shortlick

TheLick-CarnegieExoplanetSurvey:A3.
1MPlanetintheHabitableZoneoftheNearbyM3VStarGliese581StevenS.
Vogt1,R.
PaulButler2,E.
J.
Rivera1,N.
Haghighipour3,GregoryW.
Henry4,andMichaelH.
Williamson4Received;acceptedms-press1UCO/LickObservatory,UniversityofCalifornia,SantaCruz,CA950642DepartmentofTerrestrialMagnetism,CarnegieInstitutionofWashington,5241BroadBranchRoad,NW,Washington,DC20015-13053InstituteforAstronomyandNASAAstrobiologyInstitute,UniversityofHawaii-Manoa,Honolulu,HI968224TennesseeStateUniversity,CenterofExcellenceinInformationSystems,3500JohnA.
MerrittBlvd.
,Box9501,Nashville,TN.
37209-1561–2–ABSTRACTWepresent11yearsofHIRESprecisionradialvelocities(RV)ofthenearbyM3VstarGliese581,combiningourdatasetof122precisionRVswithanex-istingpublished4.
3-yearsetof119HARPSprecisionRVs.
Thevelocitysetnowindicates6companionsinKeplerianmotionaroundthisstar.
Dierentialphotometryindicatesalikelystellarrotationperiodof94daysandrevealsnosignicantperiodicvariabilityatanyoftheKeplerianperiods,supportingplanetaryorbitalmotionasthecauseofalltheradialvelocityvariations.
Thecombineddatasetstronglyconrmsthe5.
37-day,12.
9-day,3.
15-day,and67-dayplanetspreviouslyannouncedbyBonlsetal.
(2005),Udryetal.
(2007),andMayoretal.
(2009).
Theobservationsalsoindicatea5thplanetinthesystem,GJ581f,aminimum-mass7.
0Mplanetorbitingina0.
758AUorbitofperiod433daysanda6thplanet,GJ581g,aminimum-mass3.
1Mplanetorbitingat0.
146AUwithaperiodof36.
6days.
TheestimatedequilibriumtemperatureofGJ581gis228K,placingitsquarelyinthemiddleofthehabitablezoneofthestarandoeringaverycompellingcaseforapotentiallyhabitableplanetaroundaverynearbystar.
Thatasystemharboringapotentiallyhabitableplanethasbeenfoundthisnearby,andthissoonintherelativelyearlyhistoryofprecisionRVsurveys,indicatesthatη,thefractionofstarswithpotentiallyhabitableplanets,islikelytobesubstantial.
Thisdetection,coupledwithstatisticsoftheincompletenessofpresent-dayprecisionRVsurveysforvolume-limitedsamplesofstarsintheimmediatesolarneighborhoodsuggeststhatηcouldwellbeontheorderofafewtensofpercent.
Ifthelocalstellarneighborhoodisarepre-sentativesampleofthegalaxyasawhole,ourMilkyWaycouldbeteemingwithpotentiallyhabitableplanets.
–3–Subjectheadings:stars:individual:GJ581HIP74995–stars:planetarysystems–astrobiology–4–1.
IntroductionTherearenownearly500knownextrasolarplanets,anddiscoveryworkcontinuesapaceonmanyfronts:byradialvelocities(RV),gravitationalmicrolensing,transitsurveys,coronography,nullinginterferometry,andastrometry.
ByfarthemostproductivediscoverytechniquetodatehasbeenthroughtheuseofprecisionRVstosensethebarycentricreexvelocityofthehoststarinducedbyunseenorbitingplanets.
Inrecentyears,theworld'sleadingRVgroupshaveimprovedprecisiondowntothe1ms1level,andevenbelow,extendingdetectionlevelsintotherangeofplanetswithmasseslessthan10M,commonlyreferredtoas"Super-Earths".
Thislevelofprecisionisnowbringingwithinreachoneoftheholygrailsofexoplanetresearch,thedetectionofEarth-sizeplanetsorbitinginthehabitablezones(HZ)ofstars.
NearbyKandMdwarfsoerthebestpossibilityofsuchdetections,astheirHZ'sarecloserin,withHZorbitalperiodsintherangeofweekstomonthsratherthanyears.
Theselowmassstarsalsoundergolargerreexvelocitiesforagivenplanetmass.
Tothisend,wehavehadatargetlistof400nearbyquietKandMdwarfsunderprecisionRVsurveywithHIRESatKeckforthepastdecade.
Oneofthesetargets,thenearbyM3VstarGJ581(HIP74995),hasreceivedconsiderableattentioninrecentyearsfollowingtheannouncementbyBonlsetal.
(2005),hereafterBonls05,ofa5.
37-dayhot-Neptune(GJ581b,orsimplyplanet-b)aroundthisstar.
Morerecently,theGenevagroup(Udryetal.
2007),hereafterUdry07,announcedthedetectionoftwoadditionalplanets(cand-d)inthissystem,oneclosetotheinneredgeoftheHZofthisstarandtheotherclosetotheouteredge.
Planet-cwasreportedtohaveaperiodof12.
931daysandmsini=5.
06Mwhereasplanet-dwasreportedtohaveaperiodof83.
4daysandmsini=8.
3M.
TheGenevagroup'sannouncementofplanet-cgeneratedconsiderableexcitementbecauseofitssmallminimummass(5M,wellbelowthemassesoftheicegiantsof–5–oursolarsystemandpotentiallyintheregimeofrockyplanetsorSuper-Earths)anditslocationneartheinneredgeoftheHZofthisstar.
AnassumedBondalbedoof0.
5yieldedasimpleestimateof320Kfortheequilibriumtemperatureoftheplanet,suggestingthepossibilitythatitwasahabitableSuper-Earth.
However,amoredetailedanalysisbySelsisetal.
(2007),thatincludedthegreenhouseeectandthespectralenergydistributionofGJ581,concludedthatplanet-c'ssurfacetemperatureismuchhigherthantheequilibriumtemperaturecalculatedbyUdry07andthatitisunlikelytohostliquidwateronitssurface.
Selsisetal.
(2007)concludedthatbothplanetscanddaredemonstrablyoutsidetheconservativeHZofthisstar,butthatgivenalargeatmosphere,planet-dcouldharborsurfaceliquidwater.
Chylek&Perez(2007)reachedasimilarconclusionthatneitherplanetscnordisintheHZ,butthatplanet-dcouldachievehabitabilityprovidedagreenhouseeectof100Kdeveloped.
Moreover,iftheseplanetsaretidallyspin-synchronized,planet-ccouldconceivablyhaveatmosphericcirculationpatternsthatmightsupportconditionsofhabitability.
vonBlohetal.
(2007)alsoconcludedthatplanet-cistooclosetothestarforhabitability.
Theyargue,however,thatifplanet-dhasathickatmosphereandistidallylocked,itmayliejustwithintheouteredgeoftheHZ.
BothvonBlohetal.
(2007)andSelsisetal.
(2007)concludethatplanet-dwouldbeaninterestingtargetfortheplannedTPF/Darwinmissions.
Beustetal.
(2008)studiedthedynamicalstabilityandevolutionoftheGJ581systemusingtheorbitalelementsofUdry07,whichtheyintegratedforwardfor108years.
Theyobservedboundedchaos(seee.
g.
Laskar(1997)),withsmall-amplitudeeccentricityvariationsandstablesemi-majoraxes.
Theirconclusionswereunaectedbythepresenceofanyas-yet-undetectedouterplanets.
Ondynamicalstabilitygrounds,theywereabletoexcludeinclinationsi≤10(wherei=0isface-on).
Lastyear,Mayoretal.
(2009),hereafterMayor09,publishedavelocityupdatewherein–6–theyrevisedtheirpreviousclaimofan8Mplanetorbitingwithan83-dayperiod,toa7.
1Mplanetorbitingat67-days,citingconfusionwithaliasingfortheformerincorrectperiod.
Mayor09alsoreportedanotherplanetinthesystemat3.
148dayswithaminimummassof1.
9M.
Theyalsopresentedadynamicalstabilityanalysisofthesystem.
Inparticular,theadditionofthe3.
15dplanet,GJ581e,greatlystrengthenedtheinclinationlimitforthesystem.
Theplanetwasquicklyejectedforsysteminclinationslessthan40.
Thisdynamicalstabilityconstraintimpliesanupperlimitof1.
6tothe1/sinicorrectionfactorforanyplanet'sminimummass(assumingcoplanarorbits).
Mostrecently,DawsonandFabrycky(2010)publishedadetailedstudyoftheeectsofaliasingontheGJ581datasetofMayor09.
Theyconcludedthatthe67-dayperiodofGJ581cremainsambiguous,andfavoredaperiodof1.
0125daysthatproducedaliasesatboth67daysand83days.
TheGliese581systemexertsanoutsizefascinationwhencomparedtomanyoftheotherexoplanetarysystemsthathavebeendiscoveredtodate.
Theintereststemsfromthefactthattwoofitsplanetslietantalizinglyclosetotheexpectedthresholdforstable,habitableenvironments,onenearthecooledge,andonenearthehotedge.
WehavehadGJ581undersurveyatKeckObservatoryforoveradecadenow.
Inthispaper,webring11yearsofHIRESprecisionRVdatatobearonthisnearbyexoplanetsystem.
Ournewdatasetof122velocities,whencombinedwiththepreviouslypublished119HARPSvelocities,eectivelydoublestheamountofRVsavailableforthisstar,andalmosttriplesthetimebaseofthosevelocitiesfrom4.
3yearsto11years.
WeanalyzethecombinedprecisionRVdatasetanddiscusstheremarkableplanetarysystemthattheyreveal.
2.
RadialVelocityObservationsTheRVspresentedhereinwereobtainedwiththeHIRESspectrometer(Vogtetal.
1994)oftheKeckItelescope.
TypicalexposuretimesonGJ581were600seconds,–7–yieldingatypicalS/Nratioperpixelof140.
DopplershiftsaremeasuredbyplacinganIodineabsorptioncelljustaheadofthespectrometerslitintheconvergingf/15beamfromthetelescope.
ThisgaseousabsorptioncellsuperimposesarichforestofIodinelinesonthestellarspectrum,providingawavelengthcalibrationandproxyforthepointspreadfunction(PSF)ofthespectrometer.
TheIodinecellissealedandtemperature-controlledto50±0.
1CsuchthatthecolumndensityofIodineremainsconstant(Butleretal.
1996).
FortheKeckplanetsearchprogram,weoperatetheHIRESspectrometerataspectralresolvingpowerR≈70,000andwavelengthrangeof3700–8000A,thoughonlytheregion5000–6200A(withIodinelines)isusedinthepresentDoppleranalysis.
DopplershiftsfromthespectraaredeterminedwiththespectralsynthesistechniquedescribedbyButleretal.
(1996).
TheIodineregionisdividedinto700chunksof2Aeach.
Eachchunkproducesanindependentmeasureofthewavelength,PSF,andDopplershift.
Thenalmeasuredvelocityistheweightedmeanofthevelocitiesoftheindividualchunks.
InAugust2004,weupgradedthefocalplaneofHIREStoa3-chipCCDmosaicofatterandmoremodernMIT-LincolnLabsCCD's.
NozeropointshiftinourRVpipelinewasincurredfromthedetectorupgrade.
Rather,thenewCCDmosaiceliminatedahostofphotometricproblemswiththepreviousTek2048CCD(non-atfocalplane,non-linearityofCTE,chargediusioninthesiliconsubstrate,overly-largepixels,andothers).
Thedeleteriouseectsofalltheseshortcomingscanbereadilyseenaslargeruncertaintiesonthepre-August2004velocities.
Inearly2009,wesubmittedapapercontainingourRVsuptothatdateforGJ581thatdisputedthe83-dayplanetclaimofMayor09.
Oneofthereferees(fromtheHARPSteam)kindlyraisedtheconcern(basedpartlyonourlargervalueforapparentstellarjitter)thatwemayhavesomeresidualsystematicsthatcouldbeaectingthereliabilityofsomeofourconclusions.
IntheprecisionRVeldtherearenosuitablestandardsbywhich–8–teamscanevaluatetheirperformanceandnoiselevels;so,itisrarebutalsoextremelyusefulforteamstobeabletocheckeachotherusingoverlappingtargetstars,likeGJ581,forinter-comparison.
So,wetooktheHARPSteam'sconcernstoheartandwithdrewourpapertogatheranotherseasonofdata,todoadetailedreanalysisofouruncertaintyestimates,andtoscrutinizeour15-year1500-stardatabaseforevidenceofundiscoveredsystematicerrors.
Soonafterwewithdrewour2009paper,Mayor09publishedarevisedmodelwhereintheyalteredtheir83-dayplanetperiodto66.
8days(citingconfusionbyyearlyaliases)andalsoannouncedanadditionalplanetinthesystemnear3.
15days.
Forourpart,asaresultofourpreviousyear'sintrospection,wediscoveredthattheprocessbywhichwederiveourstellartemplatespectrawasintroducingasmallcomponentofadditionaluncertaintythataddedabout17%toourmeaninternaluncertainties.
Thisadditionalnoisesourcestemsfromthedeconvolutionprocessinvolvedinderivingstellartemplatespectra.
ThisprocessworksquitewellforGandKstars,butitispronetoextranoisewhenappliedtoheavilyline-blanketedMdwarfspectra.
WehaveincludedthisinourpresentreporteduncertaintiesforGJ581,andareworkingonimprovementstothetemplatedeconvolutionprocess.
Furthermore,ourexistingtemplateforthisstar,takenmanyyearsago,wasnotuptothetaskofmodelingRVvariationamplitudesdowninthefewms1regime.
So,overthepastyear,weobtainedamuchhigherqualitytemplateforGJ581.
TheHIRESvelocitiesofGJ581arepresentedinTable1,correctedtothesolarsystembarycenter.
Table1liststheJDofobservationcenter,theRV,andtheinternaluncertainty.
Thereporteduncertaintiesreectonlyonetermintheoverallerrorbudget,andresultfromahostofsystematicerrorsfromcharacterizinganddeterminingthePSF,detectorimperfections,opticalaberrations,eectsofunder-samplingtheIodinelines,etc.
Twoadditionalmajorsourcesoferrorarephotonstatisticsandstellarjitter.
Theformeris–9–alreadyincludedinourTable1uncertainties.
Thelattervarieswidelyfromstartostar,andcanbemitigatedtosomedegreebyselectingmagnetically-inactiveolderstarsandbytime-averagingoverthestar'sunresolvedlow-degreesurfacep-modes.
Thebestmeasureofoverallprecisionforanygivenstarissimplytomonitoranensembleofplanet-freestarsofsimilarspectraltype,chromosphericactivity,andapparentmagnitude,observedatsimilarcadenceandoverasimilartimebase.
Figures2,3,and4ofButleretal.
(2008)show12MdwarfswithB-V,Vmagnitude,andchromosphericactivitysimilartoGJ581.
Inanysuchensemble,itisdiculttoknowhowmuchoftheroot-mean-square(RMS)oftheRVsisduetoas-yet-undiscoveredplanetsandtostellarjitter.
However,thesestarsdoestablishthatourdecade-longprecisionisbetterthan3ms1forMdwarfsbrighterthanV=11,includingcontributionsfromstellarjitter,photonstatistics,undiscoveredplanets,andsystematicerrors.
3.
PropertiesofGJ581ThebasicpropertiesofGJ581werepresentedbyBonls05andUdry07andwill,forthemostpart,simplybeadoptedhere.
BrieyrecappingfromBonls05andUdry07,GJ581isanM3Vdwarfwithaparallaxof159.
52±2.
27mas(distanceof6.
27pc)withV=10.
55±0.
01andB-V=1.
60.
TheparallaxandphotometryyieldabsolutemagnitudesofMV=11.
56±0.
03andMK=6.
86±0.
04.
TheV-bandbolometriccorrectionof2.
08(Delfosseetal.
1998)yieldsaluminosityof0.
013L⊙.
TheK-bandmass-luminosityrelationofDelfosseetal.
(2000)indicatesamassof0.
31±0.
02M⊙,andthemass-radiusrelationsofChabrier&Barae(2000)yieldaradiusof0.
29R⊙.
Beanetal.
(2006)reportthe[Fe/H]ofGJ581tobe-0.
33,whileBonls05report[Fe/H]=-0.
25.
Bothresultsareconsistentwiththestarbeingslightlymetal-poor,inmarkedcontrasttomostplanet-bearingstarsthatareofsuper-solarmetallicity.
Johnson&Apps(2009)presentedabroadband(V-K)–10–photometricmetallicitycalibrationforMdwarfsthat,inconjunctionwiththestar'sbroadbandmagnitudesimpliesametallicityof[Fe/H]=-0.
049.
Mostrecently,Rojas-Ayalaetal.
(2010)estimatedthemetallicityat-0.
02,whileSchlaufmanandLaughlin(2010)citeametallicityof-0.
22.
Thus,GJ581appearstobebasicallyofsolarorslightlysub-solarmetallicity,yethasproducedatleast4ormorelow-massplanets.
However,thisisnocauseforsurprise.
Laughlinetal.
(2004)andIda&Lin(2005)havearguedthattheformationoflow-massplanetsshouldnotbeundulyaectedbymodestlysubsolarmetallicity.
Udry07reportGJ581tobeoneoftheleastactivestarsontheHARPSM-dwarfsurvey,withBonls05reportinglinebisectorshapesstabledowntotheirmeasurementprecisionlevels.
Udry07reportameasuredvsini≤1kms1.
TheythusndGJ581tobequiteinactivewithanageofatleast2Gyr.
OurmeasurementoflogR′hk=5.
39leadstoanestimate(Wright2005)of1.
9ms1fortheexpectedRVjitterduetostellarsurfaceactivityandanageestimateof4.
3Gyr.
4.
PhotometricObservationsPrecisephotometricobservationsofplanetaryhostcandidatestarsareusefultolookforshort-term,low-amplitudebrightnessvariabilityduetorotationalmodulationinthevisibilityofstarspotsandplages(see,e.
g.
,Henry,Fekel,&Hall1995).
Long-termbrightnessmonitoringofthesestarsenabledbyourautomatictelescopescandetectbrightnesschangesduetothegrowthanddecayofindividualactiveregionsaswellasbrightnessvariationsassociatedwithstellarmagneticcycles(Henry1999;Lockwoodetal.
2007;Halletal.
2009).
Therefore,photometricobservationsofplanetarycandidatestarshelptodeterminewhethertheobservedradialvelocityvariationsarecausedbystellaractivity(spotsandplages)orreexmotionduetothepresenceoforbitingcompanions.
Quelozetal.
(2001)andPaulsonetal.
(2004)havedocumentedseveralexamplesofsolar-typestarswhoseperiodicradial–11–velocityvariationswerecausedbystellaractivity.
GJ581hasalsobeenclassiedasthevariablestarHOLibrae,thoughWeis(1994)reporteditsshort-termvariabilitytobeatmost0.
006magnitudes.
Udry07reportthestartobeconstanttowithinthe5millimagGenevaphotometrycatalogprecisionofV=10.
5stars.
WeacquirednewphotometricobservationsofGJ581intheJohnsonVbandduringthe2007and2008observingseasonswithanautomated0.
36mSchmidt-CassegraintelescopecoupledtoanSBIGST-1001ECCDcamera.
ThisTennesseeStateUniversitytelescopewasmountedontheroofofVanderbiltUniversity'sDyerObservatoryinNashville,Tennessee.
DierentialmagnitudeswerecomputedfromeachCCDimageasthedierenceinbrightnessbetweenGJ581andthemeanoffourconstantcomparisonstarsinthesameeld.
AmeandierentialmagnitudewascomputedfromusuallytenconsecutiveCCDframes.
Outliersfromeachgroupoftenimageswereremovedbasedona3σtest.
Ifthreeormoreoutlierswerelteredfromanygroupoftenframes(usuallytheresultofnon-photometricconditions),theentiregroupwasdiscarded.
Oneortwomeandierentialmagnitudeswereacquiredeachclearnight;ournaldatasetconsistsof203meandierentialmagnitudesspanning530nights.
Our203photometricobservationsareplottedinthetoppanelofFigure1;theyscatterabouttheirmeanwithastandarddeviationof0.
0049mag.
Aperiodogramoftheobservations,basedonleast-squaressinets,isshowninthesecondpanel,resultinginabest-tperiodof94.
2±1.
0days.
ThatrotationperiodisquitesimilartotherotationalperiodofanotherimportantMdwarfplanethost,GJ876,andgivesaddedcondencetothecurrentndings.
ItisalsoconsistentwithGJ581'slowactivityandageestimate.
Inthethirdpanel,weplottheobservationsmodulothe94.
2-dayphotometricperiod,whichwetaketobethestar'srotationperiod.
Aleast-squaressinetontherotationperiodgives–12–asemi-amplitudeof0.
0030±0.
0004mag.
Thewindowfunctionfortherotationperiodisplottedinthebottompanel.
Fiveofthesixradialvelocityperiodsdiscussedbelowareindictedbyverticaldottedlinesinthesecondandfourthpanels;ourdatasetisnotlongenoughtoaddressthe433-dayperiodofGJ581f.
Aswillbeshownbelow,noneoftheveperiodscoincidewithanysignicantdipintheperiodogram.
5.
OrbitalAnalysisWeobtained122RVswiththeHIRESspectrometeratKeck.
Thedatasetspans10.
95yearswithapeak-to-peakamplitudeof37.
62ms1,anRMSvelocityscatterof9.
41ms1,andameaninternaluncertaintyof1.
70ms1.
Figure2(toppanel)presentstheRVstabulatedinTable1,combinedwiththeHARPSRVspublishedbyMayor09.
The122(red)hexagonpointsaretheHIRESobservations,whiletheHARPSobservationsareshownas(blue)trianglepoints.
Azero-pointosetof1.
31ms1wasremovedbetweenthetwodatasets,andFigure2hasthisosetincluded.
TheHARPSdataconsistof119observationsatareportedmedianuncertaintyof1.
10ms1andextendingover4.
3years.
Thepeak-to-peakamplitudeoftheHARPSdatasetis39.
96ms1.
Thecombineddatasethas241velocities,withamedianuncertaintyof1.
30ms1.
Fortheorbitalts,weusedtheSYSTEMICConsole(Meschiarietal.
2009;Meschiari&Laughlin2010).
Weassumecoplanarorbitswithi=90and=0.
Uncertaintiesarebasedon1000bootstraptrials.
WetakethestandarddeviationsofthettedparameterstothebootstrappedRVsastheuncertaintiesinthettedparameters.
ThettedmeananomaliesarereportedatepochJD2451409.
762.
Theassumedmassofthecentralstaris0.
31M⊙.
Foralltspresentedhere,wexedtheeccentricitiesatzerosincetheamplitudesareallquitesmallandextensivemodelingrevealedthatallowingeccentricitiestooatforanyorallofthe6planetsdoesnotsignicantlyimprovetheoverallt.
–13–Fig.
1.
—(Top):PhotometricV-bandobservationsofGJ581acquiredduringthe2007and2008observingseasonswithanautomated0.
36mimagingtelescope.
(SecondPanel):Periodogramanalysisoftheobservationsgivesthestar'srotationperiodof94.
2days.
(ThirdPanel):Thephotometricobservationsphasedwiththe94.
2-dayperiodrevealtheeectofrotationalmodulationinthevisibilityofphotosphericstarspotsonthebrightnessofGJ581.
(Bottom):Windowfunctionofthe94.
2-dayrotationperiod.
Theradialvelocityperiodsof5ofthe6planetarycompanionsareindicatedbyverticaldottedlinesinthesecondandfourthpanels.
–14–Fig.
2.
—Toppanel:CombinedRVdataofGJ581fromHIRES(redhexagons)andHARPS(bluetriangles).
Lowerpanel:spectralwindow–15–ThepowerspectrumofthesamplingwindowisshowninthelowerpanelofFigure2.
Asexpected,thereissomespuriouspowercreatedbythesamplingtimesnearperiodsof1.
003d(thesolardayinsiderealdayunits),29.
5d(thelunarsynodicmonth),180d(1/2year),and364d(1year),allartifactsofthenightly,monthly,andyearlyperiodsontelescopescheduling.
ThetoppanelofFigure3showsthepowerspectrumoftheRVdata.
FollowingGilliland&Baliunas(1987)(hereafterGB87),inFigure3,weuseanerror-weightedversionoftheLomb-Scargleperiodogram.
ThehorizontallinesintheperiodogramsinFigure3roughlyindicatethe0.
1%,1.
0%,and10.
0%FalseAlarmProbability(FAP)levelsfromtoptobottom.
TodeterminebetterestimatesoftheFAPsoftheprominentpeaksintheperiodograms,wedenethenoise-weightedpowerinaprominentpeakwith(GB87)p0=N4x20σ20,(1)whereNisthenumberofobservations,x0istheRVhalf-amplitudeimpliedbythepeak,andσ20isthevarianceinthedataorresidualspriortottingouttheimpliedplanet.
Additionally,wecanalsodenepowerinaprominentpeakas(Cumming(2004)):p0=(N2)2(χ2constantχ2circ)χ2circ,(2)whereχ2circisthereducedchi-squaredforacirculartat/neartheperiodimpliedbythepeakandχ2constantisthereducedchi-squaredforaconstantRVmodelofthedataorresiduals.
Estimationofthefalse-alarmprobabilityofagivenpeakrequiresknowledgeofthenumberofindependentfrequencies,Minthedataset.
Giventhehighlyunevensampling,MconsiderablyexceedsourN=241Dopplervelocitymeasurements.
UsingtheMonte-CarloprocedureoutlinedbyPressetal.
(1992),wendthatM=2525.
TheFAPisthechancethatapeakashighas,orhigherthan,thatobservedinthe–16–Fig.
3.
—Fromtoptobottom,powerspectraoftheresidualstothe0-,1-,2-,3-,4-,5-,and6-planetsolutions,respectively.
Thehorizontallinesineachperiodogramroughlyindicatethe0.
1%,1.
0%,and10.
0%FalseAlarmProbability(FAP)levelsfromtoptobottom.
–17–periodogramwouldoccurbychance,Pr(p0,M)=1[1exp(p0)]M.
(3)Ingeneral,wendthatMisroughlythesameforbothdenitionsofp0above.
NotethattherearediscrepanciesbetweenourFAPsquotedbelowandtheFAPlinesshowninFigure3.
Hereweexplainthereasonsforthesediscrepancies.
The(raw)powerlevelsshowninFigure3arebasedonEquations1and2inGB87.
TheFAPlinesarebasedonthemethodtocalculatethenumberofdegreesoffreedom,M,suggestedinSection13.
7ofPressetal.
(1992),exceptthatweassumeaGaussiandistributionwithastandarddeviationequaltothevelocityscatterofthedataorresiduals.
However,theFAPswequotebelowforeachttedplanetareforpowerlevelsdenedbyEquation2above.
Figure3showsthepowerspectraoftheresidualsoftheRVdatafromthebestKepleriantsformodelswithnplanets(withnrangingfrom0to6).
Theeccentricitiesareheldxedat0throughoutthettingprocess.
Thedominantspikeinthetoppanelisat5.
368daysandisthewell-knownHot-Neptune(GJ581b)rstreportedbyBonls05.
Thepowerimpliesaminimum-massmsini=15.
6Mcompanionina0.
041AUorbit.
Thereducedchi-squaredstatistic(using5freeparameters)forthis1-planettis8.
426,withanRMSof3.
65ms1.
TheestimatedFAPis6.
8*10306,inkeepingwiththeextremelystrongdetection.
ThesecondpaneldowninFigure3showsthepowerspectrumoftheresidualstothe1-planett.
Thispowerspectrumisdominatedbyapeakat12.
92days.
A2-planettforthe12.
92-daypeak(planet-crstreportedbyUdry07)revealsaminimum-mass5.
5Mplanetina0.
073AUorbit.
The2-planettachievesareducedchi-squaredstatistic(using8freeparameters)of4.
931,andanRMSof2.
90ms1.
TheestimatedFAPis2.
3*1033.
So,the12.
92-dayplanet-crstreportedbyUdry07alsoseemswell-conrmed.
–18–ThethirdpaneldownofFigure3showsthepowerspectrumoftheresidualsofthe2-planetmodel.
AsMayor09found,thenextobviouspeaktotisthemaximumpeakinthegroupnear67days.
Mayor09foundthatthisgroupisasetof3,withthetruepeakat67days,and1-yearaliasesnear59and82days(1/671/3651/82,and1/67+1/3651/57).
Weexploredvariousttingbranchesinvolvingthe59dand82dpeaksforplanetd.
Fittingforthe59-daypeakleftpronouncedresidualsatboth67and82days.
Fittingoutthe82-daypeakleftpronouncedresidualpeaksnear59days,37daysand158days.
Neitherthe59-daynorthe82-dayttingbranchesledtonalsolutionsthatwereasgoodasthe67-daybranch.
WethereforeconcurwithMayor09thatthe67-dayisthecorrectchoiceforplanetd.
Attothe66.
9-daypeakindicatesaminimum-mass4.
4Mplanetina0.
218AUorbit.
The3-planettresultsinareducedchi-squaredstatistic(using11freeparameters)of4.
207,withanRMSof2.
72ms1.
TheestimatedFAPis2.
5*106.
Thus,the67-day3rdplanetannouncedbyMayor09seemswell-supportedbythepresentdataset.
Atthispoint,therearealsosimilar-powerpeakspresentverynear1.
00day,bothaboveandbelow.
These"near-1-day"peaksappearfrequentlyinourRVdatasetsandtypicallyarisefromaliasingeects,asdiscussedindetailbyDawsonandFabrycky(2010).
Theyareduepartlytothefactthatexoplanetobservationsaredoneonlyatnight.
DawsonandFabrycky(2010)lookedcarefullyattheHARPSdatasetforGJ581andconcludedthatitremainsunclearwhethertheperiodofGJ581dis67days,or83days,oreventheirpreferredvalueof1.
0125days,andthatfurtherobservationswererequiredtoresolvetheambiguity.
Inourexperience,RVpowerfromastarbeingorbitedbylegitimateplanetsroughlyinthe20–90periodrangecanfeedsubstantialamountsofthatpowerintopeaksverynear1.
00day,bybeatingwiththesiderealandsolardays.
Thus,whileitmaybepossibleonrareoccasiontoencounteratrueplanetorbitingagivenstarwithaperiodverynear1.
00day,thiswillbetheexceptionalcase,andnotverycompellingfromapurely–19–Bayesianpointofview.
Inaddition,onecanonlyusethisalternativeonceinasystemtoexplainawayasuspectedplanetpeakupatalongerperiod.
Multiplelongerperiodpeakswouldrequiremultipleplanetsatorverynear1.
00day,andthatisdynamicallyuntenable.
Tolookintothismorecarefully,weintentionallyobtainedsomeextendedcadenceoverthecourseofnightsonMay21-25,June21-23,andagainonJuly30-31,2010.
Wethencarefullyexaminedtheperiodogramoftheresidualsofthetwo-planett.
Theperiodogramhastwoprominentpeaksat66.
9645daysand1.
0126dayswithrawpowersof129.
070and124.
310,respectively.
Theratioofthepowerlevelsis1.
038.
WegeneratedmockRVsetsbasedontwomodels.
First,wetookthethree-planettwiththethirdplanetat1.
0126daysandscrambledtheresiduals1000times.
WettwoplanetstoeachmockRVset.
Wethenexaminedtheperiodogramsoftheresiduals.
Inparticular,wemeasuredhowfrequentlytheratioofthepowerlevelsatthetwoperiodsexceeds1.
038.
Thenwerepeatedthisprocedurewiththethirdplanetat67days.
Wefoundthatthe67-daymodeldoesanoverwhelminglybetterjobatproducingperiodogramswhichresembletheperiodogramoftheactualresiduals.
OurMonteCarloresultsindicatea93.
6%probabilitythat67daysisthecorrectperiod.
ThefourthpanelofFigure3showstheperiodogramoftheresidualsfromthe3-planett.
AswasfoundalsobyMayor09,thenextobviouspeaktotisthe3.
15-dayone,previouslyreportedbyMayor09.
AKeplerianttothispeakindicatesaplanetina0.
028AUorbitwithaperiodof3.
149daysandminimummassofonly1.
7M(smallerbyabout10%thanthatfoundbyMayor09).
The4-planettachievesareducedchi-squaredstatistic(using14freeparameters)of3.
463andanRMSof2.
43ms1.
TheestimatedFAPofthepeakis1.
9*108.
So,the3.
15-dplanet-eannouncedbyMayor09alsoseemswell-conrmedbythecombineddatasetandmayevenbeabout10%lowerinmassthanrstreported.
ThefthpaneldowninFigure3showstheperiodogramoftheresidualstoourbest–20–4-planett.
Here,therearetwo(nearly)equalpowerpeaksintheresidualspowerspectrum,near37daysand445days.
Ingeneral,ourexperiencehasshownthatitismuchharder,withagivendataset,togeneratecoherentpoweratlongerperiods.
So,betweentwopeaksofequalpower,theonewiththelongerperiodisusuallymoresignicant.
So,wetthe445-daypeaknext,thoughtheremainingbranchesofthettingtreeandnalsolutionarenotsignicantlyalteredbyttingthe37-daypeakrstinstead.
Attothe445-daypeakindicatesaminimum-mass6.
8Mplanetina443-day0.
770AUorbit.
The5-planettachievesareducedchi-squaredstatistic(using17freeparameters)of2.
991andanRMSof2.
30ms1.
TheestimatedFAPofthepeakis9.
5*105.
This5thplanetthusappearsstatisticallywell-justiedbythepresentdataset.
ThesixthpaneldowninFigure3showstheperiodogramoftheresidualstothe5-planett.
Alonedominantpeakremainsnear37days.
Thispeakshowstheextremenarrownessexpectedofatrulycoherentsignal,that,ifKeplerianandreal,wouldhaveastrictlyxedperiodandphaseforits110cyclesspanningthepast11yearsofthedataset.
Attothispeakindicatesaplanetofminimum-mass3.
1M,ona36.
56-dayorbitofsize0.
146AU.
Ourbest6-planett(again,assumingcircularorbits)achievesareducedchi-squaredstatistic(using20freeparameters)of2.
506andanRMSof2.
12ms1.
TheestimatedFAPofthe37-daypeakis2.
7*106.
Thus,this6thplanetalsoseemsstatisticallywell-justiedbythepresentdataset.
Finally,thebottompanelofFigure3showstheperiodogramoftheresidualsofthe6-planett.
This6-planetmodelleavesnoremainingpeaksofconsequencetotatthistime.
Theresidualpeaknear59dayshasbeenvisibleallthewayupthestackofpanelsinFigure3andisapparentlyassociatedwiththeyearlyaliasinvolvedwiththe67-day,aspointedoutbyMayor09.
IthasaFAP(usingthedenitionforpowerinEquation1)ofonly0.
186.
Thephasedcurveatthisperiodshowssignicantphasegapsinboththe–21–HARPSandHIRESdatasetsduetotheconstraintofspectroscopicobservationsofbrightstarsmostlyreceivingonlybrightorgreylunartime.
Suchphasegapsfurtherincreasethechancesofafalsealarmhere.
A59-dayplanetisalsocompletelydynamicallyuntenable(evenwiththeassumptionthatallorbitsarecircular).
Wewonderedhowmanyoftheseplanetsareindependentlyconrmedbyeachdataset.
ThisisdiculttoanswerastheKeplerianttingtreeprocessdoesnotholdpreviousplanetsxedasthenextplanetisoptimizedintheprocess.
Sowelookedatrunningthettingprocessbackwards.
ForeachindependentHARPSandHIRESdataset,wesubtractedourmodelofthesystem(aslistedinTable2)fromthedata,givingasetofresiduals.
ThereexmotionscorrespondingtotheplanetsinourRVmodelwerethenaddedbackinsequentially.
Theadvantagetothisapproachisthatthereisnooptimizationandresultingparameterdriftbetweenperiodograms,andoneseesthesometimesnon-intuitiveresultofaddingaknownsignal.
Thisprocessshowedusthatthecharacterizationofthesystemrequiresthecombinationofbothdatasets.
Figure4showsthisreversesequenceofinjectingbest-tstellarreexmotionateachKeplerianperiodbackintovelocityresidualsforeachdataset.
ThesetofpanelsontheleftshowthesequencefortheHIRESdataset,whilethepanelsontherightshowthesamesequencefortheHARPSdataset.
Thetoppaneloneachsideshowstheperiodogramoftheresidualsafterttingoutall6planets.
Ineachsuccessivepanel,theperiodoftheinjectedsignalisdenotedbyaredverticaltickmark.
ThesecondpanelontheleftofFigure4showstheeectofinjectingthe37-daysignalintotheHIRESresiduals.
The37-daysignalisclearlyvisibleintheHIRESdatasetaloneandmanifestsatthecorrectperiod.
The3rdpanelontheleftofFigure4revealsthatthe433-daysignalisalsovisibleandalsomanifestsnearitstrueperiod.
The4thpanelontheleftillustratesthataddinginthe3.
15-daysignalgeneratespowerprimarilyatthe–22–Fig.
4.
—TheeectofsequentiallyaddingsignalinreverseorderateachKeplerianperiodbackintotheresidualsofeachdatasetforGJ581.
PanelsontheleftshowtheresultsfortheHIRESdataset,whilethoseontherightshowtheresultsfortheHARPSdataset.
Thetoppanelsshowtheperiodogramsoftheresidualsfromthe6-planett.
Theannotationsandredverticaltickmarksineachpanelindicatetheperiodofthelastinjectedsignalpriortocomputingeachperiodogram.
–23–non-intuitiveperiodofabout26days.
ThespectralwindowoftheHIRESsamplingtimeshaspeaksat29.
53,363.
24,1.
003,and179.
72days.
This26-daypeakcouldthusbedrawingpowerfromatleastthreesources1)alunaraliasofthe36.
6-dayplanet,2)ahalf-yearaliasofthe66.
9-dayplanet,and3)bothaone-dayandahalf-yearaliasofthe3.
15-dayplanet.
ThesealiasingandsamplingeectsproducedbytheparticularHIRESdatatimestampsrenderthe3.
15-dayplanetinconspicuousinthepowerspectrumoftheHIRESdatatakenalone.
The5thpanelontheleftrevealsthatinjectingthe67-daysignalmakesthesituationmoreconfusing,byintroducingmorepeaks.
Thisdemonstratesthatthecombinationofbothdatasetsisrequiredtoseethisplanetclearly,apparentlybecauseitisnearanintegermultipleofthelunarmonthwhichresultsindicultiesgettingcompletephasecoverage.
The6thpanelontheleftshowsthatinjectingthesignalfromthe12.
9-dayplanetleadstoanothercuriousresult,producingpoweratseveralotherfrequenciesasidefromthetrue12.
9-dayperiodicity.
Finally,thebottompanelontheleftshowstheinjectionofthe5.
4-dayplanet'ssignal.
Here,theplanet'samplitudeissolargethatitssignalisoverwhelminglymanifestedattheproperperiod.
FortheHARPSdatasetalone,the2ndpanelontherightinFigure4showsthatinjectingthe37-dsignalgeneratespowerinsteadnear23dayswhenviewedthroughthecomplexlteroftimestampsanduncertaintiesspecictotheHARPSdatapoints.
Apparently,theHARPSdatasetaloneisnotabletoreliablysensethisplanet.
The3rdpanelontherightillustratesthataddinginthe433-daysignalgeneratespowerbothnear433andatitsyearlyaliasnear200days.
The4thpanelontherightshowsthattheinjectedsignalfromthe3.
15-dayplanetalsomanifestswellintheHARPSdatasetaloneanddoesnotgeneratepowerat26daysashappenedwiththeHIRESdataset.
Thisisapparentlyaresultofmanyoftheirobservingrunsthatgarneredlongblocksofcontiguousnightswithhighandsustainedcadence.
The5thpanelontherightshowsthatthesignalinjectedfromthe67-dayperiodshowsupverywellandattheexpectedperiod,ankedalsobyitsyearly–24–aliasesnear59and82days.
The6thand7thpanelsontherightshowthatthesignalsfromthe12.
9-dayand5.
4-dayplanetsalsomanifestquitereliablyintheHARPSdatasetalone.
So,insummary,itisclearthat,althoughmostoftheseplanetsignalsdoshowupindependentlyineachdataset,thesituationisconfusedbyaliasingwithpeaksinthespectralwindowcausedbythespecictimestampsuniquetoeachdataset.
Itisreallynecessarytocombinebothdatasetstosensealltheseplanetsreliably.
AsummaryofourbestKepleriantwith(forced)circularorbitsispresentedinTable2.
ThettedmeananomaliesarereportedatepochJD2451409.
762.
Thenalparametersshownhereareslightlydierentthanthosequotedforthetsalongthettingtreeandrepresentourbestoverallmodel.
Uncertainties(inparentheses)oneachquantityaredeterminedfrom1000bootstraptrialsfromwhichwetakethestandarddeviationsofthettedparameterstothebootstrappedRVsastheuncertainties.
WealsocalculateduncertaintieswithaMarkov-chainMonteCarloestimator,andbothareingoodagreement.
The6-planetall-circulartachievesareducedchi-squaredparameterof2.
6503andanRMSof2.
118ms1.
Allowingeccentricitytooatforanyorallofthe6planetsdidnotproduceanysignicantimprovementintheoverallqualityofthet,eitherinthereducedchi-squaredstatistic,inRMS,orinrequiredstellarjitter.
Giventheverysmallamplitudesofthesignals,itisnotaltogethersurprisingthatalmostallofthettedeccentricitiesarestatisticallyconsistentwithzero.
Ourbesttindicatesthat,ifoneallowsastellarjitterof1.
4ms1,thereducedchi-squaredstatisticdropsto1.
0.
ThisjitterestimateagreesquitewellwiththatofMayor09,whofoundavalueof1.
2ms1fromtheir4-planett.
Littleisknownaboutthelowerboundsofjitterforanystar.
IfthetruestellarRVjitterisevenlessthanthis,therecouldyetbemoreplanetsinthesystemthatfurtherprecisionRVdatamightreveal.
Butwealsonditremarkablethatthisstar'sjitterhasnotexceeded1.
4ms1overthe–25–11-yearextentofthedataandthattheentiredatasetcanbettothislevelofprecisionbyonly6circularorbits(20freeparameters).
Backingoutthestellarjitterinthequadraturesumimpliesthat,withthisdataset,weareabletotrackthemotionofthe6planetarycompanionsaroundGJ581toaprecisionof1.
6ms1over11years.
Figure5showsthephasedbarycentricreexvelocitiesofthehoststardueindividuallytoeachcompanioninthesystem.
Exceptforthe2ndpanel,theordinatescalinghasbeenheldconstanttosimplifyinter-comparisonofthevariousplanets.
Wealsoexploredmanysolutionsetsallowingeccentricitiestooatforsomeoralloftheplanets.
Asmentionedabove,noneproducedanysignicantimprovementinoveralltquality.
Moreover,mostmodelsquicklybecameunstableonceeccentricitiesrosemuchabove0.
2orso.
Ourverybesteccentrictsbenettedprimarilyfromallowingeccentricityonthe67-dayand37-dayplanets'orbitswiththesetwoplanetsparticipatinginasecularresonance.
Wealsocarefullyexaminedtheeectsofincludingdynamicsinthettingprocess.
TheSYSTEMICConsoleincludesaGragg-Bulirsch-Stoerintegratorthatcanbeusedtomodelplanet-planetgravitationalinteractions.
WendthatdynamicaleectshaveaninsignicanteectonimprovingthetpresentedinTable2,andthe6-planetsystemappearsdynamicallystableoveratleasta50Myrtimescale.
Wealsoexploredthepossibilityofsettinglimitsontheinclinationofthesystemfromdynamicalstabilityexperiments.
Mayor09hadfoundthatthedynamicalstabilityoftheir4-planetsystem,particularlythestabilityofthe3.
15-dayplanet,imposedalowerboundofabout40fortheinclinationofthesystem(presumedco-planar).
Thus,eachofGJ581'splanetscouldnotbemoremassivethanabout1.
6timestheirminimummass.
Wendthat,throughstabilityconsiderations,all-circularorbitsolutionsonlyveryweaklyconstraintheinclinationofthesystem.
Planetarymasseshavetobeincreasedbya–26–Fig.
5.
—Phasedreexbarycentricvelocitiesofthehoststardueindividuallytotheplanetsat3.
15days,5.
37days,12.
9days,37days,67days,and433daysfromtheall-circulartofTable2.
Filled(red)hexagonpointsarefromKeckwhilelled(blue)trianglesarefromHARPS.
–27–factor>10toprovokeinstabilityinlessthan50Myr,andthattranslatestoalowerboundontheinclinationofonly6.
Eccentricitiesdoplayaroleinsettingalowerlimittotheinclination.
Floatingeccentricitysolutionswithmassfactors(1/msini)>1.
4areunstable.
Evenifonlyloweccentricities(45.
Itseemslikelythatsmalleccentricitiesareprobablypresentinsomeorevenalloftheseorbits.
However,sincewecannotprovethatsmalleccentricitiesarepresent,theinclinationcan'tyetreallybedenitivelyconstrained.
Table3givesthesemi-amplitudesofleast-squaressinetsofthephotometricobservations(Figure1)correspondingtoeachoftheradialvelocityperiodsmodeledinthispaper.
TheseupperlimitstobrightnessvariabilityareallverysmallandsupportiveofKeplerianmotionofplanetarycompanionsasthecauseofalltheradialvelocityvariations.
Figure6showsasimpletopviewofthesystem,withtheaxeslabeledinAU.
Forreference,theorbitsofEarth,Venus,andMercuryareoverlaidasblue,green,andreddashedlinesrespectively.
TheentireGJ581systemwouldtcomfortablywithintheEarth'sorbit.
AndthebasicstructureoftheGJ581system(withitsnearlyall-circularorbitsandatightinnerclutchofplanetsaccompaniedbyamuchmoredistantouterplanet)isinsomerespectseerilyreminiscentofthenearlyall-circularorbitsofourownsolarsystem,withitsinnerclutchofterrestrialplanetsandattendantdistantJupiter.
6.
Characteristicsofthe37-dayplanetTheGJ581systemhasasomewhatcheckeredhistoryofhabitableplanetclaims,soabriefhistoricalreviewoftheallegedpropertiesofthevariousplanetsinthissystem–28–Fig.
6.
—TopviewoftheGJ581system.
Forreference,theorbitsofEarth,Venus,andMercuryareoverlaidasdashedblue,green,andredlinesrespectively.
–29–isappropriate.
Boththe12.
9-dayand83-dayplanetsreportedbyUdry07wereinitiallythoughtlikelytobehabitableplanets.
However,furtheranalysisbyothers(previouslydescribedintheintroduction)showedthatthe12.
9-dayplanetwaslikelytoohotandthe83-daytoocoldtosupporthabitability.
Twoyearslater,whenMayor09revisedtheperiodofthe83-dayplanetto67days,thatplanet'sprospectsforhabitabilityincreasedsomewhat,despitethefactthat,ataminimummassof7.
1M,andamaximummassofupto11.
4M,thedistinctionbetweenarockyplanetandanice-giantbecomesuncertain.
Thenewmass,asderivedhereis5.
6–8.
4M.
ButevenwithaBondalbedoof0,atitsdistanceof0.
218AUfromthestar,ignoringtheeectsofthestar'sspectralenergydistribution,thatplanet'smaximumequilibriumtemperaturewouldbeonly203K.
However,ifconrmed,the37-dayplanetcandidateoersasolidcaseforapotentiallyhabitableplanetinthisverynearbysystem.
ThebestKeplerianttothedataindicatesa3.
1Mplanetinacircular36.
6-dayorbitofsemi-majoraxis0.
146AU.
ThedynamicalstabilityinvestigationspresentedbyMayor09alsoimposealowerboundontheorbitalplaneinclination,constrainingtheupperboundonthemassofGJ581gtobenomorethan1.
6timesitsminimummass.
Wendasimilarboundofabout1.
4assumingnoneoftheorbitaleccentricitiesexceed0.
2.
So,thelikelymassforthisplanetcandidateis3.
1–4.
3M.
UsingtheresultsofSeageretal.
(2007),theradiusofGJ581gisexpectedtobe1.
3–1.
5RifhomogeneousandcomposedprimarilyoftheperovskitephaseofMgSiO3(Earth-like),or1.
7–2Rifwater-ice.
Allradiiarepredictedtobe20%smalleriftheplanetisdierentiated,sotheplanetislikelytohavearadiusbelow1.
5R.
Themassandradiusestimatesimplyasurfacegravityof1.
1–1.
7g,verynearthatoftheEarth.
Selsisetal.
(2007)oeradetailedsummaryofconditionsforexoplanethabitability,withspecicreferencetotheGJ581system,butcautionedthattherearemanyfactorsthataecthabitability.
Distancefromthestarisbutoneofthesefactors.
Aplanetmaynothave–30–formedwithorretainedsucientwater.
Gravitymaybetooweaktoholdanatmosphereagainstphotodissociative-escapeprocesses.
TheplanetmightmaintainanactivegeologicalcycletoreplenishatmosphericCO2.
OraplanetmayhaveaccretedamassiveH2-Heenvelopethatwouldkeepthesurfacepressuretoohightopreventwaterfromexistingnearthesurfaceinliquidform.
Selsisetal.
(2007)arguethatavoidingthelasttwoscenariosrequiresaplanet'smasstoberoughlyintherangeof0.
5–10M.
GJ581geasilysatisesthismasscondition.
Selsisetal.
(2007)alsomakethepointthatanecessaryandsucientconditionforhabitabilityisthatTeqmustbelowerthanabout270K.
Theequilibriumtemperature(Selsisetal.
2007)isgivenbyT4eq=L(1-A)/(16πa2σ),whereσistheStefan-Boltzmannconstant,aistheorbitalradius,andAistheBondalbedo(thefractionofpoweratallwavelengthsscatteredbackintospace).
Thisformulaassumesasphericalplanetwiththeenergythatisabsorbedoverthestarlithemispherebeinguniformlyreradiatedovertheentiresurfaceoftheplanet.
TheBondalbedodoesnothoweverdependsolelyonthegeometricandphysicalcharacteristicsoftheplanet,butalsoonthespectralenergydistributionofthehoststar.
Mstarsemitalargeamountoftheirradiationintheinfrared.
Asaresult,sincethegreenhouseeectworksbyabsorbinginfraredradiation,thesurfacetemperatureswouldbehigherthanpredictedbysuchsimplecalculations.
Thethickness,density,andcompositionoftheatmospherealsosignicantlyinuencethegreenhouseeect.
Theseinturnareultimatelyinuencedbytheplanet'smassandradius(itssurfacegravity)andinternalstructure.
Thechaoticprocessesthatoperatedduringtheplanet'sformationanditssubsequentevolutiondeterminetheplanet'smass,radius,andinternalstructure.
Sotheproblemiscomplexandclearlyover-simpliedbythisformula.
Nevertheless,weestimatetheequilibriumtemperaturegivenL=0.
0135L⊙forthehoststar.
WeassumeaBondalbedofortheplanetofA=0.
3,atypicalvalueforobjectsin–31–theinnerSolarSystem(Earth'sBondalbedois0.
29).
Forthe36.
6-dayplanetcandidate,itssemi-majoraxisof0.
146AUleadstoanequilibriumtemperatureof228K.
IfinsteadtheBondalbedoisassumedtobe0.
5,theequilibriumtemperaturebecomes209K.
Thisplanetcandidatewouldthusappeartoalsosatisfyanothernecessaryconditionforhabitability,thatTeq200)tohaveareasonablechanceatbeingabletodetectsuchsmallamplitudesignals.
So,thecurrentextentofthevariousRV-basedexoplanetsurveysimpliesanincompletenessfactorof116/9orafactorof13increaseinthe1.
7%lowerlimit,makingηatleast22%.
Lookingalittlefurtherout,to10pc,thereareabout302F,G,K,andMdwarfs.
Ofthese,wecouldndevidenceintheliteratureforonly125thatareundersurveyandonlyabout10ofthesetargetedstarsthathavemorethan200observations.
So,havingtheSunandGliese581betheonlyknownhabitableexoplanetsystemsinavolume-limitedsampleoutto10pcwouldimplyalowerlimitforηof2/302timesasurveyincompletenessfactoror302/10,orabout20%.
Lookingfurtheroutstill,to12pc,thereareabout530starsandonlyabout179underprecisionRVsurvey,withonly13ofthesestarshavingatleast200observations.
Thosenumberstranslatetoalowerlimit–34–forηof2/530timesasurveyincompletenessfactoror530/13,orabout15%.
Conclusionsdrawnfromeverlargerlocalvolume-limitedsampleshavediminishingcredibilityasthesurveyincompletenessrisesdramaticallywithincreasingstellarcountwithsurveyvolume.
Anotherunavoidableincompletenessfactorinvolvestherandominclinationsofexoplanetorbits.
Assumingrandominclinations,(1cos30)orabout13%ofthestarsinanyvolume-limitedsamplewouldbeexpectedtohaveorbitalinclinations≤30(withrespecttotheplaneofthesky).
Weresuchsystemstoharborplanets,theirobservedKvalueswouldbeatleastafactorof2lessthanifedge-on.
Forexample,theKvalueforGJ581gisonly1.
3ms1.
Anadditionalfactorof2declineinKforthose13%ofsimilarstarsthatareatlowinclinations(andalsoharborhabitableplanets)wouldbringtheobservablereexvelocityamplitudedownto0.
65ms1,atorbelowtheexpectedstellarjitterfortheeventhequieteststars.
Withtoday'slargesttelescopesandcutting-edgeRVprecision(1ms1),forstarsasfaintastypicalnearbyMdwarfs,photonstatisticsdominatetheerrorbudgetand,incombinationwithstellarjitter,makeroutineandwholesaledetectabilityofsuchlowKvaluesextremelyunlikelygiventheavailablecadenceofthepresentsurveys.
Wecanconservativelyexpectanotherfactorofatleast13%incompletenesscorrectioninourpresentsurveysofthisvolume-limitedsample.
So,ndingahabitableexoplanetsystemthissoonamongthenearestfewhundredsofstarsinthelocalstellarneighborhood,inspiteofthepresenthighlevelofsurveyincompletenessandincludingourownsolarsystemalsoasahabitablesystemimpliesthatηcouldbeontheorderofafewtensofpercent.
–35–8.
SummaryWehavepresented11yearsofprecisionHIRESRVdataforGJ581.
Our122velocities,whencombinedwiththe119high-qualityHARPSvelocitiesofMayor09indicate6companionsinKeplerianmotionaroundthisstar.
Thedatastronglyconrmthe5.
37-dayplanet-b,the12.
9-dayplanet-c,the67-dayplanet-d,andthe3.
15-dayplanet-ecandidatespreviouslyannouncedbyBonls05,Udry07,andMayor09.
Thedataalsoindicatetwomoreplanetsinthissystema7.
0M433-dayplanetanda3.
1M36.
6-dayplanet.
Thelatterorbitssquarelyinthehabitablezoneofthestar.
TheNationalAcademyofScience'srecentlyreleased2010AstronomyandAstrophysicsDecadalreportlists"seekingnearbyhabitableplanets"asoneofitstopthreeobjectivesforthecomingdecade.
Forthepastdecade,theDopplervelocitymethodhasbeenthemostproductivechannelforplanetdetection.
Incomingyears,RVdetectionwillalmostcertainlycontinuetodelineatetheclosestandastrobiologicallymostcompellingplanets,limitedmostlybyavailabletelescopetime.
AstheRVamplitudesoftrulyhabitableplanetsarenearthedetectionlimit,collaborationbetweenleadingteamswouldbeextremelyhelpful.
TheplanetcandidateGJ581gpresentedhere,ifconrmed,oersacompellingcaseforapotentiallyhabitableplanet,butitsRVsignaturerequiredthecombinedpowerofextensiveHARPS+HIRESdatasets.
RVprecisionsapproaching1ms1,andcadencesofhundredsofobservationsonthequieteststarsarenecessarytosecurelydetectsuchlow-massplanets.
GJ581doesseemtobeoneofthoseveryquietstars,withanapparentstellarjitterofnomorethan1.
4ms1.
Remarkably,thestarhasmaintainedthislowlevelofjitterfor11yearsnow.
Astraightforwardandverycost-eectivewaytorealizethe2010Decadalreport'sgoalofseekingnearbyhabitableplanets,withouttheneedtodevelopanewgenerationof"advanced"precisionopticalorinfraredspectrometers,istobuilddedicated6-8meterclass–36–AutomatedPlanetFindertelescopes,oneineachhemisphere.
Suchdedicatedtelescopes,instrumentedwithtoday'sstate-of-the-artprecisionradialvelocityspectrometers,likeHARPSorHIRESorMagellan'snewPFS(PlanetFinderSpectrometer)could,withinafewshortyears,providethenecessarycadencesofhundredsofobservationsonallofthenearbyquietG,K,andMdwarfstarswithin10pc,inallprobabilityrevealingmanyothernearbypotentiallyhabitableplanets.
RidingonthecoattailsofexistingengineeringbycloselycopyingtheMagellan6.
5-mtelescopes,eachfacilitycouldprobablybebuilt(andinstrumentedwithaprecisionRVspectrometer)forabout$50million,or$100milliontotalfortelescopesinbothhemispheres.
Indeed,ifηisreallyashighasseveraltensofpercent(orisevenonlynomorethanafewpercent)havingonlyasingleplanetnderinonehemispherecouldaccomplishprettymuchthesamegoal,foramere$50million.
Withthissinglecapitalinvestment,onecouldmakesure,swift,andcost-eectiveprogressononeofthe2010Decadalreport'sthreeprimarysciencegoals.
Finally,itisimportanttokeepinmindthat,thoughall6planetspresentedherearewell-supportedbythecalculatedreducedchi-squaredstatisticsandalsobyseveraldierentvariantsofFAPstatistics,andtheentire6-planetsystemisconsistentwiththecombineddatasetfrombothteams,cautioniswarrantedasmostofthesignalsaresmall.
Andtheremayyetbeunknownsystematicerrorsineitherorbothdatasets.
Forexample,Pontetal.
(2010)haverecentlyconcludedfromadetailedanalysisofHARPSCoRoT-7datathat"Onthewhole,thereisamountingbodyofevidencethatunexplainedvariationsatthe5-10ms1levelmayexistinHARPSRVsfortargetsinthebrightnessrangeofCoRoT-7.
"GJ581isonlyaboutamagnitudebrighterthatCoRoT-7,soitmaynotbecompletelyoutofthequestionthatHARPSdataforGJ581mightalsobeaectedbysuchunexplainederrors.
Andtobecompletelyfair,theHIRESdatasetcouldalsohaveundiscoveredsystematicerrorslurkingwithin.
Thisisverydicultworkandthereisnoshameordishonorinuncoveringresidualsystematicerrorsattheselevelsofprecision.
Collegialandunabashed–37–inter-teamcomparisonsonstarslikeGJ581andGJ876willbecrucialtoquantifyingthetrueprecisionlimitsofanyteam'sdatasets.
Finally,becauseoftheverysmallamplitudesinvolved,allowingsignicanteccentricitiesintotheKeplerianttingtreemayyieldviablealternatesolutions.
Here,phasegapsindatasetsbecomeproblematicalasttingroutinesgenerallyalloweccentricitytoutilizethesegaps,drivinguptheeccentricityarticiallytoenhancethequalityofthet,andhidingmuchofthevelocityswingfromeccentricityinthephasegap.
Suchsituationssometimesresultinmisleadingsolutionsthatcanoverlookormaskadditionalplanetsinthesystem.
Conrmationbyotherteamsthroughadditionalhigh-precisionRVswouldbemostwelcome.
ButifGJ581gisconrmedbyfurtherRVscrutiny,themerefactthatahabitableplanethasbeendetectedthissoon,aroundsuchanearbystar,suggeststhatηcouldwellbeontheorderofafewtensofpercent,andthusthateitherwehavejustbeenincrediblyluckyinthisearlydetection,orwearetrulyonthethresholdofasecondAgeofDiscovery.
SSVgratefullyacknowledgessupportfromNSFgrantAST-0307493.
RPBgratefullyacknowledgessupportfromNASAOSSGrantNNX07AR40G,theNASAKeckPIprogram,andfromtheCarnegieInstitutionofWashington.
NHacknowledgessupportfromtheNASAAstrobiologyInstituteunderCooperativeAgreementNNA04CC08AattheInstituteforAstronomy,UniversityofHawaii,andNASAEXOBgrantNNX09AN05G.
GWHandMHWacknowledgesupportbyNASA,NSF,TennesseeStateUniversity,andtheStateofTennesseethroughitsCentersofExcellenceprogram.
TheworkhereinisbasedonobservationsobtainedattheW.
M.
KeckObservatory,whichisoperatedjointlybytheUniversityofCaliforniaandtheCaliforniaInstituteofTechnology,andwethanktheUC-KeckandNASA-KeckTimeAssignmentCommitteesfortheirsupport.
WealsoacknowledgethecontributionsoffellowmembersofourpreviousCalifornia-CarnegieExoplanetteaminhelpingtoobtainsomeoftheearlierRVspresentedinthispaper.
We–38–alsowishtoextendourspecialthankstothoseofHawaiianancestryonwhosesacredmountainofMaunaKeaweareprivilegedtobeguests.
Withouttheirgeneroushospitality,theKeckobservationspresentedhereinwouldnothavebeenpossible.
Finally,SSVwouldliketoextendaveryspecialthankstohiswifeZarminaDastagirforherpatience,encouragement,andwisecounsel.
Andeventhough,ifconrmed,thehabitableplanetpresentedhereinwillociallybereferredtobythenameGJ581g,itshallalwaysbeknowntoSSVas"Zarmina'sWorld".
Facilities:Keck.
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ThismanuscriptwaspreparedwiththeAASLATEXmacrosv5.
2.
–43–Table1.
RadialVelocitiesforGJ581JDRVerror(-2450000)(ms1)(ms1)1409.
762226.
961.
891586.
14605-10.
243.
221704.
912130.
472.
892003.
95507-4.
373.
652100.
86678-19.
452.
222161.
730963.
352.
192162.
7316510.
732.
382335.
150246.
872.
332487.
79326-7.
303.
772712.
05433-10.
962.
102828.
877087.
752.
253077.
15398-7.
183.
183239.
82508-2.
502.
603426.
14551-2.
744.
823748.
16323-4.
971.
963754.
14596-8.
681.
973932.
805882.
401.
953960.
8377112.
141.
903961.
772794.
381.
573962.
77418-4.
972.
40–44–Table1—ContinuedJDRVerror(-2450000)(ms1)(ms1)3963.
81985-9.
921.
783982.
7806914.
041.
924130.
14636-14.
791.
844131.
16220-4.
582.
584139.
161551.
601.
924246.
81907-4.
501.
184247.
92767-9.
211.
844248.
82815-7.
841.
484249.
902816.
451.
384250.
8129218.
171.
954251.
819427.
611.
304255.
797717.
353.
624277.
7699617.
111.
684278.
7813814.
061.
714279.
78247-10.
602.
034285.
78969-15.
082.
544294.
84381-0.
042.
044300.
81847-0.
761.
834304.
7987216.
632.
244305.
805452.
611.
45–45–Table1—ContinuedJDRVerror(-2450000)(ms1)(ms1)4306.
83201-8.
052.
314307.
83943-8.
031.
474308.
820161.
741.
274309.
8056813.
321.
264310.
8027111.
191.
264311.
79457-4.
401.
234312.
79306-7.
141.
134313.
801768.
141.
454314.
8223013.
671.
354318.
79357-5.
911.
444335.
751665.
831.
354336.
7842514.
681.
844339.
72676-8.
582.
694343.
74861-0.
292.
064345.
74397-5.
821.
944461.
174583.
572.
134545.
095184.
981.
954546.
0781317.
481.
524547.
077159.
062.
744547.
99454-3.
972.
45–46–Table1—ContinuedJDRVerror(-2450000)(ms1)(ms1)4600.
9889613.
542.
034601.
90368-8.
332.
694633.
86049-6.
471.
494634.
86134-12.
301.
274635.
87975-5.
691.
194636.
8869012.
262.
074637.
8850215.
381.
564638.
94288-1.
081.
404639.
91382-11.
271.
394640.
92943-6.
501.
954641.
902675.
641.
334643.
884560.
951.
744666.
84246-7.
601.
254667.
84194-8.
112.
074671.
85435-9.
711.
334672.
83453-3.
241.
004673.
849738.
111.
034686.
827942.
602.
224688.
77854-9.
571.
964689.
778803.
131.
29–47–Table1—ContinuedJDRVerror(-2450000)(ms1)(ms1)4701.
7921117.
511.
174702.
8125011.
351.
724703.
80853-1.
731.
544704.
80341-7.
991.
204717.
7288714.
811.
484718.
737845.
102.
034719.
73866-4.
931.
864720.
73430-14.
791.
464721.
73009-9.
861.
334722.
740363.
801.
584723.
739086.
851.
624903.
15067-14.
412.
085021.
91811-10.
111.
435022.
912861.
391.
865024.
950129.
321.
575049.
860104.
910.
905050.
8070613.
450.
795051.
840435.
281.
175052.
86710-8.
122.
095053.
79905-10.
890.
80–48–Table1—ContinuedJDRVerror(-2450000)(ms1)(ms1)5201.
1572016.
101.
585202.
157349.
801.
615203.
14807-8.
371.
535258.
155842.
442.
225260.
1337916.
542.
115338.
81312-4.
840.
535338.
90357-3.
101.
595338.
98795-1.
621.
335339.
06181-1.
561.
825340.
053719.
911.
635340.
8660011.
621.
385340.
952609.
870.
585341.
033516.
690.
765341.
79524-1.
630.
805342.
00395-1.
670.
885342.
06383-5.
261.
465369.
93610-15.
901.
405370.
87580-14.
211.
485371.
934296.
731.
135408.
89194-0.
402.
00–49–Table1—ContinuedJDRVerror(-2450000)(ms1)(ms1)5409.
7668415.
211.
485409.
8668215.
681.
98Table2.
OrbitalParametersforGJ581PlanetCandidatesPlanetPeriodKmsiniaMeanAnomalya(days)(ms1)(M)(AU)()FAPSb5.
36841(0.
00026)12.
45(0.
21)15.
6(0.
3)0.
0406163(1.
3e-6)276.
1(4.
9)6.
8e-306c12.
9191(0.
0058)3.
30(0.
19)5.
6(0.
3)0.
072993(2.
2e-5)33(19)2.
3e-33d66.
87(0.
13)1.
91(0.
22)5.
6(0.
6)0.
21847(2.
8e-4)56(27)2.
5e-6e3.
14867(0.
00039)1.
66(0.
19)1.
7(0.
2)0.
0284533(2.
3e-6)267(40)1.
9e-8f433(13)1.
30(0.
22)7.
0(1.
2)0.
758(0.
015)118(68)9.
5e-5g36.
562(0.
052)1.
29(0.
19)3.
1(0.
4)0.
14601(1.
4e-4)271(48)2.
7e-6aThettedmeananomaliesarereportedatreferenceepochJD2451409.
762.
–50–Table3.
PhotometricSemiamplitudesModulotheRadialVelocityPeriodsPlanetaryPeriodSemi-amplitudePlanet(days)(mag)b5.
368410.
00045±0.
00044c12.
91910.
00083±0.
00044d66.
870.
00129±0.
00044e3.
148670.
00061±0.
00045f433···g36.
5620.
00058±0.
00047Note.
—Thedatasetisinsucienttoaddressthe433dayperiod.