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Astron. Nachr./AN000,No.00,1–6(0000)/DOIpleasesetDOI! Light curve solutions of the ultrashort-period Kepler binaries(cid:63) D.Kjurkchieva1,(cid:63)(cid:63)andD.Dimitrov2 1 DepartmentofPhysics,ShumenUniversity,115Universitetska,9700Shumen,Bulgaria 2 InstituteofAstronomyandNAO,BulgarianAcademyofSciences,Tsarigradskoshossee72,1784Sofia,Bulgaria Received...2014,accepted...2014 Publishedonlinelater 5 1 Keywords binaries:close–binaries:eclipsing–methods:dataanalysis–stars:fundamentalparameters–stars:indi- 0 vidual(KID4921906,KID1572353,KID8108785,KID6309193,KID12055255,KID9532219) 2 Wecarriedoutlightcurvesolutionsoftheultrashort-periodbinarieswithMScomponentsobservedbyKepler.Allsix n targetsturnedoutalmostinthermalcontactwithcontactorslightlyovercontactconfigurations.Twoofthem,KID4921906 a andKID6309193,arenoteclipsingbutrevealellipsoidalandspotvariability.OneofthecomponentsofKID8108785 J exhibitsinherent,quasi-sinusoidal,small-amplitudevariability.KID12055255turnedoutaveryrarecaseofultrashort- 1 periodovercontactbinaryconsistingoftwoMdwarfs.OurmodelingindicatedthatthevariabilityofKID9532219isdue 2 toeclipsesbutnottoδSctpulsationsasitwaspreviouslysupposed. ] R (cid:13)c 0000WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim S h. 1 Introduction logicalclassificationanddeterminationoftheglobalparam- p etersofsomesystemsoftheKeplerEBcatalog. - o Most of the contact binaries consisting of solar-type com- Several individual Kepler EBs were studied in details r ponents have orbital periods within 0.25 d < P < 0.7 d. (e.g., Southworth et al. 2011; Steffen et al. 2011; Welsh et t s Rucinski (1992) found that they show a short-period limit al.2011;Winnetal.2011).Thispaperisdevotedtostandard a at about 0.22 d. But the modern large surveys allowed to (”manual”)lightcurvesolutionsoftheultrashort-periodbi- [ discover targets beyond this limit (Maceroni & Rucinski nariesfromtheKeplerEBcatalog. 1 1997;Maceroni&Montalban2004;Weldrake2004;Rucin- v ski2006,2007;Pribullaetal.2009;Lohretal.2014;Qian 8 2 Selectionoftargetsandpreliminary etal.2014,etc.). 3 preparationofthedata 0 The well-studied binaries with periods around and be- 5 low cut-off limit (ultrashort-period systems) and MS com- 0 Asacontinuationofourinterestinbinarieswithextremely ponents are quite rare but important objects for the astro- . small orbital periods (Dimitrov & Kjurkchieva 2010), we 1 physics,especiallyforthestellarevolution. 0 reviewedtheKeplerEBcatalog.Itcontains22targetswith Until two decades ago the statistics of contact binaries 5 periods P < 0.23 d (for better statistics we put an upper 1 wasparticularlyaffectedbythetrendtodiscoverrelatively limit 0.23 d that is slightly bigger than the cut-off limit of : largelight-curveamplitudes,butveryrecently,thehugesur- v 0.22d). veys (ROTSE, MACHO, ASAS, SuperWASP, etc.) led to i Although Prsa et al. (2011) reported about visual in- X discoveriesofmanylow-amplitudesystems. spectionofeverytargetandcullingabout27%oftheirini- r Lately,Kepler providesunique,unprecedentedprecise, a tial sample as nonEBs (RR Lyr-, γ Dor-, δ-Sct type stars), extendedandnearlyuninterrupteddatasetforalargenum- we carried out new visual review of the chosen 22 targets. berandvarietyofstars.Abovetwothousandseclipsingbi- Weconcludedthat13ultrashort-periodstarsareδ Sctvari- naries(EBs)wereidentifiedandincludedintheKeplerEB ablesduetotheshapeoftheircurves(KID10417986,KID catalog (Prsa et al. 2011, further PRSA11; Slawson et al. 8912468, KID 8758716, KID 10855535, KID 9612468, 2011).Accordingtotheinitialclassificationthesamplecon- KID8912730,KID9898401,KID7375612,KID5872696, sistsof1261detached,152semidetached,469overcontact KID 10684673, KID 6699679, KID 6287172, KID binaries, 137 ellipsoidal variables (they are not EBs!), and 11825204).Ourclassificationofthesestarsissupportedby 146 uncertain systems. The automated fitting of the light theirhightemperatures(above6000K). curvesbyapolynomialchainandtheartificialintelligence Oneultrashort-periodstar,KID9472174,turnedoutto basedtierEBAI(Prsaetal.2008)wereusedforthemorpho- betheknownsdB+dMbinary2M1938+4603. The shapes of the light curves of two ultrashort-period (cid:63) DatafromKepler (cid:63)(cid:63) Correspondingauthor:e-mail:[email protected] targets,KID8288741andKID12350008,seemasthoseof detached eclipsing systems (with almost flat maxima) but (cid:13)c 0000WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim 2 D.Kjurkchieva&D.Dimitrov:Lightcurvesolutionsoftheultrashort-periodKeplerbinaries their amplitudes of 1–2 mmag and periods are absolutely inappropriate for such configurations. Our preliminary at- temptstoreproducetheirdatarequiredenormousbigthird light.ThismeansthatKID8288741andKID12350008are notthetruevariablestars.Itismeaninglesstomodelthese databecausetheobtainedparameterswouldnotbereliable. Matuevic et al. (2012) noted that the automated classifica- tion and modeling of Kepler EBs, even with locally lin- ear embedding, failed for small amplitudes (∼0.001 mag). KID8288741andKID12350008aresuchcasesbuttherea- sontoberemovedfromthefurtheranalysisisthediscrep- ancybetweenthelightcurveshapeappropriatefordetached eclipsingbinaryandthenegligibleamplitudeofvariability (smallereventhanthoseofellipsoidalvariations). Asaresultoftheselectionprocedurewegatheredsam- ple of six ultrashort-period binaries: KID 4921906, KID 1572353, KID 8108785, KID 6309193, KID 12055255, KID 9532219. More conclusive confirmation of their du- Fig.1 The light curve of KID 4921906 and our fit (top) plicity would be spectroscopic data. The objects would re- andthecorrespondingresiduals(bottom) quire8m-classtelescopeduetolowbrightnessandshortpe- riodatthesametime.Anotherpossibilityforproperclassifi- cationisthecolor-perioddiagram(Duerbeck,1997)butthe presenceofthirdcomponentorcloseneighborcanalterthe colorinformation.Sowewillusetheimportantcriterionfor sureclassificationofthetargets:thesuccessfulreproducing oftheirlightcurvesbyeffectsofduplicity. Table 1 presents information for our 6 targets from the Kepler EB catalog: Kepler magnitude m ; epoch T of K 0 theprimaryminimum;orbitalperiodP;meantemperature T ;metallicity[Fe/H];radiusR;logg;reddeningE(B-V); m typeofconfiguration;ratioT /T ofthetemperaturesofthe 2 1 components;filloutfactorFF;crowding(anumberbetween 0and1thatspecifiesthefractionoffluxintheoptimalpho- tometric aperture due to the target star with respect to the totalfluxfromallsources). Morethan50000pointsareavailableforeachtargetin Fig.2 The light curve of KID 1572353 and our fit (top) the Kepler archive. The detailed review of these data re- andthecorrespondingresiduals(bottom) vealed that the shape of the light curves almost did not changeduringthedifferentobservationalquarters.However thelevelsofmaximaandminimaandtheamplitudesofthe 3 Lightcurvesolutions lightcurvesofthemosttargetschangedconsiderablyduring the different quarters causing the big thickness of the total The shapes of the light curves (Figs. 1-6) implied that our lightcurves(fromallquarters).Thiseffectisprobablydue targets are nearly contact or overcontact systems that was to problems of the satellite steering and automated reduc- expected for their short orbital periods. The depths of the tionofthedata.Thatiswhyweassumedthatitisreasonable twominimaofthemostcurvesareclosethatmeansthatthe tomodeldatafromseveralconsecutivequartersratherthan binariesarealmostinthermalcontact.Thesmalllightam- alldatasimultaneously.Moreover,weestablishedthatitis plitudesofsometargetspointatloworbitalinclinationsand more appropriate to use the raw Kepler data and to make consequently, considerable contributions of the ellipsoidal ownreductionandde-trending(Dimitrovetal.2012). variations. We chose to model the data from quarters Q0 and Q1 Taking into account the foregoing considerations we for all targets excepting KID 9532219 which observations carried out modeling of the photometric data by the code beganlater.TheirfoldedlightcurvesarepresentedinFigs. PHOEBE(Prsa&Zwitter2005)usingthefollowingproce- 1-6. dure. (cid:13)c 0000WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim www.an-journal.org Astron.Nachr./AN(0000) 3 Table1 ParametersofthetargetsfromtheEBcatalog KeplerID mK T0-2400000 P Tm [Fe/H] R logg E(B-V) Type T2/T1 FF crowd [mag] [days] [days] [K] [R(cid:12)] 4921906 15.203 54965.148704 0.213732 4800 -0.394 0.99 4.41 0.109 OC 0.958 1.033 0.648 1572353 15.234 55001.306290 0.228900 4470 -0.261 0.77 4.54 0.076 OC 0.883 1.051 0.9 8108785 14.757 54964.641700 0.228840 4354 -0.298 0.67 4.61 0.053 OC 0.855 0.414 0.921 6309193 13.674 55002.434080 0.212500 5367 -0.383 1.09 4.38 0.098 OC 1.012 1.01 0.92 12055255 15.866 54964.966610 0.220950 4093 0.106 0.73 4.50 0.066 ? ? ? 0.566 9532219 16.118 55001.945246 0.198155 5031 -0.539 1.06 4.38 0.159 ? ? ? ? Fig.3 The light curve of KID 8108785 and our fit (top) andthecorrespondingresiduals(bottom) Fig.4 The light curve of KID 6309193 and our fit (top) andthecorrespondingresiduals(bottom) Initially the primary temperature was fixed as T =T . 1 m The mean target temperatures T (Table 1) have been es- m timated using dedicated pre-launch ground-based optical multi-color photometry plus Two Micron All Sky Survey (2MASS)J,K,andH magnitudes(Skrutskieetal.,2006). We varied the secondary temperature T , mass ratio q, 2 orbitalinclinationiandpotentialsΩ (andsimultaneously 1,2 relativeradiir andfilloutfactorsFF ).Inordertore- 1,2 1,2 produce the O’Connell effect we added cool spots on the primary and varied their parameters: longitude β, latitude λ,angularsizeαandtemperaturefactork =T /T . sp 1 Weadoptedcoefficientsofgravitybrightening0.32and reflection effect 0.5 appropriate for late stars. The limb- darkening coefficients were chosen according to the tables ofVanHamme(1993). Finally, we varied the component temperatures around T tosearchforthebestfit. m The derived parameters of the targets corresponding to our light curve solutions are given in Table 2 while Table 3 presents information about the spot parameters. The for- malPHOEBEerrorsofthefittedparametersarequitesmall (Tables2-3)duetothehighprecisionoftheKeplerdata. ItshouldbenotedthattheephemeridesfromtheKepler Fig.5 ThelightcurveofKID12055255andourfit(top) EB catalogue (PRSA11) did not lead to the best fits. For andthecorrespondingresiduals(bottom) thisaimwevariedtheparameter”shift”ofPHOEBEwhich finalvaluesaregivenincolumn2ofTable2. www.an-journal.org (cid:13)c 0000WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim 4 D.Kjurkchieva&D.Dimitrov:Lightcurvesolutionsoftheultrashort-periodKeplerbinaries Table2 Parametersofthebestlightcurvesolutions KID shift i q T1,2 T2/T1 Ω1,2 FF1,2 r1m,2ean l1 config variability [◦] [K] 4921906 0.0126 21.04±0.02 0.5977±0.0005 4528±14 0.960 3.0634±0.0002 0.0 0.424 0.66 C ellipsoidal 4348±12 3.0634±0.0002 0.0 0.334 (26,4) (0,47) (0.958) (OC) 1572353 -0.01923 43.84±0.02 0.9577±0.0003 4525±20 0.945 3.688±0.0003 0.0 0.383 0.58 C grazing 4277±13 3.688±0.001 0.0 0.374 eclipses (33) (0.29) (0.883) (OC) 8108785 0.00147 61.78±0.02 0.8309±0.0003 4711±4 0.901 3.4664±0.0004 0.0 0.395 0.62 C eclipses 4246±3 3.4664±0.0006 0.0 0.360 (69.9) (0.33) (0.855) (OC) 6309193 -0.0196 13.445±0.014 0.8007±0.0003 5435±2.5 0.874 3.4165±0.0005 0.0 0.398 0.68 C ellipsoidal 4751±2 3.4165±0.0005 0.0 0.359 (21) (0.60) (1.012) (OC) 12055255 0.0128 39.79±0.05 0.9637±0.0005 3701±8 1.011 3.6326±0.0022 0.128 0.392 0.55 OC grazing 3744±10 3.6936±0.0012 0.019 0.377 eclipses (?) (?) (?) (?) 9532219 0.00647 68.42±0.06 0.9320±0.0022 4950±22 0.983 3.5687±0.0022 0.172 0.398 0.55 OC eclipses 4867±21 3.5873±0.0028 0.164 0.388 (?) (?) (?) (?) Note:Cmeanscontactbinaries,OC-overcontactsystems in defining the shapes of their light curves and the eclipse depths.Hence,thevaluesofthephotometricmassratiofor ultrashort-periodKeplerbinariesshouldbeconsideredwith highconfidence. There are differences between our solutions and those obtainedbyautomatedfittingcitedintheKeplerEBcatalog (thevaluesinparenthesesinTable2). (1) ThemostorbitalinclinationsinPRSA11arebiggerthan ours. (2) The mass ratios in PRSA11 are considerably smaller thanourvalues(Table2). (3) Wehadtoassumeathirdlightl onlyforKID9532219 3 (Table3)whilethevaluesofthisparameterinPRSA11 werenonzerosfortheallsixtargets.Wefoundaweaker starclosetoKID9532219(atdistancearound6arcsec) that could explain the presence of l in the light curve 3 solutionofthistarget. (4) TherearenovaluesofthepotentialsΩ (andthusof 1,2 Fig.6 The light curve of KID 9532219 and our fit (top) the relative radii r and fillout factors FF ) as well 1,2 1,2 andthecorrespondingresiduals(bottom) as of relative luminosities in PRSA11 that means that theautomatedmodellingleadstoapproximateresults. Table3 Parametersofthespotsandthirdlightofthetar- There are several explanations for the differences be- gets tween our ”manual” solutions and those of the automated KID β λ α k l3 fitting. [◦] [◦] [◦] 4921906 75.0±0.1 88.1±0.1 11.0±0.1 0.901±0.001 0 (a) The EBAI method fixes l3 = 1 - crowding while this 1572353 91.5±0.1 329.9±0.1 17.6±0.1 0.900±0.002 0 parameterisinvokedinourprocedureonlywhenasat- 8108785 126.3±0.2 279.6±0.3 24.9±0.2 0.939±0.001 0 6309193 63.9±0.1 338.4±0.1 10.3±0.2 0.940±0.001 0 isfactoryfitisimpossibleforanycombinationofthepa- 12055255 59.6±0.2 89.9±0.2 14.9±0.2 0.900±0.001 0 rameters. The bigger value of l requires bigger light 9532219 81.5±0.6 70.09±0.04 10.1±0.7 0.914±0.007 0.78 3 amplitude and correspondingly bigger orbital inclina- tion. Moreover, due to the correlation between third The synthetic curves corresponding to the parameters light and mass ratio for partially eclipsing binaries the of our light curve solutions are shown in Figs. 1-6 as red biggerthirdlightleadstothelargermassratioforfixed continuouslines. inclinationangle. Thederivedphotometricmassratiorequiresaspecialat- (b) AlthoughalllightcurvesexhibitO’Connelleffect(Figs. tention.Usuallythisparameterneedsspectralobservations. 1-6)theEBAImethoddoesnottakeintoaccounttheef- Butthespectralmassratioforshort-periodbinarieswithfast fectfromspots.Thentheresultsoftheautomatedmod- rotationisquiteimpreciseduetothelineblendingwhilethe ellingshouldbeassumedasfirstapproximationsofthe geometricaleffectsandmassratioaremuchmoreimportant fittedparameters. (cid:13)c 0000WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim www.an-journal.org Astron.Nachr./AN(0000) 5 4 Analysisoftheresults 5 Conclusions Ourinvestigationaddedsixnewmemberstothesmallfam- The analysis of our light curve solutions of the ultrashort- ily of the studied ultrashort-period binaries with MS com- periodbinariesfromtheKeplerdatabaseledtoseveralcon- ponents. clusions. Allsixtargetsturnedouttobecontactorslightlyover- contactconfigurationswhichcomponentsarealmostinther- (1) The configurations of all targets are almost the malcontact.Twotargets,KID4921906andKID6309193, same: 4 of them are contact binaries (KID 4921906, are not eclipsing but reveal ellipsoidal and spot variabil- KID 1572353, KID 8108785, KID 6309193) and 2 ity. KID 12055255 is very rare case of ultrashort-period are slightly overcontact systems (KID 12055255 and binary consisting of two M dwarfs. We established that KID9532219). KID 9532219 is an eclipsing binary but not a δ Sct vari- (2) Two targets, KID 4921906 and KID 6309193, are ableasitwaspreviouslysupposed.Oneofthecomponents noneclipsing systems. The registration of their low- ofKID8108785exhibitsinherent,quasi-sinusoidal,small- amplitude ellipsoidal and rotational (due spots) vari- amplitudevariability. ability is possible due to the high Kepler accuracy. The analysis of the results showed that reliable global There are quite many objects of this type in the Ke- parameters of the Kepler binaries might be obtained only pler EB catalog and hence, it should be called catalog bystandardmethodoflightcurvesolutions.Theautomated ofphotometrically-doublestars. EBAI method models the Kepler data quite roughly. Obvi- (3) To model the data of KID 9532219 we had to assume ously, the numerous and exclusive precise Kepler data de- considerablecontributionofathirdlightl .Itoriginates 3 servepreciselightcurvesolutionsbythestandardway. probably from the close neighbor. We do not exclude thisfainterstartobethetruevariablebecausethesizeof Acknowledgements. We used the live version of the Kepler EB theKeplerpixelsprojectedontothesky(4arcsec)cou- catalog from http://keplerEBs.villanova.edu. The research was supported partly by funds of project RD 08-244 of Scientific pled with the high star density near the Galactic plane Foundation od Shumen University. This publication makes use leadtoanon-negligiblelikelihoodofassociatinganEB of data products from the Two Micron All Sky Survey, which eventwiththewrongstar(PRSA11). is a joint project of the University of Massachusetts and the In- (4) ThetargetKID12055255isveryrarecaseofultrashort- fraredProcessingandAnalysisCenter/CaliforniaInstituteofTech- period binary consisting of two M dwarfs. The system nology,fundedbytheNationalAeronauticsandSpaceAdminis- seemstobeovercontact.Wearenotawareofanyover- tration and the National Science Foundation. This research also contactbinaryconsistingofMdwarfs. hasmadeuseoftheUSNOFSImageandCatalogueArchiveop- (5) Feldmeier et al. (2011) classified the target erated by the United States Naval Observatory, Flagstaff Station KID 9532219 as a δ Sct variable (from their ground- (http://www.nofs.navy.mil/data/fchpix/). based photometric observations of the Kepler FoV for Theauthorsaregratefultoanonymousrefereeforthevaluable the pre-launch survey). The Kepler data and our mod- notesandpropositions. elingcertainlyrevealthatthistarget(oritsneighbor)is eclipsingbinary. References (6) RecentlyKID6309193wasnotedas”false”intheKe- pler EB catalog. Our modeling showed that it is not DimitrovD.,KjurkchievaD.,2010,MNRAS406,2559 eclipsing star but its light curve can be reproduced by DimitrovD.,KjurkchievaD.,RadevaV.,2012,BlgAJ18c,81 DuerbeckH.,1997,IBVSNo4513 ellipsoidalvariationsofbinary.Howeverwedonotex- FeldmeierJ.etal.,2011,AJ142,2 cludethealternativetheobservedvariabilitytobeinher- Lohr,M.E.;Hodgkin,S.T.;Norton,A.J.;Kolb,U.C.,2014,A& enttosomeofitstwoconsiderablyfainterneighbors(at A563A,34 distancesaround4.5arcsecand7arcsec). MaceroniC.,MontalbanJ.,2004,A&A426,577 (7) The ripples in the residuals of KID 8108785 (Fig. 3) MaceroniC.,RucinskiS.M.,1997,PASP109,782 seem to be quasi-sinusoidal with period of 55 min and MatuevicG.etal.,2012,AJ143,123 amplitudeof0.005mag.Althoughthisvariabilityisvis- PribullaT.,VankoM.,HambalekL.,2009,IBVSNo.5886 PrsaA.,ZwitterT.,2005,ApJ628,426 ibleduringallphases,itcouldbeexplainedbyinherent PrsaA.etal.,2008,ApJ687,542 changesofsomeofthecomponentsofthissystemdue PrsaA.etal.,2011,AJ141,83 toitssmallorbitalinclination. QianS.-B.etal.,2014,CoSka43,290 PribullaT.etal.,2009,AJ137,3646 Although all considered light curves reveal O’Connell RucinskiS.,DuerbeckH.,1997,PASP109,1340 RucinskiS.,1992,AJ103,960 effect and are reproduced by cool spots we have not stud- RucinskiS.,2006,MNRAS368,319 ied long-term light curve changes as a result of the evolu- RucinskiS.,2007,MNRAS382,393 tionofthesesurfaceinhomogeneities.Todothisoneshould SkrutskieM.F.etal.,2006,AJ,131,1163 havedetailedinformationabouttheproblemsofthesatellite SlawsonR.etal.,2011,AJ142,160 steeringwhichintroducedifferenttrendsintothedata. SouthworthJ.etal.,2011,MNRAS414,3740 www.an-journal.org (cid:13)c 0000WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim 6 D.Kjurkchieva&D.Dimitrov:Lightcurvesolutionsoftheultrashort-periodKeplerbinaries SteffenJ.etal.,2011,MNRAS417L,31 VandenbergD.,ClemJ.,2003,AJ126,778 VanHammeW.,1993,AJ106,2096 Weldrake D., Sackett P., Bridges T., Freeman K., 2004, AJ 128, 736 WelshW.etal.,2011,ApJS197,4 WinnJ.etal.,2011,ApJ741L,1 (cid:13)c 0000WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim www.an-journal.org