What causes the large extensions of red-supergiant atmospheres? Comparisons of interferometric observations with 1-D hydrostatic, 3-D convection, and 1-D pulsating model atmospheres

1.3 MB·English

by  B. Arroyo-Torres

Astronomy&Astrophysicsmanuscriptno.RSG+models˙v3 (cid:13)c ESO2015
January8,2015
What causes the large extensions of red-supergiant atmospheres?
Comparisons of interferometric observations with 1-D hydrostatic, 3-D
⋆
convection, and 1-D pulsating model atmospheres
B.Arroyo-Torres1,M.Wittkowski2,A.Chiavassa3,M.Scholz4,5,B.Freytag6,J.M.Marcaide1,7,P.H.Hauschildt8,
P.R.Wood9,andF.J.Abellan1
1 Dpt.AstronomiaiAstrof´ısica,UniversitatdeVale`ncia,C/Dr.Moliner50,46100,Burjassot,Spaine-mail:[email protected]
5 2 ESO,Karl-Schwarzschild-St.2,85748,GarchingbeiMu¨nchen,Germany
1 3 LaboratoireLagrange,UMR7293,Universite´ deNiceSophia-Antipolis,CNRS,ObservatoiredelaCoˆtedAzur,BP.4229,06304
0 NiceCedex4,France
2 4 Zentrum fu¨r Astronomie der Universita¨t Heidelberg (ZAH),Institut fu¨r Theoretische Astrophysik, Albert-Ueberle-Str. 2, 69120
Heidelberg,Germany
n 5 SydneyInstituteforAstronomy,SchoolofPhysics,UniversityofSydney,SydneyNSW2006,Australia
a 6 DepartmentofPhysicsandAstronomyatUppsalaUniversity,Regementsva¨gen1,Box516,SE-75120Uppsala,Sweden
J 7 DonostiaInternationalPhysicsCenter,PaseodeManuelLardizabal4,20018Donostia-SanSebastia´n,Spain

7 8 HamburgerSternwarte,Gojenbergsweg112,21029,Hamburg,Germany
9 ResearchSchoolofAstronomyandAstrophysics,AustralianNationalUniversity,CotterRoad,WestonCreekACT2611,Australia

]
R Received24October2014;Accepted23December2014
S
. ABSTRACT
h
p Aims.This research has two main goals. First, we present the atmospheric structure and the fundamental parameters of three red
- supergiants(RSGs),increasingthesampleofRSGsobservedbynear-infraredspectro-interferometry.Additionally,wetestpossible
o
mechanismsthatmayexplainthelargeobservedatmosphericextensionsofRSGs.
r
t Methods.Wecarriedoutspectro-interferometricobservationsoftheRSGsV602Car,HD95687,andHD183589inthenear-infrared
s K-band(1.92-2.47µm)withtheVLTI/AMBERinstrumentatmediumspectralresolution(R∼1500).Tocategorizeandcomprehend
a
the extended atmospheres, we compared our observational results to predictions by available hydrostatic PHOENIX, available 3-D
[
convection,andnew1-Dself-excitedpulsationmodelsofRSGs.

1 Results.Ournear-infraredfluxspectraofV602Car,HD95687,andHD183589arewellreproducedbythePHOENIXmodelatmo-
v spheres.Thecontinuumvisibilityvaluesareconsistentwithalimb-darkeneddiskaspredictedbythePHOENIXmodels,allowingusto
0 determinetheangulardiameterandthefundamentalparametersofoursources.Nonetheless,inthecaseofV602CarandHD95686,
6 thePHOENIXmodelvisibilitiesdonotpredictthelargeobservedextensionsofmolecularlayers,mostremarkablyintheCObands.
5 Likewise,the3-Dconvectionmodelsandthe1-DpulsationmodelswithtypicalparametersofRSGsleadtocompact atmospheric
1 structures as well, which are similar to the structure of the hydrostatic PHOENIX models. They can also not explain the observed
0 decreasesinthevisibilitiesandthusthelargeatmosphericmolecularextensions.ThefullsampleofourRSGsindicatesincreasing
. observedatmosphericextensionswithincreasingluminosityanddecreasingsurfacegravity,andnocorrelationwitheffectivetemper-
1
atureorvariabilityamplitude.
0
Conclusions.ThelocationofourRSGsourcesintheHertzsprung-Russelldiagramisconfirmedtobeconsistentwiththeredlimitsof
5
recentevolutionarytracks.TheobservedextensionsoftheatmosphericlayersofoursampleofRSGsarecomparabletothoseofMira
1
stars.Thisphenomenonisnotpredictedbyanyoftheconsideredmodelatmospheresincludingavailable3-Dconvectionandnew1-D
:
v pulsationmodelsofRSGs.ThisconfirmsthatneitherconvectionnorpulsationalonecanlevitatethemolecularatmospheresofRSGs.
i OurobservedcorrelationofatmosphericextensionwithluminositysupportsascenarioofradiativeaccelerationonDoppler-shifted
X
molecularlines.
r
a Keywords.supergiants–Star:fundamentalparameters–Star:atmospheres–Star:individual:V602Car,HD95687andHD183589.
1. Introduction of Mira-variable AGB stars (mass-loss rates of 10−6M /yr –
⊙
10−4M /yr, Wood et al. 1983, 1992), this mechanism is better
⊙
Redsupergiant(RSG)starsareknowntolosemasswithmass-
understood.ThetheoreticalmodelsthatexplaintheMiramass-
loss rates of 2 × 10−7M /yr – 3 × 10−4M /yr (de Beck et al.
⊙ ⊙ lossprocessarebasedonpulsationsthatextendtheatmospheres
2010), and they are one of the major sources of the chemical
toradiiwheredustcanform,andsubsequentlyonradiativepres-
enrichment of galaxies and of dust in the universe, along with
sureondustgrainsthatdrivesthewind(e.g.,Bladhetal.2013).
asymptoticgiantbranch(AGB)starsandsupernovae.Currently,
InthecaseofvariableRSGs,theamplitudeofthelightcurvesis
themechanismofmasslossofRSGstarsandsemi-regularorir-
aboutone-thirdofthatofMiras(e.g.,Woodetal.1983),sothat
regular AGBs is not known in detail. Nevertheless, in the case
pulsation is expected to play a less dominant role (cf. Josselin
& Plez 2007). Other mechanisms that might give rise to mass
⋆ Based onobservations made withtheVLTInterferometer (VLTI)
loss in the RSGs are convection and rotation (e.g., Langer &
atParanalObservatoryunderprogrammeID091.D-0275
1
B.Arroyo-Torresetal.:LargeextensionsofRSGatmospheres
Heger1999).Constraintsonthemechanismsthatlevitatetheat- inmedium-resolutionmode(R ∼1500)intheK-2.1µmandK-
mospheresofRSGsarethusfundamentalforourunderstanding 2.3µmbands.Theintegrationtime(DIT)ofeachframewas20
ofthemass-lossprocessofRSGstars. ms. Our data were observed as sequences of cal-sci-cal (cal is
ObservationsofMiravariablestarsusingtheIOTAorVLTI calibrator and sci is our target),with 5 scans for each of them.
interferometersshow evidenceof molecularlayers lying above Table1liststhedetailedinformationaboutourobservationsand
thephotosphericlayers(e.g.,Perrinetal.2004;Wittkowskietal. thecalibratorusedforeachtarget.Table2showsthecalibrators
2008, 2011). Theoretical dynamic model atmospheres (Ireland usedforourobservationstogetherwiththeirangulardiameters.
etal.2004a,2004b,2008,2011;Scholzetal.2014)canexplain WeselectedthemfromtheESOCalibrationSelectorCalVin,in
reasonablywell these molecularlayersfor Miras. On the other turnbasedonthecatalogofLafrasseetal.(2010).
hand, interferometric observations of RSGs also indicate the DuringtheacquisitionofoneAMBERframe,thereareop-
presence of extended molecular layers (CO and water), which ticalpathfluctuations(jitter)thatproducefringemotions.These
cannot be explained by hydrostatic model atmospheres (Perrin motionsreducethe squaredvisibility by a factor e−σ2φ, FINITO
et al. 2005; Ohnakaetal. 2011, 2013; Wittkowskiet al. 2012). factor, where σ is the fringe phase standard deviation over
φ
The red supergiant VX Sgr (Chiavassa et al. 2010a) showed a the frame acquisition time. This attenuation is corrected in the
goodagreementwithMiramodels,althoughtheyhaveverydif- science data by the calibration provided the FINITO factors
ferentstellarparametersthanexpectedforthissource. are similar in science and calibrator (more information in the
Thispaperisconceivedaspartofaseriesofthreeprevious AMBERUserManual1).
papers(Wittkowskietal.2012;Arroyo-Torresetal.2013,2014). As a first step we selected the scans such that the FINITO
Inthesepreviousworks,wepresentedtheatmospherestructure factorsweresimilarbetweencalandscidata.Afterthat,weob-
and the fundamentalparametersof a sample of four RSG stars tainedthevisibilitydatafromourselectedAMBERobservations
andfivecoolgiantstars.Onegoalofthecurrentpaperistoadd using the 3.0.7 version of the amdlib data reduction package
three red supergiants and thus to increase this sample. On the (Tatullietal.2007;Chellietal.2009).Thisincludedtheremoval
otherhand,ourpreviousworksshowedthattheobservedvisibil- ofthebadpixelmapandthecorrectionfortheflatcontribution.
itydataoftheRSGsandofoneoftheredgiants,βPeg,indicate Afterwards,wecalculatedthepixel-to-visibilitymatrix(P2VM)
largeextensionsofthemolecularlayers,similarasthoseprevi- tocalibrateourdatafortheinstrumentaldispersiveeffects, and
ously observedfor Mira variablestars (Wittkowskiet al. 2008, obtained the interferometricobservables (visibility and closure
2011).ThiswasnotpredictedbyhydrostaticPHOENIXmodelat- phase). Next, we appended all scans of the same source taken
mospheres.However,thespectraofallourstarswerereproduced consecutively,selectedandaveragedtheresultingvisibilitiesof
wellby the PHOENIXmodels. Thisindicatesthatthe molecular each frame using appropriate criteria. In our case, the criteria
opacitieswereadequatelyincludedinthesemodelatmospheres, werebasedontheflux(weselectedallframeshavingfluxdensi-
butthattheyweretoocompactcomparedtoobservations.Inor- tiesthreetimeshigherthanthenoise)andonthesignal-to-noise
der to understand the processes that may explain the extended ratio(S/N).Weonlyused80%oftheremainingframeswithbest
molecularlayers,thesecondgoalofthispaperisto investigate S/N2.
the effects of realistic three-dimensional(3-D)radiativehydro- Using scripts of IDL (Interactive Data Language), which
dynamical(RHD)simulationsofstellarconvectionaswellasof have been developed by us, we performed the absolute wave-
one-dimensional(1-D)self-excitedpulsationmodelsontheex- length calibrationby correlatingthe AMBER flux spectra with
tensionsofRSGatmospheres.Theseprocesseswerepreviously a reference spectrum, that of the star BS 4432 (spectral type
discussedaspossiblemechanismstolevitateRSGatmospheres K4.5 III, similar to our calibrators; Lanc¸on & Wood 2000). A
(Chiavassaetal.2010a,2011a). relative flux calibration of the targets was performed by using
Inthispaper,inadditiontostudyingRSGs,wealsoreferto the instrumental response, estimated by the calibrators and the
asymptotic giant branch stars (AGBs), Mira variable stars, and BS4432spectrum.Finally,calibratedvisibilityspectrawereob-
redgiantstars.AGBstarsarelowandintermediatemassevolved tained by using the average of two transfer function measure-
starsbeforetheyevolvetowardhottertemperaturesintheHRdi- mentstakenbeforeandaftereachsciencetargetobservation.In
agram.Mirastarsarelong-periodlarge-amplitudevariableAGB the case of V602 Car (25-26 April), HD 95687 (24-25 April)
stars. With red giants we refer to giants on the first red giant andHD 183589(03-04August),weonlyusedthefirstcalibra-
branch. tor,becausetheothercalibratorhadverydifferentFINITOfac-
Our work is structured as follows: In Sect. 2, we describe torsandtheirvisibilitieswerenotofsufficientquality.Theerror
ourAMBERobservationsandthedatareduction.InSect.3we of the transferfunctionwas calculatedas in our previouswork
present the results obtained from the PHOENIX model fitting (Arroyo-Torresetal.2013,2014).
andthefundamentalparameters.InSect.4,wecharacterizethe
extensions of the atmospheres. In Sect. 5, we show the results
3. Results
obtained from the comparison with the convection and pulsa-
tion modelsandwe discussalternativemechanisms.Finally,in We compared our observational data to synthetic data pro-
Sect.6,wesummarizeourresultsandconclusions. videdbyagridofPHOENIXmodelatmospheres(version16.03,
Hauschildt & Baron 1999 from Arroyo-Torres et al. 2013).
These models are based on a hydrostatic atmosphere, local
2. Observationsanddatareduction thermodynamic equilibrium and spherical geometry. The best-
fit PHOENIX model is obtained from an iterative process using
We observed V602 Car (Simbad spectral type M3-M4 I),
the continuum band around 2.25µm, as explained by Arroyo-
HD 95687 (M3 Iab), and HD 183589 (K5 Ib) with the ESO
Torres et al. (2013). The final values for the used PHOENIX
Very Large Telescope Interferometer(VLTI), utilizing three of
the Auxiliary Telescopes of 1.8m diameter, and the AMBER 1 http://www.eso.org/sci/facilities/paranal/instruments/amber/doc.html
instrument(AstronomicalMulti-BEamcombineR)withtheex- 2 see AMBER Data Reduction Software User Manual;
ternal fringe tracker FINITO (Petrov et al. 2007). We worked http://www.jmmc.fr/doc/approved/JMMC-MAN-2720-0001.pdf
2
B.Arroyo-Torresetal.:LargeextensionsofRSGatmospheres
Table1.VLTI/AMBERobservations
Target(Sp.type) Date Mode Baseline Projectedbaseline PA Calibrator
2013- K-(µm) m deg
04-04 2.1 A1-G1-K0 75.86/80.02/127.8 91/21/55
V602Car(M3-M4I) 04-04 2.3 A1-G1-K0 79.89/68.52/112.6 130/48/93 HR4164-zCar
04-26 2.3 D0-H0-G1 63.22/58.73/64.46 71/-172/125
04-04 2.1 A1-G1-K0 73.06/80.57/128.6 80/14/45
HD95687(M3Iab) 04-04 2.3 A1-G1-K0 79.94/71.35/117.5 121/43/85 HR4164-zCar
04-25 2.3 D0-H0-G1 56.88/53.89/69.30 104/-153/153
05-04 2.1 D0-I1-G1 78.89/45.56/63.26 99/-134/134
HD183589(K5Ib) 07-29 2.3 D0-I1-G1 69.75/46.61/55.98 99/-134/141 38Aql-HR7404
08-04 2.1 A1-G1-K0 88.87/67.14/126.2 -145/-72/-114
Notes.Detailsofourobservations.TheprojectedbaselineistheprojectedbaselinelengthfortheATVLTIbaselineused,andPAistheposition
angleofthebaseline(norththrougheast).
2.5 0.5
V602 Car K-2.3 (25-26 April) a) de V602 Car K-2.3 (25-26 April)UD (Θ2.25µm= 5.11 mas) b)
x 2.0 VLTI/AMBER plitu 0.4 VLTI/AMBER PHOENIX (ΘRoss= 5.25 mas)
u m
d fl 1.5 y a 0.3
malize 1.0 sibilit 0.2
Nor ed vi
0.5 ar 0.1
u
q
S
0.0 0.0
2100 2200 2300 2400 2200 2300 2400
Wavelength (nm) Wavelength (nm)
8
as) VV6L0T2I /CAaMr KBE-2R.3 (25-26 April) c) 40 V602 Car K-2.3 (25-26 April) d)
meter (m 67 G1-H0-D0 e (deg) 20 VLTI/AMBER
dia has 0
sk 5 e p
di ur
m os -20
or 4 Cl
Unif -40
3
2100 2200 2300 2400 2150 2200 2250 2300 2350 2400 2450
wavelength (nm) Wavelength (nm)
Fig.1.Normalizedflux(a),squaredvisibilityamplitudes(b),UDdiameters(c),andclosurephases(d)fortheexampleofV602Car
obtainedwiththeMR-K2.3µmsetting,on26April2013.Inblacktheobserveddata,inbluetheUDmodel,andinredthePHOENIX
model.
modelatmosphereare:ForV602Car,T =3400K,log(g)=-0.5; curve)andthebest-fitPHOENIXmodelatmosphere(redcurve).
eff
for HD 95687, T =3400K, log(g)=0.0; and for HD 183589, Thedataandbest-fitmodelsfortheremainingdataareshownin
eff
T =3700K, log(g)=1.0. For all cases, we used a model with theonlineappendix(Figs.2–6).
eff
solar metallicity and a micro-turbulent velocity of 2km/s. We Thenormalizedfluxspectrashowtypicalspectraofredsu-
choseamassof20M⊙forV602CarandHD95687andof1M⊙ pergiantsintheKband(cf.Lanc¸onetal.2007;Arroyo-Torreset
forHD183589.Wechosealowmassof1M⊙ forthelattertar- al.2013).Thefluxvariationsatwavelengthsbelowabout2.0µm
get,becausethefinalparametersindicatethatitisasourcewith are due to a higher noise level, possibly caused by the lower
lower luminosity and thus lower mass compared to the other atmospherictransmission. In the K-2.3 band,we observea de-
RSGsources.Wenotethatthestructureoftheatmosphereisnot creasingfluxlongwardsof2.25µm andstrongabsorptionlines
verysensitivetovariationsofthemass(Hauschildtetal.1999). ofCO.ThesyntheticspectraofthePHOENIXmodelatmosphere
Certainly,anyofthosestructurevariationsarebelowthelevelof areinagoodagreementwithourfluxspectraincludingtheCO
thedetectabilityofourinterferometer. bandheads.This indicates that the opacitiesof CO are well re-
Fig. 1 shows as an example the resulting normalized flux, producedbythePHOENIXmodelatmosphere.
squaredvisibilityamplitude,uniformdiskdiameter,andclosure Thecontinuumvisibilityvaluesnear2.25µmareconsistent
phase data for one of our sources, V602 Car, obtained on 26 withthepredictionsbythePHOENIXmodelatmospheresforall
April2013.Alsoshownarethebest-fituniformdiskmodel(blue oursources.InthecaseofHD183589,thevisibilityspectrumis
3
B.Arroyo-Torresetal.:LargeextensionsofRSGatmospheres
Table2.Calibrationsources 1.2
e V602 Car UD
d
HR4164 SpeKct1raIlIItype Angula1r.6d4ia±m0e.1te2r(mas) mplitu 01..80 VLTI/AMBER PHOENIX
zCar M6 1.54±0.11 y a
3H8RA7q4l04 KK32III 21..2127±±00..0028 sibilit 0.6
vi 0.4
d
e
uar 0.2
featurelessandconsistentwiththePHOENIXmodelatmosphere q
S
predictionacrossthewholeobservedwavelengthrange.Inpar- 0.0
ticular,thevisibilityspectrumofthissourcedoesnotshowfea- 0 50 100 150 200 250 300
Spatial frequency (1/arcsec)
turesatthelocationsoftheCObandheads,whicharevisiblein
the flux spectrum, indicating a compact atmospheric structure 1.2
e HD 95687 UD
wheretheCOlayersarelocatedclosetothecontinuum-forming d
u 1.0 VLTI/AMBER PHOENIX
layers.Nonetheless,V602CarandHD95687showlargedrops plit
ofthevisibilityintheCObandheadsbetween2.3µmand2.5µm m 0.8
a
thatarenotreproducedbythePHOENIXmodelatmosphere.The y
synthetic PHOENIX visibility spectra show features in the CO bilit 0.6
lines, but these are much weaker than the observed features. visi 0.4
This effect is also reflected in the panels showing the uniform ed
diskdiameter.ThesizeincreasesofUDfitsattheCObandheads uar 0.2
q
areabout40%forV602Carand20%forHD95687,whilethe S
0.0
PHOENIXmodelspredictUDsizeincreasesbelow5%.Thesere-
0 50 100 150 200 250 300
sultsindicatethatthesesourcesexhibitalargecontributionfrom Spatial frequency (1/arcsec)
extended atmospheric layers in the CO bands. The PHOENIX
1.2
modelstructuresaretoocompactcomparedtoourobservations e HD 183589 UD
d
fyoorntdhe2s.e3tµwmo,swouhriccehsm.Wayeablesocaoubsseedrvbeyapmseoundooto-cnoicndtiencuruemasecobne-- plitu 1.0 VLTI/AMBER PHOENIX
m 0.8
tributions from CO or by contributions from water vapor. We y a
observed the same phenomenon previously for the red super- bilit 0.6
giantsVYCMa(Wittkowskietal.2012),AHSco,UYSct,and si
KW Sgr (Arroyo-Torreset al. (2013), as well as for the small- d vi 0.4
amplitudepulsatingredgiantsRSCap(Marti-Vidaletal.2011), uare 0.2
BKVir(Ohnakaetal.2012),αTau(Ohnaka2013b),andβPeg q
S
(Arroyo-Torresetal.2014). 0.0
The closure phase data of our sources in the 4th panels of 0 50 100 150 200 250 300
Spatial frequency (1/arcsec)
Fig.1andFigs.2–6showvariationswithinthenoiselevel,and
are thus are not indicative of deviations from point symmetry. Fig.7.Squaredvisibilityamplitudesinthecontinuumbandpass
However,since our measurementslie in the first visibility lobe for V602 Car, HD 95687, and HD 183589 (from top to bot-
andthe noise levelis relativelyhigh,we cannotexcludeasym- tom)asafunctionofspatialfrequency.Eachpointrepresentsan
metriesonscalessmallerthantheobservedstellardisk.Wenote average of data pointswithin the continuumbandpassat 2.15–
that there are points in the observed closure phases whose de- 2.25µm.Shownaredataofallobservingdatesandbothspectral
viationfromzeroislargerthantheerrorbars.Ingeneral,small setups.Theredlinesindicatethebest-fitUDmodelsandtheblue
deviationsfromzeroclosurephasesmightindicateasymmetries lines(oftenindistinguishablefromthered)thebest-fitPHOENIX
in layers corresponding to certain atomic or molecular bands models.Thedashedlinesindicatethe maximumandminimum
aspreviouslyobservedforRSGs bye.g.,Ohnakaetal. (2011), visibilitycurves,fromwhichweestimatedtheangulardiameter
Wittkowskietal.(2012),Ohnakaetal.(2013).However,itisnot errors.
clearwhetherinourcasethisdeviationarerealorwhetherthey
correspondto systematic uncertaintiesofthe data reduction,as
forinstanceduetothebadpixelmask.
and0.93forHD183589.Themodelfitsusedallavailabledata
takenduringallnightsandwith anyofthetwo spectralsetups,
3.1.Estimateoftheangulardiameter
asbothsetupsincludethecontinuumbandnear2.25µm.Tab.3
Thecontinuumbandnear2.25µmappearstobelargelyfreeof liststheresultingbest-fitRosselandangulardiametersaswellas
contaminationsbymolecularlayers.Thus,fitsofPHOENIXmod- thebest-fitUDdiameters.Fig.7showsthecontinuumvisibility
elsto the continuumbandallow usto estimate reliableangular dataasafunctionofspatialfrequencytogetherwiththebest-fit
diametersofoursources.Theangulardiameter,obtainedinthis PHOENIXandUDmodels.Theerrorsofthecontinuumvisibili-
way, correspondsto the size of the outermostmodellayer (0% ties data were computedas an averageof the individualerrors,
intensity radius). To estimate the Rosseland angular diameter whereas, the errorsof the angular diameter are estimated from
(corresponding to the layer where the Rosseland optical depth the differencesbetween the visibility curveslying at the maxi-
equals2/3),wemultipliedourvalueoftheangulardiameterby mumandminimumofourdataasshownbythedashedlinesin
theratiobetweentheRosselandlayerandtheoutermostmodel Fig. 7. Deviatingvisibility pointsarecausedbyremainingsys-
layer. This ratio was 0.92 for V602 Car, 0.95 for HD 95687, tematic uncertainties of the absolute visibility calibration. The
4
B.Arroyo-Torresetal.:LargeextensionsofRSGatmospheres
Table3.Summaryofestimatedangulardiameters 6
40 M
RSGs sun
V602Car HD95687 HD183589 6 2 32 Msun
θUD(mas) 4.94±0.75 3.17±0.50 2.95±0.50 13 5 2250 MMsun
θRoss(mas) 5.08±0.75 3.26±0.50 3.04±0.50 7 sun
5 4 1- AH Sco 15 M
sun
8 2- UY Sct 12 M
sun
5000 3-KW Sgr 9 M
14 Dyck et al. 1998 sun
Levesque et al. 2005 4- Betelgeuse 7 M
sun
Effective temperature (K) 3344050500000000 1234567....... AUKVBVVeHYWYX6t0e SSCS2lSg ccgMgCeotr ru a a sr e 911111.01234 H..... εNβψγD O H U PP1cy e8ePtag3 ga 5 v8 9 9 3v5an14 1B18e3l7le 12et al.16 200091125 log (L/L)sun34 19111130215 5678911-----01 VVVHH -- YX6DDεβ 0O CS91P258c gMeC63trga85ar789 543 MMMsssuuunnn
8. HD 95687 15. RS Cap
12 - NU Pav
2500 RGs 13- ψ Peg
K0 K5 M4 14 - γ Hya
Spectral type
15 - RS Cap
14
Fig.8.Effectivetemperatureversusspectraltypeofoursources, 2
together with calibrations of the effective temperature scale by 3.8 3.6 3.4 3.2 3.0 2.8
Dyck etal. (1998), Levesqueet al. (2005), andvan Belle et al. log (T [K])
eff
(2009).Also includedarepreviousmeasurementsofRSGsand
redgiantsaslistedinthemaintext.InbluearetheRSGsandin Fig.9. Location of our sources in the HR diagram, compared
redtheredgiants. toevolutionarytracksfromEkstro¨metal.(2012)formassesof
3M , 4M , 5M , 7M , 9M , 12M , 15M , 20M , 25M ,
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
32M , and 40M . The solid lines indicate modelswithout ro-
⊙ ⊙
tation,andthedashedlineswithrotation.Alsoshownareprevi-
dataofV602Carincludetwopointsnearthefirstvisibilitynull,
ouslymeasuredsourcesaslistedinthemaintext.Inbluearethe
whichincreasestheprecisionofthebest-fitangulardiameter.
RSGstars,andinredtheredgiants.
3.2.Fundamentalparameters
Weestimatedthefundamentalstellarparametersofoursources
to place them on the HR diagram. In particular we calculated In Fig. 8, we plot the resulting effective temperatures vs.
the effective temperature, the luminosity, the Rosseland-mean spectral types of our targets. For comparison, we include the
radius, the bolometric flux, and the distance in the same way calibrations of the effective temperature scale by Dyck et al.
as described in detail by Arroyo-Torreset al. (2014). We used (1998) for coolgiants stars, by van Belle et al. (2009) forcool
the BVJHKsmagnitudesfromKharchenko(2001) andCutriet giants stars and RSG stars, and by Levesque et al. (2005) for
al.(2003)andtheIRASfluxfromIRAS(1988).Toconvertthe only RSGs. Fig. 9 shows the position of our targets in the HR
magnitudes into fluxes, we used the zero values from Johnson diagram,together with evolutionarytracks from Ekstro¨m et al.
(1965)andCohenetal.(2003).Todereddenthefluxvalueswe (2012). Both figures also include the RSGs from our previous
usedthecolorexcessmethodappliedto(V-K)andbasedonin- studies(VYCMafromWittkowskietal.2012;AHSco,UYSct,
trinsiccolorsfromDucatietal.(2001),asdescribedinArroyo- KWSgrfromArroyo-Torresetal.2013),aswellasBetelgeuse
Torresetal.(2014). based on the data by Ohnaka et al. (2011) and VX Sgr based
V602CarandHD95687belongtotheclusterCAROB2and onthedistancebyChenetal.(2007)andtheangularradiusby
we usethedistanceasdeterminedbyHumphreysetal.(1978). Chiavassaetal.(2010a),analyzedbyusinArroyo-Torresetal.
ForHD183589,weusedthedistancevaluefromvanLeeuwen (2013).Finally,weincludedtheredgiantstarsfromMart´ı-Vidal
(2007). Lastly, the effective temperature is estimated from the etal.(2011)andArroyo-Torresetal.(2014).Allsourcesarecon-
angular diameter and the bolometric flux, the luminosity from sistent within their errors with the different calibrations of the
the bolometric flux and the distance, and the Rosseland radius effective temperature scale and with the red limits of the evo-
from the Rosseland angular diameter and the distance. We as- lutionary tracks. The positions on the HR diagram of our new
sumeda 15%errorin the flux, anda 10%errorin the distance sourcesareclosetoevolutionarytrackscorrespondingtoanini-
for HD 183589.For V602Car andHD 95687,we used the er- tialmassof20-25M⊙withoutrotationor15-20M⊙withrotation
rorsfromHumphreysetal.(1978).Theerrorsintheluminosity, (V602Car),12-15M⊙withoutrotationor9-15M⊙withrotation
effective temperature and radius were estimated by error prop- (HD 95687),5-12M⊙ withoutrotation or 7-9M⊙ with rotation
agation. The resulting fundamentalparameters and their errors (HD183589).HD183589maythusalsobea(super-)AGBstar
arelistedinTable4. andnotaRSGstar(Siess2010).
TheradiusandluminosityofHD183589suggestthatthisis We note that the red giants with luminosities below
a source oflower luminosityand thuslowermass comparedto log(L/L ) ∼ 4 are located systematically to the right of the
⊙
theotherobservedRSGsources.ItisatthelimitbetweenRSG Ekstro¨m tracks, and that a better agreement for these sources
andsuper-AGBstars.Thevisibilityfunctionsresemblethoseof can be found using the STAREVOL grid (Lagarde et al.
theredgiantsasobservedbyArroyo-Torresetal.(2014),which 2012),whichincludesthermalinemixingunlikeEkstro¨m’sgrid
donotshowindicationsofanextendedmolecularlayer. (Arroyo-Torresetal.2014).
5
B.Arroyo-Torresetal.:LargeextensionsofRSGatmospheres
Table4.FundamentalparametersofV602Car,HD95687,andHD183589.
Parameter V602Car HD95687 HD183589 Ref.
F (10−10Wm−2) 11.30±1.69 4.84±0.73 5.49±0.82 1
bol
d(pc) 1977±75 1977±75 621±62 2
L(1031W) 5.28±0.89 2.26±0.38 0.25±0.06 1,2
log(L/L ) 5.14±0.17 4.77±0.17 3.82±0.25 -
⊙
θ (mas) 5.08±0.75 3.17±0.50 2.95±0.50 Thiswork
Ross
R(R ) 1050±165 674±109 197±39 2,4
⊙
T (K) 3432±263 3467±282 3709±322 3,5
eff
log(T ) 3.54±0.08 3.54±0.08 3.57±0.09 -
eff
log(g) -0.30±0.16 -0.14±0.14 0.80±0.17 thiswork
M(M ) 20-25 12-15 7-12 6
⊙
Notes. 1: Kharchenko (2001), Cutri et al. (2003), IRAS (1988); 2: Humphreys et al. (1978) - HD 95687, V602 Car (cluster CAR OB2); van
Leeuwen(2007)-HD183589; 6:ValuesobtainbythepositionofthestarsintheHRdiagramwiththeevolutionarytracksfromEkstro¨metal.
(2012);Weassumeda15%errorintheflux.ThedistanceerrorwasbasedonthevaluesfromHumphreysetal.(1978)byV602CarandHD95687.
FromHD183589,weassumeda10%errorinthedistance.Theerrorsintheluminosity,effectivetemperatureandradiuswereestimatedbyerror
propagation.
4. Characterizationoftheextensionofthe
4 Mira RW Vel UY Sct molecularatmosphere
AH Sco
Wecharacterizedtheobservedextensionsofthemolecularlay-
22V /V(cont)(CO) 23 X HWya Vel KW SgVr60V2Y C CaMr a etsetrarssrsianaffnoedrcdtMetrhiretoamsb.teaWtrtsee,rwaulhsnoidcewhrasantlastnotdoexhchooiwmbiptthaerexetfetuhnneddebademhmeanovtliaeolcrupolaafrraRlmaSyeG--
RGs ers(cf.,e.g.,Wittkowskietal.2011).Weusedtheratiooftheob-
RSGs
servedvisibilitiesinthecontinuumband(averagebetween2.27
β Peg R Cnc HD 95687
1 ε Oct and 2.28µm) and the first (2-0) CO line at 2.294µm as an ob-
servational indication of the contribution from extended atmo-
2 3 4 5 6 7 spheric CO layers. Since this ratio dependson the value of the
log(L/L_sun) visibility in the continuum (V2 ), i.e. on how well the source
cont
wasresolved,welimitedthestudytocontinuumsquaredvisibil-
4 UY Sct RW Vel ities between 0.2 and 0.4, a rangewhere the visibility function
is nearly linear. Although this approach may be limited by the
AH Sco
limitedspectralresolutionofourobservationsofR ∼1500and
22V /V(cont)(CO) 23 KWV S6g0r2 Car VY CMa X HyaW Vel bfeovyrotlahveefidrlosstwtacronsmu.mpabreirsoonfoofbsthereveaxtitoennssipoenrssoofuRrcSeG,itstiasraspapnrdoportihaeter
RSGs Fig.10showstheresultingratios(V2 /V2 )foroursources
β PegHD 95687 RGs Mira R Cnc vs. log(L/L⊙) and ∆V, considering thecRonStGsCOby Wittkowski et
1 ε Oct al.(2012),Arroyo-Torresetal.(2013)andthiswork(notrepre-
sent HD 183589because their visibilities in the continuumare
0 1 2 3 4 5 6 7
greater than 0.4), as well as the giants from Arroyo-Torres et
∆ V
al. (2014). Results forMira stars obtainedby Wittkowskiet al.
Fig.10.Ratiobetweenthesquarevisibilityinthecontinuum(av- (2011) are also shownfor comparison.Fig. 11 showsthe same
erage between 2.27 and 2.28µm) and the square visibility in visibility ratio but only for the RSG sample. In this case, we
the CO (2-0) line vs. log(L/L ) (top) and the variability am- show the visibility ratio vs. L/L , log(g), and T . Also shown
⊙ ⊙ eff
plitude (bottom) for a sample of RSGs in blue (Arroyo-Torres are the ranges of the predicted visibility ratios based on the
et al. 2013; Wittkowski et al. 2012; this work), AGB stars in PHOENIXmodelatmospheres,aswellasbasedon3-DRHDsim-
red (Arroyo-Torreset al. 2014) and Mira variable stars in ma- ulations,whichwillbediscussedinthenextsection.
genta (Wittkowskiet al. 2011) for visibilities in the continuum
Fig.10showsthatthegiantstars(red)areconsistentwiththe
between 0.2 and 0.4. The dotted black lines show the range of
PHOENIXmodelsandtheconvectionmodels(RHDsimulations).
predictionsbythebest-fitPHOENIXmodelofthesesources,the
βPegshowsanatmosphericextensionlargerthanpredictedby
dashedorangetherangeofpredictionsbythebest-fitRHDsim-
thePHOENIXmodels,howeveritisrelativelysmallanditdoes
ulation.Bothlinesoverlap.
notshow up with any significanceusing this metric of plotting
(V2 /V2 ).TheothergiantstarsdonotshowanextendedCO
cont CO
band(thevisibilitiesinthecontinuumareverysimilar tothose
intheCO(2-0)line).TheRSG(blue)andMirastars(magenta)
showamoreextendedCOlayerandthereforetheyarenotcon-
sistentwithhydrostaticmodelsorconvectionmodels.TheRSG
andMirastarsshowsimilaratmosphericextensions.
6
B.Arroyo-Torresetal.:LargeextensionsofRSGatmospheres
observedonlyforluminositiesbeyond∼1∗105L andforsur-
⊙
4 UY Sct facegravitiesbelowlog(g)∼0.
AH Sco
V2(CO) 3 KW Sgr VY CMa 5. Comparisonswithconvectionandpulsation
V /2(cont) 2 V602 Car models
Inthefollowingwediscussphysicalmechanismsthathavebeen
HD 95687 discussedaspossibledriversoftheobservedlargeextensionsof
1 RSG atmospheres.In particular,we discuss convectionmodels
andpulsationmodels.Pulsationmodelshavebeensuccessfulto
1•105 2•105 3•105 4•105 5•105 6•105 explainobservedatmosphericextensionsofMira-variableAGB
L/L_sun starswithshockfrontspassingthroughtheatmospheres.
4 UY Sct
5.1.3-DRHDsimulations
AH Sco
O) 3 The3-Dradiation-hydrodynamicssimulationsofredsupergiant
2V(C VY CMa starswerecomputedwithCO5BOLD(Freytagetal.2012).The
2V /(cont) 2 KW VS6g0r2 Car )choydderosodlyvneasmtihcescaonudpnleodn-elqoucaaltiorandsiaotfivceoemnperregsysitbrlaens(pmoargtnoentoa-
Cartesian grid. The ”star-in-a-box” geometry is used and the
HD 95687 computational domain is a cubic grid equidistant in all direc-
1
tions; the same open boundary condition is employed for all
sidesof thecomputationalbox.The tabulatedequationofstate
0.5 0.0 -0.5 -1.0 -1.5
takes the ionization of hydrogenand helium and the formation
log(g) [cgs]
ofH moleculesintoaccount.Theopacitytablesaregrayoruse
2
afrequency-binningscheme.
4 UY Sct
Themainmodelparametersare(Chiavassaetal.2011a):the
AH Sco stellarmass(enteringthegravitationalpotential),theinputlumi-
V2(CO) 3 VY CMa nthoesietqyuinattihoen-coofr-es,taatnedatnhdeaobpuancditayntcaebsleths.atAwveerreaguesevdaltuoecsoonfstsrtuecl-t
V /2(cont) 2 KW Sgr V602 Car ldaerrirvaeddiufsr,oemffeacrteivlaexteedmmpeordaetlu(rCe,haianvdassusarfeatcealg.r2a0v0it9y,2h0a1ve1at)o.be
The models show large-scale convection cells (several in
HD 95687
1 RSGs and only one to two for AGB stars) that span the entire
convectiveenvelopeandhavelifetimesofyears.Onthesurface,
4200 4000 3800 3600 3400 3200 3000 therearesmallershorter-livedcellsthatresemblesolargranules.
Effective temperature [K] AccordingforinstancetoSamadietal.(2001),convectiveflows
exciteacoustic wavesthroughturbulentReynoldsstresses (i.e.,
Fig.11.Ratiobetweenthesquarevisibilityinthecontinuum(av-
essentially velocities)and turbulententropyfluctuations.In the
eragebetween2.27and2.28µm)andthesquarevisibilityinthe
partofthe3-DRHDsimulationsthatcomprisesthestellarinte-
CO (2-0) line vs. log(L/L ) (top), log(g) (middle), and the ef-
⊙ rior,botharelargestinorclosetothedowndrafts.Accordingly,
fective temperature (bottom) for the sample of RSGs (Arroyo-
acousticwavesareproducedmostlyinthedowndrafts,andpar-
Torresetal.2013;Wittkowskietal.2012;thiswork).Thedotted
ticularly during merging of downdrafts. While the fast down-
blacklinesshowtherangeofpredictionsbythebest-fitPHOENIX
drafts themselves actually impede the outward propagation of
modelofthesesources,andthedashedorangetherangeofpre-
thewaves,thewavesspreadintothesurroundingupflowregions
dictionsbythebest-fitRHDsimulation.Bothlinesareoverlap.
in which they can easily reach the stellar surface. When these
Thedashedgraylines,inthetopandmiddle,showlinearfits.
wavesreachthethinandcoldphotosphericlayers,theysteepen
intoshocksthattravelthroughtheatmospherewithadecreasing
densityofthepost-shockgas.Theirinduceddynamicalpressure
exceedsthethermalgaspressureleadingtoasignificantincrease
Fig.11suggestsacorrelationbetweenthevisibilityratioof inthedensityscaleheight.
ourRSGsandtheluminosityandsurfacegravity,whichisindi- We used the pure-LTE radiative transfer Optim3D
catedbylinearfits(dashedgraylines).Thecorrelationsindicate (Chiavassa et al. 2009) to compute intensity maps from
anincreasingatmosphericextensionwithincreasingluminosity three of these RHD simulations. This code take the Doppler
and with decreasing surface gravity. We do not observe a cor- shifts occurring due to convective motions into account. The
relation between observed atmospheric extension and effective radiative transfer equation is solved monochromatically using
temperature or variability amplitude. In the case of Mira stars, pre-tabulated extinction coefficients as a function of tempera-
wedonotobserveanycorrelation.Thelackofacorrelationbe- ture, density, and wavelength. The lookup tables are computed
tween visibility ratio and the luminosity and/or surface gravity for the same chemical compositions as the RHD simulations
suggeststhatdifferentprocessesmayberesponsibleforextend- using the same extensiveatomic and molecularcontinuumand
ing the atmospherein RSGs and Miras. On the other hand, we line opacity data as the latest generation of MARCS models
notethatconsiderableatmosphericextensionsforRSGstarsare (Gustafssonetal.2008).
7
B.Arroyo-Torresetal.:LargeextensionsofRSGatmospheres
Thethreeredsupergiant(RSG)simulationsareshowninthe 5.2.Pulsationmodels
Table 5. On the other hand, we also tried the higher resolution
simulation(4013gridpoints)st36gm00n05(alsointable5).We
Self-excited pulsation models of Mira-variable AGB stars
consideredseveralsnapshotsforeachsimulationandcomputed
(Ireland et al. 2004a, 2004b, 2008, 2011; Scholz et al. 2014)
intensitymapsinthewavelengthrange1.90-2.60µmwithacon-
havebeensuccessfultodescribeinterferometricobservationsof
stantspectralresolutionofR=λ/δ ∼ 20000.Moreover,forev-
λ these sources, including their extended atmospheric molecular
erywavelength,atop-hatfilterincluding5wavelengthscloseby
layers (Woodruff et al. 2009, Wittkowski et al. 2011, Hillen et
hasbeenconsidered.Intotal,about70000imagesforeverysim-
al. 2012). The observed visibility spectra of our RSG sources
ulation snapshot have been computed to cover the wavelength
showsimilarfeaturesasthoseofMirastars,inparticularatthe
rangeoftheobservations.
CObandheads(seeSect.3.3).Wehavethusasafirststepinves-
Then, using the method explained in detail in Chiavassa et tigatedwhetherpulsatingmodelatmospheresofMira variables
al.(2009),wecomputedazimuthallyaveragedintensityprofiles. canprovideagoodfittoourRSGstarsaswell,althoughthestel-
Theseprofileswereconstructedusingringsregularlyspacedin larparameters,inparticularmassandluminosity,areverydiffer-
µ (whereµ = cos(θ) with θ the anglebetweenthe line of sight entandvariabilityamplitudesofRSGsaretypicallylowerbya
andtheradialdirection). factorof2-3comparedtoMiras(Woodetal.1983).Weusedthe
recentCODEXmodelseriesbyIrelandetal.(2008,2011)and,as
Finally, we averaged the monochromatic intensity profiles
anexample,havefoundbest-fitmodelstothedataofV602Car
to match the spectral channels of the individual observations
asshowninFig.1.Fig.14showsoneofthebest-fitCODEXmod-
(we reduced the spectral resolution to AMBER observations).
elscomparedtothesedata.Theshownmodelismodel261460
Afterward,weestimatedthesyntheticvisibilityofeachbaseline
oftheo54series.Theo54seriesisdesignedtodescribethepro-
usingtheHankeltransforminthesamewayasforthePHOENIX
totypeMiravariableomiCetiwithanon-pulsatingparentstarof
modelsdescribedabove.
M=1.1M , L=5400L ,R=216R , P=330days.Model261460
⊙ ⊙ ⊙
Fig. 12 shows the intensity images at a continuum wave-
isamodelatphase0.2withinaparticularlyextendedcycle,with
length (2.20µm) and at the CO (2-0) line (2.294µm), together L=7420L and T =3154K. The modeldoes not show all ob-
⊙ eff
withtheazimuthallyaveragedintensityprofilesfortheexample
servationaldetails,inparticularthedetailedoverallslopeofthe
ofthesnapshotofmodelst35gm03n07.Theintensityimagesil-
fluxandvisibility spectra.However,itdoesmatchthe dropsof
lustrate that the intensity in the CO line is lower by a factor of
theCO bandheadsinthevisibility spectrum.Fig. 15showsthe
about 2 compared to the intensity in the continuum, which is
intensityprofileofthismodel,inthecontinuum(2.25µm)andin
consistent with observed flux spectra such as in Fig. 1 for the
theCO(2-0)line(2.294µm),asanillustrationofwhichkindof
example of V602 Car. In the images, the linear intensity range
atmosphericextensionisrequiredtodescribetheobservedvisi-
is between 0 and 130000erg/s/cm2/A. Keeping the same scale
bilitydata.TheintensityprofileintheCOlineextendstobeyond
seems to reduce the apparent luminosity of the CO image and
2Rosselandradii,comparedtoanextensionofafewpercentas
thusalsothecontrastbetweenbrightanddarkregions,however
predictedbythe3-DRHDsimulationsofRSGs(Fig.12).
itistheopposite.TheimageofCOhasapseudo-continuumcon-
tribution due to CO opacities that increase the surface contrast As a nextstep, we calculated a new pulsation modelbased
anddecreasethelevelofthestructures,inparticularatthelimb. on stellar parametersthatare typicalfor an RSG star: the non-
TheCOlinesurfacelooksslightlymoreextended(purplecolor pulsating parentstar has M=15M , L=1.26·105L , R=954R ,
⊙ ⊙ ⊙
closetothestellarlimbinthefigure12,centralpanel)butonly and its effective temperature is about 3600K. The pulsation
byafewpercent(∼7%,estimatedfromFig.12bottompanelat period of this model is about 750days. These parameters are
the0%intensity) close to the star V602 Car discussed above (T =3432±263K,
eff
Fig. 13 (top and middle panels) shows the example of our L=(1.35±0.23)·105L⊙, R=1050±165R⊙, P=645days). Fig. 16
V602CardataofFig.1comparedwiththe3-DRHDsimulation shows the radius variation of selected mass zones of this pul-
ofFig.12. Inthe bottompanel,we showthepredictedsquared sation model, the velocity at the photosphere, and the visual
visibility amplitudesof the best-fit PHOENIXmodelto our data light curve.The amplitude of the photosphericradiusvariation
ofV602Car(cf.Fig.1)comparedtothoseoftheRHDsimula- is about 10% with radial velocities of up to about 5km/sec.
tion of Fig. 12. The model-predictedvisibility curvesof the 3- The model reproduces the amplitude of the visual light curve
DRHD simulationareverysimilartothehydrostaticPHOENIX of V602Car of about1-1.5mag.Whilst shock frontsenter the
model at the AMBER resolution and can thus not explain the stellar atmospherein a typicalCODEXmodelofa Mira variable
largeobservedatmosphericextensionsofRSGstars. atorbelowopticaldepth1,leadingtoageometricextensionof
the stellar atmosphere of the order a few Rosseland radii (e.g.,
TheresultsaresimilarforalltheRHDsimulationsemployed
Ireland et al. 2011), it turns out that no shock fronts reach at
in this work. In summary, it appears from the visibility curves
anyphasetheatmosphericlayersincaseoftheRSGmodel.We
that the atmospheric extension of RHD simulations is compa-
alsocomputedahigheramplitudeversionofthismodelwithV
rable to typical hydrostaticPHOENIXmodelwithin the spectral
mag., velocity, and radius amplitudes that are larger by a fac-
resolutionoftheactualobservations.
tor of 2–3. Although the surface movesin and out more, there
RHDsimulationsofRSGsdonotleadtoaconsiderablein- are still no shocks in the atmospheric layers. We note that the
creaseoftheradius.However,thesituationmaybedifferentfor movingphotospheremightinduceshocksathigherradii,beyond
theAGBsimulations(Freytag&Ho¨fner2008),wheretheratio theregionofthesemodels,wherethedensityisverylow.This,
of the pressure scale height to the stellar radius is larger, giv- however,couldalsonotexplaintheobservedatmosphericexten-
ingrisetorelativelylargerconvectivestructures,tolarger-scale sionsabovethephotosphericlayers.Inourtestmodel,theratio
wavesandshocks,andfinallytoanoticeableincreaseofthestel- (r(τ = 10−4) − r(τ = 1))/r(τ = 1) which roughly
Ross Ross Ross
larradius.Thus,shockwavesinAGBsimulationsmayexplain measures the atmospheric extension is only 0.04 at four sam-
the atmospheric extension we see in the observations of Mira ple phases (-0.02, 0.27, 0.52, 0.76), and we see hardly depth-
stars. dependentoutflow/infallvelocitiesbelow4 km/s(Fig.16).For
8
B.Arroyo-Torresetal.:LargeextensionsofRSGatmospheres
Table5.RHDsimulationsofredsupergiantstarsusedinthiswork.
model grid M L T R logg
pot eff ⋆
[gridpoints] [M ] [L ] [K] [R ] [cgs]
⊙ ⊙ ⊙
st35gm03n07a 2353 12 91932±1400 3487±12 830.0±2.0 −0.335±0.002
st35gm03n13b 2353 12 89477±857 3430±8 846.0±1.1 −0.354±0.001
st36gm00n06 2553 6 23994±269 3660±11 391.3±1.5 0.010±0.004
st36gm00n05b 4013 6 24233±535 3710±20 376.7±0.5 0.047±0.001
Notes.a)usedinChiavassaetal.2009,2010b,2011b.b)Chiavassaetal.2011a
comparison,thePHOENIXmodelplottedinFig.1hasanexten- ofthesecancurrentlyexplaintheobservedmajorextensionsof
sionof0.04aswell. theatmospheresofRSGs.
A few test computations with higher parent-star luminos- A large number of spectroscopic and interferometric stud-
ity (3 105L⊙) and higher mass (25 and 15M⊙) yield similar iesofRGsandRGSsshowthatclassicalmodelsdonotexplain
results. This means that the hydrostatic approximation should the extended atmospheresof these sources (Tsuji 2003, 2008).
be well suited for calculating the stratification of the RSG at- Studies of resolved 12µm spectra of red giant and supergiant
mosphere. We note in this context that the atmospheric scale stars show strong absorption lines of OH and H O, which are
2
height,H ∝ Teff ∗R2/M,whichwouldbeanapproximatemea- evenlargerthanexpectedfroma classical photospherewithout
sureoftheatmosphericextensionincaseofastaticstellaratmo- a MOLecular sphere around the stars (Ryde et al. 2002, 2003,
sphere,isofthesameorderofmagnitudefortypicalMirasand 2006a,2006b).
for typical RSGs. For, e.g., the o54 model of the CODEX series
Hereby,thenew1-Dpulsationtestmodelsshowvelocityam-
thathasaboutoCetparametersandtheaboveRSGmodel,one
plitudes below about 10km/sec. These velocity amplitudes are
finds H(o54)/H(RSG)= 0.7andverysmallatmosphericexten-
consistent with observed long-term average velocity curves of
sions H(o54)/R(o54)∼0.023/µ and H(RSG)/R(RSG)∼0.008/µ.
Betelgeuse of ∼9km/sec (Gray 2008, Fig. 6) and of a sample
Themeanmolecularweightisµ∼1.3foranormalsolarelement
ofRSGsof≤10km/sec(Josselin&Plez2007).These1-Dpul-
mixture with atomic hydrogen (molecular hydrogen is formed
sationmodelsarealsoconsistentwithtypicalamplitudesofthe
only in the high layers of the Mira models). We also note that
long-periodvisuallightcurvesofRSGsof1–3mag.
H/Risapproximatelytheratio(gasparticlethermalkineticen-
ergy)/(gravitationalpotentialat the stellar surface).In the RSG Inadditiontotheselong-termaveragevelocitycurves,which
model,thetypicalgasparticlehasaspeedof∼8km/sintheat- we interpretas being caused by orderedpulsation motionsand
mospherewhereaspulsationvelocitiesareonly∼3km/s.Hence, which are well explained by the new 1-D pulsation models,
thepulsationenergyisonly∼14%oftheparticlethermalenergy Gray (2008) and Josselin & Plez (2007) also report on higher
and,therefore,doesnotleadtosignificantatmosphericextension velocity gradients and turbulent motions in the atmospheres
on short time scales with velocities of up to 30km/sec. These
ofthemodels.
were explained by granulation and giant convection cells ac-
Overall,thepulsationmodelsfortypicalparametersofRSG
companied by short-lived oscillations. In addition, Ohnaka et
stars lead to compact atmospheres with extensions similar to
al. (2011, 2013) reported on interferometric observations of
those of the PHOENIX and RHD models discussed above, and
Betelgeuse and Antares at two epochs each, which confirmed
canthusalsonotexplaintheobservedextensionsofthemolec-
time variable atmospheric velocities of up to 20–30km/sec.
ularlayers.
Theysuggestedthatthesemotionsarerelatedtothewinddriving
mechanism.Theyalsoconcludedthatthedensityoftheextended
outer atmospheres of Antares and Betelgeuse are significantly
5.3.Discussiononalternativemechanisms
higherthan predictedby current3-D RHD simulations, so that
We showed in Sects. 3 and 4 that our interferometric observa- convectionalonecannotexplaintheformationoftheextended
tionsofRSGsprovideevidenceofextendedmolecularlayersfor atmospheres. This conclusion is confirmed by our direct com-
a sample of RSGs with luminosities between about1×105L parisonsof interferometricdata and synthetic visibilities based
⊙
and5×105L andeffectivetemperaturesbetweenabout3350K on current 3-D RHD simulations, and for a larger sample of 6
⊙
and 3750K. These extensionsare comparableto those of Mira additionalRSGs.
variableAGBstars,whichtypicallyreachtoafewphotospheric Current 3-D RHD simulations of RSGs are still limited in
radii. Furthermore, our observations of RSGs indicate correla- spatial resolution. However, we can compare older models of
tionsofincreasingatmosphericextensionwithincreasinglumi- RSGswithlownumericalresolution(2353gridpoints)andnew
nosityanddecreasingsurfacegravity,whereconsiderableexten- models with better resolution (4013 grid points). On the other
sions of the CO (2-0) line are observed for luminosities above hand, we also have better resolved models of AGB stars and
∼1∗105L⊙ andforsurfacegravitiesbelowlog(g)∼0. even better resolved local models of solar-type stars – with a
Comparisonsofourinterferometricdatatoavailable1-Dhy- rangeofresolutions.Fromthesecomparisons,weconcludethat
drostaticPHOENIXmodelatmospheres,new1-dpulsationmod- future RSG simulations with higher resolution are indeed im-
els, and available 3-D RHD simulations show that all of these portantanddesirable,butthatwedonotexpecttheatmospheric
theoreticalmodelsresultinverysimilarsyntheticvisibilityval- velocity fields due to convection and pulsations alone to grow
uesfortheparametersofourobservations.Theyindicateacom- enoughtoremotelyreachtheamplitudenecessarytogiveamol-
pactatmosphericstructurefor all consideredmodels,and none sphereextensionofafewstellarradiiasobserved.
9
B.Arroyo-Torresetal.:LargeextensionsofRSGatmospheres
Josselin & Plez (2007) suggested that high velocities and Grunhutetal.(2010),Aurie`reetal.(2010),andBedecarrax
steepvelocitygradients,possiblycausedbyconvectivemotion, etal.(2013)detectedweak(<1G)magneticfieldsinonethirdof
generatelineasymmetries,thatturbulentpressuredecreasesthe theirsampleoflatetypesupergiants,withtheirsensitivitylimit.
effectivegravity,andthatthisdecreasecombinedwithradiative They suggested that magnetic fields are generated by dynamo
pressureonlinesinitiatesthemassloss.Thesphericallysymmet- action, and that weak fields may be excited in all cool super-
ricCODEXMiramodelatmospheresdo,indeed,shownoticeable giants.Ithasbeendiscussedthatmagneticfieldsmayalsoplay
radiative acceleration a which significantly affects the effec- aroleinthemass-lossprocessofRSGstarsalongsideotherpro-
rad
tivegravityintheatmosphericlayers(e.g.,Fig.6withEq.1in cesses as discussed above. Thirumalai & Heyl (2012) recently
Ireland et al. 2008), but still without any net outward acceler- presentedamagnetizedhybridwindmodelforBetelgeuse,com-
ation. One should realize that the pulsation-generated very ir- biningaWeber-Davisstellarwindwithdustgrains,thatwasable
regular velocity stratification (resulting in irregular ρ(r), e.g., toliftstellarmaterialupfromthephotosphereandintothecir-
Figs. 14/15/16 in Ireland et al. 2011 and Fig. 2 in Scholz et cumstellarenvelope.Oneofus(BF) recentlyproduceda setof
al. 2014) favors large a because of substantial line shifts. 5-M -RSGRHDmodelswithoutandwithmagneticfield.These
rad ⊙
Velocity (outward/inward)variationscan be quite strong,up to first simulationswith magnetic fields did notsignificantly alter
a few km/s between shock fronts, apart from the big “jumps” the stratification of the model, however, more calculations are
at shock front positions. The new RSG pulsation models de- needtoreacharealconclusion.Wealsonotethatthegoodover-
scribed in Sect. 5.2 do not show this velocity stratification be- all fit of the hydrostatic PHOENIX models in the continuum
havior.However,theyarealsosolelybasedonlongtermvelocity bands means that the temperature structure vs. optical depth is
variationscausedbypulsationmotion.Itisplausiblethatmuch roughlycorrect,so thatadditionalheatingof the atmosphereis
steepervelocitygradientsonshortertimescales,asreportedby notamissingmechanism.Inaddition,rigidrotationordifferen-
Gray (2008), andnotincludedin these models, mightgenerate tialrotation(e.g.,arapidlyrotatingcore)areprocessesthatare
accelerationsonDoppler-shiftedmolecularlinesthatsufficiently notincludedinourmodelsbutmaycontributetotheatmospheric
extend the molecular atmosphere. Although already suggested extensionandtothemass-lossprocess.
in 2007,more detailedcalculationsof this effectfor RSGs and
itsimplementationinthe3-DRHDsimulationsarestillpending
6. Summaryandconclusions
andarealsooutsidethescopeofthepresentpaper.Ourobserved
correlationofincreasingatmosphericextensionwithincreasing Our spectro-interferometric observations with AMBER are a
luminosityanddecreasingsurfacegravity(cf.Fig.11)supports goodtoolforstudyingthecontinuum-forminglayerandmolec-
sucharadiativelydrivenextensionoftheatmospheresofRSGs. ularlayersseparatelyandforconstrainingtheatmosphericstruc-
ture of RSGs. We used the continuum near 2.2µm, which is
The proposed scenario of radiation pressure on Doppler- mostlyfreeofmolecularcontamination,toestimatetheangular
shifted lines is in a a way reminiscent of what happens in the diametersofthetargets.Togetherwithestimatesofthedistances
windsofhotstars.However,itshouldbenotedthat–unlikefor and the bolometric fluxes, we also derived fundamentalstellar
hot stars– RSGs form dust at larger radii (typically ∼20 stellar parameterssuchastheluminosity,theRosselandradius,andthe
radii, Danchi et al. 1994) so radiation pressure on dust cannot effectivetemperature.
occurinthewindaccelerationzone(Josselin& Plez,2007).In With the effective temperature and the luminosity, we lo-
the case of RSGs, the proposed radiative pressure on molec- cated our targets in the HR diagram. Their locations are close
ular lines may only levitate the molecular atmosphere up to to evolutionary tracks that correspond to initial masses of 20-
radii where dust can form (as suggested by Josselin & Plez, 25/15-20M (V602 Car), 12-15/9-15M (HD 95687), and 5-
⊙ ⊙
2007), analogous to shock fronts for Miras, albeit not lifting 12/7-9M (HD183589)withorwithoutrotation.Alltargetpo-
⊙
the material outside the gravitational potential. However, the sitions are consistent with the red limits of recentevolutionary
detailed dust formation, condensation sequence, and mass-loss tracks. HD 183589 shows a lower luminosity and thus lower
mechanisms are also not yet fully understood in the case of mass compared to our other sources. It may more likely be a
oxygen-rich AGB stars (cf., e.g., Karovicova et al. 2013 for a (super-)AGBstarinsteadofaRSGstar.
recent discussion). Recent indications based on a polarimetric The near-infrared spectra of all our target are reproduced
aperture masking technique (Norris et al. 2012) and on mid- wellbyhydrostaticPHOENIXmodelatmospheres,includingthe
infrared interferometry (Wittkowski et al. 2007; Karovicova et CO bands.We hadobservedthesamebehaviorinourprevious
al.2011,2013)pointtowardtransparentdustgrainsformingal- project(Wittkowskietal.2012,Arroyo-Torresetal.2013).
ready at relatively small radii of about 1.5 stellar radii. These TheobservedvisibilitycurvesofoursampleofRSGsshow
may be grains of amorphous Al O and/or magnesium-rich largedropsintheCO(2.3–2.5µm)andpartlyintheH O(1.9–
2 3 2
iron-free (“forsterite”) silicates, while iron-rich silicates form 2.1µm) bands, indicating major extensions of the atmospheric
at larger radii. Verhoelstet al. (2006) founda similar evidence molecularlayers.Asafirstcharacterizationoftheextensions,we
foramorphousaluminaintheextendedatmosphereoftheRSG calculatedthesquarevisibilityratiosbetweenthenearbycontin-
Betelgeuseascloseas∼1.4stellarradii,whileiron-richsilicates uumandtheCO(2-0)bandhead.Moredetailedobservationsus-
indeed had an inner radius of 20 stellar radii in their model. ingalargernumberofdatapoints,possiblyimagingcampaigns,
However, Kamin´ski et al. (2013) do not observe the presence and a higher spectral resolution to better isolate the CO band-
of AlO in the inner outflow in the spectrum obtained with the headaredesirableforamoreaccuratedescriptionoftheexten-
UltravioletandVisualEchelleSpectrograph(UVE)atthe Very sions. Nevertheless, we observed a linear correlation between
Large Telescope (VLT). On the other hand, they have detected thevisibilityratiosofourRSGsandtheluminosityandsurface
AlO-bearinggasinthewind-accelerationzone,outto20R .If gravity,indicatinganincreasingatmosphericextensionwithin-
∗
thepresenceoftransparentgrainsisconfirmedatsmallradiiof creasing luminosity and decreasing surface gravity. With that,
∼1.5stellar radii, itwouldplay a crucialrole forthe dustcon- weobservedconsiderableatmosphericextensionsofRSGsonly
densation sequence and the overall mass-loss process of both forluminositiesbeyond∼105L andforsurfacegravitiesbelow
⊙
oxygen-richAGBstarsandRSGs. log(g) ∼0.We didnotobserveacorrelationwitheffectivetem-
10