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Mem.S.A.It.Vol.79,3 (cid:13)c SAIt 2008 Memoriedella Photometri binaries in (cid:12)fty Globular Clusters A. P. Milone1 G. Piotto1 L. R. Bedin2 A. Sarajedini4 1 DipartimentodiAstronomia, Universita` diPadova,Vicolodell’Osservatorio3,Padova, 8 I-35122,Italy 0 2 SpaceTelescopeScienceInstitute,3700SanMartinDrive,Baltimore,MD21218,USA 0 3 Department of Astronomy, University of Florida, 211 Bryant Space Science Center, 2 Gainesville,FL32611,USA n a J Abstract. TheHST/ACSSurveyofGalacticglobularclusters(GGCs)isaHSTTreasury projectaimedatobtaininghighprecisionphotometryinalargesampleofglobularclusters. 1 ThehomogeneousphotometriccatalogsthathasbeenobtainedfromthesedatabyAnderson 2 etal.(2008)representsagoldenmineforalotofastrophysicalstudies. ] InthispaperweusedthecatalogtoanalysethepropertiesofMS-MSbinarysystemsfrom h asampleoffiftyGGCs.Wemeasuredthefractionofbinaries(dividedindifferentgroups), p studiedtheirradialdistributionandconstrainedthemassratiodistribution.Weinvestigated - possible relations between the fraction of binaries and the main parameters of their host o GGCs. r t Wefoundasignificantanti-correlationbetweenthebinaryfractioninaclusteranditsabso- s luteluminosity(mass). a [ Keywords. stellardynamics–methods:observational–techniques:photometric–bina- 1 ries:general–stars:PopulationII–globularclusters:general v 7 7 1. Introduction low mass X ray binaries are believed to rep- 1 resentevolutionarystagesofclosebinarysys- 3 KnowledgeofthebinaryfrequencyinGlobular . tem. The determination of the fraction of bi- 1 Clusters(GCs)isoffoundamentalimportance naries plays a foundamental step towards the 0 foralotofastrophisicalstudies. understanding of the evolution of these pecu- 8 Binaries play an important role in the dy- liar objects. Furthermore, binary stars intro- 0 namical evolution of a clusters. Interactions ducesystematicerrorsin thedeterminationof : v with hard binaries pump kinetic energy into themainsequence(MS)fiduciallineandmove i the cluster core,slowingthe corecollapsand, X it toward red colorswith respectto its correct eventually,causingthecoretoreexpand,ifthe position. r numberofbinariesislargeenough.Ingeneral, a Finally,acorrectdeterminationofthemass binaries are a foundamentalingredient in any and luminosity functions requires a correct dynamicalevolutionmodelofaGC. measureofthefractionofbinaries. Exoticstellarobjects,likeBlueStragglers, cataclismic variables, millisecond pulsars and Up to now, three main techniques have been used to measure the fraction ob binaries Sendoffprintrequeststo:A.P.Milone inGGCs(Hutetal.1992). 4 Miloneetal.:PhotometricbinariesinfiftyGCs Thefirstoneidentifiesbinariesbymeasur- In this paper, we analyse the catalogs ob- ing their radial velocity variation (eg. Latham tained by Anderson et al. (2008) from HST 1996).Thismethodrelieswiththedetectionof ACS/WFC data.We exploitedboththehome- each individual binary system but, due to the geneityofthisdataset,andthehighphotomet- limitsinsensibilityofspectroscopy,thesestud- ricaccuracyofthemeasurestoderivethefrac- ies are possible only for the brightest GGCs tion of binaries in the central regions of fifty stars. GGCs. Thesecondtecniqueisbasedonthesearch forphotometricvariables(eg.Mateo1996).As 2. OutliersintheColorMagnitude wellasthepreviousone,itisabletoinferspe- Diagram cificpropertiesofeachbinarysystem(likethe measure of orbital period, mass ratio, orbital Binaries that are able to survive in the dense inclination).Unfortunatly,itisbiased towards enviroment of a globular cluster are so close binarieswithshortperiodsandlargeorbitalin- that even the Hubble Space Telescope (HST) clination.Moreoverthesetecniqueshavealow isnotabletoseparatetheirsinglecomponents. discovery efficency and are very expensive in For this reason, light coming from each star termsoftelescopetimebecauseitisnecessary will combine, and the binary system will ap- torepeatmeasuresintime. pearasasinglepointlikesource. Athirthapproach,thatisbasedontheanal- In this paper we will take advantage from ysis of the numberof stars located on the red thisinstrumentallimittosearchforbinariesby side of the main sequence (MS) ridge line analisingtheirpeculiarpositionintheCMD. (MSRL)mayrepresentamoreefficientmethod In the most general case, if we consider tomeasurethefractionofbinariesinacluster twostarsina binarysystemandindicatewith forseveralreasons: m ,m ,F andF theirrespectivemagnitudes 1 2 1 2 and fluxes, a simple algebric count demon- – availability of a large number (thousands) stratethatthebinarywillappearasasingleob- of stars makes it a statistically roboust jectwithamagnitude: method; – it is cheep in terms of observationaltime: m =m −2.5log(1+ F1) twofiltersareenoughfordetectingbinaries bin 1 F2 andrepeatedmeasuremetsarenotneeded. InthecaseofabinaryformedbytwoMSstars – it is sensitive to binaries with any orbital (MS-MS), fluxes are related to stellar masses periodandinclination (M , M ), and its luminosity depends on the 1 2 mass ratio q = M /M (in the following we 2 1 Thisapproachhavebeenusedbyothergroups will assume M < M , q < 1). The bina- 2 1 (seeSollimaetal.2007andreferenceswithin) ries formed by an equal mass pair form a se- to study the population of binaries in GGCs. quenceparalleltoMS,and∼ 0.75magnitudes Therelativesmallnumberofclustersthathave brighter. When the masses of the two compo- been analized is consequence of the intrinsic nentsaredifferent,thebinarywillappearred- difficultiesofthemethod: derandbrighterthantheMSanditwillbelo- cated in a CMD region on the red side of the – highphotometricqualityisrequired; MSRL. – in some cases, the differential reddening An obious consequence of this analysis is spreadstheMSandmakesitmoredifficult that our capability in detecting binaries de- toisolatethebinarysequence; pends meanly by the photometric quality of – an accurate analysis of photometric er- the data. Binaries with large mass ratios have rors as well as a correct estimate of field alargedistancefromMSRLandarerelatively contaminationarenecessarytodisantangle easy to be detected. On the contrary, a small realbinariesfrombadphotometryandfield massratiopushesbinariesneartheMSRLand stars. makesithardtoseparatethemfromsingleMS Miloneetal.:PhotometricbinariesinfiftyGCs 5 stars.Moreover,thepoorerphotometryoffaint starslimitstheluminosity(mass)rangewhere theycanbedetectedandstudied. 3. Method Thelimitedphotometricprecisionmakesitim- possible to measure the overall population of binarieseveninasmallregionofclusters.For this reason, in this paper, we do not pretend to measure the global fraction of binaries in a cluster, but will limit our study to particu- larsubsamplesofthem.Eachgroupisformed byobjectsthatshareallthesamepropertiesin termsofluminosityandmassratio. Weisolatedthreesamplesofhighmassra- tiobinaries(definedasthebinarysystemswith, q>0.5,0.6and0.7)andseparatelystudiedthe properties of each group. In addition we de- Fig.1. Grey areas are the regions of the rivedalsotheglobalfractionofbinaries. NGC6121CMDadoptedtoselectallthe(sin- We performedour study in the magnitude gleandbinary)clusterstars(right)andthecan- range3.75<∆(IF814W)<0.75belowthemain didatebinarieswithq>0.6(left)inarangeof3 sequenceturnoff.Theextremesofthisinterval I magnitudes. F814W willbeindicatedwithI andI . bright faint – theridgelineforanequalmassbinarysys- 3.1.Highqbinaryfraction temontheredside. Inordertomeasurethefractionofhighqbina- The third region(A ) containsall the binaries ries, we dividedthe CMD in two regions(see 3 with q ∼ 1 thatare shiftedbyphotometricer- Fig.1): rorstotherightofanequalmassbinariesfidu- Aregion(A)thatincludesalltheMSsingle cialline.ItisadiajenttotheregionA anditis starsandthebinarieswithaprimarystarwith 2 I > I > I .Itisformedbythreesubre- limitatedbytheridgelineforanequalmassbi- bright faint narysystemshiftedincolorbythreetimesthe gions. The first one (A ) includes all the MS 1 main sequence photometric dispersion on the single stars and MS-MS binaries with small leftside. mass ratios; it is limited by dashed lines in Thesecondregion Bisdefinedasthepor- Fig.1andcorrespondstotheCMDportionwith tion of the region (A) on the red side of the acolordistancefromtheMSridgelinesmaller trackformedbyabinarystarwithq = q and thanthreetimestheMSdispersion;thesecond tr itincludesallthebinariesformedbyaprimary (A ) includes all the binary candidates with 2 star with I > I > I and a mass ra- highmassratios.InFig.1itcorrespondstothe bright faint tiosgreaterthanathreasholdvalue(q ).Inthis CMD portiononthe redside ofthe A region tr 1 workweseparatelystudiedthe samplesofbi- andisdelimitedby: narieswithmassratioslargerthanq =0.5,0.6 tr – the track formed by a binary system with and0.7. a primary star with I = I and a mass Unfortunatly, regions A and B are popu- bright ratiorangingfrom0to1onthetop; latedbyfieldstars,whilechancesuperposition – thecorrespondingtrackforabinarysystem oftwounrelatedstars(apperentbinaries)may withaprimarystarofmassI onthebot- reproduce the behaviour of a genuine binary faint tom; system. 6 Miloneetal.:PhotometricbinariesinfiftyGCs To estimate the quantity of back- 4. Results ground/foreground objects that casually We investigated if the fraction of binaries de- overlapthe cluster CMD we used the galactic pends on the radial distance from the cluster models of Girardi et al. (2008) (with the center. To this aim we divided the ACS field ecception of seven clusters, where we could into four concentric annuli, each containing isolate field stars through proper motions). roughly the same number of stars, and mea- The fraction of apperent binaries has been suredthefractionofbinariesineachofthem. quantifiedbyperformingartificialstartests. In (at least) the ∼ 60 % of the 37 GGCs Wefurtherappliedathetecniquedescribed with good photometry in the innermost re- in Milone et al. 2008 to correct the spread in gions,binariesaremorecentrallyconcentrated color caused by differential reddening and/or thansingleMSstars.Intheotherobjects,their spatiallydependentzeropointphotometricer- distribution is consistent with a flat distribu- rors. tion, probably, as a consequence of the small In order to measure the fraction of high radialcoverageofourfieldofview. massratioqbinaries,westartedbyderivingthe In the following, we present preliminary observednumbersofstarsinregionsA(NA ) OBS resultsthatinvolvebinariesselected fromdif- and B (NB ). Then we evaluated the corre- ferentclusterregions: OBS sponding values of arificial stars (NA and NB )andfieldstars(NA andNB ART)The – insidethecoreradius(ICORE sample); ART FIELD FIELD – betweenthe core and the half-massradius correctnumbersofreal,fieldandartificialstars (HMsample); are calculated as N = P1/c, where c is the i i – outsidethehalf-massradius(O sample). HM completeness. Even if data used in this paper are homoge- Highmassbinaryfractioniscalculatedas neous as they came from the same observ- ingfacility(ACS/HST)andhavebeenreduced f = NOBBS−NFBIELD − NABRT adoptingthesametecniques,theirphotometric bin NA −NA NA OBS FIELD ART quality(andcompleteness)mayvaryfromone cluster to the other, mainly, as a consequence 3.2.Theglobalbinaryfraction ofthedifferentstellardensities. For this reason, it was possible to include InthecaseofMS-MSbinarieswithsmallmass in the I sample only 35 out50 GGCs. In CORE ratios, thedistancefromtheMSRL is compa- addition,thelimitedACSfieldofviewreduced rabletothesizeofphotometricerrorsincolor. thenumberofGGCswithHM andO sam- HM Thereforetheseobjectsappearmixedtosingle plesto46and29respectively. stars, and a more sophisticate statistical anal- Weexploredpossiblerelationsbetweenthe ysis is required to derive their contribution to fraction of binaries and the main parameters theglobalfractionofbinaries. oftheirhostGGCsabsolutevisualmagnitude, In order to estimate the global fraction of metallicity,collisionalparameter,coreandhalf binarysystemsweadoptedastatisticalmethod massrelaxationtime,centraldensityandcon- which is based on the comparison of the ob- centration(fromHarrisetal.1996,2003). served data with more then 10,000 simulated We found an highly significant anticorre- CMDsenrichedbydifferentfractionsofbina- lationbetweenthebinaryfractionandthetotal rieswithagiven f(q).Detailsofthistecnique clusterluminositywithclusterswithfainterab- are outside the purpose of this work and will soluteluminosityhavehigherbinaryfractions. be expleined in a farcoming paper (Milone et This anti-correlationis shown in Fig.2 for the al. 2008). We want emphasize here that the I sample and in Figs.3 and for the HM CORE adopted statistical approach is very sensitive (bottom panel) and O (upper panel) sam- HM to small inaccuracies and the results that we ples. present are to be considered just as approxi- Asimilaranticorrelationhasbeenfoundby mateestimatesoftherealfractionofbinaries Piotto et al (2004) and Moretti et al. (2008) Miloneetal.:PhotometricbinariesinfiftyGCs 7 Fig.4. Fractionofbinarieswithq>0.5inthe coreasafunctionofthecollisionalparameter (Daviesetal.2004) Fig.2. Fraction of binaries with q > 0.5, 0.6 and 0.7 and global fraction of binaries in the coreasafunctionofthehostGGCsluminosity. duetoencountersasdescribedbyDaviesetal. (2004). We found only a marginalcorrelation betweenthebinaryfractionandtheclustercol- lisionalparameter References Anderson, J., Sarajedini, A., Bedin, L. R., King,I.R.,Piotto,etal.,submittedtoApJ Davies, M. B., Piotto, G., & De Angeli, F., 2004,MNRAS,349,129 GirardiL.,etal.,inpreparation HarrisW.E.,1996,AJ,112,1487 Hutp.etal.,1992,PASP,104,981 Mateo M., 1996 in ”The Origins, Evolution and Destinies of Binary Stars in Clusters”, E. F. Milone & J. C. Mermilliod eds., San FranciscoASPConf.Ser.,90,21 Milone,A.P.,Piotto,G.,Bedin,L.R.,etal.,in preparation Moretti, A., De Angeli, F., & Piotto, G., sub- Fig.3. Fraction of binaries with q > 0.5 for mittedtoA.&A theO (top)andHMsamples(bottom) HM Piotto, G., De Angeli, F., King, I. R., et al. 2004,ApJ,604,L109 Sollima A., Ferraro F. R., Fusi Pecci F, between the frequency of blue stragglers and SarajediniA.,2007,MNRAS,380,781 the luminosity of the cluster. It is very tempt- ing to connect BSS and binaries populations in GGCs: the BSS frequency can be in fact related to the evolution of the binary fraction