William B Hubbard

Interests

Teaching

Upper division and graduate courses in planetary physics

Research

Physics of planetary interiorsExoplanetsEvolution of jovian planetsStellar occultations by planetary bodies

Courses

No activities entered.

Scholarly Contributions

Journals/Publications

• {Hubbard}, W., , B. (2016). A Preliminary Jupiter Model. \apj, 820, 80.
• {Kaspi}, Y., {Davighi}, J., {Galanti}, E., , W. (2016). The gravitational signature of internal flows in giant planets: Comparing the thermal wind approach with barotropic potential-surface methods. \icarus, 276, 170-181.
• {Militzer}, B., {Soubiran}, F., {Wahl}, S., , W. (2016). Understanding Jupiter's interior. Journal of Geophysical Research (Planets), 121, 1552-1572.
• {Wahl}, S., {Hubbard}, W., , B. (2016). Tidal Response of Preliminary Jupiter Model. \apj, 831, 14.
• {Wisdom}, J., , W. (2016). Differential rotation in Jupiter: A comparison of methods. \icarus, 267, 315-322.
• {Kaspi}, Y., {Galanti}, E., {Hubbard}, W., , J. (2015). "{The Juno and Cassini gravity measurements: probing the interior dynamics of Jupiter and Saturn}". European Planetary Science Congress 2015, held 27 September - 2 October, 2015 in Nantes, France, Online at http://meetingorganizer.copernicus.org/EPSC2015, id.EPSC2015-509, 10, EPSC2015-509.
• Hubbard, W. B., Schubert, G., Kong, D., & Zhang, K. (2014). On the Convergence of the Theory of Figures. Icarus, 242, 138-141.
• {Murphy}, N., {Jefferies}, S., {Hart}, M., {Hubbard}, W., {Showman}, A., {Hernandez}, G., , L. (2014). "{Planetary Doppler Imaging}". AGU Fall Meeting Abstracts.
• Hubbard, W. B. (2013). Concentric maclaurin spheroid models of rotating liquid planets. Astrophysical Journal, 768(1).
  More info

  Abstract: 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. © 2013. The American Astronomical Society. All rights reserved.
• Militzer, B., & Hubbard, W. B. (2013). Ab initio equation of state for hydrogen-helium mixtures with recalibration of the giant-planet mass-radius relation. Astrophysical Journal, 774(2).
  More info

  Abstract: Using density functional molecular dynamics simulations, we determine the equation of state (EOS) for hydrogen-helium mixtures spanning density-temperature conditions typical of giant-planet interiors, ∼0.2-9 g cm-3 and 1000-80,000 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 EOS table with 391 density-temperature points is constructed and the results are presented in the form of a 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 that 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." © 2013. The American Astronomical Society. All rights reserved.
• Hubbard, W. B. (2012). High-precision Maclaurin-based models of rotating liquid planets. Astrophysical Journal Letters, 756(1).
  More info

  Abstract: We present an efficient numerical self-consistent field method for calculating a gravitational model of a rotating liquid planet to spherical harmonic degree ∼30 and a precision ∼10-12 in the external gravity field. The method's accuracy is validated by comparing results, for Jupiter rotation parameters, with the exact Maclaurin constant-density solution. The method can be generalized to non-constant density. © © 2012. The American Astronomical Society. All rights reserved.
• Hubbard, W. B., Dougherty, M. K., Gautier, D., & Jacobson, R. (2009). The interior of saturn. Saturn from Cassini-Huygens, 75-81.
  More info

  Abstract: A source of uncertainty in Saturn interior models is the lack of a unique rotation rate to be ascribed to the deep (metallic-hydrogen) interior. As a result, models are not uniquely constrained by measured gravitational multiple coefficients. Further uncertainty is associated with the effect of a multiplicity of rotation periods due to zonal flows of unknown magnitude and depth (and therefore unknown mass). Nevertheless, the inference that Saturn has a large core of mass 15-20 M e (Earth masses) is robust. The equation of state of dense hydrogen-helium mixtures is one area where uncertainty has been much reduced, thanks to new first-principles simulations. However, because there is still uncertainty in Saturn's interior temperature profile, a variety of mantle metallicities and core masses could still fit the constraints, and the question of interior helium separation is still unsettled. © 2009 Springer Science+Business Media B.V.
• Hubbard, W. B., McCarthy, D. W., Kulesa, C. A., Benecchi, S. D., Person, M. J., Elliot, J. L., & Gulbis, A. A. (2009). Buoyancy waves in Pluto's high atmosphere: Implications for stellar occultations. Icarus, 204(1), 284-289.
  More info

  Abstract: 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. © 2009 Elsevier Inc.
• Militzer, B., & Hubbard, W. B. (2009). Comparison of Jupiter interior models derived from first-principles simulations. Astrophysics and Space Science, 322(1-4), 129-133.
  More info

  Abstract: 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.
• Widemann, T., Sicardy, B., Dusser, R., Martinez, C., Beisker, W., Bredner, E., Dunham, D., Maley, P., Lellouch, E., Arlot, J. -., Berthier, J., Colas, F., Hubbard, W. B., Hill, R., Lecacheux, J., Lecampion, J. -., Pau, S., Rapaport, M., Roques, F., , Thuillot, W., et al. (2009). Titania's radius and an upper limit on its atmosphere from the September 8, 2001 stellar occultation. Icarus, 199(2), 458-476.
  More info

  Abstract: On September 8, 2001 around 2 h UT, the largest uranian moon, Titania, occulted Hipparcos star 106829 (alias SAO 164538, a V = 7.2, K0 III star). This was the first-ever observed occultation by this satellite, a rare event as Titania subtends only 0.11 arcsec on the sky. The star's unusual brightness allowed many observers, both amateurs or professionals, to monitor this unique event, providing fifty-seven occultations chords over three continents, all reported here. Selecting the best 27 occultation chords, and assuming a circular limb, we derive Titania's radius: RT = 788.4 ± 0.6 km (1 - σ error bar). This implies a density of ρ = 1.711 ± 0.005 g cm-3 using the value G M = (2.343 ± 0.006) × 1011 m3 s-2 derived by Taylor [Taylor, D.B., 1998. Astron. Astrophys. 330, 362-374]. We do not detect any significant difference between equatorial and polar radii, in the limit req - rpo = - 1.3 ± 2.1 km, in agreement with Voyager limb image retrieval during the 1986 flyby. Titania's offset with respect to the DE405 + URA027 (based on GUST86 theory) ephemeris is derived: Δ αT cos (δT) = - 108 ± 13 mas and Δ δT = - 62 ± 7 mas (ICRF J2000.0 system). Most of this offset is attributable to a Uranus' barycentric offset with respect to DE405, that we estimate to be: Δ αU cos (δU) = - 100 ± 25 mas and Δ δU = - 85 ± 25 mas at the moment of occultation. This offset is confirmed by another Titania stellar occultation observed on August 1st, 2003, which provides an offset of Δ αT cos (δT) = - 127 ± 20 mas and Δ δT = - 97 ± 13 mas for the satellite. The combined ingress and egress data do not show any significant hint for atmospheric refraction, allowing us to set surface pressure limits at the level of 10-20 nbar. More specifically, we find an upper limit of 13 nbar (1 - σ level) at 70 K and 17 nbar at 80 K, for a putative isothermal CO2 atmosphere. We also provide an upper limit of 8 nbar for a possible CH4 atmosphere, and 22 nbar for pure N2, again at the 1 - σ level. We finally constrain the stellar size using the time-resolved star disappearance and reappearance at ingress and egress. We find an angular diameter of 0.54 ± 0.03 mas (corresponding to 7.5 ± 0.4 km projected at Titania). With a distance of 170 ± 25 parsecs, this corresponds to a radius of 9.8 ± 0.2 solar radii for HIP 106829, typical of a K0 III giant. © 2008 Elsevier Inc.
• McCarthy, D. W., Hubbard, W. B., Kulesa, C. A., Benecchi, S. D., Person, M. J., Elliot, J. L., & Gulbis, A. A. (2008). Long-wavelength density fluctuations resolved in Pluto's high atmosphere. Astronomical Journal, 136(4), 1519-1522.
  More info

  Abstract: Near-infrared measurements of the occultation of star P445.3 by Pluto on 2007 March 18 reveal that Pluto's upper atmosphere (200-400 km altitude) is unexpectedly dynamic. At a wavelength of 1.6 μm, numerous vertical fluctuations (8-20 km) of density are detected with unprecedented signal-to-noise ratio. These fluctuations are achromatic, nearly limb-aligned, and fully resolved along a 1000 km path over a pressure range of 0.1-0.7 μbar (0.01 to 0.07 Pa). Vertical wavelength increases with altitude indicating a high-frequency cutoff operating on a broad-band spectrum of buoyancy ("gravity") waves generated deeper in Pluto's atmosphere. © 2008. The American Astronomical Society. All rights reserved.
• Militzer, B., Hubbard, W. B., Vorberger, J., Tamblyn, I., & Bonev, S. A. (2008). A massive core in Jupiter predicted from first-principles simulations. Astrophysical Journal, 687(1 PART 2), L45-L48.
  More info

  Abstract: Hydrogen-helium mixtures at conditions of Jupiter's interior are studied with first-principles computer simu-lations. 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 the standard model for the formation of hydrogen-rich giant planets. Our nominal model has about 4 Earth masses of planetary ices in the H-He-rich mantle, a result that is, within a modeling uncertainty of 6 Earth masses, consistent with abundances measured by the 1995 Galileo entry probe mission, 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 ob-servable effect on the high-order gravity field. © 2008. The American Astronomical Society. All rights reserved. Printed in U.S.A.
• Militzer, B., Hubbard, W. B., Vorberger, J., Tamblyn, I., & Bonev, S. A. (2008). A massive core in Jupiter predicted from first-principles simulations. Astrophysical Journal, 688(1 PART 2), L45-L48.
  More info

  Abstract: Hydrogen-helium mixtures at conditions of Jupiter's interior are studied with first-principles computer simu-lations. 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 the standard model for the formation of hydrogen-rich giant planets. Our nominal model has about 4 Earth masses of planetary ices in the H-He-rich mantle, a result that is, within a modeling uncertainty of 6 Earth masses, consistent with abundances measured by the 1995 Galileo entry probe mission, 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 ob-servable effect on the high-order gravity field. © 2008. The American Astronomical Society.
• Person, M. J., Elliot, J. L., Gulbis, A. A., Zuluaga, C. A., Babcock, B. A., McKay, A. J., Pasachoff, J. M., Souza, S. P., Hubbard, W. B., Kulesa, C. A., McCaarthy, D. W., Benecchi, S. D., Levine, S. E., Bosh, A. S., Ryan, E. V., Ryan, W. H., Meyer, A., Wolf, J., & Hill, J. (2008). Waves in Pluto's upper atmosphere. Astronomical Journal, 136(4), 1510-1518.
  More info

  Abstract: Observations of the 2007 March 18 occultation of the star P445.3 (2UCAC 25823784; R = 15.3) by Pluto were obtained at high time resolution at five sites across the western United States and reduced to produce light curves for each station using standard aperture photometry. Global models of Pluto's upper atmosphere are fitted simultaneously to all resulting light curves. The results of these model fits indicate that the structure of Pluto's upper atmosphere is essentially unchanged since the previous occultation observed in 2006, leading to a well-constrained measurement of the atmospheric half-light radius at 1291 5 km. These results also confirm that the significant increase in atmospheric pressure detected between 1988 and 2002 has ceased. Inversion of the Multiple Mirror Telescope Observatory light curves with unprecedented signal-to-noise ratios reveals significant oscillations in the number density, pressure, and temperature profiles of Pluto's atmosphere. Detailed analysis of this highest resolution light curve indicates that these variations in Pluto's upper atmospheric structure exhibit a previously unseen oscillatory structure with strong correlations of features among locations separated by almost 1200 km in Pluto's atmosphere. Thus, we conclude that these variations are caused by some form of large-scale atmospheric waves. Interpreting these oscillations as Rossby (planetary) waves allows us to establish an upper limit of less than 3 m s -1 for horizontal wind speeds in the sampled region (radius 1340-1460 km) of Pluto's upper atmosphere. © 2008. The American Astronomical Society. All rights reserved.
• Burrows, A., Hubeny, I., Budaj, J., & Hubbard, W. B. (2007). Possible solutions to the radius anomalies of transiting giant planets. Astrophysical Journal, 661(1 I), 502-514.
  More info

  Abstract: We calculate the theoretical evolution of the radii of all 14 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. Although 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. © 2007. The American Astronomical Society. All rights reserved.
• Hubbard, W. B., Hattori, M. F., Burrows, A., & Hubeny, I. (2007). A mass function constraint on extrasolar giant planet evaporation rates. Astrophysical Journal, 658(1 II), L59-L62.
  More info

  Abstract: The observed mass function for all known extrasolar giant planets (EGPs) varies approximately as M-1 for mass M between ∼0.2 Jupiter masses (MJ) and ∼5 MJ. In order to study evaporation effects for highly irradiated EGPs in this mass range, we have constructed an observational mass function for a subset of EGPs in the same mass range but with orbital radii
• Hubbard, W. B., Hattori, M. F., Burrows, A., Hubeny, I., & Sudarsky, D. (2007). Effects of mass loss for highly-irradiated giant planets. Icarus, 187(2), 358-364.
  More info

  Abstract: 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. [Baraffe, I., Selsis, F., Chabrier, G., Barman, T.S., Allard, F., Hauschildt, P.H., Lammer, H., 2004. Astron. Astrophys. 419, L13-L16] predict the highest rate, based on the theory of Lammer et al. [Lammer, H., Selsis, F., Ribas, I., Guinan, E.F., Bauer, S.J., Weiss, W.W., 2003. Astrophys. J. 598, L121-L124]. Scaling the theory of Watson et al. [Watson, A.J., Donahue, T.M., Walker, J.C.G., 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. © 2006 Elsevier Inc. All rights reserved.
• Militzer, B., & Hubbard, W. B. (2007). Implications of shock wave experiments with precompressed materials for giant planet interiors. AIP Conference Proceedings, 955, 1395-1398.
  More info

  Abstract: This work uses density functional molecular dynamics simulations of fluid helium at high pressure to examine how shock wave experiments with precompressed samples can help characterizing the interior of giant planets. In particular, we analyze how large of a precompression is needed to probe a certain depth in a planet's gas envelope. We find that precompressions of up to 0.1, 1.0, 10, or 100 GPa are needed to characterized 2.5, 5.9, 18, to 63% of Jupiter's envelope by mass. © 2007 American Institute of Physics.
• Vorberger, J., Tamblyn, I., Bonev, S. A., Militzer, B., & Hubbard, W. B. (2007). Properties of dense fluid hydrogen and helium and implications for giant gas planets. 34th EPS Conference on Plasma Physics 2007, EPS 2007 - Europhysics Conference Abstracts, 31(1), 219-222.
• Boss, A. P., Butler, R. P., Hubbard, W. B., Ianna, P. A., Kürster, M., Lissauer, J. J., Mayor, M., Meech, K. J., Mignard, F., Penny, A. J., Quirrenbach, A., Tarter, J. C., & Vidal-Madjar, A. (2005). Working group on extrasolar planets. Proceedings of the International Astronomical Union, 1(T26A), 183-186.
• Hubbard, W. B. (2005). Hydrogen EOS at megabar pressures and the search for Jupiter's core. Astrophysics and Space Science, 298(1-2), 129-134.
  More info

  Abstract: The interior structure of Jupiter serves as a benchmark for an entire astrophysical class of liquid-metallic hydrogen-rich objects with masses ranging from ~0.1M J to ~80M J (1M J = Jupiter mass = 1.9e30 g), comprising hydrogen-rich giant planets (mass < 13M J) and brown dwarfs (mass > 13M J but ~ < 80M J), the so-called substellar objects (SSOs). Formation of giant planets may involve nucleated collapse of nebular gas onto a solid, dense core of mass ~0.04M J rather than a stellar-like gravitational instability. Thus, detection of a primordial core in Jupiter is a prime objective for understanding the mode of origin of extrasolar giant planets and other SSOs. A basic method for core detection makes use of direct modeling of Jupiter's external gravitational potential terms in response to rotational and tidal perturbations, and is highly sensitive to the thermodynamics of hydrogen at multi-megabar pressures. The present-day core masses of Jupiter and Saturn may be larger than their primordial core masses due to sedimentation of elements heavier than hydrogen. We show that there is a significant contribution of such sedimented mass to Saturn's core mass. The sedimentation contribution to Jupiter's core mass will be smaller and could be zero. © Springer 2005.
• Burrows, A., Hubeny, I., Hubbard, W. B., Sudarsky, D., & Fortney, J. J. (2004). Theoretical radii of transiting giant planets: The case of OGLE-TR-56b. Astrophysical Journal Letters, 610(1 II), L53-L56.
  More info

  Abstract: 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 HD 209458b seems larger than the radii of the recently discovered OGLE family of extremely close-in transiting planets suggests that HD 209458b 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.
• Fortney, J. J., & Hubbard, W. B. (2004). Effects of helium phase separation on the evolution of extrasolar giant planets. Astrophysical Journal Letters, 608(2 I), 1039-1049.
  More info

  Abstract: 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 0.15MJ-3.0MJ. 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 0.15MJ object and ∼10 Gyr for a 3.0M 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 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 gigayears. 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.
• Hubbard, W. B. (2004). The core problem. Nature, 430(7004), 32-33.
• Young, R. E., Atkinson, D., Atreya, S., Banfield, D., Beebe, R., Bolton, S., Briggs, G., Crisp, D., Cutts, J., Drake, M., Esposito, L., Galal, K., Hubbard, W., Hunten, D., Ingersoll, A., Kerzhanovich, V., Kolawa, E., Laub, B., Fuk, L. i., , Mahaffy, P., et al. (2004). Summary of the Boulder Entry Probe Workshop April 21-22, 2003, Boulder, Colorado, USA. European Space Agency, (Special Publication) ESA SP, 13-20.
  More info

  Abstract: The Solar System Exploration Decadal Survey (SSEDS) identified several high priority Solar System Key Science Questions that should be addressed by entry probes/landers, or that should be addressed simultaneously by both probes/landers and remote sensing types of observations. These Key Science Questions are directly relevant to Goals and Objectives of the NASA Strategic Plan and Office of Space Science Strategic Plan. In this report we define entry probes/landers as spacecraft that sample in-situ a planetary atmosphere, and planetary surface if there is one. The Entry Probe Workshop grew out of a community concern that if entry probes/landers were to be a viable mission option for addressing the overarching questions identified in the SSEDS in the coming 10-15 years, significant resources must be applied to key technology areas immediately. The major science objectives requiring entry probes and the key technology development areas for probes are described.
• Burrows, A., Sudarsky, D., & Hubbard, W. B. (2003). A Theory for the Radius of the Transiting Giant Planet HD 209458B. Astrophysical Journal Letters, 594(1 I), 545-551.
  More info

  Abstract: Using a full frequency-dependent atmosphere code that can incorporate irradiation by a central primary star, we calculate self-consistent boundary conditions for the evolution of the radius of the transiting planet HD 209458b. Using a well-tested extrasolar giant planet evolutionary code, we then calculate the behavior of this planet's radius with age. The measured radius is in fact a transit radius that resides high in HD 209458b's inflated atmosphere. Using our derived atmospheric and interior structures, we find that irradiation plus the proper interpretation of the transit radius can yield a theoretical radius that is within the measured error bars. We conclude that if HD 209458b's true transit radius is at the lower end of the measured range, an extra source of core heating power is not necessary to explain the transit observations.
• Fortney, J. J., & Hubbard, W. B. (2003). Phase separation in giant planets: Inhomogeneous evolution of Saturn. Icarus, 164(1), 228-243.
  More info

  Abstract: We present the first models of Jupiter and Saturn to couple their evolution to both a radiative-atmosphere grid and to high-pressure phase diagrams of hydrogen with helium and other admixtures. 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 propose 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 Yatoms = 0.185, in agreement with recent estimates. We also explore the possibility of internal separation of elements heavier than helium, and find that, alternatively, such separation could prolong Saturn's cooling to its known age and effective temperature under a realistic phase diagram and heavy element abundance (in which case Saturn's Yatoms would be solar but heavier elements would be depleted). In none of these scenarios does Jupiter's interior evolve to any region of helium or heavy-element immiscibility: Jupiter evolves homogeneously to the present day. We discuss the implications of our calculations for Saturn's primordial core mass. © 2003 Elsevier Inc. All rights reserved.
• Fortney, J. J., Sudarsky, D., Hubeny, I., Cooper, C. S., Hubbard, W. B., Burrows, A., & Lunine, J. I. (2003). On the indirect detection of sodium in the atmosphere of the planetary companion to HD 209458. Astrophysical Journal Letters, 589(1 I), 615-622.
  More info

  Abstract: 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 millibars in the planet's atmosphere. These clouds have significant vertical extent and optical depth because of 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 H2, 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.
• Hubbard, W. (2003). Pluto's atmospheric surprise. Nature, 424(6945), 137-138.
  More info

  PMID: 12853938;Abstract: Last year, for the first time in 14 years, an alignment of stars with Pluto created an opportunity to observe the atmosphere of this most remote of planets. Though tenuous, the atmosphere has, remarkably, expanded.
• Raynaud, E., Drossart, P., Matcheva, K., Sicardy, B., Hubbard, W. B., Roques, F., Widemann, T., Gladstone, G. R., Waite, J. H., Nadeau, D., Bastien, P., Doyon, R., Hill, R., Rieke, M. J., & Marley, M. (2003). The 10 October 1999 HIP 9369 occultation by the northern polar region of Jupiter: Ingress and egress lightcurves analysis. Icarus, 162(2), 344-361.
  More info

  Abstract: The occultation of bright star HIP9369 by the northern polar region of Jupiter was observed from four locations in North and South America, providing four data sets for ingress and egress. The inversion of the eight occultation lightcurves provides temperature profiles at different latitudes ranging from 55°N to 73.2°N. We estimate the errors on the profiles due to the uncertainties of the inversion method and compare the value of the temperature at the deepest level probed (∼ 50 μbar) with previous observations. The shape of the temperature gradient profile is found similar to previous investigations of planetary atmospheres with propagating and breaking gravity waves. We analyze the small scale structures in both lightcurves and temperature profiles using the continuous wavelet transform. The calculated power spectra of localized fluctuations in the temperature profiles show slopes close to -3 for all eight profiles. We also isolate and reconstruct the three-dimensional geometry of a single wave mode with vertical and horizontal wavelengths of respectively 3 and 70 km. The identified wave is consistent with the gravity wave regime, with a horizontal phase speed nearly parallel to the planetary meridian. Nevertheless, the dissipation of the corresponding wave in Jupiter's stratosphere should preclude its detection at the observed levels and an acoustic wave cannot be ruled out. © 2003 Elsevier Science (USA). All rights reserved.
• Hubbard, W. B., Burrows, A., & Lunine, J. I. (2002). Theory of giant planets. Annual Review of Astronomy and Astrophysics, 40, 103-136.
  More info

  Abstract: Giant planet research has moved from the study of a handful of solar system objects to that of a class of bodies with dozens of known members. Since the original 1995 discovery of the first extrasolar giant planets (EGPs), the total number of known examples has increased to ∼80 (circa November 2001). Current theoretical studies of giant planets emphasize predicted observable properties, such as luminosity, effective temperature, radius, external gravity field, atmospheric composition, and emergent spectra as a function of mass and age. This review focuses on the general theory of hydrogen-rich giant planets; smaller giant planets with the mass and composition of Uranus and Neptune are not covered. We discuss the status of the theory of the nonideal thermodynamics of hydrogen and hydrogen-helium mixtures under the conditions found in giant-planet interiors, and the experimental constraints on it. We provide an overview of observations of extrasolar giant planets and our own giant planets by which the theory can be validated.
• Burrows, A., Hubbard, W. B., Lunine, J. I., & Liebert, J. (2001). The theory of brown dwarfs and extrasolar giant planets. Reviews of Modern Physics, 73(3), 719-765.
  More info

  Abstract: Straddling the traditional realms of the planets and the stars, objects below the edge of the main sequence have such unique properties, and are being discovered in such quantities, that one can rightly claim that a new field at the interface of planetary science and astronomy is being born. This article extends the previous review of Burrows and Liebert (1993) and describes the essential elements of the theory of brown dwarfs and giant planets. It discusses their evolution, atmospheric composition, and spectra, including the new spectroscopic classes L and T. Particular topics which are important for an understanding of the spectral properties include the effects of condensates, clouds, molecular abundances, and atomic opacities. Moreover, it discusses the distinctive features of these extrasolar giant planets that are irradiated by a central primary, in particular, their reflection spectra, albedos, and transits. Overall, the theory explains the basic systematics of substellar-mass objects over three orders of magnitude in mass and age, and a factor of 30 in temperature.
• Geissler, P. E., Smyth, W. H., McEwen, A. S., Ip, W., Belton, M. J., Johnson, T. V., Ingersoll, A. P., Rages, K., Hubbard, W., & Dessler, A. J. (2001). Morphology and time variability of Io's visible aurora. Journal of Geophysical Research A: Space Physics, 106(A11), 26137-26146.
  More info

  Abstract: Clear-filter imaging of Io during the Galileo nominal and extended missions recorded diffuse auroral emissions in 16 distinct observations taken during 14 separate eclipses over a two year period. These images show that the morphology and time variability of the visible aurora have several similarities to Io's far ultraviolet emissions. The orbital leading hemisphere of Io is consistently brighter than the trailing hemisphere, probably due to a greater concentration of torus electrons in the wake region of the satellite. The locations of the polar limb glow and the bright equatorial glows appear to correlate with Io's System III longitude. Unlike the far ultraviolet emissions, the visible aurorae are enhanced near actively venting volcanic plumes, probably because of molecular emission by SO2. Copyright 2001 by the American Geophysical Union.
• Hubbard, W. B., Fortney, J. J., Lunine, J. I., Burrows, A., Sudarsky, D., & Pinto, P. (2001). Theory of extrasolar giant planet transits. Astrophysical Journal Letters, 560(1 PART 1), 413-419.
  More info

  Abstract: We present a synthesis of physical effects influencing the observed light curve 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 for planetary orbital radii less than a few AU. Using a generic model for the atmosphere of EGP HD 209458b, we perform a fit to the best available transit light-curve data and infer that this planet has a radius at a pressure of 1 bar, R1, equal to 94,430 km, with an uncertainty of ∼500 km arising from plausible uncertainties in the atmospheric temperature profile. We predict that R will be a function of wavelength of observation, with a robust prediction of at least ±1% variations at infrared wavelengths where H2O opacity in the high EGP atmosphere dominates.
• Burrows, A., Guillot, T., Hubbard, W. B., Marley, M. S., Saumon, D., Lunine, J. I., & Sudarsky, D. (2000). On the radii of close-in giant planets. Astrophysical Journal Letters, 534(1 PART 2), L97-L100.
  More info

  Abstract: The recent discovery that the close-in extrasolar giant planet HD 209458b transits its star has provided a first-of-its-kind measurement of the planet's radius and mass. In addition, there is a provocative detection of the light reflected off of the giant planet τ Bootis b. Including the effects of stellar irradiation, we estimate the general behavior of radius/age trajectories for such planets and interpret the large measured radii of HD 209458b and τ Boo b in that context. We find that HD 209458b must be a hydrogen-rich gas giant. Furthermore, the large radius of a close-in gas giant is not due to the thermal expansion of its atmosphere but to the high residual entropy that remains throughout its bulk by dint of its early proximity to a luminous primary. The large stellar flux does not inflate the planet but retards its otherwise inexorable contraction from a more extended configuration at birth. This implies either that such a planet was formed near its current orbital distance or that it migrated in from larger distances (≥0.5 AU), no later than a few times 107 yr of birth.
• Elliot, J. L., Person, M. J., McDonald, S. W., Buie, M. W., Dunham, E. W., Millis, R. L., Nye, R. A., Olkin, C. B., Wasserman, L. H., Young, L. A., Hubbard, W. B., Hill, R., Reitsema, H. J., Pasachoff, J. M., McConochie, T. H., Babcock, B. A., Stone, R. C., & Francis, P. (2000). The Prediction and Observation of the 1997 July 18 Stellar Occultation by Triton: More Evidence for Distortion and Increasing Pressure in Triton's Atmosphere. Icarus, 148(2), 347-369.
  More info

  Abstract: A variety of CCD astrometric data was used to predict the location of the path for the occultation of the star we have denoted "Tr176" by Triton, which occurred on 1997 July 18, and was visible from locations in northern Australia and southern North America. A network of fixed and portable telescopes equipped with high-speed photometric equipment was set up to observe the event, with the following observational goals: (i) mapping the central flash (to establish the global shape of Triton's atmosphere at about 20-km altitude by modeling the detailed shape of the central flash), (ii) obtaining one or more light curves of high signal-to-noise ratio from a large telescope (to accurately determine the thermal structure of Triton's atmosphere), and (iii) obtaining light curves distributed across Triton's disk (to probe the thermal structure of Triton's atmosphere above different areas and to establish the shape of the atmosphereat about 100-km altitude by modeling the half-light surface). Although the large, fixed telescopes proved to be outside of the occultation shadow and observations with some of the portable telescopes were foiled by clouds, light curves were successfully recorded from Brownsville, Texas, and Chillagoe, Queensland. These were combined with data from another group to determine the radius and shape of the half-light surface in Triton's atmosphere and the equivalent-isothermal temperatures at the sub-occultation latitudes on Triton. A circular solution for the half-light surface (projected into Triton's shadow) yielded a radius of 1439±10 km. However, the data are indicative of a global shape more complex than a sphere. Such a figure is most likely caused by strong winds. Light-curve models corresponding to the best fitting circular and elliptical atmospheres were fit to the data. The mean pressure at 1400-km radius (48-km altitude) derived from all of the data was 2.23±0.28 μbar for the circular model and 2.45±0.32 μbar for the elliptical model. These values suggest a global pressure increase at this level since a previous Triton occultation in 1995 August. The mean equivalent-isothermal temperature at 1400 km was 43.6±3.7 K for the circular model and 42.0±3.6 K for the elliptical model. Within their (sometimes large) uncertainties, the equivalent-isothermal temperatures agree for all Triton latitudes probed. © 2000 Academic Press.
• Hubbard, W. B. (1999). Gravitational Signature of Jupiter's Deep Zonal Flows. Icarus, 137(2), 357-359.
  More info

  Abstract: Calculations predict that, if Jupiter's observed zonal flows persist to a depth ~1000 km below the cloud layers (corresponding to a pressure ~10 kbar), they will produce gravity anomalies on the order of a few mgal in high-degree zonal components of the gravitational field, referenced to the field expanded to tenth degree. This signature would be detectable by a low-periapse Jupiter orbiter with a sensitivity to accelerations at the same level as the Galileo orbiter. © 1999 Academic Press.
• Hubbard, W. B., Guillot, T., Marley, M. S., Burrows, A., Lunine, J. I., & Saumon, D. S. (1999). Comparative evolution of Jupiter and Saturn. Planetary and Space Science, 47(10-11), 1175-1182.
  More info

  Abstract: We present evolutionary sequences for Jupiter and Saturn, based on new non-gray model atmospheres, which take into account the evolution of the solar luminosity and partitioning of dense components to deeper layers. The results are used to set limits on the extent to which possible interior phase separation of hydrogen and helium may have progressed in the two planets. When combined with static models constrained by the gravity field, our evolutionary calculations constrain the helium mass fraction in Jupiter to be between 0.20 and 0.27, relative to total hydrogen and helium. This is consistent with the Galileo determination. The helium mass fraction in Saturn's atmosphere lies between 0.11 and 0.21, higher than the Voyager determination. Based on the discrepancy between the Galileo and Voyager results for Jupiter, and our models, we predict that revised observational results for Saturn will yield a higher atmospheric helium mass fraction relative to the Voyager value. © 1999 Elsevier Science Ltd. All rights reserved.
• Liebert, J., & Hubbard, W. B. (1999). Big planets and little stars. Nature, 400(6742), 316-317.
• Sicardy, B., Ferri, F., Roques, F., Lecacheux, J., Pau, S., Brosch, N., Nevo, Y., Hubbard, W. B., Reitsema, H. J., Blanco, C., Carreira, E., Beisker, W., Bittner, C., Bode, H. -., Bruns, M., Denzau, H., Nezel, M., Riedel, E., Struckmann, H., , Appleby, G., et al. (1999). The Structure of Titan's Stratosphere from the 28 Sgr Occultation. Icarus, 142(2), 357-390.
  More info

  Abstract: A dozen lightcurves obtrained during the ground-based observations of the occulation of 28 Sgr by Titan (3 July 1989) are reanalyzed. Profiles of density and temperature between altitude levels z of 290 and 500 km (pressures p from 110 to 1.4 μbar) are derived. A mean number- density scale height of 50.5±1.4 km is found with no significant difference between immersion and emrsion. Two in-version layers are observed at 425 and 450-455 km, respectively (p ~7 μbar and p ~4 μbar), with an increase in temperature of about 10 K in less than Δz=10 km. These layers are visible both at immersion and at emersion, at latitudes ranging from 46°S to 20°N, and are thus global features of the stratosphere. The profiles of temperature gradients exhibit a clear cutoff at the adiabatic lapse rate, indicating that fluctuations lead to marginal convective instabilities. Although ray crossing can also cause an apparent cut-off of the temperature gradients, we estimate it probably does not play an important role in the observed cutoff, at least for the larger structures under study. The vertical power spectra of fluctuations show a general power law behavior, with an exponent close to -3, between vertical wavelengths of ~5 and 50 km. The finite stellar diameter and ray crossings can distort the real spectra, and we can only conclude that the original power spectra have slopes between -2 and -3. The horizontal structure of the atmosphere exhibits typical aspect (horizontal-to-vertical) ratios of 15-45, with a tail in the distribution with values as high as 100-200 for some structures. Finally, the horizontal spectrum of fluxtuations is a power law with an exponent close to -4 (between horizontal wavelengths of ~25 and 250 km), if we assume it is separable from the vertical spectrum. © 1999 Academic Press.
• Trilling, D. E., Benz, W., Guillot, T., Lunine, J. I., Hubbard, W. B., & Burrows, A. (1999). Migration and evolution of extrasolar planets. Physics and Chemistry of the Earth, Part C: Solar, Terrestrial and Planetary Science, 24(5), 553-556.
  More info

  Abstract: Giant planets in circumstellar disks can migrate inward from their initial (formation) positions at several AUs. Inward radial migration of the planet is caused by torques between the planet and the disk; outward radial migration of the planet is caused by torques between the planet and the spinning star, and by torques due to Roche lobe overflow and consequent mass loss from the planet. We present self-consistent numerical considerations of the problem of migrating giant planets by summing torques on planets for various physical parameters of the disk and of planets. We find that Jupiter-mass planets can stably arrive and survive at small heliocentric distances, thus reproducing observed properties of some of the recently discovered extra-solar planets. The range of fates of massive planets is broad, and some perish by losing all their mass onto the central star during Roche lobe overflow, while others survive for the lifetime of the central star. Surviving planets cluster into two groups when examined in terms of final mass and final heliocentric distance: those which have lost mass and those which have not. Some of the observed extrasolar planets fall into each of these two exclusive classes. We also find that there is an inner boundary for planets' final heliocentric distances, caused by tidal torques with the central star. Planets in small orbits are shown to be stable against atmospheric loss.
• Trilling, D. E., Benz, W., Guillot, T., Lunine, J. I., Hubbard, W. B., & Burrows, A. (1998). Orbital evolution and migration of giant planets: modeling extrasolar planets. Astrophysical Journal Letters, 500(1 PART I), 428-439.
  More info

  Abstract: Giant planets in circumstellar disks can migrate inward from their initial (formation) positions. Radial migration is caused by inward torques between the planet and the disk, by outward torques between the planet and the spinning star, and by outward torques due to Roche lobe overflow and consequent mass loss from the planet. We present self-consistent numerical considerations of the problem of migrating giant planets. Summing torques on planets for various physical parameters, we find that Jupiter-mass planets can stably arrive and survive at small heliocentric distances, thus reproducing observed properties of some of the recently discovered extrasolar planets. Inward migration timescales can be approximately equal to or less than disk lifetimes and star spindown timescales. Therefore, the range of fates of massive planets is broad and generally comprises three classes: (I) planets that migrate inward too rapidly and lose all their mass; (II) planets that migrate inward, lose some but not all of their mass, and survive in very small orbits; and (III) planets that do not lose any mass. Some planets in class III do not migrate very far from their formation locations. Our results show that there is a wide range of possible fates for Jupiter-mass planets for both final heliocentric distance and final mass. © 1998. The American Astronomical Society. All rights reserved.
• Burrows, A., Marley, M., Hubbard, W. B., Lunine, J. I., Guillot, T., Saumon, D., Freedman, R., Sudarsky, D., & Sharp, C. (1997). A nongray theory of extrasolar giant planets and brown dwarfs. Astrophysical Journal Letters, 491(2 PART I), 856-875.
  More info

  Abstract: We present the results of a new series of nongray calculations of the atmospheres, spectra, colors, and evolution of extrasolar giant planets (EGPs) and brown dwarfs for effective temperatures below 1300 K. This theory encompasses most of the mass/age parameter space occupied by substellar objects and is the first spectral study down to 100 K. These calculations are in aid of the multitude of searches being conducted or planned around the world for giant planets and brown dwarfs and reveal the exotic nature of the class. Generically, absorption by H2 at longer wavelengths and H2O opacity windows at shorter wavelengths conspire to redistribute flux blueward. Below 1200 K, methane is the dominant carbon bearing molecule and is a universal diagnostic feature of EGP and brown dwarf spectra. We find that the primary bands in which to search are Z (∼1.05 μm), J (∼1.2 μm), H (∼1.6 μm), K (∼2.2 μm), M (∼5 μm), and N (∼10 μm), that enhancements of the emergent flux over blackbody values, in particular in the near infrared, can be by many orders of magnitude, and that the infrared colors of EGPs and brown dwarfs are much bluer than previously believed. In particular, relative to J and H, the K band flux is reduced by CH4 and H2 absorption. Furthermore, we conclude that for Teff's below 1200 K most or all true metals may be sequestered below the photosphere, that an interior radiative zone is a generic feature of substellar objects, and that clouds of H2O and NH3 are formed for Teff's below ∼400 and ∼200 K, respectively. This study is done for solar-metallicity objects in isolation and does not include the effects of stellar insulation. Nevertheless, it is a comprehensive attempt to bridge the gap between the planetary and stellar realms and to develop a nongray theory of objects from 0.3MJ ("Saturn") to 70MJ (∼0.07 M⊙). We find that the detection ranges for brown dwarf/EGP discovery of both ground- and space-based telescopes are larger than previously estimated. © 1997. The American Astronomical Society. All rights reserved.
• Guillot, T., Gautier, D., & Hubbard, W. B. (1997). New constraints on the composition of jupiter from Galileo measurements and interior models. Icarus, 130(2), 534-539.
  More info

  Abstract: Using the helium abundance measured by Galileo in the atmosphere of Jupiter and interior models reproducing the observed external gravitational field, we derive new constraints on the composition and structure of the planet. We conclude that, except for helium which must be more abundant in the metallic interior than in the molecular envelope, Jupiter could be homogeneous (no core) or could have a central dense core up to 12M⊕. The mass fraction of heavy elements is less than 7.5 times the solar value in the metallic envelope and between 1 and 7.2 times solar in the molecular envelope. The total amount of elements other than hydrogen and helium in the planet is between 11 and 45M⊕. © 1997 Academic Press.
• Hubbard, W. B. (1997). Lensing by Triton's atmosphere. Science, 278(5337), 403-404.
  More info

  PMID: 9381144;
• Hubbard, W. B. (1997). Neptune's deep chemistry. Science, 275(5304), 1279-1280.
  More info

  PMID: 9064785;
• Olkin, C. B., Elliot, J. L., Hammel, H. B., Cooray, A. R., McDonald, S. W., Foust, J. A., Bosh, A. S., Buie, M. W., Millis, R. L., Wasserman, L. H., Dunham, E. W., Young, L. A., Howell, R. R., Hubbard, W. B., Hill, R., Marcialis, R. L., McDonald, J. S., Rank, D. M., Holbrook, J. C., & Reitsema, H. J. (1997). The thermal structure of Triton's atmosphere: Results from the 1993 and 1995 occultations. Icarus, 129(1), 178-201.
  More info

  Abstract: This paper presents new results about Triton's atmospheric structure from the analysis of all ground-based stellar occultation data recorded to date, including one single-chord occultation recorded on 1993 July 10 and nine occultation lightcurves from the double-star event on 1995 August 14. These stellar occultation observations made both in the visible and in the infrared have good spatial coverage of Triton, including the first Triton central-flash observations, and are the first data to probe the altitude level 20-100 km on Triton. The small-planet lightcurve model of J. L. Elliot and L. A. Young (1992,Astron. J.103,991-1015) was generalized to include stellar flux refracted by the far limb, and then fitted to the data. Values of the pressure, derived from separate immersion and emersion chords, show no significant trends with latitude, indicating that Triton's atmosphere is spherically symmetric at ~50-km altitude to within the error of the measurements; however, asymmetry observed in the central flash indicates the atmosphere is not homogeneous at the lowest levels probed (~20-km altitude). From the average of the 1995 occultation data, the equivalent-isothermal temperature of the atmosphere is 47 ± 1 K and the atmospheric pressure at 1400-km radius (~50-km altitude) is 1.4 ± 0.1 μbar. Both of these are not consistent with a model based on Voyager UVS and RSS observations in 1989 (D. F. Strobel, X. Zhu, M. E. Summers, and M. H. Stevens, 1996,Icarus120,266-289). The atmospheric temperature from the occultation is 5 K colder than that predicted by the model and the observed pressure is a factor of 1.8 greater than the model. In our opinion, the disagreement in temperature and pressure is probably due to modeling problems at the microbar level, since measurements at this level have not previously been made. Alternatively, the difference could be due to seasonal change in Triton's atmospheric structure. © 1997 Academic Press.
• Burrows, A., Hubbard, W. B., Lunine, J. I., Guillot, T., Saumon, D., Marley, M., & Freedman, R. S. (1996). Theoretical models of extrasolar giant planets. Nuclear Physics B - Proceedings Supplements, 51(2), 76-85.
  More info

  Abstract: The recent discoveries of giant planets around nearby stars has galvanized the planetary science community, astronomers, and the public at large. Since direct detection is now feasible, and is suggested by the recent acquisition of G1229 B, it is crucial for the future of extrasolar planet searches that the fluxes, evolution, and physical structure of objects from Saturn's mass to 15 Juipter masses be theoretically investigated. We discuss our first attempts to explore the characteristics of extrasolar giant planets (EGPs), in aid of both NASA's and ESA's recent plans to search for such planets around nearby stars.
• Bus, S. J., Buie, M. W., Schleicher, D. G., Hubbard, W. B., Marcialis, R. L., Hill, R., Wasserman, L. H., Spencer, J. R., Millis, R. L., Franz, O. G., Bosh, A. S., Dunham, E. W., Ford, C. H., Young, J. W., Elliot, J. L., Meserole, R., Olkin, C. B., McDonald, S. W., Foust, J. A., , Sopata, L. M., et al. (1996). Stellar occultation by 2060 Chiron. Icarus, 123(2), 478-490.
  More info

  Abstract: A 14th magnitude double star was occulted by 2060 Chiron on 1993 November 7. Observations of this event were obtained from five locations in California. An occultation by Chiron's nucleus was recorded at one of these sites, while a possible graze by the nucleus was seen at the next closest location. If this possible graze represents a true detection of the nucleus, Chiron's radius is determined to be 89.6 ± 6.8 km, assuming a circular outline for the shape. If the nucleus was not seen at the second location, Chiron's radius is only constrained as being greater than 90.2 ± 6.5 km. The presence of dust in Chiron's inner coma was also detected in four of the five occultation datasets. Lightcurve features were identified that may be explained by narrow, collimated jets of material, and by a much larger region of dust distributed asymmetrically about Chiron's nucleus. Periodic fluctuations in the dust may have been detected in one of the lightcurves. If this periodicity is real, and is induced as a result of Chiron's rotation, then a minimum expansion velocity for the dust is found to be ∼40 m sec-1. © 1996 Academic Press, Inc.
• Marley, M. S., Saumon, D., Guillot, T., Freedman, R. S., Hubbard, W. B., Burrows, A., & Lunine, J. I. (1996). Atmospheric, evolutionary, and spectral models of the brown dwarf Gliese 229 B. Science, 272(5270), 1919-1920.
  More info

  PMID: 8658164;Abstract: Theoretical spectra and evolutionary models that span the giant planet- brown dwarf continuum have been computed based on the recent discovery of the brown dwarf Gliese 229 B. A flux enhancement in the 4- to 5-micrometer wavelength window is a universal feature from jovian planets to brown dwarfs. Model results confirm the existence of methane and water in the spectrum of Gliese 229 B and indicate that its mass is 30 to 55 jovian masses. Although these calculations focus on Gliese 229 B, they are also meant to guide future searches for extrasolar giant planets and brown dwarfs.
• Saumon, D., Hubbard, W. B., Burrows, A., Guillot, T., Lunine, J. I., & Chabrier, G. (1996). A theory of extrasolar giant planets. Astrophysical Journal Letters, 460(2 PART I), 993-1018.
  More info

  Abstract: We present a broad suite of models of extrasolar giant planets (EGPs), ranging in mass from 0.3 to 15 Jupiter masses. The models predict luminosity (both reflected and emitted) as a function of age, mass, deuterium abundance, and distance from parent stars of various spectral types. We also explore the effects of helium mass fraction, rotation rate, and the presence of a rock-ice core. The models incorporate the most accurate available equation of state for the interior, including a new theory for the enhancement of deuterium fusion by electron screening, which is potentially important in these low-mass objects, The results of our calculations reveal enormous sensitivity of EGPs to the presence of the parent star, particularly for G and earlier spectral types. They also show a strong sensitivity of the flux contrast in the mid-infrared, between parent star and EGP, to the mass and age of the EGPs. We interpret our results in terms of search strategies for ground- and space-based observatories in place or anticipated in the near future. © 1996. The American Astronomical Society. All rights reserved.
• Burrows, A., Saumon, D., Guillot, T., Hubbard, W. B., & Lunine, J. I. (1995). Prospects for detection of extra-solar giant planets by next-generation telescopes. Nature, 375(6529), 299-301.
  More info

  Abstract: THE construction of several large ground-based telescopes1,2 and the anticipated launches of new space-based ones3-5, have prompted renewed interest in the means by which extra-solar planets might be discovered1,6,7-11. The direct detection of light from such a planet would be the most compelling means of discovery, and it may soon be technically feasible1,6. Jupiter has traditionally been used as a benchmark for observability, but extra-solar giant planets could have a wide range of masses and ages12, and could be significantly brighter than Jupiter. Here we present calculations estimating the optical and infrared fluxes of extra-solar giant planets with a range of ages, and demonstrate the conditions under which they will be observable with several new telescopes. Giant planets with masses greater than that of Jupiter, and younger than about 1 billion years, are the best targets, and they should be visible using the generation of telescopes now under construction. © 1995 Nature Publishing Group.
• Elliot, J. L., Olkin, C. B., Dunham, E. W., Ford, C. H., Gilmore, D. K., Kurtz, D., Lazzaro, D., Rank, D. M., Temi, P., Bandyopadhyay, R. M., Barroso, J., Barucci, A., Bosh, A. S., Buie, M. W., Bus, S. J., Dahn, C. C., Foryta, D. W., Hubbard, W. B., Lopes, D. F., , Marcialis, R. L., et al. (1995). Jet-like features near the nucleus of Chiron. Nature, 373(6509), 46-49.
  More info

  Abstract: CONSIDERED as a comet, the object 2060 Chiron is unusual in two respects: it exhibits outbursts at very large distances from the Sun1-3, and its nucleus is much larger than that of any other known comet4,5. It is, however, similar in size to the recently discovered Kuiper-belt objects6 - a population of objects with orbits beyond Neptune, which are a possible source of short-period comets. This has led to the conjecture that Chiron is related to these objects, but its chaotic orbit has brought it much closer to the Sun7. Here we report observations of a recent stellar occultation by Chiron which permit the identification of several features associated with Chiron's coma. The observation of discrete, jet-like features provides evidence that the coma material originates from just a few, small active areas, rather than from uniform sublimation, and that the particles in at least one of these features have radii greater than 0.25 μm. The observations also suggest the presence of material in the plane of Chiron's orbit and are consistent with a gravitationally bound coma. Finally, the present data, and those from a previous occultation8, constrain the radius of Chiron to lie between 83 and 156 km.
• Saumon, D., Bergeron, P., Lunine, J. I., Hubbard, W. B., & Burrows, A. (1994). Cool zero-metallicity stellar atmospheres. Astrophysical Journal Letters, 424(1), 333-344.
  More info

  Abstract: Very low mass stars and brown dwarfs have low effective temperatures and their atmospheric opacities are provided by heavy elements which form a host of strongly absorbing molecules. We present a study of the atmospheres and emergent spectra of these objects in the limiting case of zero metallicity. A grid of atmosphere models is presented, based on updated opacities for H/He mixtures, in particular for the collision-induced absorption by H2 which plays an important role in these atmospheres. The emergent spectra bear little resemblance to the corresponding blackbody emission and become bluer as the effective temperature is lowered. The atmosphere models are coupled with interior calculations to obtain accurate physical and photometric characteristics for the low-mass end of the zero-metallicity main sequence. This provides a useful boundary in the Hertzsprung-Russel diagram to interpret observations of low-metallicity stars.
• Stansberry, J. A., Lunine, J. I., Hubbard, W. B., Yelle, R. V., & Hunten, D. M. (1994). Mirages and the Nature of Pluto's Atmosphere. Icarus, 111(2), 503-513.
  More info

  Abstract: We present model occultation lightcurves demonstrating that a strong thermal inversion layer at the base of Pluto's stratosphere can reproduce the minimum flux measured by the Kuiper Airborne Observatory (KAO) during the 1988 occultation of a star by Pluto. The inversion layer also forms the occultation equivalent of a mirage at a radius of 1198 km, which is capable of hiding tropospheres of significant depth. Pluto's surface lies below 1198 km, its radius depending on the depth of the troposphere. We begin by computing plausible temperature structures for Pluto's lower atmosphere, constrained by a calculation of the temperature of the atmosphere near the surface. We then trace rays from the occulted star through the model atmosphere, computing the resultant bending of the ray. Model light curves are obtained by summing the contribution of individual rays within the shadow of Pluto on Earth. We find that we can reproduce the KAO lightcurve using model atmospheres with a temperature inversion and no haze. We have explored models with tropospheres as deep as 40 km (implying a Pluto radius of 1158 km) that reproduce the suite of occultation data. Deeper tropospheres can be fitted to the data, but the mutual event radius of 1150 km probably provides a lower bound. If Pluto has a shallow or nonexistent troposphere, its density is consistent with formation in the solar nebula with modest water loss due to impact ejection. If the troposphere is relatively deep, implying a smaller radius and larger density, signficant amounts of water loss are required. © 1994 Academic Press. All rights reserved.
• Burrows, A., Hubbard, W. B., Saumon, D., & Lunine, J. I. (1993). An expanded set of brown dwarf and very low mass star models. Astrophysical Journal Letters, 406(1), 158-171.
  More info

  Abstract: We present in this paper updated and improved theoretical models of brown dwarfs and late M dwarfs (VLMs) The evolution and characteristics of objects between 0.01 and 0.2 M⊙ are exhaustively investigated and special emphasis is placed on their properties at early ages (106-108 yr). The dependence on the helium fraction deuterium fraction, and metallicity of the masses, effective temperature and luminosities at the edge of the hydrogen main sequence are calculated. We derive luminosity functions for representative mass functions and compare our predictions to recent cluster data. We show that there are distinctive features in the theoretical luminosity functions that can serve as diagnostics of brown dwarf physics. A zero-metallicity model is presented as a bound to or approximation of a putative extreme halo population. This study is a continuation of that of Burrows Hubbard, & Lunine (1989) and is meant to provide an expanded set of standard stellar models both just above and below the lower main-sequence edge for comparison with the new data in clusters, binaries, and in the field.
• Chabrier, G., Saumon, D., Hubbard, W. B., & Lunine, J. I. (1992). The molecular-metallic transition of hydrogen and the structure of Jupiter and Saturn. Astrophysical Journal Letters, 391(2), 817-826.
  More info

  Abstract: Recently, a new equation of state for hydrogen which predicts a molecular-metallic phase transition at finite temperature has become available. It is combined with a helium equation of state, and the resulting thermodynamic description of H/He mixtures is used to compute interior models of Jupiter and Saturn, subject to the constraints of the measured gravitational harmonics of both planets. We discuss the inferred heavy element abundance distribution in their interiors and the possible consequences on their formation. In particular, the Z-element enhancement and smaller core in Saturn relative to Jupiter, a conclusion of this study, may indicate a depletion of water ice in the Jupiter formation zone. In a companion paper, we investigate the effect of the molecular-metallic phase transition on the thermal evolution of Jupiter, Saturn, and brown dwarfs.
• Saumon, D., Hubbard, W. B., Chabrier, G., & M., H. (1992). The role of the molecular-metallic transition of hydrogen in the evolution of Jupiter, Saturn, and brown dwarfs. Astrophysical Journal Letters, 391(2), 827-831.
  More info

  Abstract: An equation of state for hydrogen which predicts a molecular-metallic phase transition at finite temperatures has become available recently. A companion paper addresses the issue of the internal structures of Jupiter and Saturn, as derived with this new equation of state. Here we study the effect of this phase transition on the cooling histories of these two giant planets and of substellar brown dwarfs. The phase transition alters the present age of Jupiter and of Saturn by a few percent. Interestingly, the cooling of brown dwarfs is most strongly affected at the time when the interior adiabat crosses the critical point of the phase transition.
• Hubbard, W. B., Nellis, W. J., Mitchell, A. C., Holmes, N. C., Limaye, S. S., & Mccandless, P. C. (1991). Interior structure of Neptune: Comparison with Uranus. Science, 253(5020), 648-651.
  More info

  PMID: 17772369;Abstract: Measurements of rotation rates and gravitational harmonics of Neptune made with the Voyager 2 spacecraft allow tighter constraints on models of the planet's interior. Shock measurements of material that may match the composition of Neptune, the so-called planetary "ice," have been carried out to pressures exceeding 200 gigapascals (2 megabars). Comparison of shock data with inferred pressure-density profiles for both Uranus and Neptune shows substantial similarity through most of the mass of both planets. Analysis of the effect of Neptune's strong differential rotation on its gravitational harmonics indicates that differential rotation involves only the outermost few percent of Neptune's mass.
• Podolak, M., Hubbard, W. B., & Stevenson, D. J. (1991). Models of Uranus' interior and magnetic field. Uranus, 29-61.
  More info

  Abstract: Our understanding of Uranus' interior structure comes from the results of theoretical models. In this chapter, the methods for computing such models are reviewed. The various physical assumptions employed are discussed and their strengths and weaknesses are assessed. The accretion theory of the formation of the planets is summarized and the implications for the structure and composition of Uranus are presented. The results of the most recent modeling efforts are then discussed. The implications of these model results are examined for their bearing on three important questions. First, the anomalously low internal heat source of the planet compared to its insolation, second, the strongly tilted dipole of the magnetic field and finally the chemistry of Uranus' atmosphere and deep interior. The implications of these models for theories of the formation of Uranus are discussed. -from Authors
• Hubbard, W. B., Burrows, A., & Lunine, J. I. (1990). The initial mass function for very low mass stars in the Hyades. Astrophysical Journal, 358(2 PART 2), L53-L55.
  More info

  Abstract: We have computed theoretical luminosity functions at various evolutionary ages for stars and substellar objects (brown dwarfs), spanning the mass range 0.03 < M < 0.2 M⊙. These functions constrain the distribution of very low mass objects in a star cluster of known age. In this Letter we compare our calculations with a 1988-1989 survey of faint members of the Hyades cluster by Leggett and Hawkins, a cluster whose age is 6 × 108 yr. The comparison shows that the survey does not reach sufficiently low luminosities to reveal brown dwarfs. We obtain a strong constraint on the initial mass function (IMF) for very low mass stars in the Hyades and infer that its IMF does not increase with decreasing mass for the mass interval investigated here. Our results imply at most a moderate contribution from brown dwarfs to the cluster mass, and to the Galaxy's mass if the Hyades are representative of the Galaxy as a whole.
• Hubbard, W. B., Hunten, D. M., Reitsema, H. J., Brosch, N., Nevo, Y., Carreira, E., Rossi, F., & Wasserman, L. H. (1990). Results for Titan's atmosphere from its occultation of 28 Sagittarii. Nature, 343(6256), 353-355.
  More info

  Abstract: ON 3 July 1989 the bright K giant star 28 Sgr was occulted by Saturn's largest moon, Titan. This event, which was predicted by Wasserman1, offered a unique opportunity to probe Titan's extensive nitrogen-rich atmosphere in an altitude range not investigated by the Voyager 1 spacecraft2,3. Our group observed the occultation from three stations in the Mediterranean area, and here we examine the data set. We derive average mesospheric temperatures of ∼180 K, with evidence for lateral and vertical atmospheric inhomogeneities on scales ranging from ∼10-1,000 km. Our results are consistent with published models4of Titan's mesosphere. © 1990 Nature Publishing Group.
• Hubbard, W. B., Yelle, R. V., & Lunine, J. I. (1990). Nonisothermal Pluto atmosphere models. Icarus, 84(1), 1-11.
  More info

  Abstract: We calculate the thermal profile of a model Pluto atmosphere containing a substantial number fraction of methane molecules, taking into account the heating of the atmosphere by absorption of solar infrared flux and the cooling by conductive transport to the planet's surface. We assume an equilibrium temperature of the high atmosphere equal to 106°K and an atmospheric composition with an appreciable fraction of molecules heavier than methane (such as, perhaps, CO or N2). For surface pressures of a few microbars, we find that an appreciable temperature gradient must exist close to the surface. The predicted stellar occultation lightcurve for such a Pluto atmosphere agrees with observations, suggesting that an inferred Pluto haze layer may not exist. Instead, similar effects on the lightcurve could be produced by the strong temperature gradient near the surface. Our alternative model implies that Pluto's solid surface probably lies in the vicinity of 1180 km from the planet's center and that the normal and tangential optical depth of the atmosphere is quite negligible. We calculate an upper limit to the escape rate for the model atmosphere deduced here and find that the minimum time for depletion of the atmospheric methane inventory is about 30 Earth years. © 1990.
• Marley, M. S., Lunine, J. I., & Hubbard, W. B. (1990). The periodicities in the infrared excess of G29-38: An oscillating brown dwarf?. Astrophysical Journal, 348(1 PART 2), L37-L40.
  More info

  Abstract: We have investigated the oscillatory behavior of brown dwarfs. The observed periodicities in the infrared excess of the white dwarf Giclas 29-38 are consistent with low-degree, intermediate radial order p-mode oscillations of a brown dwarf companion to the white dwarf. These oscillation modes have the correct frequencies, act on observable layers of the atmosphere, and may be excited to sufficient amplitudes to explain the observations.
• Hubbard, W. B., & Marley, M. S. (1989). Optimized Jupiter, Saturn, and Uranus interior models. Icarus, 78(1), 102-118.
  More info

  Abstract: We present models of Jupiter, Saturn, and Uranus which exactly match recent accurate determinations of these planets' gravitational harmonics. The models are computed to third order in the rotational disturbance to the total potential and are based upon a method for inverting the gravitational data. For Jupiter and Saturn, a range of gravity models is calculated to test the possibility of a reduction of density in the outer layers due to helium depletion. The results, which are based upon an improved equation of state for molecular hydrogen, indicate that major helium depletion has not occurred in the outer (molecular hydrogen) layers of Jupiter or Saturn, or if it has, that its effect on the density profile is masked by the presence of other, denser, components. Jupiter is found to be slightly enhanced in heavy elements with respect to solar composition, but the density profile of its hydrogen-rich layers generally agrees rather well with a theoretical profile for solar composition. The deviations from such a profile are more pronounced in the case of Saturn. Uranus models have considerable uncertainty; one successful model resembles the ice-rich model of M. Podolak and R.T. Reynolds (1987, Icarus 70, 31-36), but is fitted to a newer value of J4. Our Uranus model has a substantial enrichment of heavy elements at depth, but little separation of the ice from the rock component. All of the Jovian planets appear to have central cores of non-hydrogen-helium material which are of similar mass (about 10-15 Earth masses). For Jupiter and Saturn, our calculations yield a gravitational harmonic J6 which is in agreement with observation, but suggest that this quantity, along with harmonics of higher degree and order, is likely to be more useful for constraining the nature of fluid currents in outer layers rather than deep static structure. © 1989.
• Hubbard, W. B., Hunten, D. M., Dieters, S. W., Hill, K. M., & Watson, R. D. (1988). Occultation evidence for an atmosphere on Pluto. Nature, 336(6198), 452-454.
  More info

  Abstract: On 9 June 1988, Pluto occulted a 12th magnitude star1. Several observations of the occultation were obtained from Australia, New Zealand, and the south Pacific2 and indicated that the initial decline in stellar flux was gradual, as would be expected if the starlight was defocused by an extended atmosphere around the planet. Here we interpret data obtained from the 1- telescope at the University of Tasmania, Hobart, in terms of a theory for occultation by an atmosphere whose thickness is comparable to the planetary radius. The data can be satisfactorily fitted with a methane atmosphere at plausible pressures and temperatures. The surface pressures inferred from this single chord are uncertain by an order of magnitude, but are consistent with spectroscopic constraints. © 1988 Nature Publishing Group.
• Marley, M. S., & Hubbard, W. B. (1988). Thermodynamics of dense molecular hydrogen-helium mixtures at high pressure. Icarus, 73(3), 536-544.
  More info

  Abstract: Current equations of state of dense molecular hydrogen-helium mixtures are not experimentally verified beyond densities of ∼0.3 g cm-3. We have used effective intermolecular pair potentials derived from recent shock wave experiments on liquid hydrogen (W.J. Nellis, A.C. Mitchell, M. van Thiel, G.J. Devine, R.J. Trainor, and N. Brown 1983, J. Chem. Phys. 79, 1480-1486) and helium (W.J. Nellis, N.C. Holmes, A.C. Mitchell, R.J. Trainor, G.K. Governo, M. Ross, and D.A. Young 1984, Phys. Rev. Lett. 53, 1248-1251) in Monte Carlo simulations of mixtures of hydrogen and helium at densities up to 1.2 g cm-3. A model interaction Helmholtz free energy has been derived which accurately reproduces the results of the Monte Carlo calculations. This free energy also reproduces the experimental data to densities of ∼0.6 g cm-3. The equation of state derived from the free energy expression will be useful in preparing improved interior models of the Jovian planets, especially Saturn. The pressure of the molecular hydrogen to metallic hydrogen presumed first-order phase transition is also calculated. Uncertainties in the rotational and vibrational frequencies of the compressed hydrogen molecule translate into an uncertain transition pressure of 3-5 Mbar. © 1988.
• Hubbard, W. B., Nicholson, P. D., Lellouch, E., Sicardy, B., Brahic, A., Vilas, F., Bouchet, P., McLaren, R. A., Millis, R. L., Wasserman, L. H., Elias, J. H., Matthews, K., McGill, J. D., & Perrier, C. (1987). Oblateness, radius, and mean stratospheric temperature of Neptune from the 1985 August 20 occultation. Icarus, 72(3), 635-646.
  More info

  Abstract: The occultation of a bright (K∼6) infrared star by Neptune revealed a central flash at two stations and provided accurate measurements of the limb position at these and several additional stations. We have fitted this data ensemble with a general model of an oblate atmosphere to deduce the oblateness e and equatorial radius a0 of Neptune at the 1-μbar pressure level, and the position angle pn of the projected spin axis. The results are e=0.0209±0.0014, a0=25269±10 km, pn=20.1°±1°. Parameters derived from fitting to the limb data alone are in excellent agreement with parameters derived from fitting to central flash data alone (E. Lellouch, W.B. Hubbard, B. Sicardy, F. Vilas, and P. Bouchet, 1986, Nature 324, 227-231), and the principal remaining source of uncertainty appears to be the Neptune-centered declination of the Earth at the time of occultation. As an alternative to the methane absorption model proposed by Lellouch et al., we explain an observed reduction in the central flash intensity by a decrease in temperature from 150 to 135°K as the pressure rises from 1 to 400 μbar. Implications of the oblateness results for Neptune interior models are briefly discussed. © 1987.
• Millis, R. L., Wasserman, L. H., Franz, O. G., Nye, R. A., Oliver, R. C., Kreidl, T. J., Jones, S. E., Hubbard, W., Lebofsky, L., Goff, R., Marcialis, R., Sykes, M., Frecker, J., Hunten, D., Zellner, B., Reitsema, H., Schneider, G., Dunham, E., Klavetter, J., , Meech, K., et al. (1987). The size, shape, density, and Albedo of Ceres from its occultation of BD+8°471. Icarus, 72(3), 507-518.
  More info

  Abstract: The occultation of BD+8°471 by Ceres on 13 November 1984 was observed photoelectrically at 13 sites in Mexico, Florida, and the Caribbean. These observations indicate that Ceres is an oblate spheroid having an equatorial radius of 479.6±2.4 km and a polar radius of 453.4±4.5 km. The mean density of this minor planet is 2.7 g/cm3±5%, and its visual geometric albedo is 0.073. While the surface appears globally to be in hydrostatic equilibrium, firm evidence of real limb irregularities is seen in the data. © 1987.
• Hubbard, W. B. (1986). 1981N1: A Neptune Arc?. Science, 231(4743), 1276-1278.
  More info

  Abstract: An object in the vicinity of Neptune detected in 1981 by simultaneous stellar occultation measurements at observatories near Tucson, Arizona, was interpreted as a new Neptune satellite. A reinterpretation suggests that it may have instead been a Neptune arc similar to one observed in 1984. The 1981 object, however, did not occult the star during simultaneous observations at Flagstaff, Arizona. This result constrains possible arc geometries.
• Hubbard, W. B., Brahic, A., Sicardy, B., Elicer, L. -., Roques, F., & Vilas, F. (1986). Occultation detection of a neptunian ring-like arc. Nature, 319(6055), 636-640.
  More info

  Abstract: The apparent closest approach of the star SAO186001 to Neptune was observed photoelectrically on 22 July 1984 at Cerro Tololo Inter-American Observatory. A 32% signal drop lasting about 1.2 s was probably caused by a partially transparent arc of material at a distance of 67,000 km from Neptune. Neptune's arc(s) do not vary smoothly with azimuth, unlike the rings of other jovian planets. © 1986 Nature Publishing Group.
• Lellouch, E., Hubbard, W. B., Sicardy, B., Vilas, F., & Bouchet, P. (1986). OCCULTATION DETERMINATION OF NEPTUNE'S OBLATENESS AND STRATOSPHERIC METHANE MIXING RATIO.. Nature, 324(6094), 227-231.
  More info

  Abstract: The occultation of a star by Neptune on 20 August 1985 was observed at 2. 2 mu m wavelength with telescopes at the European Southern Observatory (ESO) and the Cerro Tololo Inter-American Observatory (CTIO). The detection of a 'central flash' midway between immersion and emersion has allowed the determination of Neptune's oblateness, epsilon , and the atmospheric extinction at 2. 2 mu m, which is related to the stratospheric methane mixing ratio. It is found that epsilon equals (2. 08// minus //0//. //1//8** plus **0**. **1**9) multiplied by 10** minus **2 and, assuming a stratospheric temperature of 120 K, a value of 0. 6% (with an uncertainty of a factor of 10) is inferred for the methane mixing ratio (CH//4/H//2) at 0. 3 mbar. The latter value may indicate supersaturation of methane in Neptune's stratosphere.
• Iglesias, C. A., DeWitt, H. E., Lebowitz, J. L., MacGowan, D., & Hubbard, W. B. (1985). Low-frequency electric microfield distributions in plasmas. Physical Review A, 31(3), 1698-1702.
  More info

  Abstract: We evaluate the low-frequency component electric microfield distribution at a charged point, i.e., the field distribution due to ions, possibly of different species, which interact through an electron-screened potential. The method employed is an adaptation of the adjustable-parameter exponential (APEX) approximation previously developed for the high-frequency component and involves a noninteracting-quasiparticle representation of the electron-screened ions designed to yield the correct second moment of the microfield distribution. The APEX results are compared to Monte Carlo simulations, and we find good agreement. © 1985 The American Physical Society.
• Hubbard, W. B. (1984). INTERIOR STRUCTURE OF URANUS.. NASA Conference Publication, 291-325.
  More info

  Abstract: This paper discusses key measurements which are diagnostic of Uranus' interior structure and evolutionary history, and reviews their present status. Typical interior models have chondritic cores, but have the bulk of their mass in an envelope consisting of an 'ice'-component, principally water. The total amount of free hydrogen in the planet cannot exceed approximately 1-2 earth masses. Measurements of the gravitational moments of Uranus are beginning to be accurate enough to constrain models, but are limited in utility by uncertainty in the rotation period. The outermost planetary layers have a gravitationally significant quantity of denser material ('ice'-component? ) in addition to hydrogen and helium.
• Horedt, G. P., & Hubbard, W. B. (1983). Two-and three-layer models of Uranus. The Moon and the Planets, 29(3), 229-236.
  More info

  Abstract: We present simple two-layer models of Uranus with rocky core and polytropic envelope satisfying exactly the observed mass, radius and the gravitational moments. The models show that the value of the fourth order zonal harmonic is J4 ≲-38×10-6, while J6 ≈ 10-6. More elaborate threelayer models fail to satisfy the observational constraints of the ice/rock ratio and/or of the rotation period. We conclude that three-layer models with uniform chemical composition in each layer may be too restrictive. More realistic models should account for variable chemical composition within each layer. © 1983 D. Reidel Publishing Company.
• Hubbard, W. B., & Horedt, G. P. (1983). Computation of Jupiter interior models from gravitational inversion theory. Icarus, 54(3), 456-465.
  More info

  Abstract: A method for deriving a planetary interior model which exactly satisfies a set of N gravitational constraints is implemented. For Jupiter, recent spacecraft measurements provide the mass, radius at a standard pressure level, rotation law, multipole moments of the internal mass distribution, and constraints on the internal composition and temperature distribution. By appropriate iterations, interior models are found which exactly satisfy these constraints. The models are assumed to have constant chemical composition and constant specific entropy in the hydrogenic envelope. The derived pressure-density relation in the outer envelope depends sensitively on the observational uncertainty in the mass multipole moment J4. Models are not forced to fit the more indirectly derived constraints, which are instead used as consistency checks. For a helium mass fraction in the envelope (Y) equal to 0.20, the inferred pressure at a mass density ≈ 0.2 g/cm3 is about a factor of 2 higher than would be indicated by experimental hydrogen shock compression data in the relevant pressure range of 105 to 106 bar. The inferred pressure distribution is in much better agreement with the shock data for a nominal Y = 0.30 ± 0.05. This value of Y is interpreted in terms of an enhancement in the envelope, by a factor of order 5 over solar abundance, of species primarily consisting of CH4, NH3, and possibly H2O. The same method is applied to Saturn, but existing uncertainties in Saturn's gravitational parameters are still too large to allow useful conclusions about the composition of its envelope. © 1983.
• Hubbard, W. B. (1982). Effects of differential rotation on the gravitational figures of Jupiter and Saturn. Icarus, 52(3), 509-515.
  More info

  Abstract: It is assumed that observed zonal currents in the atmospheres of Jupiter and Saturn correspond to a state of permanent rotation, and that the angular velocity is constant on cylindrical surfaces parallel to the rotation axis. The equation of hydrostatic equilibrium for a rotating planet is solved under these restrictive assumptions, and the effect of the hypothesized rotation state on the planet's gravity harmonics and external shape is investigated. Spacecraft data on zonal currents are used to derive nearly model-independent corrections to the first four zonal gravity harmonic coefficients, which can be used to correct observed gravity harmonics to values appropriate for solid-body rotation. If the assumed rotation state is applicable, then zonal currents lead to measurable topography of isopycnic surfaces with respect to the reference fihure defined by the magnetospheric rotation period and the gravity harmonics. The amplitude of the topography is on the order of 5 km for Jupiter and 60 km for Saturn. © 1982.
• Hubbard, W. B. (1982). Structure of the Martian atmosphere from ε-Gem occultation observations. Advances in Space Research, 2(2), 103-106.
  More info

  Abstract: We have collected information about Martian atmospheric scale heights derived from observations of the occultation of ε{lunate} Gem by Mars on April 8, 1976. The observations give data in the altitude range ∼50 to 80 km. A rough, unweighted average of results so far available yields a temperature of ∼165°K. Excursions of ∼±40°K about this mean may be present as a function of both altitude and areographic coordinates. © 1982.
• Reitsema, H. J., Hubbard, W. B., Lebofsky, L. A., & Tholen, D. J. (1982). Occultation by a possible third satellite of Neptune. Science, 215(4530), 289-291.
  More info

  Abstract: The 24 May 1981 close approach of Neptune to an uncataloged star was photoelectrically monitored from two observatories separated by 6 kilometers parallel to the occultation track. An 8.1-second drop in signal, recorded simultaneously at both sites, is interpreted as resulting from the passage of a third satellite of Neptune in front of the star. From the duration of the event, the derived minimum diameter for an object sharing Neptune's motion is 180 kilometers. If the object was in Neptune's equatorial plane and there are no significant errors in the prediction ephemeris, the object was located at a distance of 3 Neptune radii from Neptune's center. Copyright © 1982 AAAS.
• Hubbard, W. B. (1981). Interiors of the giant planets. Science, 214(4517), 145-149.
  More info

  Abstract: Unlike the terrestrial planets, the giant planets-Jupiter, Saturn, Uranus, and Neptune-have retained large amounts of the carbon, nitrogen, and oxygen compounds that were present in their zone of formation. A smaller fraction of the available hydrogen and helium was retained. The distribution and relative amounts of these components in the interiors of the Jovian planets can be inferred from theoretical and experimental data on equations of state and from the planets' hydrostatic equilibrium response to rotation. Copyright © 1981 AAAS.
• Hubbard, W. B., & Reitsema, H. J. (1981). SCINTILLATION AT TWO OPTICAL FREQUENCIES.. Applied Optics, 20(18), 3227-3232.
  More info

  Abstract: Stellar scintillation data were obtained on a single night at a variety of zenith distances and azimuths, using a photon-counting photometer recording at 100 Hz simultaneously at wavelengths of 0. 475 mu m and 0. 870 mu m. Orientable apertures of 42-cm diam separated by 1 m were used to establish the average upper atmosphere wind direction and velocity. Dispersion in the earth's atmosphere separates the average optical paths at the two wavelengths, enabling a reconstruction of the spatial cross-correlation function for scintillations to be made, independent of assumptions about differential fluid motions. Although there is evidence of a complicated velocity field, scintillation power was predominantly produced by levels at pressures of 130 plus or minus 30 mbar. The data are not grossly inconsistent with layers of isotropic Kolmogorov turbulence, but there is some evidence for deviation from the Kolmogorov spectral index and/or anisotropy.
• Ross, M., DeWitt, H. E., & Hubbard, W. B. (1981). Monte Carlo and perturbation-theory calculations for liquid metals. Physical Review A, 24(2), 1016-1020.
  More info

  Abstract: Monte Carlo calculations of the thermodynamic properties of a pseudopotential metal fluid, approximating lithium, were carried out over a wide range of temperatures and densities. The calculations were compared with the predictions of variational perturbation theories employing the hard sphere, soft sphere, and the one component plasma (OCP) as reference systems. The OCP predictions are in better agreement with Monte Carlo pressures, but are comparable for energies. The OCP reference system has the lower Helmholtz free energy at all points studied. © 1981 The American Physical Society.
• Anderson, J. D., Null, G. W., Biller, E. D., Wong, S. K., Hubbard, W. B., & MacFarlane, J. J. (1980). Pioneer Saturn celestial mechanics experiment. Science, 207(4429), 449-453.
  More info

  Abstract: During the Pioneer Saturn encounter, a continuous round-trip radio link at S band (∼2.2 gigahertz) was maintained between stations of the Deep Space Network and the spacecraft. From an analysis of the Doppler shift in the radio carrier frequency, it was possible to determine a number of gravitational effects on the trajectory. Gravitational moments (J2 and J 4) for Saturn have been determined from preliminary analysis, and preliminary mass values have been determined for the Saturn satellites Rhea, Iapetus, and Titan. For all three satellites the densities are low, consistent with the compositions of ices. The rings have not been detected in the Doppler data, and hence the best preliminary estimate of their total mass is zero with a standard error of 3×10-6 Saturn mass. New theoretical calculations for the Saturn interior are described which use the latest observational data, including Pioneer Saturn, and state-of-the-art physics for the internal composition. Probably liquid H2O and possibly NH 3 and CH4 are primarily confined in Saturn to the vicinity of a core of approximately 15 to 20 Earth masses. There is a slight indication that helium may likewise be fractionated to the central regions. Copyright © 1980 AAAS.
• Hubbard, W. B. (1980). INTRINSIC LUMINOSITIES OF THE JOVIAN PLANETS.. Reviews of geophysics and space physics, 18(1), 1-9.
  More info

  Abstract: The author reviews available data and theories on the size and nature of interior power sources in the Jovian planets. Broad band infrared measurements indicate that Jupiter and Saturn have interior heat fluxes about 150 and 50 times larger, respectively, than the terrestrial value. While Neptune has a modest heat flux ( similar 5 times terrestrial), it is clearly detected by earth-based measurements. Only Uranus seems to lack a detectable interior heat flow. Various models, ranging from simple cooling to gravitational layering to radioactivity, are discussed. Current evidence seems to favor a cooling model in which the escape of heat is regulated by the atmosphere. This model seems capable of explaining phenomena such as the uniformity of effective temperature over Jupiter's surface and the different emission rates of Uranus and Neptune. In such a model the heat radiated from the atmosphere may derive from depletion of a thermal reservoir in the interior, or it may derive from separation of chemical elements during formation of a core. Calculations indicate that in the earlier stages of cooling, Jupiter and Saturn may have more homogeneous abundances of hydrogen and helium and radiate energy derived from simple cooling. At a subsequent phase (which may be later than the present time), hydrogen and helium will separate and supply gravitational energy. Either model is consistent with a hot, high-luminosity origin for the Jovian planets.
• Hubbard, W. B., & MacFarlane, J. J. (1980). Theoretical predictions of deuterium abundances in the Jovian planets. Icarus, 44(3), 676-682.
  More info

  Abstract: Using current concepts for the origin of the Jovian planets and current constraints on their interior structure, we argue that the presence of large amounts of "ice" (H2O, CH4, and NH3) in Uranus and Neptune indicates temperatures low enough to condense these species at the time Uranus and Neptune formed. Yet such low temperatures imply orders-of-magnetude fractionation effects for deuterium into the "ice" component if isotopic equilibration can occur. Our models thus imply that Uranus and Neptune should have a D/H ratio at least four times primordial, contrary to observation for Uranus. We find that the Jovian and Saturnian D/H should be close to primordial regardless of formation scenario. The Uranus anomaly could indicate that there was a strong initial radial gradient in D/H in the primordial solar nebula, or that Uranus is so inactive that no significant mixing of its interior has occurred over the age of the solar system. Observation of Neptune's atmospheric D/H may help to resolve the problem. © 1980.
• Hubbard, W. B. (1979). On the atmosphere with exponential turbulence. Icarus, 39(3), 473-478.
  More info

  Abstract: We present an exact calculation for the photon-average bending angle and intensity produced during occultation of a point source by an isothermal atmosphere with an exponential height dependence of turbulent power. The calculation is performed via an expansion in powers of the gradients of average refractivity and turbulent power. Conditions for the validity of the expansion are discussed. We compare results with other expressions, for the same distribution of refractivity, recently presented by V. R. Eshleman and B. S. Haugstad. Discrepancies are noted. Certain properties of photon averages, which may be of importance for the reduction of occultation data, are discussed. © 1979.
• Hubbard, W. B. (1978). Comparative thermal evolution of Uranus and Neptune. Icarus, 35(2), 177-181.
  More info

  Abstract: We extend a Jovian convective-cooling model to Uranus and Neptune. The model assumes that efficient interior convection prevails, so that escape of interior heat is governed by the radiative properties of the atmosphere. A comparison of the thermal evolution of Uranus and Neptune indicates that the larger amount of solar radiation absorbed in Uranus' atmosphere tends to differentially suppress the escape of interior heat. The model is shown to be consistent with recent infrared observations of the thermal balance of Uranus and Neptune, and with the presumed age of these planets. © 1978.
• Hubbard, W. B., & Anderson, J. D. (1978). Possible flyby measurements of Galilean satellite interior structure. Icarus, 33(2), 336-341.
  More info

  Abstract: Flyby encounters of the Galilean satellites from a Jupiter orbiter spacecraft could yield information about the second-degree gravity harmonics of these satellites. We have calculated the expected values of these harmonics for a range of plausible interior models in hydrostatic equilibrium. Because the satellites respond to comparable perturbations from rotation and tides, an independent test of hydrostatic equilibrium is feasible. For Io and Ganymede, the expected measurement accuracy from a nominal encounter should make possible an excellent discrimination from the ensemble of interior models. For Europa, a qualitative distinction between near-uniform and centrally condensed models seems feasible. Only for Callisto is the proposed experiment of marginal value. © 1978.
• Hubbard, W. B., Jokipii, J. R., & Wilking, B. A. (1978). Stellar Occultations by turbulent planetary atmospheres: A wave-optical theory including a finite scale height. Icarus, 34(2), 374-395.
  More info

  Abstract: A generalized wave-optical theory of stellar occultations by a turbulent planetary atmosphere is developed. The finite scale height of the atmosphere is retained for the first time. It is found that the finite scale height of the atmosphere affects the scintillations observed during the occultation in a number of ways which are most easily understood in terms of an effective Fresnel scale. We demonstrate the validity of a phase-changing screen approximation for occultation by a turbulent atmosphere in parameter ranges of general interest. Using this approximation various statistical properties of the fluctuating intensity are calculated explicitly. We present expressions for the total scintillation power, correlation function of the intensity, the cross-correlation at two frequencies, and its application to refractivity determinations. All of these expressions are given as a function of occultation depth and of parameters of the mean atmosphere and turbulence. © 1978.
• Hubbard, W. B. (1977). The Jovian surface condition and cooling rate. Icarus, 30(2), 305-310.
  More info

  Abstract: A theory which is almost fully analytic is used to investigate Jupiter's cooling rate. We find that a simple model of contraction with adiabatic interior structure gives a total cooling time to the present which is in good agreement with the age of the solar system. The interplay between the surface condition and the cooling rate is exhibited and discussed. The current rate of change of the effective temperature is calculated to be -1°K/0.145×109 yr. Discrepancies with fully numerical investigations of the Jovian age and cooling rate are noted. © 1977.
• Hubbard, W. B. (1977). Wave optics of the central spot in planetary occultations. Nature, 268(5615), 34-35.
  More info

  Abstract: THE detection of a bright central spot1 during the occultation of ε Geminorum by Mars2 has demonstrated that an exponential planetary atmosphere can act as a lens with somewhat peculiar properties. In the course of a general study of certain wave-optical phenomena in planetary occultations, we have carried out an investigation into the diffraction nature of the central spot, which has not been previously considered in occultation theory. Some of the results are presented in this letter, along with implications for possible future experiments. © 1977 Nature Publishing Group.
• Hubbard, W. B. (1977). de Sitter's theory flattens Jupiter. Icarus, 30(2), 311-313.
  More info

  Abstract: A correction to the Galilean satellite ephemerides indicated by the observations of 1973 mutual eclipse and occultation phenomena acts to reduce significantly the discrepancy between the dynamical oblateness of Jupiter measured by spacecraft and the optical oblateness measured by the 1971 β Sco occultations. © 1977.
• Hubbard, W. B., & Jokipii, J. R. (1977). Stellar occultations by turbulent planetary atmospheres: A heuristic scattering model. Icarus, 30(3), 531-536.
  More info

  Abstract: A model of ray refraction by an isothermal atmosphere with a scattering screen at the center of bending is used to generate analytic results which simulate the effects of real atmospheric turbulence on occultations. Calculations are carried through for scattering which is constant with height and for exponential height dependence. The effect of the scattering is to bias the the mean intensity of the occulted source, and hence systematically to distort bending angles and height differences obtained from inversion of the intensity data. However, the effect is of order 〈δε{lunate}2〉/ε{lunate}2 for either model, where 〈δε{lunate}2〉 is the mean square scattering angle and ε{lunate} is the average bending angle. The effect turns out to be small for plausible turbulence, since 〈δε{lunate}2〉/gfe2 is of approximately the same order as the relative mean square density fluctuation. Thus the random effects of turbulence are unlikely to be a source of large systematic error in occultations, provided that the data can be meaningfully averaged either temporally or over a number of occultation events. © 1977.
• Hubbard, W. B., Coyne, G. V., Gehrels, T., Smith, B. A., & Zellner, B. H. (1977). Observations of Uranus occultation events. Nature, 268(5615), 33-34.
  More info

  Abstract: A PRELIMINARY analysis of photometric data obtained by Zellner at the Perth Observatory during the Uranus appulse to SA0 158687 on 10 March 1977 shows at least three brief occultation events which appear to coincide with portions of a Uranian ring system reported by Elliot et al.1. No occultation by Uranus itself occurred at Perth. Our group also obtained an observation by Smith with a portable telescope from the vicinity of Mauritius. The data are marginal due to variable transparency but it seems clear that there was no occultation by Uranus which diminished the stellar intensity by more than 50%. No ring events were observed from Mauritius due to the onset of a rain shower. Our observations at Perth, along with the null result from Mauritius, can be combined with other available data2-5 to improve the deduction of the geometry of the ring features, and to obtain a preliminary upper limit to the radius of Uranus. © 1977 Nature Publishing Group.
• Jokipii, J. R., & Hubbard, W. B. (1977). Stellar occultations by turbulent planetary atmospheres: The Beta Scorpii events. Icarus, 30(3), 537-550.
  More info

  Abstract: Possible manifestationsof turbulent scattering in the 1971 Beta Scorpii occultations by Jupiter are critically examined. Lack of detailed correlation between light curves observed at 60-km separations on the Jovian limb argues against a detailed layering hypothesis. An approximate calculation shows that the observed features of the light cuves can be explained in terms of a model for which "spikes" are scintillations caused by Jovian atmospheric turbulence. A significant number of paired spikes are a consequence of the model if the occulted star is binary with an appropriate orientation. The statistical properties of spikes for Beta Scorpii A and C are predicted from Rytov theory for Kolmogorov turbulence and compared with the available observations. Finally, we discuss the effects of turbulent scattering on the temperature profile which is obtained by averaging over the effect of the spikes. © 1977.
• Hubbard, W. B. (1976). Ray propagation in oblate atmospheres. Icarus, 27(3), 387-389.
  More info

  Abstract: We evaluate the departures from Bouguer's law for the case of an oblate atmosphere. We show that, to lowest order, the plane of refraction is defined by the normal to the atmosphere at closest approach. In next order, however, the ray path is "warped" by the oblateness, which changes slightly the plane of refraction. © 1976.
• Slattery, W. L., & Hubbard, W. B. (1976). Thermodynamics of a solar mixture of molecular hydrogen and helium at high pressure. Icarus, 29(2), 187-192.
  More info

  Abstract: The thermodynamic properties of a model molecular hydrogen and helium mixture are calculated in the strongly interacting region of 0.005 to 0.3 cm-3 for a range of temperatures that are of interest for the envelopes of the Jovian planets. Computed adiabats fit the gravity data and boundary conditions from model atmospheres of Jupiter. © 1976.
• Hubbard, W. B. (1975). Comparison of geometrical effects in radio and stellar occultations. Icarus, 26(2), 175-177.
  More info

  Abstract: An important difference between the radio and stellar occultation techniques for probing planetary atmospheres is that a crucial equation relating refraction angle with ray impact parameter is solved in opposite directions in the two techniques. The solution is tolerant of small geometrical errors for stellar occultations but, unfortunately, not for radio occultations. © 1975.
• Hubbard, W. B. (1975). Interior structure of Uranus. Icarus, 24(3), 285-291.
  More info

  Abstract: A mission to Uranus will permit definitive measurements of fundamental parameters of Uranus' interior structure, such as radius, rotation, magnetic moment, atmospheric composition, and gravitational harmonics. We briefly discuss the utility of such data for constraining interior models. © 1975.
• Hubbard, W. B. (1974). Inversion of gravity data for giant planets. Icarus, 21(2), 157-165.
  More info

  Abstract: We derive approximate inversion formulas which permit the calculation of the density on an interior level surface of a rotating planet from observed values of J2, J4, and J6, given that the planet is in hydrostatic equilibrium and that the density near the surface varies smoothly with depth. The method gives information about a level surface which is, respectively, about 3000 km (Jupiter), 3600 km (Saturn), 1000 km (Uranus), and 500 km (Neptune) below the mean surface of the planet. The value of J4 gives the density gradient on this surface, while J6 depends on the second derivative of the density with depth as well. However, J6 serves primarily as a check on the inversion model since its value is mainly determined by J4. We discuss the application of the method in determining abundances. © 1974.
• Hubbard, W. B. (1974). Tides in the giant planets. Icarus, 23(1), 42-50.
  More info

  Abstract: Goldreich and Soter's (Icarus 5, 375-389, 1966) discussion of tidal dissipation in the Jovian planets is reexamined for planetary models which possess an appreciable internal heat source. The tidal torque produced in a fully liquid planet is calculated as a function of the average viscosity in the interior. Turbulent viscosity, which is produced by the convection of internal heat to the surface, seems to be capable of producing small (∼ few per cent) changes in the orbits of the innermost satellites of Jupiter over the age of the solar system. The basic regularity of many of the giant planet satellite systems is probably due to other, perhaps primordial, causes. © 1974.
• Hubbard, W. B., Trubitsyn, V. P., & Zharkov, V. N. (1974). Significance of gravitational moments for interior structure of Jupiter and Saturn. Icarus, 21(2), 147-151.
  More info

  Abstract: We present the case for liquid models of Jupiter and Saturn. We then discuss the information which can be obtained about their interior structure from a knowledge of their gravitational moments, and we discuss the nature of presently available data and data which will be necessary to fully exploit future results. © 1974.
• Hubbard, W. B. (1973). The significance of atmospheric measurements for interior models of the major planets. Space Science Reviews, 14(3-4), 424-432.
  More info

  Abstract: We present a discussion of proposed models for interior processes in Jupiter and Saturn, and discuss how these models can be tested by atmospheric measurements by space vehicles. The importance of measurements at Uranus and Neptune is also discussed. © 1973 D. Reidel Publishing Company.
• Hubbard, W. B., & Smoluchowski, R. (1973). Structure of Jupiter and Saturn. Space Science Reviews, 14(5), 599-662.
  More info

  Abstract: Understanding of the planetary interiors depends upon our knowledge of the equations of state and of the transport properties of matter at high pressures and temperatures. The present status of this knowledge in relation to hydrogen and helium is discussed in detail including electrical and thermal conductivity, viscosity, diffusivity, etc. On this basis the various possible models of the internal structure of Jupiter and of Saturn are presented and their agreement with observational constraints such as the multipole gravitational coefficients analyzed. Relevance of planetary magnetic fields, basic atmospheric information and the Great Red Spot of Jupiter to the models of the interiors are discussed. © 1973 D. Reidel Publishing Company.
• Hubbard, W. B. (1972). Thermodynamics of hydrogen-helium mixtures at high pressure and finite temperature. Physics of the Earth and Planetary Interiors, 6(1-3), 65-68.
  More info

  Abstract: We review a technique for calculating thermodynamic quantities for mixtures of light elements at high pressure, in the metallic state. Ensemble averages are calculated with Monte Carlo techniques and periodic boundary conditions. Interparticle potentials are assumed to be coulombic, screened by the electrons in dielectric function theory. This method is quantitatively accurate for alloys at pressures above about 10 Mbar. An alloy of equal parts hydrogen and helium by mass appears to remain liquid and mixed for temperatures above about 3000 K, at pressures of about 15 Mbar. The additive volume law is satisfied to within about 10%, but the Grüneisen equation of state gives poor results. A calculation at 1300 K shows evidence of a hydrogen-helium phase separation. © 1972.
• Taylor, G. E., O'Leary, B., Flandern, T. V., Bartholdi, P., Owen, F., Hubbard, W. B., Smith, B. A., Smith, S. A., Fallon, F. W., Devinney, E. J., & Oliver, J. (1971). Occultation of beta Scorpii C by Io on May 14, 1971 [3]. Nature, 234(5329), 405-406.

Proceedings Publications

• {Wahl}, S., {Hubbard}, W., , B. (2016, oct). Tidal Response of Jupiter and Saturn from CMS calculationsTidal Response of Jupiter and Saturn from CMS calculations. In AAS/Division for Planetary Sciences Meeting Abstracts, 48.
• {Davighi}, J., {Kaspi}, Y., {Galanti}, E., , W. (2015, nov). "{The gravity signature of atmospheric dynamics on giant planets: comparing the potential-theory and thermal-wind approaches}". In AAS/Division for Planetary Sciences Meeting Abstracts, 47.
• {Hubbard}, W. (2014, nov). "{Validity of the ''Laplace Swindle'' in Calculation of Giant-Planet Gravity Fields}". In AAS/Division for Planetary Sciences Meeting Abstracts, 46.

Poster Presentations

• Kaspi, Y., Showman, A., Hubbard, W., Aharonson, O., & Helled, R. (2014, Fall). Atmospheric confinement of jet streams on Uranus and Neptune. American Astronomical Society, DPS meeting #45.
  More info

  #312.22
• Hubbard, W. (2013, Fall). High-Precision Simulation of the Gravity Field of Rapidly-Rotating Barotropes in Hydrostatic Equilibrium. American Geophysical Union.
  More info

  Abstract #: P21C-1745
• Hubbard, W. (2013, Fall). Implications of a New Ab-Initio H-He Equation of State for Giant Planet Structure. American Geophysical Union.
  More info

  Abstract #: MR14A-08
• Hubbard, W. B. (2013, May). Juno: revealing Jupiter’s depths. SpaceFest V. Tucson, AZ.
• Kaspi, Y., Galanti, E., Hubbard, W., & Davighi, J. (2013, Fall). Estimating the depth of the zonal jet streams on Jupiter and Saturn through inversion of gravity measurements by Juno and Cassini. American Geophysical Union.
  More info

  Abstract #: P21C-1740
• Militzer, B., & Hubbard, W. (2013, Fall). Ab Initio Equation of State Calculations for Jupiter's Interior. American Geophysical Union.
  More info

  Abstract #: P11B-05
• Hubbard, W. B. (2012, December). Juno and the Interior of Jupiter. Exploring Giant Planets on NIF: Workshop. Livermore, CA.
• Hubbard, W. B. (2012, July). The Juno mission to Jupiter. Big Bend AstronomersMcDonald Observatory.
• Hubbard, W. B. (2012, July). The Juno mission to Jupiter. Tucson Amateur Astronomers Assoc. Tucson, AZ.
• Hubbard, W. B. (2012, June). The Juno mission to Jupiter. SpaceFest IV. Tucson, AZ.

Others

• Hubbard, W. B. (2013, Fall). Blitzer Award for Excellence in the Teaching of Physics and Related Sciences.
• Hubbard, W. B. (2012, Fall). NASA Group Achievement Award for Juno proposal.