265Publications of the Astronomical Society of the Pacific, 114:265–283, 2002 March䉷 2002. The Astronomical Society of the Pacific. All rights reserved. Printed in U.S.A.Planet Formation in the Outer Solar SystemScott J. KenyonSmithsonian Astrophysical Observatory, 60 Garden Street, Cambridge, MA 02138; [email protected] 2001 December 5; accepted 2001 December 5; published 2002 February 8ABSTRACT. This paper reviews coagulation models for planet formation in the Kuiper belt, emphasizing linksto recent observations of our and other solar systems. At heliocentric distances of 35–50 AU, single-annulus andmultiannulus planetesimal accretion calculations produce several 1000 km or larger planets and many 50–500 kmobjects on timescales of 10–30 Myr in a minimum-mass solar nebula. Planets form more rapidly in more massivenebulae. All models yield two power-law cumulative size distributions, with for radii⫺qN ∝ rqp 3.0–3.5Ckm and for radii km. These size distributions are consistent with observations of Kuiper⫺2.5r ⲏ 10 N ∝ rrⱗ 1Cbelt objects acquired during the past decade. Once large objects form at 35–50 AU, gravitational stirring leads toa collisional cascade where 0.1–10 km objects are ground to dust. The collisional cascade removes 80%–90% ofthe initial mass in the nebula in ∼1 Gyr. This dust production rate is comparable to rates inferred for a Lyr, b Pic,and other extrasolar debris disk systems.1. INTRODUCTIONRecent observations indicate that nearly all low- andintermediate-mass stars are born with massive circumstellardisks of gas and dust. Most young pre–main-sequence starswith ages of ∼1 Myr have gaseous disks with sizes of 100 AUor larger and masses of ∼0.01 M,(Beckwith 1999; Lada 1999).Many older main-sequence stars have dusty debris disks withsizes of 100–1000 AU (Aumann et al. 1984; Smith & Terrile1984; Gaidos 1999; Habing et al. 1999; Song et al. 2001;Spangler et al. 2001). Current source statistics suggest that thepercentage of stars with observable disks declines from ∼100%among the youngest stars to less than 10% for stars more than1 Gyr old (Backman & Paresce 1993; Artymowicz 1997; Lada1999; Lagrange, Backman, & Artymowicz 2000).Models for the formation of our solar system naturally beginwith a disk. In the 1700s, Immanuel Kant and the Marquis deLaplace proposed that the solar system collapsed from a gas-eous medium of roughly uniform density (Kant 1755; Laplace1796). A flattened gaseous disk—the protosolar nebula—formed out of this cloud. The Sun contracted out of materialat the center of the disk; the planets condensed in the outerportions. Although other ideas have been studied since La-place’s time, this picture has gained widespread acceptance.Measurements of the composition of the Earth, Moon, andmeteorites support a common origin for the Sun and planets(e.g., Harris 1976; Anders & Grevesse 1989). Simulations ofplanet formation in a disk produce objects resembling knownplanets on timescales similar to the estimated lifetime of theprotosolar nebula (Safronov 1969; Greenberg et al. 1978; Weth-erill & Stewart 1993; Pollack et al. 1996; Alexander & Agnor1998; Levison, Lissauer, & Duncan 1998; Kokubo & Ida 2000;Kortenkamp & Wetherill 2000; Chambers 2001).The Kuiper belt provides a stern test of planet formationmodels. In the past decade, observations have revealed severalhundred objects with radii of 50–500 km in the ecliptic planeat distances of ∼35–50 AU from the Sun (Jewitt & Luu 1993;Luu & Jewitt 1996; Gladman & Kavelaars 1997; Jewitt, Luu,& Trujillo 1998; Chiang & Brown 1999; Luu, Jewitt, & Trujillo2000; Gladman et al. 2001). The total mass in these Kuiperbelt objects (KBOs), ∼0.1 , suggests a reservoir of materialM丣left over from the formation of our solar system (Edgeworth1949; Kuiper 1951). However, this mass is insufficient to allowthe formation of 500 km or larger KBOs on timescales of∼5 Gyr (Ferna´ndez & Ip 1981; Stern 1995; Stern & Colwell1997a; Kenyon & Luu 1998).The Kuiper belt also provides an interesting link betweenlocal studies of planet formation and observations of disks andplanets surrounding other nearby stars. With an outer radius ofat least 150 AU, the mass and size of the Kuiper belt is com-parable to the masses and sizes of many extrasolar debris disks(Backman & Paresce 1993; Artymowicz 1997; Lagrange et al.2000). Studying planet formation processes in the Kuiper beltthus can yield a better understanding of evolutionary processesin other debris disk systems.Making progress on planet formation in the Kuiper belt andthe dusty disks surrounding other stars requires plausible the-ories that make robust and testable predictions. This paper re-views the coagulation theory for planet formation in the outersolar system (for reviews on other aspects of planet formation,see Mannings, Boss, & Russell 2000). After a short summaryof current models for planet formation, I consider recent nu-merical calculations of planet formation in the Kuiper belt and266 KENYON2002 PASP, 114:265–283Fig. 1.—Top view of the solar system. The yellow filled circle is the Sun.Colored ellipses indicate the orbits of Jupiter (red), Saturn (cyan), Uranus(green), Neptune (dark blue), Pluto (black), and the scattered KBO 1996 TL66(magenta). The black dots represent 200 classical KBOs randomly distributedin a band between 42 and 50 AU. The bar at the lower right indicates a distanceof 40 AU.describe observational tests of these models. I conclude witha discussion of future prospects for the calculations along withsuggestions for observational tests of different models of planetformation.2. BACKGROUNDFigure 1 shows the geometry of the outer part of our solarsystem. Surrounding the Sun at the center, four colored ellipsesindicate the orbits of Jupiter (red), Saturn (cyan), Uranus (green),and Neptune (dark blue). The black ellipse plots the orbit ofPluto, which makes two orbits around the Sun for every threeof Neptune. Roughly 20% of currently known KBOs, the Plu-tinos, have similar orbits. The black dots represent 200 KBOsrandomly placed in the classical Kuiper belt, objects in roughlycircular orbits outside the 3 : 2 resonance with Neptune. A fewKBOs outside this band lie in the 2 : 1 orbital resonance withNeptune. The eccentric magenta ellipse indicates the orbit of oneKBO in the scattered Kuiper belt (Luu et al. 1997). The totalmass in classical KBOs is ∼0.1 ; the mass in scattered KBOsM丣and KBOs
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