L143The Astrophysical Journal, 585:L143–L146, 2003 March 10䉷 2003. The American Astronomical Society. All rights reserved. Printed in U.S.A.HALTING PLANET MIGRATION BY PHOTOEVAPORATION FROM THE CENTRAL SOURCEIsamu Matsuyama,1Doug Johnstone,2and Norman Murray3,4Received 2002 November 26; accepted 2003 January 31; published 2003 February 13ABSTRACTThe recent discovery of Jupiter mass planets orbiting at a few AU from their stars complements earlierdetectionsof massive planets on very small orbits. The short-period orbits strongly suggest that planet migration has occurred,with the likely mechanism being tidal interactions between the planets and the gas disks out of which theyformed. The newly discovered long-period planets, together with the gas giant planets in our solar system, showthat migration is either absent or rapidly halted in at least some systems. We propose a mechanism for haltingtype II migration at several AU in a gas disk. Photoevaporation of the disk by irradiation from the central starcan produce a gap in the disk at a few AU, preventing planets outside the gap from migrating down to the star.This would result in an excess of systems with planets at or just outside the photoevaporation radius.Subject headings: accretion, accretion disks — planetary systems: formation —planetary systems: protoplanetary disks — planets and satellites: formation —solar system: formation1. INTRODUCTIONIt is believed that gas giants do not generally form at smallorbital distances from the central star (Boss 1995). Thus, anatural explanation for extrasolar planets orbiting close to thecentral star is that these planets formed farther away in theprotoplanetary disk and migrated inward to where they are nowobserved. A variety of mechanisms have been proposed toexplain planet migration: the interaction between a planet anda planetesimal disk (Murray et al. 1998), the gravitational in-teraction between two or more Jupiter mass planets (Rasio &Ford 1996), and the tidal gravitational interaction between theplanet and the surrounding disk gas (Goldreich & Tremaine1979, 1980). The last mechanism, focused on in this Letter, isexpected to be dominant at early times, since the surroundinggaseous disk is required for the formation of planets.If the perturbation exerted on the disk by the planet is small,the disk structure is not greatly altered, and the planet movesinward relative to the surrounding gas (Ward 1997). This typeof migration is referred to as “type I.” However, if the planetis large, it may open a gap in the disk (Goldreich & Tremaine1980). The planet is locked to the disk and moves either inwardor outward in lockstep with the gaseous disk. This slower mi-gration is referred to as “type II.”We propose a mechanism for halting type II migration: pho-toevaporation driven by radiation from the central star. Theplanet’s final location is consistent with the solar system andthe growing class of extrasolar planets with nearly circularorbits outside of a few AU (see Tinney et al. 2002, Fig. 4).Photoevaporation by the central star was proposed by Shu,Johnstone, & Hollenbach (1993) and Hollenbach et al. (1994)as a way to remove a gas disk. Hollenbach, Yorke, & Johnstone(2000) generalized the discussion, describing the variety ofpossible disk removal mechanisms: accretion, planet formation,stellar encounters, stellar winds or disk winds, and photoevap-1Department of Astronomy and Astrophysics, University of Toronto, 60 St.George Street, Room 1403, Toronto, ON M5S 3H8, Canada; [email protected] Research Council Canada, Herzberg Institute of Astrophysics, 5071West Saanich Road, Victoria, BC V9E 2E7, Canada; [email protected] Institute for Theoretical Astrophysics, University of Toronto, 60 St.George Street, Toronto, ON M5S 3H8, Canada; [email protected] Research Chair in Astrophysics.oration by ultraviolet photons from the central source or mas-sive external stars. Hollenbach et al. (2000) concluded that thedominant mechanisms for a wide range of disk sizes are viscousaccretion and photoevaporation, operating in concert within thedisk. In this Letter, we consider photoevaporation by the centralsource and viscous accretion.2. MODELThe model for disk removal used here is developed in apaper by Matsuyama, Johnstone, & Hartmann (2003) and issimilar to that used by Clarke, Gendrin, & Sotomayor (2001).In addition, we assume a planet with a large mass, which opensa narrow gap in the disk, and assume that planet migrationproceeds in lockstep with the disk evolution (type II migration).The gas disk orbiting the central star with the local Kepleriancircular velocity is axisymmetric and geometrically thin. Con-sidering angular momentum and mass conservation of a diskannulus at a radius, R, with kinematic viscosity, , the disknsurface density evolution can be described by (Pringle 1981)⭸S 3 ⭸⭸1/2 1/2p R (nSR ) , (1)[]⭸tR⭸R ⭸Rwhere S is the disk surface density and t is the disk evolutionarytime. We adopt the standard a-parameterization of Shakura &Sunyaev (1973) and write where csis the soundn p acH,sspeed at the disk midplane and H is the disk thickness. Hart-mann et al. (1998) estimate and a disk mass⫺2 ⫺3a ∼ 10 –10∼0.01–0.2 M,for T Tauri stars (TTSs). For the modeled disktemperature distribution, (D’Alessio et al. 1998), the⫺1/2T ∝ Rdviscosity takes the simple form, . Given a solutionn(R) ∝ Rfor equation (1), we find the drift velocity,3 ⭸1/2v p ⫺ (nSR ), (2)R1/2SR ⭸Rand describe the evolution of the disk stream lines.The EUV ( A˚) photons from the central star and thel! 912accretion shock (we refer to these photons as the EUV photonsfrom the central source) are capable of ionizing hydrogen andevaporating material from the disk surface. PhotoevaporationL144 HALTING PLANET MIGRATION BY PHOTOEVAPORATION Vol. 585Fig. 1.—Snapshots of the surface density for a fiducial model under theinfluence of viscous diffusion and photoevaporation from the central source. Themodel corresponds to and an initial disk mass, . The⫺3a p 10 M(0) p 0.03 M,short-dashed line indicates the location of the gravitational radius, and the long-dashed line corresponds to the minimum surface density for gap formation byphotoevaporation. The solid curves represent67 7t p 0, 10 , 10 , 3.6 # 10 ,77777774.2 # 10 , 4.7 # 10 , 5.2 # 10 , 5.7 # 10 , 6.2 # 10 , 6.7 # 10 , 7.2 # 10 ,. The gap structure starts777 77.7 # 10 , 8.2 # 10 , 8.7 #
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