arXiv:astro-ph/0701485v1 16 Jan 2007LECTURE NOTES ON THE FORMATION ANDEARLY EVOLUTION OF PLANETARY SYSTEMSPhilip J. ArmitageJILA, 440 UCB, University of Colorado, Boulder, CO80309-0440These notes provide an introduction to the theory of the formation and early evolution of planetarysystems. Topics covered include the structure, evolution and dispersal of protoplanetary disks;the formation of planetesimals, terrestrial and gas giant planets; and orbital evolution due to gasdisk migration, planetesimal scattering, and planet-planet interactions.ContentsI. Introduction 1A. Critical Solar System Observations 21. Architecture 22. Mass and angular momentum 23. Minimum mass Solar Nebula 24. Resonances 25. Minor bodies 36. Ages 37. Satellites 3B. Extrasolar Planets 31. Detection methods and biases 32. Observed properties 4II. Protopla netary Disks 6A. The star formation context 6B. Passive circumstellar disks 71. Vertical structure 72. Radial temperature profile 83. Spectral energy distribution (SED) 94. Sketch of more complete models 9C. Actively accreting disks 101. Diffusive evolution equation 102. Solutions 113. Temperature profile 134. Origin of angular momentum transport 135. Layered disks 156. Disk dispersal 16D. The condensation sequence 17III. Planet Formation 19A. Planetesimal formation 201. Dust settling 202. Radial drift of particles 213. The Goldreich-Ward mechanism 23B. Growth beyond planetesimals 271. Gr avitational focusing 272. Gr owth versus fragmentation 283. Shear versus dispersion dominated encounters 284. Gr owth r ates 295. Isolation mass 306. Coagulation equation 307. Overview of terrestrial planet formation 31C. Gas giant formation 321. Core accretion model 322. Gr avitational instability model 343. Compar ison with observations 35IV. Evolution of Planetary Systems 36A. Gas disk migration 361. Conditions for resonance 372. Gr avitational torques at resonances 383. Type I migration 384. Type II m igration 405. The Type II migration rate 416. Stochastic migration 417. Eccentricity evolution during migration 428. Observational evidence for inner holes 42B. Planetesimal disk migration 431. Solar System evidence 432. The Nice model 43C. Planet-planet scattering 441. Hill stability 442. Scattering and exoplanet eccentricities 46Acknowledgements 47References 48I. INTRODUCTIONThe theoretical study of planet formation has a longhistory. Many of the fundamental ideas in the theoryof terrestrial planet formation were laid out by Safronov(1969) in his classic monograph ‘Evolution of the Pro-toplanetary Cloud and Formation of the Earth and thePlanets’, while the essential elements of the core accre-tion theory for gas giant formation were in place by theearly 1980’s (Mizuno, 1980). A wealth of new data overthe last decade — including observations of protoplan-etary disks, the discovery of the Solar System’s KuiperBelt, and the detection of numerous extrasolar planeta rysystems — has led to renewed interest in the problem.Although these obs e rvatio ns have confirmed some exist-ing predictions, they have also emphasized the need toexplore new theoretical avenues. The major questionsthat work in this field seeks to answer include:• How did the terrestrial and giant planets for m?• How much evolution in the orbits of planets takesplace at early times?• Is the architecture of the Solar System typical?• How common are habitable planets?The main goal of these notes is to provide a suc c inc tintroduction to the critical concepts necessary to under-stand planet formation. Before de lving into theory, how-ever, we first briefly review the basic observational prop-erties of the Solar System and of ex trasolar planeta rysystems tha t a theory of planet formation mig ht aspireto explain.2TABLE I Basic propert ies of planets in the Solar Systema/AU eMp/gMercury 0.387 0.206 3.3 × 1026Venus 0.723 0.007 4.9 × 1027Earth 1.000 0.017 6.0 × 1027Mars 1.524 0.093 6.4 × 1026Jupiter 5.203 0.048 1.9 × 1030Saturn 9.537 0.054 5.7 × 1029Uranus 19.189 0.047 8.7 × 1028Neptune 30.070 0.009 1.0 × 1029A. Critical Solar S ystem Observations1. ArchitectureThe orbital properties and masse s of the planets in theSolar System are listed in Table I (the values here aretaken from the JPL web site). The basic architecture ofour Solar System comprises 2 gas giants (Jupiter and Sat-urn) composed primarily of hydrogen and helium, thoughnot of Solar compo sition. Saturn is known to have a sub-stantial core. Descending in mass there are then 2 icegiants (Uranus and Neptune) composed of water, am-monia, methane, slica tes and meta ls, plus low mass hy-drogen / helium atmospheres ; 2 large terrestrial planets(Earth and Venus) plus two smaller terrestrial planets(Mercury and Mars). Apart from Mercury, all of theplanets have low eccentricities and orbita l inclinations.They orbit in a plane that is approximately perpendicu-lar to the Solar ro tation ax is (7◦misalignment ang le ).In the Solar System, the giant and terrestrial planetsare cle arly segregated in orbital radius. Moreover, thegiant planets occupy a zone of o rbital radii that coincideswith where we expect the protoplanetary disk to havebeen cool enoug h for ices to have been pr e sent. This isa significant o bserva tion in the classical theory of giantplanet formatio n.2. Mass and angular momentumThe mass of the Sun is M"=1.989 × 1033g, madeup of hydrogen (fraction by mass X =0.73), helium(Y =0.25) and ‘metals’ (Z =0.02). One obs e rves im-mediately that most of the heavy elements in the SolarSystem are found in the Sun – if we assume that most ofthe mass in the Sun passed through a disk at some junc-ture during the star formation process this means tha tplanet formatio n need not be very efficient.The angular momentum budget for the Solar Systemis dominated by the orbital angular momentum of theplanets. The angular momentum in the Solar rota tion is,L"" k2M"R2"Ω, (1)assuming for simplicity solid body rotation. TakingΩ = 2.9 × 10−6s−1and adopting k2=0.1 (roughlyappropriate for a sta r with a radiative core), L""3 × 1048gcm2s−1. By comparison, the orbital angularmomentum of Jupiter is ,LJ= MJ!GM"a =2×1050gcm2s−1. (2)That the Solar System’s angular momentum is over-whelmingly in the planets is not terribly surprising,though exactly how the angular velocity of low mass starsevolves at early times remains a subject of active research(Herbst et al., 2007).3. Minimum mass Solar NebulaWe can use the observed mas
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