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Astronomy&Astrophysicsmanuscriptno.sori-amber (cid:13)c ESO2008 February2,2008 LE ⋆ J, H, K spectro-interferometry of the Mira variable S Orionis M.Wittkowski1,D.A.Boboltz2,T.Driebe3,J.-B.LeBouquin4 F.Millour3 K.Ohnaka3,andM.Scholz5,6 1 ESO,Karl-Schwarzschild-Str.2,85748GarchingbeiMu¨nchen,Germany,e-mail:[email protected] 2 USNavalObservatory,3450MassachusettsAvenue,NW,Washington,DC20392-5420,USA 3 Max-Planck-Institutfu¨rRadioastronomie,AufdemHu¨gel69,53121Bonn,Germany 8 4 ESO,Casilla19001,Santiago19,Chile 0 5 Institutfu¨rTheoretischeAstrophysikderUniv.Heidelberg,Albert-Ueberle-Str.2,69120Heidelberg,Germany 0 6 InstituteofAstronomy,SchoolofPhysics,UniversityofSydney,SydneyNSW2006,Australia 2 Received...;accepted... n a J ABSTRACT 3 Aims.WepresentJ,H,Kspectrallydispersedinterferometrywithaspectralresolutionof35fortheMiravariableSOrionis.Weaim atmeasuringthediametervariationasafunctionofwavelengththatisexpectedduetomolecularlayerslyingabovethecontinuum- ] h formingphotosphere.Ourfinalgoalisabetterunderstandingofthepulsatingatmosphereanditsroleinthemass-lossprocess. p Methods.VisibilitydataofSOriwereobtainedatphase0.78withtheVLTI/AMBERinstrumentusingthefringetrackerFINITOat - 29spectralchannelsbetween1.29µmand2.32µm.Apparentuniformdisk(UD)diameterswerecomputedforeachspectralchannel. o Inaddition,thevisibilitydataweredirectlycomparedtopredictionsbyrecentself-exciteddynamicmodelatmospheres. r Results.S Ori shows significant variations inthe visibilityvalues asafunction of spectral channel that can only bedescribed by t s aclear variation intheapparent angular sizewithwavelength. Theclosurephase values are closetozero atall spectral channels, a indicatingtheabsenceofasymmetricintensityfeatures.TheapparentUDangulardiameterissmallestatabout1.3µmand1.7µmand [ increasesbyafactorof∼1.4around2.0µm.TheminimumUDangulardiameteratnear-continuumwavelengthsisΘ =8.1±0.5mas, UD correspondingtoR∼420R .TheSOrivisibilitydataandtheapparentUDvariationscanbeexplainedreasonablywellbyadynamic 1 ⊙ atmospheremodelthatincludesmolecularlayers,particularlywatervaporandCO.Thebest-fittingphotosphericangulardiameterof v themodelatmosphereisΘ =8.3±0.2mas,consistentwiththeUDdiametermeasuredatnear-continuumwavelengths. 4 Phot Conclusions.ThemeasuredvisibilityandUDdiametervariationswithwavelengthresembleandgenerallyconfirmthepredictionsby 9 recentdynamicmodelatmospheres.ThesesizevariationswithwavelengthcanbeunderstoodastheeffectsfromwatervaporandCO 5 layerslyingabovethecontinuum-formingphotosphere.Themajorremainingdifferencesbetweenobservationsandmodelprediction 0 areverylikelyduetoanimperfectmatchofthephaseandcyclecombinationbetweenobservationandavailablemodels. . 1 Keywords.Techniques:interferometric–Stars:AGBandpost-AGB–Stars:atmospheres–Stars:individual:SOri 0 8 0 : 1. Introduction ingofpulsationandmassloss.ObservedradiiofMirastarshave v beenfoundtodifferfordifferentopticalandinfraredbandpasses Xi Mira stars are low-mass, large-amplitude, long-period variable (e.g. Thompson et al. 2002; Mennesson et al. 2002; Ireland et stars on the AGB, evolving toward the planetary nebula and r al. 2004; Perrin et al. 2004; Eisner et al. 2007), and this has a white dwarfphases. Theyexhibita mass-loss rate on the order beenattributedtothepresenceofmolecularlayerslocatedabove of∼10−6M /yearthatsignificantlyaffectsthefurtherstellarevo- ⊙ the continuum-forming photosphere. Here, we present both a lutionandisoneofthemostimportantsourcesforthechemical spectro-interferometric observation of the Mira star S Ori that enrichmentoftheinterstellarmedium.Thedustcondensationse- coversthenear-infrared J, H, and K bandssimultaneouslyata quence,the wind-drivingmechanism,and the role of pulsation spectralresolutionof35andacomparisontorecentself-excited are currentlynotwell understood,in particularforoxygen-rich dynamicmodelatmospheres. AGBstars(Woitkeetal.2006;Ho¨fner&Andersen2007).The pulsatingatmospheresof Mirastars can becomeveryextended becauseofdynamiceffectsincludingshockfronts,andtheyare SOriisaMiravariablestarwithspectraltypeM6.5e–M9.5e verycoolintheirouterparts.Here,moleculescanform,which andV magnitude7.2–14.0(Samusetal.2004).WeuseaJulian for O-rich stars are most importantly H2O, CO, TiO, and SiO DateoflastmaximumbrightnessT0 = 2453190days,aperiod (Tsujietal.1997;Tejetal.2003;Ohnaka2004).Wittkowskiet P = 430 days (as in Wittkowski et al. 2007), and the distance al.(2007)foundforthecaseofSOrithatAl O dustcondenses of 480 pc ± 120 pc from van Belle et al. (2002). The broad- 2 3 withintheextendedatmosphereatphase-dependentdistancesof band near-infrared K UD angular diameter of S Ori has been 1.8–2.4photosphericradii.Thisextendedatmosphere,whichis measuredbyvanBelleetal.(1996),Millan-Gabetetal.(2005), characterizedbyphase-dependenttemperatureanddensitystrat- andBoboltz&Wittkowski(2005)tovaluesbetween9.6masand ifications, the presence of molecular layers, and the formation 10.5mas at different phases. Joint VLTI/MIDI and VLBA/SiO of dust, is thus of particular interest for our better understand- maserobservationsbyWittkowskietal.(2007)haveshownthat SOriexhibitssignificantphase-dependenciesoftheatmospheric ⋆ Based onobservations made withtheVLTInterferometer (VLTI) extension and dust shell parameters with photospheric angular atParanalObservatoryunderprogramID080.D-0691 diametersbetween7.9masand9.7mas. 2 M.Wittkowskietal.:J,H,Kspectro-interferometryoftheMiravariableSOrionis Table1.Observationlog.Nightstarting12October2007,JD2454386. Target Purpose Θ DIT Time Φ B [m] PA AM Seeing τ LD Vis p p 0 [mas] [msec] [UTC] E0-G0/G0-H0/E0-H0 deg [′′] [msec] 45Eri Calibrator(K3II-III) 2.15±0.04 25 08:03-08:07 16.0/31.9/47.9 -107 1.1 1.3 1.3 45Eri Calibrator(K3II-III) 2.15±0.04 50 08:09-08:12 16.0/32.0/48.0 -107 1.1 1.3 1.3 γEri Checkstar(M0.5IIIb) 8.74±0.09 25 08:22-08:26 15.6/31.2/46.8 -104 1.1 1.4 1.2 γEri Checkstar(M0.5IIIb) 8.74±0.09 50 08:28-08:32 15.5/31.0/46.5 -104 1.1 1.4 1.2 SOri Sciencetarget 25 08:45-08:49 0.78 15.9/31.8/47.8 -107 1.1 1.3 1.3 SOri Sciencetarget 50 08:52-08:57 0.78 16.0/31.9/47.9 -107 1.1 1.3 1.3 αHor Calibrator(K2III) 2.76±0.03 25 09:14-09:18 14.5/28.9/43.3 -91 1.1 1.2 1.4 αHor Calibrator(K2III) 2.76±0.03 50 09:21-09-24 14.3/28.7/43.0 -90 1.1 1.4 1.2 SOri Sciencetarget 25 09:36-09:40 0.78 15.9/31.8/47.7 -106 1.1 1.5 1.1 2. Observationsanddatareduction framesbasedonS/R.Weverifiedthatkeepingupto80%ofthe best frames based on SNR did not significantly change the re- Weobtainednear-infraredJ, H,K interferometryofSOriwith sults.TheSOriandγErivisibilitydatawerecalibratedforeach the instrument AMBER (Petrov et al. 2007) in low-resolution DITvalueseparatelyusingthe45EriandαHorcalibrationstar mode at the ESO VLTI using the fringe tracker FINITO and data. After calibration, the different calibrated S Ori and γ Eri threeVLTIAuxiliaryTelescopes(ATs)on12October2007(JD data were averaged. The errors of the calibrated visibility data 2454386).TheATswerepositionedonstationsE0,G0,andH0. include the statistical error of averaging the single frames, the ThedateofobservationcorrespondstoavisualphaseΦVis=0.78, errorsofthecalibrationstars’angulardiameters,andthevaria- with an uncertainty of about 0.1. The details of the observing tionoftheavailabletransferfunctionmeasurements. sequenceare listed in Table 1, includingthe projectedbaseline lengths (B ) and position angles (PA ), the airmass (AM), and p p theopticalseeingandcoherencetime.Ambientconditionswere 3. Results notverygoodbut stable. The airmasswas the same for all observations.Datawererecordedusingtwodifferentdetectorinte- Figures1 and 2 show the resulting visibility and closure phase grationtimes(DITs)of25msecand50msec. dataforSOriandforthecheckstarγEri,respectively.Thegaps TheVLTIfringe-trackerFINITOrecordsfringesonthetwo inthevisibilitydataaround1.45µmand1.85µmcorrespondto shortestbaselinesusing70%oftheH-bandlight.Outputsignals the regions between the bands. Also shown are the best fitting areprocessedinrealtimeandusedtocompensateforthefringe models of a UD with a constant diameter, of a Gaussian disk motionduetoatmosphericturbulence.Owingtothelowcoher- with a constant diameter, and of atmosphere models. The lat- encetimeduringtheobservations,FINITOwasonlyabletopro- ter are for S Ori the M18nmodel(describedin detail below in videaverageperformancesof0.2–0.4µmRMS(tobecompared Sect. 4), andforγ ErianATLAS9 modelatmosphere(Kurucz with 0.1µm RMS achieved in good conditions). Nevertheless 1993) with T =3750K, logg=1.5, and solar chemical abun- eff such a performance is sufficient for increasing the signal-to- danceasexpectedforγEri(Bordeétal.2002).Thecomparison noiseratio(S/R)oftheAMBERdataandstabilizingthetransfer oftheSOrivisibilitydatatothedynamicmodelatmosphereis function.Allobservationsusedherewereobtainedwithexactly describedindetailbelowinSect.4. thesameFINITOcontrollerparameters,whichisimportantfor The calculation of synthetic visibility values and the fits to avoidingsystematicbiasesincalibratingtheabsolutevisibility. theinterferometricdatawereperformedasinWittkowskietal. In addition to S Ori, the two calibration stars 45 Eri and (2006,2007).ThefittedangulardiameteroftheGaussianmodel α Hor were observed close in time, as was γ Eri. The last is a correspondsto the FWHM, that of the plane-parallelATLAS9 regularnon-pulsatingM0.5giantwithawell-knownangulardi- modeltothe0%intensity(limb-darkened)radius,andthatofthe ametersimilarto thatof SOriwhichis notexpectedto exhibit M18nmodeltothe1.04µm(photospheric)radius(asdefinedin strongeffectsfrommolecularlayers.Thisdataisusedtocheck Irelandetal.2004b).Thebest-fitangulardiametersare that any strong wavelength-dependentfeaturesfound for S Ori SOri:Θ =10.8mas;Θ =6.9mas;Θ =8.3mas UD Gaussian M18n arenotcausedbyanysystematiceffectsoftheinstrument.The γEri:Θ =8.5mas;Θ =8.9mas. UD ATLAS9 spectraltypesandangulardiametersofthecalibrationandcheck Theerrorsareσ∼0.2mas starsarefromBordeétal.(2002). The visibility data of the check star γ Eri can be described Raw visibility andclosurephase valueswere computedus- well by a UD of constant diameter and by the ATLAS9 model ing the latest version of the amdlib package (version 2.0 beta atmosphere.Therearenosignificantwavelength-dependentde- 2b)andtheyorickinterfaceprovidedbytheAMBERconsor- viationsbetweenmeasuredvisibilitydataandtheUDmodel.It tium and the Jean-Marie Mariotti Center. Absolute wavelength isnotyetclearwhethertherelativelylow J-bandvisibilitiesfor correlationwas performedby correlatingthe raw spectra of all theG0-H0baselineandthedeviationsintheclosurephaseval- fourstarswithamodeloftheatmospherictransmissionwiththe uesnearthefliparecausedbyanasymmetricstellarsurfacefea- samespectralresolution.Inparticular,weusedaplateauinthe tureorasystematiccalibrationuncertainty.Notethattheangular transmissioncurveatλ ∼2.0µm.Theoffsetwithrespecttothe diameterofγEribasedonagivenmodeliswell-constrainedby original wavelength table was 3 spectral channels (0.1µm at a thepositionofthevisibilityminimum,whichisindependentof wavelength of 2.0µm). We estimated the error of the absolute an absolute visibility calibration. The resulting angular diame- wavelengthcalibrationto1pixel(∼0.03µm).Individualframes ter ΘATLAS9=8.9±0.2mas is consistent with the value given in were averaged after frame selection keeping 70% of the best Bordeétal.(2002)ofΘLD=8.74±0.09mas. framesbasedonpiston(toremovetheframeswhentheFINITO The visibility data of S Ori show significant wavelength- loop was notclosed) and outof these keeping30% of the best dependent features clearly deviating from UD and Gaussian M.Wittkowskietal.:J,H,Kspectro-interferometryoftheMiravariableSOrionis 3 1.2 0.4 quared visibility amplitude 00001.....24680 SVE 0LO-TGriI0/AMBER, UGMDa1u8snsian quared visibility amplitude 000...123 SVG L0O-TrHiI/0AMBER UGMDa1u8snsian quared visibility amplitude 000...011505 SVE 0LO-THriI0/AMBER UGMDa1u8snsian Closure phase (deg) 1230000000 SVE 0LO-TGriI0/A-HM0BER UGMDa1u8sns S S S 0.0 0.0 0.00 1200 1400 1600 1800 2000 2200 2400 1200 1400 1600 1800 2000 2200 2400 1200 1400 1600 1800 2000 2200 2400 1200 1400 1600 1800 2000 2200 2400 Wavelength (nm) Wavelength (nm) Wavelength (nm) Wavelength (nm) Fig.1.MeasuredSOrivisibilitydatacomparedtomodelsofaUDwithaconstantdiameter(reddashedlines),ofaGaussiandisk ofconstantdiameter(greendashedline),andofthe M18natmospheremodel(bluesolidline).Forthe projectedbaselinelengths andanglesseeTable1. 1.2 0.6 quared visibility amplitude 00001.....24680 γVE 0EL-rTGiI0/AMBER, UADTLAS 9 quared visibility amplitude 00000.....12345 γVG EL0-rTHiI/0AMBER UADTLAS 9 quared visibility amplitude 000...011505 γVE 0EL-rTHiI0/AMBER UADTLAS 9 Closure phase (deg) 1230000000 γVE 0EL-rTGiI0/A-HM0BER UADTLAS 9 S S S 0.0 0.0 0.00 1200 1400 1600 1800 2000 2200 2400 1200 1400 1600 1800 2000 2200 2400 1200 1400 1600 1800 2000 2200 2400 1200 1400 1600 1800 2000 2200 2400 Wavelength (nm) Wavelength (nm) Wavelength (nm) Wavelength (nm) Fig.2.Measuredγ Erivisibilitydata comparedto modelsof a UD with a constantdiameter(red dashedline)and ofan ATLAS9 modelatmospherewithT =3750K,logg=1.5,solarchemicalabundance(bluesolidline).Fortheprojectedbaselinelengthsand eff anglesseeTable1. withtheSOriphotosphericangulardiametersbetween7.9mas s) S Ori M18n 1.6 at phase 0.55 and 9.7mas at phase 1.15 derived in Wittkowski a m 12 VLTI/AMBER (E0-G0-H0) et al. (2007) based on VLTI/MIDI data and modelingwith dy- meter ( 1.4UD) ndaumstischmelol.dTelhaetsmeopshpohteorsepshaenridcaanragduilaatrivdeiatmraentsefresramreodaelsloofcothne- k dia 10 1.2min( seitsatel.n2t0w0i7th).pWreivthiotuhsebardooapdtbeadnddismtaenacseurteomSeOntrsi,(cthf.eWanigttukloawrsdki-i m dis 8 1.0UD/ ameterΘUD=8.1±0.5mascorrespondstoaradius418±130R⊙. or nif U HO CO HO CO 0.8 4. ComparisontodynamicMirastaratmosphere 6 2 2 1200 1400 1600 1800 2000 2200 2400 models Wavelength (nm) Fewdynamicatmospheremodelsforoxygen-richMirastarsare Fig.3. S Ori UD diameter values as a function of wavelength availablethatincludetheeffectsofmolecularlayers.ThePand comparedtothepredictionbytheM18nmodelatmosphere.Also Mmodelseries(Irelandetal.2004a,2004b)arecompleteself- indicated are the positions of H2O and CO bandsafter Lançon excited dynamic model atmospheres of Mira stars designed to &Wood(2000). match the prototype oxygen-rich Mira stars o Cet and R Leo. They have been used successfully for comparisons to recent broadbandinterferometricdataofoCetandRLeo(Woodruffet models of constant diameter on all three baselines. This indi- al.2004;Fedeleetal.2005).ComparedtooCetandRLeo,SOri catesvariationsintheapparentangulardiameter.TheSOriclo- isaslightlycoolerMiravariablewith alongerperiod,ahigher sure phase values are consistent with zero at all spectral chan- main-sequence precursor mass, and a larger radius. However, nels,indicatingtheabsenceofasymmetricfeaturesintheinten- when scaled to variability phases between 0 and 1 and to the sitydistribution.InordertocharacterizethevariationofSOri’s correspondingangularsizeonthesky,thegeneralmodelresults angulardiameterasa functionof wavelength,we fitted UD di- arenotexpectedtobedramaticallydifferentforSOricompared ameterstothedataofeachspectralchannelseparately.Figure3 tooCetandRLeo(cf.thediscussioninWittkowskietal.2007). showsthe resultingUD diametervaluesasa functionofwave- The M model series was chosen to model the atmosphere of length.NotethattheintensityprofileofaMirastarisgenerally S Ori by Wittkowski et al. (2007) as the currently best avail- notexpectedtobeclosetoaUDandthatthisapproachcanonly able optionto describe Mira star atmospheres.Monochromatic givearoughestimateofSOri’scharacteristicsizeasafunction center-to-limbvariations (CLVs) at 46 angles between 0 and 5 ofwavelength.FitsofGaussianfunctionsleadtosimilarresults. R basedonthePandMmodelswererecomputedforthewave- p The apparentUD angulardiameter shows clear variationswith lengthrangefrom1–2.5µminstepsof0.001µm. wavelength. It is smallest at about 1.3µm and 1.7µm and in- The P and M dynamic model atmospheres predict signifi- creases by a factor of ∼1.4 around 2.0µm. The minimum UD cant changes in the monochromatic radius R = R (τ = 1), λ λ λ angulardiameterofSOriatthenear-continuumwavelengthsis causedbymolecularlayersthatlieabovethecontinuum-forming Θ =8.1±0.5mas.Thisresultatvisualphase0.78isconsistent photosphereandsignificantlyaffectcertainbandpasses.Figure4 UD 4 M.Wittkowskietal.:J,H,Kspectro-interferometryoftheMiravariableSOrionis R)p2.5 Model M16n, Phase 1+0.60 3.0 R)p2.5 Model M18n, Phase 1+0.84 2.5 R)p2.5 Model M20, Phase 2+0.05 2.0 hromatic radius R (λ112...050 122...505R/min(R)λλhromatic radius R (λ112...050 112...050R/min(R)λλhromatic radius R (λ112...050 11..05R/min(R)λλ c c c no 1.0 no no Mo 0.5 H2O CO H2O CO Mo 0.5 H2O CO H2O CO 0.5 Mo 0.5 H2O CO H2O CO 0.5 1200 1400 1600 1800 2000 2200 2400 1200 1400 1600 1800 2000 2200 2400 1200 1400 1600 1800 2000 2200 2400 Wavelength (nm) Wavelength (nm) Wavelength (nm) Fig.4.Monochromaticτ = 1 Mira star radiipredictedbythe M modelseriesforthe exampleof the M16n(modelphase 1.60), λ M18n(1.84),andM20(2.05)models.Theredlineindicatesthemodelcontinuumradiusexcludingatomicandmolecularfeatures. The spectral resolution of the model is 0.001µm. Also indicated are the positions of H O and CO bands after Lançon & Wood 2 (2000). showsthemonochromaticradiusR =R (τ =1)inunitsofthe shape compared to M18n (as seen for instance in the case of λ λ λ non-pulsatingparent star radius for the example of three mod- M20),andatthe sametime a justasstrongbutbroader1.9µm els of the series. It illustrates the strong phase dependence of feature(asforinstanceinthecaseofM16n).Itisquitepossible themolecularlayers.ThemodelsareM16n(modelphase1.60), that such a combination of the two water-vapor features could M18n(1.84),andM20 (2.05)models.The redlines denotefor appear for a model of another phase-cycle combination. Also, comparison the R values solely based on the continuum radi- somedifferencesbetweenMmodelpredictionsandobservations λ ation excludingall atomic and molecularfeatures. Also shown of S Ori are expected due to the different stellar parametersof arethepositionsoftheH OandCObandsafterLançon&Wood SOricomparedtotheparentstaroftheMmodelseries.Finally, 2 (2000) and references therein. The most prominentfeatures of differences can also be caused by remaining uncertainties in thesemodelcurvesinthenear-infraredregionaretwowaterva- the absolute calibration of visibility values and of the wave- por features around 1.4µm and 1.9µm, and also CO features lengthscale. TheSOridustshellofτ =1.5–2.5asmodeledin V around 1.6µm and 2.4µm. The strengths, shapes, and widths Wittkowski et al. (2007) is not expected to have a noticeable ofthesemolecularfeaturesdependstronglyonthestellarphase effect on our near-infraredvisibility data, because its contribu- (and also on cycle), as is evident from the comparison of the tiontothevisibilitywasalreadysmallat8µm andbecausethe threemodelcurves.Also,therelativestrengthsofthemolecular visibilitydataarecalibratedseparatelyforeachspectralchannel. featuresvarieswithstellarphase. In summary, our AMBER observations of S Ori generally Model M18n provides the best formal fit to our S Ori confirmthepredictionsbytheMmodelseriesandwefindthat AMBER visibility data out of the 20 available phase and cy- the observedvariation of diameter with wavelength can be un- clecombinationsoftheMseries.Thesyntheticvisibilityvalues derstood as the effect of phase-dependentwater vapor and CO basedontheM18nmodelcomparedtoourAMBERobservation layers lying above the photosphere. The M model series can areindicatedinFig.1.Here,theangularphotosphericdiameter be used reasonably well to model the atmosphere of a Mira correspondingto the 1.04µm (photospheric)modelradius (de- star such as S Ori and to derive a reliable photospheric radius finedinIrelandetal.2004b)isΘ =8.3±0.2mas,consistent M18n basedonbroadbanddata.Moresuchobservationsareneededto with the UD diameter at near-continuum wavelengths 1.3µm confirmandconstrainthemodelpredictionsin moredetailand and 1.7µm of Θ =8.1±0.5mas. The theoretical R (τ = 1) UD λ λ to monitor the predicted phase dependenceof the strength and radiiinFig.4cannotbecompareddirectlytotheUDdiameters characteristicsofthemolecularlayers.Simultaneouslyobtained derivedfromourAMBERdata(Fig.3),becauseofthedifferent spectrawouldbeavaluableaddition. spectral resolution and because the model-predicted CLVs can beverydifferentfromaUDmodel(sothatdifferentradiusdef- Acknowledgements. WeacknowledgewiththankstheuseoftheAMBERdata initions are not equal). The translation of the model prediction reductionsoftwarefromtheJMMC(version2.0beta2b). intoaUDdiameterdependsontheexactshapeofthebandpass- averaged CLV and the baselines used. To compare the model predictionsto the measured UD values in Fig. 3, we fitted UD References diameters to the synthetic visibility values of the M18n model Boboltz,D.A.,&Wittkowski,M.2005,ApJ,618,953 usingexactlythesamespectralchannels,baselineconfiguration, Borde´,P.,Coude´ duForesto,V.,Chagnon,G.,&Perrin,G.2002,A&A,393, and fit method as for our AMBER data. The resulting model 183 prediction for the UD diameter as a function of wavelength is Eisner,J.A.,Graham,J.R.,Akeson,R.L.,etal.2007,ApJ,654,L77 shown in Fig. 3, in comparison to the values derived from the Fedele,D.,Wittkowski,M.,Paresce,F.,etal.2005,A&A,431,1019 Ho¨fner,S.,&Andersen,A.C.2007,A&A,465,L39 observation. Ireland,M.,Tuthill,P.,Robertson,G.,etal.2004,ASPConf.Proc.310,327 Figures 1 and 3 show that our AMBER visibility data can Ireland,M.J.,Scholz,M.,&Wood,P.R.2004a,MNRAS,352,318 Ireland,M.J.,Scholz,M.,Tuthill,P.,&Wood,P.2004b,MNRAS,355,444 bedescribedreasonablywellbythedynamicatmospheremodel Kurucz, R. 1993, Limbdarkening for 2 km/s grid (No. 13): [+0.0] to [-5.0]. M18n. 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