Mass Of Heavy Elements Research Articles

Fate of a remnant solid disk around an eccentric giant planet

The composition of giant planets' atmospheres is an important tracer of their formation history. While many theoretical studies investigate the heavy-element accretion within a gaseous protoplanetary disk, the possibility of solid accretion after disk dissipation has not been explored. Here, we focus on the case of a gas giant planet excited to an eccentric orbit and assess the likelihood of solid accretion after disk dissipation. We follow the orbital evolution of the surrounding solid materials and investigate the scattering and accretion of heavy elements in the remnant solid disks. We perform N-body simulations of planetesimals and embryos around an eccentric giant planet. We consider various sizes and orbits for the eccentric planet and determine the fate of planetesimals and embryos. We find that the orbital evolution of solids, such as planetesimals and embryos, is regulated by weak encounters with the eccentric planet rather than strong close encounters. Even in the region where the Safronov number is smaller than unity, most solid materials fall onto the central star or are ejected from the planetary system. We also develop an analytical model of the solid accretion along the orbital evolution of a giant planet, where the accretion probability is obtained as a function of the planetary mass, radius, semi-major axis, eccentricity, inclination, and solid disk thickness. Our model predicts that sim 0.01-0.1 $M_ of solids is accreted onto an eccentric planet orbiting in the outer disk ($ The accreted heavy-element mass increases (decreases) with the eccentricity (inclination) of the planet. We also discuss the possibility of collisions of terrestrial planets and find that $ of the hot Jupiters formed via high-eccentric migration collide with a planet of $10M_ However, we find that solid accretion and collisions with terrestrial planets are minor events for planets in the inner orbit, and a different accretion process is required to enrich eccentric giant planets with heavy elements.

Missing metals in DQ stars: a compelling clue to their origin

ABSTRACT White dwarf stars frequently experience external pollution by heavy elements, and yet the intrinsically carbon-enriched DQ spectral class members fail to exhibit this phenomenon, representing a decades-old conundrum. This study reports a high-resolution spectroscopic search for Ca ii in classical DQ white dwarfs, finding that these stars are stunted both in pollution frequency and heavy element mass fractions, relative to the wider population. Compared to other white dwarf spectral classes, the average external accretion rate is found to be at least three orders of magnitude lower in the DQ stars. Several hypotheses are considered which need to simultaneously account for (i) an apparent lack of accreted metals, (ii) a dearth of circumstellar planetary material, (iii) an observed deficit of unevolved companions in post-common envelope binaries, (iv) relatively low helium mass fractions, and remnant masses that appear smaller than for other spectral classes, (v) a high incidence of strong magnetism, and (vi) modestly older disc kinematics. Only one hypothesis is consistent with all these constraints, suggesting DQ white dwarfs are the progeny of binary evolution that altered both their stellar structures and their circumstellar environments. A binary origin is already suspected for the warmer and more massive DQ stars, and is proposed here as an inclusive mechanism to expose core carbon material, in a potential evolutionary unification for the entire DQ spectral class. In this picture, DQ stars are not descended from DA or DB white dwarfs that commonly host dynamically active planetary systems.

NGTS-30 b/TOI-4862 b: An ~1 Gyr old 98-day transiting warm Jupiter

Long-period transiting exoplanets bridge the gap between the bulk of transit- and Doppler-based exoplanet discoveries, providing key insights into the formation and evolution of planetary systems. The wider separation between these planets and their host stars results in the exoplanets typically experiencing less radiation from their host stars; hence, they should maintain more of their original atmospheres, which can be probed during transit via transmission spectroscopy. Although the known population of long-period transiting exoplanets is relatively sparse, surveys performed by the Transiting Exoplanet Survey Satellite (TESS) and the Next Generation Transit Survey (NGTS) are now discovering new exoplanets to fill in this crucial region of the exoplanetary parameter space. This study aims to characterise a new long-period transiting exoplanet by following up on a single-transit candidate found in the TESS mission. The TOI-4862 system was monitored using a combination of photometric instruments (TESS, NGTS, and EulerCam) and spectroscopic instruments (CORALIE, FEROS, HARPS, and PFS) in order to determine the period, radius, and mass of the long-period transiting exoplanet NGTS-30\,b/TOI-4862\,b. These observations were then fitted simultaneously to determine precise values for the properties and orbital parameters of the exoplanet, as well as the refined stellar parameters of the host star. We present the discovery of a long-period (P = 98.29838pm 0.00010 day) Jupiter-sized (0.928pm 0.032 R$_ J $; 0.960pm 0.056 M$_ J $) planet transiting a 1.1 Gyr old G-type star, one of the youngest warm Jupiters discovered to date. NGTS-30\,b/TOI-4862\,b has a moderate eccentricity $), meaning that its equilibrium temperature can be expected to vary from 274$^ $ K to 500$^ $ K over the course of its orbit. Through interior modelling, NGTS-30\,b/TOI-4862\,b was found to have a heavy element mass fraction of $ $ and a heavy element enrichment ($ p / Z_ star $) of $20^ $, making it metal-enriched compared to its host star. NGTS-30\,b/TOI-4862\,b is one of the youngest well-characterised long-period exoplanets found to date and will therefore be important in the quest to understanding the formation and evolution of exoplanets across the full range of orbital separations and ages.

TOI-4201: An Early M Dwarf Hosting a Massive Transiting Jupiter Stretching Theories of Core Accretion* *This paper includes data gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile.

We confirm TOI-4201 b as a transiting Jovian-mass planet orbiting an early M dwarf discovered by the Transiting Exoplanet Survey Satellite. Using ground-based photometry and precise radial velocities from NEID and the Planet Finder Spectrograph, we measure a planet mass of 2.59−0.06+0.07 M J, making this one of the most massive planets transiting an M dwarf. The planet is ∼0.4% of the mass of its 0.63 M ⊙ host and may have a heavy-element mass comparable to the total dust mass contained in a typical class II disk. TOI-4201 b stretches our understanding of core accretion during the protoplanetary phase and the disk mass budget, necessitating giant planet formation to take place either much earlier in the disk lifetime or perhaps through alternative mechanisms like gravitational instability.

Towards a new era in giant exoplanet characterisation

Determining the composition of giant exoplanets is crucial for understanding their origin and evolution. However, planetary bulk composition is not measured directly but must be deduced from a combination of mass-radius measurements, knowledge of the planetary age and evolution simulations. Accurate determinations of stellar ages, mass-radius measurements, and atmospheric compositions from upcoming missions can significantly improve the determination of the heavy-element mass in giant planets. In this paper we first demonstrate the importance of an accurate age measurement, as expected from Plato, in constraining planetary properties. Well-determined stellar ages can reduce the bulk-metallicity uncertainty by up to a factor of two. We next infer the bulk metallicity of warm giants from the Ariel mission reference sample and identify the Ariel high-priority targets for which a measured atmospheric metallicity can clearly break the degeneracy in the inferred composition. We show that knowledge of the atmospheric metallicity can broadly reduce the bulk-metallicity uncertainty by a factor of four to eight. We conclude that accurate age determinations from Plato and atmospheric measurements by Ariel and the James Webb Space Telescope will play a key role in revealing the composition of giant exoplanets.

Heavy-element accretion by proto-Jupiter in a massive planetesimal disc, revisited

ABSTRACT Planetesimal accretion is a key source for heavy-element enrichment in giant planets. It has been suggested that Jupiter’s enriched envelope is a result of planetesimal accretion during its growth, assuming it formed in a massive planetesimal disc. In this study, we simulate Jupiter’s formation in this scenario. We assume in situ formation and perform N-body simulations to infer the solid accretion rate. We find that tens-Earth masses of planetesimals can be captured by proto-Jupiter during the rapid gas accretion phase. However, if several embryos are formed near Jupiter’s core, which is an expected outcome in the case of a massive planetesimal disc, scattering from the embryos increases the eccentricity and inclination of planetesimals and therefore significantly reduces the accretion efficiency. We also compare our results with published semi-analytical models and show that these models cannot reproduce the N-body simulations especially when the planetesimal disc has a large eccentricity and inclination. We show that when the dynamical evolution of planetesimals is carefully modelled, the total mass of captured planetesimals Mcap,tot is 2M⊕ ≲ Mcap,tot ≲ 18M⊕. The metallicity of Jupiter’s envelope can be explained by the planetesimal accretion in our massive disc model despite the low accretion efficiency coming from the high eccentricity and inclination of planetesimals. Our study demonstrates the importance of detailed modelling of planetesimal accretion during the planetary growth and its implications to the heavy-element mass in gaseous planets.

Constraining the origin of giant exoplanets via elemental abundance measurements

The origin of close-in giant planets is a key open question in planet formation theory. The two leading models are (i) formation at the outer disk followed by migration and (ii) in situ formation. In this work we determine the atmospheric composition of warm Jupiters for both formation scenarios. We perform N-body simulations of planetesimal accretion interior and exterior to the water ice-line for various planetary formation locations, planetary masses, and planetesimal sizes to estimate the accreted heavy-element mass and final planetary composition. We find that the two models differ significantly: migrating giant planets have 2–14 times higher metallicities than planets that form in situ. The ratio between refractories and volatiles is found to be above one for migrating planets but below 0.4 for planets that form in situ. We also identify very different trends between heavy-element enrichment and planetary mass for these two formation mechanisms. While the metallicity of migrating planets is found to increase with decreasing planetary mass, it is about constant for in situ formation. Our study highlights the importance of measuring the atmospheric composition of warm Jupiters and its connection to their formation and evolutionary paths.

First-principles study on the ultralow lattice thermal conductivity of BiSeI

Thermoelectric materials have received widespread attention for decades. An important way to find high-efficiency thermoelectric materials is to find materials with ultralow thermal conductivity. Here, we have studied the lattice thermal conductivity of the quasi-one-dimensional semiconductor BiSeI through first-principles calculations. It is found that the thermal conductivity of BiSeI has a large anisotropy due to its quasi-one-dimensional structure. Particularly, BiSeI has ultralow lattice thermal conductivities of 0.28 and 0.34 W/m⋅K along the a and c axes at room temperatures. The lattice thermal conductivity of BiSeI along the b axis is also quite low, which is 1.54 W/m⋅K at room temperatures. It is shown that the quasi-one-dimensional crystal structure and heavy element mass of BiSeI result in low phonon group velocities and short phonon lifetimes, which inevitably lead to ultralow thermal conductivity. Our work implies that BiSeI is a potential thermoelectric material if its electric conductivity could be enhanced in experiments.

Possible In Situ Formation of Uranus and Neptune via Pebble Accretion

The origin of Uranus and Neptune is still unknown. In particular, it has been challenging for planet formation models to form the planets in their current radial distances within the expected lifetime of the solar nebula. In this paper, we simulate the in situ formation of Uranus and Neptune via pebble accretion and show that both planets can form within ∼3 Myr at their current locations, and have final compositions that are consistent with the heavy element to H–He ratios predicted by structure models. We find that Uranus and Neptune could have been formed at their current locations. In several cases a few earth masses (M ⊕ ) of heavy elements are missing, suggesting that Uranus and/or Neptune may have accreted ∼1–3 M⊕ of heavy elements after their formation via planetesimal accretion and/or giant impacts.

A low accretion efficiency of planetesimals formed at planetary gap edges

Observations and models of giant planets indicate that such objects are enriched in heavy elements compared to solar abundances. The prevailing view is that giant planets accreted multiple Earth masses of heavy elements after the end of core formation. Such late solid enrichment is commonly explained by the accretion of planetesimals. Planetesimals are expected to form at the edges of planetary gaps, and here we address the question of whether these planetesimals can be accreted in large enough amounts to explain the inferred high heavy element contents of giant planets. We performed a series of N-body simulations of the dynamics of planetesimals and planets during the planetary growth phase, taking gas drag into account as well as the enhanced collision cross section caused by the extended envelopes. We considered the growth of Jupiter and Saturn via gas accretion after reaching the pebble isolation mass and we included their migration in an evolving disk. We find that the accretion efficiency of planetesimals formed at planetary gap edges is very low: less than 10% of the formed planetesimals are accreted even in the most favorable cases, which in our model corresponds to a few Earth masses. When planetesimals are assumed to form beyond the feeding zone of the planets, extending to a few Hill radii from a planet, accretion becomes negligible. Furthermore, we find that the accretion efficiency increases when the planetary migration distance is increased and that the efficiency does not increase when the planetesimal radii are decreased. Based on these results, we conclude that it is difficult to explain the large heavy element content of giant planets with planetesimal accretion during the gas accretion phase. Alternative processes most likely are required, such as accretion of vapor deposited by drifting pebbles.

Understanding the interior structure of gaseous giant exoplanets with machine learning techniques

Context. Characterizing the interiors of gaseous giant exoplanets is currently one of the main objectives in exoplanetary sciences. In particular, the planetary heavy-element mass provides a critical constraint on planet formation from exoplanetary systems. However, gas giant exoplanets show large diversities in thermal states and their interior properties vary across a wide magnitude range. Forward modeling of their interiors exhibits a larger degeneracy with respect to rocky exoplanets. Aims. We applied machine learning techniques based on mixture density networks (MDNs) to investigate the interiors of gaseous giant exoplanets. We aim to provide a well-trained MDN for quick and efficient predictions. Methods. Based on our current knowledge of gas giants in the Solar System, we discussed an effect of model uncertainties on planetary interiors and presented a data set for gas giants with masses between 0.1 and 10 Jupiter masses using two-layer interior models. Then, MDNs were constructed to train the generated data set and their performance was evaluated in order to achieve a well-trained one. Results. The MDN using planetary mass and radius as inputs exhibits the well-known degeneracy of interior models. The surface temperature of a planet bears constraints on the thermal state of planetary interiors, and adding it as additional input considerably breaks the degeneracy of possible interior structures. The MDN with inputs of mass, radius, and surface temperature is found to show excellent performance in predicting the interior properties of gaseous giant exoplanets, although these interior properties span over a very wide range. We also applied the well-trained MDN to four gas giants in the Solar System and beyond. The MDN predictions are in good agreement with the interior model solutions within the observational and systematic uncertainties. Conclusions. We offer a convenient and powerful tool available online providing knowledge of the interiors of gaseous giant exoplanets in addition to rocky exoplanets, which could be helpful for our understanding of planet formation in diverse protoplanetary environments.

Determination of Multi Elements in Tobacco Plant of Northeast India by Neutron Activation Analysis and Atomic Absorption Spectrometry.

Even when cultivated in uncontaminated soils, tobacco plant has higher propensity to extract and accumulate trace elements. The concentrations (mass fractions) of essential elements (K, Ca, Mg, Na, Cl, Mn, Fe, Cu, and Zn) and 28 non-essential elements in tobacco plant (leaves, stem, and root) of Northeast India and their respective soils were quantitatively measured. Hg mass fraction in all samples analyzed were found to be < 10mg/kg. The heavy element mass fractions of tobacco are weakly correlated to different soil parameters. The bioconcentration factor values indicated that Cd (7) is selectively absorbed and translocated in the tobacco leaves compared to Zn (1.7), Cu (1.5), Ni (0.12), and Pb (0.1). Under acidic soil conditions, tobacco plant efficiently absorbed and translocated Cl- ion with great ease, whereas it may be a very low accumulator of rare-earth elements. The mass fractions of Mn, Cu, Sb, Cs, Rb, and Pb are very similar to the "reference plant," whereas significantly higher mass fractions of Al, Sc, Ti, Zr, Hf, Ta, Th, and U are present in the roots of tobacco plant relative to the "reference plant." Principal component analysis has revealed that Northeast Indian tobacco can be clearly differentiated from other varieties of tobaccos used in different countries because of their element profiles.

The mass budget necessary to explain ‘Oumuamua as a nitrogen iceberg

Recently, a nitrogen iceberg was proposed as a possible origin for the first interstellar object, 1I/2017 U1, also known as ‘Oumuamua. Here, we show that the mass budget in exo-Pluto planets necessary to explain the detection of ‘Oumuamua as a nitrogen iceberg chipped off from a planetary surface requires a mass of heavy elements exceeding the total quantity locked in stars with 95% confidence, making the scenario untenable because only a small fraction of the mass in stars ends in exo-Plutos.

The Nature and Composition of Jupiter’s Building Blocks Derived from the Water Abundance Measurements by the Juno Spacecraft

Abstract The microwave radiometer on board the Juno spacecraft provided a measurement of the water abundance found to range between ∼1 and 5.1 times the protosolar abundance of oxygen in the near-equatorial region of Jupiter. Here, we aim to combine this up-to-date oxygen determination, which is likely to be more representative of the bulk abundance than the Galileo probe subsolar value, with the other known measurements of elemental abundances in Jupiter, to derive the formation conditions and initial composition of the building blocks agglomerated by the growing planet, and that determine the heavy element composition of its envelope. We investigate several cases of formation of icy solids in the protosolar nebula (PSN), from the condensation of pure ices to the crystallization of mixtures of pure condensates and clathrates in various proportions. Each of these cases corresponds to a distinct solid composition whose amount is adjusted in the envelope of Jupiter to match the O abundance measured by Juno. The volatile enrichments can be matched by a wide range of planetesimal compositions, from solids exclusively formed from pure condensates or from nearly exclusively clathrates, the latter case providing a slightly better fit. The total mass of volatiles needed in the envelope of Jupiter to match the observed enrichments is within the ∼4.3–39 M ⊕ range, depending on the crystallization scenario considered in the PSN. A wide range of masses of heavy elements derived from our fits is found to be compatible with the envelope’s metallicity calculated from current interior models.

Core-collapse supernova explosion theory.

Most supernova explosions accompany the death of a massive star. These explosions give birth to neutron stars and black holes, and eject solar masses of heavy elements. However, determining the mechanism of explosion has been a half-century journey of great numerical and physical complexity. Here we present the status of this theoretical quest and the physics and astrophysics upon which its resolution seems to depend. The delayed neutrino-heating mechanism is emerging as the key driver of supernova explosions, but there remain many issues to address, such as the chaos of the involved dynamics.

Growth of Jupiter: Formation in disks of gas and solids and evolution to the present epoch

The formation of Jupiter is modeled via core-nucleated accretion, and the planet's evolution is simulated up to the present epoch. Throughout the phases when the planet acquires most of its heavy-element content, the calculation of solids' accretion accounts for interactions with an evolving disk of planetesimals. The phase of growth from an embryo of a few hundred kilometers in radius until the time when the accretion of gas overtakes solids' accretion was presented by D'Angelo et al. (2014), and the same numerical methods are applied here. Those calculations followed the formation for about 4 × 105 years, until the epoch when the heavy-element and hydrogen/helium masses wereMZ ≈ 7.3 andMXY ≈ 0.15 Earth's masses (M⊕), respectively, and ṀXY≈ṀZ. Herein, the calculation is continued through the phase when MXYgrows to equalMZ, at which age, about 2.4 × 106 years, the total mass of the planet isMp ≈ 20M⊕. About 9 × 105 years later,Mpis approximately 60M⊕and MZ ≈ 16M⊕, three-quarters of which are delivered by planetesimals larger than 10km in radius. Around this epoch, the contraction of the envelope dictates gas accretion rates a few times 10−3M⊕per year, initiating the regime of disk-limited accretion, whereby the planet can accrete all the gas provided by the disk, and its evolution is therefore tied to disk's evolution. Growth is continued by constructing simplified models of protosolar accretion disks that evolve through viscous diffusion, winds, and accretion on the planet. Jupiter's formation ends after ≈ 3.4–4.2Myr, depending on the applied disk viscosity parameter, when nebula gas disperses. The young Jupiter is 4.5–5.5 times as voluminous as it is presently and thousands of times as luminous, ~10−5L⊙. The heavy-element mass is ≈ 20M⊕. The evolution proceeds through the cooling and contraction phase, in isolation except for solar irradiation. After 4570Myr, the age of the solar system, radius and luminosity of the planet are within 10% of current values, accounting also for uncertainties in the power absorbed from the Sun. During formation, and soon thereafter, the planet exhibits features, e.g., luminosity and effective temperature, that may probe aspects of the latter stages of formation, if observable. These possibly distinctive features, however, seem to disappear within a few tens of Myr

The origin of the high metallicity of close-in giant exoplanets

Context. Recent studies suggest that in comparison to their host star, many giant exoplanets are highly enriched with heavy elements and can contain several tens of Earth masses of heavy elements or more. Such enrichment is considered to have been delivered by the accretion of planetesimals in late formation stages. Previous dynamical simulations, however, have shown that planets cannot accrete such high masses of heavy elements through “in situ” planetesimal accretion. Aims. We investigate whether a giant planet migrating inward can capture planetesimals efficiently enough to significantly increase its metallicity. Methods. We performed orbital integrations of a migrating giant planet and planetesimals in a protoplanetary gas disc to infer the planetesimal mass that is accreted by the planet. Results. We find that the two shepherding processes of mean motion resonance trapping and aerodynamic gas drag inhibit the planetesimal capture of a migrating planet. However, the amplified libration allows the highly-excited planetesimals in the resonances to escape from the resonance trap and to be accreted by the planet. Consequently, we show that a migrating giant planet captures planetesimals with total mass of several tens of Earth masses if the planet forms at a few tens of AU in a relatively massive disc. We also find that planetesimal capture occurs efficiently in a limited range of semi-major axis and that the total captured planetesimal mass increases with increasing migration distances. Our results have important implications for understanding the relation between giant planet metallicity and mass, as we suggest that it reflects the formation location of the planet – or more precisely, the location where runaway gas accretion occurred. We also suggest the observed metal-rich close-in Jupiters migrated to their present locations from afar, where they had initially formed.

Signature of helium rain and dilute cores in Jupiter's interior from empirical equations of state

Measurements of Jupiter's gravity field by Juno have been acquired with unprecedented precision, but uncertainties in the planet’s hydrogen–helium equation of state (EOS) and the hydrogen–helium phase separation have meant that differences remain in the interior model predictions. We deduce an empirical EOS from Juno gravity field observations in terms of the hydrostatic equation and then investigate the structure and composition of Jupiter by comparison of the empirical EOS with Jupiter's adiabats obtained from the physical EOS. The deduced helium mass fraction suggests depletion of helium in the outermost atmosphere and helium concentration in the inner molecular hydrogen region, which is a signature of helium rain in Jupiter's interior. The deduced envelope metallicity (the heavy-element mass fraction) is as high in the innermost envelope as 11–13 times the solar value. Such a high metallicity provides sharp support to the dilute core model with the heavy elements dissolved in hydrogen and expanded outward. No matter how the core mass is varied, the empirical EOS derived from the two-layer interior model generally suggests higher densities in the innermost envelope than does the best-fit Jupiter's adiabat; this result is, again, a signature of dilute cores in Jupiter's interior. Moreover, no matter the core mass, the empirical EOS is found to exhibit an inflexion point in the deep interior, around 10 Mbar, which can be explained as the combined effect of helium concentration in the upper part and dilute cores in the lower part.

Jupiter formed as a pebble pile around the N2 ice line

Context. The region around the H2O ice line, due to its higher surface density, seems to be the ideal location to form planets. The core of Jupiter, as well as the cores of close-in gas giants are therefore thought to form in this region of the disk. Nevertheless, constraining the formation location of individual planets has proven to be difficult. Aims. We aim to use the nitrogen abundance in Jupiter, which is around four times solar, in combination with Juno constraints on the total mass of heavy elements in Jupiter to narrow down its formation scenario. Methods. Different pathways of enrichment of the atmosphere of Jupiter are considered, such as the accretion of enriched gas, pebbles, and planetesimals, and their implications for the oxygen abundance of Jupiter are discussed. Results. The super-solar nitrogen abundance in Jupiter necessitates the accretion of extra N2 from the proto-solar nebula. The only location of the disk where this can happen is outside or just inside the N2 ice line. These constraints favor a pebble accretion origin of Jupiter, from the perspective of composition and planet formation. We predict that Jupiter’s oxygen abundance is between 3.6 and 4.5 times solar.

Understanding Jupiter’s deep interior: the effect of a dilute core

Context. The Juno spacecraft has significantly improved the accuracy of low-order even gravitational harmonics. It has been demonstrated that a dilute core is helpful to interpret Juno’s gravity measurements. However, introducing a dilute core adds a new degree of freedom to Jupiter’s interior models in addition to the uncertainties in the equations of state for hydrogen and helium. Aims. We present four-layer structure models for Jupiter where a dilute core region is added above a central compact core of rocks. The effect of the dilute core on the structure and composition of Jupiter is investigated in detail. Combined with current knowledge of Jupiter’s composition and thermal state, we aim to obtain information on the dilute core. Also, we investigate the effect of equations of state for hydrogen and helium on the predictions of the core mass and heavy element abundance. Methods. In the four-layer structure model, the heavy element abundances in the outer two envelopes and the mass of the compact core were adjusted to reproduce Jupiter’s equatorial radius as well as Juno’s gravity observations. Different dilute core configurations were constructed in terms of its size and composition and different equations of state for hydrogen and helium were used in interior structure calculations. Optimized calculations were then performed to investigate the effect of dilute cores and equations of state on Jupiter’s internal structure and composition. Results. It is found that the absolute values of J6 and J8 tend to decrease as helium becomes more depleted in the dilute core region. Most interior structure calculations seem to prefer an inward decrease of the helium mass fraction from the metallic envelope to the dilute core region. We also show that the core mass and heavy element abundance in Jupiter are dependent upon the rock-to-ice ratio in the dilute core region, the temperature jump from the molecular to metallic envelope, and the equations of state for hydrogen and helium. The resulting heavy-element mass in the core is generally larger than the three-layer structure models owing to the heavy elements dissolved in the dilute core region, and the global heavy-element abundance is in good agreement with the available dilute-core predictions.