Editing Planetary migration (section)

==== Type II migration ====
A planet massive enough to open a gap in a gaseous disk undergoes a regime referred to as <em>Type&nbsp;II disk migration</em>. When the mass of a perturbing planet is large enough, the tidal torque it exerts on the gas transfers angular momentum to the gas exterior of the planet's orbit, and does the opposite interior to the planet, thereby repelling gas from around the orbit. In a Type&nbsp;I regime, viscous torques can efficiently counter this effect by resupplying gas and smoothing out sharp density gradients. But when the torques become strong enough to overcome the viscous torques in the vicinity of the planet's orbit, a lower density annular gap is created. The depth of this gap depends on the temperature and viscosity of the gas and on the planet mass. In the simple scenario in which no gas crosses the gap, the migration of the planet follows the viscous evolution of the disk's gas. In the inner disk, the planet spirals inward on the viscous timescale, following the accretion of gas onto the star. In this case, the migration rate is typically slower than would be the migration of the planet in the Type&nbsp;I regime. In the outer disk, however, migration can be outward if the disk is viscously expanding. A Jupiter-mass planet in a typical protoplanetary disk is expected to undergo migration at approximately the Type II rate, with the transition from Type&nbsp;I to Type&nbsp;II occurring at roughly the mass of Saturn, as a partial gap is opened.<ref name=dangelo_etal_2003 /><ref name=dangelo_lubow_2008 /> 

Type II migration is one explanation for the formation of [[hot Jupiter]]s.<ref name="Armitage_2007">{{Cite journal |last1=Armitage |first1=Phillip J. |title=Lecture notes on the formation and early evolution of planetary systems |arxiv=astro-ph/0701485 |bibcode=2007astro.ph..1485A|year=2007 }}</ref> In more realistic situations, unless extreme thermal and viscosity conditions occur in a disk, there is an ongoing flux of gas through the gap.<ref name=lubow_dangelo_2006>{{cite journal |author1=Lubow, S. |author2=D'Angelo, G. |title=Gas flow across gaps in protoplanetary disks |journal=The Astrophysical Journal |date=2006 |volume=641 |issue=1|pages=526–533 |doi=10.1086/500356 |arxiv=astro-ph/0512292 |bibcode=2006ApJ...641..526L|s2cid=119541915 }}</ref> As a consequence of this mass flux, torques acting on a planet can be susceptible to local disk properties, akin to torques at work during Type&nbsp;I migration. Therefore, in viscous disks, Type&nbsp;II migration can be typically described as a modified form of Type I migration, in a unified formalism.<ref name=dangelo_lubow_2008>{{cite journal |author1=D'Angelo, G. |author2=Lubow, S. H. |title=Evolution of migrating planets undergoing gas accretion |journal=The Astrophysical Journal |date=2008 |volume=685 |issue=1 |pages=560–583 |doi=10.1086/590904 |arxiv=0806.1771 |bibcode=2008ApJ...685..560D|s2cid=84978 }}</ref><ref name=dangelo_lubow_2010 /> The transition between Type&nbsp;I and Type&nbsp;II migration is generally smooth, but deviations from a smooth transition have also been found.<ref name=dangelo_etal_2003>{{cite journal |author1=D'Angelo, G. |author2=Kley, W. |author3=Henning T. |title=Orbital migration and mass accretion of protoplanets in three-dimensional global computations with nested grids| journal=The Astrophysical Journal |date=2003 |volume=586 |issue=1 |pages=540–561 |doi=10.1086/367555 |arxiv=astro-ph/0308055 |bibcode=2003ApJ...586..540D|s2cid=14484931 }}</ref><ref name=masset_etal_2006>{{cite journal |author1=Masset, F.S. |author2=D'Angelo, G. |author3=Kley, W. |title=On the migration of protogiant solid cores |journal=The Astrophysical Journal |date=2006 |volume=652 |issue=1 |pages=730–745 |doi=10.1086/507515 |arxiv=astro-ph/0607155 |bibcode=2006ApJ...652..730M|s2cid=17882737 }}</ref> In some situations, when planets induce eccentric perturbation in the surrounding disk's gas, Type&nbsp;II migration may slow down, stall, or reverse.<ref name=dangelo_etal_2006>{{cite journal |arxiv=astro-ph/0608355 |title=Evolution of Giant Planets in Eccentric Disks |journal=The Astrophysical Journal |volume=652 |issue=2 |pages=1698–1714 |last1=D'Angelo |first1=Gennaro |last2=Lubow |first2=Stephen H. |last3=Bate |first3=Matthew R. |year=2006 |doi=10.1086/508451 |bibcode=2006ApJ...652.1698D|s2cid=53135965 }}</ref>

From a physical viewpoint, Type I and Type II migration are driven by the same type of torques (at Lindblad and co-rotation resonances). In fact, they can be interpreted and modeled as a single regime of migration, that of Type I appropriately modified by the perturbed gas surface density of the disk.<ref name=dangelo_lubow_2008 /><ref name=dangelo_lubow_2010 />