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Orbital Evolution of Planets around Intermediate-Mass Giants M. Kunitomo∗, M. Ikoma∗, B. Sato∗, Y. Katsuta† and S. Ida∗ 1 1 ∗DepartmentofEarthandPlanetarySciences,TokyoInstituteofTechnology,2-12-1Ookayama, 0 Meguro-ku,Tokyo152-8551,Japan 2 †DepartmentofCosmosciences,HokkaidoUniversity,Kita10Nishi8,Kita-ku,Sapporo060-0810, n Japan a J 8 Abstract. Aroundlow-andintermediate-mass(1.5-3M⊙)redgiants,noplanetshavebeenfound 1 inside0.6AU.Suchapaucityisnotseeninthecaseof1M⊙ mainsequencestars.Inthisstudy,we examinethe possibility that short-periodplanetswere engulfedby their hoststar evolvingoff the ] mainsequence.Todoso, wehavesimulatedtheorbitalevolutionofplanets,includingthe effects P of stellar tide and mass loss, to determinethe critical semimajoraxis, a , beyondwhich planets E crit survivethe RGB expansionof their hoststar. We have foundthata changesdrastically around . crit h 2 M⊙:Inthe lower-massrange,acrit ismorethan1 AU, whileacrit isassmallasabout0.2AU in p thehigher-massrange.Comparisonwithmeasuredsemimajoraxesofknownplanetssuggeststhat - thereisalackofplanetsthatonlyplanetengulfmentneveraccountsforinthehigher-massrange. o Whether the lack is real affects our understanding of planet formation. Therefore, increasing the r t number of planet samples aroundevolved intermediate-massstars is quite meaningfulto confirm s a robustnessofthelackofplanets. [ Keywords: exoplanet,planetarysystem–formationandevolution,tide 1 PACS: 97.82.Fs,96.15.Bc,96.15.Wx v 8 5 INTRODUCTION 4 3 1. According to recent radial velocitysurveys for GK giants, it appears that there is a lack 0 ofgiantplanets inside0.6AU [18, 13]. Such apaucity is notseen around Sun-likestars 1 whichoftenharborshort-periodplanetssuchashotJupiters.Onepossibilityisthatsuch 1 : a property is primordial; namely, short-period giant planets (SPGPs) are not present v around BA dwarfs originally. Another possibility is that SPGPs were removed during i X theevolutionoftheirhoststar, whichis tobeexploredin thispaper. r A starevolvesoffthemainsequence(MS)towardsthered-giant branch(RGB), after a exhaustionofhydrogenatitscenter.Then,oncethecentralheliumignites,thestarenters a next stable phase called the horizontal branch (HB). Most of the giants with detected planets are thought to be on their HB. Before reaching the HB, namely, in the RGB phase, the star expands substantially, becomes highly luminous, and loses substantial mass,whichshouldaffect orbitsofsurroundingplanets. Villaver & Livio [23], following Sato et al. [18], examined what happened around evolvingintermediate-mass stars to understand the observed lack of SPGPs around GK giants.TheydemonstratedthatJovian-massplanetsinitiallyorbitingat<∼1AUaround 2-3M⊙starsundergoorbitaldecayduetostellartide,endingupbeingswallowedbytheir hoststar.However,theymadenoquantitativecomparisonwithobservation. The purpose of this paper is to examine whether planet engulfment by host stars is responsible for the lack of SPGPs, by making a quantitative comparison between the limits of existence of SPGPs predicted theoretically and suggested observationally. To thisend,wederiveacriticalsemimajoraxisbeyondwhichplanetssurvivethehoststar’s RGBphase, and investigateitssensitivityto stellarparameters. PHYSICAL MODEL We simulate the evolution of circular orbit of a planet during its host star’s evolution. Theeffectsofstellartideandmasslossonplanetaryorbitareincluded.Weneglectother competing processes such as the frictional and gravitational drag forces by stellar wind andchangeintheplanetmassduetostellar-windaccretionandevaporation,whichwere evaluated to be negligible by Villaver & Livio [23] and Duncan & Lissauer [4]. Thus, weintegrate 1da k M M R 8 M˙ =−6 p 1+ p ⋆ − ⋆, (1) a dt T M (cid:18) M (cid:19)(cid:18) a (cid:19) M ⋆ ⋆ ⋆ whereaisthesemimajoraxis,t istime,M istheplanet’smass,M andR arethemass p ⋆ ⋆ and radius of the host star, respectively, and k is the apsidal motion constant, and T is the eddy turnover timescale. The first term on the right-hand side represents the effect of stellar tide [7]. Since an RGB star is a slow rotator, we assume no stellar rotation, which means that the stellar tide always causes orbital decay of the planet. As for the parameters for stellar tide such as k and T, we have followed Rasio et al. [15] and Villaver& Livio[23]. The second term on the right-hand side of equation (1) represents orbital migration duetostellarmassloss(M˙ <0).WeusetheReimers’parameterisationforstellarmass ⋆ loss[16],namely,M˙ =−4×10−13h L R /M ,whereh isthemass-lossparameter;M˙ ⋆ ⋆ ⋆ ⋆ ⋆ isinM⊙yr−1 andM⋆, L⋆, and R⋆ arein solarunits. We simulate stellar evolution directly with the code MESA v2258 [14] to calculate M , R , M˙ , and parameters relevant to stellar tide as a function of time t. In this ⋆ ⋆ ⋆ calculation in this paper, the effect of convective overshooting is not included (see Kunitomoet al. [10]for theresultswithovershooting). ORBITAL EVOLUTION AND SURVIVAL LIMIT Figure1 showstheorbitalevolutionofplanets around stars with masses of2M⊙ (upper panel)and3M⊙(lowerpanel);themetallicityissolar(Z⋆=0.02)inthecalculations.The solidlinesrepresenttheevolutionofthestellarradiusR .Theorbitofa1M planetwith ⋆ J different initial semimajor axes (dotted lines) has been integrated from the host-star’s zero-age main sequence until the planet’s semimajor axis falls below the stellar radius (a<R )oruntilthebeginningofAsymptoticGiantBranch (AGB) thermalpulse. ⋆ OfspecialinterestinthisstudyiswhetherplanetssurvivetheRGBandHBphasesof their host star. As seen in the upper panel of Fig. 1, the 2M⊙ star expands up to 0.5 AU at theRGB-tip and consequentlyswallowsplanetswhoseinitialsemimajoraxes, a , are i smaller than 1.1 AU. The planet that starts out at 1.2 AU is pulled by the host star, but 2.5 2 U] 1.5 A e[ c n a t Dis 1 0.5 0 800 900 1000 1100 Time[Myr] 0.35 0.3 0.25 U] A 0.2 e[ c n a t 0.15 s Di 0.1 0.05 0 200 250 300 350 400 450 Time[Myr] FIGURE 1. Evolution of semimajor axes of Jupiter-mass planets (dotted lines) and the radius of the solar-metallicitystar(solidline)forM⋆ =2M⊙ (upperpanel)and3M⊙(bottompanel). it barely survives the RGB/HB phases. We define a critical initial semimajor axis, a , crit belowwhichplanets endup being engulfedby theirhoststarat somepointon theRGB or HB. In the present case, a = 1.2 AU. (Hereafter, we sometimes call the critical crit initialsemimajoraxisthesurvivallimit.)Asforthe3M⊙ star(thelowerpanelofFig.1), the RGB-tip radius is as small as 0.13 AU. As a consequence, even a planet starting 3 2 U] 1 A e[ 0.8 c n a Dist 0.6 0.4 0.2 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3 FIGURE2. Comparisonbetweenthecriticalsemimajoraxisa (solidline)andmeasuredsemimajor crit axes of detected exoplanets (symbols with error bars). The theoretical curve is for stellar metallicity Z=0.01andplanetarymassM =6M .Inthiscalculation,theeffectofovershootingisnotincluded. p J out at 0.20 AU can avoid engulfment during the RGB and HB phases. As seen in these panels, the survival limit is sensitiveto the mass of host stars. While a =1.2 AU for crit the2M⊙ star,acrit =0.20AU forthe3M⊙ star. COMPARISON WITH OBSERVATION We compare measured semimajor axes of known planets around GK giants with the criticalsemimajoraxisthatwehavederivedinFig.2.Thosemeasuredstellarmassesand planetarysemimajoraxesaretakenfromtheliterature[e.g.,22].Twofactscanbefound inthisfigure: First, theobservationalerrors beingtaken intoaccount,itwouldbefairto say that all the known planets are outside the survival limit. Therefore, it is not denied that SPGPs (a < a ) were swallowed by their host star on the RGB. Second, around crit giantsofM⋆ >2.4M⊙, planetsexistfarfrom acrit. In otherwords, planetengulfmentby hoststarsseemsnot tobethemainreason forthelack ofSPGPs. AnotherpossibilityisthatthelackofSPGPs isprimordial—theremaybeanystellar- mass-dependent processes that hinder formation of SPGPs around 2-3M⊙ stars. For example, Burkert & Ida [1] proposed that a decreasing-with-stellar-mass lifetime of protoplanetary disks could become comparable with or shorter than the timescale of the type-II migration of giant planets. They then demonstrated that the observed period valley between the hot-Jupiter and cool-Jupiter classes is more pronounced for planets orbitingFstars(1.2-1.5M⊙)thanGKstars(0.8-1.2M⊙).Applyingtheideatohigh-mass stars (1.5-3.0M⊙), Currie [2] demonstrated that SPGPs are rarely formed around high- massstars. Obviously we need more samples of giant planets and smaller planets orbiting high- massstarstoconfirmconclusionswehavederivedinthispaperandtounderstandstellar- mass-dependenceofplanetformation,whichisalsohelpfulinunderstandingtheorigins anddiversityofplanetarysystemsaroundsolar-typestars.Therefore,furthersurveysfor planetsaroundgiantsare highlyencouraged. ACKNOWLEDGMENTS Wewouldliketoexpressourgratitudetothefollowingpersons:B.PaxtonandA.Dotter kindly helped us install and use the stellar-evolution code MESA and modified it upon our request. M. Fujimoto and T. Suda gave useful comments about stellar evolution. We had fruitful discussion on this study with Y. Hori and T. Nakamoto. This work is supportedpartly byJapan Society forthePromotionofScience (JSPS). REFERENCES 1. Burkert,A.,&Ida,S.2007,ApJ,660,845 2. Currie,T.2009,ApJ,694,L171 3. deMedeiros,J.R.,etal.2009,A&A,504,617 4. Duncan,M.J.,&Lissauer,J.J.1998,Icarus,134,303 5. 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