1992ApJ. . .384. .624P binary systemsstartedin1988(cf.Panetal.1990). color astrometry(Colavita,Shao,&Staelin1987),starposition stellar diametermeasurement(Shaoetal.1987;Hutter determination (Mozurkewichetal.1988;Shao1990),and published describingtheinstrument(Shaoetal.1988),two- tions andstellardiameters.Aseriesofpapershasbeen Wilson, California,hasbeenusedinitiallytomeasurestarposi- fringe-tracking datarecordedovera75sinterval,followed by 20024. a 5smeasurementofthetotaldarkcountandskybackground. were 22and25nm,respectively.Theapertureforthenarrow- widths ofthe800and550nmchannels,whichwereanalyzed, Laboratory, Washington,DC20375. band channelswasusually2.5cm.Eachscanofastarincludes nm, thedatafromthischannelwerenotusedhere.Theband- narrow-band channelswithtypicalcenterwavelengthsof 800, provides 36differentlengthsfrom3to32morientedN-S. a wide-bandchannelat700nmforfringetracking,andthree 550, and450nm.Becauseoflowsignal-to-noiseratioat 450 Fringes areobservedsimultaneouslyinfourspectralchannels: 1989; Mozurkewichetal.1991).Theobservationprogramof The AstrophysicalJournal,384:624-633,1992January10 © 1992.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. 4 3 2 1 Postaladdress:Interferometries,Inc., Vienna,VA22182. The MarkIIIStellarInterferometer,locatedonMount Postaladdress:SFAInc.,Landover, MD20785. Postaladdress:CenterforAdvanced SpaceSensing,NavalResearch Postaladdress:UniversitiesSpace Research Associates,Washington,DC For binaryobservations,avariablebaselineisused,which tions, thecolorindicesbetween550nmand800forprimarycompanionaredeterminedas Am =1.82±0.04magat800nmand1.99550nm.Incorporatingphotometricobserva- In addition,themagnitudedifferencebetweentwocomponentshasbeenmeasured,yielding 96?6960 ±0?0013,eccentricitye=0.5270.004,andepochofperiastronpassageTJD2,447,374.77±0.15. position angleofascendingnodeQ=104?16+0?25,longitudeperiastronœ77?310?32,periodP interferometric data.Usingbothandspectroscopicobservations,thedefinitiveorbitalelements with thespectroscopicresults.However,threeoftheseelements,i.e.,a",i,andQ,canonlybeobtainedfrom calculated utilizingobservationsfromtheMarkIIIStellarInterferometeronlyandareinexcellentagreement milliarcsecond measurementprecisionatopticalwavelengths.AlloftheorbitalelementsaAndhavebeen Subject headings:binaries:visual—instrumentation:interferometersstars:individual(aAndromedae) are determinedasfollows:angularsemimajoraxisa"=0'.'02415±0'.'00013,inclination¿105?66+0?22, using theMarkIIIStellarInterferometer.ObservationsofaAndin1988and1989clearlydemonstratesub- — 0.11±0.03magand+0.070.05mag,respectively. The visualorbitofthespectroscopicbinaryaAndhasbeendeterminedindependentlydata © American Astronomical Society • Provided by the NASA Astrophysics Data System 123 J. ThomasArmstrong,DavidMozurkewich,MaddaliVivekanand,CraigS.Denison, DETERMINATION OFTHEVISUALORBITSPECTROSCOPICBINARY 1. INTRODUCTION NRL/USNO OpticalInterferometerProject,USNavalObservatory,Washington,DC20392 a ANDROMEDAEWITHSUBMILLIARCSECONDPRECISION Optical SciencesandApplicationSection,JetPropulsionLaboratory,Pasadena,CA91109 Department ofAstronomy,CaliforniaInstituteTechnology,Pasadena,CA91125 42 Richard S.Simon,andKennethJ.Johnston Michael ShaoandM.MarkColavita Received 1991April12;acceptedMay31 ABSTRACT Xiaopei Pan 624 AND lengths isalsopresented.Finally,theimplicationsofthese ed next.Theorbitalelementsofthissystemarethencalculated will bedescribedfirst.TheobservationsonaAndarepresent- star systemsisdividedintofour steps,discussedbelow. results onthephysicalparametersofsystemaredescribed. The magnitudedifferenceofthissystematdifferentwave- results fromspectroscopy.Predictionsoftheorbitalmotion of minutes, andatotalof160-200scanscanbemadeeachnight. few seconds.Afterrecordingfringe-trackingdataoveraperiod is loadedbyanobserver.Foreachscan,thesiderostatsand a Andaremadeandcomparedwithmeasurementdata. using interferometricdataonlyandarecomparedwith the star. Usually, 15-25scanspernightarescheduledforeachbinary dark countandskybackground.Ascantypicallytakes 3 delay linesslewtothetargetstar.Afterangletrackerhas instrument. Atthebeginningofeachnight,anobservationlist of 75s,thesiderostatsareoffsetforameasurementtotal Under normalseeingconditions,fringescanbeacquiredina acquired andlockedonthestar,fringeacquisitionbegins. Selected referencestarswithdiametersequaltoorsmallerthan 1 masareobservedperiodicallyduringthenight. Analysis oftheinterferometric dataforthestudyofbinary In thispaper,datareductionofthebinarystarobservations The MarkIIIStellarInterferometerisafullyautomated 2. DATAREDUCTIONOFBINARY STAROBSERVATIONS 1992ApJ. . .384. .624P 52 1/2 caused bythefinitebandwidthoffilters,weapproximate where B,andarethethreecomponentsofbaseline fringe visibility,Viscalculatedforeach0.5speriodusing parameters arecalculatedandaveragedto0.5s.Thesquared tive wavelengthofeachchannel, 2,asfollows: the stellarspectrumwithablackbodyandcalculateeffec- declination andhourangleofthestar. the unbiasedestimator interferometer is4ms.Intheinitialprocessing,fringe vector intheequatorialcoordinatesystem,andôhare the (~75 s),andthermsof5spointswithinscanisused integrated to5s.Thesespointsareaveragedascan is givenby<7=iV.Wediscardthoseframeswhosephoton criterion weadoptedtorejectdatapoints. count exceedsthemeanvalueby5aormore.Thisisonly photon noisehasaPoissondistribution,itsstandarddeviation photons perframe,thephotonnoisetermdominates.Since variance ofthephotonfluxineachframeisgivenbysum caused by,forexample,radiofrequencyinterferenceinthe calculated as the zeropointoflasermetrologysystem.Thetwocom- unit vectortothestar,andCisdelayoffset,representing given byD=B•s+C,whereisthebaselinevector, as anestimateofthemeasurementerrorscan(J. the visibilitychannels,becauseofrelativelylownumber a photonnoisetermandanatmosphericscintillationterm;for detector electronics,adataqualificationstepistakenhere.The rection inthepreviousexpression. nearest fivedarkcountmeasurementsisthenusedasthecor- measurements exceeding3aarediscarded.Theaverageofthe each nightarediscarded.Darkcountmeasurementsoverthe a realquantity. (R < 1); $ïandd"aretheangular diameters(equivalent ponents oftheprojectedbaselinevectoronu-vplane are remaining intervalaretheneditedtoremoveerroneouspoints: path-length strokeismatchedtothecenterwavelength. each channelareadjustedelectronicallysothattheeffective xyz surements, dataduringtwilightatthebeginningandendof average over126frames(cf.Shaoetal.1988).Thebinwidthsin correction normalizedto4ms;and<...)denotesatime per frame;Disthetotaldarkcountandskybackground each offourtimebinsduringthepath-lengthmodulation where A,B,C,andDarethenumberofdetectedphotonsin eff stroke; V=A+BCDisthetotalnumberofphotons scan 2 r 2 5 In these In ordertoperformafirst-ordercorrectionforthebias The basicframeratefordatarecordingwiththeMarkIII After thisqualificationstep,the0.5sFmeasurementsare Asusedinthispaper,fringevisibility referstofringevisibilityamplitude-expressionsR istheintensityratiooftwocomponents For atwo-elementinterferometer,thefringepositionDis In ordertoavoiderrorsinfringevisibilitymeasurements On thebasisofdarkcountandskybackgroundmea- 2 % B= —Bsin<5cosh—/i+Ô,(3) vxyz V =(n/2K(A-C)+(B—D)-V>/
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