Precise radial velocities of giant stars. IV. A correlation between surface gravity and radial velocity variation and a statistical investigation of companion properties

0.28 MB·English

by  S. Hekker

Astronomy&Astrophysicsmanuscriptno.8321astroph (cid:13)c ESO2008
February2,2008
⋆
Precise radial velocities of giant stars. IV.
A correlation between surface gravity and radial velocity variation and a
statistical investigation of companion properties.
8
0 S.Hekker1,2,I.A.G.Snellen1,C.Aerts3,4,A.Quirrenbach1,5,S.Reffert5,andD.S.Mitchell6
0
2
1 LeidenObservatory,LeidenUniversity,P.O.Box9513,2300RALeiden,TheNetherlands
n
2 RoyalObservatoryofBelgium,Ringlaan3,1180Brussels,Belgium
a
3 InstituutvoorSterrenkunde,KatholiekeUniversiteitLeuven,Celestijnenlaan200D,3001Leuven,Belgium
J
4 DepartmentofAstrophysics,UniversityofNijmegen,P.O.Box9010,6500GLNijmegen,TheNetherlands
4
5 ZAH,LandessternwarteHeidelberg,Ko¨nigstuhl12,D-69117Heidelberg,Germany

6 CaliforniaPolytechnicStateUniversity,SanLuisObispo,CA93407,USA
]
h
p Received¡date¿;accepted¡date¿
-
o
r ABSTRACT
t
s
a Context.Since1999, wehavebeenconducting aradialvelocitysurveyof 179KgiantsusingtheCoude´ AuxiliaryTelescopeatUCO/Lick
[ observatory.Atpresent∼20−100measurementshavebeencollectedperstarwithaprecisionof5to8ms−1.Ofthestarsmonitored,145(80%)

showradialvelocity(RV)variationsatalevel>20ms−1,ofwhich43exhibitsignificantperiodicities.
1
v Aims.Ouraimistoinvestigatepossiblemechanism(s)thatcausetheseobservedRVvariations.Weintendtotestwhetherthesevariationsare
1 intrinsicinnature,orpossiblyinducedbycompanions,orboth.Inaddition,weaimtocharacterisetheparametersofthesecompanions.
4 Methods.ArelationbetweenloggandtheamplitudeoftheRVvariationsisinvestigatedforallstarsinthesample.Furthermore,thehypothesis
7 that all periodic RV variations are caused by companions is investigated by comparing their inferred orbital statistics with the statistics of
0 companionsaroundmainsequenceF,G,andKdwarfs.
1. Results.AstrongrelationisfoundbetweentheamplitudeoftheRVvariationsandlogginKgiantstars,assuggestedearlierbyHatzes&
0 Cochran(1998).However,mostofthestarsexhibitingperiodicvariationsarelocatedabovethisrelation.TheseRVvariationscanbesplitina
8 periodiccomponentwhichisnotcorrelatedwithloggandarandomresidualpartwhichdoescorrelatewithlogg.Comparedtomain-sequence
0 dwarfstars,KgiantsfrequentlyexhibitperiodicRVvariations.InterpretingtheseRVvariationsasbeingcausedbycompanions, theorbital
: parametersaredifferentfromthecompanionsorbitingdwarfs.
v
Conclusions.Intrinsic mechanisms play an important role in producing RV variations in K giants stars, as suggested by their dependence
i
X on logg. However, it appears that periodic RV variations areadditionalto these intrinsic variations, consistent with them being caused by
r companions. If indeed the majority of the periodic RV variations in K giants is interpreted as due to substellar companions, then massive
a planetsaresignificantlymorecommonaroundKgiantsthanaroundF,G,Kmain-sequencestars.
Keywords.stars:variables–techniques:radialvelocities
1. Introduction stars, but detections around an A star (Gallandetal. 2006)
and several subgiants (Johnsonetal. (2006), Johnsonetal.
For more than a decade, radialvelocity observationswith ac-
(2007)) have also been reported recently. Moreover, 10
curacies of order ms−1 have been within reach (see for in-
giant stars were reported to have sub-stellar companions
stanceMarcy&Butler(2000)andQuelozetal.(2001)).Even
(ι Draconis (K2III) Frinketal. (2002), HD104985 (G9III)
accuracies of less than 1 ms−1 (Pepeetal. 2003) are possi-
Satoetal. (2003), HD47526 (K1III) Setiawanetal. (2003),
ble now. With these observations, more than 200 sub-stellar
HD13189 (K2II-III) Hatzesetal. (2005), HD11977 (G5III)
companionshavebeendiscoveredbymeasuringthereflexmo-
Setiawanetal. (2005), Pollux (K0III) Hatzesetal. (2006),
tions of their parent stars. Most of these sub-stellar compan-
Reffertetal. (2006), 4UMa (K1III) Do¨llingeretal. (2007),
ions have been detected around F, G and K main sequence
NGC2423No3andNGC4349No127Lovis&Mayor(2007),
Sendoffprintrequeststo:S.Hekker,
email:[email protected]
⋆ BasedondataobtainedatUCO/LickObservatory,USA
2 S.Hekkeretal.:Preciseradialvelocitiesofgiantstars.IV.
and recently HD17092 (K0III) Niedzielskietal. (2007))1. In
addition to searches for extra-solar companions, radial veloc-
ity observations prove to be very useful for detecting solar-
likeoscillationsinstarswithturbulentatmospheres,suchasthe
dwarfαCenA(e.g.Beddingetal.2006),thesubgiantProcyon
(e.g.Eggenbergeretal.2004:Martic´etal.2004)andthegiant
ǫ Ophiuchi(e.g.DeRidderetal.2006).
With techniques for accurate radial velocity observations
at hand, a survey was started in 1999 to verify whether K
giants are stable enough to be used as astrometric refer-
encestarsforSIM/PlanetQuest(SpaceInterferometryMission)
(Frinketal.2001).Thissurveycontains179starsandusesthe
Coude´ Auxiliary Telescope (CAT) at University of California
Observatories / Lick Observatory, in conjunction with the
HamiltonEchelleSpectrograph.Thesurveyhasrecentlybeen
expandedtoabout380giantsandisstillongoing.Fortheanal-
ysis described in the present paper only data from the initial
179starsareused.
From this survey, companions have been announced for ι
Draconis (Frinketal. 2002) and Pollux (Reffertetal. 2006).
Starswithradialvelocityvariationsoflessthan20ms−1 have
beenpresentedasstablestarsbyHekkeretal.(2006).Inaddi-
tion, some binaries discoveredwith this survey,as well as an
extensive overview of the sample, will be presented in forth-
comingpapers.
Fig.1. Radial velocity variations as a function of phase for a
As almost all of the stars show significant radial velocity
star(HIP34693)withahighlysignificantperiod(top),withits
variations,weinvestigateherewhichmechanismcausesthese
periodogram(bottom).Thedashedlineintheperiodogramin-
variations.Non-periodicradialvelocityvariations,oftheorder
dicatesthesignificancethreshold.
oftheinvestigatedtimescales,aremostlikelycausedbysome
intrinsicmechanism,whiletheperiodicvariabilitycanalsobe
causedbycompanions.We also investigatethe characteristics
ofthesecompanions. about80−100atλ = 5500Å, yieldinga radialvelocitypre-
InSect.2,theradialvelocityobservationsaredescribedin cision of 5 − 8 ms−1. As we are looking for radial velocity
detail.In Sect. 3,the relationbetweenthe observedradialve- variationsoforder10to100ms−1,thisisadequateandhence
locityamplitudeandsurfacegravityisinvestigated.InSect.4, noattempthasbeenmadetoreachthe3ms−1 accuracywhich
weexplorethehypothesisthatallperiodicradialvelocityvari- isinprinciplepossiblewiththissetup(Butleretal.1996).For
ationsare causedbysub-stellarcompanions,andwe compare thedeterminationoftheradialvelocitiesthepipelinedescribed
the inferred orbital parameters with those obtained for sub- by Butleretal. (1996) is used. In this pipeline, a template io-
stellar companionsorbiting main sequence stars. Our conclu- dine spectrum and a template spectrum of the target star ob-
sionsarepresentedinSect.5. tainedwithoutaniodinecellinthelightpathareusedtomodel
thestellarobservationswithasuperposediodinespectrum.The
Dopplershiftisafreeparameterinthismodel.Notethatwith
2. Radialvelocityvariations thismethodtheabsoluteradialvelocityisnotmeasured,butthe
radialvelocityrelativetothestellartemplateisobtained.
Theinitial179starsselectedfortheradialvelocitysurveyare
All 179 stars are subjected to a period search. The peri-
usedinthepresentwork.Thesestarshavebeenselectedfrom
odicity of the radial velocity variations is determined first of
theHipparcoscatalogue(Perryman&ESA1997),basedonthe
all from a classical Lomb-Scargle(LS) periodogram(Scargle
criteriadescribedbyFrinketal.(2001).Theselectedstarsare
1982).Thesignificancethresholdissetto6σ,wherethenoise
all brighter than 6 mag, are presumably single and have pho-
level is determined from the average power of the residual
tometric variations < 0.06 mag in V. The survey started in
Scargle periodogram for frequencies between 0 and 0.03 cy-
1999atLickObservatoryusingtheCoude´AuxiliaryTelescope
clesperday(c/d)(0.35µHz)andafrequencystepof0.00001
(CAT)inconjunctionwiththeHamiltonEchelleSpectrograph
c/d(0.12·10−3µHz).Weadoptedtheconventionalmethodof
(R=60000). The system with an iodine cell in the light path
iterativesinewavefitting (‘prewhitening’)to searchforsubse-
hasbeendescribedbyMarcy&Butler(1992)andValentietal.
quentfrequencies(Kuschnigetal. 1997). In Figs 1 and2, the
(1995). With integration times of up to thirty minutes for the
radial velocity variation as a function of phase is shown for
fainteststars(m = 6 mag)we reacha signalto noiseratio of
v
twostars.TheperiodofthestarinFig.1ishighlysignificant,
1 For updated information on sub-stellar companions, see while the one in Fig. 2 is close to the significance threshold.
http://exoplanet.euandhttp://exoplanets.org. Periodogramsareshowninthebottompanelsofthesefigures.
S.Hekkeretal.:Preciseradialvelocitiesofgiantstars.IV. 3
Table1.Singlestarswithsignificantfrequencies.
star frequency period frequency period
µHz days µHz days
HIP3419 0.0638 181 0.1197 97
HIP7607 0.0216 536
HIP7884 0.0184 629
HIP13905 0.0223 519
HIP16335 0.0197 588
HIP19011 0.0252 459
HIP21421 0.0203 570 0.0448 237
HIP23015 0.0151 767 0.0073 1586
HIP23123 0.0135 857
HIP31592 0.0144 804
HIP33160 0.0226 512
HIP34693 0.0380 305
HIP36616 0.0033 3507 0.0389 298
HIP37826 0.0194 597
HIP38253 0.0171 677
HIP39177 0.0133 870
HIP40526 0.0172 673
HIP46390 0.0233 497
HIP47959 0.0187 619
HIP53229 0.0022 5261
HIP53261 0.0149 777
HIP57399 0.0196 591
HIP64823 0.0021 5512
Fig.2. Radial velocity variations as a function of phase for a
HIP69673 0.0382 303 0.0187 619
star(HIP7607)withaperiodclosetothesignificancethreshold
HIP73133 0.0014 8267 0.0157 737
(top), with its periodogram (bottom). The dashed line in the HIP73620 0.0226 512
periodogramindicatesthesignificancethreshold. HIP74732 0.0233 497
HIP75458 0.0226 512
HIP79540 0.0203 570
AsproperlyemphasizedbyCummingetal.(1999),suchaclas-
HIP80693 0.0022 5261 0.0198 585
sicalperiodsearchmaynotbeappropriateforunevenlyspaced
HIP84671 0.0251 461
sparsedata,eventhoughwesetthesignificancelevelatacon-
HIP85139 0.2895 40
servativelyhighlevel.Inordertocheckthis,wehavedonean HIP85355 0.0258 449 0.0056 2067
additionalLSanalysisafterprewhiteningtheoriginaldatabya HIP85693 0.0175 661
linearpolynomial.Thisledalmostalwaystothesamefrequen- HIP87808 0.0153 757
cies.Weonlyacceptedafrequencywhenitwasfoundtomeet HIP88048 0.0218 531 0.0029 3991
the significance criterion for both these analyses. The signifi- HIP91117 0.0303 382
cantfrequenciesarelistedinTable1. HIP109023 0.0199 582
HIP109492 0.0217 533
HIP109602 0.0130 890
3. Radialvelocityamplitude-surfacegravity HIP109754 0.0189 612
relation HIP113562 0.0401 289 0.0472 245
HIP114855 0.0639 181
Hatzes&Cochran(1998)alreadyinvestigatedtheoriginofthe
observedradialvelocitiesinKgiantstars.Althoughtheirsam-
ple contained only 9 stars, they suggested that the amplitude and Kurucz model atmospheres which include overshooting
oftheradialvelocityincreaseswithdecreasingsurfacegravity (Castellietal.1997).Theseauthorsestimatedtheerroronlogg
(logg).Inlowersurfacegravityittakeslongertodecreasethe tobe0.22dexfromthescatterfoundinacomparisonwithlit-
velocityofamovingparcelwhichresultsinlargeramplitudes eraturevalues.Adetaileddescriptionofthestellarparameters
andtherelationsuggestedbyHatzes&Cochran(1998)would forindividualstarsandacomparisonwithliteraturevaluesare
thereforebeevidenceforpulsationsorrotationalmodulationas availableinHekker&Mele´ndez(2007)andisthereforeomit-
themechanismfortheselongperiodradialvelocityvariations. tedhere.
Forthepresentsample,loggvaluesweredeterminedspec- In Fig. 3, we show half of the peak-to-peak value of the
troscopicallybyHekker&Mele´ndez(2007),by imposingex- observedradialvelocityvariationsasafunctionofloggforK
citation and ionisation equilibrium of iron lines through stel- giantsinoursample.Acleartrendisvisiblebetweenincreasing
lar models. The equivalent width of about two dozen care- radialvelocityvariationsin single stars, anddecreasinglogg,
fully selected iron lines were used for a spectroscopic LTE whichprovidesastrongindicationthat,atleastforalargefrac-
analysis based on the 2002version of MOOG (Sneden 1973) tion of stars in our sample, the observed radial velocity vari-
4 S.Hekkeretal.:Preciseradialvelocitiesofgiantstars.IV.
Fig.3.Half ofthe peak-to-peakvariationof theradialvelocityas a functionofsurfacegravity(logg).Theblue ◦indicatethe
singlestarswithperiodicradialvelocityvariations(seetextforperiodicitycriteria),thered(cid:3)indicatesinglestarswithrandom
radialvelocityvariations,and stellar binaries(companionmass > 100M ) are indicatedwith black ⋄ symbols.(Coloursare
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only visible in the online version of the paper.) The solid line is the best fit through the random single stars, the dotted line
indicates the 1σ interval around the best fit and the dashed line indicates the 3.5σ interval. Single stars with a higher radial
velocityamplitudethanexpectedbasedontheirloggvalue(morethan3.5σabovethebestfit)areindicatedbyarrows.Sixof
the8starswithperiodicradialvelocityvariationsandlogg < 1.6areclassified brightgiantsorsupergiants(Perryman&ESA
1997).
ations are induced by a mechanism intrinsic to the star. This fittedveryaccuratelywithaKeplerianorbitofasinglenearly
trendispresentforstarswithrandomaswellasstarswithperi- sinusoidalsub-stellarcompanion.
odicradialvelocityvariations.Also,nearlyallstarswithperi- Inordertoinvestigatethesimultaneousoccurrenceofsub-
odicradialvelocityvariationsandlogg≥1.6arelocatedabove stellarcompanionsandoscillationsingiants,thebestKeplerian
the fitin Fig.3. Sevensingle starshavea higherradialveloc- fitsaresubtractedfromtheobservedradialvelocityvariations
ityvariationthanexpectedbasedontheirloggvalue,i.e.they ofboththebinariesandthesinglestarswithsignificantperiodic
are situated more than 3.5σ abovethe best fit for the relation radialvelocityvariations.Thehalfpeak-to-peakvaluesofthese
obtainedforsinglestars.Thesestarsareindicatedwitharrows residualsareplottedasa functionofsurfacegravityinFig.4,
inFig.3.TheradialvelocityvariationobservedforHIP53229 also showingthe linear fitthroughthe non-periodicstars, and
maybeduetoastellarcompanioninawideorbit,withaperiod theamplitudesofthesubtractedperiodicsignals.Therearesev-
much longerthan the observationtime span. Due to this long eralinterestingpointstomakeaboutthisgraph.Firstly,almost
periodthecompanionmass,and,therefore,the(sub-)stellarna- allperiodicstarsshowlargerradialvelocityvariationsthanpre-
ture,is still veryuncertain.HIP33152is classified asa super- dictedbytherelationfoundfornon-periodicstars,butwhenthe
giant. The observed radial velocity variations for HIP80693, periodicities are removed, their residual radial velocity varia-
HIP36616,andHIP88048canbefittedwithtwoKeplerianor- tions follow the same relation as found for the non-periodic
bits, while HIP75458 can be explained by an eccentric sub- stars. This could be interpreted as evidence for both intrinsic
stellar companion (Frinketal. 2002) and an additional linear (non-periodicradialvelocityvariation)andextrinsic(periodic
trend,indicatingacompanioninawideorbit.HIP34693canbe variations)mechanismsplayingaroleinthesestars.Secondly,
S.Hekkeretal.:Preciseradialvelocitiesofgiantstars.IV. 5
Fig.4. Top: Half of the peak-to-peakvariation of the radial velocity as a function of surface gravity (logg), as in Fig. 3, but
showingonlythosestarswithperiodicradialvelocityvariations(blue◦)andstellarbinaries(black⋄).Theblue+andblack×
symbolsindicatetheamplitudeoftheradialvelocityvariationsforthesestarsaftersubtractionoftheKeplerianfits.(Coloursare
onlyvisibleinthe onlineversionofthepaper.)Thesolid lineindicatesthelinearfitthroughthe starswith non-periodicradial
velocityvariations(fromFig.3).Bottom:AmplitudesofthesubtractedKeplerianfitsasafunctionoflogg.
thereisnocorrelationbetweentheamplitudeofthesubtracted 4. CompanionInterpretation
periodic signal and logg, which providesadditional evidence
From the analysis of the correlation between radial velocity
forthepresenceofcompanions.Thirdly,almostall(8outof9)
amplitude and surface gravity we have evidence for the pres-
stars with logg ≤ 1.6 exhibit periodic variations. If these in-
ence of both intrinsic variabilityand companionsin at least a
deedhaveanextrinsicmechanism,itwouldmeanthat∼ 90%
fractionoftheKgiantstarswithperiodicradialvelocityvaria-
of these stars have sub-stellar companions.However,froman
tions.Inordertostudythecharacteristicsofthesecompanions,
astrophysicalpoint of view, stars with such low surface grav-
we take the hypothesisthat the periodic radial velocity varia-
ities are alreadyvery high on the giant branchor even on the
tionsdetectedin43ofourKgiantstars,excludingbinaries,are
asymptoticgiantbranch.Attheselowgravities,starscannotbe
caused by sub-stellar companions. Under this hypothesis, we
constantanymore,astheouterlayersaresodilutedthatinsta-
investigatethestatisticalpropertiesoftheorbitalparametersof
bilities occur easily, either periodic or random. Stated differ-
thesampleandcomparethesewiththestatisticalpropertiesof
ently,thesestarsareveryclosetothesemi-regulars,whichare
companionsorbitingF,GandKdwarfs.
ontheir way to becomeMira variables.Hence,these periodic
According to our analysis, 55 stars in the sample would
variationscouldwellbeintrinsic.
have a single companion, and 11 stars multiple companions.
6 S.Hekkeretal.:Preciseradialvelocitiesofgiantstars.IV.
Twenty-three (22 single and 1 in a multiple system) of these
companions have msini larger than 100 M and should be
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interpretedas stellar binaries.By advancingthe multiple sub-
stellarsystemsforwardintimeviaaRunga-Kuttaintegration,
we investigated the stability of the systems, taking into ac-
countthemutualinteractionsofthecompanions.Withthe or-
bitalparametersthatminimiseχ2takenatfacevalue,wefound
thatmostoftheinferredsub-stellarmultiplesystemswouldbe
’likelyunstable’,with a changein semi-majoraxis> 1%and
< 10%,or’unstable’withachangeinsemi-majoraxis> 10%
onatimescaleof100yearsduetocompanion-companionin-
teraction.
However, the inferred stability depends on the starting
epoch of the computations, as well as on the orbital parame-
ters,whichmightchangewithanincreasingnumberofobser-
vations. Furthermore, there is no guarantee that the obtained Fig.5.Ahistogramofmsiniofinferredcompanionmassesor-
χ2 minimumis a globalminimum.Therefore,stars with mul- biting K giants in our sample. The dashed line indicates the
tiple inferred sub-stellar companions that seem to be unsta- rise of planet masses M−1.05 from 10 M down to Saturn
Jup
ble, might also have stable solutions. One could also use the massesforsub-stellarcompanionsaroundmainsequencestars
equationsfordynamicalstabilitydescribedbyGladman(1993) (Marcyetal. 2005), normalised to the number of stars in our
and Marcyetal. (2001). Gladman (1993) also notes that the sample.
Hill stability criteria for companions in initially eccentric or-
bitsmaynotbemet,butthatthesystemsmaystillbefoundto
beempiricallyquitestableforalongperiodoftime.Inorderto
drawa firmconclusiononthe stability ofa particularsystem,
amorethoroughinvestigationisneeded,aswellasdatawitha
longertimebase,whichisbeyondthescopeofthispaper.
For all stars with periodic radial velocity variations, we
checked the Hipparcos (Perryman&ESA 1997) photometry.
We checkedperiodogramsfor significantfrequenciesclose to
the obtainedradialvelocity period,and plotted the photomet-
ric valuesphased with the radialvelocityperiod. None of the
starsshowphotometricvariationsrelatedtotheobservedradial
velocityvariations.
The massdistributionof ourK giantsampleis notknown
very well. The stellar masses are typically between 1 and 4
M⊙. Hence most of their main sequence progenitors should
have been of A or F spectralclass. The distribution of orbital Fig.6.Zoomin onthelowendofthe companionmassdistri-
parameters of sub-stellar companions orbiting A and F main butionofinferredsub-stellarcompanionsorbitingKgiantstars
sequencestarsisstillunknown.Thecoreaccretionmodelpre- inoursurvey,shownaspercentageofthetotalnumberofstars
dictsmoregiantplanetsaroundmoremassivestars,sothatthe inthesample(grayhistogram).Thehatchedhistogramshows
distributionoforbitalparametersofsub-stellarcompanionsor- the distribution of companionmasses orbiting main sequence
bitingF,GandKmain-sequencestarsprobablycannotserveas starsasshowninFig.1ofMarcyetal.(2005),asapercentage
a proxy.However,itshouldbeinstructivetocomparethetwo ofthetotalnumberofstarsintheirsample.Thecrosshatched
distributions. areaaremainsequencestarswithcompanionsatasemi-major
Sincethedatapresentedherespan∼ 2500days,radialve- axissmallerthan0.3AU(seeFig.7).
locityvariationswithlongerperiodsareuncertain,and,there-
fore, not taken into consideration. Companions with periods
dwarf statistics around F, G and K main sequence stars for
exceeding the observation time span are also excluded from
which onlyvery few companionsare foundwith msini > 15
theF,G,andKmainsequencestarstatistics.
M around more than thousand stars. This is known as the
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brown dwarf desert and is possibly caused by migration and
mergingofbrowndwarfsinaviscousdiskwithamassatleast
4.1.Massdistribution
comparable to the brown dwarf mass (Armitage&Bonnell
Fig. 5 shows the distribution of inferred companion masses 2002).
of our K giant sample. First, notice that 30% of the inferred The dashed line in Fig. 5 indicates the rise of sub-stellar
companionswouldhavemassesinthebrowndwarfregime15 companion masses M−1.05 from 10 M down to Saturn
Jup
M <msini<80M .Thisisinsharpcontrasttothebrown massesformainsequencestars(Marcyetal.2005),normalised
Jup Jup
S.Hekkeretal.:Preciseradialvelocitiesofgiantstars.IV. 7
Fig.7. Semi-major axis distribution of inferred K giant com- Fig.8.Perioddistributionoftheobservedradialvelocityvari-
panionsinoursample(grayhistogram),shownasapercentage ations shown as a fraction of all significant periods (gray
of the total number of stars in the sample. The hatched his- histogram). The period distribution of main sequence stars
togram shows the distribution for F, G and K main sequence (Butleretal.2006)isshowninthehatchedhistogram,asafrac-
stars as shown in Fig. 2 of Marcyetal. (2005), as a percent- tion of the total number of observed companions. The cross
age ofthe totalnumberof stars in theirsample. Themain se- hatched area are main sequence stars with a semi-major axis
quence stars with a companion orbiting at a semi-major axis smallerthan0.3AU(seeFig.7).
smallerthan0.3AUarecross-hatched.Thesearealsoindicated
inFigs6and8.
4.3.Perioddistribution
In Fig. 8 the period distribution of the observed radial veloc-
ity variationsisshownandcomparedwith thecompanionpe-
to the number of stars in our sample. We use a two-sided
riod distribution of dwarfs. The large fraction of F, G and K
Kolmogorov-Smirnov test (Pressetal. 1992) (hereafter KS-
dwarf companions with orbital periods shorter than 100 days
test) to compare the M−1.05 fit and the mass distribution
correspondstotheoneswithsemi-majoraxissmallerthanap-
(msini < 80 M ) of our sample and find a probability of
Jup proximately0.3AU.Theclose-inshort-periodcompanionsare
0.05% (0.002% for msini < 28 M ) that these are identi-
Jup not present around K giants, while about 80% of these stars
cal. This implies that inferred sub-stellar companions around
with observed radial velocities have periods ranging between
K giantsin oursamplehavehighermassescomparedtocom-
400and800days.AKS-testrevealsaprobabilityoflessthan
panionsaroundF,GandKmainsequencestars.
0.0001%for the two distributions to be identical. The proba-
Fig. 6 shows the low-mass companion distribution of our bilityremainsbelowthislevel,whenthecompanionsorbiting
survey.MostKgiantcompanionswouldhaveinferredmasses mainsequencestarswithasemi-majoraxis<0.3AUareomit-
between 2 and 8 MJup, while the fraction of companions or- ted.
biting F, G and K dwarfs strongly decreases with increasing
msini.
4.4.Eccentricitydistribution
Fig. 9 shows the distribution of companion eccentricities for
4.2.Semi-majoraxisdistribution
Kgiantsinoursampleandfordwarfs.Companionsofdwarfs
Thedistributionofthecompanions’semi-majoraxisisshown withperiodslessthan20daysareexcluded,asthesemightbe
inFig.7.Noinferredcompanionswithsemi-majoraxissmaller tidally circularised. The fraction of companion eccentricities
than0.3AUarepresentintheKgiantsample,possiblydueto < 0.3forthegiantsis75%comparedto 50%forcompanions
increasedstellarradiiofgiants.Thefractionofstarswithanin- orbitingF, GandKdwarfs.TheKS-testshowsthatthesedis-
ferredcompanionwithasemi-majoraxisbetween1and3AU tributionsarenearlyidentical(97%).
ismuchhigheramongtheKgiantscomparedtotheF,GandK
dwarfs.AcomparisonbetweenthetwodistributionswithaKS-
4.5.Ironabundance
test reveals a probability for the two distributions to be iden-
tical of 11%. This increases to 32% when omitting the main Companion occurrence correlates strongly with the abun-
sequencestarswithsemi-majoraxis< 0.3AU.Theincreasing dance of heavy elements (see for instance Gonzalez (1997),
incompletenessbeyond3 AU, dueto the limited time span of Fischer&Valenti (2005) and Santosetal. (2005)), such that
surveys,ispresentinbothsamplesasthesurveyscoveracom- F, G, and K dwarf stars with supersolar abundance are more
parableamountoftime.Thisincompletenesscannotcausethe likely to harbour sub-stellar companions (about 50% of the
significantdifferenceinthepeakbetween1and3AU. stars with 0.3 < [Fe/H] < 0.5). The increase of the fraction
8 S.Hekkeretal.:Preciseradialvelocitiesofgiantstars.IV.
Fig.9. Distribution of eccentricities for possible companions Fig.10. Iron abundance [Fe/H] distribution of K giant stars
around K giants in our sample (gray histogram) shown as a with periodicradialvelocityvariationsshownasapercentage
fraction of all possible sub-stellar companions in the sample. of the total number of observed stars with iron abundance in
Thehatchedhistogramistheeccentricitydistributionofcom- the same interval. The numbers above each bar on the his-
panionsaroundmainsequencestars(Butleretal.2006)shown togram indicate the ratio of stars with a significant periodic
as a fraction of all companions around main sequence stars. radial velocity variation to the total number of stars in each
Companions with periods shorter than 20 days are excluded bin. The error bars are calculated assuming Poisson statistics
fromthelattersampleasthesemightbetidallycircularised. (i.e.,the percentageof starswith periodicradialvelocitiesdi-
vided by the square rootof the number of stars with periodic
radialvelocities).Thedashedlineisthepowerlawderivedfor
of F, G andK dwarfsharbouringcompanionswith increasing
the increasing trend in the fraction of stars with companions
metallicity is well fitted with a power law, yielding a prob-
asafunctionofmetallicityofF,GandKmainsequencestars
ability for such a star to harbour a companion to be: P =
(Fischer&Valenti2005).
0.03·[(NFe/NH)/(NFe/NH)⊙]2.0(Fischer&Valenti2005).
InFig.10theironabundancedistributionofstarswithpe-
riodicradialvelocityvariationsisshownasapercentageofthe
totalnumberofobservedstarswithironabundanceinthesame Almost all of the lowest logg stars show periodic varia-
interval. The iron abundance is determined spectroscopically tions.Itmaybepossiblethatstarswithsuchlowsurfacegravity
byimposingexcitationandionisationequilibriuminironlines cannotbe constantand thatin these dilute atmospheresinsta-
andisdescribedbyHekker&Mele´ndez(2007).Themaximum bilities can occur very easily, and therefore may be periodic,
iron abundance of a K giant star in our sample is 0.29 and, butnotextrinsic.
therefore,wedonotprobethehighmetallicityregioninwhich Based on the evidence that extrinsic mechanism(s) play a
F,GandKdwarfsaremostlikelytoharbouracompanion. roleforKgiantstarswithperiodicradialvelocityvariationswe
ThemeanmetallicityoftheKgiantsintheentiresampleis investigated the hypothesis that this periodic signal is caused
−0.12dex,whilethemeanmetallicityofthestarswithperiodic by the reflex motion of sub-stellar companionsorbiting these
radial velocity variations, presented in Fig. 10, is −0.13 dex. stars.Wepresentedthecharacteristicsoftheorbitalparameters
Nocorrelationbetweencompanionoccurrenceandabundance, of these companions and compared them with the known or-
similartotheonewhichispresentfordwarfstars,isfoundin bitalparametersofsub-stellarcompanionsorbitingF,GandK
thissampleofgiantstars. dwarfs.
About 25% of the stars in our sample have radial veloc-
ity variations with significant periodicity, and could possibly
5. DiscussionandConclusion
harbour a sub-stellar companion, while approximately only
The tight correlation we found between logg and half of the 8% of the 1330 F, G and K main sequence stars investigated
peak-to-peakradialvelocityvariationsseemstoindicatethata byMarcyetal.(2005)haveasub-stellarcompanion.Recently
largefractionof the observedradialvelocityvariationsin our Johnsonetal. (2007) and Lovis&Mayor (2007) showed that
sampleofKgiantsisinducedbymechanism(s)intrinsictothe thenumberofcompanionharbouringstarsincreaseswithmass.
stars.Wealsopresentevidencethatbothintrinsicandextrinsic Thegiantsinthepresentsamplehavetypicalmassesbetween
mechanisms play a role. The stars with a significant periodic 1and4M⊙ andareingeneralmoremassivethanthemainse-
signal are almost all located above the radial velocity ampli- quencestarsinvestigatedforcompanions.So,thehighpercent-
tudevs.loggrelation,butwhentheperiodicsignalisremoved, age is qualitativelyin agreementwith the results from the lit-
theresidualsshowthesametrendasforthenon-periodicstars. erature.Furthermore,Lovis&Mayor(2007)suggestthatmore
Furthermore, no correlation is present between the amplitude massivestarsformmoremassiveplanetarysystemsthanlower
oftheperiodicsignalandlogg. mass stars. Figs 5 and 6 show that we find, in general, more
S.Hekkeretal.:Preciseradialvelocitiesofgiantstars.IV. 9
massive companions around the more massive K giants than preparation)becausetheamountofsuchdataathandtodayis
arepresentaroundF,GandKdwarfs. insufficienttoaddsignificantlytotheconclusionsofthispaper.
The highpercentageof more massive companionsaround
themoremassiveKgiantstarswouldalsobecompatiblewith Acknowledgements. WethankDebraFischer,GeoffMarcyandPaul
the core accretion model. This model predicts very few giant Butlerforusefuldiscussionsandthedevelopmentoftheinstrumenta-
planets,butarelativelylargenumberofplanetswiththemass tionandsoftwareforthedeterminationoftheradialvelocitiesatLick
ofNeptuneorsmalleraroundMdwarfs(Laughlinetal.2004: Observatory.Inaddition,wethanktheentirestaffatLickObservatory
Ida&Lin 2005). This is mainly the result of a much reduced fortheirexcellentsupport.Finally,wewouldliketothanktheanony-
surfacedensityofthediskandtheresultingshorterdiskevolu- mousrefereeforvaluablecommentsandsuggestions.
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