t a j ,491:856 875,1997december20 1997

THE ASTROPHYSICAL JOURNAL, 491 :856È875, 1997 December 201997. The American Astronomical Society. All rights reserved. Printed in U.S.A.(

A NONGRAY THEORY OF EXTRASOLAR GIANT PLANETS AND BROWN DWARFS

A. M. W. B. J. I. T. D.BURROWS,1 MARLEY,2 HUBBARD,3 LUNINE,3 GUILLOT,4 SAUMON,5R. D. AND C.FREEDMAN,6 SUDARSKY,1 SHARP1

Received 1997 May 27; accepted 1997 August 4

ABSTRACTWe 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 e†ective temperatures below 1300 K.This theory encompasses most of the mass/age parameter space occupied by substellar objects and is theÐrst spectral study down to 100 K. These calculations are in aid of the multitude of searches being con-ducted or planned around the world for giant planets and brown dwarfs and reveal the exotic nature ofthe class. Generically, absorption by at longer wavelengths and opacity windows at shorterH2 H2Owavelengths conspire to redistribute Ñux blueward. Below 1200 K, methane is the dominant carbonbearing molecule and is a universal diagnostic feature of EGP and brown dwarf spectra. We Ðnd thatthe primary bands in which to search are Z (D1.05 km), J (D1.2 km), H (D1.6 km), K (D2.2 km), M(D5 km), and N (D10 km), that enhancements of the emergent Ñux over blackbody values, in particularin the near infrared, can be by many orders of magnitude, and that the infrared colors of EGPs andbrown dwarfs are much bluer than previously believed. In particular, relative to J and H, the K bandÑux is reduced by and absorption. Furthermore, we conclude that for below 1200 K mostCH4 H2 TeffÏsor all true metals may be sequestered below the photosphere, that an interior radiative zone is a genericfeature of substellar objects, and that clouds of and are formed for below D400 andH2O NH3 TeffÏsD200 K, respectively. This study is done for solar-metallicity objects in isolation and does not includethe e†ects of stellar insulation. Nevertheless, it is a comprehensive attempt to bridge the gap between theplanetary and stellar realms and to develop a nongray theory of objects from (““ Saturn ÏÏ) to0.3MJ 70MJ(D0.07 We Ðnd that the detection ranges for brown dwarf/EGP discovery of both ground- andM

_).

space-based telescopes are larger than previously estimated.Subject headings : planetary systems È stars : atmospheres È stars : interiors È

stars : low-mass, brown dwarfs

1. INTRODUCTION

After years of slow progress and ambiguous, but tantaliz-ing, observations of objects in the Ðeld and in young clus-ters, the study of brown dwarfs via reÑex stellar motion,Ðlter photometry, and spectroscopy has Ðnally come into itsown. The direct detection of Gl229B et al.(Oppenheimer

et al. et al.1995 ; Nakajima 1995 ; Matthews 1996 ; Geballeet al. et al. et al. et al.1996 ; Marley 1996 ; Allard 1996 ; Tsuji

was a watershed because Gl229B displays methane1996)spectral features and low surface Ñuxes that are unique toobjects with e†ective temperatures (in this case, Teff D 950K) below those at the solar-metallicity main-sequence edge(D1750 K, et al. D2000 K, et al.Burrows 1993 ; Bara†e

In addition, the almost complete absence of spectral1995).signatures of metal oxides and hydrides (such as TiO, VO,FeH, and CaH) is in keeping with theoretical predictionsthat these species are depleted in the atmospheres of all butthe youngest (hence, hottest) substellar objects and aresequestered in condensed form below the photosphere (see

1 Department of Astronomy and Steward Observatory, University ofArizona, Tucson, AZ 85721.

2 Department of Astronomy, New Mexico State University, Box 30001/Department 4500, Las Cruces, NM 88003.

3 Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ85721.

4 Department of Meteorology, University of Reading, P.O. Box 239,Whiteknights, Reading RG6 6AU, UK.

5 Department of Physics and Astronomy, Vanderbilt University, Nash-ville, TN 37235.

6 Space Physics Research Institute, NASA Ames Research Center,Mo†ett Field, CA 94035.

°° and et al. et al.2.6, 3.2, 3.3 ; Lunine 1989 ; Marley 1996).This convergence between theory and observation shouldnot obscure the fact that the study of the atmospheres,spectra, colors, and evolution of substellar objects is still inits infancy. Though predictions of luminosity, andTeff,radius evolution versus mass and composition have beenavailable for almost a decade Rappaport, & Joss(Nelson,

& Mazzitelli Hubbard, &1985 ; DÏAntona 1985 ; Burrows,Lunine Nelson, & Chou1989 ; Dorman, 1989 ; Stevenson

et al. et al.1991 ; Stringfellow 1991 ; Burrows 1993 ; Bara†eand predictions for the colors and spectra of hot1995)

K), young brown dwarfs have been available for a(Z1600few years & Hauschildt to date there has been(Allard 1995),no complete theory of the evolution of the colors, spectra,and structure of brown dwarfs with temperatures belowD1300 K. This is true despite the fact that, for most of themass-age space occupied by brown dwarfs in the galaxy, Teffis indeed below 1300 K. To remedy this situation, we herepresent the Ðrst nongray theory of the evolution, spectra,and colors of brown dwarfs down to of 100 K.TeffÏsThis sweep of and the e†ective physical equivalenceTeffÏsbetween equal-mass extrasolar giant planets (EGPs) andbrown dwarfs allows our theory to apply, without modiÐ-cation, to EGPs as well. It is sensible to distinguish EGPsand brown dwarfs on the basis of their origins : browndwarfs form like stars but are too light to burn hydrogenstably on the main sequence, and EGPs form out of proto-planetary disks by accretion. The di†erent birth paths nodoubt lead to di†erent metallicities, rotation rates, andorbital characteristics, and in the giant planet case to thepresence of an ““ ice/rock ÏÏ core Hubbard, &(Podolak,

856

NONGRAY THEORY OF EXTRASOLAR GIANT PLANETS AND BROWN DWARFS 857

Pollard However, in the main it is not the origin, but1993).the mass, composition, age, and proximity of a hydrogen-dominated object to a star that determines its spectral sig-natures and evolution. An objectÏs pedigree is not anobvious observable.

We have already published a general theory of extrasolargiant planets with masses from to where0.3MJ 15MJ, MJdenotes a Jupiter mass (D0.001 et al.M

_) (Burrows 1995 ;

et al. et al. When we publishedSaumon 1996 ; Guillot 1996).these EGP models, no such objects had been identiÐed.Now, Doppler spectroscopy alone has revealed about 20objects in the giant planet/brown dwarf regime, includingcompanions to q Boo, 51 Peg, t And, 55 Cnc, o CrB, 70 Vir,16 Cyg B, and 47 UMa et al. et al.(Noyes 1997 ; Butler

et al. & Butler &1997 ; Cochran 1997 ; Marcy 1996 ; ButlerMarcy & Queloz et al.1996 ; Mayor 1995 ; Latham 1989).However, our old theory assumed that EGPs emit likeblackbodies. While this assumption is not bad for somewavelength stretches in the mid-infrared, it can be spectacu-larly o† in bands of interest for direct detection. TheGl229B campaign taught us that. The nongray theory wedevelop in this paper encompasses masses from to0.3MJand is in aid of the multitude of direct searches for70MJ7substellar objects, be they ““ planets ÏÏ or brown dwarfs, uponwhich the worldÏs astronomical community has now collec-tively embarked and reports ; et al.(TOPS ExNPS Leger

In order to maintain a reasonable focus, we limit1993).ourselves to solar-metallicity & Grevesse(Anders 1989)objects in isolation and ignore the e†ects of stellar inso-lation et al. A subsequent paper will address(Guillot 1996).the consequences of proximity to a central star and ofvarying metallicity.

In we describe our calculational techniques and the° 2,opacity and thermodynamic data that we used. Section 3covers the physics of the atmospheres of brown dwarfs andEGPs and includes a discussion of temperature/pressure/composition proÐles and the location of convective andradiative zones. In we describe the evolution of objects° 4,with masses from to from saturns to M0.3MJ 200MJ,dwarfs, and provide a global view of the giant planet/browndwarf/M dwarf model continuum. contains aSection 5comprehensive discussion of the near- and mid-infraredspectra of EGPs and brown dwarfs as a function of massand age, as well as and gravity. Our major results are toTeffbe found in this section. presents the IR colors andSection 6magnitudes from the J through the N bands and demon-strates just how unlike blackbodies these objects can be.Search and discovery techniques using Doppler spectros-copy, astrometry, transits, and microlensing are rapidlymaturing, but it is only via direct photometric and spectro-scopic characterization that substellar objects will really beunderstood. In we summarize the salient features of the° 7,nongray theory and list some of the ground- and space-based telescopes and searches for which it should proveuseful.

2. INPUT PHYSICS

The ingredients for a theory of EGPs and brown dwarfsinclude (1) equations of state for metallic hydrogen/heliummixtures and molecular atmospheres, (2) chemical equi-librium codes and thermodynamic data to determine themolecular fractions, (3) scattering and absorption opacitiesfor the dominant chemical species, (4) an atmosphere code

7 For a brown dwarf, K for Gyr.70MJ Teff \ 1300 Z4

to calculate temperature/pressure proÐles and to identifythe radiative and convective zones, (5) an algorithm forconverting a grid of atmospheres into boundary conditionsfor evolutionary calculations, (6) a Henyey code, and (7) aradiative transfer code to provide emergent spectra. In prin-ciple, the calculation of the atmosphere, involving as it doesradiative transfer, and the calculation of the emergent spec-trum are done together. However, as long as the thermalproÐles obtained with the atmosphere code are accurate,one can employ these proÐles, but with another more accu-rate and higher resolution transfer scheme, to calculateemergent spectra. Though we use the k-coefficient methodto calculate the atmosphere proÐles, we are free to employother radiative transfer schemes to obtain spectra.

In the evolutionary calculations, we use the Saumon,Chabrier, & Van Horn equation of state in the metal-(1995)lic and high-density molecular regimes. For solar metal-licity, near and above brown dwarf/EGP photospheres,throughout most of their lives the dominant equilibriumform of carbon is not CO & LoddersCH4, (Fegley 1996),that of oxygen is and that of nitrogen is either orH2O, N2depending upon Hydrogen is predominantly inNH3, Teff.the form of Silicates and metals are found at highH2.optical depths and temperatures. Clouds of andNH3 H2Ocan form for below D200 and D400 K, respectively.TeffÏsWhile for this new model suite we have precipitated speciesaccording to their condensation curves, we have not consis-tently incorporated the e†ects of the associated clouds. If aspecies has condensed, it is left at its saturated vapor pres-sure. Though the proper inclusion of the radiative transfere†ects of clouds is deferred to a later work, in °° and we2.6 3discuss the basic physics of such clouds for betweenTeffÏs100 and 1300 K (see also et al. and speculateLunine 1989)on their role in spectrum formation.

2.1. OpacitiesWater is an important source of opacity in EGPs and

brown dwarfs, particularly when the many lines that orig-inate from highly excited energy levels are considered. Aseries of databases have recently become available that arebased on theoretical calculations that employ a variety ofquantum mechanical methods Jensen, &(Polyansky,Tennyson & Rothman &1994 ; Wattson 1992 ; PartridgeSchwenke In particular, Partridge & Schwenke have1997).calculated the potential energy surface and dipole momentfunction using an ab initio method. This energy surface wasempirically adjusted to improve the Ðt between predictionsand the HITRAN 92 database et al. for(Rothman 1992)

The overall accuracy in wavenumber and intensity isJ [ 5.good and the data have already been used to identify pre-viously unidentiÐed sunspot lines as water lines &(CarbonGoorvitch The 10, 25, 50, 75, and 90 percentiles of the1996).errors in the line positions as compared to HITRAN are :[0.11, [0.04, [0.01, 0.02, and 0.07 cm~1. This databaseallows the inclusion of many predicted lines that are unob-served in the lab and only become important at highertemperatures, since they arise from highly excited levels.This can be particularly important in opacity windows, i.e.,regions where the water opacity reaches a local minimum,but where many weak, high-excitation lines may occur.Depending upon the temperature of the layer, and theassumed abundance of water, well over 2.0] 108 linescould be required for a calculation at the highest tem-peratures, while far fewer lines are needed at lower tem-

858 BURROWS ET AL. Vol. 491

peratures. We use this new Partridge & Schwenke H2Odatabase. (Note that the model published by et al.Marleyused an earlier version of the Schwenke data with1996

fewer lines.)For other than we used databases that go beyondH2O,

what is available in the HITRAN database et al.(RothmanThe limitations of HITRAN are a consequence of the1998).

cuto† in line strength that is imposed at a temperature of296 K. Weaker lines, including those that are unobservableat room temperature, are excluded by this cuto†, althoughthey may become much stronger as the temperature climbsto well above 300 K. In addition, in HITRAN lines whoseanalysis is lower in quality may have been excluded. Sincein our application we are interested in the total opacity onlyover fairly broad regions in wavenumber, we can acceptlines whose positions and strengths may not be known withthe highest precision. This makes available databases withfar more lines than HITRAN. The GEISA database

et al. can also be a source of additional lines,(Husson 1994)as its line strength cuto† is lower than that of HITRAN.Additional lines have been obtained from theoretical calcu-lations et al.(Tyuterev 1994 ; Goorvitch 1994 ; Tipping

& Rothman and from other1990 ; Wattson 1992)researchers prior to publication (L. R. Brown 1997, privatecommunication). This has resulted in databases for CH4and of 1.9] 106 lines, for CO of 99,000 lines, forCH3Dof 11,400 lines, for of 11,240 lines, and for ofNH3 PH3 H2S179,000 lines.

Modeled continuum opacity sources include H~ and H2~opacity and collision-induced absorption (CIA) of andH2helium & Frommhold & Borysow(Borysow 1990 ; ZhengThe latter is a direct function of pressure and a major1995).

process in EGP/brown dwarf atmospheres.We employed the formulation of et al. forRages (1991)

Rayleigh scattering, important at shorter wavelengths. Notethat our opacity model is currently grain-free.

2.2. L ine ProÐlesFor our calculations, when the data are available, the line

widths for the various molecules are assumed to be due toor broadening. Currently, such data are avail-H2 H2 ] He

able for & Plymate Lynch, &H2O (Brown 1996 ; Gamache,Brown CO et al. & Severin1996), (Bulanin 1984 ; LeMoal

(Margolis L. R. Brown 1997, private1986), CH4 1993, 1996 ;communication), Lacome, & TarragoPH3 (Levy, 1994),and & Peterson These data wereNH3 (Brown 1994).derived from laboratory measurements, and the width foreach line was derived from a Ðt to the available data as afunction of the value of J and the other relevant rotationalquantum numbers. Because these measurements typicallycover only one or more vibrational bands, it is necessary toassume that any vibrational dependence of the widths isvery small, since the same Ðt is used for all bands. For otherspecies, it may be necessary to use the air-broadened widthsdue to and perhaps making an adjustment by aN2 O2,constant factor if any information is available on the rela-tive efficiency of versus broadening for the molecule.H2 N2This is still quite uncertain and may vary from species tospecies.

2.3. Calculation of the Atmosphere Structures and SpectraWe construct model atmospheres employing an

approach similar to that used to derive temperature proÐlesfor the outer planets et al. and Titan(Marley 1996) (McKay,

Pollack, & Courtin The model consists of a series of1989).up to 60 homogeneous plane-parallel layers. The bottom ofthe lowermost layer is placed at a depth of up to 300 bars,the top of the uppermost at 0.5 mbar. Levels, whichseparate layers, are spaced approximately evenly in log P.The current model considers 101 spectral intervals from0.87 km to 2.5 cm.

A trial temperature proÐle is adjusted until the entireatmosphere is in radiative equilibrium. The model is judgedto be in radiative equilibrium when the temperature proÐleresults in zero net Ñux across each level in the radiativeregion of the atmosphere. Layers in which the radiativelapse rate exceeds the adiabatic lapse rate are then deemedconvective. The lapse rate is adjusted only one layer at atime and a new radiative-convective equilibrium proÐle iscomputed after the lapse rate in each layer is adjusted. Thisapproach allows for the presence of multiple convectionzones and works very well for the solar Jovian planets

et al. The scaling arguments of &(Marley 1996). IngersollPollard suggest that the fractional di†erence between(1982)the actual temperature proÐle and an adiabat is less than10~4 for Jovian atmospheres. Indeed, the computed radi-ative lapse rate above our convection zones is close to theconvective rate, so that any error in the temperature proÐle(and, thus, in see will be small. However,Teff [ T10 ; ° 2.7)the assumption that the temperature gradient is strictlyadiabatic in convective zones is not appropriate for TeffÏsabove 2000 K et al. a regime occupied by(Burrows 1989),the youngest and most massive brown dwarfs and Mdwarfs.

Fluxes are computed using the two-stream source func-tion technique et al. The intensity is integrated(Toon 1989).over Ðve angular Gauss points in each hemisphere. Thistechnique is rapid and is well suited for application to inho-mogeneous, multiple-scattering atmospheres. Some imple-mentations of the two-stream method have variousshortcomings, which the Source Function scheme et(Toonal. is designed to overcome. SpeciÐcally, this tech-1989)nique gives exact Ñuxes et al. in the limit of(Toon 1989)pure absorption, yet still gives good accuracy with a scat-tering atmosphere. Toon et al. Ðnd the source functionapproach produces layer emissivities that agree with anexact calculation to better than 1% over a three-decaderange of layer optical depths for a nonscattering atmo-sphere. When scattering is present, the approach still con-serves Ñux and produces layer emissivities accurate to atleast 10%.

In a Gliese 229B-like model, the integrated Rayleigh scat-tering optical depth over the entire model column domi-nates other opacity sources only for wavelengths less than0.9 km. Thus, for the vast majority of spectral intervals inour cloud-free calculations the two-stream source functiontechnique provides exceptionally accurate Ñuxes.

2.4. T he k-Coefficient MethodThe k-coefficient method et al. &(Goody 1989 ; Lacis

Oinas is widely used in planetary atmosphere model-1991)ing. The earlier use of the ODF technique & Gus-(Saxnertafsson which can be related to the1984),k-coefficient/cumulative probability method by a simplemathematical transform, may leave the impression that thismethod is always subject to large errors when applied tohot gases with many atmospheric layers. However, theapplication of this technique to a mixture of gases that has

No. 2, 1997 NONGRAY THEORY OF EXTRASOLAR GIANT PLANETS AND BROWN DWARFS 859

already been combined using the equilibrium mixing ratiosbefore the calculation of the cumulative probability dis-tribution, diminishes many of the problems associated bothwith the mapping technique used in the work of Saxner &Gusta†son, and with newer techniques that have beendeveloped to convolve probability distributions of individ-ual gases into a combined, equivalent distribution (Goodyet al. For the calculations described in this paper, we1989).have generated extensive tables of k-coefficients for equi-librium mixtures at given temperatures and pressures, inwhich we interpolate as we converge to a consistent atmo-spheric structure. This is particularly important in reducingthe problem caused by large changes in the band structureof the molecular opacity from one layer to the next due, forexample, to dissociation or changes in relative abundance.Hence, it is possible for the cumulative probability distribu-tions, and thus correlated kÏs, to look very similar for thetwo approaches, even though in one case, since the opacityis changing its distribution in frequency, radiation couldescape between the lines in transparent regions, but not inthe other. Errors can accumulate if the wrong order is fol-lowed in calculating the k-coefficients. In our case, the factthat the gases have already been mixed before the k-coefficients are derived greatly diminishes the probabilitythat these sorts of problems will occur in moving from onelayer to the next, given that in our models there is not alarge change in temperature between layers. Typical errorsfor test cases in planetary atmospheres (that include use ofthe convolution technique for probability distributions) arebetween 1% and 10% (Grossman & Grant 1992, 1994a,1994b).

After we perform the line-by-line calculations for eachindividual molecule, the resulting opacity Ðles are put on acommon frequency scale. Then, they are combined into oneÐle for the total opacity using the appropriate mixing ratiosfor each molecule. The abundance of the various constitu-ents is determined by a chemical equilibrium calculationand condensation (°° and At temperatures below2.5 2.6).the condensation point of a given constituent, the abun-dance is set equal to the saturation vapor pressure. In thek-coefficient method, this summed Ðle is then broken upinto a large number (D100) of frequency blocks coveringthe entire spectrum. The creation of the block structureallows one to avoid solving the transfer equation at a verylarge number of individual frequency points et al.(Goody1989).

One constructs a distribution function of all the opacitieswithin each frequency block. This technique takes all theopacities (at each wavenumber) from the line-by-line calcu-lation, sorts them according to value (independent ofwavenumber), and places them in logarithmically spacedbins. Note that this destroys the relationship between aparticular value of the opacity and the wavenumber whereit occurred. This distribution (number of points that fall ineach bin vs. opacity) is then normalized and converted intoa cumulative distribution. The distribution is now thecumulative number of points at each bin versus the opacityof that bin. After the proper normalization, this now givesthe cumulative probability versus opacity, i.e., the probabil-ity that an opacity is less than or equal to a given value.This distribution is then inverted using interpolation to givethe Ðnal cumulative probability distribution. The abscissa isnow the probability normalized to run from 0 to 1.0 and theordinate is opacity and runs from the minimum to the

maximum value of the opacity within the window.Because the Ðnal distribution is now uniform in probabil-

ity space, it is possible to integrate this distribution to Ðndthe total opacity in each window. We perform this integra-tion by extracting values at appropriate Gauss points.These values, sometimes called correlated kÏs, can be usedwith the appropriate Gauss weights to represent the totalopacity in a given window.

The transmission, T , as a function of absorber columnmass, u, within a layer for a given spectral interval is thenexpressed as

T (u)\ ;i

wie~kiu , (1)

where the are Gauss weights and the are equivalentwi

kimonochromatic absorption coefficients.

Within each spectral interval the equation of radiativetransfer is solved eight times as a monochromatic equationof transfer, once for each term in the expansion in equation

with the continuum opacities identical for each of the(1),computations. The Ñuxes thus obtained are then summed,with the terms weighted by the to obtain the total Ñux inw

i,

the spectral interval.The accuracy of the approach is controlled by the width

of the model spectral intervals and the number of Gausspoints used. To improve the sensitivity to small fractions ofvery strong lines in a given spectral interval, we employ adouble Gaussian quadrature. The Ðrst four Gauss pointsprovide for the integral over the weakest 88% of the lines.The remaining four points take the integration over theremaining probability interval. Accuracy can be compro-mised if the spectral shape of the molecular opacity within agiven interval changes with depth in the model, usuallybecause of conversion of one species to another. Thus, wehave carefully chosen the individual spectral intervals tominimize such e†ects. Experimentation with the currentspectral intervals reveals that computed temperature pro-Ðles are not sensitive to a further increase in their number.Although the Ñux is computed in only D100 spectral inter-vals, in each interval an exact calculation is performed at 8Gauss points. The opacity at each Gauss point results froman exact calculation of the molecular opacity at severalthousand points in that interval. Thus, substantially moreinformation enters into the Ñux computation than simplythe opacity at 100 points.

During model runs, the k-coefficients at an arbitrarytemperature-pressure point are computed by interpolationwithin the k-coefficient grid. Opacities are interpolatedin log P-1/T space to follow the variation of constituentsalong the vapor pressure curve.

2.5. Chemical Equilibrium CalculationsFor this paper, the chemical equilibrium calculations

were performed with the ATLAS code and data fromThe Kurucz reaction constants are inaccu-Kurucz (1970).

rate at low temperatures, but, fortunately, the NH3] N2and conversions that occur in EGPs and brownCH4] COdwarfs do so in regions of T -P space for which the Kuruczreaction constants are accurate. Condensation of CH4,Fe, and was included using data fromNH3, H2O, MgSiO3various sources, including & KauzmannEisenberg (1969),the of Chemistry and Physics andHandbook (1993),

Handbook of Chemistry Following FegleyLangeÏs (1979).& Lodders we assumed that Al, Ca, Ti, and V(1994, 1996),


surface used for evolutionary calculations presented in this paperFIG. 1.ÈTeff [ T10-g

were removed either by condensation or were dissolved insilicate grains at about the condensation tem-MgSiO3perature. These atoms are important because they lead tomolecules that are strong light absorbers, such as TiO andVO. However, they have not been detected in the giantplanets of our solar system and should not be present inrelatively cool objects such as the brown dwarf Gl229B

et al. Our results are in excellent agreement(Marley 1996).with those of Fegley & Lodders (1994, 1996).

2.6. Condensation ProcessesThe principal e†ect of cloud formation is the removal of

molecular species from the gas phase into the solid or liquidphase. For a single component system that does not interactchemically with other species (i.e., water) cloud formationoccurs at a pressure level (““ cloud base ÏÏ) where the partialpressure of the gaseous species just exceeds its saturationvapor pressure. The saturation vapor pressure is givenapproximately by the Clausius-Clapeyron relationship,P\ Be~A@T, where B and A are weak functions of tem-perature. A is the latent heat of condensation (per mole)divided by the universal gas constant. At lower pressures(higher altitudes) in the atmosphere, the abundance of thegas phase species drops o† in this inverse-exponentialfashion. Since A/T [ 1, the fallo† is steep and the gaseousspecies does not contribute to the emergent spectral dis-tribution at pressures much above the cloud base.

There are several complications to the above simplepicture. The Ðrst is supersaturation. Because the radius ofcurvature of cloud particles or droplets adds an additionalsurface energy to the condensed phase, the cloud base is

usually elevated above the pressure level at which the ratioof partial pressure to saturation vapor pressure is unity (thisis the supersaturation ratio). In the case of terrestrial clouds,the threshold ratio may be 1.2 ; in certain cold environmentslacking particulates to serve as nucleation sites, the valuemay be as high as 2 (such as in Neptune ; Allen, &Moses,Yung Because of the high temperatures at the unity1992).optical depth level in objects such as Gl229B, we ignoresupersaturation ; variations of a few tens of percent in thesupersaturation are not discernable in its spectra.

The second complication is that for most condensablespecies the temperature variation of A cannot be ignored intwo cases : near the liquid-vapor critical point and overlarge ranges of temperature. Because our models span alarge temperature range, this is a concern for the majorcloud-forming species, in particular water. For water, weuse multiterm polynomial and exponential Ðts for the liquidand solid phases from & KauzmannEisenberg (1969).These are suitable for temperatures from well below the icepoint to the critical temperature.

The third complication is that many cloud-forming ele-ments are not incorporated in the same molecular species inthe gaseous and condensed phases, but instead a chemicalreaction occurs associated with the condensation process.To correctly characterize cloud formation requires that weincorporate it into the chemical equilibrium computationsdescribed above ; cloud formation occurs for particular ele-ments when the phase with the minimum Gibbs free energyis the condensed phase. The only species we consider herefor which this is an issue is the magnesium silicate, MgSiO3.Convenient expressions for the resulting condensation aregiven in & Lewis We are currently pre-Barshay (1976).


paring a more comprehensive set of condensation curves forminor species using a Gibbs energy minimization routine,the results of which will be presented in a subsequent paper.

versus2.7. Teff T10As in our previous papers, we parameterize the speciÐc

entropy of the fully convective deep interior of an EGP bywhich is the temperature that the interior isentropeT10,would have if extrapolated to a pressure of 10 bars, and

which may or may not equal the actual atmospheric tem-perature at 10 bars.

We construct a surface by making a splined ÐtTeff-T10-gto the grid of nongray model atmospheres augmented withadditional points from gray model atmospheres,Teff-T10-gas presented in et al. The resulting surface isSaumon (1996).shown in The points used to deÐne this surface areFigure 1.shown as dots. Open dots represent the previous (grayatmosphere) relations from Saumon et al., and the soliddots are the new (nongray atmosphere) calculations. Toillustrate the domain actually traversed by EGP models,three evolutionary trajectories of EGPs with masses of 1MJ(left), (middle), and (0.04 right) are shown.10MJ 42MJ M

_;

The earliest portions of the evolution tracks are shown asdotted lines starting at an age of 10~3 Gyr and ending at anage of 10~1 Gyr. Subsequent evolution is shown as a solidline, which ends at a maximum age of 10 Gyr for the 1MJand models, and at 20 Gyr for the model. Evol-10MJ 42MJution of objects with ages greater than 0.1 Gyr is well con-strained by our nongray grid.

3. ATMOSPHERES

3.1. Radiative and Convective Zonesshows proÐles of atmospheric pressure as a func-Figure 2

tion of temperature calculated in our grid of nongraymodels. In this Ðgure, the surface gravity g is held constantat 2200 cm s~2 (close to the value for Jupiter), and takesTeffthe values 128 K (lowest curve), and 200È1000 K (highestcurve) in steps of 100 K. This sequence does not preciselyrepresent an evolutionary sequence for a Jupiter-massobject because g actually decreases with increasing inTeffsuch an object. The heavy dot represents the photosphere,which is not a well-deÐned region in a nongray model atmo-sphere, but which we approximate as the region in the

FIG. 2.ÈAtmospheric pressure-temperature proÐles for EGPs withsurface gravity Ðxed at 2200 cm s~2 and 900, 800, 700, 600,Teff \ 1000,500, 400, 300, 200, and 128 K.

atmosphere where the local temperature Convec-T \ Teff.tion zones, where the local value of dT /dP is essentiallyequal to the adiabatic value, are shown as dashed lines ; asusual, radiative zones appear where the local value ofdT /dP is subadiabatic. Various chemical boundaries, dis-cussed below, are shown as lighter lines : solid for a changein equilibrium for chemical species and dashed for forma-tion of condensed phases of a single species. The observedP-T relation for Jupiter et al. is(Lindal 1992 ; Sei† 1996)shown as a dot-dashed line.

Note in that a detached radiative zone appearsFigure 2in the hotter models at temperatures around 1500È2000 K.The physical origin of this zone is the near coincidence of aminimum in the CIA opacity as a function of wavelengthwith the maximum of the local Planck function, as orig-inally discovered by et al. Guillot et al. haveGuillot (1994).determined that a detached radiative zone is likely also tobe present in Jupiter at temperatures between 1200 and2900 K. Not only is the detached radiative zone of interestin its own right, but it is important for the evolution ofEGPs because it causes the speciÐc entropy in the upper-most convection zone to be higher than the speciÐc entropyin the deepest convection zone. Thus, an EGP in which thiszone appears will evolve slightly more rapidly than it wouldin the absence of the zone. That is, for a given value of Teff,the central temperature will be lower than would be calcu-lated without allowing for the detached radiative zone.

The models shown in do not extend to sufficientFigure 2depth at and 200 K to include the detached radi-Teff \ 128ative zone. Thus, the relation between and for theseTeff T10models is slightly incorrect. However, as discussed by

et al. and & Pollard theGuillot (1994) Ingersoll (1982),di†erence between the radiative gradient and the adiabaticgradient in the radiative zone is small, so that the cumula-tive error in calculating is at the level of or smaller thanT10other e†ects which we neglect in this paper, such as inso-lation from a moderately distant (D5 A.U.) companion star.

Figures and portray the calculated atmospheric3, 4, 5, 6proÐles for surface gravities of 104, 3 ] 104, 105, and3 ] 105 cm s~2. As the gravity increases, the photosphericpressure increases, but the dependence of the photo-Teffspheric pressure is weak. For all gravities, an extended orsecond radiative zone is a generic feature of the atmo-

FIG. 3.ÈAtmospheric pressure-temperature proÐles for EGPs withsurface gravity Ðxed at 104 cm s~2 and 600, 500, 400, 200, andTeff \ 800,128 K.


FIG. 4.ÈAtmospheric pressure-temperature proÐles for EGPs withsurface gravity Ðxed at 3 ] 104 cm s~2 and 900, 700, 300, 200,Teff \ 1100,and 128 K.

spheres. This will have consequences for the mixing of non-equilibrium species into the observable layers.

3.2. Equilibrium and Condensation L inesFigures depict temperature/pressure proÐles, on2È6

which are superimposed the equilibrium condensation lines

FIG. 5.ÈAtmospheric pressure-temperature proÐles for EGPs withsurface gravity Ðxed at 105 cm s~2 and 1100, 900, 700, 500,Teff \ 1200,250, 200, and 128 K. Cooler models show some numerical noise at lowpressures arising from ammonia condensation.

FIG. 6.ÈAtmospheric pressure-temperature proÐles for EGPs withsurface gravity Ðxed at 3 ] 105 cm s~2 and 1100, 900, 700, 200,Teff \ 1200,and 128 K.

for various species. For Jovian-type e†ective temperaturescondensation of ammonia and water occur near the photo-sphere. Even for objects as warm as K, waterTeff \ 500condensation occurs, but it does so at altitudes well abovethe photosphere in the atmosphere, and at pressures so lowthat (1) the actual cloud particle density is rather small and(2) the cloud particles are expected to fall out of the atmo-sphere rapidly. We therefore expect such a tenuous watercloud to play a much more minor role in the radiativebalance and spectral appearance than in the cooler objectsfor which the water cloud is potentially quite massive (as insimplistic Jupiter models).

Interestingly, among cloud-forming species that areabundant by virtue of cosmic composition, a relatively largegap occurs between water and less volatile species. Sulfur-bearing condensates of iron sulÐdes (not shown in theÐgures) might be present in the e†ective temperature rangearound 500 K. Beyond that, magnesium silicate and ironclouds are expected to form around the photosphere forobjects with e†ective temperature exceeding 1000 K. All ofthe relationships between e†ective temperature and cloudformation are modestly sensitive to the e†ective gravity.

Also shown in Figures are lines deÐning equal gas-2È6phase abundances of methane and carbon monoxide and ofammonia and nitrogen. Le ChatelierÏs principle demandsthat the hydrate species dominate at the lower tem-peratures. Hence, below D1200 and D600 K, methane andammonia, respectively, are the dominant carbon and nitro-gen species. Between D600 and D1200 K, and canN2 CH4coexist. This illustrates that Gl229B is a threshold objectthat may contain some amounts of CO in addition to CH4.It is also possible that the atmosphere of Gl229B containsdetectable amounts of ammonia, because, even though it isa minor species, it is spectroscopically active.

3.3. CloudsCloud formation depletes a gas-phase absorber from

certain regions of the atmosphere ; if this occurs around thephotosphere, the resulting radiative balance and emergentÑux distribution are modiÐed. Because of condensation, weexpect that the gaseous water bands will disappear forobjects with e†ective temperature below about 400 K. Weexpect the disappearance of silicate or iron features belowabout 1000 K (depending modestly on surface gravity).Despite the general complexity of cloud formation physics,in all the giant planets in the solar system, we see discreteclouds near the intercepts of the temperature/partial pres-sure curves and the condensation curves, implying thatthere is rain-out and that simple estimates for the locationof a cloud deck are useful. Furthermore, our calculationsimply that for above the and condensationTeffÏs H2O NH3temperatures (e.g., near that of Gl229B), the atmosphere isradiative above the grain cloud, so we do not expect grainsto be convected to the photosphere for below 1300 KTeffÏs(see Figs. 2È6).

Beyond predicting where the water and ammonia bandsshould disappear due to condensation, the spectral andradiative e†ects of clouds are difficult to quantify. Simplemodels in which clouds are uniformly distributed over thesurface of the EGP and are characterized by a single parti-cle size, fail to take account of atmospheric dynamics, whichcan lead to dramatic changes in the e†ects of clouds. Inparticular, convective processes lead to growth in the meanparticle size, as well as a potentially heterogeneous distribu-


tion of clouds across the disk of the object. In the case ofwater and magnesium silicates, the latent heat of conden-sation increases the mean upwelling velocity and can exag-gerate these e†ects, as quantiÐed by et al. TheLunine (1989).simple model of the transport processes in magnesium sili-cate clouds presented in Lunine et al. suggests particle sizesin the range of 100 microns are possible by coalescence,much larger than the micron-sized particles one wouldassume from simple condensation. The radiative propertiesof a cloud clearly depend upon the actual particle size, aswell as the large-scale cloud morphology (broken orcontinuous).

The importance of these processes is seen in Jupiter.Earth-based, and Voyager spectra, along with theoreticalmodeling, show that the spectroscopic e†ects of waterclouds di†er from those predicted by the simplest conden-sation models et al. Galileo probe results(Carlson 1987).

et al. demonstrate directly that global(Niemann 1996)dynamical processes combined with condensation lead to astrongly heterogeneous distribution of water clouds acrossJupiterÏs disk. Thus, in the archetypal example of a giantplanet, the simple assumptions about cloud formation andtheir impact on radiative processes fail. Likewise, onNeptune the methane clouds are distributed in a manifestlyheterogeneous fashion.

For these reasons we have chosen not to model explicitlythe spectral and radiative e†ects of condensed species. Our

opacity and transfer models are grain-free. To do otherwisewith the available information remains an unconstrainedexercise, but higher resolution spectra on objects such asGl229B could provide constraints for such cloud modeling.

4. EVOLUTIONARY MODELS

In et al. and et al. weBurrows (1995) Saumon (1996),published cooling curves for EGPs and small brown dwarfsthat were based upon our then-current atmosphere models.For this paper, we have updated the CIA, andH2 H2O,

opacities and the grid. Consequently, the evo-CH4 T10-Tefflutionary tracks have changed, but generally by no morethan 10% in luminosity at any given time, for any givenmass. In this section, we present these latest cooling tracksand do so in the larger context of the M dwarf/browndwarf/EGP continuum. The Ðgures in this section cover 3orders of magnitude in mass and encapsulate the character-istics of the entire family of substellar objects and the tran-sition to stars.

portrays the luminosity versus time for objectsFigure 7from SaturnÏs mass to 0.2 The early plateaux(0.3MJ) M

_.

between 106 and 108 yr are due to deuterium burning,where the initial deuterium mass fraction was taken to be2 ] 10~5. Deuterium burning occurs earlier, is quicker, andis at higher luminosity for the more massive models, but itcan take as long as 108 yr for a object. The mass15MJbelow which less than 50% of the ““ primordial ÏÏ deuterium

FIG. 7.ÈEvolution of the luminosity (in of solar-metallicity M dwarfs and substellar objects vs. time (in yr) after formation. The stars, ““ brownL_

)dwarfs ÏÏ and ““ planets ÏÏ are shown as solid, dashed, and dot-dashed curves, respectively. In this Ðgure, we arbitrarily designate as ““ brown dwarfs ÏÏ thoseobjects that burn deuterium, while we designate those that do not as ““ planets.ÏÏ The masses (in label most of the curves, with the lowest threeM

_)

corresponding to the mass of Saturn, half the mass of Jupiter, and the mass of Jupiter.


is burnt is et al. On this and sub-D13MJ (Burrows 1995).sequent Ðgures in this section, we have arbitrarily classed as““ planets ÏÏ those objects that do not burn deuterium and as““ brown dwarfs ÏÏ those that do burn deuterium, but notlight hydrogen. While this distinction is physically moti-vated, we do not advocate abandoning the deÐnition basedon origin. Nevertheless, the separation into M dwarfs,““ brown dwarfs,ÏÏ and giant ““ planets ÏÏ is useful for parsingby eye the information in the Ðgures.

In the bumps between 10~4 and 10~3 andFigure 7, L_between 108 and 109 yr, seen on the cooling curves of

objects from 0.03 to 0.08 are due to silicate andM_

M_

,iron grain formation. These e†ects, Ðrst pointed out by

et al. occur for between 2500 and 1300Lunine (1989), TeffÏsK. The presence of grains a†ects the precise mass and lumi-nosity at the edge of the main sequence. Since grain andcloud models are problematic, there still remains much tolearn concerning their role and how to model them (° 3.3and et al.Allard 1997).

depicts the central temperature versusFigure 8 (Tc)

central density for a variety of masses between(oc) 0.3MJand 0.237 Superposed are isochrones from 106.5 toM

_.

109.5 yr. For the M dwarfs, the central temperature gener-ally rises until the object has stabilized as a star. However,near the bottom edge of the main sequence the central tem-perature actually decreases slightly just before stabilizing.The central density always increases with time. The highest

densities are achieved by the massive brown dwarfs andhover near 1000 g cm~3 for solar metallicity. They arehigher for lower metallicities, reaching a peak of D2000 gcm~3 at zero metallicity et al. The era(Burrows 1993).during which increases is rather brief for the ““ planets ÏÏT

cand they spend most of their time cooling throughout. The““ brown dwarfs ÏÏ nicely straddle these two regimes.

The trajectories for a given mass are universalFigure 8curves, independent of the metallicity and atmospheremodel. They depend solely upon the equation of state andthe fact that the structures are fully convective in the inte-rior. However, the positions of the isochrones do dependupon the model speciÐcs and vary with metallicity andboundary conditions. Note that the isochrones shear per-ceptibly near the ““ brown dwarf ÏÏ-““ planet ÏÏ interface. Notunexpectedly, this is a consequence of the onset of deute-rium burning.

For a given ““ brown dwarf ÏÏ or EGP mass (in M_),

connects the observables (in K) and gravity (g,Figure 9 Teffin cgs). The dashed curves are the isochrones. As is clearfrom the Ðgure, gravity maps fairly directly onto mass andfor no mass does g change by more than a factor of 2 after108 yr. Modeling the spectrum of a substellar object willyield estimates of and g. With these estimates,Teff Figure 9can be used to infer the mass and the age simultaneously. Infact, for a given composition and model, only two quantitiesare needed to derive all others. Bolometric luminosity and

FIG. 8.ÈEvolutionary tracks of central density (in g cm~3) vs. central temperature (in K) for stars (solid lines), ““ brown dwarfs ÏÏ (dashed lines), and ““ giantplanets ÏÏ(dot-dashed lines), as in The isochrones are drawn as gray curves and are labeled in yr. The pronounced wave in the isochrones betweenFig. 7. log10about and 6 is due to deuterium burning. A given mass deÐnes a unique relationship between central temperature and density that islog10 T

c\ 5.5

independent of metallicity. The only e†ect of the metallicity is to change the rate at which the central temperature and density evolve and the positions of theisochrones.


FIG. 9.ÈEvolutionary tracks of gravity (in cm s~2) vs. e†ective temperature (in K) for ““ brown dwarfs ÏÏ (solid lines) and ““ planets ÏÏ (dashed lines). Thelog10isochrones are gray curves and are labeled in yr. In all cases, gravity increases with time. Initially, for the more massive brown dwarfs, the e†ectivelog10temperature is roughly constant, or slightly increasing, before decreasing inexorably at later times. This Ðgure depicts how and gravity map onto massTeffand age.

age can be used to yield mass and radius. E†ective tem-perature and mass can provide age and luminosity. Our Ðtto the UKIRT spectrum of Gl229B et al.(Marley 1996 ;

et al. et al. see alsoGeballe 1996 ; Matthews 1996 ;

et al. gave K andOppenheimer 1995) Teff D 900È1000g D 105B0.5 cm s~2. Reading o† of one obtains aFigure 9,mass between and with a best value near20MJ 60MJ, 35MJ,and an age between 108.5 and 109.5 yr. The wide range in

TABLE 1

EVOLUTION OF A PLANET1MJlog t Teff R log T

clog o

c(Gyr) (K) log L /L_

(109 cm) (K) (g cm~3) L nuclear/L

[2.990 . . . . . . 839.9 [4.851 12.33 4.684 0.130 0.000[2.780 . . . . . . 767.4 [5.053 11.70 4.673 0.168 0.000[2.567 . . . . . . 699.7 [5.257 11.13 4.658 0.205 0.000[2.365 . . . . . . 631.7 [5.474 10.64 4.641 0.239 0.000[2.156 . . . . . . 575.9 [5.671 10.20 4.620 0.272 0.000[1.944 . . . . . . 515.5 [5.898 9.81 4.595 0.303 0.000[1.734 . . . . . . 455.1 [6.145 9.47 4.567 0.331 0.000[1.520 . . . . . . 397.6 [6.407 9.17 4.536 0.356 0.000[1.312 . . . . . . 347.5 [6.664 8.93 4.505 0.377 0.000[1.101 . . . . . . 304.0 [6.919 8.71 4.474 0.394 0.000[0.898 . . . . . . 267.9 [7.157 8.53 4.442 0.410 0.000[0.682 . . . . . . 235.9 [7.397 8.34 4.406 0.427 0.000[0.474 . . . . . . 209.0 [7.625 8.18 4.367 0.443 0.000[0.261 . . . . . . 184.8 [7.856 8.01 4.326 0.459 0.000[0.050 . . . . . . 163.9 [8.081 7.86 4.283 0.474 0.000

0.155 . . . . . . 145.3 [8.306 7.71 4.236 0.488 0.0000.363 . . . . . . 128.1 [8.541 7.58 4.185 0.502 0.0000.571 . . . . . . 112.4 [8.783 7.45 4.132 0.517 0.0000.778 . . . . . . 98.9 [9.020 7.33 4.076 0.532 0.0000.982 . . . . . . 86.4 [9.268 7.22 4.016 0.547 0.000


radius (in cm) vs. e†ective temperature in K), with decreasing to the right. This plot has the advantage over an H-R diagram inFIG. 10.Èlog10 (Teff, Teffthat considerably more detail can be shown over the range of conditions considered. In all cases, radius decreases with time. As depicted in for theFig. 9,more massive brown dwarfs the e†ective temperature initially increases before decreasing.

inferred Gl229B parameters is a direct consequence of theweakness of our current constraints on g.

depicts the evolution of radius with whichFigure 10 Teff,at later times is an ersatz age. JupiterÏs current radius is near7 ] 109 cm. In some sense, a plot is a compactradiusÈTeffH-R diagram, since, while luminosities for the family range

9 orders of magnitude during a Hubble time, radii vary farless. Note that initially it takes longer for more massiveobjects to shrink, but that isochrones are not very muchdi†erent from constant-radius lines at later times. Note alsothat the lowest mass objects (e.g., Saturn) tend to havelarger radii at earlier times and smaller radii at later times.

TABLE 2

EVOLUTION OF A PLANET5MJlog t Teff R log T

clog o



[2.998 . . . . . . 1814.0 [3.482 12.79 5.214 0.625 0.000[2.792 . . . . . . 1689.0 [3.664 11.96 5.211 0.699 0.000[2.582 . . . . . . 1494.0 [3.929 11.26 5.202 0.767 0.000[2.380 . . . . . . 1352.0 [4.144 10.74 5.191 0.824 0.000[2.176 . . . . . . 1228.0 [4.351 10.26 5.173 0.880 0.000[1.973 . . . . . . 1094.0 [4.587 9.85 5.151 0.932 0.000[1.772 . . . . . . 967.3 [4.832 9.50 5.125 0.978 0.000[1.571 . . . . . . 848.7 [5.086 9.22 5.097 1.018 0.000[1.368 . . . . . . 740.6 [5.345 8.98 5.067 1.053 0.000[1.163 . . . . . . 643.8 [5.609 8.77 5.038 1.083 0.000[0.961 . . . . . . 561.6 [5.863 8.60 5.009 1.108 0.000[0.749 . . . . . . 489.0 [6.120 8.44 4.978 1.131 0.000[0.534 . . . . . . 424.8 [6.379 8.30 4.947 1.152 0.000[0.332 . . . . . . 373.1 [6.617 8.18 4.917 1.170 0.000[0.131 . . . . . . 327.9 [6.853 8.07 4.886 1.186 0.000

0.083 . . . . . . 285.4 [7.105 7.96 4.853 1.202 0.0000.297 . . . . . . 248.5 [7.356 7.87 4.819 1.216 0.0000.502 . . . . . . 218.3 [7.591 7.79 4.786 1.229 0.0000.712 . . . . . . 193.2 [7.812 7.71 4.750 1.241 0.0000.920 . . . . . . 172.8 [8.015 7.63 4.711 1.253 0.000


FIG. 11.ÈH-R diagram: luminosity (in vs. (in K) for various masses labeled on the Ðgure in Due to the large range in luminosity and the nearL_

) Teff M_

.degeneracy of the tracks of substellar objects at late stages of evolution, it is not possible to represent with adequate detail the whole H-R diagram as oneÐgure. Accordingly, the low-temperature and low-luminosity tail of the H-R diagram is shown in the inset ; note that the axes are scaled di†erently, butotherwise correspond to those on the main Ðgure. For additional clarity, several masses have been omitted in the inset. We have labeled the observedpositions of Jupiter and Saturn as points ““ J ÏÏ and ““ S,ÏÏ respectively & Conrath As discussed in all substellar objects decrease in luminosity(Pearl 1991). Fig. 7,monotonically, though during the early phases deuterium burning slows the evolution. As the ““ brown dwarfs ÏÏ and ““ planets ÏÏ cool to their cold radii, theirtracks in the lower right of the H-R diagram correspond closely to curves of constant radius. Moreover, in the late phases of evolution, due to the very weakdependence of radius on mass, the curves of the lower mass objects become degenerate.

In addition, at a given the higher the mass the smallerTeff,the radius, while at a given age (after 108 yr) radii generallydecrease with mass. Not obvious from the plot is the factthat the maximum cold radius occurs for a mass near 4MJ.

is a theoristÏs H-R diagram for the ““ brownFigure 11dwarfs ÏÏ and giant ““ planets.ÏÏ The inset is a continuation ofthe Ðgure down to low luminosities and The currentTeffÏs.Jupiter and Saturn are superposed for comparison &(Pearl

TABLE 3

EVOLUTION OF A PLANET/BROWN DWARF10MJlog t Teff R log T

clog o



[2.987 . . . . . . 2318.0 [2.934 14.72 5.466 0.772 0.000[2.779 . . . . . . 2238.0 [3.065 13.57 5.475 0.868 0.000[2.572 . . . . . . 2153.0 [3.208 12.44 5.480 0.975 0.001[2.372 . . . . . . 2006.0 [3.405 11.42 5.478 1.082 0.001[2.165 . . . . . . 1720.0 [3.732 10.66 5.468 1.170 0.003[1.959 . . . . . . 1539.0 [3.971 10.11 5.454 1.239 0.004[1.750 . . . . . . 1370.0 [4.214 9.64 5.435 1.302 0.005[1.540 . . . . . . 1221.0 [4.452 9.24 5.412 1.358 0.004[1.329 . . . . . . 1080.0 [4.698 8.89 5.384 1.409 0.003[1.129 . . . . . . 951.4 [4.947 8.61 5.353 1.451 0.002[0.925 . . . . . . 824.3 [5.220 8.37 5.321 1.488 0.002[0.715 . . . . . . 710.5 [5.499 8.18 5.287 1.518 0.001[0.507 . . . . . . 616.0 [5.764 8.02 5.253 1.544 0.001[0.301 . . . . . . 535.4 [6.022 7.88 5.220 1.566 0.000[0.097 . . . . . . 464.3 [6.283 7.76 5.188 1.585 0.000

0.114 . . . . . . 404.0 [6.536 7.66 5.154 1.601 0.0000.326 . . . . . . 351.7 [6.788 7.56 5.121 1.617 0.0000.540 . . . . . . 305.5 [7.042 7.48 5.086 1.630 0.0000.740 . . . . . . 267.8 [7.280 7.41 5.053 1.642 0.0000.942 . . . . . . 235.0 [7.515 7.34 5.020 1.653 0.000


TABLE 4

EVOLUTION OF A 0.04 BROWN DWARFM_

(42MJ)

log t Teff R log Tc

log oc(Gyr) (K) log L /L

_(109 cm) (K) (g cm~3) L nuclear/L

[2.982 . . . . . . 2847.0 [1.812 35.48 5.777 0.347 0.439[2.780 . . . . . . 2857.0 [1.850 33.73 5.795 0.408 0.900[2.573 . . . . . . 2860.0 [1.864 33.13 5.801 0.430 0.943[2.372 . . . . . . 2866.0 [1.886 32.16 5.812 0.466 0.909[2.172 . . . . . . 2881.0 [1.962 29.16 5.847 0.586 0.632[1.967 . . . . . . 2883.0 [2.287 20.04 5.977 1.061 0.000[1.765 . . . . . . 2842.0 [2.537 15.47 6.058 1.397 0.000[1.557 . . . . . . 2774.0 [2.754 12.64 6.110 1.660 0.000[1.357 . . . . . . 2677.0 [2.957 10.75 6.138 1.871 0.000[1.155 . . . . . . 2537.0 [3.171 9.35 6.146 2.052 0.000[0.948 . . . . . . 2340.0 [3.414 8.31 6.134 2.207 0.000[0.743 . . . . . . 2035.0 [3.736 7.58 6.103 2.327 0.000[0.537 . . . . . . 1635.0 [4.164 7.18 6.070 2.397 0.000[0.331 . . . . . . 1451.0 [4.404 6.91 6.037 2.447 0.000[0.125 . . . . . . 1296.0 [4.630 6.67 5.998 2.493 0.000

0.077 . . . . . . 1127.0 [4.900 6.47 5.954 2.532 0.0000.278 . . . . . . 968.6 [5.184 6.32 5.911 2.564 0.0000.487 . . . . . . 820.7 [5.490 6.19 5.867 2.590 0.0000.699 . . . . . . 680.9 [5.828 6.09 5.828 2.609 0.0000.903 . . . . . . 586.2 [6.098 6.02 5.794 2.624 0.0001.113 . . . . . . 511.7 [6.344 5.96 5.758 2.638 0.000

Conrath Importantly, constant mass trajectories1991).never cross and it is only for objects below that tem-25MJperatures below 400 K are reached within 1010 yr. Figures

collectively summarize the model space within which7È11substellar objects reside. Tables and contain the1, 2, 3, 4results of evolutionary calculations for objects with massesof and 0.04 The numbers in1MJ, 5MJ, 10MJ, M

_(D42MJ).them represent the latest atmospheric and opacity calcu-

lations at solar metallicity.

5. EGP AND BROWN DWARF SPECTRA

There are a few major aspects of EGP/brown dwarfatmospheres that bear listing and that uniquely character-ize them. Below of 1300 K, the dominant equilibriumTeffÏscarbon molecule is not CO, and below 600 K theCH4,dominant nitrogen molecule is not As discussedNH3, N2.in the major opacity sources are and° 2, H2, H2O, CH4,For below D400 K, water clouds form at orNH3. TeffÏsabove the photosphere and for below 200 K, ammoniaTeffÏsclouds form (viz., Jupiter). Collision-induced absorption of

partially suppresses emissions longward of D10 km.H2The holes in the opacity spectrum of that deÐne theH2Oclassic telluric IR bands also regulate much of the emissionfrom EGP/brown dwarfs in the near infrared. Importantly,the windows in and the suppression by conspire toH2O H2force Ñux to the blue for a given The upshot is an exoticTeff.spectrum enhanced relative to the blackbody value in the Jand H bands (D1.2 and D1.6 km, respectively) by as muchas 2 to 10 orders of magnitude, depending upon InTeff.addition, as decreases below D1000 K, the Ñux in the MTeffband (D5 km) is progressively enhanced relative to theblackbody value. While at 1000 K there is no enhancement,at 200 K it is near 105. Hence, the J, H, and M bands are thepremier bands in which to search for cold substellar objects.The Z band (D1.05 km) is also super-blackbody over this

range. However, there is a feature in the Z bandTeff NH3that is not in our database. This will likely reduce the Ñux inthis band for the cooler models. Even though K band (D2.2km) Ñuxes are generally higher than blackbody values, H2

and absorption features in the K band decrease itsCH4importance relative to J and H. As a consequence of theincrease of atmospheric pressure with decreasing theTeff,anomalously blue J[K and H[K colors get bluer, notredder.

For this paper, we calculated low-resolution spectra from0.9 to 2500 km, though we focus our discussions on the 1È10km region. A grid of spectra in space was calcu-Teff-gravitylated. As stated in for the evolutionary calculations° 2.7,described in a grid was also constructed. The° 4, Teff-T10evolutionary calculations were used to map mass and ageonto and gravity, which were then used to interpolate inTeffthe grid of spectra to Ðnd the spectra and colors at any massand age. This procedure proved to be quite robust for TeffÏsbetween 1250 and 100 K. The spectra we present are forobjects in isolation and ignore the transport e†ect of clouds.As stated in omitting the direct e†ects of clouds has° 3.3,consequences, for below 400 K the formation of H2Oclouds partially depletes the spectrum of the vaporH2Ofeatures that deÐne it at higher temperatures. Note that thepresence or absence of clouds strongly a†ects the reÑectionalbedos of EGPs and brown dwarfs In par-(Marley 1998).ticular, when there are clouds at or above the photosphere,the albedo in the optical is high. Conversely, when cloudsare absent, the albedo in the mostly absorbing atmosphereis lower.

depicts the objectÏs surface Ñux versus wave-Figure 12length for representative from 130 to 1000 K at aTeffÏsgravity of 3.0 ] 104 cm s~2. The corresponding massesrange from to and the corresponding agesD13MJ D16MJrange from 0.25 to 7 Gyr. Superposed on are theFigure 12positions of various prominent molecular bands and the J,H, K, and M bands. As is clear from the Ðgure, deÐnesH2Omuch of the spectrum, but and modify it in usefulCH4 H2ways. absorption features near 1.65 km, 2.2 km, andCH43.3 km are particularly relevant, the latter two decreasingthe K and L@ (D3.5 km) band Ñuxes, respectively. nearNH36 km becomes important below 250 K and the featureCH4around 7.8 km deepens with decreasing However, itTeff.

1 2 3 4 5 6 7 8 9 10-18

-16

-14

-12

-10

-8

-6

-4 J H K M


FIG. 12.ÈSurface Ñux (in ergs cm~2 s~1 Hz~1) vs. wavelength (in km)from 1 to 10 km for of 130, 200, 300, 500, 600, 700, and 1000 K, at aTeffÏssurface gravity of 3.0 ] 104 cm s~2. Shown are the positions of the J, H, K,and M bands and various molecular absorption features. See the text fordiscussion.

should be noted that in Jupiter the 7.8 km absorptionfeature is inverted into a stratospheric emission feature.Since a stratosphere requires UV Ñux from the primary oranother energy deposition mechanism, our models do notaddress this possibility. In addition, we Ðnd that andH2Ofeatures near 6 km make the band from 5.5 to 7 kmNH3less useful for searching for brown dwarfs and EGPs.

depicts spectra between 1 and 40 km at a detec-Figure 13tor 10 pc away from objects with age 1 Gyr and massesfrom through portrays the spectra for1MJ 40MJ. Figure 14the same parameters, but from 1 to 10 km. Superposed onthe former are the corresponding blackbody curves andsuperposed on both are putative sensitivities for the threeNICMOS cameras ISO et al.(Thompson 1992), (Benvenuti

SIRTF & Werner and Gemini/1994), (Erickson 1992),

FIG. 13.ÈFlux (in kJy) at 10 pc vs. wavelength (in km) from 1 to 40 kmfor 1, 5, 10, 20, 30, and models at 1 Gyr. Superposed for comparison40MJare the corresponding blackbody curves (dashed lines) and the putativesensitivities of the three NICMOS cameras, ISO, Gemini/SOFIA, andSIRTF. NICMOS is denotes with large black dots, ISO with thin, darklines, Gemini/SOFIA with thin, light lines, and SIRTF with thicker, darklines. At all wavelengths, SIRTFÏs projected sensitivity is greater thanISOÏs. SOFIAÏs sensitivity overlaps with that of ISO around 10 km. Forother wavelength intervals, the order of sensitivity is SIRTF [ Gemini/SOFIA [ ISO, where ““ [ ÏÏ means ““ is more sensitive than.ÏÏ Note thesuppression relative to the blackbody values at the longer wavelengths.

FIG. 14.ÈFlux at 10 pc (in kJy) vs. wavelength (in km) for the samemodels depicted in but for a wavelength range of 1 to 10 km.Fig. 13,Shown are the positions of the J, H, K, and M bands and various molecu-lar absorption features. Also included are the estimated sensitivities ofNICMOS, ISO, Gemini/SOFIA, and SIRTF, as described in the captionto Fig. 13.

SOFIA Kurz, & Oschmann(Mountain, 1994 ; Ericksondemonstrates how unlike a blackbody an1992). Figure 13

EGP spectrum is. Note on the sup-Figure 13 H2-inducedpression at long wavelengths and the enhancement atshorter wavelengths. For example, the enhancement at 5km for a 1 Gyr old, extrasolar planet is by 4 orders of1MJmagnitude. Implicit in is the enhancement aroundFigure 13the N band (D10 km) for below 200 K.TeffComparison with the sensitivities reveals that the rangefor detection by SIRTF at 5 km of a 1 Gyr old, object1MJin isolation is near 100 pc. The range for NICMOS in H fora 1 Gyr old, object is approximately 300 pc, while for a5MJcoeval object it is near 1000 pc. These are dramatic40MJnumbers that serve to illustrate both the promise of the newdetectors and the enhancements we theoretically predict.

Figures and portray the evolution from15, 16, 17, 18, 190.1 to 5 Gyr of the spectra from 1 to 10 km of objects withmasses of 1, 5, 10, 15, The higher curves are for the20MJ.younger ages. These cooling curves summarize EGP/brown

FIG. 15.ÈFlux (in kJy) at 10 pc vs. wavelength (in km) from 1 to 10 kmfor a object at ages of 0.1, 0.5, 1.0, and 5.0 Gyr. Superposed are the1MJpositions of the J, H, K, and M bands and the corresponding blackbodycurves (dashed), as well as the estimated sensitivities of the three NICMOScameras, ISO, Gemini/SOFIA, and SIRTF (see caption to Fig. 13).


FIG. 16.ÈFlux (in kJy) at 10 pc vs. wavelength (in km) from 1 to 10 kmfor a object at ages of 0.1, 0.5, 1.0, and 5.0 Gyr. Superposed are the5MJpositions of the J, H, K, and M bands and the estimated sensitivities of thethree NICMOS cameras, ISO, Gemini/SOFIA, and SIRTF.

FIG. 17.ÈFlux (in kJy) at 10 pc vs. wavelength (in km) from 1 to 10 kmfor a object at ages of 0.1, 0.5, 1.0, and 5.0 Gyr. Superposed are the10MJpositions of the J, H, K, and M bands, the estimated sensitivities of thethree NICMOS cameras, ISO, Gemini/SOFIA, and SIRTF, and the posi-tions of various of the important molecular absorption features.

FIG. 18.ÈFlux (in kJy) at 10 pc vs. wavelength (in km) from 1 to 10 kmfor a object at ages of 0.1, 0.5, 1.0, and 5.0 Gyr. Superposed are the15MJpositions of the J, H, K, and M bands and the estimated sensitivities of thethree NICMOS cameras, ISO, Gemini/SOFIA, and SIRTF.

FIG. 19.ÈFlux (in kJy) at 10 pc vs. wavelength (in km) from 1 to 10 kmfor a object at ages of 0.1, 0.5, 1.0, and 5.0 Gyr. Superposed are the20MJpositions of the J, H, K, and M bands, the estimated sensitivities of thethree NICMOS cameras, ISO, Gemini/SOFIA, and SIRTF, and the posi-tions of various of the important molecular absorption features.

dwarf spectra and their evolution but are merely representa-tive of the suite of models now available. Note that thescales change from Figures and to Figures and15 16 17È19that, for comparison, blackbody curves are superposed on

(the ““ Jupiter ÏÏ model). Figures and includeFigure 15 17 19identiÐcations of some of the molecular features. Figure 19suggests that SIRTF will be able to see at 5 km a 5 Gyr old,

object in isolation out to D400 pc and that NICMOS20MJwill be able to see at J or H a 0.1 Gyr old object with thesame mass out to D2000 pc. As shown in the JFigure 15,and H Ñux enhancements over blackbody values for the

model after 0.1 Gyr are at least 10 orders of magnitude.1MJHowever, it must be remembered that these models do notinclude a reÑected light component from a primary. Formany combinations of primary and orbital separation, thisreÑected component can dominate in the near IR.

6. INFRARED COLORS

From the spectra described in the previous section, wehave calculated infrared colors and produced color-colorand color-magnitude diagrams. Figures and20, 21, 22, 23,

are representative color-magnitude diagrams for objects24with masses from to for ages of 0.5, 1.0, and 5.03MJ 40MJ,Gyr. Figures and are color-color diagrams for the25 26same models. For comparison, included in these Ðgures arethe corresponding blackbody curves, hot, young browndwarf or extremely late M dwarf candidates such as LHS2924, GD 165B, Calar 3, and Teide 1 (Kirkpatrick, Henry,& Simons Rebolo, & Martin1994, 1995 ; Zapatero-Osorio,

and a sample of M dwarfs from These1997), Leggett (1992).Ðgures collectively illustrate the unique color realmsoccupied by extrasolar giant planets and brown dwarfs.

Figures and portray the fact that the K and J20 21versus J[K infrared H-R diagrams loop back to the bluebelow the edge of the main sequence and are not continua-tions of the M dwarf sequence into the red. The di†erencebetween the blackbody curves and the model curves isbetween 3 and 10 mag for J versus J[K, more for K versusJ[K. Gl229B Ðts nicely on these theoretical isochrones.The suppression of K by and features is largelyH2 CH4


FIG. 20.ÈAbsolute J vs. J[K color-magnitude diagram. Theoreticalisochrones are shown for t \ 0.5, 1, and 5 Gyr, along with their blackbodycounterparts. The di†erence between blackbody colors and model colors isstriking. The brown dwarf, Gliese 229B et al. the(Oppenheimer 1995),young brown dwarf candidates Calar 3 and Teide 1 (Zapatero-Osorio,Rebolo, & Martin and late M dwarfs LHS 2924 and GD165B1997),(Kirkpatrick, Henry, & Simons are plotted for comparison.1994, 1995)The lower main sequence is deÐned by a selection of M dwarf stars fromLeggett (1992).

responsible for this anomalous blueward trend withdecreasing mass and As Figures and demon-Teff. 22 23strate, the Ðt to Gl229B in H is not as good. This is also trueof the Ðt to L @. Since both H and L @ have signiÐcant CH4features in them, we surmise that incompleteness or errors

FIG. 21.ÈAbsolute K vs. J[K color-magnitude diagram. Otherwise asin Fig. 20.

FIG. 22.ÈAbsolute J vs. J[H color-magnitude diagram. Otherwise asin Fig. 20.

in the opacity database is the culprit. As FiguresCH4 22and also show, J[H actually reddens with decreasing23

but only marginally and is still 1.5È4 mag bluer thanTeff,the corresponding blackbody. That the J[H and H[Kcolors of EGPs and brown dwarfs are many magnitudesblueward of blackbodies is a Ðrm conclusion of this work.

Superposed on the color-color diagrams (Figs. and25 26)are model colors for stars at the edge of the main sequencefor metallicities from solar to 10~3 times solar. For thenonsolar calculations, the atmospheres of & Haus-Allard

FIG. 23.ÈAbsolute H vs. J[H color-magnitude diagram. Otherwise asin Fig. 20.


FIG. 24.ÈAbsolute H vs. H[K color-magnitude diagram. Otherwiseas in Fig. 20.

childt were used to generate the corresponding(1995) Teff-relations employed by our evolutionary code (SaumonT10et al. 1998, in preparation). A glance at these numbers andthose in the zero-metallicity paper of et al.Saumon (1994)reveals that we expect the lower metallicity models to popu-late the bluer regions below the depicted model lines.However, we have yet to calculate precise numbers for non-solar metallicities with the new algorithms and opacities ofthis paper.

Tables and depict the infrared magnitudes and colors5 6for various gravities and Also included are N bandTeffÏs.magnitudes and M[N colors. We employed the transmis-

FIG. 25.ÈJ[H vs. H[K color-color diagram. The edge of the mainsequence as a function of metallicity, from our calculations employing

& Hauschildt atmosphere models, is shown for metallicitiesAllard (1995)from [M/H]\ 0 (top) to [M/H]\ [3 (bottom) (Saumon et al. 1998, inpreparation). Otherwise as in Fig. 20.

sion curves of & Brett and toBessell (1988) Bessell (1990)deÐne the photometric bandpasses and the model of Vegaby & Bell for the calibration of the magni-Dreiling (1980)tude scale. As and Figures suggest, theTable 5 20È24brightnesses in the near IR are quite respectable. Table 6shows that colors generally get bluer with increasing gravity(except for K[L @, which shows the opposite trend). ForJ[H, the e†ect may be only D0.2 mag per decade ingravity and for the problematic H[K color it is perhaps

TABLE 5

ABSOLUTE MAGNITUDES OF SYNTHETIC BD/EGPS, [M/H]\ 0.0a

g Teff(cm s~2) (K) MJ

MH

MK

ML{ M

MM

N

105 . . . . . . . . . . 1000.0 15.35 14.99 15.62 13.34 12.56 11.70800.0 16.44 16.01 17.09 14.13 13.14 12.37600.0 17.91 17.40 19.27 15.18 13.94 13.26500.0 18.96 18.39 20.96 15.94 14.49 13.88

3 ] 104 . . . . . . 1000.0 14.96 14.52 14.98 12.99 12.12 12.15800.0 16.04 15.54 16.40 13.83 12.71 11.84600.0 17.49 16.92 18.43 14.94 13.51 12.77400.0 20.33 19.69 22.97 16.97 14.96 14.27300.0 22.62 21.91 26.74 18.58 16.08 15.40

104 . . . . . . . . . . 1000.0 14.66 14.11 14.26 12.70 11.70 10.59800.0 15.82 15.23 15.88 13.66 12.39 11.42600.0 17.27 16.61 17.89 14.84 13.24 12.44400.0 19.76 19.31 21.86 16.74 14.64 13.83

3 ] 103 . . . . . . 1000.0 13.97 13.15 13.05 12.31 11.16 10.10800.0 15.42 14.64 15.00 13.38 11.97 10.97600.0 17.17 16.48 17.44 14.72 12.97 12.05400.0 19.84 19.40 21.49 16.77 14.49 13.59200.0 24.60 24.03 28.84 19.93 16.58 15.72

a We employed the transmission curves of & Brett andBessell (1988) Bessell (1990)to deÐne the photometric bandpasses and the model of Vega by & BellDreiling (1980)for the calibration of the magnitude scale.


FIG. 26.ÈJ[K vs. K[L@ color-color diagram. Otherwise as in Fig. 25.

D0.4 mag per decade. However, for K[L @ it is D0.8 magper decade, though one must recall that L @ is not wellmodeled. Nevertheless, in principle these colors can collec-tively be used as crude gravity diagnostics.

7. CONCLUSIONS AND FUTURE WORK

During the past 2 years, scientists and the public at largehave been galvanized by the discovery of planets and browndwarfs around nearby stars and by evidence for ancient lifeon Mars et al. These extraordinary Ðndings(McKay 1996).have dramatically heightened interest in the age-old ques-tions of where we came from and whether we are unique inthe cosmos. NASA has outlined a program to detect planet-ary systems around nearby stars that may become a futurefocus of NASA and its central, unifying scientiÐc theme inthe next century. This vision is laid out in the ofExplorationNeighboring Planetary Systems hereafter ExNPS)(1996,Roadmap (see also the Report and has beenTOPS 1992)

expanded to include the Origins of life, planets, galaxies,and the universe.

The next generation planet and brown dwarf searchesand studies will be conducted by NICMOS, SIRTF,Gemini/SOFIA, ISO, NGST, LBT the MMT(Angel 1994),conversion, the VLT, Keck I and II, COROT (transits),DENIS, 2MASS, UKIRT, and IRTF, among other plat-forms. For close companions, advances in adaptive optics,interferometry, and coronagraphs will be necessary to dis-entangle the light of companion and primary.

The models we have generated of the colors and spectraof EGPs and brown dwarfs are in aid of this quest fororigins and of the discovery and characterization of sub-stellar objects around nearby stars and in the Ðeld. We havecreated a general nongray theory of objects from to0.3MJbelow D1300 K using the best input physics and70MJsome of the best numerical tools available, but muchremains to be done. In particular, the opacity of and aCH4proper treatment of silicate/iron, and clouds areH2O, NH3future challenges that must be met before the theory can beconsidered mature. Furthermore, the e†ects of stellar inso-lation, addressed only approximately in et al.Saumon

and et al. must be incorporated con-(1996) Guillot (1996),sistently. Since the near IR signature of proximate substellarcompanions will be signiÐcantly altered by a reÑected com-ponent, a theory of albedos in the optical and in the near IRmust be developed. For speciÐcity, we focussed in this paperupon objects in isolation and did not include the complicat-ing parameters of central star and semimajor axis. However,it will be useful to predict the signatures of speciÐc systemswith known orbital characteristics, primaries, and ages,such as q Boo, 51 Peg, t And, 55 Cnc, o CrB, 70 Vir, 16 Cyg,and 47 UMa.

Nevertheless, our theoretical calculations lead to certaingeneral conclusions :

and dominate the spectrum below1. H2O, H2, CH4K. For such most or all true metals areTeff D 1200 TeffÏs,sequestered below the photosphere.2. Though EGP colors and low-resolution spectra

depend upon gravity, this dependence is not strong.However, high-resolution spectra may provide usefulgravity diagnostics.

TABLE 6

COLOR INDICES OF SYNTHETIC BD/EGPS, [M/H]\ 0.0

g Teff(cm s~2) (K) J[H J[K H[K K[L @ M[N

105 . . . . . . . . . . 1000.0 0.35 [0.28 [0.63 2.28 0.87800.0 0.43 [0.65 [1.08 2.96 [0.77600.0 0.51 [1.36 [1.87 4.09 [0.68500.0 0.57 [2.00 [2.57 5.02 [0.62

3 ] 104 . . . . . . 1000.0 0.44 [0.02 [0.46 1.99 0.98800.0 0.50 [0.37 [0.87 2.58 [0.87600.0 0.57 [0.94 [1.51 3.49 [0.74400.0 0.63 [2.64 [3.27 5.99 [0.69300.0 0.71 [4.12 [4.83 8.17 0.68

104 . . . . . . . . . . 1000.0 0.55 0.40 [0.15 1.55 0.11800.0 0.59 [0.06 [0.65 2.22 [0.97600.0 0.66 [0.62 [1.28 3.05 [0.80400.0 0.46 [2.10 [2.56 5.12 [0.81

3 ] 103 . . . . . . 1000.0 0.82 0.92 0.10 0.74 1.07800.0 0.78 0.42 [0.36 1.62 [1.00600.0 0.69 [0.28 [0.97 2.73 [0.92400.0 0.45 [1.65 [2.10 4.73 [0.90200.0 0.56 [4.25 [4.81 8.91 0.86


3. The primary bands in which to search are Z, J, H, K,M, and N. K is not as good as J or H.

4. Enhancements and suppressions of the emergent Ñuxrelative to blackbody values can be by many orders of mag-nitude.

5. Objects that were considered from their low TeffÏsK) to be undetectable in the near IR may not be.([6006. The infrared colors of EGPs and brown dwarfs are

much bluer than the colors previously derived using eitherthe blackbody assumption or primitive nongray models.

7. In some IR colors (e.g., J[K), an object gets bluer, notredder, with age and for a given age, lower mass substellarobjects are bluer than higher mass substellar objects.

8. For a given composition, only two observables arenecessary to constrain a substellar objectÏs parameters. Forinstance, given only and gravity, one can derive mass,Teffage, and radius.

9. The existence of an interior radiative zone seems to bea generic feature of substellar objects with from D200TeffÏsto 1000 K, and might also obtain for below D200 K.TeffÏsThe appearance and extent of such a radiative zone is afunction of gravity.

10. Clouds of and are formed for belowH2O NH3 TeffÏsD400 and D200 K, respectively. Their formation will a†ectthe colors and spectra of EGPs and brown dwarfs in waysnot yet fully characterized.

We thank R. Angel, W. Benz, S. Kulkarni, J. Liebert, B.Oppenheimer, G. Rieke, G. Schneider, S. Stolovy, and N.Woolf for a variety of useful contributions. This work wassupported under NSF grants AST 93-18970 and AST 96-24878 and under NASA grants NAG 5-2817, NAGW-2250,and NAG 2-6007.

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