William B. Hubbard

A Nongray Theory of Extrasolar Giant Planets and Brown Dwarfs

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 ?m), J (~1.2 ?m), H (~1.6 ?m), K (~2.2 ?m), M (~5 ?m), and N (~10 ?m), 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 Teffs 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 Teffs 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.

The theory of brown dwarfs and extrasolar giant planets

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.An inking roller assembly wherein the rollers are driven and there being an impositive driving connection between the driven roller and the driving shaft therefor and the roller is driven by impact of the imprinting head and the roller as the roller is struck by the imprinting head, the rollers also being associated with pumping rollers and smoothing rollers for properly distributing the ink and the inking rollers having novel end plates which return the excess ink into the roller. The imprinting head intermittently impacts against limited areas of the inking roller periphery and then moves out of contact with the inking roller to cause the same to thereafter roll freely and thus override the drive imparted thereto by the impositive or one way driving means so that the imprinting head is caused to strike the periphery of the inking roller in different areas randomly.

Orbital Evolution and Migration of Giant Planets: Modeling Extrasolar Planets

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.

Giant Planets at Small Orbital Distances

Using Doppler spectroscopy to detect the reflex motion of the nearby star, 51 Pegasi, Mayor & Queloz (1995) claim to have discovered a giant planet in a 0.05 AU, 4.23 day orbit. They estimate its mass to be in the range 0.5-2 Jupiter masses, but are not able to determine its nature or origin. Including the effects of the severe stellar insolation implied, we extend the theory of giant planets we have recently developed to encompass those at very small orbital distances. Our calculations can be used to help formulate search strategies for luminous planets in tight orbits around other nearby stars. We calculate the radii and luminosities of such giant planets for a variety of compositions (H/He, He, H2O, and olivine), the evolutionary tracks for solar-composition gas giants, and the geometry of the Hayashi forbidden zone in the gas-giant mass regime. We show that such planets are stable and estimate the magnitude of classical Jeans evaporation and of photodissociation and loss due to EUV radiation. In addition, we demonstrate that for the mass range quoted, such planets are well within their Roche lobes. We show that the strong composition dependence of the model radii and the distinctive spectral signatures provide clear diagnostics that might reveal 51 Peg Bs nature, should interferometric or adaptive-optics techniques ever succeed in photometrically separating planet from star.

Atmospheric, evolutionary, and spectral models of the brown dwarf Gliese 229 B

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.

A Theory of extrasolar giant planets

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 type. 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 the 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.

An expanded set of brown dwarf and very low mass star models

We present in this paper updated and improved theoretical models of brown dwarfs and late M dwarfs. The evolution and characteristics of objects between 0.01 and 0.2 solar mass are exhaustively investigated and special emphasis is placed on their properties at early ages. 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.

Theory of Extrasolar Giant Planet Transits

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.

Thermal Conduction by Electrons in Stellar Matter

Abstract : Tables of electron conduction opacity are presented which incorporate recent advances in the theory of electron conduction in stellar matter. The following effects are included: (a) electorn-ion and electron-electron collisions; (b) electron-electron, electron-ion, and ion-ion correlations and shielding; (c) correct treatment of the low-temperature low-density regime where Born approximation fails. A calculation of electron thermal conductivity in the ion solid state is presented. Relativistic effects are not included. Tables are presented for hydrogen, helium carbon, red giant core composition, and solar composition over a range of density from (10 to the minus 5.75 power)g/cc to one million g/cc, and a range of temperature from 1000 to 1 billion degrees K. Regions where the theory breaks down are excluded. (Author)

On the Radii of Close-in Giant Planets.

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 planets radius and mass. In addition, there is a provocative detection of the light reflected off of the giant planet tau 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 tau 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.