arXiv subjects

W. B. Hubbard

Publications and source records attributed to W. B. Hubbard.

At least 19 recordsLinked to original sources

arXiv2023

Saturn's Interior After the Cassini Grand Finale

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.

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arXiv2023

Jupiter's interior from Juno: Equation-of-state uncertainties and dilute core extent

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. 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. We carried out an extensive exploration of the parameter space and studied a wide range of interior models using Markov chain Monte Carlo (MCMC) simulations. To consider the uncertainty on the equation of state, we allowed for modifications of the equation of state in our calculations. 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. 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.

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arXiv2022

Jupiter's inhomogeneous envelope

While Jupiter's massive gas envelope consists mainly of hydrogen and helium, the key to understanding Jupiter's formation and evolution lies in the distribution of the remaining (heavy) elements. Before the Juno mission, the lack of high-precision gravity harmonics precluded the use of statistical analyses in a robust determination of the heavy-elements distribution in Jupiter's envelope. In this paper, we assemble the most comprehensive and diverse collection of Jupiter interior models to date and use it to study the distribution of heavy elements in the planet's envelope. We apply a Bayesian statistical approach to our interior model calculations, reproducing the Juno gravitational and atmospheric measurements and constraints from the deep zonal flows. Our results show that the gravity constraints lead to a deep entropy of Jupiter corresponding to a 1 bar temperature 5-15 K higher than traditionally assumed. We also find that uncertainties in the equation of state are crucial when determining the amount of heavy elements in Jupiter's interior. Our models put an upper limit to the inner compact core of Jupiter of 7 Earth masses, independently on the structure model (with or without dilute core) and the equation of state considered. Furthermore, we robustly demonstrate that Jupiter's envelope is inhomogenous, with a heavy-element enrichment in the interior relative to the outer envelope. This implies that heavy element enrichment continued through the gas accretion phase, with important implications for the formation of giant planets in our solar system and beyond.

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arXiv2019

Models of Saturn's Interior Constructed with Accelerated Concentric Maclaurin Spheroid Method

The Cassini spacecraft's Grand Finale orbits provided a unique opportunity to probe Saturn's gravity field and interior structure. Doppler measurements yielded unexpectedly large values for the gravity harmonics J_6, J_8, and J_10 that cannot be matched with planetary interior models that assume uniform rotation. Instead we present a suite of models that assume the planet's interior rotates on cylinders, which allows us to match all the observed even gravity harmonics. For every interior model, the gravity field is calculated self-consistently with high precision using the Concentric Maclaurin Spheroid (CMS) method. We present an acceleration technique for this method, which drastically reduces the computational cost, allows us to efficiently optimize model parameters, map out allowed parameter regions with Monte Carlo sampling, and increases the precision of the calculated J_2n gravity harmonics to match the error bars of the observations, which would be difficult without acceleration. Based on our models, Saturn is predicted to have a dense central core of 15-18 Earth masses and an additional 1.5-5 Earth masses of heavy elements in the envelope. Finally, we vary the rotation period in the planet's deep interior and determine the resulting oblateness, which we compare with the value from radio occultation measurements by the Voyager spacecraft. We predict a rotation period of 10:33:34 h +- 55s, which is in agreement with recent estimates derived from ring seismology.

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arXiv2017

Comparing Jupiter interior structure models to Juno gravity measurements and the role of a dilute core

The Juno spacecraft has measured Jupiter's low-order, even gravitational moments, $J_2$--$J_8$, to an unprecedented precision, providing important constraints on the density profile and core mass of the planet. Here we report on a selection of interior models based on ab initio computer simulations of hydrogen-helium mixtures. We demonstrate that a dilute core, expanded to a significant fraction of the planet's radius, is helpful in reconciling the calculated $J_n$ with Juno's observations. Although model predictions are strongly affected by the chosen equation of state, the prediction of an enrichment of $Z$ in the deep, metallic envelope over that in the shallow, molecular envelope holds. We estimate Jupiter's core to contain an 7--25 Earth mass of heavy elements. We discuss the current difficulties in reconciling measured $J_n$ with the equations of state, and with theory for formation and evolution of the planet.

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arXiv2016

A Preliminary Jupiter Model

In anticipation of new observational results for Jupiter's axial moment of inertia and gravitational zonal harmonic coefficients from the forthcoming Juno orbiter, we present a number of preliminary Jupiter interior models. We combine results from ab initio computer simulations of hydrogen-helium mixtures, including immiscibility calculations, with a new nonperturbative calculation of Jupiter's zonal harmonic coefficients, to derive a self-consistent model for the planet's external gravity and moment of inertia. We assume helium rain modified the interior temperature and composition profiles. Our calculation predicts zonal harmonic values to which measurements can be compared. Although some models fit the observed (pre-Juno) second- and fourth-order zonal harmonics to within their error bars, our preferred reference model predicts a fourth-order zonal harmonic whose absolute value lies above the pre-Juno error bars. This model has a dense core of about 12 Earth masses, and a hydrogen-helium-rich envelope with approximately 3 times solar metallicity.

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arXiv2013

Concentric Maclaurin spheroid models of rotating liquid planets

I present exact expressions for the interior gravitational potential V of a system of N concentric constant-density (Maclaurin) spheroids. I demonstrate an iteration procedure to find a self-consistent solution for the shapes of the interfaces between spheroids, and for the interior gravitational potential. The external free-space potential, expressed as a multipole expansion, emerges as part of the self-consistent solution. The procedure is both simpler and more precise than perturbation methods. One can choose the distribution and mass densities of the concentric spheroids so as to reproduce a prescribed barotrope to a specified accuracy. I demonstrate the method's efficacy by comparing its results with several published test cases.

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arXiv2013

Ab Initio Equation of State for Hydrogen-Helium Mixtures with Recalibration of the Giant-Planet Mass-Radius Relation

Using density functional molecular dynamics simulations, we determine the equation of state for hydrogen-helium mixtures spanning density-temperature conditions typical of giant planet interiors, ~0.2-9 g/cc and 1000-80000 K for a typical helium mass fraction of 0.245. In addition to computing internal energy and pressure, we determine the entropy using an ab initio thermodynamic integration technique. A comprehensive equation of state (EOS) table with 391 density-temperature points is constructed and the results are presented in form of two-dimensional free energy fit for interpolation. Deviations between our ab initio EOS and the semi-analytical EOS model by Saumon and Chabrier are analyzed in detail, and we use the results for initial revision of the inferred thermal state of giant planets with known values for mass and radius. Changes are most pronounced for planets in the Jupiter mass range and below. We present a revision to the mass-radius relationship which makes the hottest exoplanets increase in radius by ~0.2 Jupiter radii at fixed entropy and for masses greater than ~0.5 Jupiter mass. This change is large enough to have possible implications for some discrepant "inflated giant exoplanets".

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arXiv2009

Buoyancy waves in Pluto's high atmosphere: Implications for stellar occultations

We apply scintillation theory to stellar signal fluctuations in the high-resolution, high signal/noise, dual-wavelength data from the MMT observation of the 2007 March 18 occultation of P445.3 by Pluto. A well-defined high wavenumber cutoff in the fluctuations is consistent with viscous-thermal dissipation of buoyancy waves (internal gravity waves) in Pluto's high atmosphere, and provides strong evidence that the underlying density fluctuations are governed by the gravity-wave dispersion relation.

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arXiv2008

Comparison of Jupiter Interior Models Derived from First-Principles Simulations

Recently two groups used first-principles computer simulations to model Jupiter's interior. While both studies relied on the same simulation technique, density functional molecular dynamics, the groups derived very different conclusions. In particular estimates for the size of Jupiter's core and the metallicity of its hydrogen-helium mantle differed substantially. In this paper, we discuss the differences of the approaches and give an explanation for the differing conclusions.

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arXiv2008

A Massive Core in Jupiter Predicted From First-Principles Simulations

Hydrogen-helium mixtures at conditions of Jupiter's interior are studied with first-principles computer simulations. The resulting equation of state (EOS) implies that Jupiter possesses a central core of 14-18 Earth masses of heavier elements, a result that supports core accretion as standard model for the formation of hydrogen-rich giant planets. Our nominal model has about 2 Earth masses of planetary ices in the H-He-rich mantle, a result that is, within modeling errors, consistent with abundances measured by the 1995 Galileo Entry Probe mission (equivalent to about 5 Earth masses of planetary ices when extrapolated to the mantle), suggesting that the composition found by the probe may be representative of the entire planet. Interior models derived from this first-principles EOS do not give a match to Jupiter's gravity moment J4 unless one invokes interior differential rotation, implying that jovian interior dynamics has an observable effect on the measured gravity field.

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arXiv2007

Possible Solutions to the Radius Anomalies of Transiting Giant Planets

We calculate the theoretical evolution of the radii of all fourteen of the known transiting extrasolar giant planets (EGPs) for a variety of assumptions concerning atmospheric opacity, dense inner core masses, and possible internal power sources. We incorporate the effects of stellar irradiation and customize such effects for each EGP and star. Looking collectively at the family as a whole, we find that there are in fact two radius anomalies to be explained. Not only are the radii of a subset of the known transiting EGPs larger than expected from previous theory, but many of the other objects are smaller than the default theory would allow. We suggest that the larger EGPs can be explained by invoking enhanced atmospheric opacities that naturally retain internal heat. This explanation might obviate the necessity for an extra internal power source. We explain the smaller radii by the presence in perhaps all the known transiting EGPs of dense cores, such as have been inferred for Saturn and Jupiter. Importantly, we derive a rough correlation between the masses of our "best-fit" cores and the stellar metallicity that seems to buttress the core-accretion model of their formation. Though many caveats and uncertainties remain, the resulting comprehensive theory that incorporates enhanced-opacity atmospheres and dense cores is in reasonable accord with all the current structural data for the known transiting giant planets.

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arXiv2006

Effects of mass loss for highly-irradiated giant planets

We present calculations for the evolution and surviving mass of highly-irradiated extrasolar giant planets (EGPs) at orbital semimajor axes ranging from 0.023 to 0.057 AU using a generalized scaled theory for mass loss, together with new surface-condition grids for hot EGPs and a consistent treatment of tidal truncation. Theoretical estimates for the rate of energy-limited hydrogen escape from giant-planet atmospheres differ by two orders of magnitude, when one holds planetary mass, composition, and irradiation constant. Baraffe et al. (2004, A&A 419, L13-L16) predict the highest rate, based on the theory of Lammer et al. (2003, Astrophys. J. 598, L121-L124). Scaling the theory of Watson et al. (1981, Icarus 48, 150-166) to parameters for a highly-irradiated exoplanet, we find an escape rate ~102 lower than Baraffe's. With the scaled Watson theory we find modest mass loss, occurring early in the history of a hot EGP. In this theory, mass loss including the effect of Roche-lobe overflow becomes significant primarily for masses below a Saturn mass, for semimajor axes = 0.023 AU. This contrasts with the Baraffe model, where hot EGPs are claimed to be remnants of much more massive bodies, originally several times Jupiter and still losing substantial mass fractions at present.

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arXiv2004

Theoretical Radii of Transiting Giant Planets: The Case of OGLE-TR-56b

We calculate radius versus age trajectories for the photometrically-selected transiting extrasolar giant planet, OGLE-TR-56b, and find agreement between theory and observation, without introducing an ad hoc extra source of heat in its core. The fact that the radius of HD209458b seems larger than the radii of the recently discovered OGLE family of extremely close-in transiting planets suggests that HD209458b is anomalous. Nevertheless, our good fit to OGLE-TR-56b bolsters the notion that the generic dependence of transit radii on stellar irradiation, mass, and age is, to within error bars, now quantitatively understood.

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arXiv2004

Effects of Helium Phase Separation on the Evolution of Extrasolar Giant Planets

We build on recent new evolutionary models of Jupiter and Saturn and here extend our calculations to investigate the evolution of extrasolar giant planets of mass 0.15 to 3.0 M_J. Our inhomogeneous thermal history models show that the possible phase separation of helium from liquid metallic hydrogen in the deep interiors of these planets can lead to luminosities ~2 times greater than have been predicted by homogeneous models. For our chosen phase diagram this phase separation will begin to affect the planets' evolution at ~700 Myr for a 0.15 M_J object and ~10 Gyr for a 3.0 M_J object. We show how phase separation affects the luminosity, effective temperature, radii, and atmospheric helium mass fraction as a function of age for planets of various masses, with and without heavy element cores, and with and without the effect of modest stellar irradiation. This phase separation process will likely not affect giant planets within a few AU of their parent star, as these planets will cool to their equilibrium temperatures, determined by stellar heating, before the onset of phase separation. We discuss the detectability of these objects and the likelihood that the energy provided by helium phase separation can change the timescales for formation and settling of ammonia clouds by several Gyr. We discuss how correctly incorporating stellar irradiation into giant planet atmosphere and albedo modeling may lead to a consistent evolutionary history for Jupiter and Saturn.

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arXiv2003

Effects of Helium Phase Separation on the Evolution of Giant Planets

We present the first models of Saturn and Jupiter to couple their evolution to both a radiative-atmosphere grid and to high-pressure phase diagrams of hydrogen with helium. The purpose of these models is to quantify the evolutionary effects of helium phase separation in Saturn's deep interior. We find that prior calculated phase diagrams in which Saturn's interior reaches a region of predicted helium immiscibility do not allow enough energy release to prolong Saturn's cooling to its known age and effective temperature. We explore modifications to published phase diagrams that would lead to greater energy release, and find a modified H-He phase diagram that is physically reasonable, leads to the correct extension of Saturn's cooling, and predicts an atmospheric helium mass fraction Y_atmos in agreement with recent estimates. We then expand our inhomogeneous evolutionary models to show that hypothetical extrasolar giant planets in the 0.15 to 3.0 Jupiter mass range may have T_effs 10-15 K greater than one would predict with models that do not incorporate helium phase separation.

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arXiv2003

On the Indirect Detection of Sodium in the Atmosphere of the Planetary Companion to HD 209458

Using a self-consistent atmosphere code, we construct a new model of the atmosphere of the transiting extrasolar giant planet HD 209458b to investigate the disparity between the observed strength of the sodium absorption feature at 589 nm and the predictions of previous models. For the atmospheric temperature-pressure profile we derive, silicate and iron clouds reside at a pressure of several mbar in the planet's atmosphere. These clouds have significant vertical extent and optical depth due to our slant viewing geometry and lead to increased absorption in bands directly adjacent to the sodium line core. Using a non-LTE sodium ionization model that includes photoionization by stellar UV flux, collisional processes with H_2, and radiative recombination, we show that the ionization depth in the planet's atmosphere reaches ~1/2 mbar at the day/night terminator. Ionization leads to a slight weakening of the sodium feature. We present our baseline model, including ionization and clouds, which falls near the observational error bars. The sensitivity of our conclusions to the derived atmospheric temperature-pressure profile is discussed.

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arXiv2001

Theory of Extrasolar Giant Planet Transits

We present a synthesis of physical effects influencing the observed lightcurve of an extrasolar giant planet (EGP) transiting its host star. The synthesis includes a treatment of Rayleigh scattering, cloud scattering, refraction, and molecular absorption of starlight in the EGP atmosphere. Of these effects, molecular absorption dominates in determining the transit-derived radius $R$. Using a generic model for the atmosphere of EGP HD209458b, we perform a fit to the best available transit lightcurve data, and infer that this planet has a radius at a pressure of 1 bar, $R_1$, equal to 94430 km. We predict that $R$ will be a function of wavelength of observation, with a robust prediction of variations of $\pm 1$% at infrared wavelengths where H$_2$O opacity in the high EGP atmosphere dominates.

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