging from 104 to 106 cm2 s−1 and (2) efficient conversion of C2H2 and NH3 into the Carlson et al. (2016) chromophore. Thus, the enhanced red coloring of the GRS may be due to the combined effects of (1) the relatively high, 0.2-bar cloudtop where ammonia ice and gas are delivered to prime photo-dissociation altitudes, by (2) powerful convection, which also delivers acetylene from depth created by (3) lightning, which is itself a by-product and indicator of powerful convection, and aided by (4) the vortex nature of the GRS, which helps to confine and concentrate the chromophore as it forms over time within the GRS anticyclone.

Proper Frequencies of a Rotating Two-layer Spheroidal Liquid Mass: A Jupiter Model

We establish the first six proper frequencies for the series of figures of our heterogeneous models. For this purpose, we use the second-order virial equations as developed by Chandrasekhar. The main aim is to know if the figures are stable. We consider all types of figures: those with an oblate or prolate nucleus, with ρn > ρa, as well as the cases with ρn < ρa. We attempt here also to fit our two-layer model to the planet Jupiter, using its known gravitation obtained by the Juno mission, along with other accepted facts. It is found that the model reproduces reasonably well the observed gravitational moments. Further, it comes out that Jupiter rotates differentially, with a mean period of 9.92 hr, agreeing with the recognized one.

Model of Jupiter's Current Sheet With a Piecewise Current Density

AbstractWe develop a new empirical model of Jupiter's equatorial current sheet or magnetodisk, constructed by combining successful elements from several previous models. The new model employs a disk‐like current of constant north‐south thickness in which the current density is piecewise dependent on the distance ρ from Jupiter's dipole axis, proportional to ρ−1 at distances between ∼7 and ∼30 RJ and again at distances between ∼50 and ∼95 RJ, and to be continuous in value but proportional to ρ−2 at distances between. For this reason we term the model the Piecewise Current Disk model. The model also takes into account the curvature of the magnetodisk with distance and azimuth due to finite radial propagation speed and solar wind effects. It is taken to be applicable in the radial distance range between ∼5 and ∼60 RJ. Optimized parameters have been determined for Juno magnetic field data obtained on Perijove‐01, with the model showing overall the lowest root‐mean‐square deviation from the data compared with similarly optimized earlier models.

New Models of Jupiter in the Context of Juno and Galileo

Abstract Observations of Jupiter’s gravity field by Juno have revealed surprisingly low values for the high-order gravitational moments, considering the abundances of heavy elements measured by Galileo 20 years ago. The derivation of recent equations of state for hydrogen and helium, which are much denser in the megabar region, exacerbates the conflict between these two observations. In order to circumvent this puzzle, current Jupiter model studies either ignore the constraint from Galileo or invoke an ad hoc modification of the equations of state. In this paper, we derive Jupiter models that satisfy constraints of both Juno and Galileo. We confirm that Jupiter’s structure must encompass at least four different regions: an outer convective envelope, a region of compositional and thus entropy change, an inner convective envelope, an extended diluted core enriched in heavy elements, and potentially a central compact core. We show that in order to reproduce Juno and Galileo observations, one needs a significant entropy increase between the outer and inner envelopes and a lower density than for an isentropic profile, which is associated with some external differential rotation. The best way to fulfill this latter condition is an inward-decreasing abundance of heavy elements in this region. We examine in detail the three physical mechanisms that can yield such a change of entropy and composition: a first-order molecular-metallic hydrogen transition, immiscibility between hydrogen and helium, or a region of layered convection. Given our present knowledge of hydrogen pressure ionization, a combination of the two latter mechanisms seems to be the most favored solution.

Convective Models of Jupiter’s Zonal Jets with Realistic and Hyper-Energetic Excitation Source

Numerical simulations of Jupiter’s zonal jets are presented, which are generated with realistic and hyper energetic source. The models are three dimensional and nonlinear, applied to a gas that is convective, stratified and compressible. Two solutions are presented, one for a shallow 0.6% envelope, the other one 5% deep. For the shallow model (SM), Jupiter’s small energy flux was applied with low kinematic viscosity. For the deep model (DM), the energy source and viscosity had to be much larger to obtain a solution with manageable computer time. Alternating zonal winds are generated of order 100 m/s, and the models reproduce the observed width of the prograde equatorial jet and adjacent retrograde jets at 20° latitude. But the height variations of the zonal winds differ markedly. In SM the velocities vary radially with altitude, but in DM Taylor columns are formed. The dynamical properties of these divergent model results are discussed in light of the computed meridional wind velocities. With large planetary rotation rate Ω, the zonal winds are close to geostrophic, and a quantitative measure of that property is the meridional Rossby number, Rom. In the meridional momentum balance, the ratio between inertial and Coriolis forces produces Rom = V2/ΩLU, U zonal, V meridional winds, L horizontal length scale. Our analysis shows that the meridional winds vary with the viscosity like ν1/2. With much larger viscosity and meridional winds, the Rossby number for DM is much larger, Rom(DM) >> Rom(SM). Compared to the shallow model with zonal winds varying radially, the deeper and more viscous model with Taylor columns is much less geostrophic. The zonal winds of numerical models in the literature tend to be independent of the energy source, in agreement with the present results. With 104 times larger energy flux, the zonal winds for DM only increase by a factor of 3, and the answer is provided by the zonal momentum budget with meridional winds, VU/L = ΩV, yielding U = ΩL, independent of the source. The same relationship produces the zonal Rossby number, Roz = U/ΩL, of Order 1, which is commonly used as a dimensionless measure of the zonal wind velocities.

A re-analysis of the Jovian radio emission as seen by Cassini-RADAR and evidence for time variability

After more than a decade of operation at Titan and Saturn, the Cassini RADAR instrument is considered well understood and calibrated. In light of the recent Juno mission which is exploring the inner magnetosphere and the atmosphere of Jupiter, it is worthwhile to reconsider the original measurements of Cassini at Jupiter. The better instrument knowledge in combination with a better understanding of the ammonia distribution of Jupiter has allowed for revising the synchrotron flux density to 1.10 ± 0.07 Jansky, a factor of 2.5 larger than the initial estimate (Bolton et al., 2002). The forward model reduced uncertainties pertaining to the spacecraft pointing using a Markov-Chain Monte Carlo algorithm and constrained simultaneously a brightness model of Jupiter with a disk-averaged brightness temperature of 158.6 ± 2.4 K and depletion of ammonia at the poles (limb darking coefficient, p = 0.05). The flux density spectrum for the 2001 measurement campaign reveals a depletion of energetic electrons (>30 MeV) in contrast to an undisturbed electron population at lower energies. Comparing the Cassini radio maps to Very Large Array maps revealed a redistribution of energetic particles to higher latitudes, indicating enhanced pitch angle scattering for energetic particles. This kind of behavior has been observed in the terrestrial Van Allen belts and could be caused by the resonance of energetic electrons with electromagnetic ion cyclotron waves. We used a simplified analytic expression to determine the feasibility of this process at Jupiter. Although this process is not feasible under nominal conditions, a 10-fold enhancement of the cold plasma density, caused for example by extreme UV events, or volcanic eruptions on Io, could lead to rapid pitch angle scattering of electrons, and the subsequent removal of these particles by the atmosphere.

A study of Babylonian planetary theory I. The outer planets

In this study I attempt to provide an answer to the question how the Babylonian scholars arrived at their mathematical theory of planetary motion. Although no texts are preserved in which the Babylonians tell us how they did it, from the surviving Astronomical Diaries we have a fairly complete picture of the nature of the observational material on which the scholars must have based their theory and from which they must have derived the values of the defining parameters. Limiting the discussion to system A theory of the outer planets Saturn, Jupiter and Mars, I will argue that the development of Babylonian planetary theory was a gradual process of more than a century, starting sometime in the fifth century BC and finally resulting in the appearance of the first full-fledged astronomical ephemeris around 300 BC. The process of theory formation involved the derivation of long “exact” periods by linear combination of “Goal–Year” periods, the invention of a 360° zodiac, the discovery of the variable motion of the planets and the development of the numerical method to model this as a step function. Longitudes of the planets in the Babylonian zodiac could be determined by the scholars with an accuracy of 1° to 2° from observations of angular distances to Normal Stars with known positions. However, since the sky is too bright at first and last appearances of the planets and at acronychal rising for nearby stars to be visible, accurate longitudes as input for theoretical work could only be determined when the planets were near the stationary points in their orbits. In this study I show that the Babylonian scholars indeed based their system A modeling of the outer planets on planetary longitudes near stations, that their system A models of Saturn and Jupiter provided satisfactory results for all synodic phenomena, that they realized that their system A model of Mars did not produce satisfactory results for the second station so that separate numerical schemes were constructed to predict the positions of Mars at second station from the model at first station, and finally that their system A model for Mars provided quite poor predictions of the longitude of Mars at first and last appearances over large stretches of the zodiac. I further discuss ways in which the parameters of the system A models may have been derived from observations of the outer planets. By analyzing contemporaneous ephemerides from Uruk of four synodic phenomena of Jupiter from the second century BC, I finally illustrate how the Babylonian scholars may have used observations of Normal Star passages of planets to choose the initial conditions for their ephemerides.

Empirical models of Jupiter’s interior from Juno data

Context. The Juno spacecraft has significantly improved the accuracy of gravitational harmonic coefficients J4, J6 and J8 during its first two perijoves. However, there are still differences in the interior model predictions of core mass and envelope metallicity because of the uncertainties in the hydrogen-helium equations of state. New theoretical approaches or observational data are hence required in order to further constrain the interior models of Jupiter. A well constrained interior model of Jupiter is helpful for understanding not only the dynamic flows in the interior, but also the formation history of giant planets. Aims. We present the radial density profiles of Jupiter fitted to the Juno gravity field observations. Also, we aim to investigate our ability to constrain the core properties of Jupiter using its moment of inertia and tidal Love number k2 which could be accessible by the Juno spacecraft. Methods. In this work, the radial density profile was constrained by the Juno gravity field data within the empirical two-layer model in which the equations of state are not needed as an input model parameter. Different two-layer models are constructed in terms of core properties. The dependence of the calculated moment of inertia and tidal Love number k2 on the core properties was investigated in order to discern their abilities to further constrain the internal structure of Jupiter. Results. The calculated normalized moment of inertia (NMOI) ranges from 0.2749 to 0.2762, in reasonable agreement with the other predictions. There is a good correlation between the NMOI value and the core properties including masses and radii. Therefore, measurements of NMOI by Juno can be used to constrain both the core mass and size of Jupiter’s two-layer interior models. For the tidal Love number k2, the degeneracy of k2 is found and analyzed within the two-layer interior model. In spite of this, measurements of k2 can still be used to further constrain the core mass and size of Jupiter’s two-layer interior models.

A New Model of Jupiter's Magnetic Field From Juno's First Nine Orbits

AbstractA spherical harmonic model of the magnetic field of Jupiter is obtained from vector magnetic field observations acquired by the Juno spacecraft during its first nine polar orbits about the planet. Observations acquired during eight of these orbits provide the first truly global coverage of Jupiter's magnetic field with a coarse longitudinal separation of ~45° between perijoves. The magnetic field is represented with a degree 20 spherical harmonic model for the planetary (“internal”) field, combined with a simple model of the magnetodisc for the field (“external”) due to distributed magnetospheric currents. Partial solution of the underdetermined inverse problem using generalized inverse techniques yields a model (“Juno Reference Model through Perijove 9”) of the planetary magnetic field with spherical harmonic coefficients well determined through degree and order 10, providing the first detailed view of a planetary dynamo beyond Earth.

AbInitio Calculation of the Miscibility Diagram for Hydrogen-Helium Mixtures.

We use finite-temperature density functional theory coupled to classical molecular dynamics simulation to calculate the miscibility gap of hydrogen-helium mixtures. The van der Waals density functional (vdW-DF) theory is used, which leads to lower demixing temperatures compared to computations using the Perdew-Burke-Ernzerhof functional. Our calculations suggest that current Jupiter models are most likely too hot to allow demixing in the interior. A Jupiter isentrope based on our vdW-DF data is presented. Our demixing phase diagram still predicts phase separation in Saturn, but in a significantly reduced fraction of its volume.

Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2015

This report continues the practice where the IAU Working Group on Cartographic Coordinates and Rotational Elements revises recommendations regarding those topics for the planets, satellites, minor planets, and comets approximately every 3 years. The Working Group has now become a “functional working group” of the IAU, and its membership is open to anyone interested in participating. We describe the procedure for submitting questions about the recommendations given here or the application of these recommendations for creating a new or updated coordinate system for a given body. Regarding body orientation, the following bodies have been updated: Mercury, based on MESSENGER results; Mars, along with a refined longitude definition; Phobos; Deimos; (1) Ceres; (52) Europa; (243) Ida; (2867) Steins; Neptune; (134340) Pluto and its satellite Charon; comets 9P/Tempel 1, 19P/Borrelly, 67P/Churyumov–Gerasimenko, and 103P/Hartley 2, noting that such information is valid only between specific epochs. The special challenges related to mapping 67P/Churyumov–Gerasimenko are also discussed. Approximate expressions for the Earth have been removed in order to avoid confusion, and the low precision series expression for the Moon’s orientation has been removed. The previously online only recommended orientation model for (4) Vesta is repeated with an explanation of how it was updated. Regarding body shape, text has been included to explain the expected uses of such information, and the relevance of the cited uncertainty information. The size of the Sun has been updated, and notation added that the size and the ellipsoidal axes for the Earth and Jupiter have been recommended by an IAU Resolution. The distinction of a reference radius for a body (here, the Moon and Titan) is made between cartographic uses, and for orthoprojection and geophysical uses. The recommended radius for Mercury has been updated based on MESSENGER results. The recommended radius for Titan is returned to its previous value. Size information has been updated for 13 other Saturnian satellites and added for Aegaeon. The sizes of Pluto and Charon have been updated. Size information has been updated for (1) Ceres and given for (16) Psyche and (52) Europa. The size of (25143) Itokawa has been corrected. In addition, the discussion of terminology for the poles (hemispheres) of small bodies has been modified and a discussion on cardinal directions added. Although they continue to be used for planets and their satellites, it is assumed that the planetographic and planetocentric coordinate system definitions do not apply to small bodies. However, planetocentric and planetodetic latitudes and longitudes may be used on such bodies, following the right-hand rule. We repeat our previous recommendations that planning and efforts be made to make controlled cartographic products; newly recommend that common formulations should be used for orientation and size; continue to recommend that a community consensus be developed for the orientation models of Jupiter and Saturn; newly recommend that historical summaries of the coordinate systems for given bodies should be developed, and point out that for planets and satellites planetographic systems have generally been historically preferred over planetocentric systems, and that in cases when planetographic coordinates have been widely used in the past, there is no obvious advantage to switching to the use of planetocentric coordinates. The Working Group also requests community input on the question submitting process, posting of updates to the Working Group website, and on whether recommendations should be made regarding exoplanet coordinate systems.

Photochemistry, mixing and transport in Jupiter’s stratosphere constrained by Cassini

In this work, we aim at constraining the diffusive and advective transport processes in Jupiter’s stratosphere, using Cassini/CIRS observations published by Nixon et al. (2007,2010). The Cassini–Huygens flyby of Jupiter on December 2000 provided the highest spatially resolved IR observations of Jupiter so far, with the CIRS instrument. The IR spectrum contains the fingerprints of several atmospheric constituents and allows probing the tropospheric and stratospheric composition. In particular, the abundances of C2H2 and C2H6, the main compounds produced by methane photochemistry, can be retrieved as a function of latitude in the pressure range at which CIRS is sensitive to. CIRS observations suggest a very different meridional distribution for these two species. This is difficult to reconcile with their photochemical histories, which are thought to be tightly coupled to the methane photolysis. While the overall abundance of C2H2 decreases with latitude, C2H6 becomes more abundant at high latitudes. In this work, a new 2D (latitude-altitude) seasonal photochemical model of Jupiter is developed. The model is used to investigate whether the addition of stratospheric transport processes, such as meridional diffusion and advection, are able to explain the latitudinal behavior of C2H2 and C2H6. We find that the C2H2 observations are fairly well reproduced without meridional diffusion. Adding meridional diffusion to the model provides an improved agreement with the C2H6 observations by flattening its meridional distribution, at the cost of a degradation of the fit to the C2H2 distribution. However, meridional diffusion alone cannot produce the observed increase with latitude of the C2H6 abundance. When adding 2D advective transport between roughly 30 mbar and 0.01 mbar, with upwelling winds at the equator and downwelling winds at high latitudes, we can, for the first time, reproduce the C2H6 abundance increase with latitude. In parallel, the fit to the C2H2 distribution is degraded. The strength of the advective winds needed to reproduce the C2H6 abundances is particularly sensitive to the value of the meridional eddy diffusion coefficient. The coupled fate of these methane photolysis by-products suggests that an additional process is missing in the model. Ion-neutral chemistry was not accounted for in this work and might be a good candidate to solve this issue.

Jupiter’s evolution with primordial composition gradients

Recent formation and structure models of Jupiter suggest that the planet can have composition gradients and not be fully convective (adiabatic). This possibility directly affects our understanding of Jupiter’s bulk composition and origin. In this Letter we present Jupiter’s evolution with a primordial structure consisting of a relatively steep heavy-element gradient of 40 M⊕. We show that for a primordial structure with composition gradients, most of the mixing occurs in the outer part of the gradient during the early evolution (several 107 yr), leading to an adiabatic outer envelope (60% of Jupiter’s mass). We find that the composition gradient in the deep interior persists, suggesting that ~40% of Jupiter’s mass can be non-adiabatic with a higher temperature than the one derived from Jupiter’s atmospheric properties. The region that can potentially develop layered convection in Jupiter today is estimated to be limited to ~10% of the mass.

A complete study of the precision of the concentric MacLaurin spheroid method to calculate Jupiter’s gravitational moments

A few years ago, Hubbard (2012, ApJ, 756, L15; 2013, ApJ, 768, 43) presented an elegant, non-perturbative method, called concentric MacLaurin spheroid (CMS), to calculate with very high accuracy the gravitational moments of a rotating fluid body following a barotropic pressure-density relationship. Having such an accurate method is of great importance for taking full advantage of the Juno mission, and its extremely precise determination of Jupiter gravitational moments, to better constrain the internal structure of the planet. Recently, several authors have applied this method to the Juno mission with 512 spheroids linearly spaced in altitude. We demonstrate in this paper that such calculations lead to errors larger than Juno’s error bars, invalidating the aforederived Jupiter models at the level required by Juno’s precision. We show that, in order to fulfill Juno’s observational constraints, at least 1500 spheroids must be used with a cubic, square or exponential repartition, the most reliable solutions. When using a realistic equation of state instead of a polytrope, we highlight the necessity to properly describe the outermost layers to derive an accurate boundary condition, excluding in particular a zero pressure outer condition. Providing all these constraints are fulfilled, the CMS method can indeed be used to derive Jupiter models within Juno’s present observational constraints. However, we show that the treatment of the outermost layers leads to irreducible errors in the calculation of the gravitational moments and thus on the inferred physical quantities for the planet. We have quantified these errors and evaluated the maximum precision that can be reached with the CMS method in the present and future exploitation of Juno’s data.

On the libration collinear points in the restricted three – body problem

Abstract In the restricted problem of three bodies when the primaries are triaxial rigid bodies, the necessary and sufficient conditions to find the locations of the three libration collinear points are stated. In addition, the Linear stability of these points is studied for the case of the Euler angles of rotational motion being θ i = 0, ψi + φi = π/2, i = 1, 2 accordingly. We underline that the model studied in this paper has special importance in space dynamics when the third body moves in gravitational fields of planetary systems and particularly in a Jupiter model or a problem including an irregular asteroid.

Scattering V-type asteroids during the giant planet instability: a step for Jupiter, a leap for basalt

V-type asteroids are a taxonomic class whose surface is associated to a basaltic composition. The only known source of V-type asteroids in the Main Asteroid Belt is (4) Vesta, that is located in the inner part of the belt. However, many V-type asteroids cannot be dynamically linked to Vesta., in particular, those asteroids located in the middle and outer parts of the Belt. Previous works have failed to find mechanisms to transport V-type asteroids from the inner to the middle and outer belt. In this work we propose a dynamical mechanism that could have acted on primordial asteroid families. We consider a model of the giant planets migration known as the jumping Jupiter model with five planets. Our study is focused on the period of 10 Myr that encompasses the instability phase of the giant planets. We show that, for different hypothetical Vesta-like paleo-families in the inner belt, the perturbations caused by the ice giant that is scattered into the asteroid belt before being ejected from the solar system, are able to scatter V-type asteroids to the middle and outer belt. Based on the orbital distribution of V-type candidates identified from the Sloan Digital Sky Survey and the VISTA Survey colours, we show that this mechanism is efficient enough provided that the hypothetical paleo-family originated from a 100 to 500 km crater excavated on the surface of (4) Vesta. This mechanism is able to explain the currently observed V-type asteroids in the middle and outer belt, with the exception of (1459) Magnya.

Jupiter’s Formation and Its Primordial Internal Structure

Abstract The composition of Jupiter and the primordial distribution of the heavy elements are determined by its formation history. As a result, in order to constrain the primordial internal structure of Jupiter, the growth of the core and the deposition and settling of accreted planetesimals must be followed in detail. In this paper we determine the distribution of the heavy elements in proto-Jupiter and determine the mass and composition of the core. We find that while the outer envelope of proto-Jupiter is typically convective and has a homogeneous composition, the innermost regions have compositional gradients. In addition, the existence of heavy elements in the envelope leads to much higher internal temperatures (several times 104 K) than in the case of a hydrogen–helium envelope. The derived core mass depends on the actual definition of the core: if the core is defined as the region in which the heavy-element mass fraction is above some limit (say, 0.5), then it can be much more massive (∼15 ) and more extended (10% of the planet’s radius) than in the case where the core is just the region with 100% heavy elements. In the former case Jupiter’s core also consists of hydrogen and helium. Our results should be taken into account when constructing internal structure models of Jupiter and when interpreting the upcoming data from the Juno (NASA) mission.

Jupiter internal structure: the effect of different equations of state

Heavy elements, even though its smaller constituent, are crucial to understand Jupiter formation history. Interior models are used to determine the amount of heavy elements in Jupiter interior, nevertheless this range is still subject to degeneracies due to uncertainties in the equations of state. Prior to Juno mission data arrival, we present Jupiter optimized calculations exploring the effect of different model parameters in the determination of Jupiter's core and heavy element's mass. We perform comparisons between equations of state published recently. The interior model of Jupiter is calculated from the equations of hydrostatic equilibrium, mass and energy conservation, and energy transport. The mass of the core and heavy elements is adjusted to match Jupiter's observational constrains radius and gravitational moments. We show that the determination of Jupiter interior structure is tied to the estimation of its gravitational moments and the accuracy of equations of state of hydrogen, helium and heavy elements. The location of the region where Helium rain occurs as well as its timescale are important to determine the distribution of heavy elements and helium in the interior of Jupiter. We show that differences find when modeling Jupiter's interior with recent EOS are more likely due to differences in the internal energy and entropy calculation. The consequent changes in the thermal profile lead to different estimations of the mass of the core and heavy elements, explaining differences in recently published Jupiter interior models. Our results help clarify differences find in Jupiter interior models and will help the interpretation of upcoming Juno data.

TIDAL RESPONSE OF PRELIMINARY JUPITER MODEL

ABSTRACT In anticipation of improved observational data for Jupiter’s gravitational field, from the Juno spacecraft, we predict the static tidal response for a variety of Jupiter interior models based on ab initio computer simulations of hydrogen–helium mixtures. We calculate hydrostatic-equilibrium gravity terms, using the non-perturbative concentric Maclaurin Spheroid method that eliminates lengthy expansions used in the theory of figures. Our method captures terms arising from the coupled tidal and rotational perturbations, which we find to be important for a rapidly rotating planet like Jupiter. Our predicted static tidal Love number, , is ∼10% larger than previous estimates. The value is, as expected, highly correlated with the zonal harmonic coefficient J 2, and is thus nearly constant when plausible changes are made to the interior structure while holding J 2 fixed at the observed value. We note that the predicted static k 2 might change, due to Jupiter’s dynamical response to the Galilean moons, and find reasons to argue that the change may be detectable—although we do not present here a theory of dynamical tides for highly oblate Jovian planets. An accurate model of Jupiter’s tidal response will be essential for interpreting Juno observations and identifying tidal signals from effects of other interior dynamics of Jupiter’s gravitational field.