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The Kuiper Belt

Michael E. Brown

fin 10 January 1992, a freighter en route from Hong\rf Kong to Tacoma, Washington, got caught in a storm inthe northern Pacifrc Ocean, and shipping containers frlledwjth 29 000 plastic bathtub toys were lost overboard. Tbnmonths later, brightly colored ducks, turtles, beavers, andfrogs began showing up on beaches all along the coast ofAlaska. Seattle-based oceanographers Curtis Ebbesmeyerand James Ingraham quickly realized that they had a mas-sive inadvertent experiment on their hands. In their re-search, the two had been studying wind and sea circula-tion in the northwest Pacific by'systematically droppingsmall numbers of labeled floats from fixed locations andhoping for their recovery. As they well knew, scientists un-derstood the physics behind the winds and currents, butthe large numbers of different interactions that occurmade precise prediction difficult---even with the help oflarge computer models. The bathtub toys provided a wind-fall of data that would allow the two oceanographers tochart out winds and currents and understand the complexinteractions in more detail than was previously possiblewith their more limited data.

Like oceanographers trying with a paucity of observa-tions to understand the complexities of currents, as-tronomers studying the formation and evolution of theouter Solar System have had, until recently, few data pointsaround which to spin their theories. The outer Solar Sys-tem's four giant planets were each created and movedaround by a complex suite ofinteractions. Tlying to piecetogether all ofthose interactions to discern a history wouldbe like trying to use just four large shipwrecks washedashore to understand the flows ofall ofthe oceans'currents.

The breakthrough for astronomers came a few monthsbefore the frrst plastic ducks hit the beaches near Sitka,Alaska, in November 1992. After a long search, David Je-witt of the University of Hawaii and Jane Luu, then of theUniversity of Califorriia, Berkeley, found a single faint,slowly moving object in the sky.l After they followed it fora few days, they realized that they had found the frrst ob-ject beyond Neptune since Clyde Tombaugh discoveredPluto in 1930.

Today, more than 800 additional members of what isnow known as the Kuiper belt have been discovered in theouter Solar System.2 Their existence is forcing a change in

the picture that astronomers held justa decade ago of the outer Solar Sys-tem's dynamical evolution. In manyways, Kuiper belt objects behave liketest particles that trace the gravita-tional effects of the giant planets' re-arrangements and perturbations. Thehundreds of such objects strewnthroughout the outer Solar System

give cbncrete data that allow astronomers to trace the his-tory of that system-as surely as tracing the routes of hun-dreds ofplastic bathtub toys washed on beaches shows thewinds and currents ofthe northern Pacifrc.

Early expectationsThe prediction of a belt of small bodies, or planetesimals,beyond the orbit of Neptune was made in 1950 by GerardKuiper, pictured in frgure 1, who used a seemingly weakbut ultimately correct line of argument. Kuiper proposeda method to conceptually reconstruct the initial disk of gasand dust from which the entire Solar System formed. Hebegan by taking Jupiter, smashing it flat, and spreadingits entire mass into an annulus centered around the orbitofthe giant planet. That annulus represented the regionof the nebula that went into making Jupiter. Kuiper knew,however, that some material initially in that part of thenebula must have been lost, because Jupiter has a higherabundance ofelements heavier than hydrogen and heliumthan the Sun does. So he added a little more mass to theannulus to make up for the lost hydrogen and helium andbring that region ofthe theoretical nebula to solar compo-sition. Kuiper applied the same procedure to the remain-ing giant planets and to the terrestrial planets. (The ter-restrial planets have lost almost all oftheir hydrogen andhelium so a large amount of extra material had to be addedin.) His method yields an approximate reconstruction ofthe mass distribution of the initial nebula similar to themore modern reconstruction displayed in frgure 2.

Kuiper noted that the surfaee density of the nebulasmoothly dropped from the inside to the outside until, be-yond Pluto, the flensity plummeted. He reasoned that thenebula should not have an abrupt edge and that beyondPluto was a realm where densities were never high enoughto form large bodies, but where small icy objects existedinstead. Furthermore, he suggested that the outer regioncould be the source for the comets that periodically comeblazing through the inner Solar System. When Kuiper for-mulated his argument, Pluto was thought to be massiveenough not to fall below the straight interpolating line infigu.re 2. Nowadays, astronomers regard the Kuiper beltas lying beyond the orbit of Neptune.

Almost four decades after Kuiper's analysis, MartinDuncan, Thomas Quinn, and Scott Tremaine, all then ofthe University of Toronto, took advantage of the growingpower of computers to simulate the long-term gravita-

@ 2004 American Institute ol Physics, S-0031-9228-O4O4-O2O-7 April 2004 Physics Today 49

tional influence of planets and showed that one class ofcomets-the Jupitei-family comets-were best explainedby the existence ofa band ofsmall bodiesjust beyond Nep-tune's orbit. They named that group of bodies the Kuiperbelt.3 Jewitt and-Luu found the first object in the hypoth-esized Kuiper beltjust five years later, in 1992'

The edge of the Solar System?One of the frrst surprises after the discovery of the Kuip-erbelt was that it appea"s to contain only about IVo of themass needed to make up for the deficit noted by Kuiper'Even more interesting, early studies by Alan Stern at theSouthwest Research Institute in Boulder, Colorado, sug-gested that the Kuiper belt did not even contain enoughirass to have formeditself.a That is, building up the largestKuiper belt objects from the gradual accumulation of the.-.lle" objecti-the typical way in which solid bodies inthe Solar System are iliought to form-would have takenlonger than the age of the Solar System-

Figure 2 suggests a possible resolutiot to the discrep-"tt"y n6t"d by Stern. There one sees that the asteroid beltalso appearsio have an anomalously low density. The lossofthe vast majority ofthe original asteroids !s an expectedconsequence of thei" interaction with nearby Jupiter'-Asimilar type of process is likely to have taken place in theouter Solar Sys-em, where an initially much more massiveKuiper belt was severely depleted by interaction withnearby Neptune.

An interesting potential consequence ofthe local lossin the Kuiper belt iJthat somewhere beyond the influenceof Neptun^e, the Kuiper belt might increase in density by

50 April 2004 PhYsics TodaY

a factor of 100 or more. As gleater numbers of objectsbegan to be detected, however, it became clear that thetro--b"" of Kuiper belt objects decreases dramatically be-yond about 43 AU. (An astronomical unit, or AU, is themean distance from the Sun to Earth; Pluto, for instance,is on average 39.5 AU from the Sun.)

For many years, arguments circulated that the drop-off was a simpie consequence of more distant Kuiper beltobjects'beingmuch fainter. After all, t}rre Ur2 decrease inlight intensity happens twice for Kuiper belt objects----onceoi th" way fiom the Sun to the object and again on theway back to Earth. Thus, an object at 50-AU is only(40i50)4 = 0.41 times as bright as one at 40 AU. But threeyears ago, separate analyses by Lynne Allen (then at theUniversity of Michigan' Ann Arbor) and colleagues, and byChad Truiilo and me showed that the lack of detectionswas statistically signifrcant even when one takes into ac-count the expected dimming of distant objects.s The trueradial distribution ofKuiper belt objects has a strong peak

at about 43 AU and decreases quickly beyond that' Mymost recent analysis rules out a resumption of Kuiper beltdensities 100 times that of the known Kuiper belt to a dis-tance of more than 100 AU.6 It appears that astronomershave truly found the edge-or at least an edge-of oursolar system at about 50 AU. Many known Kuiper belt ob-jects tiavel out beyond that edge, but their orbits all re-

iurn to the inner dense region of the Kuiper belt. No knownobjects exist exclusively beyond 50 AU.

The existence of an abrupt edge was what led Kuiperto suggest the presence ofan unseen band ofplanetesimals

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of the nebular disk from whichmed may be estimated by spreading thelanet into an annulus and adding a littlewhat was thought to have been lost. As

rtes, the density falls fairly regularly withbut one sees precipitous density drops:roid belt and beyond Neptune's orbit.is in astronomical units (AU), where 1l mean distance from the Sun to Earth.

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to begin with. Some astronomers have theorized that theKuiper belt does indeed continue outward and that its bod-ies become significantly smaller or darker, but no physi-cally plausible reason for such an abrupt change has beenfound. Shigeru Ida ofthe Tbkyo Institute ofTbchnology andcolleagues have proposed that a close encounter with apassing star could have stripped material from the outeredge of the Solar System.T Such an encounter would haveleft a clear signature in the inclinations of the remainingKuiper belt objects, and I have shown that this signatureis absent.8 I have long speculated that one or more mod-erately large planets remain to be discovered in the outerSolar System and that the missing mass is tied up in thosebodies. Although Tlujillo and I have surveyed most of thearea where such planets would likely be found, we havenot uncovered anything larger than Quaoar (frgure B),about half the size of Pluto. We're continuing to look.

[As this article goes to press, we'ue rnade two new dis-coueries that sornewhat alter the picture painted in this sec-tion. The Kuiper belt object 2004 DW may be euen largerthan Quaoar. That object's orbit is well within the SI-AUbelt edge, but we haue found a second large object far out-side the edge. Its highly elliptical orbit takes it from a min-imum distance of 76 AU from the Sun to a maximum ofaround 900 AU. This object, we belieue, is the first of whatwill proue to be a large population of new objects in the Oortclourl' a band of cornets belieued, prior to our discouery, torun from 75 000 to 150 000 AU. To read more about thetwo newly discouered objects, see http:llwww.gps.caltech.edu l-mbrown.l

PlutinosInaddition to expecting a much higher mass for the Kuiperbelt than has been observed, astronomers had initially as-sumed that the Kuiper belt would be a quiescent, smoothlyvarying band of objects slowly decaying in density with dis-tance from the Sun. They figured objects would be in rel-a-tively circular (that is, low eccentricity) orbits, althoughobjects elosest to Neptune might have slightly higher ec-centricities owing to the gravitational influence of thegiant planet.

The true picture of the Kuiper belt that has emergedfrom the first decade of observations is dramaticallv dif-ferent from those initial expectations. As shown in figure4, the Kuiper belt contains multiple complex dynamicalstructures. Those are the clues that allow one to untanglethe complex interactions and begin to understand theearly evolution of the outer Solar System.

The first unusual structure noted in the Kuiper belt wasthe pileup of objects with semimajor €l:res of approximately39AU and moderate to large eccentricities. Pluto is a mem-ber of that population, which collectively has come to beknown as the Plutinos. An important clue to the origin ofPluto and the Plutinos is that they are situated in B:2 meanmotion resonance with Neptune. That is, while Neptune cir-cles three times around the Sun, a Plutino circles twice.

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For many years, astronomers considered the curiousresonance of the orbits of Neptune and Pluto to be a fortu-itous coincidence that prevented close encounters betweenthe two planets (even though their orbits cross) and so al-lowed Pluto to suryive. It was hypothesized that many otherPluto-sized objects might have existed at one time but thatone by one they had close encounters with Neptune andwere scattered away. In 1993, however, Renu Malhotra ofthe University of Arizona, Thcson, realized that Pluto's or-bital resonance and high eccentricity-though unusual-would be expected if, at some point in the past, Neptune'sorbit had slowly expanded outward and Pluto had been cap-tured and pushed outward (see the box on page 5B).e Sliecalcr4ated that Neptune would need to have moved by asmuch as 10 AU to explain the orbit of Pluto. Also, the move-ment of Neptune must have been quite smooth or Plutowould have escaped the resonance.

Resonance capture could naturally explain the orbitof Pluto and the Plutinos, but why would Neptune's orbitexpand? Almost a decade before the discovery ofthe firstKuiper belt object, the answer was provided by Juan Fer-nandez (Max Planck Institute for Nuclear Physics) andWing Ip (Max Planck Institute forAeronomy), who exam-ined the interaction between Neptune and the small bod-ies left over after the formation of the giant planets.l0

The key to the explanation is simple eonservation ofmomentum. As small bodies approach Neptune and arescattered inward toward the other planets or outward to-ward the edge of the Solar System, Neptune must move atiny amount in the opposite direction. In general, Neptunehas an equal probability ofscattering an object inward oroutward and thus moving outward or inward, respectively.But objects scattered outward by Neptune tend to remaingravitationally bound to the Sun and tend to eventuallyhave another close encounter with Neptune. The net effec1is that objects scattered outward do nothing to Neptune'sorbit. Objects scattered inward, however, have a muchsmaller chance of coming back, as they are likely to hit orgravitationally interact with one of the other giant plan-ets. Ifan object gets close to Jupiter, it will likely be thrownout of our solar system completely. The bottom line is thatNeptune scatters more objects inward than outward andthus itself moves outward.

The other giant planets move, too, as they scatter ob-jects. Uranus and Saturn, like Neptune, tend to scattermore objects inward than outward, and so move fartherfrom the Sun. Jupiter has no interior giant planets, so ittends to scatter more objects outward than inward and

April 2004 Physics Today 51

move closer to the Sun.The smoothness of the planetary migration, which

plays an important part in whether objects are resonantlycaptured, is a function ofthe size and number ofobjects inthe nebular disk. Large numbers of small objects will leadto a smooth migration, and a smaller number of larger ob-jects will make the migration jumpy and cause objects tobe lost from the resonances.

The idea oflarge-scale migration ofgiant planets, asproposed by Fernandez and Ip, did not really catch on withastronomers until Malhotra suggested that the pileup ofPlutinos is an inescapable consequence ofthat migration.After Malhotra's paper, the idea that the giant planets mi-grated became an instant part ofthe standard lore oftheearly evolution of the outer Solar System.

Scattered and classical beltsAnother striking aspect of the Kuiper belt's structure, ev-ident in frgure 4, is the long tail of objects at high semi-major axis and high eccentricity. Notwithstanding thegreat distances beyond the Sun to which those objectstravel, they all have orbits that return them to the mainregion of the Kuiper belt, well inside the 50-AU edge. Thatthe majority ofthose objects have closest approaches to theSun of around 30 Au-the length of Neptune's semimajoraxis-is a giveaway as to their origin. They are the rem-nants ofthe scattering and migration process that pushedNeptune outward. They must have had a close encounterwith Neptune sometime in the past and are now on largeeccentric orbits that will eVentually lead them into moreclose encounters.ll Some of them will be scattered inwardand eventually make their way into the inner Solar Sys-tem to join the Jupiter-family comets visible today.

The frnal Kuiper belt structure displayed in figure 4comprises bodies in relatively circular orbits betweenabout 41 and 48 AU. Those bodies most resemble the ear-liest expectation of what Kuiper belt objects would be andthus have become known as classical Kuiper belt objects.But a close look at the classical Kuiper belt shows thateven it is not pristine and undisturbed as originally envi-sioned by astronomers. I have shown that the classical ob-jects appear to be two separate superimposed populations:

one, a low-inclination dynamically unperturbed popula-tion and the second, a much-higher-inclination dynamically stirred population.8

The existence of dynamically hot and cold populationsin the same place was perceived to be almost as odd as apot of water on the stove's being half scalding and halftepid. No simple process can start with a dynamically un-excited collection of objects and excite half of them whileleaving the other half unperturbed. One seems forced toconclude that the two separate populations were made atdifferent times, different places, or both, and that they arenow fortuitously superimposed. Hal Levison and Sternfound interesting evidence that supported the separateformation of the two populations and showed that thelargest objects in the Kuiper belt are all part of the dy-namically hot population.l2 Tfujillo and I found that theunexcited cold population is distinctly different in colorfrom the hot counterpart.ls (The colors are difficult to in-terpret, though, because no one knows what they actuallymean.) Both frndings suggest that the different dynamicalpopulations ofthe classical belt are physically distinct andarose separately. It thus appears that the cold classicalpopulation, which consists only of small red bodies, is thepristine part of the Kuiper belt. (But read on-appear-ances may be deceiving.) Everything else originated else-where, presumably in the denser regions closer to the Sunwhere the larger bodies could more easily have formed.Somehow, the bodies in the Kuiper belt that are not pris-tine were transported to where we see them today.

A nice explanation for the coexistence ofthe two pop-ulations was published last year by Rodney Gomes of theObservat6rio Nacional in Brazil.la Gomes used powerfulcomputer simulations and suggested that the hot popula-tion is a consequence of the migration of Neptune.

Previous work had, of necessity, considered theprocesses of scattering and migration separately. Butsteady increases in computer speed allowed Gomes to com-bine the two processes and see their interplay. He foundthat sometimes objects could be scattered into high-incli-nation orbits that intersect the region of the classicalKuiper belt. If Neptune were not migrating, those objectswould eventually have another close encounter with Nep-

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tune and scatter elsewhere. But thanks to Neptune's mi-gration, objects could occasionally remain trapped in theseemingly odd high-inclination orbits. Thus the coexistencedilemma seems resolved: The small, red, dSmamically coldobjects in the outer Solar System are the only objects thatactually formed in place; the larger high-inclination popu-lation is an interloper from deeper within the Solar System.

That the cold population formed in place is a criticalad hoc assumption that was forced on Gomes. In his sim-ulations, Neptune always migrated to the very edge of thenebular disk. Tlo make Neptune stop its migration at itscurrent location, Gomes had to end that disk at 30 AU. Toaccount for the primordial cold classical Kuiper belt be-grnning at around 40 AU, Gomes had to artificially put aband ofobjects beyond the 30-AU disk edge. No plausibleexplanation for his initial configuration could be found, yetat the time, no other way could be found to both stop Nep-tune at its correct location and to allow for the classicalKuiper belt.

It all gets pushed outSeveral months later, Levison and Alessandro Morbidelli,at the Observatoire de la C6te d'Azur, devised a scheme tosolve the mystery of how the 30-AU location of Neptunecould be consistent with a Kuiper belt edge at 50 AU.15They noted that the edge appears to coincide nicely witht}lLe2:l mean motion resonance of Neptune at 48AU. Theyhypothesized that the near equality oflocation was not acoincidence and suggested that the entire Kuiper belt-in-

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its equilibrium orbit, with slow oscillations of its semimajoraxis, eccentricity, and orbital velocity.

lf, however, Neptune's semimajoraxis expands by a smallqmount-as astronomers think has occurred-Neptune's or-bial velocity slows, so the closest approach occurs a littlepast the equilibrium position. The Kuiper belt object's orbitand eccentricity slightly expand as the object works towardits new equilibrium. Continued smooth outward movemenlof Neptune will cause continued movement of the Kuiperbelt object and a continued increase in the obiect's eccen-tricity. lf Neptune's orbit ever jumps by too large an amount,however, the objeA may not be able to reestablish its equi-librium. ln that case, it will be lost from the resonance and itsorbit will cease to expand.

cluding the supposedly primordial cold objects-had beenpushed out by the process ofresonance capture. With thehelp of continually advancing computer power, they ex-arnined Neptune's migration through a massive disk ofparticles that ended at 30 AU. The computer advances al-lowed them to resolve the disk into an ever increasingnumber of ever smaller objects. The results were surpris-ing: Not only did Levison and Morbidelli get the expectedcapture into the 3:2 and.2:1 resonances, but some objectsthat had initially been pushed out to the 2:1 resonancethen dropped out ofthe resonance and ended up with loweccentricities in the region ofthe classical Kuiper belt. Theappearance ofthe low-eccentricity objects was a surprisebecause astronomers had always assumed that the reso-nance capture and pushing out of an object would monot-onically increase its eccentricity.

So, how did the low-eccentricity objects arise? When acomputer simulation gets sufficiently complicated, under-standing the results is almost as difficult as understand-ing the real universe. But the advantage in a simulationis that one can change things and see what happens. Lev-ison and Morbidelli reran their simulation but changed themass of each Kuiper belt object to zero. They then had toprescribe an artificial outward force on Neptune to have itmigrate through the now massless (and thus momentum-less) disk ofobjects. They found that, in contrast to the re-sults with the massive disk, the eccentricities increased.When they further analyzed their simulations, Levisonand Morbidelli found an effect not previously noticed. The

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April 2004 Physics Today 53

Kuiper belt objects that are captured into resonances areindividually small, but collectively, they exert a torque onNeptune that causes its orbit to precess. That orbital pre-cession, in turn, creates a back reaction on the Kuiper beltobjects that causes the eccentricities of each object to os-cillate. When Neptune's migration is suffrciently jumpy'some ofthe objects fall out ofthe 2:1 resonance as they arebeing pushed outward. Those objects have a range ofec-centricities similar to that seen in the classical Kuiper belt.

In the Levison and Morbidelli scheme, all of theKuiper belt objects were formed inside the present loca-tion of Neptune and were carried out as Neptune migrated.The edge ofthe belt occurs at the location ofthe 2:1 reso-nance because that is the most distant resonance able tocapture and move objects outward. Intuitively, it appearsdifficult to reconcile the scheme with the physical differ-ences in the hot and cold classical populations. But whenthe dynamics become sufficiently complicated, intuitionoften does not serve very well. To date, computer power isinsufficient to determine if the processes described by Lev-ison and Morbidelli wiII segregate objects from differentregions ofthe initial nebula into hot and cold populations.

A coherent storyCombining the new ideas discussed here yields a coherentand possibly even correct picture ofthe formation and evo-lution of the outer Solar System. The story goes like this.First, the nebular disk was much smaller than previouslyexpected: It must have had an edge at 30 AU for Neptuneto be there now. Neptune (and Uranus) could have beenwell inside 20 AU, which, incidentally, would relieve thelong-standing problem that it is difficult to form thoseplanets at their current locations. Neptune and the othergiants, as they began to migrate through the disk ofplan-etesimals, pushed out some objects in resonances and scat-tered others into elliptical and high-inclination orbits. Theforce of the resonantly captured planetesimals on Neptunecaused that planett orbit to precess, which in turn causedeccentricities of the planetesimals being pushed out to os-cillate rather than simply to increase. As Neptune mi-grated, some of the scattered objects became stranded inthe dynamically hot classical belt. Others fell out of the 2:1resonance due to Neptune's occasional large jumps and be-came the cold classical belt. The story ends when Neptunereaches the edge of the disk at 30 AU and we are left withthe arrangement we have today.

IfKuiper were to recreate his construction ofthe ini-tial Solar System nebula based on this story, he would findthe density near the Sun was increased and that all themass of the giant planets was inside about 20 AU. Onething would remain similar, though: The disk would end,now at 30 AU. Kuiper might think to himself, "It doesn't

54 April 2004 Physics Today

seem natural that the Solar System should have such anabrupt edge."And he might begin to look for a new answerto his dilemma.

The full story is not yet known. Many advances willcome with the always increasing ability of computer sim-ulations to include more and more particles interacting inincreasingly realistic ways. But in the end, even if as-tronomers know all of the relevant forces, computer mod-eling will not be enough. The final answers are likely tocome after finding one single plastic duck, unexpectedlywashed ashore in, say, Ireland, and using it to trace thecomplex paths of the many forces that move plastic ducksand Kuiper belt objects to where they are found today.

ReferencesD. Jewitt, J. Luu, Nature 362, 730 (1993).See the list updated daily at http://cfa-www.harvard. edu./iau,/Ephemerides/Distant/index. html.M. Duncan, T. Quinn, S. TYemaine, Astron. J. 94, 1330(1987).S. A. Stern, Astron. J. 110, 856 (1995).R. L. Allen, G. M. Bernstein, R. Malhotra,Astrophys. J. 549,L24l (2OOl); C. A. Trujillo, M. E. Brown, Astrophys. J. 554,L95 (2001).A. Morbidelli, M. E. Brown, in a sppcial isste of Earth, Moon,and Planets (in press).S. Ida, J. Larwood, A. Burkett, Astrophys. J. 528,351 (2000).M. E. Brown, Astron. J. l2l,2804 (2001).R. Malhotra, Nature 365,819 (1993).J. Fernandez, W.lp, Icarus 58, 109 (1984).H. Levison, M. Duncan, Science 276, 1670 (1997).H. Levison, S. A. Stern,Astron. J. f21, 1730 (2001).C. A. Tlujillo, M. E. Brown, Astrophys. J. 566,LI25 (2002).R. Gomes. Icarus 161.404 (2003).H. Levison, A. Morbidelli, Nature 426, 419 (2003).

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