Editing Planetary migration (section)

== Types of migration ==
There are many different mechanisms by which planets' orbits can migrate, which are described below as disk migration (Type&nbsp;I migration, Type&nbsp;II migration, or Type&nbsp;III migration), tidal migration, planetesimal-driven migration, gravitational scattering, and Kozai cycles and tidal friction. This list of types is not exhaustive or definitive: Depending on what is most convenient for any one type of study, different researchers will distinguish mechanisms in somewhat different ways.

Classification of any one mechanism is mainly based on the circumstances in the disk that enable the mechanism to efficiently transfer energy and/or angular momentum to and from planetary orbits. As the loss or relocation of material in the disk changes the circumstances, one migration mechanism will give way to another mechanism, or perhaps none. If there is no follow-on mechanism, migration (largely) stops and the stellar system becomes (mostly) stable.

=== Disk migration ===
<em>Disk migration</em> arises from the gravitational force exerted by a sufficiently massive body embedded in a disk on the surrounding disk's gas, which perturbs its density distribution.  By the [[Reaction (physics)|reaction]] principle of [[classical mechanics]], the gas exerts an equal and opposite gravitational force on the body, which can also be expressed as a [[torque]].  This torque alters the [[angular momentum]] of the planet's orbit, resulting in a variation of the [[semi-major axis]] and other orbital elements.  An increase over time of the semi-major axis leads to ''outward migration'', i.e., away from the star, whereas the opposite behavior leads to ''inward migration''.

Three sub-types of disk migration are distinguished as Types&nbsp;I, II, and III. The numbering is '''not''' intended to suggest a sequence or stages.

==== Type I migration ====
Small planets undergo <em>Type&nbsp;I disk migration</em> driven by torques arising from Lindblad and co-rotation resonances. [[Lindblad resonance]]s excite [[spiral density wave]]s in the surrounding gas, both interior and exterior of the planet's orbit.  In most cases, the outer spiral wave exerts a greater torque than does the inner wave, causing the planet to lose angular momentum, and hence migrate toward the star. The migration rate due to these torques is proportional to the mass of the planet and to the local gas density, and results in a migration timescale that tends to be short relative to the million-year lifetime of the gaseous disk.<ref name=li2011>{{cite book |author1=Lubow, S.H. |author2=Ida, S. |chapter=Planet Migration |bibcode=2010exop.book..347L |title=Exoplanets |publisher=University of Arizona Press, Tucson, AZ |editor=Seager, S. |pages=347–371 |date=2011 |chapter-url=http://www.uapress.arizona.edu/Books/bid2263.htm |arxiv=1004.4137}}</ref>  Additional co-rotation torques are also exerted by gas orbiting with a period similar to that of the planet. In a reference frame attached to the planet, this gas follows [[horseshoe orbit]]s, reversing direction when it approaches the planet from ahead or from behind. The gas reversing course ahead of the planet originates from a larger semi-major axis and may be cooler and denser than the gas reversing course behind the planet. This may result in a region of excess density ahead of the planet and of lesser density behind the planet, causing the planet to gain angular momentum.<ref name="Paadekooper_Mellema_2006">{{cite journal |last1=Paardekooper |first1=S.-J. |last2=Mellema |first2=G. |title=Halting type&nbsp;I planet migration in non-isothermal disks |journal=Astronomy and Astrophysics |date=2006 |volume=459 |issue=1 |pages=L17–L20 |doi=10.1051/0004-6361:20066304|arxiv=astro-ph/0608658 |bibcode=2006A&A...459L..17P|s2cid=15363298 }}</ref><ref name="Brasser_etal_2017">{{cite journal |last1=Brasser |first1=R. |last2=Bitsch |first2=B. |last3=Matsumura |first3=S. |title=Saving super-Earths: Interplay between pebble accretion and type&nbsp;I migration |date=2017 |arxiv=1704.01962 |doi=10.3847/1538-3881/aa6ba3 |volume=153 |issue=5 |journal=The Astronomical Journal |page=222 |bibcode=2017AJ....153..222B|s2cid=119065760 |doi-access=free }}</ref> 

The planet mass for which migration can be approximated to Type&nbsp;I depends on the local gas pressure [[scale height]] and, to a lesser extent, the kinematic [[viscosity]] of the gas.<ref name="li2011" /><ref name=dangelo_lubow_2010 /> In warm and viscous disks, Type I migration may apply to larger mass planets. In locally isothermal disks and far from steep density and temperature gradients, co-rotation torques are generally overpowered by the [[Lindblad resonance|Lindblad]] torques.<ref name=tanaka_etal_2002>{{cite journal |author1=Tanaka, H. |author2=Takeuchi, T. |author3=Ward, W.R. |title=Three-Dimensional Interaction between a Planet and an Isothermal Gaseous Disk: I. Corotation and Lindblad Torques and Planet Migration
|journal=The Astrophysical Journal |date=2002 |volume=565 |issue=2 |pages=1257–1274 |doi=10.1086/324713 |bibcode=2002ApJ...565.1257T |doi-access=free }}</ref><ref name=dangelo_lubow_2010>{{cite journal |author1=D'Angelo, G. |author2=Lubow, S.H. |title=Three-dimensional disk-planet torques in a locally isothermal disk |journal=The Astrophysical Journal |date=2010 |volume=724 |issue=1 |pages=730–747 |doi=10.1088/0004-637X/724/1/730 |arxiv=1009.4148 |bibcode=2010ApJ...724..730D|s2cid=119204765 }}</ref> Regions of outward migration may exist for some planetary mass ranges and disk conditions in both local isothermal and non-isothermal disks.<ref name=dangelo_lubow_2010 /><ref name="Lega_etal_2014">{{cite journal |last1=Lega |first1=E. |last2=Morbidelli |first2=A. |last3=Bitsch |first3=B. |last4=Crida |first4=A. |last5=Szulágyi |first5=J. |title=Outwards migration for planets in stellar irradiated 3D discs |journal=Monthly Notices of the Royal Astronomical Society |date=2015 |volume=452 |issue=2 |pages=1717–1726 |doi=10.1093/mnras/stv1385 |doi-access=free |arxiv=1506.07348 |bibcode=2015MNRAS.452.1717L|s2cid=119245398 }}</ref> The locations of these regions may vary during the evolution of the disk, and in the local-isothermal case are restricted to regions with large density and/or temperature radial gradients over several pressure scale-heights. Type I migration in a local isothermal disk was shown to be compatible with the formation and long-term evolution of some of the observed [[Kepler (spacecraft)|Kepler]] planets.<ref name=dangelo_bodenheimer_2016>{{Cite journal |author1=D'Angelo, G. |author2=Bodenheimer, P. |title=In-situ and ex-situ formation models of Kepler&nbsp;11 planets |journal=The Astrophysical Journal |year=2016 |volume=828 |issue=1 |at=id. 33 (32 pp.) |doi=10.3847/0004-637X/828/1/33 |arxiv=1606.08088 |bibcode=2016ApJ...828...33D|s2cid=119203398 |doi-access=free }}</ref> The rapid accretion of solid material by the planet may also produce a "heating torque" that causes the planet to gain angular momentum.<ref name="Benitez_Llambay_etal_2015">{{cite journal |last1=Benítez-Llambay |first1=Pablo |last2=Masset |first2=Frédéric |last3=Koenigsberger |first3=Gloria |author3-link=Gloria Suzanne Koenigsberger Horowitz |last4=Szulágyi |first4=Judit |title=Planet heating prevents inward migration of planetary cores |journal=Nature |date=2015 |volume=520 |issue=7545 |pages=63–65 |doi=10.1038/nature14277 |pmid=25832403 |arxiv=1510.01778 |bibcode=2015Natur.520...63B|s2cid=4466971 }}</ref>

==== 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 />

==== Type III disk migration ====
<em>Type III disk migration</em> applies to fairly extreme disk / planet cases and is characterized by extremely short migration timescales.<ref name=masset_2003>{{cite journal |author1=Masset, F.S. |author2=Papaloizou, J.C.B. |title=Runaway migration and the formation of hot Jupiters |journal=The Astrophysical Journal |date=2003 |volume=588 |issue=1 |pages=494–508 |doi=10.1086/373892 |arxiv=astro-ph/0301171 |bibcode=2003ApJ...588..494M|s2cid=7483596 }}</ref><ref name=dangelo_2005>{{cite journal |author1=D'Angelo, G. |author2=Bate, M.R.B. |author3=Lubow, S.H. |title=The dependence of protoplanet migration rates on co-orbital torques |journal=Monthly Notices of the Royal Astronomical Society |date=2005 |volume=358 |issue=2 |pages=316–332 |doi=10.1111/j.1365-2966.2005.08866.x |doi-access=free |arxiv=astro-ph/0411705 |bibcode=2005MNRAS.358..316D|s2cid=14640974 }}</ref><ref name="dangelo_lubow_2008"/> Although sometimes referred to as "runaway migration", the migration rate does not necessarily increase over time.<ref name="masset_2003"/><ref name=dangelo_2005 /> '''Type&nbsp;III''' migration is driven by the co-orbital torques from gas trapped in the planet's [[Lagrangian point|libration regions]] and from an initial, relatively fast, planetary radial motion. The planet's radial motion displaces gas in its co-orbital region, creating a density asymmetry between the gas on the leading and the trailing side of the planet.<ref name="dangelo_lubow_2008"/><ref name="li2011"/> Type III migration applies to disks that are relatively massive and to planets that can only open partial gaps in the gas disk.<ref name="li2011"/><ref name="dangelo_lubow_2008"/><ref name="masset_2003"/> Previous interpretations linked Type&nbsp;III migration to gas streaming across the orbit of the planet in the opposite direction as the planet's radial motion, creating a positive feedback loop.<ref name=masset_2003 /> Fast outward migration may also occur temporarily, delivering giant planets to distant orbits, if later Type&nbsp;II migration is ineffective at driving the planets back.<ref name="Pierens_Raymond_2016">{{cite journal |last1=Pierens |first1=A. |last2=Raymond |first2=S.N. |title=Migration of accreting planets in radiative discs from dynamical torques|journal=Monthly Notices of the Royal Astronomical Society |date=2016 |volume=462 |issue=4 |pages=4130–4140 |doi=10.1093/mnras/stw1904 |doi-access=free |arxiv=1608.08756 |bibcode=2016MNRAS.462.4130P|s2cid=119225370 }}</ref>

=== Gravitational scattering ===
{{main|Gravitational scattering}}

Another possible mechanism that may move planets over large orbital radii is <em>gravitational scattering</em> by larger planets or, in a protoplanetary disk, gravitational scattering by over-densities in the fluid of the disk.<ref name="cloutier">{{cite journal |author=R. Cloutier |author2=M-K. Lin |title=Orbital migration of giant planets induced by gravitationally unstable gaps: the effect of planet mass |journal=Monthly Notices of the Royal Astronomical Society |arxiv=1306.2514 |date=2013 |bibcode=2013MNRAS.434..621C |doi=10.1093/mnras/stt1047 |volume=434 |issue=1 |pages=621–632|doi-access=free |s2cid=118322844 }}</ref> In the case of the [[Solar System]], Uranus and Neptune may have been gravitationally scattered onto larger orbits by close encounters with Jupiter and/or Saturn.<ref name="thommes">{{cite journal |author=E. W. Thommes |author2=M. J. Duncan |author3=H. F. Levison |title=The Formation of Uranus and Neptune among Jupiter and Saturn |journal=Astronomical Journal |arxiv=astro-ph/0111290 |date=2002 |volume=123 |issue=5 |pages=2862 |doi=10.1086/339975 |bibcode=2002AJ....123.2862T|s2cid=17510705 }}</ref><ref name="Gomes" /> Systems of exoplanets can undergo similar dynamical instabilities following the dissipation of the gas disk that alter their orbits and in some cases result in planets being ejected or colliding with the star.

Planets scattered gravitationally can end on highly eccentric orbits with perihelia close to the star, enabling their orbits to be altered by the tides they raise on the star. The eccentricities and inclinations of these planets are also excited during these encounters, providing one possible explanation for the observed eccentricity distribution of the closely orbiting exoplanets.<ref name="Ford_Rasio_2008">{{cite journal |last1=Ford |first1=Eric B. |last2=Rasio |first2=Frederic A. |title=Origins of Eccentric Extrasolar Planets: Testing the Planet-Planet Scattering Model |journal=The Astrophysical Journal |date=2008 |volume=686 |issue=1 |pages=621–636|doi=10.1086/590926 |arxiv=astro-ph/0703163 |bibcode=2008ApJ...686..621F|s2cid=15533202 }}</ref> The resulting systems are often near the limits of stability.<ref name="Raymond_etal_2009">{{cite journal |last1=Raymond |first1=Sean N. |last2=Barnes |first2=Rory |last3=Veras |first3=Dimitri |last4=Armitage |first4=Phillip J. |last5=Gorelick |first5=Noel |last6=Greenberg |first6=Richard |title=Planet-Planet Scattering Leads to Tightly Packed Planetary Systems |journal=The Astrophysical Journal Letters |date=2009 |volume=696 |issue=1 |pages=L98–L101 |doi=10.1088/0004-637X/696/1/L98 |arxiv=0903.4700 |bibcode=2009ApJ...696L..98R|s2cid=17590159 }}</ref> As in the Nice model, systems of exoplanets with an outer disk of planetesimals can also undergo dynamical instabilities following resonance crossings during planetesimal-driven migration. The eccentricities and inclinations of the planets on distant orbits can be damped by [[dynamical friction]] with the planetesimals with the final values depending on the relative masses of the disk and the planets that had gravitational encounters.<ref name="Raymond_etal_2010">{{cite journal |last1=Raymond |first1=Sean N. |last2=Armitage |first2=Philip J. |last3=Gorelick |first3=Noel |title=Planet-Planet Scattering in Planetesimal Disks: II. Predictions for Outer Extrasolar Planetary Systems |journal=The Astrophysical Journal |date=2010 |volume=711 |issue=2 |pages=772–795 |doi=10.1088/0004-637X/711/2/772|arxiv=1001.3409 |bibcode=2010ApJ...711..772R|s2cid=118622630 }}</ref>

=== Tidal migration ===
Tides between the star and planet modify the semi-major axis and orbital eccentricity of the planet. If the planet is orbiting very near to its star, the tide of the planet raises a bulge on the star. If the star's rotational period is longer than the planet's orbital period the location of the bulge lags behind a line between the planet and the center of the star creating a torque between the planet and the star. As a result, the planet loses angular momentum and its semi-major axis decreases with time.

If the planet is in an eccentric orbit the strength of the tide is stronger when it is near perihelion. The planet is slowed the most when near perihelion, causing its aphelion to decrease faster than its perihelion, reducing its eccentricity. Unlike disk migration – which lasts a few million years until the gas dissipates – tidal migration continues for billions of years. Tidal evolution of close-in planets produces semi-major axes typically half as large as they were at the time that the gas nebula cleared.<ref>{{cite arXiv |title=Tidal evolution of close-in extra-solar planets |first1=Brian |last1=Jackson |first2=Richard |last2=Greenberg |first3=Rory |last3=Barnes |quote=Submitted [for publication] on 4 Jan 2008 |date=4 Jan 2008|eprint = 0801.0716|class = astro-ph}}</ref>

===Kozai cycles and tidal friction===
{{See also|Kozai mechanism}}
A planetary orbit that is inclined relative to the plane of a binary star can shrink due to a combination of Kozai cycles and tidal friction. Interactions with the more distant star cause the planet's orbit to undergo an exchange of eccentricity and inclination due to the Kozai mechanism. This process can increase the planet's eccentricity and lower its perihelion enough to create strong tides between the planet on the star increases. When it is near the star the planet loses angular momentum causing its orbit to shrink. 

The planet's eccentricity and inclination cycle repeatedly, slowing the evolution of the planets semi-major axis.<ref name="Fabrycky_Tremaine_2007">{{cite journal |last1=Fabrycky |first1=Daniel |last2=Tremaine |first2=Scott |title=Shrinking Binary and Planetary Orbits by Kozai Cycles with Tidal Friction |journal=The Astrophysical Journal |date=2007 |volume=669 |issue=2 |pages=1298–1315 |doi=10.1086/521702 |arxiv=0705.4285 |bibcode=2007ApJ...669.1298F|s2cid=12159532 }}</ref> If the planet's orbit shrinks enough to remove it from the influence of the distant star the Kozai cycles end. Its orbit will then shrink more rapidly as it is tidally circularized. The orbit of the planet can also become retrograde due to this process. Kozai cycles can also occur in a system with two planets that have differing inclinations due to gravitational scattering between planets and can result in planets with retrograde orbits.<ref name="Noaz_etal_2011">{{cite journal |last1=Naoz |first1=Smadar |last2=Farr |first2=Will M. |last3=Lithwick |first3=Yoram |last4=Rasio |first4=Frederic A. |last5=Teyssandier |first5=Jean|title=Hot Jupiters from secular planet-planet interactions |journal=Nature |date=2011 |volume=473 |issue=7346 |pages=187–189 |doi=10.1038/nature10076 |arxiv=1011.2501 |bibcode=2011Natur.473..187N |pmid=21562558|s2cid=4424942 }}</ref><ref name="Nagasawa_etal_2008">{{cite journal |last1=Nagasawa |first1=M. |last2=Ida |first2=S. |last3=Bessho |first3=T. |title=Formation of Hot Planets by a Combination of Planet Scattering, Tidal Circularization, and the Kozai Mechanism |journal=The Astrophysical Journal |date=2008 |volume=678 |issue=1 |pages=498–508 |doi=10.1086/529369 |arxiv=0801.1368 |bibcode=2008ApJ...678..498N|s2cid=14210085 }}</ref>

===Planetesimal-driven migration===
The orbit of a planet can change due to gravitational encounters with a large number of planetesimals. <em>Planetesimal-driven migration</em> is the result of the accumulation of the transfers of angular momentum during encounters between the planetesimals and a planet. For individual encounters the amount of angular momentum exchanged and the direction of the change in the planet's orbit depends on the geometry of the encounter. For a large number of encounters the direction of the planet's migration depends on the average angular momentum of the planetesimals relative to the planet. If it is higher, for example a disk outside the planet's orbit, the planet migrates outward, if it is lower the planet migrates inward. The migration of a planet beginning with a similar angular momentum as the disk depends on potential sinks and sources of the planetesimals.<ref name="Levison_etal_2007" /> 

For a single planet system, planetesimals can only be lost (a sink) due to their ejection, which would cause the planet to migrate inward. In multiple planet systems the other planets can act as sinks or sources. Planetesimals can be removed from the planet's influence after encountering an adjacent planet or transferred to that planet's influence. These interactions cause the planet's orbits to diverge as the outer planet tends to remove planetesimals with larger momentum from the inner planet influence or add planetesimals with lower angular momentum, and vice versa. The planet's resonances, where the eccentricities of planetesimals are pumped up until they intersect with the planet, also act as a source. Finally, the planet's migration acts as both a sink and a source of new planetesimals creating a positive feedback that tends to continue its migration in the original direction.<ref name="Levison_etal_2007" /> 

Planetesimal-driven migration can be damped if planetesimals are lost to various sinks faster than new ones are encountered due to its sources. It may be sustained if the new planetesimals enter its influence faster than they are lost. If sustained migration is due to its migration only, it is called runaway migration. If it is due to the loss of planetesimals to another planet's influence, it is called forced migration.<ref name="Levison_etal_2007">{{cite book |last1=Levison |first1=H.F. |last2=Morbidelli |first2=A. |last3=Gomes |first3=R. |last4=Backman |first4=D. |title=Protostars and Planets V |chapter=Planet Migration in Planetesimal Disks |date=2007 |publisher=University of Arizona Press |pages=669–684 |chapter-url=http://www.lpi.usra.edu/books/PPV/8045.pdf |access-date=6 April 2017}}</ref> For a single planet orbiting in a planetesial disk the shorter timescales of the encounters with planetesimals with shorter period orbits results in more frequent encounters with the planetesimals with less angular momentum and the inward migration of the planet.<ref name="Kirsh_etal_2009">{{cite journal |last1=Kirsh |first1=David R. |last2=Duncan |first2=Martin |last3=Brasser |first3=Ramon |last4=Levison |first4=Harold F. |title=Simulations of planet migration driven by planetesimal scattering |journal=Icarus |date=2009 |volume=199 |issue=1 |pages=197–209 |doi=10.1016/j.icarus.2008.05.028 |bibcode=2009Icar..199..197K}}</ref> Planetesimal-driven migration in a gas disk, however, can be outward for a particular range of planetesimal sizes because of the removal of shorter period planetesimals due to gas drag.<ref name="Capobianco_eal_2011">{{cite journal |last1=Capobianco |first1=Christopher C. |last2=Duncan |first2=Martin |last3=Levison |first3=Harold F. |title=Planetesimal-driven planet migration in the presence of a gas disk |journal=Icarus |date=2011 |volume=211 |issue=1 |pages=819–831 |doi=10.1016/j.icarus.2010.09.001 |arxiv=1009.4525 |bibcode=2011Icar..211..819C|s2cid=118583564 }}</ref>