Editing Planetary migration (section)

==== 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>