Orbital Stability of a Protoplanet System under a Drag Force Proportional to the Random Velocity

Publications of the Astronomical Society of Japan

Emori, Hiroyuki¹  Iwasaki, Kazunori¹  Nakazawa, Kiyoshi¹  Tanaka, Hidekazu¹ 

[1] Department of Earth and Planetary Sciences, Faculty of Science, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551

关键词: Earth;    instabilities;    "planets and satellites: formation";    "Stokes-type drag force";   

DOI  :  10.1093/pasj/54.3.471

学科分类：天文学(综合)

来源: Oxford University Press

【 摘 要 】

Weinvestigatedtheeffectsofatidalinteractionwithagasdiskandthedynamicalfrictionwithaplanetesimaldiskontheorbitalinstabilityofaprotoplanetsystem.Botheffectsareexpressedasthedragforce,whichisproportionaltotherandomvelocityofaprotoplanet.Wecalculatednumericallytheorbitsof5protoplanetswiththesameseparationdistanceunderthedrag-forceeffectandexaminedtheorbitalinstabilitytimeunderthedragforce,$$T_{mathrm{inst}}^{mathrm{df}}$$.Wefoundthat$$T_{mathrm{inst}}^{mathrm{df}}$$canbecomemuchlargerthantheinstabilitytimeunderthedrag-freecondition,andthattheonsetoftheorbitalinstabilityispreventedwhentheseparationdistanceexceedsacriticalvalue.Weobtainedarelationbetweenthecriticalseparationdistanceandthesurfacedensityofthegasorplanetesimaldisk.Byapplyingthisrelation,wefoundthat,fortheformationofterrestrialplanetsfromaprotoplanetsystemwithatypicalorbitalseparation(i.e.,$$sim10$$Hillradii),thesurfacedensityofthenebulargasmustbereducedtoaboutone-thousandthofthatintheminimum-massnebulamodel.Terrestrialplanetswouldbeformedaftersuchadepletionofthesolarnebula.

【 授权许可】

Unknown