Chapter3

Photometricvariability in theold openclusterM 67I. Clustermembersdetectedin X-rays

MaureenvandenBerg, KeivanG. Stassun,FrankVerbunt& RobertD. Mathieusubmitted to Astronomy & Astrophysics

Abstract – We studyphotometricvariability amongthe optical counterpartsof X-ray sourcesin theold openclusterM 67. Thetwo puzzlingbinariesbelow thegiantbrancharebothvariables:for S1113the photometricperiodis compatiblewith the orbital period,S1063eithervarieson a periodlongerthantheorbital period,or doesnot vary periodically. For thespectroscopicbinariesS999,S1070andS1077 the photometricandorbital periodsaresimilar. Anothernew periodicvariableis the main-sequencestarS1112,not known to bea binary. An increaseof thephotometricperiodin theW UMasystemS1282(AH Cnc) is in agreementwith a previously reportedtrend. Six of theeightvariableswe detectedare binarieswith orbital periodsof 10 daysor lessand equalphotometricand orbitalperiods.ThisconfirmstheinterpretationthattheirX-ray emissionarisesin thecoronaof tidally lockedmagneticallyactive stars.No variability wasfoundfor thebinarieswith orbital periodslongerthan40days;theirX-ray emissionremainsto beexplained.

31

CHAPTER 3

3.1 Introduction

Twentyfivemembersof theold openclusterM 67havebeendetectedin X-rays(Belloni etal.1998).At theageof M 67 (4 Gyr, Dinescuet al. 1995)therotationof singlestarsis too slowto generatedetectableX-rays.Therefore,theX-ray emissionof many M 67 sourcesprobablyarisesin interactingbinaries.Indeed,onesourceis known to bea cataclysmicvariable.Ninesourcesarebinarieswith orbitalperiodsof 10daysor less,presumablyRSCVn typesystems,whoseX-rays aredueto thecoronaeof magneticallyactive starsforcedto corotateby tidalinteraction(seeTable3.2). However, not all X-ray sourcesarebinaries,e.g. onesourceis ahotwhitedwarf, andsomeothersarestarswhichdo notshow signsof binarity.

Therearefive peculiarbinarieswhoseevolutionarystatuseswe currentlydo not under-stand.They arefound in thecolour-magnitudediagramin locationswhich cannotberepro-ducedby combiningthelight from any two memberson themainsequence,subgiantand/orgiantbranches.Two of themhave longorbital periodswhichexcludestrongtidal interaction.A sixth binary with a long orbital period lies to the blue of the giant branchwhich canbeexplainedby thesuperpositionof thelight of agiantanda turnoff star.

A spectroscopicstudy of thesepeculiarsystemswas presentedin van den Berg et al.(1999)[Chapter2]. Herewe reportour photometricstudyof thesesourcesandof otherX-ray sourcesthathappento be in the samefields of view. The photometryof S1082will bepublishedseparately(vandenBerg et al. 2001)[Chapter5]. Theobservationsandanalysesaredescribedin Sect.3.2.Resultsarepresentedin Sect.3.3,followedby theinterpretationanddiscussion– includingcomparisonwith earlierwork – in Sect.3.4. Sect.3.5summarisesourconclusions.Thevariability of starsnot detectedin X-raysbut includedin our observationswill bethesubjectof PaperII (Stassunet al., in preparation)[Chapter4].

3.2 Data and analysis

3.2.1 Observations

U , B, V , I andGunni photometrywasobtainedwith the 0.90-mtelescopeat Kitt Peak,the0.91-mESODutchTelescopeatLaSillaandthe1-mJacobusKapteynTelescopeonLaPalma.Combined,thefiveobservationrunsspanaperiodof two years(seeTable3.1).Fig.3.1showsthelocationof theobservedfields.During run 1 weatherconditionsweregoodwith a typicalseeingof 0���� 9 to 1���� 4. The observationsweremadeduring andaroundfull moonbut moonillumination wasnot a problem. Weatherconditionsduring runs2 and3 weregood,witha typical seeingof 1� ��� 6. During run 4 the typical seeingwas1���� 5 while the quality of someimageswasaffectedby the brightnessof the nearbymoon. The same,at a seeingbetween1���� 5 and3

���, is truefor thelastrun, thatin additionwastroubledby partialcloudiness.This is

reflectedin therelatively largeerrorsof thelasttwo runs.Every X-ray sourceof Belloni et al. (1998)wasmonitoredin at leastonerun, exceptfor

thefaintcataclysmicvariableEUCncandthehotwhitedwarf. Themainpurposeof run1 was

32

PHOTOMETRIC VARIABILITY IN M 67 I.

Figure3.1: A 35x 35arcmin2 regionof M 67centredonthestarS783.Thecoordinatesof thesourcesin thisfield aretakenfrom theUSNO-A1.0catalogue.Theareasmonitoredin thefiveobservationrunsareindicatedby thesquares(seealsoTable3.1). Theopencirclesmarktheopticalcounterpartsto theX-ray sourcesthat arediscussedin this paper;the diamondmarksS1082that we discusselsewhere(vandenBerg etal. 2001)[Chapter5].

to monitorvariability of S1113andS1063,of run 2 to monitorS1113andof runs3 to 5 tomonitorS1082. This meansthatexposuretimeswerechosento optimisethemeasurementsof thesestars.During run 5, five additionalfieldscontainingX-ray sourceswereobservedinB andV onceor twicepernightto searchfor obvioussignsof variability. As S364andS1237areverybrightstars(seeTable3.2)thequalityof theimagesof fainterstarsin thesefieldsarepoor. This affectsthequality of the light curvesof theX-ray sourcesin thefield of view ofS1237(i.e. S1242,S1270andS1282).

3.2.2 Data reduction and light curve solution

StandardIRAF routineswereusedto removethebiassignalandflatfieldtheimages.Aperturephotometryfor all the starswas donewith the DAOPHOT.PHOT task. For eachindividualrun, sourcecountswereextractedwithin a fixedradiuswith a valuedependingon theseeingconditions.Thestarsin M 67areseparatedwell enoughto avoid problemsof crowding.

The light curve solution was computedwith the algorithm of ensemblephotometryasdescribedby Honeycutt (1992).In thismethod,themagnitudesof all thestarsonevery frame

33

CHAPTER 3

Run

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34

PHOTOMETRIC VARIABILITY IN M 67 I.

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1993

);fo

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with

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for

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.

35

CHAPTER 3

areusedto createan ensembleaveragewith respectto which the brightnessvariationsaredefined.Framesthathave a large offset from this average(e.g. dueto badseeing)show upasdeviant observationsandcanbe excluded. For a given star, errorswereassignedto thedatapointsby estimatingthetypical spreadin the light curvesof starsof similar magnitude.In mostcasesthe formal errorsfrom the PHOT taskarenegligible; if not, we usedthis errorinstead.Thedifferentdatasetswereanalysedindividually.

As exposuretimeswerechosento optimisethemeasurementsof theX-ray sourcesin eachfield, thephotometricprecisionasa functionof stellarbrightnessvariesfrom onerun to thenext. Generallyspeaking,thephotometricprecisionof thebrightest(unsaturated)starsin ourexposuresis flat-field limited to 5–10mmag.This precisionlevel typically holdsfor starsupto 2–2.5magfainterthanthe brightestsources,andthenbecomesphoton-noiselimited anddegradesfor still fainterstars.ThebestoverallprecisionwasachievedonourKitt Peakframes(run1; Table3.1),for whichthebrighteststars(B � 12,V � 12,I � 11� 5) haveσmag 0.007,0.005,0.005in B, V , andI, respectively. Theprecisionbeginsto degradeataround14thmag.For thefaintestsources,atabout18.5mag,theprecisionis 0.05–0.1mag.Wereferthereaderto PaperII [Chapter4] for a full discussionof thephotometricprecisionin our observations.

A simplezero-pointshift is appliedto the measurementsin eachfilter to roughly placethe instrumentalmagnitudeson an absolutescaleasdescribedin PaperII [Chapter4]. Thelight andcolour curvesthat arepresentedin Fig.3.3-3.5show the variationswith respecttothemeanmagnitudeandcolour(seeTable2 of PaperII) [Table4.2].

3.2.3 Search for variability

Our searchfor variability is a two-stepprocess.First we performa χ2-teston the individuallight curvesfor eachfilter for eachrun, to calculatetheprobabilitythatthelight curvesof theX-ray sourcesarecompatiblewith beingconstant.As theintrinsicpropertiesof thevariabilityneednot be thesamein light curvesof differentruns(in particularfor brightnessvariationsdue to spots),we considereachlight curve separately. To remove accidentaloutliers, theminimumandmaximumdatapointsareexcluded.A staris labeledasa probablevariableiftheprobability for beingconstantis smallerthan0.3%in any of the light curves. Eight starsaremarked asprobablevariables(seecolumnvar in Table3.2). For six of thesestarsthevariability is notdetectedin every light curve. In mostcaseswecanascribethis to differencesin sensitivity betweenrunsor betweendifferentfiltersof acertainrun,or to differentdurationsof runs. For S1063, S1070 and S1077 it seemsthat the variability itself haschangedasdiscussedbelow.

We next performa Lomb-Scargle time-seriesanalysis(Scargle 1982)to searchfor peri-odicity in thelight curves. In caseswhenmultiple light curvesin a givenfilter aremarkedasvariable,thoselight curvesarecombinedfor theperiodsearch;no distinctionwasmadebe-tweenI andGunni. If theresultingperioddoesnotproduceasmoothfoldedlight curve,datafrom differentrunsareanalysedseparately;thiswill beindicatedfor eachsourcein Sect.3.3.A periodogramis computedwith 1000frequenciesbetweenaminimumandmaximumperiod

36

PHOTOMETRIC VARIABILITY IN M 67 I.

Pmin andPmax correspondingto twice the typical samplingperiodandthe full lengthof thelongestobservation run, respectively (seeTable3.1). We choosethe periodof the highestpeakin theperiodogramasour first estimatefor periodicity in thedata.However, aswill bediscussedbelow, external informationoften leadsus to immediatelyneighbouringpeaksofcomparablesignificance.

Photometricperiodshave beendeterminedpreviously for thetwo contactbinariesS1036(Gilliland et al. 1991)andS1282(e.g.Kurochkin1979).Therefore,we look for periodsin anarrow window insteadof therangelimited by Pmin andPmax. In bothcases,we find thatthepower at half thephotometricperiodis far higherthanat thephotometricperiod,dueto thesymmetryin thelight curve. For S1036wesearchfor periodsbetween0.215and0.225days,for S1282between0.175and0.185days. Theperiodogramis computedfor 5000pointstoincreasetheresolution.

An estimatefor thechancedetectionof a period,i.e. theprobability that the light curvedoesnot have the periodicity indicatedby the highestpeak,is expressedby the false-alarmprobability. In thecaseof theLomb-Scargle periodogramthefalse-alarmprobabilityfollowsthe expression:1 �

1 exp � z ��� m, wherez is the heightof the peakandm is the numberof independentfrequencies.Horne& Baliunas(1986)demonstratedthat this numbercanbesmallerthanthenumberof datapointsespeciallyin setsof unevenlysampleddata.Thevalueof m is obtainedby fitting thisexpressionto aprobabilitydistributiongeneratedby measuringthemaximumpeakheightsin periodogramsof 5000simulatedrandomdatasetswith thesametime-samplingandthesamespreadin themeasurementsastheactuallight curve.

Photometricperiodswith a false-alarmprobability smallerthan 1% are summarisedinTable3.2. Thesecorrespondto the positionof the highestpeakin the periodogramunlessindicatedotherwise.To estimatetheerror in thebestperiodwe proceedasfollows. For thecorrectperiod the light curvesdefinedby the first and last observationscoincide. A smallchangedP in theperiodcausesa smallphaseshift:dφ T ��� P � dP �� T � P, whereT is thetime spanof thedataset.For eachlight curve we estimate,by visual inspection,a maximumdφmax for which the light curvesdo not split perceptibly. This correspondsto a maximumacceptableperiodchangeof

dPP dφmaxP

T � dφmaxP(3.1)

Thevaluefor dφmax thatwechooseis listedin Table3.2.

3.3 Results

We have divided the sourcesinto periodically(Sect.3.3.1)or non-periodically(Sect.3.3.2)varying stars. The periodically varying starsare two W UMa systems,four spectroscopicbinariesandonestarnot known to beabinary, i.e. S1112.

37

CHAPTER 3

3.3.1 Periodic variables

W UMa systems

TheW UMa light curvesareplottedversusphotometric phasewherephase0 correspondstothemomentof photometricprimaryminimum(seeFig. 3.3).

S 1282 is theW UMa variableAH Cncdiscoveredby Kurochkin(1960). Theperiodogramsof the total B andV datasetsshow peakswith a spacingof � 4 10� 5 and � 6 10� 4 daysdueto the two-yearandthe two-monthgapsin our observations,respectively (seeFig.3.2).The highestpeaksin the B andV periodogramsarefound at 0.180226and0.180270days,respectively, which correspondsto two neighbouringpeaksin the periodogram.We foldedthedataontwice thoseperiodsbut find thatthepeakat0.180226daysrepresentsbestthetrueperiod:whenwe usethelongerperiod,thedeeperprimaryminimaof thefirst run fall on topof thesecondaryminimaof thefourth run. Thuswe concludethat thephotometricperiodis0.360452days.I datawereonly obtainedduringrun 1 andcannotprovideanequallypreciseperiod.

In additionto short-termvariationson a time scaleof roughly 9 to 10 years,Kurochkin(1979)findsa secularincreaseof theperiodof AH Cnc.His ephemerisfor theprimarymini-mumis:

Min I 2441740� 7166� 27��� 0�d36044098� 53� E� 1�d56� 38� 10� 10E2 (3.2)

Thisephemerispredictsaperiodduringthetimeof ourobservationsbetween0.3604447daysand0.3604479days,in agreementwith our result. We note that periodchangesof similarmagnitudehavebeenfoundfor othercontactbinaries.

Weobserveno significantcolourchangesin V I andB V .

S 1036, or EV Cnc,wasdiscoveredto beacontactbinaryby Gilliland etal. (1991)whoreporta periodof 0.44125days.TheB andV periodogramsshow fine structurefrom the two-yearandtwo-monthgapsin thedata. In bothsets,that includedatafrom run 1, 4 and5, we findthesamebestperiodof 0.22078days.Whenfoldedon this period,thelight curvesshow thesameeffect of interchangingprimaryandsecondaryminimaasdescribedfor S1282.Properphasingis obtainedwith theperiodof 0.22072daysderivedfrom thepeaknext to thehighest.Theperiodthat correspondsto thehighestpeakin theperiodogramof the I datais 0.22091days,but againinterchangesminima. The periodof 0.22072dayscoincideswith a nearbypeakof similarheight.U datawereonly obtainedduringrun5 andcannotprovideanequallypreciseperiod.In Fig. 3.3thelight curvesarefoldedon thedoubleperiodof 0.44144days.

A light curve foldedon theperiodgivenby Gilliland et al. shows that this periodcannotbecorrectfor theepochof our observations.SinceGilliland et al. do not specifytheerror intheperiod,wecannottell whethertheperiodhaschangedsignificantly.

Weseeno significantchangesin any of thecoloursU V , B V or V I.

38

PHOTOMETRIC VARIABILITY IN M 67 I.

Figure3.2: Periodogramsfor thevariablestars. The arrow indicatesthephotometricperiodor halfthephotometricperiodlistedin Table3.2. Thedottedline marksthepositionof theorbital periodforS1070,S1077andS1113,half theorbital periodfor S999andthepositionof theperiodaspredictedby Kurochkin(1979)for S1282.Thehorizontalerrorbarsgive our estimatefor theuncertaintyin theperiod.

39

CHAPTER 3

Figure3.3: Light curvesof thetwo contactbinariesS1036(EV Cnc)andS1282(AH Cnc)foldedonthenewly derivedperiods(seeTable3.2).Datafrom differentobservingrunsaremarkedwith differentsymbols:opencirclesfor run1, filled circlesfor run4 andopentrianglesfor run5.

Spectroscopic binaries

We note that the light curvesof the spectroscopicbinariesaregivesas function of orbitalphasewherephase0 correspondsto themomentof maximumpositive radialvelocity of theprimarystar(primaryreceding).

S 999 TheB andV dataof thefirst runshow variability with asemi-amplitudeof � 0� 03mag.Only theperiodfoundin theB datahasafalse-alarmprobabilitysmallerthan1%. Thehighestpeakin theperiodogramis foundat 4.6� 1.0days(Fig. 3.2),but this perioddoesnot producea smoothlight curve. We suggestthat the peakat 4.6 daysis a harmonicof photometricvariationonor neartheorbitalperiodof 10.06days.Notethatthedurationof thefirst runwas10nights,soourperiodsearchdoesnotextendupto theorbitalperiod.Gilliland etal. (1991)reportaperiodof 9.79days(noerroris given)with anamplitudeof only 0.013mag.

In Fig.3.4wefold theB andV dataontheorbitalperiod.Accordingto theorbitalsolutionof Mathieuet al. (1990),theminimumbrightnessoccursaroundorbital phase0. TheB Vcolourdoesnot varysignificantly.

S 1070 A period of 2.6� 0.1 daysis detectedin the B andV light curves of run 3 with asemi-amplitudeof thevariationof � 0� 03mag.

Thephotometricpropertiesof S1070havechangedwith respectto run1. If thevariations

40

PHOTOMETRIC VARIABILITY IN M 67 I.

seenin thethird run (σ � 0� 014magin V ) werepresentin thefirst run, they wouldhavebeendetected.

In Fig. 3.4 all dataof run 3 arefoldedon theorbital periodwhich is compatiblewith thephotometricperiod.Thephotometricminimumoccursaroundorbitalphase0.1-0.2(ephemerisfrom Lathametal.,privatecommunication).TheV Gunni colourcurveshowsperiodicvari-ationswith asemi-amplitudeof � 0� 03magsuchthatthestarbecomesbluerasit getsbrighter.

S 1077 All light curvesof thisstararemarkedasvariableexceptfor theU andB dataof run5,probablydueto thereducedsensitivity of run 5, andtheV andI dataof run 1. Thelattercanpointata realabsenceof variationascouldbethecasein S1070;thevariationsof run3 (σ �0.018magin V ) werenotseenin run1. In theperiodogramsof thecombineddatapeakswitha false-alarmprobability smallerthan1% arefound near0.6 and1.3 days. However, whenfoldedon theseperiods,thelight curvesdonot look smooth.Thereforewealsoanalyseddataof thedifferentrunsseparately. Only thelight curvesof run3, with thehighestprecision,looksmoothwhenfoldedontheperiodsof about1.4days(seeTable3.2)whichhaveafalse-alarmprobabilitysmallerthan1% only in B, V andGunni. This perioddoesnot correspondto thehighestpeakin theV periodogram,which is foundat 0.60days. Thesemi-amplitudeof thevariationis small, � 0� 03magin V .

Thephotometricperiodis compatiblewith theorbital period;we considerthelatterto bethe true period for the photometricvariability. The dataof run 3 are folded on the orbitalperiodin Fig. 3.4. Thephotometricminimumoccursaroundphase0.9-0.Thecoloursdo notvarysignificantly.

S 1113 As alreadynotedby Kaluzny & Radczynska(1991)thisstaris aphotometricvariable.In our observations,the B andV datacover the longesttimespanandcanthereforeprovidethe mostaccuratephotometricperiod. The periodogramis computedfor 25000periodstomake the period bins smaller than the accuracy of our period determination(0.001). Theperiodogram(seeFig. 3.2) againshows fine structurewith a spacingasexpectedfrom thetwo-yeargapbetweenruns1 and5. Themaximumpeakindicatesa periodof 2.833� 0.001days,which is not compatiblewith the orbital period. The orbital periodcorrespondsto aneighbouringpeakin theperiodogramat 2.822� 0.001days(in V ; 2.823� 0.001daysin B).Given the lack of significantdifferencein peakheights,thephotometricandorbital periodsmay be the same. Therefore,the light curves in Fig. 3.4 are folded on the orbital period.For the B light curve we find a similar result. The periodsfound in the U and I bandarecompatible,but lessaccurate(seeTable3.2).

Datatakenduringdifferentrunsat thesameorbital phasegive rise to scatterin the lightcurve, asseenin the top panelof Fig. 3.4. This could be explainedif the amplitude,phaseand/ortheperiodof thevariability haschangedbetweentheruns.Whenanalysedseparately,thelight curvesof run1 and2 giveaperiodof 2.8� 0.1and2.83� 0.03days,respectively; theuncertaintyis too large to detecta periodchange.Assumingthat the photometricperiodistheorbital periodwe concludethat theamplitudeor thephaseof thevariationshaschanged,

41

CHAPTER 3

Figure3.4: Light curvesof S1112(foldedon thephotometricperiod)andof S999,S1070,S1077.Datafrom differentobservingrunsaremarked with differentsymbols:opencirclesfor run 1, filledtrianglesfor run2, andopensquaresfor run3.

42

PHOTOMETRIC VARIABILITY IN M 67 I.

Figure3.4 – continued:Light curvesof S1113(folded on the orbital period). Datafrom differentobservingrunsaremarkedwith differentsymbols:opencirclesfor run1, filled trianglesfor run2, andopentrianglesfor run5.

43

CHAPTER 3

eitherof which is possibleif thevariationis causedby astarspot.We show separatelythe light andcolourcurvesfrom runs1 and3 in the lower panelsof

Fig. 3.4. Thecolourvariationis significantonly in V I in run 1 andB V andV Gunniin run 3, suchthatthestarbecomesbluerasit brightens.

S 1112

The dataof the first (B, V , I) andsecond(V ) runsshow variability but only in the B andVlight curvesdo we find significantperiodsof 2.7� 0.2 and2.65� 0.03days,respectively. InFig. 3.4thedataarefoldedon thelatterperiod.Theamplitudeof thevariationis againsmall,only � 0� 04mag.Weakcolourvariationsareonly seenin V Gunni andappearto bein phasewith thelight curve; thestarbecomesbluerasit brightens.No informationon binarity fromradial-velocitymeasurementsexistsfor this star.

3.3.2 Non-periodic variable: S 1063

Photometricvariability of thisstarup to 0.18magwasinferredby Racine(1971)from thedifferencesbetweenpublishedvaluesof themagnitude.Rajamohanetal. (1988)andKaluzny& Radczynska(1991)alsonotedits variability, but only the latter provide light curves(forDecember9 to 15 1986,seeFig. 3.5). This binary wasincludedin all our runsexcept thesecond.Thelight curvesof run 1 and3 clearlyshow variability (seeFig. 3.5)on a long timescale. The variability during run 1 is similar to that observed by Kaluzny & Radczynska.Thelongestinterval of continuousobservationwaseighteenconsecutivenightsduringrun 3,which is almostthe lengthof theorbital period(18.39days). Thereforeduring any onerunwecouldnothaveestablishedperiodicityon theorbital period.

Data from run 1 and3 werecombinedto look for periodsup to 18 days. The highestpeaksin theperiodogramarefoundbetween17and18days,all with afalse-alarmprobabilitysmallerthan1%. However, thefoldedlight curvesshow noconvincingperiodicity. Therefore,noactualperiodis specifiedin Table3.2.

Theamplitudeof thevariationincreasestowardstheblue.

3.4 Discussion

We have studiedthe optical photometricpropertiesof X-ray sourcesin M 67. Eight photo-metric variables,including threenew variables,were found amongthe twenty two sourcesthatarediscussedin thispaper. In all casestheamplitudesof thevariationsaresmall,rangingfrom 0.03to 0.4magin V .

44

PHOTOMETRIC VARIABILITY IN M 67 I.

Figure3.5: Light curvesandcolourcurvesof S1063.Datafrom differentobservingrunsaremarkedasin Fig. 3.3. Thedatafrom Kaluzny & Radczynka(1991)of December9-151986areincludedontheleft; thebrightnessvariationsaredefinedwith respectto themeanmagnitudeof thelight curve.

Thelight curvesof thetwocontactbinariesS1036andS1282arisethroughpartialeclipsesandellipsoidalvariationsof thetidally deformedstars.TheirX-raysarebelievedto beemittedby thehotcoronaeof themagneticallyactivecomponents.

Theprimaryandsecondaryeclipsesof contactbinariesusuallyareof similar depth.Thishasbeeninterpretedasevidencethatbothstarshave almostthesametemperature,which inturn is evidencefor energy exchangebetweenthetwo starsin contact.Unequaldepthsof theprimary andsecondaryeclipsesthenimplies differenttemperaturesfor both stars,i.e. poorthermalcontact. The thermalcontactcanbe suppressedwhenthe systembecomes(semi-)detached.It hasbeensuggestedthatsuchphasesof poorthermalcontactoccurperiodicallyincontactbinaries(Lucy & Wilson1979).In view of this interpretationit mayappearsurprisingthatweseeunequaleclipsesbut no evidenceof colouri.e. temperaturevariationsin S1036.

S1036is interestingaseitheran immediateprogenitorof a contactbinary, or becauseit

45

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is in thesemi-detachedphaseof thethermalcycle of a contactbinary. Theupperlimit on thecolourvariationsin S1036is about0.05in B V (Fig. 3.3). Radial-velocity measurementsarerequiredto determinetheevolutionarystatusof this systemandto convert theupperlimitto thecolourvariationsinto anupperlimit on temperaturedifference.

The small amplitudeof the S1036light curve indicateseithera small inclination or anextrememassratio (e.g. Rucinski 1997). In a volume-limitedsampleof contactbinaries,Rucinski(1997) found that only two amongthe 98 systemshave light curveswith unequalminima. Oneof thosetwo alsohasa relatively small amplitudeof variationof about0.25mag.

Another featureof W UMa light curvesassociatedwith unequaleclipsesis that at firstquadrature(phase0.25)thestaris brighterthanat secondquadrature(phase0.75). This hasbeenexplainedwith a hot spoton the secondary, possiblyasa resultof masstransferin asemi-detachedsystem(e.g.Rucinski1997).Thiseffect is alsovisible in S1036.

Within thetwo yearsof ourobservationsweseeevidencefor variability of thelight curveof S1282: thesecondaryminimumof run 1 appearsto belessdeepandflatterthanobservedin run 4. A similar variation was seenby Gilliland et al. (1991) who notedthat in theirobservationsof 1988thesecondaryeclipsehadaflat shape,while theobservationsby Whelanet al. (1979)donefrom 1973to 1976showeda roundedsecondaryminimum. Thetimescaleof thesevariationsis indicativeof thepresenceof spots.

The light curvesof theperiodicvariablesS999,S1070,S1077andS1113displayonlyonemaximumper cycle. S1113andS1070alsoshow colour variationsin phasewith thebrightness.For all four systemsthereis indication for variability in the light curves. Theamplitudeof thevariationin S999is differentin ourobservationsandthoseof Gilliland etal.(1991);in S1070andS1077therehaslikely beena changebetweenrun 1 andrun 3 andinS1113betweenrun1 and2. Theshorttimescaleof thisvariationis anindicationof brightnessmodulationsby spots.Remarkably, in all casestheminimumoccursaroundorbital phase0.Wehaveno explanationfor this.

All four systemsarespectroscopicbinarieswith photometricperiodscompatiblewith theorbital period. Thecircularorbital periods,their X-ray luminosity, andtheCaII K emissionin thecaseof S999,S1077andS1113(Pasquini& Belloni 1998,vandenBerg et al. 1999[Chapter2]) make thesestarslikely candidatesfor magneticallyactivesystemsdueto oneorbothstarsbeingtidally locked. This wasalreadysuggestedby Belloni et al. (1998)andourlight curvessupporttheir interpretation.

Thelight curveof S1112showslow-amplitudeperiodiclight andcolourvariationssimilarto thoseseenin thesefour binaries. This star hasnot beenmonitoredfor radial-velocityvariationsbut the X-ray luminosity and the light curve are typical for magneticallyactivesystemswhichsuggeststhatS1112is abinarywith anorbital periodof about2.65days.

We do not understandthevariability thatwe observe for S1063.Thesourceshows spec-troscopicsignaturesof magneticactivity (van denBerg et al. 1999)[Chapter2]. However,if oneof the starsin this binary would be corotatingnearperiastron,we expecta rotationperiodof 14.6 days(Eq. 42 of Hut 1981)which is excludedby the observationsof run 3.

46

PHOTOMETRIC VARIABILITY IN M 67 I.

Figure 3.6: Visual magnitudeversusorbital period of the M 67 binariesdetectedin X-rays. Thesizeof the symbol is a measurefor the logarithmof the X-ray luminosity (0.1-2.4keV, in erg s� 1)asindicatedin thefigure. Eccentricbinariesareindicatedwith triangles,binarieswith eccentricitiescompatiblewith zero (within the 3σ-error) with circles. Filled symbolsare systemsfor which wedetectedphotometricvariability. S1112is indicatedwith afilled square.

We concludethateitherthestardoesnot vary periodicallyor that theperiodof variability islongerthan18days.Moreobservationscoveringalongertimespanarerequiredto understandthe natureof the variability. Our findingsarein contrastwith thesuggestionby Kaluzny &Radczynska(1991)thatS1063,aswell asS1113,arehighly evolvedW UMa-typebinaries.

3.5 Conclusion

Of the twenty two X-ray sourcesin M 67 thatwe discuss,sixteenarespectroscopicbinarieswith known orbital periods.Our survey for opticalphotometricvariablesamongtheseX-raysourceshasestablishedeight variables. Seven of theseareamongthe sixteenbinaries,thebinary statusof the eighth, S1112, is not yet known. In addition, Gilliland et al. (1991)observed periodicoptical variationin threemoreof the X-ray binarieswith amplitudestoolow to bedetectedby us:S1019(semi-amplitude0.015mag),S1242(semi-amplitude0.0025mag)andS1040(semi-amplitude0.012)mag.Thustenof thesixteenX-ray binariesin M 67areopticalvariablesat the �

�0.01maglevel.

Belloni et al. (1998)havesuggestedthatrapidstellarrotationresultingfrom tidal lockingresultsin enhancedmagneticactivity andX-ray emission.Fig.3.6showsthevisualmagnitudeversusorbital periodof thespectroscopicbinaries.With theexceptionof S1040andS1112,all variableshave orbital periodslessthan20 daysandV � 15. In all casesbut S1019and

47

CHAPTER 3

S1063, the photometricperiod is equalto the orbital period or, in the caseof S1242, theorbitalperiodnearperiastron.Evidentlytidal lockinghasbeenestablished,leadingto rotationof at leasttheprimarystarthat is morerapidthantypical for solar-massstarsat 4 Gyr. Thusour resultsestablishakey premiseof theBelloni et al. (1998)picturefor theX-ray emission.Furthermore,if the causeof the observed optical variability is indeedspot modulationofthe observed flux, thenthe presenceof the requiredlarge spotsis consistentwith enhancedmagneticactivity in thesestars. The X-ray emissionand optical variability propertiesofS1019andS1063requirefurtherinvestigation.

Threebinarieswerenot detectedasvariablesdespitetheir shortorbital periods.S972 isthefaintestof thebinarysampleatV 15� 37,andsoits variability mayhavegoneundetected.TheX-ray luminositiesof S1045(Porb 7� 6 days)andS1234(Porb 4� 3 days)areamongthe lowestof the binary X-ray sourcesandindicatelow activity levels; this canexplain theabsenceof optical variability dueto spots.Rajamohanet al. (1998)have notedS1234asapossibleopticalvariable(semi-amplitude� 0� 16mag)whichsuggeststhattime-variability ofthespotphenomenoncanalsoexplain theabsenceof opticalvariation.

Theinterpretationof S1040andof theremainingthreeX-ray binariesS760,S1072andS1237maybethemostchallenging.All have longorbital periods.Giventheirwider separa-tionstidal lockingis notexpectedandsotheconsequentstellarrotationsmaybecharacteristicof singlestars.As such,their lackof largespotsandconsequentphotometricvariability is notasurprise.Nonetheless,thesebinariesareX-ray sources.TheirX-ray emissionremainsto beexplained.

No large radial-velocity variationswere found for S775 and S1270 (σ is 0.9 km s� 1

in 12 observationsspanning5200daysand0.7km s� 1 in 7 observationsspanning800days,respectively, seeMathieuetal. 1986);if thesestarsarebinariestheirperiodsmustberelativelylong. Thustheir X-ray luminosities,asthoseof S364,S628andS1027for which no radial-velocity informationis available,remainunexplained.

Acknowledgements – The authorswish to thank Magiel Janson,Rien Dijkstra, GertieGeertsema,RemonCornelisseandGijs Nelemansfor obtainingpartof thedatausedin thepaper. We alsowantto thankDavid Lathamfor computingpreliminaryorbital solutionsfor four spectroscropicbinariestosupportthis research;theradial-velocity measurementsarepartof a largerstudyof M 67 binariescar-riedoutby D. Latham,A. Milone andR.D.Mathieu.TheKitt PeakNationalObservatoryis partof theNationalOptical AstronomyObservatories,which is operatedby the Associationof UniversitiesforResearchin Astronomy, Inc. (AURA) undercooperative agreementwith theNationalScienceFounda-tion. TheJacobusKapteyn Telescopeis operatedontheislandof La Palmaby theIsaacNewtonGroupin theSpanishObservatorio del Roquede los Muchachosof the Instituto deAstrofisicadeCanarias.TheDutch0.91-mTelescopeis operatedat La Silla by theEuropeanSouthernObservatory. IRAF isdistributedby theNationalOpticalAstronomyObservatories,whichareoperatedby theAssociationofUniversitiesfor Researchin Astronomy, Inc., undercooperative agreementwith theNationalScienceFoundation.MvdB is supportedby theNetherlandsOrganizationfor ScientificResearch(NWO).

48

PHOTOMETRIC VARIABILITY IN M 67 I.

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