A&A479,L21–L24(2008) Astronomy DOI:10.1051/0004-6361:20079237 & (cid:1)c ESO2008 Astrophysics Letter to the Editor (cid:1) 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.2,85748GarchingbeiMünchen,Germany e-mail:[email protected] 2 USNavalObservatory,3450MassachusettsAvenue,NW,Washington,DC20392-5420,USA 3 Max-Planck-InstitutfürRadioastronomie,AufdemHügel69,53121Bonn,Germany 4 ESO,Casilla19001,Santiago19,Chile 5 InstitutfürTheoretischeAstrophysikderUniv.Heidelberg,Albert-Ueberle-Str.2,69120Heidelberg,Germany 6 InstituteofAstronomy,SchoolofPhysics,UniversityofSydney,SydneyNSW2006,Australia Received12December2007/Accepted29December2007 ABSTRACT Aims.WepresentJ,H,Kspectrallydispersedinterferometrywithaspectralresolutionof35fortheMiravariableSOrionis.Weaim atmeasuringthediametervariationasafunctionofwavelengththatisexpectedduetomolecularlayerslyingabovethecontinuum- formingphotosphere.Ourfinalgoalisabetterunderstandingofthepulsatingatmosphereanditsroleinthemass-lossprocess. Methods.VisibilitydataofSOriwereobtainedatphase0.78withtheVLTI/AMBERinstrumentusingthefringetrackerFINITO at 29 spectral channels between 1.29µm and 2.32µm. Apparent uniform disk (UD) diameters were computed for each spectral channel.Inaddition,thevisibilitydataweredirectlycomparedtopredictionsbyrecentself-exciteddynamicmodelatmospheres. Results.SOrishowssignificantvariationsinthevisibilityvaluesasafunctionofspectralchannelthatcanonlybedescribedbyaclear variationintheapparentangularsizewithwavelength.Theclosurephasevaluesareclosetozeroatallspectralchannels,indicating theabsenceofasymmetricintensityfeatures.TheapparentUDangulardiameterissmallestatabout1.3µmand1.7µmandincreases by a factor of ∼1.4 around 2.0µm. The minimum UD angular diameter at near-continuum wavelengths is Θ = 8.1±0.5mas, UD correspondingtoR∼420R(cid:3).TheSOrivisibilitydataandtheapparentUDvariationscanbeexplainedreasonablywellbyadynamic atmospheremodelthatincludesmolecularlayers,particularlywatervaporandCO.Thebest-fittingphotosphericangulardiameterof themodelatmosphereisΘ =8.3±0.2mas,consistentwiththeUDdiametermeasuredatnear-continuumwavelengths. Phot Conclusions.ThemeasuredvisibilityandUDdiametervariationswithwavelengthresembleandgenerallyconfirmthepredictions by recent dynamic model atmospheres. These size variations with wavelength can be understood as the effects from water vapor andCOlayerslyingabovethecontinuum-formingphotosphere. Themajorremainingdifferencesbetweenobservationsandmodel predictionareverylikelyduetoanimperfectmatchofthephaseandcyclecombinationbetweenobservationandavailablemodels. Keywords.techniques:interferometric–stars:AGBandpost-AGB–stars:atmospheres–stars:individual:SOri–stars:mass-loss 1. Introduction betterunderstandingofpulsationandmassloss.Observedradii of Mira stars have been found to differ for different optical Mira stars are low-mass, large-amplitude, long-period variable andinfraredbandpasses(e.g.Thompsonetal.2002;Mennesson stars on the AGB, evolving toward the planetary nebula and etal.2002;Irelandetal.2004a;Perrinetal.2004;Eisneretal. white dwarf phases. They exhibita mass-loss rate on the order 2007), and this has been attributed to the presence of molec- of∼10−6M(cid:3)/yearthatsignificantlyaffectsthefurtherstellarevo- ular layers located above the continuum-formingphotosphere. lutionandisoneofthemostimportantsourcesforthechemical Here, we present both a spectro-interferometricobservation of enrichmentoftheinterstellarmedium.Thedustcondensationse- the Mira star S Ori that covers the near-infrared J, H, and K quence, the wind-drivingmechanism,and the role of pulsation bandssimultaneouslyat a spectralresolutionof 35 and a com- are currentlynotwellunderstood,in particularfor oxygen-rich parisontorecentself-exciteddynamicmodelatmospheres. AGBstars(Woitkeetal. 2006;Höfner&Andersen2007).The SOriisaMiravariablestarwithspectraltypeM6.5e–M9.5e pulsatingatmospheresofMira starscan becomeveryextended andV magnitude7.2−14.0(Samusetal.2004).WeuseaJulian becauseofdynamiceffectsincludingshockfronts,andtheyare DateoflastmaximumbrightnessT = 2453190days,aperiod verycoolintheirouterparts.Here,moleculescanform,which P = 430 days (as in Wittkowski et0al. 2007), and the distance for O-rich stars are most importantly H2O, CO, TiO, and SiO of 480 pc ± 120 pc from van Belle et al. (2002). The broad- (Tsuji et al. 1997; Tej et al. 2003; Ohnaka 2004). Wittkowski band near-infrared K UD angular diameter of S Ori has been et al. (2007) found for the case of S Ori that Al O dust 2 3 measuredbyvanBelleetal.(1996),Millan-Gabetetal.(2005), condenses within the extended atmosphere at phase-dependent andBoboltz&Wittkowski(2005)tovaluesbetween9.6masand distances of 1.8−2.4 photospheric radii. This extended atmo- 10.5mas at different phases. Joint VLTI/MIDI and VLBA/SiO sphere,whichischaracterizedbyphase-dependenttemperature maserobservationsbyWittkowskietal.(2007)haveshownthat and density stratifications, the presence of molecular layers, SOriexhibitssignificantphase-dependenciesoftheatmospheric and the formation of dust, is thus of particular interest for our extension and dust shell parameters with photospheric angular diametersbetween7.9masand9.7mas. (cid:1) BasedonobservationsmadewiththeVLTInterferometer(VLTI)at ParanalObservatoryunderprogramID080.D-0691. Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20079237 Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. 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PERFORMING ORGANIZATION US Naval Observatory,3450 Massachusetts Avenue, REPORT NUMBER NW,Washington,DC,20392-5420 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S) 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited 13. SUPPLEMENTARY NOTES 14. ABSTRACT 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 18. NUMBER 19a. NAME OF ABSTRACT OF PAGES RESPONSIBLE PERSON a. REPORT b. ABSTRACT c. THIS PAGE Same as 4 unclassified unclassified unclassified Report (SAR) Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 L22 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] [ms] [UTC] E0-G0/G0-H0/E0-H0 deg [(cid:4)(cid:4)] [ms] 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 1.2 0.4 Squared visibility amplitude 00001.....24680 SVE 0LO-TGriI0/AMBER, UGMDa1u8snsian Squared visibility amplitude 000...123 SVG L0O-TrHiI/0AMBER UGMDa1u8snsian Squared visibility amplitude 000...011505 SVE 0LO-THriI0/AMBER UGMDa1u8snsian Closure phase (deg) 1230000000 SVE 0LO-TGriI0/A-HM0BER UGMDa1u8sns 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.MeasuredSOrivisibilitydatacompared tomodelsofaUDwithaconstantdiameter(reddashedlines),ofaGaussiandiskofconstant diameter(greendashedline),andoftheM18natmospheremodel(bluesolidline).FortheprojectedbaselinelengthsandanglesseeTable1. 1.2 0.6 Squared visibility amplitude 00001.....24680 γVE 0EL-rTGiI0/AMBER, UADTLAS 9 Squared visibility amplitude 00000.....12345 γVG EL0-rTHiI/0AMBER UADTLAS 9 Squared visibility amplitude 000...011505 γVE 0EL-rTHiI0/AMBER UADTLAS 9 Closure phase (deg) 1230000000 γVE 0EL-rTGiI0/A-HM0BER UADTLAS 9 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.MeasuredγErivisibilitydatacomparedtomodelsofaUDwithaconstantdiameter(reddashedline)andofanATLAS9modelatmosphere withTeff =3750K,logg=1.5,solarchemicalabundance(bluesolidline).FortheprojectedbaselinelengthsandanglesseeTable1. 2. Observationsanddatareduction thesameFINITOcontrollerparameters,whichisimportantfor avoidingsystematicbiasesincalibratingtheabsolutevisibility. Weobtainednear-infraredJ,H, K interferometryofSOriwith In addition to S Ori, the two calibration stars 45 Eri and the instrument AMBER (Petrov et al. 2007) in low-resolution α Hor were observed close in time, as was γ Eri. The last is a mode at the ESO VLTI using the fringe tracker FINITO and regularnon-pulsatingM0.5giantwithawell-knownangulardi- three VLTI Auxiliary Telescopes (ATs) on 12 October 2007 ametersimilar to thatofSOriwhichisnotexpectedto exhibit (JD 2454386). The ATs were positioned on stations E0, G0, strongeffectsfrommolecularlayers.Thisdataisusedtocheck and H0. The date of observationcorrespondsto a visual phase that any strong wavelength-dependentfeatures found for S Ori ΦVis = 0.78, with an uncertainty of about 0.1. The details of are notcausedbyanysystematiceffectsoftheinstrument.The the observingsequencearelisted inTable1,includingthe pro- spectraltypesandangulardiametersofthecalibrationandcheck jected baseline lengths (Bp) and position angles (PAp), the air- starsarefromBordéetal.(2002). mass(AM),andtheopticalseeingandcoherencetime.Ambient Raw visibility and closure phase values were computed conditionswere not very goodbut stable. The airmass was the sameforallobservations.Datawererecordedusingtwodiffer- using the latest version of the amdlib package (version 2.0 beta 2b) and the yorick interface provided by the AMBER entdetectorintegrationtimes(DITs)of25msand50ms. consortiumandtheJean-MarieMariottiCenter.Absolutewave- TheVLTIfringe-trackerFINITOrecordsfringesonthetwo lengthcalibrationwasperformedbycorrelatingtherawspectra shortestbaselinesusing70%oftheH-bandlight.Outputsignals of all four stars with a model of the atmospheric transmission areprocessedinrealtimeandusedtocompensateforthefringe withthesamespectralresolution.Inparticular,weusedaplateau motionduetoatmosphericturbulence.Owingtothelowcoher- inthetransmissioncurveatλ ∼ 2.0µm.Theoffsetwithrespect encetimeduringtheobservations,FINITOwasonlyabletopro- totheoriginalwavelengthtablewas3spectralchannels(0.1µm videaverageperformancesof0.2−0.4µmRMS(tobecompared at a wavelength of 2.0µm). We estimated the error of the ab- with 0.1µm RMS achieved in good conditions). Nevertheless solute wavelength calibration to 1pixel (∼0.03µm). Individual such a performance is sufficient for increasing the signal-to- frameswereaveragedafterframeselectionkeeping70%ofthe noiseratio(S/R)oftheAMBERdataandstabilizingthetransfer best frames based on piston (to remove the frames when the function.Allobservationsusedherewereobtainedwithexactly FINITO loopwas notclosed)andoutof these keeping30%of M.Wittkowskietal.:J,H,Kspectro-interferometryoftheMiravariableSOrionis L23 s) S Ori M18n 1.6 The visibility data of S Ori show significant wavelength- a dependent features clearly deviating from UD and Gaussian m 12 VLTI/AMBER (E0-G0-H0) eter ( 1.4D) mindoidcealtsesovfarciaotniosntasnitndthiaemapetpearreonntanagllultahrrdeieambeatseerl.inTehse.STOhirsi k diam 10 1.2min(U cclhoasnunreelsp,hiansdeicvaatliunegstahree acbosnesniscteenotfwaisthymzmereotraict afellatsupreecstrianl dis D/ the intensity distribution. In order to characterize the variation m 8 1.0U of S Ori’s angular diameter as a function of wavelength, nifor we fitted UD diameters to the data of each spectral channel U HO CO HO CO 0.8 separately. Figure 3 shows the resulting UD diameter values 6 2 2 as a function of wavelength. Note that the intensity profile of 1200 1400 1600 1800 2000 2200 2400 a Mira star is generally not expected to be close to a UD and Wavelength (nm) that this approach can only give a rough estimate of S Ori’s Fig.3.SOriUDdiametervaluesasafunctionofwavelengthcompared characteristicsizeasafunctionofwavelength.FitsofGaussian tothepredictionbytheM18nmodelatmosphere.Alsoindicatedarethe functions lead to similar results. The apparent UD angular positionsofH2OandCObandsafterLançon&Wood(2000). diameter shows clear variations with wavelength. It is smallest at about 1.3µm and 1.7µm and increases by a factor of ∼1.4 thebestframesbasedonS/R.Weverifiedthatkeepingupto80% around 2.0µm. The minimum UD angular diameter of S Ori ofthebestframesbasedonS/Rdidnotsignificantlychangethe at the near-continuum wavelengths is ΘUD = 8.1 ± 0.5mas. This result at visual phase 0.78 is consistent with the S Ori results. The S Ori and γ Eri visibility data were calibrated for photospheric angular diameters between 7.9mas at phase each DIT value separately using the 45 Eri and α Hor calibra- tion star data. After calibration, the different calibrated S Ori 0.55 and 9.7mas at phase 1.15 derived in Wittkowski et al. (2007) based on VLTI/MIDI data and modeling with dynamic and γ Eri data were averaged.The errors of the calibrated vis- model atmospheres and a radiative transfer model of the ibility data include the statistical error of averaging the single dust shell. These photospheric angular diameters are also frames,theerrorsofthecalibrationstars’angulardiameters,and consistent with previous broadband measurements (cf. thevariationoftheavailabletransferfunctionmeasurements. Wittkowskietal.2007).WiththeadopteddistancetoSOri,the angular diameter Θ = 8.1±0.5mas correspondsto a radius UD 3. Results 418±130R(cid:3). Figures 1 and 2 show the resulting visibility and closure phase 4. ComparisontodynamicMirastaratmosphere dataforSOriandforthecheckstarγEri,respectively.Thegaps models inthevisibilitydataaround1.45µmand1.85µmcorrespondto the regions between the bands. Also shown are the best fitting Fewdynamicatmospheremodelsforoxygen-richMirastarsare models of a UD with a constant diameter, of a Gaussian disk availablethatincludetheeffectsofmolecularlayers.ThePand with a constant diameter, and of atmosphere models. The lat- Mmodelseries(Irelandetal.2004b,c)arecompleteself-excited ter are forS Orithe M18nmodel(describedin detailbelow in dynamicmodelatmospheresofMirastarsdesignedtomatchthe Sect. 4),andforγ Erian ATLAS9 modelatmosphere(Kurucz prototype oxygen-rich Mira stars o Cet and R Leo. They have 1993)withTeff =3750K,logg=1.5,andsolarchemicalabun- beenusedsuccessfullyforcomparisonstorecentbroadbandin- danceasexpectedforγEri(Bordéetal.2002).Thecomparison terferometric data of o Cet and R Leo (Woodruff et al. 2004; oftheSOrivisibilitydatatothedynamicmodelatmosphereis Fedele et al. 2005). Compared to o Cet and R Leo, S Ori is a describedindetailbelowinSect.4. slightlycoolerMiravariablewithalongerperiod,ahighermain- The calculation of synthetic visibility values and the fits to sequence precursor mass, and a larger radius. However, when the interferometricdatawere performedasinWittkowskietal. scaled to variability phases between 0 and 1 and to the corre- (2006,2007).ThefittedangulardiameteroftheGaussianmodel spondingangularsize onthe sky,the generalmodelresultsare correspondsto the FWHM, that of the plane-parallelATLAS9 notexpectedtobedramaticallydifferentforSOricomparedto modeltothe0%intensity(limb-darkened)radius,andthatofthe o CetandR Leo(cf.the discussioninWittkowskietal.2007). M18nmodeltothe1.04µm(photospheric)radius(asdefinedin The M model series was chosen to model the atmosphere of Ireland et al. 2004c). The best-fit angular diameters are S Ori: S Ori by Wittkowski et al. (2007) as the currently best avail- ΘUD = 10.8mas;ΘGaussian = 6.9mas;ΘM18n = 8.3mas;γEri: able option to describeMira star atmospheres. Monochromatic Θ =8.5mas;Θ =8.9mas.Theerrorsareσ∼0.2mas. center-to-limbvariations(CLVs)at46anglesbetween0and5R UD ATLAS9 p The visibility data of the check star γ Eri can be described based on the P and M models were recomputed for the wave- well by a UD of constant diameter and by the ATLAS9 model lengthrangefrom1−2.5µminstepsof0.001µm. atmosphere.Therearenosignificantwavelength-dependentde- The P and M dynamic model atmospheres predict signifi- viationsbetweenmeasuredvisibilitydataandtheUDmodel.It cant changes in the monochromatic radius R = R (τ = 1), λ λ λ isnotyetclearwhethertherelativelylow J-bandvisibilitiesfor causedbymolecularlayersthatlieabovethecontinuum-forming theG0-H0baselineandthedeviationsintheclosurephaseval- photosphereandsignificantlyaffectcertainbandpasses.Figure4 uesnearthefliparecausedbyanasymmetricstellarsurfacefea- shows the monochromatic radius R = R (τ = 1) in units λ λ λ tureorasystematiccalibrationuncertainty.Notethattheangular of the non-pulsatingparentstar radiusforthe exampleof three diameterofγEribasedonagivenmodeliswell-constrainedby models of the series. It illustrates the strong phase dependence thepositionofthevisibilityminimum,whichisindependentof of the molecular layers. The models are M16n (model phase anabsolutevisibilitycalibration.Theresultingangulardiameter 1.60), M18n (1.84), and M20 (2.05) models. The red lines de- Θ = 8.9±0.2mas is consistent with the value given in note for comparison the R values solely based on the con- ATLAS9 λ Bordéetal.(2002)ofΘ =8.74±0.09mas. tinuum radiation excluding all atomic and molecular features. LD L24 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)λλ hromatic radius R (λ112...050 112...050R/min(R)λλ hromatic radius R (λ112...050 11..05R/min(R)λλ noc 1.0 noc noc 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 =1MirastarradiipredictedbytheMmodelseriesfortheexampleoftheM16n(modelphase1.60),M18n(1.84),and λ M20(2.05)models.Theredlineindicatesthemodelcontinuumradiusexcludingatomicandmolecularfeatures.Thespectralresolutionofthe modelis0.001µm.AlsoindicatedarethepositionsofH OandCObandsafterLançon&Wood(2000). 2 Also shown are the positions of the H O and CO bands after uncertaintiesin the absolute calibrationof visibility valuesand 2 Lançon&Wood(2000)andreferencestherein.Themostpromi- of the wavelength scale. The S Ori dust shell of τ = 1.5−2.5 V nent features of these model curves in the near-infraredregion asmodeledinWittkowskietal.(2007)isnotexpectedtohavea aretwowatervaporfeaturesaround1.4µmand1.9µm,andalso noticeableeffectonournear-infraredvisibilitydata,becauseits CO features around 1.6µm and 2.4µm. The strengths, shapes, contributionto the visibility was alreadysmallat 8µm and be- and widths of these molecular features depend strongly on the causethevisibilitydataarecalibratedseparatelyforeachspec- stellarphase(andalsooncycle),asisevidentfromthecompari- tralchannel. sonofthethreemodelcurves.Also,therelativestrengthsofthe In summary, our AMBER observations of S Ori generally molecularfeaturesvarieswithstellarphase. confirm the predictions by the M model series and we find Model M18n provides the best formal fit to our S Ori thatthe observedvariationof diameterwith wavelengthcan be AMBER visibility data out of the 20 available phase and cy- understood as the effect of phase-dependent water vapor and clecombinationsoftheMseries.Thesyntheticvisibilityvalues CO layers lying above the photosphere. The M model series basedontheM18nmodelcomparedtoourAMBERobservation canbeusedreasonablywelltomodeltheatmosphereofaMira areindicatedinFig.1.Here,theangularphotosphericdiameter star such as S Ori and to derive a reliable photospheric radius correspondingto the 1.04µm (photospheric)modelradius(de- basedonbroadbanddata.Moresuchobservationsareneededto finedinIrelandetal.2004c)isΘ =8.3±0.2mas,consistent confirmandconstrainthe modelpredictionsinmoredetailand M18n with the UD diameter at near-continuum wavelengths 1.3µm to monitor the predicted phase dependence of the strength and and1.7µmofΘ = 8.1±0.5mas.ThetheoreticalR (τ = 1) characteristicsofthemolecularlayers.Simultaneouslyobtained UD λ λ radiiinFig.4cannotbecompareddirectlytotheUDdiameters spectrawouldbeavaluableaddition. derivedfromourAMBERdata(Fig.3),becauseofthedifferent Acknowledgements. WeacknowledgewiththankstheuseoftheAMBERdata spectral resolution and because the model-predicted CLVs can reductionsoftwarefromtheJMMC(version2.0beta2b). beverydifferentfromaUDmodel(sothatdifferentradiusdef- initions are not equal). The translation of the modelprediction intoaUDdiameterdependsontheexactshapeofthebandpass- References averaged CLV and the baselines used. To compare the model Boboltz,D.A.,&Wittkowski,M.2005,ApJ,618,953 predictionstothemeasuredUDvaluesinFig.3,wefittedUDdi- Bordé,P.,CoudéduForesto,V.,Chagnon,G.,&Perrin,G.2002,A&A,393, ameterstothesyntheticvisibilityvaluesoftheM18nmodelus- 183 ing exactly the same spectral channels, baseline configuration, Eisner,J.A.,Graham,J.R.,Akeson,R.L.,etal.2007,ApJ,654,L77 and fit method as for our AMBER data. The resulting model Fedele,D.,Wittkowski,M.,Paresce,F.,etal.2005,A&A,431,1019 Höfner,S.,&Andersen,A.C.2007,A&A,465,L39 prediction for the UD diameter as a function of wavelength is Ireland,M.,Tuthill,P.,Robertson,G.,etal.2004a,ASPConf.Proc.,310,327 shown in Fig. 3, in comparison to the values derived from the Ireland,M.J.,Scholz,M.,&Wood,P.R.2004b,MNRAS,352,318 observation. Ireland,M.J.,Scholz,M.,Tuthill,P.,&Wood,P.2004c,MNRAS,355,444 Figures 1 and 3 show that our AMBER visibility data Kurucz, R.1993, Limbdarkening for2kms−1 grid, No.13:[+0.0]to[−5.0]. KuruczCD-ROMNo.17,SmithsonianAstrophysicalObservatory can be described reasonably well by the dynamic atmosphere Lançon,A.,&Wood,P.R.2000,A&AS,146,217 modelM18n.The differencesbetween observationsand model Mennesson,B.,Perrin,G.,Chagnon,G.,etal.2002,ApJ,579,446 prediction are most likely due to an imperfect match of the Millan-Gabet,R.,Pedretti,E.,Monnier,J.D.,etal.2005,ApJ,620,961 phaseandcyclecombinationbetweenobservationandavailable Ohnaka,K.2004,A&A,424,1011 Perrin,G.,Ridgway,S.T.,Mennesson,B.,etal.2004,A&A,426,279 M models of the series. Looking at Figs. 3 and 4, it is evident Petrov,R.G.,Malbet,F.,Weigelt,G.,etal.2007,A&A,464,1 that a better fit to our AMBER data could be obtained with a Samus,N.N.,Durlevich, O.V.,&etal.2004,CombinedGeneral Catalog of model that shows a stronger 1.4µm water vapor feature of the VariableStars,GCVS4.2,2004Ed.,VizieROnlineDataCatalog,2250 sameshapecomparedtoM18n(asseenforinstanceinthecase Tej,A.,Lançon,A.,&Scholz,M.2003,A&A,401,347 ofM20),andatthesametimeajustasstrongbutbroader1.9µm Thompson,R.R.,Creech-Eakman,M.J.,&vanBelle,G.2002,ApJ,577,447 Tsuji,T.,Ohnaka,K.,Aoki,W.,&Yamamura,I.1997,A&A,320,L1 feature (as for instance in the case of M16n). It is quite pos- vanBelle,G.T.,Dyck,H.,Benson,J.,&Lacasse,M.1996,AJ,112,2147 sible that such a combination of the two water-vapor features vanBelle,G.T.,Thompson,R.R.,&Creech-Eakman,M.J2002,AJ,124,1706 could appear for a model of another phase-cycle combination. Wittkowski, M.,Hummel,C.A.,Aufdenberg,J.P.,&Roccatagliata, V.2006, Also, some differences between M model predictions and ob- A&A,460,843 servations of S Ori are expected due to the differentstellar pa- Wittkowski, M.,Boboltz, D.A.,Ohnaka, K.,Driebe, T.,&Scholz, M.2007, A&A,470,191 rameters of S Ori compared to the parent star of the M model Woitke,P.2006,A&A,460,L9 series. Finally, differences can also be caused by remaining Woodruff,H.C.,Eberhardt,M.,Driebe,T.,etal.2004,A&A,421,703