Table Of ContentDRAFTVERSIONFEBRUARY3,2008
PreprinttypesetusingLATEXstyleemulateapjv.10/09/06
MICROLENSINGSEARCHFORPLANETSWITHTWOSIMULTANEOUSLYRISINGSUNS
CHEONGHOHAN
ProgramofBrainKorea21,DepartmentofPhysics,ChungbukNationalUniversity,Chongju361-763,Korea;[email protected]
DraftversionFebruary3,2008
ABSTRACT
Among more than 200 extrasolar planet candidates discovered to date, there is no known planet orbiting
aroundnormalbinarystars. Inthispaper,wedemonstratethatmicrolensingisatechniquethatcandetectsuch
planets.Microlensingdiscoveriesoftheseplanetsarepossiblebecausetheplanetandhostbinarystarsproduce
8 perturbationsat a common region around center of mass of the binary stars and thus the signatures of both
0
planetandbinarycanbedetectedinthelightcurvesofhigh-magnificationmicrolensingevents. Therangesof
0
theplanetaryandbinaryseparationsofsystemsforoptimaldetectionvarydependingontheplanetmass. For
2
aJupiter-massplanet,wefindthathighdetectionefficiencyisexpectedforplanetslocatedintherangeof∼1
n AU–5AUfromthebinarystarswhichareseparatedby∼0.15AU–0.5AU.
a Subjectheadings:gravitationallensing–planetsandsatellites: general
J
1
3 1. INTRODUCTION
Since the first discovery by Wolszczan&Frail (1992),
]
h morethan200extrasolarplanetcandidateshavebeendiscov-
p ered. Among the currently known extrasolar planet-hosting
- stars, approximately20% are membersof binaries or multi-
o
plesystems(Haghighipour2006). Nearlyalloftheplanetsin
r
t thesesystemsrevolvearoundonlyoneofthestars. Theonly
s
exceptionistheplanetarysystemPSRB1620-26(Lyneetal.
a
[ 1988;Backeretal.1993),butthissystemconsistsofnotnor-
malstarsbutapulsarandawhitedwarf.
1 Besides the orbital configuration of the known planets in
v
binaries where the planet revolvesaround one of the widely FIG.1.—Lensinggeometryofaplanetrevolvingaroundclosebinarystars.
8 separatedbinarymembers,aplanetcanstayinastableorbit ThebigdashedcirclerepresentstheEinsteinringofamasscorrespondingto
2 thetotal massofthebinary stars. Theangleφdenotes theposition angle
if the planetis locatedwelloutside thebinarystarsand thus
8 oftheplanetasmeasuredcounterclockwisefromthebinaryaxisanddband
4 seeing the two stars as approximatelya single object. How- dpdenotetheprojectedseparationsbetweenthebinarystarsandbetweenthe
ever,suchplanets,whichwereimaginedasaplanetwithtwo planetandthebinarycenterofmass,respectively. Therightpanelshowsthe
.
1 simultaneouslyrising suns in the Star Wars saga (Tatooine), enlargedviewoftheregionaroundthebinarystars. Thefiguredrawninred
0 havenotbeenseeninplanetsearchesusingtheradialveloc- colorrepresentsthelensingcausticproducedbythelenssystem.
8
itytechniquebecausethesearchprogramsavoidshort-period ismuchsmallerthanthestar-planetseparation(seeFigure1).
0
: binarystars. Thechancetodetectsuchplanetsviathetransit Under this geometry, the lensing behavior of the triple lens
v techniqueisalsoverylowbecausetheseplanetstendtohave systemcanbegreatlysimplifiedbecausetheclosestellar bi-
Xi wideorbits. narypairandtheplanetcanbeseparatelytreated.
Planets in binary stellar systems can be detected by us- The lensing behavior of the close stellar binary pair is
ar ing the microlensing technique. Such a possibility was first mostlydescribedbythesinglemasslenslocatedatthecenter
mentioned by Bennettetal. (1999). They reported a can- ofthemassofthebinarysystemwithamassequaltothetotal
didate planet orbiting around a binary system from the ob- massofthebinary.Asmalldeviationoccursaroundthecaus-
servation and light-curve modeling of a microlensing event ticwhichformsclosetothecenterofmass.Thecausticrepre-
MACHO-97-BLG-41. However, their interpretation of this sentsthesetofsourcepositionsatwhichthemagnificationof
eventisveryspecialinthesensethatthesourcetrajectoryis apointsourcebecomesinfinite.Foraclosebinary,thecaustic
preciselyalignedwith the line connectingthe planetand the hastheshapeofanasymmetrichypocycloidwithfourcusps
center of mass of the binary. Besides, the interpretation of and the asymmetry increases as the mass ratio between the
the signalwas rejected becausea rotatingbinary-lensmodel stars, q =m /m , decreases. Here m and m representthe
b 2 1 1 2
provides an excellent fit to the observed data (Albrowetal. massesoftheheavierandlighterbinarycomponents,respec-
2000). Leeetal. (2008) also investigated the lensing signal tively.Thecausticsizedependsweaklyonthemassratio,but
of planets in binary systems. However, their analysis is re- itdecreasesrapidlywiththedecreaseofthestellarseparation.
strictedtoplanetsorbitingaroundoneofthebinarymembers. Foraclosebinary,then,theperturbationregionisconfinedto
Inthispaper,weinvestigatethefeasibilityofdetectingplanets asmallregionaroundthecenterofmassofthebinary.
with two simultaneouslyrising sunsby using the microlens- Theplanet,ontheotherhand,causesformationoftwosets
ingtechnique. of disconnected caustics. One set is located away from the
hoststar. Theothersetis locatedclose tothe planet-hosting
2. LENSINGBEHAVIOR star, which coincides with the region of the binary-induced
Thegeneralgeometryofaplanetrevolvingaroundthestars perturbation. Thelattercaustic(centralcaustic)hasanelon-
ofaclosebinaryissuchthattheseparationbetweenthestars gatedwedge-likeshape. Thesize ofthe planet-inducedcen-
2 PLANETSWITHTWOSUNS
FIG.2.—Lensingmagnificationpatternsoftriplelenssystemscomposedofaplanetrevolvingaroundbinarystars.Thelabelsaboveandontherightrepresent
theprojectedseparationsbetweenbinarystars(db)andbetweentheplanetandthecenterofmassofthebinary(dp),respectively.Ineachmap,thecoordinatesare
centeredatthepositionofthecenterofmassofthebinarystarsandthex-axisisalignedwiththebinaryaxis.Theheavierstarisontheright.Theplanetshavea
commonpositionangleofφ=45◦asmeasuredcounterclockwisefromthebinaryaxis(seeFigure1).Thegrey-scaleisdrawnsuchthatbrightertonerepresents
theregionofhighermagnification.Thefiguresdrawninsolidcurvesrepresentthelensingcaustics.ThepresentedpatternsareforaSaturn-massplanetrevolving
aroundbinarystarswithatotalmassof0.5M⊙andacompanion/primarymassratioof0.5. Thelightcurvesresultingfromthesourcetrajectoriesmarkedby
straightlineswitharrowsintheindividualpanelsarepresentedinthecorrespondingpanelsofFigure3(thicksolidcurvesinblackcolor).Thepanelsblockedby
thickblacksolidlinesshowthecaseswheretheplanetdominatestheperturbationpattern,whilethepanelsblockedbythickwhitesolidlinesshowtheopposite
caseswherethebinarystarsdominatethepattern.
tralcausticsdependsbothonthestar-planetseparationandthe
planet/starmassratio(Chungetal.2005).Theplanet-induced TABLE1
causticissmallduetothesmallmassratiooftheplanet.How- OPTIMALSEPARATIONRANGES
ever,itssizebecomesnon-negligiblewhentheplanetarysep-
planet planetary binary
arationisequivalenttotheEinsteinradius(Mao&Paczyn´ski type separation separation
1991;Gould&Loeb1992).
The small sizes of the deviation regions induced by the Jupiter-mass 1.0AU.dp.5.0AU 0.15AU.db.0.5AU
Saturn-mass 1.6AU.dp.3.8AU 0.15AU.db.0.5AU
planetandthe hostbinarystars greatly simplifythe descrip- Uranus-mass 2.0AU.dp.3.0AU 0.15AU.db.0.5AU
tion of the lensing behavior of the system. This is because
each deviation can be treated as a perturbation and thus the AU and the source size normalizedby the Einstein radiusis
lensingbehaviorofthetriplelenssystemisapproximatedas ρ=1.5×10- 3.
the superposition of those of the two sets of binary lenses InFigure3,wealsopresentthelightcurvesresultingfrom
composed of the binary star pair and the pair composed of the sourcetrajectoriesmarkedbystraightlines on the maps.
theplanetandavirtualstar locatedatthecenterofthemass In each panel, there exist three lightcurves. The thick solid
ofthebinarystarswith amassequalto thetotalmassofthe lightcurveisforthetriple-lensevent,whilethecurvesdrawn
binary. In addition,the coincidenceof the individualpertur- inredandbluecolorsareforthecaseswherethereisnoplanet
bation regions might enable to detect both signatures of the andtheplanet-hostingstarisasingleobject,respectively.
planet and host binary stars from high magnification events FromFigure2and3,wefindthattheinfluenceoftheplanet
for which the source trajectory passes close to the common andbinarystarsonthepatternofperturbationvariesdepend-
regionofperturbation. ingonthebinaryandplanetaryseparations. Whenthebinary
separationissmallandtheplanetaryseparationisequivalent
3. MAGNIFICATIONPATTERN to the Einstein radius, the planet dominates the perturbation
Withthepossibleapproximationofbinarysuperpositionin pattern.Thesecorrespondtothecasesblockedbythickblack
mind, we investigatethe magnificationpattern in the central solidlinesinFigure2. Onthecontrary,thebinarydominates
region of various triple lens systems composed of a planet theperturbationpatternwhenthebinaryseparationisconsid-
around binary stars. For this, we construct magnification erable and the planetary separation is either too large or too
map, which represents the map of lensing magnification as small comparedto the Einstein radius. These correspondto
a function of the source star position. For the construction thecasesenclosedbythickwhitesolidlinesinFigure2. For
of the map, we use the ray-shooting method. We choose eventsproducedbytheselenssystems,then,theresultingper-
this method because it allows not only simple procedure of turbationwould be well described by a binary lens of either
multiple-lensingmagnificationcomputationbutalsoeasyin- star-planetorbinarystarpair.However,forlenssystemswith
corporationofthefinite-sourceeffect. separationslocatedintheneutralregionofthed –d param-
b p
Figure 2 shows the mapsfor a Saturn-massplanetrevolv- eter space, the influencesofthe planetand stellar binaryare
ingaroundbinarystarswithatotalmassofM=0.5M⊙ and equivalentandthusitwouldbepossibletodetectbothsignals
a mass ratio of q =0.5. The labels above and on the right oftheplanetandbinarystars.
b
sideofthefigurerepresenttheprojectedseparationsbetween
binary stars (binary separation, d ) and between the planet 4. OPTIMALBINARYANDPLANETARYSEPARATIONS
b
and the center of mass of the binary (planetary separation, Then,whataretheoptimalrangesofthebinaryandplane-
dp), respectively. In each map, the coordinates are centered taryseparationsforwhichthemicrolensingtechniqueissen-
at the position of the center of mass of the binary stars and sitivetothedetectionsofplanetsorbitingaroundbinarystars.
the x-axis is aligned with the binary axis, where the heav- Inthissection,weinvestigatetheseoptimalranges.
ier star is on the right. For all tested cases, the planetshave The size of the perturbation region is proportional to the
a common position angle of φ= 45◦ as measured counter- size of the caustic. We, therefore, determine the optimalre-
clockwise from the binary axis (see Figure 1). The grey- gion in the d –d parameter space as the one within which
b p
scaleisdrawnsuchthatbrightertonerepresentstheregionof the sizes of the planet and binary-induced caustics become
highermagnification. Thefiguresdrawninsolidcurvesrep- equivalent. Figure 4 shows the regionsfound underthis ap-
resentthe caustics. Since the caustics inducedby the planet proximation for three different types of Jupiter, Saturn, and
and binary stars are small, finite-source effect would be im- Uranus-mass planets. For lens systems with planetary and
portantin magnificationpattern (Bennett&Rhie 1996). We binary separations located in the shaded region, the size ra-
considertheeffectbyassumingthatthesourcestarhasara- tiobetweenthetwotypesofcausticisintherangeof1/5≤
dius equivalent to that of the Sun. We assume that events ∆ξ /∆ξ ≤5.0, where ∆ξ and ∆ξ represent the sizes of
p b p b
are observed toward the Galactic bulge field and the dis- the planetand binary-inducedcaustics, respectively. We ap-
tancestothelensandsourceareDL=6kpcandDS=8kpc, plytwoexceptionstothisrule. Thefirstisthatif bothcaus-
respectively, by adopting those of a typical Galactic bulge ticsaretoosmall,weassumethatthesignaldetectionwould
event (Han&Gould 1995). Then, the corresponding Ein- bedifficultdueto severefinite-sourceeffect. To accountfor
stein radius is r = (4GM/c2)1/2[D (D - D )/D ]1/2 ∼ 2.5 the finite-source effect, we set the lower limit of the caustic
E L S L S
HAN 3
FIG. 3.—Lightcurvesoflensingeventscausedbytriplelenssystemscomposedofaplanetrevolvingaroundbinarystars. Thelenssystemgeometryandthe
sourcestartrajectoriesresponsiblefortheindividualeventsarepresentedinthecorrespondingpanelsofFigure2. Ineachpanel,thereexistthreelightcurves.
Thethickblacksolidlightcurveisforthetriple-lens event, whilethecurvesdrawninredandbluecolorsareforthecaseswherethereisnoplanetandthe
planet-hostingstarisasingleobject,respectively.
FIG. 4.— The optimal ranges of binary and planetary separations for binary-lens modelling was considered to be a difficult task,
whichmicrolensingtechniqueissensitivetothedetectionsofplanetsorbiting butnowit is routinelyconductedfor binaryevents. Consid-
aroundbinarystars. ering this, triple-lens modelling would be possible in future
sizeforsignaldetectionastwotimesofthesourcesize. The lensinganalysis.
secondexceptionisthatifbothcausticsaregreaterthanacer- Nevertheless,onemightthinkofseveralpossibledegener-
tain value, we assume that the chance to detect both planet ate cases to the signal of the planet orbiting a close binary
andstellarbinaryisnotsmall. Wesetthisthresholdcaustics stars. Onepossiblecaseisatriplelenssystemwhereaplanet
size as 10 times of the source size. Fromthe comparisonof orbits around one of widely separated binary stars. In this
the optimal ranges determined in this way with those of the case, the binary-producedcausticis locatedalso close tothe
neutralregionjudgedbasedoneyeinspectionofthemapsin planet-induced caustic, causing potential degeneracy. How-
Figure 2, we find good agreement. The optimalrangesvary ever,thecaustic producedbythe wide-separationbinaryhas
dependingontheplanetmass. ForaJupiter-massplanet,we a verysymmetric hypocycloidshape, while the shape of the
find thathigh detectionefficiencyis expectedfor planetslo- caustic produced by close binary stars is in general asym-
catedintherangeof1AU.dp.5AUorbitingaroundbina- metric. Therefore, the resulting patterns of the two cases
rieswithseparationsof0.15AU.db.0.5AU. Therangeof are differentand thus it would not be difficultto distinguish
theplanetaryseparationshrinksastheplanetmassdecreases. the two cases. Another possible case is a star with multi-
However, the range of the binary separation remains nearly pleplanets(Gaudietal.1998). Heretheperturbationsinthe
thesame regardlessof theplanetmass. In Table1, we sum- central region are produced by the individual planets. The
marizetheoptimalrangesforvarioustypesofplanets. planet-inducedcausticsaremuchmoreelongatedthanbinary-
It might be that planets located in some portions of the inducedcaustic. Therefore,itwouldnotbedifficulttodistin-
testeddb–dp parameterspacemightbedynamicallyunstable guishthiscase,either.
and thus the estimated optimal region is overestimated. At Planets aroundclose binarystars will be detected through
present,however,thepossibleextentoftheplanetseparation thechannelofhigh-magnificationevents. Currentmicrolens-
aroundstarsofaclosebinarysystemisanopenquestionand ingfollow-upobservations(Beaulieuetal.2006;Gouldetal.
issubjecttobetestedfromobservation.Inthissense,thecon- 2006)arefocusingontheseeventsduetotheirhighefficiency
straintofthestableregionoftheplanetaryseparationthatwill inplanetdetections(Griest&Safizadeh1998).Byusingmul-
beprovidedbythemicrolensingmethodisveryimportant. tiple telescopes located at differentlocations, these observa-
tionsenabledense and continuouscoverageof eventswhich
5. DISCUSSION
is required to detect the short-lasting signature of the planet
Interpretingthesignalsoftriple-lenssystemsisnotaneasy in binary stars. In addition, greatly enhanced source bright-
task. Withmorecompleteunderstandingoflensingbehavior nessofhigh-magnificationeventsenablesprecisionphotome-
and the development of efficient modelling codes, however, trywhichisessentialforthecharacterizationofthesignature.
suchanalysisisbeingstartedfortheanalysisofobservedlens- Therefore, we predict that planets with two simultaneously
ingevents(A.Gouldprivatecommunication). Notlongago,
4 PLANETSWITHTWOSUNS
risingsunswouldbedetectedinthenearfuture. crolensingmethodisefficientindetectingtheseplanetarysys-
tems. Discoveringplanetsorbitingaroundclose binarystars
6. CONCLUSION is difficult by using the radial velocity or transit technique.
We investigated the feasibility of detecting planets orbit- Therefore, microlensing is an important technique that can
ing close binary stars by using the microlensing technique. provideinformationaboutthese planetary systems, which is
Wepresentedthechannelforwhichonecanidentifythesig- veryimportantforourunderstandingofplanetformation.
natures of such planetary systems. We illustrated the signa-
tures for various planet-binary configurations and explained
thetendenciesofthesignatures.Wealsoestimatedtheranges This work was supported by the Science Research Center
of the binary and planetary separations for which the mi- (SRC)program.
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