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Probing the Giant Planets

Tristan Guillot

llefore 1995, most astronomers expected giant extra-lJsolar planets to orbit their stars in quasicircular or-bits at a distance of more than a few astionomical units.(1AU is the mean distance between Earth and the Sun.)tt our Solar System, the orbits of the four giant planets-Jupiter, Saturn, IJranus, and Neptune-have semimajoraxes ranging from 5.2 to 30 AU and eccentricities nolarger than 5.6Vo.

Since then, more than 100 extrasolar planets havebeen discovered, all ofthem giants with at least 107o themass of Jupiter (0.1 M,, about twice the mass of Uranusor Neptune). Much smaller Earthlike ("terrestrial") extra-solar planets would not be massive enough to be detectedby current methods.

The newly found planets are strange-not at all whatwe expected. A signifrcant fraction ofthe extrasolar giantsdetected thus far orbit extremely close to their star, thatis, at less than 0.1AU. Some semimajor axes are as smallas 0.04AU, implying a period of revolution around the starofonly about three Earth days. The archetype ofthese so-called Pegasi planets (also called "hot Jupiters") is the firstone to have been discovered: 51 Pegasi b, a roughlyJupiter-mass giant orbiting at only 0.05 AU from a sun-like star in the constellation Pegasus.l

The other fraction of extrasolar planets discoveredsince 1995 may be even stranger. As shown in frgure 1,many of them exhibit very eccentric orbits,2 quite unlikeour own giant planets. It may be, however, that Solar Sys-tem analogs are common but hard to discover. After all,Jupiter and Saturn are so far from the Sun that they take12 and 29 years, respectively, to complete an orbit. A fewplanets in frgure t have large orbits with low eccentricity.Discovering more objects like these will require patienceand improved observational techniques.

Ithasbeen very dillicult to construct a coherent sce-nario that would explain the formation of giant planets aswe see them both within and beyond our solar system. Thepresence ofclose-in planets is generally thought to be dueto early migration of planets forming in a disk of gas anddust surrounding the young central star.3 But that's notthe only possibility, and it doesn't explain why Jupiter andits sisters didn't share such a fate.

Similarly, it is not clear why extrasolar planets often

have very eccentric orbits while ourown giant planets orbit the Sun in se-date circles. Could it be that "otdi-nary" circular orbits are in fact quiteextraordinary by Galactic standards?Is our solar system an unlikely out-come of the general mechanism ofplanet formation? Or perhaps, mightextrasolar planets be formed by a dif-ferent mechanism?

These are but a few ofthe questions that confront us.There's no shortage of suggested answers, but none thusfar has given satisfaction. A large part ofthe problem isthat the so-called radiovelocimetry method used until nowto discover extrasolar planets provides only a lower limiton the planetary mass M. Relying on the tiny Doppler mod-ulation as the star is tugged to and fro by its orbitingplanet, the method determines the orbit's diameter and ec-centricity. But the inclination angle i between the normalto the orbital plane and the line of sight is unknown, andradiovelocimetry only determines the product M sini.

Of course, we do have interesting additional meas-urements. For example, it is becoming clear that stars withplanets tend to be enriched in heavy elements-meaning,in astronomers'jargon, anything other than hydrogen andhelium. That tells us something about planetary forma-tion, namely that planets probibly grew more rapidly inenvironments rich in dust. (Most heavy elements formchemical species that condense at low temperatures.) Butwe do not know two crucial properties ofthe extrasolar gi-ants: their exact masses and their sizes. Except for oneserendipitous casea-the planet HD209458b.

A planet in transitHD209458 is a faint star in Pegasus, barely visible to thenaked eye. Like 51 Pegasi, its planet has a mass close tothat of Jupiter, and a tiny semimajor axis, a mere 0.045AU.The particularity of the HD209458 system is that, as seenfrom Earth, the planet passes in front ofthe star every 3.5days. Therefore, we can measure the time it takes for theplanet to transit the stellar surface and the consequentdimming of the star (about 2Vo). Thus we can also calcu-late the planet's size, the inclination ofits orbit, and there-fore its mass.5

The radius measured for the giant planet HD20g4b8bis about SSVolarger than that ofJupiter, although its massis 30Vo less than Jupiter's. This apparent contradiction isunderstood by realizing that gaseous giant planets tend tocool slowly by infrared emission and thus contract. andthat planets heavily irradiated by their stars contractmore slowly. Jupiter itself is estimated to be contractingat a rate ofabout 3 mm per year.

The observations of HD209458b, a hundred timescloser to its star than is Jupiter, confrrmed the general the-oretical picture and showed that the planet, discovered in200O, is made mostly of hydrogen and helium.6 The studyof this transiting Jovian giant was the first confirmation

@ 2004 American Institute of Physics, S-003i-9229-0404-040-2 April 2004 Physics Today 63

that our models of planet formation were not completelyoff-track. Had HD209458b been found to have a smallerdiameter than Jupiter, it would have meant that the newplanet consists mostly of heavy material, which wouldpatently contradict our formation models.

However, the hope that we would be able to learn moreprecisely the composition of HD209458b has dwindled rap-idly. The planet's radius turned out to be slightly largerthan expected. So we're probably missing some enerrysource that prevents the planet from cooling faster.T It ap-pears that tides may be dissipating heat into the planet'sinterior and thus slowing its contraction. The energ'ysource might be the orbital enerry of an unseen eccentricgiant companion planet, or it might be winds generated inthe planet's atmosphere by the strong stellar irradiation.

Alternatively, the atmosphere may be hotter than mostmodels predict (see figure 2). We know little about meteor-ology and tides on gaseous planets. Tens ofEarth massesof heavy elqments could be mixed in with the hydrogen andhelium without our being able to tell. Better understand-ing the giant planets will require more examples of tran-siting extrasolar planets, with different masses and orbitaldistances. That's an important goal of space missions suchas COROT, Kepler and, we hope, Eddingtoa (see box 1).

In the meantime, the power of transit observationshas been demonstrated. Because we know exactly whenthe planet is due to transit in front of its star, we can makevery accurate measurements and compare the on-transitto off-transit results. In just that way, David Charbonneau

64 April 2004 Physics Today

and coworkers,s in 200L,detected the presence ofsodium in the atmosphere ofHD209458b. The sodium, itturned out, was less abun-dant than expected. But be-cause we know so little aboutthe atmospheres of these ex-otic planets, it's not yet clearwhat that means. The sodiumshortfall could, for example,be due to colder atmgspherictemperatures than expected.Or it might result from at-mospheric dynamics or non-equilibrium effects. In anycase, the observation was amilestone in the study of ex-trasolar planets, .because itshowed that we can detectconstituents in the atmos-pheres of planets millions oftimes further from us thanJupiter.

Another crucial recentdiscovery is that HD209458bis slowly losing mass. Lastyear, Alfred Vidal-Madj ar and

coworkers found that when one observes the transitingplanet at the LIV wavelength of the Lyman-a absorptionline of hydrogen, it appears three times larger than atother wavelengths.e This suggests the presence of an ex-tended, tenuous, envelope ofhydrogen escaping from theplanet as a result ofheating ofthe upper atmosphere andbombardment by ionized stellar wind. The magnitude ofthis mass loss appears to be consistent with estimatesbased on Jupiter, but scaled up by a factor 10 000 becausethe star is 100 times closer to the planet than the Sun isto Jupiter.G The Lyman-a measurements give us the firstpossibility of quantiffing such processes more preciselyand examining how gaseous planets manage to suryive soclose to their stars.

Impressive as they are, the HD209458b measure-ments tell us only about the upper atmospheres of giantgas planets. How can we better constrain their interiorcompositions? To do so, we have to learn how surface meas-urements relate to interior compositions. And to that end,we must look more carefully to the gas giants closest to us.

Our own giant planetsWe can, of course, measure very accurately the masses,sizes, and hence the mean densities'of Jupiter, Saturn,IJranus, and Neptune. The densities turn out to be quitelow-ranging from 0.7 glcml for Saturn to 1.6 g/cm3 forNeptune. For comparison, the four inner terrestrial plan-ets have mean densities near 5 glcml. One might have at-tributed the difference to the conjecture that the giantplanets have the same composition as Earth but very muchhotter. Alternatively, one could suppose that they are verymuch colder but made of light material. Of course, we'veknown for a hundred years that only the second explana-tion is valid.

Indeed, a look at the atmospheres ofthe giant planetsshows that they are made mostly of hydrogen and helium,with only traces of heavier elements. Exactly how much ofthese trace elements is present is a big question. Remotesensing cannot probe very deep, because the atmospheresbecome too opaque and because cloud formation sequestersa number of important elements in the deep regions. The

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sequestered elements include water, the main carrier ofoxygen. Being the third most abundant element in the uni-verse, oxygen is a critical but hidden component of thegiant gas planets.

The Galil.eo probe, which was sent down into the Jov-ian atmosphere in September 1995, was desigrred to detectsome of the hidden atmospheric ingredients. It success-fully probed Jupiter's atmosphere down to a pressure of 22bar. (1 bar = 105 pascals, roughly the mean sea-level at-mospheric pressure on Earth.) Thus the probe was able tomeasure accurately the abundance ofconstituents such ashelium, methane, hydrogen sulfur, neon, argon, krypton,and xenon. Except for helium and neon, all these speciesappear to be enriched by about a factor ofthree relative to

their abundances in the Sun.Ammonia was also detected, but measuring its abun-

dance posed problems because ofits tendency to stick to thewalls of the probe's mass spectrometer. The most elusivespecies, however, proved to be the one that was most soughtafter-water. The probe did detect some water, but muchless than expected, and its abundance was still rising in thelast measurements before the probe frnally fell silent.10

What does that deficit mean? In the frigid outermostprecincts ofthe Jovian atmosphere, the water is condensed.To properly measure its bulk abundance, the probe had toreach levels deep and hot enough for the water to be en-tirely vaporized. It had been thought that probing down to5 bar would suffice. Obviously, that was too optimistic.

1-he formidable promise of the transitI method of studying extrasolar planets has

led to the development of several space mis-sions dedicated to the discoverv and meas-urement of more extrasolar planets transitingin front of their stars. Canada's 15-cm MOSTtelescope, launched in August 2003, canfollow giant extrasolar planets closely orbit-ing their stars, even if they don't transit thestellar disk. Two other missions. the FrenchSpace Agency's COROT and NASA's Kepler,are due to be launched in 2006-02. The fu-ture of the European Space Agency's Ed-dington mission, originally scheduled for a2008 launch, is unclear.

These missions are designed to searchhundreds of thousands of stars for planetsranging from Pegasi giants down to Earth-sized planets. To do all that, the instrumentswill have to achieve very stable and accu-rate photometric measurements. The dim-ming of a sunlike star by a transiting giantplanet is only of order 1%; for a transitingEarth-sized planet, the dimming is 100 timesweaker still.

By comornrng tne space-Daseo ooserya- -rs'with" grouni-b*"b radiovelocimetry, we will be able to

te radii and masses of gas giants and ice giants. Fort$tramlar planets that are also very close to theirP r d l q ) l r r s r o r s d r J v v c l ) t L l v J s r v f l l s l l

be able to measure the modulation of the storls

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After the fact, the consensus of the community is that theprobe fell into a rare dry hot spot. If,s as ifan alien race de-iigned a probe for Earth's atmosphere and it just happenedto fall onto the Sahara desert. Very likely, there is morewater elsewhere on Jupiter, or at greater depths.

The only secure conclusion is that we don't under-stand the meteorology ofgiant planets. That's because themeteorology is inherently complex. We don't know how it'stied to the planet's internal structure, and data arepainfully scarce. Visible and IR observations, and eventhe deepest probe we could design, only provide skin-deepincursions into the interior. To really understand thegiant gas planets, we have to avail ourselves of anothertechnique.

GravimetryOne possible method is seismology. Solar astronomershave learned much from observing helioseismic modes'Unfortunately, it is not clear that the giant planets can os-cillate like the Sun. Attempts to measure seismic oscilla-tions on the giant planets ofthe Solar System have thusfar been inconclusive.l:

Our last resort is gravimetry. The giant planets rotatequite rapidly. The fastest is Jupiter, with a diurnal periodof t hours, 55 minutes; the slowest is lJranus, with a pe-riod of 17 hours, 14 minutes.

Therefore, all the Solar System giants are signifi-cantly flattened by centrifugal acceleration. The conse-quent departure of the gravitational field from sphericalsymmetry can be measured by careful monitoring of thetrajectory ofa spacecraft coming close to the planet, prefer-ably on a polar orbit. Roughly speaking, when the space-craft is near the equator, its trajectory is less influencedby the planet's core, and more by the outer regions, thanwhen it flies close to either pole.

For a fluid planet in the absence of tidal forces, the

where r and 0 are the radial and polar coordinates andMand Ro are the planet's mass and equatorial radius. Thefunctions PrdcoJ0) are Legendre polynomials and J*thecorresponding gravitational moments that parameterizethe cylindrically symmetric mass distribution.

The -ass and gravitational moments determined bysatellite measurements of the gravitational potentialtranslate into a constraint on the interior density profrlep(r,0). These constraints can be written

M = ! o(r,e)d,

t r, = - h I p(r,o)r2i Pr,(cos g)dr,

where dr is a volume element and the integrations are per-formed over the entire volume of the planet.

Because of the form of the Legendre polSmomials,gravitational moments of progressively higher order con-itrain the density profrle of regions closer to the planet'satmosphere. Unfortunately, only J" and Jn are presentlyknown well enough to provide useful constraints on the in-teriors ofJupiter, Saturn, IJranus, and Neptune.

The density p is itself a function of several thermody-namic variables: pressure, temperature, and composition.The pressure can be calculated quite accurately becagsegianf planets are always very close to hydrostatic equilib-iium; internal pressure equilibrates gxavity and inertialforces at all points. Determination of the internal temper-ature is more problematic. Fortunately, the giant planets

gravitational potential V just'outside the planet isgiven by

radiate more energ-Jr' than they receivefrom the Sun. We can measure the rateof energy loss and estimate how theycool. Jupiter, for example, cools bYabout 1 K per million years. We canthen infer how heat is transportedwithin the planetary interiors.

Convection appears to be the dom-inant form oftransport in Jupiter, Sat-urn, and Neptune, and probably also inIJranus. Because convection is very ef-ficient in these fluid planets, tempera-ture structure should be close to anadiabat-that is, a system that ex-changes no heat with its environment.The temperature distribution can thenbe calculated as a function of pressure,composition and the known atmos-pheric boundary conditions.

Composition is the knotty Prob-lem. It affects the temperature struc-ture and can also affect convection.That leaves an infinite number of

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solutions describing how pressure, temperature, density,and composition might depend on r. The true solution maydepend on the initial conditions.

The Gedanken Caf6To illustrate the conundrum, let's assume you're sittingcomfortably in the sun at a caf6 and you're served anespresso. I like it sweet and, in any case, our gedanken ex-periment requires sugar. Ifyou drop a sugar cube into thecup and let it dissolve, most of the sugar will stay at thebottom. If you stir the liquid gently (let's say for fear ofspilling it on your laptop), only part of the sugar will mixwith the coffee. You get a homogeneous system only if youstir vigorously enough.

An alternative method would be to drop finely granu-lated sugar instead ofcubes into the coffee. Ifthe sugar isfrne enough, it will dissolve before reaching the bottom,and very little stirring is needed. But that's only if theespresso is hot enough. If it's only lukewarrn, the sugar hasa hard time dissolving; it tends to sink to the bottom. Fi-nally, after all this preparation, let a friend arrive at thetable and try to guess, from his first sip, how much sugarthere is in the cup.

For giant planets, the problem is similar, only morecomplex. Ifthe coffee itselfis a good analog for the hydro-gen, the sugar is replaced by a mixture of helium, water,methane, ammonia, neon, and many more chemicalspecies, all ofwhich behave differently. They could, for ex-ample, either be mixed with the hydrogen or sequesteredin the deepest regions.

Part ofthe helium is believed to have fallen into theinteriors ofJupiter and Saturn. Less of it is observed intheir atmospheres than must have been present when theSolar System was formed. This sequestration is thought tobe due to a phase separation between helium and hydro-

http://www. physicstoday. org

gen in which helium-rich dropletsform and fall to deeper regions. Suchphase separation should occur at highpressures and low temperatures. Butneither laboratory experiments norcalculations have yet confirmed that itreally does happen under conditions

:,, relevant to Jupiter and Saturn. Inter-,' estingly, the Galileo probe found a,, lower concentration of neon in the

outer reaches ofJupiter than the Sunhas. That's consistent with the predic-tion that neon should efficiently dis-solve into the fallinghelium droplets.l2

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Other constituents, such as icesand silicates, may have been deliveredto the forming planet very early on, asingredients of a central solid core.They may have arrived in small piecesand mixed with the mostly hydro-

gen-helium envelope, or they may have come as large-say, Earth-sized-protoplanets. In the latter case, the ma-terials would have penetrated deep into Jupiter.

Tb make matters even more complicated, any primor-dial central core might either have remained largely intactuntil now or, like the sugar cube in our espresso cup, itmight have been eroded by convection. The spoon in thecup plays the role ofconvection in the giant planets. De-pending on the vigor and depth ofthe convection, it eitherwill or will not scoop core material up into higher precincts.

But independently ofhow you stirred the espresso, solong as it's been stirred even a little bit, you expect it to befairly homogeneous. Only the last sip might be signifr-cantly sweeter, and there might be a residue of sugar leftin the bottom of the cup. In the same way, we expect ourgiant planets, which are mostly convective, to be reason-ably well-mixed. That simplifies the problem enorrnously.We have to consider only three principal layers. ForJupiter and Saturn, they are a central core and an enve-lope that is split into a helium-rich interior and a helium-poor outer shell (see figures 3 and 4.) For Uranus and Nep-tune, the two much smaller giants, it is less clear that thisapproach is valid. Nonetheless, astronomers often'dividetheir interiors into a central rock core, a surrounding icemantle, and an outermost hydrogen-helium envelope.

Models of the planetary interiors that match all theobservational constraints conclude that Jupiter and Sat-urn consist mostly of hydrogen and helium. Saturn ap-pears to require a dense central core of L0-25 Earthmasses, while Jupiter's core has no more than 12 Earthmasses.13 lJranus and Neptune are quite different in struc-ture from their larger cousins. While Jupiter and Saturnare called gas giants, the other two are really ice giants.Indeed, for more l};ran 70Vo of their interiors, the densityprofile appears to be consistent with that of compressedwater ice. Their outer precincts appear to be gas envelopes

April 2004 Physics Today 67

N.EPTUNE

n 1 July 2004, Saturn wil l acquire a\lnew satellite. The Cassini spacecraftwill fire its engines for orbit insertion intothe Saturnian svstem. For the next fouryears, it will study Saturn's moons, rings,and magnetosphere, and also the planet'sintriguing meteorology. The spacecraftwill remotely measure the composition ofSaturn's atmosphere.

Cassini will'also determine the gravityfield much more accuratelv than hasbeen done before. Cravitational mo-ments at least up to ,1, should be deter-mined with high precision, which wouldallow a much better determination of Sat-urn's internal structure. We should thenbegin to understand the planet's interiorrotation. At present, we don't knowwhether Saturn's atmospheric winds aresuperficial or deep-rooted

Early next yeat Cassini will drqpa probe, called Huygens, into the atnegi*phere of Titan, Saturn's largest moon. TheCassini-Huygens mission is an impres.sive example of a successful cooperationbetween NASA, the European SpaceAgency, and the ltalian Space Agency.

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consisting mostly of a few Earth masses of hydrogen andhelium.la The few measurements we have don't allow amore accurate estimate of the structures of l]ranus andNeptune.

For Jupiter and Saturn, it is important also to con-sider their total content of heavy elements. Present mod-els estimate the heavy-element component at 20-30 Earthmasses for Saturn and 10--40 Earth masses for Jupiter.The uncertainty is signifrcant. Most of it is due to our lim-ited understanding of the behavior of hydrogen at ultra-high pressures on the order ofa megabar.

Shock compression experiments can now reach thesehigh pressures in the laboratory. However, two sets of suchexperiments have yielded conflicting results.ls The 1998laser-induced shock experiments at Lawrence LivermoreNational Laboratory measured a maximum density com-pression ofabout a factor of6 for hydrogen at 1 Mbar. Themore recent experiment by Marcus Knudson and cowork-ers with magneticallj' accelerated plates at Sandia Na-tional Laboratories found a maximum compression of onlyabout 4 at the same high pressure.

For Jupiter, the greater hydrogen compressibility im-plies a significantly smaller component of heavy elements.Hence the wide uncertainty range of 10-40 Earth masses.For Saturn, on the other hand, the total amounts ofheavyelements appear to be more or less independent ofhydro-gen's equation of state at ultrahigh pressure. That'smostly because the pressures in Saturn's interior aresmaller. Our hopes rest on the Cassini mission, whiehshould allow a much better determination of Saturn'sgravity field (see box 2).

Lessons and prospectsOur knowledge ofthe interior structure ofthe giant plan-ets remains vag'ue, which severely limits our progress inunderstanding how they formed. For example, one of theunexpected results from the Galileo probe is the presence

68 April 2004 Physics Today

of argon at three times the solar abundance insideJupiter's atmosphere.lo Argon is a noble gas that is ex-pected to condense in the protosolar nebula only at verylow temperature-no higher than 30 K. One therefore ex-pects that the ratio ofargon to hydrogen should be aboutthe same in Jupiter and in the Sun. The unexpectedlylarge Jovian argon abundance indicates that some physi-cal process led to the separation of argon and hydrogenduring the planet's formation. That points to relatively lowtemperatures at the time of Jupiter's formation.

One possibility is that small ice grains grabbed someof the argon in the protosolar nebula (in a process calledclathration) and that the grains were somehow efficientlybrought into Jupiter.l6 This process would imply thatwater is abundant inside the planet. Unfortunately, pres-ent models ofthe Jovian interior are too uncertain to tellus whether clathration is the correct answer.

Future high-pressure laboratory experiments on deu-terium compression and numerical calculations of the be-havior of the hydrogen-helium mixture at the relevantpressures and temperatures will give us a clearer pictureof the interiors of the giant planets. So will t}re Cassinisatellite's precise determination of Saturn's gravitationalmoments. But we'll still be missing cr-ucial pieces ofthe puzzle: the abundance ofwater in Jupiter and Saturn,and a precise knowledge ofJupiter's gravitational and mag-netic fields. Uranus and Neptune will remain mysterious.

Jupiter is the next giant planet on the agenda. It iseasier to reach than the other Solar System giants, and it'sthe one from which we can learn the most. How, specifi-cally, should we proceed? One possibility, inspired by theGalileo mission, is to send several more probes into the at-mosphere. They should be able to penetrate deeper thanthe Galileo probe-down to at least 100 bar. The Galileoprobe taught us that Jupiter's atmosphere is complex. Al-though the new probes would provide unique local data,the measurements could be diffrcult to interpret without

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prior knowledge of deep winds, meteorological structures,and so forth.

Therefore we must, first of all, learn more about theglobal structure of Jupiter's deep atmosphere. Using an or-biter that comes within 4000 km of the planet's cloud topson a polar orbit, one can get very accurate measurements ofthe planet's gravitational and magnetic fields. The meas-urement of higher-order gravitational moments would re-veal whether or not the zonal winds are rooted deep in theinterior.l? That issue is critical for understanding the mete-orology and internal structure of rapidly rotating gaseousplanets.

With a radiometer added to the spacecraft, one canmeasure variations in the deep atmosphere's temperatureand its ammonia and water abundances as a function oflatitude and longitude, down to pressures ofa few hundredbar. Using meteorological and radiative-transfer modelstogether with the most up-to-date laboratory measure-ments of molecular opacities at high temperature, one canthen disentangle the different satellite data to determineconstraints on the abundance ofwater. Thus equipped, thenext generation ofmissions to the giant planets, probablyincluding a few well-designed probes to be dropped intospecifrc locations, should do much to unlock their secrets.

Giant planets, extrasolar as well as our solar systemneighbors, retain most ofthe keys to understanding howplanets form and evolve. Their exploration began with thePioneer, Voyager, and Galileo missions. The scheduledCassini-Huygens mission to Saturn promises great scien-tific returns. But the most signifrcant void in the inven-tory of Solar System data is probably Jupiter's unknowncomposition. To understand how the Solar System formedand to acquire fundamental data that will be crucial forthe following generation of astronomers, let the explo-ration continue!

ReferencesM. Mayor, D. Queloz, Noture 378,355 (1996).G. W. Marcy, R. P. Butler, Annu. Reu. Astron. Astrophys.36,57 (1998); D. A. Fischer et al., Astrophys. J. 586, 1394 (2003);C. Perrier et al.,Astron. Astrophys.,4l0, 1039 (2003).D. N. C. Lin, P. Bodenheimer, D. C. Richardson,NatureSSO,606 (1996).There are other transiting candidates, but they have yet tobe confrrmed. See M. Konacki et al., Nature 421,507 (2003).D. Charbonneau, T. M. Brown, D. W. Latham, M. Mayor, As-trophys. J. Lett.529,lA5 (2000); G. W. Henry G. W. Marcy,R. P. Butler, S. S. Vogt, Astrophys. J. Lett.529,IAl(2000);T. Brown et al., Astrophys. J. 552,699 (2001).

6. T. Guillot et al., Astrophys. J. Lett. 460, L993 (l-996).7. P. Bodenheimer, D. N. C. Lin, R. Mardling,Astrophys. J.548,

466 (2001); T. Guillot, A. P. Showrnan, Astron. Astrophys.385, 156 (2002); l. Baraffe et al., Astron. Astrophys. 4O2, 7Ot(2003); A. Burrows, D. Sudarsky, W. B. Hubbard., Astrophys.J.594.545 (2003).D. Charbonneaw et al., Astrophys. J. iffi,377 (2002).A. Vidal-Madjar et al., Nature 422, L43 (2003).T. Owen et al, Nature 4O2,269 (1999); S. K. Atreya et al.,Planet. Space Sci. 51,105 (2003).B. Mosser, J. P. Maillard, D. M6katnia, Icarus l/U, L04(2000).

12. See abstract, M. S. Roustlon, D. J. Stevenson EOS Tlans.Arn. Geophys. Union 76,343 (1995).

13. T. Guillot, Science 2a6,72 (1999); D. Saumon, T. Guillot,Astrophys. J. (in press).

14. M. Podolak, J. I. Podolak, M. S. Marley, Planct. Space Sci.48,143 (2000).

15. G. W. Collins et a1., Science 281, 1178 (1998); M. D. Knudsonet al., Phys. Reu. Lett.90, 035505 (2003).

16. D. Gautier, F. Hersant, O. Mousis, J. I. Lunine, Astrophys.'J.

3.

4.

5.

8.9.

10.

11.

55O,227 (20Ot).17. W. B. Hubbard, lcorus 137,196 (1999). I

Physics Today 69April2OO4

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