Introduction

The extremely short orbital period of 51 Pegasi (Mayor & Queloz 1995) and the other hot Jupiters pose a problem for planet formation, not only because such systems bear little resemblance to the Solar System, but more fundamentally because the high temperatures expected in the protoplanetary disk at radii a < 0.1 AU largely preclude the possibility of in situ formation. Disk models by Bell et al. (1997) show that for typical T Tauri accretion rates of M ~ 10~8 Mq yr_1 (Gullbring et al. 1998), the midplane temperature interior to 0.1 AU exceeds 1000 K, destroying ices and, for the very closest in planets, even dust. At least the cores of these hot Jupiters must, therefore, have formed elsewhere, and subsequently migrated inward. Migration is also likely to have occurred for the larger population of extrasolar planets that now lie within the snow line in their parent disks (Bodenheimer, Hubickyj, & Lissauer 2000), though this is a more model-dependent statement since both the location of the snow line (Sasselov & Lecar 2000) and its significance for giant planet formation remain uncertain.

Orbital migration of planets involves a loss of angular momentum to either gas or other solid bodies in the system. Three main mechanisms have been proposed, all of which involve purely gravitational interactions (aerodynamic drag, which is central to the orbital evolution of meter-scale rocks, is negligible for planetary masses). The first is gravitational interaction between the planet and the gas in the protoplanetary disk.

This leads to angular momentum exchange between the planet and the gas, and resulting orbital evolution (Goldreich & Tremaine 1980; Lin, Bodenheimer & Richardson 1996). Since gas giant planets, by definition, formed at an epoch when the protoplanetary disk was still gas rich, this type of migration is almost unavoidable. It is the main subject of this article. However, further migration could also occur later on, after the gas disk has been dissipated, as a consequence of the gravitational scattering of either planetesimals (Murray et al. 1998) or other massive planets (Rasio & Ford 1996; Weidenschilling & Marzari 1996; Lin & Ida 1997; Papaloizou & Terquem 2001). Some orbital evolution from planetesimal scattering is inevitable, given that the formation of massive planets is highly likely to leave a significant mass of smaller bodies in orbits close enough to feel perturbations from the newly formed giant. In the Solar System, planetesimal scattering could have allowed substantial outward migration (Thommes, Duncan, & Levison 1999) of Uranus and Neptune—which have a small fraction of the Solar System's angular momentum—while simultaneously raising the eccentricities and inclinations of all the giant planets to values consistent with those observed (Tsiganis et al. 2005). Although this is an attractive theory for the architecture of the outer Solar System, invoking a scaled-up version of this process as the origin of the hot Jupiters is problematic. To drive large-scale migration of the typically rather massive planets seen in extrasolar planetary systems would require a comparable mass of planetesimals interior to the initial orbit of the planet. Such a planetesimal disk would, in turn, imply the prior existence of a rather massive gas disk, which would likely be more effective at causing migration than the planetesimals. Similar reservations apply to models of planet-planet scattering, which is only able to yield a population of planets at small orbital radii if multiple planet formation (with the planets close enough that they are unstable over long periods) is common. That said, the observation that most extrasolar planets have significantly eccentric orbits— which currently defies explanation except as an outcome of planet-planet scattering (Ford, Rasio, & Yu 2003)—may mean that at least some scattering-driven migration occurs in the typical system.

Figure 1 illustrates how a planet on a circular orbit interacts with the protoplanetary disk. The planet perturbs the gas as it passes by the planet, with angular momentum transport taking place at the locations of resonances in the disk—radii where a characteristic disk frequency is related to the planet's orbital frequency. For relatively low-mass perturbers, the interaction launches a trailing spiral wave in the gas disk, but is not strong enough to significantly perturb the azimuthally averaged surface-density profile. In this regime, described as Type I migration, angular-momentum transport between the planet and the gas occurs while the planet remains embedded within the protoplanetary disk. The rate of migration is controlled by the sum of the torques arising from the inner and outer Lindblad and corotation resonances, which is generally non-zero (if the sum happened to be close to zero, the planet would act as a source of angular-momentum transport in the disk (Goodman & Rafikov 2001), while remaining in place). For the parameters (sound speed, efficiency of angular-momentum transport) that are believed to be appropriate for protoplanetary disks, Type I migration occurs for planet masses Mp < 0.1 MJ, where MJ is the mass of Jupiter (Bate et al. 2003), and is most rapid as this critical mass is approached (e.g., Ward 1997). As a result, it is likely to play a particularly important role in the final assembly of giant planet cores.

At higher masses—Mp > 0.1 MJ —the angular momentum removal/deposition at the planet's inner/outer Lindblad resonances is strong enough to repel gas from an annular region surrounding the planet's orbit, forming a gap in which the surface density is reduced compared to its unperturbed value. For planets of a Jupiter mass and above, the gap is almost entirely evacuated (e.g., the right-hand panel of Figure 1), although

Figure 1. An illustration of the interaction between a planet on a fixed circular orbit with a laminar (non-turbulent) protoplanetary disk, computed from a two-dimensional (r,0) hydrody-namic simulation with a locally isothermal equation of state and a constant kinematic viscosity. In the left-hand panel showing the regime of Type I migration, a relatively low-mass planet excites a noticeable wave in the disk gas, but does not significantly perturb the azimuthally averaged surface-density profile (shown as the inset graph). In contrast, a 10 MJ planet (right-hand panel) clears an annular gap in the disk, within which the surface density is a small fraction of its unperturbed value. As the disk evolves over a viscous time scale, the planet is predicted to track the motion of the gas (either inward or outward) while remaining within the gap. This is Type II migration.

Figure 1. An illustration of the interaction between a planet on a fixed circular orbit with a laminar (non-turbulent) protoplanetary disk, computed from a two-dimensional (r,0) hydrody-namic simulation with a locally isothermal equation of state and a constant kinematic viscosity. In the left-hand panel showing the regime of Type I migration, a relatively low-mass planet excites a noticeable wave in the disk gas, but does not significantly perturb the azimuthally averaged surface-density profile (shown as the inset graph). In contrast, a 10 MJ planet (right-hand panel) clears an annular gap in the disk, within which the surface density is a small fraction of its unperturbed value. As the disk evolves over a viscous time scale, the planet is predicted to track the motion of the gas (either inward or outward) while remaining within the gap. This is Type II migration.

mass may continue to flow in a stream across the gap to enter the planet's Roche lobe (Artymowicz & Lubow 1996; Lubow, Seibert, & Artymowicz 1999). The location of the inner and outer edges of the gap are set by a balance between angular momentum exchange with the planet (which tends to widen the gap), and internal stresses within the protoplanetary disk ('viscosity,' which tends to close it). Under most circumstances, this balance acts to lock the planet into the long-term viscous evolution of the disk gas. At radii where the disk gas is moving inward, the planet migrates toward the star, all the while remaining within its gap (Lin & Papaloizou 1986). This is Type II migration, which differs from Type I not only in the presence of a gap, but also because the rate depends directly on the efficiency of angular-momentum transport within the protoplanetary disk.

In addition to these well-established migration regimes, qualitatively different behavior may occur at very low masses, and at masses intermediate between the Type I and Type II regimes. At sufficiently low masses (probably of ~10 and below), the persistent Type I torque may be overwhelmed by random torques from surface density perturbations in a turbulent protoplanetary disk (Nelson & Papaloizou 2004; Laughlin, Steinacker, & Adams 2004). This process, which is similar to the heating of Galactic stars by transient spiral arms (Carlberg & Sellwood 1985), may lead to rapid random walk migration on top of Type I drift. This could have important consequences for both core accretion (Rice & Armitage 2003) and terrestrial planet formation. Another uncertain regime lies at the transition mass (Mp « 0.1 MJ) between Type I and Type II migration, where a partial gap exists and corotation torques can be highly significant. Masset & Pa-paloizou (2003) suggested that the corotation torques could drive an instability in the direction of migration, which, if confirmed, would be extremely important for massive planet formation. Subsequent higher resolution simulations by D'Angelo, Bate, & Lubow (2005) yield a smaller contribution from the corotation region, and slower migration, but still fail to achieve numerical convergence. The possibility of runaway migration at masses just beyond the Type I threshold remains, therefore, open.

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