Catching the fish - Constraining stellar parameters for TX Psc using spectro-interferometric observations

1.4 MB·English

by  D. Klotz

Astronomy&Astrophysicsmanuscriptno.tx-psc (cid:13)c ESO2013
December11,2013
Catching the fish – Constraining stellar parameters for TXPsc
⋆
using spectro-interferometric observations
D.Klotz1,C.Paladini1,J.Hron1,B.Aringer1,S.Sacuto1,2,P.Marigo3,andT.Verhoelst4,5
1 DepartmentofAstrophysics,UniversityofVienna,Tu¨rkenschanzstrasse17,A-1180Vienna
e-mail:[email protected]
2 DepartmentofPhysicsandAstronomy,DivisionofAstronomyandSpacePhysics,UppsalaUniversity,Box516,75120,Sweden
3 DepartmentofPhysicsandAstronomyG.Galilei,UniversityofPadova,Vicolodell’Osservatorio3,I-35122Padova,Italy
4 BelgianInstituteforSpaceAeronomy(BIRA-IASB),Ringlaan-3-AvenueCirculaire,B-1180Brussels,Belgium
3 5 InstituutvoorSterrenkunde,KULeuven,Celestijnenlaan200D,3001Heverlee,Belgium
1
Received;accepted
0
2
ABSTRACT

n
a Context.Stellar parameter determination is a challenging task when dealing with galactic giant stars. The combination of dif-
J ferent investigation techniques has proven to be a promising approach. We analyse archive spectra obtained with the Short-

3 Wavelength-Spectrometer(SWS)onboardofISO,andnewinterferometricobservationsfromtheVeryLargeTelescopeMID-infrared
Interferometricinstrument(VLTI/MIDI)ofaverywellstudiedcarbon-richgiant:TXPsc.

] Aims.Theaimofthisworkistodeterminestellarparametersusingspectroscopy andinterferometry.Theobservationsareusedto
R constrainthemodelatmosphere,andeventuallythestellarevolutionarymodelintheregionwherethetracksmapthebeginningof
S thecarbonstarsequence.
. Methods.Twodifferentapproachesareusedtodeterminestellarparameters:(i)the‘classic’interferometricapproachwheretheeffec-
h
tivetemperatureisfixedbyusingtheangulardiameterintheN-band(frominterferometry)andtheapparentbolometricmagnitude;
p
(ii)parametersareobtainedbyfittingagridofstate-of-the-arthydrostaticmodelstospectroscopicandinterferometricobservations.
- Results.Wefindagood agreement betweentheparameters of thetwomethods. Theeffectivetemperatureand luminosityclearly
o
place TXPscinthe carbon-rich AGB star domain intheH-R-diagram. Current evolutionary trackssuggest that TXPscbecame a
r
t C-starjustrecently,whichmeansthatthestarisstillina‘quiet’phasecomparedtothesubsequent strong-windregime.Thisisin
s
agreementwiththeC/Oratiobeingonlyslightlylargerthan1.
a
[
Keywords.Stars:AGBandpost-AGB-Stars:atmospheres-Stars:carbon-Stars:fundamentalparameters-Techniques:interfero-
metric-Techniques:spectroscopic
1
v
4
0 1. Introduction Catalogue of Variable stars (Samusetal. 2009) with a mean
4 brightnessof ∼5mag and a peak-to-peakamplitudeof 0.4mag
0 Theasymptoticgiantbranch(AGB)isthelateevolutionarystage
in the V-band (Jorissenetal. 2011). Distance estimates range
1. of low- to intermediate- mass stars (1 − 8M⊙). On the early- from 275 to 315 pc (vanLeeuwen 2007; Claussenetal. 1987;
AGBthecarbon-to-oxygen-ratioissmallerthanone.Aftersev-
0 Bergeat&Chevallier 2005). Different ISO/SWS spectra of
3 eralthermalpulses,theatmospheresofobjectswithmassesbe- TXPsc(Jørgensenetal.2000;Gautschy-Loidletal.2004)show
1 tween 1 − 4M⊙ will very likely turn from oxygen-rich into that there is a difference in the 3µm feature between 1996
: carbon-rich because of the third dredge-up (Iben&Renzini
v and 1997. With the help of plane-parallel, hydrostatic models
1983). Good estimates of stellar parameters are needed for a
i Jørgensenetal. (2000) interpret this difference as a change in
X profound understanding of the evolution of this stage. Their
temperature of ∼100K. The photometry and spectra were suc-
determination is a challenging task because of the complex-
r cessfully modeled by Gautschy-Loidletal. (2004) with dust-
a ity of the atmospheres of these objects. It is demonstrated that
free dynamical models that reproduce the region between 1 −
the combined use of spectroscopic and interferometric observ-
5µm. They claim that the region between 8−9µm is affected
ing techniques can efficiently help to ascertain stellar parame-
almostsolelybyCS.Theauthorssuggestthatobservationsfrom
ters (e.g. Wittkowskietal. 2001, 2008, 2011; Neilson&Lester
8−9µmshowthedeepphotosphere,whiletheexpectedabsorp-
2008;Paladinietal.2011;Sacutoetal.2011a;Mart´ı-Vidaletal.
tionofHCNandC H originatingfromthehigherlayersisnot
2 2
2011). At the same time these observationsprovideconstraints
observed.Asthisobjectisalmost(carbon)dust-freewemayin-
forexistingmodelatmospheres:e.g.COMARCS(Aringeretal.
feritbecameacarbonstarquiterecently.Therefore,thisstaris
2009),Ho¨fneretal.(2003),PHOENIX(Hauschildtetal.1999),
a perfectcandidate to constrain the regionwhere the transition
ATLAS(e.g.Kurucz1993),CODEX(Irelandetal.2008,2011).
fromoxygen-tocarbon-richoccurs.
TXPsc is one of the brightest and closest carbon-rich AGB
In this work we present a study of the atmosphere and a stel-
stars. It is listed as an irregular variable in the General
lar parameter determination for TX Psc. We combine spectro-
interferometric observations of VLTI/MIDI and spectroscopic
⋆ Based on observations made with ESO telescopes at Paranal
observations from ISO/SWS and compare them to geometric,
Observatory under program IDs 74.D-0601, 60.A-9224, 77.C-0440,
hydrostatic,andevolutionarymodels.
60.A-9006,78.D-0112,84.D-0805
1
Klotzetal.:ConstrainingstellarparametersforTXPsc
calibratorobservationsis<0.2,(ii)thespectraltypeofthecali-
bratorisnotlaterthanM0.Consideringthesecriteria,fivespec-
traarederived(flaggedwith‘a’inTable1).
TXPsc is almost unresolved for baselines shorter than 32m.
Therefore, we expect that the star is unresolved by the single-
dishUTs.Thus,mostofthemid-infrared(mid-IR)fluxislocated
withinthefield-of-view(FoV)oftheUTsandconsequentlyalso
in the FoV of the ATs and ISO, which makes the spectra fully
comparabletoeachother.
2.2.ISOspectra
Three spectra of TXPsc were observed with the Short-
Wavelength-Spectrometer (SWS, deGraauwetal. 1996) on-
board of ISO (Sloanetal. 2003; Jørgensenetal. 2000). Two
spectra have a resolution of R ∼ 200 and range from 2.36 −
Fig.1.N-bandspectrallydisperseduv-coverageoftheMIDIob- 45.35µm.Theotherspectrumrangesfrom2.45−45.20µmand
servationsofTXPsc.Colourlevelsrangefrom8-11.5µm(black hasaresolutionofR ∼ 2000whichhasbeenbinnedtotheres-
toblue,respectively)withastepsizeof0.5µm.Northisupand olutionoftheotherspectra.FortheISOspectraamultiplicative
Eastisleft. error of ±10% is assumed from 2.38-4.05µm and ±5% after-
wards(Sloanetal.2003).
A description of observations and data reduction is given in
Sect.2. Modelsand approachesto derive syntheticobservables 2.3.Interferometricandspectroscopicvariability
are presented in Sect.3. The stellar parameters are derived in
IntheleftpanelofFig.2thecalibratedMIDIspectraareover-
Sect.4 and compared to state-of-the-art evolutionary tracks in
plottedtotheISO/SWSspectra.ThefluxleveloftheMIDIob-
Sect.5.AsummaryoftheresultsisgiveninSect.6.
servations is the same (within the error bars) as the ISO/SWS
spectra taken at 1996 Nov 26 and 1997 Dec 11. This suggests
that no significant cycle-to-cycle variation is expected in the
2. ObservationsandDataReduction
mid-IR. The right plot of Fig. 2 shows part of the lightcurve
Sections2.1 and 2.2 discuss the interferometric and spectro- of TXPsc in V taken from AAVSO. The spectra from 1996
scopic observations obtained with VLTI/MIDI and ISO/SWS, Nov 26/1997 Dec 11 were observed at a ’local’ visual maxi-
respectively. Section2.3 discusses possible cycle-to-cycle and mum/minimum,respectively.Inthefollowingwewillusethese
intra-cyclevariabilityofthedata. two spectra to derive the parameters of the star at different
phases.AswedonothaveanyinformationontheV magnitude
of the spectrum from 1997 May 24, this spectrum is not used
2.1.MIDIvisibilitiesandspectra
in the subsequent sections. Additionally, the phase for all the
TX Psc was observed in 2004 with the 8.2m Unit Telescopes MIDI observations is unknown. However, AAVSO visual esti-
andin2005,2006and2011withthe1.8mAuxiliaryTelescopes matesfromonespecificobserverrevealedthatnoneoftheMIDI
oftheVeryLargeTelescopeInterferometerMIDI(Leinertetal. observationsweretakenatvisualminimaormaxima.
2003). MIDI covers the N-band and provides spectrally dis- Simulationswithdust-freemodelatmospheresshowthattheef-
persedvisibilities,differentialphasesandfluxes(resolutionR= fect of pulsation on the N-band UD-radius is smaller than 0.1
230forobservationsin2004,R = 30forobservationsin2005, masat1kpc(Paladinietal. 2009).Fora star atthedistanceof
2006and2011). TX Psc thiswouldbe ∼0.3mas. Thisvalueisbeyondthelimit
The journalof available MIDI observationsis givenin Table 1 ofresolutionofMIDI.Therefore,wedonotexpectanyobserved
(electronicversiononly).Theuv-coverageisplottedinFig.1. intra-cyclevariabilityeffectthatislargerthantheerrors.Thisal-
Data are reduced using MIA+EWS 1.7.11 (Jaffe 2004; Ratzka lowstocombineallcalibratedvisibilitiesforthefurtheranalysis.
2005; Leinertetal. 2004). Observations are not used if one or
more of the selection criteria discussed in Klotzetal. (2012a)
are violated (observations that are not boldfaced in Table1). 3. Modeldescription
Uniform-diskangulardiametersandIRAS12µmfluxofthecal-
In thefollowingwe presentthe differentclasses ofmodelsand
ibratortargetsaregiveninTable2(electronicversiononly).
thederivationofsyntheticobservablesthatwillbecomparedto
As only one suitable calibrator is available per observation, a
observationsinSect.4.
standard multiplicative error of 10% is assumed for the cali-
brated visibilities (Chesneau 2007) . Some calibrated visibili-
tiesatbaselinesshorterthan∼30maresignificantlynoisierand 3.1.Hydrostaticmodels
sometimeslargerthanunityafter11.5µm.Therefore,inthefol-
Observed spectra and visibilities are compared to the grid
lowing,spectro-interferometricobservationsareconsideredonly
of spherical hydrostatic model atmospheres and spectra
forwavelengthsshorterthan11.5µm.
of Aringeretal. (2009). These models are computed with
Forthecalibratedspectraadditionalselectioncriteriaareapplied
COMARCS andaregeneratedassuminghydrostaticlocalther-
(Chesneau2007):(i)theairmassdifferencebetweenscienceand
malandchemicalequilibrium.Themolecularandatomicopaci-
1 http://www.strw.leidenuniv.nl/∼jaffe/ews/MIA+EWS- tiesaretreatedintheopacitysampling(OS)approximation.The
Manual/index.html parametersthat characterize a modelare: effective temperature
2
Klotzetal.:ConstrainingstellarparametersforTXPsc
Fig.2. Left: MIDI flux (error bars) for differentdates. Overplottedare the three ISO/SWS spectra (full lines) of TXPsc. Right:
AAVSOV-bandlightcurveofTXPsc.VerticallinesmarktheobservationdateoftheISOspectra.Colorsarethesameasintheleft
figure.
T ,metallicityZ,surfacegravityg,massM,andcarbontooxy- surfacechemicalabundancesthatmaysignificantlyvarydueto
eff
genratioC/O. thethirddredge-upepisodesandhot-bottomburning.Thetransi-
Forthisworkwelimitthesampletomodelshavingsolarmetal- tionfromC/O <1toC/O >1isfollowedaccurately,inparticu-
licityastheeffectofmetallicityisexpectedtobesmallforlow- larinthenarrowrangefrom0.95≈C/O≈1.05,whereanabrupt
resolutionspectroscopy.Additionally,thereisnoindicationfor changeinthemolecularchemistryandopacityisexpectedtooc-
largelynon-solarmetallicityfromotherpropertiesofthisstar. cur(seefigures11and16inMarigo&Aringer2009).Thispoint
The spectra cover the following parameters: 2400 ≤ T ≤ isparticularlyrelevantinthecontextofthepresentwork,asTX
eff
4000Kwithstepsof100K;Z/Z⊙ =1;−1.0≤log(g[cms−2])≤ PscisfoundtohaveasurfaceC/Oslightlyaboveunity.
+0.0; M/M = 1,2; C/O= 1.05,1.10,1.40,2.00. In order to
⊙
get precise estimates of T , additional model atmospheres
eff
were producedresulting in a grid spacingof ∆T=10K. All the 4. Stellarparameterdetermination
mainmolecularopacitiestypicalforC-starswereincluded:CO
Stellar parametersforTXPsc were determinedbya numberof
(Goorvitch&Chackerian 1994), C (Quercietal. 1974), HCN
2 authors.AsummaryisgiveninTable3.
(Harrisetal. 2006), CN (Jørgensen 1997) in the form of line
In the following two different approaches will be used to de-
lists,whileC H andC (Jorgensenetal.1989)asOSdata.CS
2 2 3 termine the stellar parameters of TXPsc: (i) in Sect.4.1 we
isnotincludedduetothelackoflinelistsandOSdata.Synthetic
use the ‘classical approach’of interferometristswhere spectro-
spectra with a resolution of 18000 are computed in the wave-
interferometric observations are used to determine the ef-
lengthrange0.8−25µm.Thespectraareconvolvedinorderto
fective temperature T ; (ii) in Sect.4.2 we follow the ap-
getthesameresolutionastheobserveddata. eff
proach of Paladinietal. (2011, P11 hereafter) where spectro-
AmongtheoutputofthesphericalradiativetransfercodeCOMA
scopic/interferometric measurements are compared to hydro-
is the monochromatic spatial intensity profile. This profile is
static models to determine T and C/O ratio and to constrain
used to calculate a syntheticvisibility profile in the mid-IRfor eff
massandlogg.
asubsetofthemodelsinthegrid.Adetaileddescriptionofthe
computation of the visibility profiles is given in Paladinietal.
(2009). 4.1.Approach1:Geometricmodels
Interferometryis a powerfultoolforconstrainingthemorphol-
3.2.Evolutionarytracks ogyandsizeofstarsandtheirenvironments.
A deviation from spherical symmetry for the circumstellar en-
The luminosity and effective temperature that are determined vironmentof TXPsc was detected by several authorsat differ-
fromhydrostaticmodelsarecomparedtothermally-pulsing(TP) ent spatial scales and wavelengths(e.g. Cruzale`besetal. 1998;
AGB evolutionary tracks from Marigo et al. (in prep). We se- Raglandetal. 2006; Sacutoetal. 2011b; Jorissenetal. 2011,
lectedTP-AGBsequenceswithan initialscaled-solarchemical Hron et al in prep.). Clearly, the circumstellar environment of
composition (Z = 0.014, Y = 0.273), where Z and Y denote TXPsc isverycomplexandmostlikelyunrelatedeffectsshape
themassfractionsofmetalsandhelium,respectively.TP-AGB themorphologyindifferentregions,resultingina largevariety
evolutionary calculations are carried out from the first thermal ofstructures.To studythegeometryoftheinnermostregionof
pulse - extracted from the PARSEC database of stellar models thestarintheN-band,thegeometricalmodelfittingtoolGEM-
(Bressanetal. 2012) - to the completeejectionof the envelope FIND(Klotzetal.2012b)wasusedtofittheMIDIinterferomet-
duetostellarwinds.TheTP-AGBtracksarebasedonnumerical ricobservationsofTXPsc.AsphericalUD-modelisabletore-
integrationsofcompleteenvelopemodelsinwhich,forthefirst producethecalibratedvisibilities,i.e.TXPsccanbeassumedto
time, molecular chemistry and gas opacities are computed on- besphericallysymmetricinthemid-IRatspatialscalesprobed
the-flywiththeÆSOPUScode(Marigo&Aringer2009).This by our MIDI observations. The reason why the asymmetrical
guaranteesa fullconsistencyofthe envelopestructurewith the structuresdetectedbyotherworksarenotobservedisthatthey
3
Klotzetal.:ConstrainingstellarparametersforTXPsc
Table3.PublishedstellarparametersofTXPsc.
Reference T logg Mass C/O θ λ d
eff θ
[K] [M ] [mas] [µm] [pc]
⊙
Laskeretal.(1973) 9.00 0.66
deVegt(1974) 8.00 0.71
Dunhametal.(1975) 10.20 0.69
Lambertetal.(1986) 3030 0.0 1.03
Claussenetal.(1987) 280
Quirrenbachetal.(1994) 2805 11.20 0.7-0.8
Richichietal.(1995) 8.38 0.55-3.60
Dycketal.(1996) 2921 11.20 2.2
Jørgensenetal.(2000) 3000 -0.5 1.02
Ohnakaetal.(2000) 3000 1.07
3100 1.17
Bergeatetal.(2001) 3115
Harrisetal.(2003) 3050 0.0 1.02
Gautschy-Loidletal.(2004) 3200 -0.3 1 1.10
Bergeat&Chevallier(2005) 3125 315
Raglandetal.(2006) 9.89 1.65
vanLeeuwen(2007) 275+34
−26
Fig.3. Left:Calibrated visibilities(symbols)versusbaselinelengthforthree differentwavelengths.Thelines representthe best-
fittingUD-modelatthegivenwavelength.Right:Spectrallydispersedangulardiameterpluserrorsfromthebest-fittingUD-model
(darkgreyshadedarea).Thelightgreyshadedareamarkstheregionthatisomittedforthemeandiameterestimation.
wereeitherdetectedatdistancesoutsidetheFoVofMIDIorat F.Kerschbaumbyfitting acombinationof blackbodiesto near-
smaller spatial scales beyondthe detectionlimitof MIDI. This IRandIRASdata2.
is supported by the differential phase measurements of MIDI, Variousdefinitionsfortheradiuscanbefoundinliterature(c.f.
whichdonotshowanydeviationfromzero.Thecalibratedvisi- reviews by Bascheketal. 1991; Scholz 2003), where the most
bilitiesareplottedtogetherwiththebest-fittingUD-modelinthe commonlyusedradiusinatmosphericmodelingistheRosseland
leftpanelofFig.3forthreedifferentwavelenghts. radius. It is defined by the distance between the center of the
The right panel of Fig.3 shows the wavelength dispersed di- star and the layer having Rosseland optical depth τ = 2.
ross 3
ameter calculated with the UD-model(dark grey shaded area). Thisradius,however,isnotanobservablequantityandobserved
The star appears larger between 8 and 9µm. According to radii have to be converted by using model considerations. In
Gautschy-Loidletal. (2004) CS is affecting this wavelength the following we will derive this conversion factor for hydro-
range. Because of this molecular contamination, this region is staticC-starsbyusingasubsetofthehydrostaticmodelsinthe
omittedandameanangulardiameterofθ=10.51±0.70masis gridof Aringeretal. (2009) to derivea mean UD-radiusin the
calculatedbyaveragingthediameterfrom9-11.5µm. mid-IR (9 − 11.5µm). This mean UD-radius is plotted versus
theRosselandradiusofthecorrespondinghydrostaticmodelin
Fig.4.Thereisaclearcorrelationbetweenthetworadii,yielding
4.1.1. Effectivetemperature
R =0.95R . (1)
Ross UD
Thetemperaturecanbedeterminedusingtheapparentbolomet-
ricmagnitudembolandtheangularRosselanddiameterθross.The 2 Method described inKerschbaum&Hron(1996a) andreferences
apparentbolometricmagnitudembol =2.26magwasderivedby therein;near-IRdatafromtheIRAScatalogueandFouqueetal.(1992).
4
Klotzetal.:ConstrainingstellarparametersforTXPsc
opticallythinandcontainsalmostnodust.
In Sect.4.2.1 and 4.2.2 low-resolution spectroscopic observa-
tionsarecomparedwithsyntheticspectraofhydrostaticmodels
tofixthefundamentalstellarparametersC/OratioandT .The
eff
overallenergydistributionaswellasthebandsofthemolecules
that are present from 2.3-6µm put strong constraints on these
parameters(Jørgensenetal.2000;Loidletal.2001;P11).
Low resolution spectroscopy does not allow to ascertain mass
and logg (Fig.6-10 in P11). To determine these parameters
Sect.4.2.3 follows the approach described in P11: spectro-
interferometric observations are compared to models of fixed
T andC/Oratiobutvaryingloggandmass.
eff
4.2.1. C/Oratio
Jørgensenetal.(2000)foundtheratiobetweenthe3µmfeature
(HCN and C H ) and the 5.1µm feature (CO and C ) to be a
2 2 3
Fig.4. Rosselandradiusofthesyntheticmodelsversusthede-
sensitivemeasureoftheC/Oratio.Inordertobeindependentof
rivedmid-IRUD-radiusofthesamemodels(crosses).Theblue
distance each model spectrum is normalized to the ISO flux at
lineisalinearfittothedata.
2.9µm (local minimum of molecular absorption, Aringeretal.
2009).Aχ2 testisappliedbetween2.9-6.0µmtocomparethe
Table 4. Stellar parametersderivedfromobservations(middle observed ISO spectra (1996 Nov 26 and 1997 Dec 11) to the
block)andcalculated(rightblock)usingapproach1. models. For both ISO spectra we find that the best solution is
obtainedwithaC/O ratioof1.05.Consideringallsolutionsly-
d θUD θRoss Teff R L ing within the 68% confidence level a C/O ratio of 1.1 can be
[pc] [mas] [mas] [K] [R⊙] [L⊙] defined as an upper limit. Due to the coarse grid spacing for
C/Othisvalueisnota strictupperlimitandnolowerlimitcan
275 10.51±0.70 9.99 3127+192 294 7406
−173 beassigned.Figs.5and6showtheISO/SWSspectrumplotted
together with models of different temperatures and C/O ratios.
280 10.51±0.70 9.99 3127+192 299 7678
−173 The upper panels draw the region around the 3µm and 5.1µm
315 10.51±0.70 9.99 3127+192 337 9717 featuretoalargerscale.Theseplotsdemonstratethatasynthetic
−173 spectrum with a C/O ratio largeror equal1.4 is not able to re-
producetheobservations,becauseitover-evaluatesthedepthof
the5.1µmfeature.ThisfindingisconsistentwiththeC/Oratios
giveninliterature(seeTable3).
This implies that for a hydrostatic C-star the Rosseland radius
canbeapproximatedbythemid-IRUD-radiusifthederivedcor- 4.2.2. Effectivetemperature
rectionfactorof0.95isapplied.
Applyingthiscorrectionfactoryieldsan angularRosselanddi- We expectthe 3µm feature to be a goodtemperatureindicator
ameter θ = 9.99mas. Together with the bolometric magni- forhydrostaticstars(P11).Consequently,inordertofindthebest
Ross
tude the distance-independenteffective temperature can be de- temperatureforTXPsc,aχ2testisusedtocomparetheobserved
rived. Using the three different distance estimates d that are ISO spectra and the modelspectra between 2.9 - 3.6µm. Only
availableforTXPsc(seeTable3)alinearradiusandluminosity model spectra lying within the confidence level of C/O (1.05,
canbecalculated.Table4liststhederivedandcalculatedstellar 1.1;seeSect.4.2.1)areusedforthistest.
parametersof approach1. Errors on the temperatureare deter- The large grid of models allows to determine Teff very pre-
minedbyusingtheerrorsonθ andbyassuminganarbitrary cisely.Allsolutionslyingwithinthe68%confidencelevelhave
UD
errorof±0.1form thataccountsforthestellarvariabilityand a temperature of 3080+70 / 3170+70K for the visual mini-
bol −60 −80
thefittingerror.Thesevaluesareinagreementwiththosegiven mum/maximum,respectively.TheupperleftpanelofFigs.5and
inliterature(seeTable3). 6showthatmodelswithhigher/lowertemperaturesdonotrepro-
ducethedepthofthe3µmfeature.
Thetemperaturederivedwithapproach1inSect.4.1.1iswithin
4.2.Approach2:Hydrostaticmodels the errors of the temperature that is derivedhere for the visual
minimumandmaximum.
The short wavelength part of the ISO spectrum of TXPsc is
We confirm the finding of Jørgensenetal. (2000) that the dif-
dominated by the 3µm feature which has contributions from
ference in the two ISO spectra can be explainedby a tempera-
HCN and C H . The 5µm feature, on the other hand, is due
2 2 ture change. The lightcurvesuggests that this difference is due
to C and the fundamental band of CO. The region from 7
3 to variability effects, but time-series spectroscopy is needed to
to 8µm is dominated by HCN and C H and according to
2 2 confirmthisfinding.
Gautschy-Loidletal. (2004) the region from 8 to 9µm is af-
fectedbyCS opacity.Thelowvariabilityinthe V-band(∆V ∼
0.4mag) justifies the use of hydrostatic models in the near- as
4.2.3. Surfacegravityandmass
wellasmid-IR.Additionally,hydrostaticmodelsareabletore-
producelargepartsoftheoverallISOaswellasMIDIspectra. Interferometric observations are compared to synthetic visi-
This indicates that the circumstellar environment of TXPsc is bilities of hydrostatic models of varying logg and mass us-
5
Klotzetal.:ConstrainingstellarparametersforTXPsc
Fig.5. ISO/SWSspectrumofTXPsc atvisualminimumfrom1997Dec11(blackline)plottedwithhydrostaticmodels(colored
lines)ofdifferenttemperatureandC/Oratio.Thebestfittingmodelisplottedingreen.Modelspectraarenormalizedtothefluxof
thecorrespondingISOspectrumat2.9µm.
Fig.6. SameasFig.5,butforatvisualmaximumfrom1996Nov21.
ing a χ2 test. All synthetic visibilities are computed for the there is also a degeneracy between distance and logg. From
best-fitting values of T and C/O-ratio from Sects.4.2.1 and current TP-AGB evolutionary calculations (e.g. Karakasetal.
eff
4.2.2. Synthetic visibilities are derived at 3 different distances: 2002;Marigo&Girardi2007,Marigoetal.inprep.)weexpect
275pc, 280pc, 315pc (vanLeeuwen 2007; Claussenetal. that a 1M TP-AGB star with solar metallicity does not make
⊙
1987; Bergeat&Chevallier 2005, respectively). In Fig.7 the thetransitiontotheC-richdomain.Thissuggeststhatthelogg
wavelength-dispersedcalibratedvisibilitiesare plottedtogether valuesinTable5foundforM =2M arethemorereliableones.
⊙
withthesyntheticvisibilitiesofthebest-fittingmodels.There- But,consideringthedegeneracyandthelimitedmasssampling
gion between 8 - 9µm is not considered in the fitting, as the (M =1,2M )inthegrid,alsomodelswithhighermasseswould
⊙
hydrostaticmodelsdonotincludetheCSopacitydata. reproduce the observed visibilities. To support this statement,
The middle block of Table5 gives the best-fitting stellar pa- oneadditionalmodelwith3M iscalculatedandoverplottedin
⊙
rameters for a given distance that were determined using ap- Fig.7asdashedline.Themodelsarealmostindistinguishable.
proach 2. It is clear from the table and from Fig.7 that, given TherightpartofTable5givesstellarparametersthatarecalcu-
the error barson the visibilities, there is a degeneracybetween latedfromthederivedlogg,massandeffectivetemperature.The
logg and mass. As the distance defines the level of visibility, luminositiesaresignificantlylargerthanthe L = 5200L used
⊙
6
Klotzetal.:ConstrainingstellarparametersforTXPsc
Fig.7. Wavelength-dispersedcalibratedvisibilitiespluserrors(darkgreyshadedarea)plottedwiththebest-fittingsyntheticvisibil-
itiesofhydrostaticmodels(fulllines).Toshowthedegeneracybetweenmassandloggonemodelwith3M isoverplotted(dotted
⊙
line).
byGautschy-Loidletal.(2004),butcomparabletoL=7700L
⊙
derivedbyClaussenetal.(1987).Theluminositiesandradiiare
also in perfect agreement with the ones determined with ap-
proach1(seeSect.4.1).
4.2.4. Photometricconstraintsonthebestmodel
The best fitting hydrostatic models of visual mini-
mum/maximum (model with lowest χ2 in Table5) are
logg,M
overplotted to the ISO and MIDI spectra as well as to pho-
tometric measurements in Fig.8. Photometric measurements
from Johnsonetal. (1966), MendozaV.&Johnson (1965) and
Catchpoleetal. (1979) were observed with the Johnson filter
system. Zero points to convert these measurements from mag-
nitudestoJanskyaretakenfromCox(2000).Thesezeropoints
arealsousedtoconvertobservationsfromBergeatetal.(1976)
andBergeat&Lunel(1980)astheauthorsclaimthattheirfilter
system is similar to the Johnson filter system. Zero points for Fig.8. Best fitting hydrostaticmodelsfor the visualminimum
2MASSphotometry(Cutrietal.2003)aregiveninCohenetal. (blackline)andmaximum(greyline).SuperimposedaretheISO
(2003). Olofssonetal. (1993) and Kerschbaumetal. (1996b) spectra of visual minimum (green line) and visual maximum
usedtheESOfiltersystem.ZeropointsaretakenfromLeBertre (blue line), MIDI spectra (violet lines) and photometric mea-
(1988)andWamsteker (1981).Noguchietal.(1981) usedtheir surements of different works (orange symbols). Model spectra
own filter system and corresponding zero points are given in arenormalizedtothefluxofthecorrespondingISOspectrumat
theirpaper. 2.9µm.
5. Comparisonwithevolutionarytracks
with solar-metallicity and C/O within a narrow interval (i.e.
WefollowtheapproachdescribedinP11andcomparethestel- 1<C/O≤1.1). As we see in Fig. 9, the TP-AGB evolutionary
larparameterswithnewevolutionarytracksofthermallypulsing tracksintheC-richregimeextendtomuchlowereffectivetem-
AGBstars(Marigoetal.,inprep). peratures than the derived values for TX Psc. This cooling is
Figure9 depictsevolutionarytracksin the regionofAGB stars mainlydrivenbytheincreaseoftheC/Oratioaftereachdredge-
intheH-Rdiagram.Overplottedarethedeterminedluminosity up episode, as well as by the progressive strengthening of the
and temperature for TXPsc for the two approaches. Only the mass-loss efficiency.The relativelywarm effective temperature
best-fitting luminosity (see Table 5) at d=280pc is plotted for ofTXPscsuggeststhatthisstarisobservedcloseafterthetran-
TXPsc.Errorsfortheluminosityareassumedtolieintheorder sitionintotheC-stardomain,inanearly‘quiet’stageinwhich
of∼40%(uncertaintyonthegivendistancemeasurement). thestrongwindhasnotyetdeveloped.Thispictureisnicelysup-
We note an encouraging agreement between the observed lo- portedbytheobservationalfindingsalreadydiscussedinthepre-
cation of TX Psc in the H-R diagram and the predicted ranges vioussections.
of luminosity and effective temperature for a carbon-rich star Itisvisible fromthe evolutionarytracksthatan AGBstar with
7
Klotzetal.:ConstrainingstellarparametersforTXPsc
Table5. Stellarparametersderivedfromobservations(middleblock)andcalculated(rightblock)usingapproach2.
d T T C/O logg M χ2 R L L
eff,min eff,max logg,M min max
[pc] [K] [K] [M ] [R ] [L ] [L ]
⊙ ⊙ ⊙ ⊙
275 3080+70 3170+70 1.05 -0.5 1 0.50 295 7019 7876
−60 −80
-0.2 2 0.50 295 7019 7876
280 3080+70 3170+70 1.05 -0.5 1 0.48 295 7019 7876
−60 −80
-0.2 2 0.53 295 7019 7876
315 3080+70 3170+70 1.05 -0.6 1 0.49 331 8836 9915
−60 −80
-0.3 2 0.53 331 8836 9915
solar metallicity will turn into a carbon-richAGB star only for Acknowledgements. TheauthorsthankAngelaBaierforfruitfuldiscussionson
masses around 2M and higher. Also, the position of TXPsc ISO spectra and Walter Nowotny for helpful discussions on SEDs and pho-
⊙
in Fig.9 suggests that the mass lies between 2 and 3M . This tometric filter systems.This workis supported bytheAustrian Science Fund
⊙
FWFunderprojectnumberAP23006.BAacknowledgessupportfromAustrian
is not in agreement with the best fitting models having 1M
⊙ Science Fund (FWF) Projects AP23006 & AP23586 and from contract ASI-
(Sect.4.2.3), but in good agreement with the models having INAFI/009/10/0.ThisresearchhasmadeuseoftheSIMBADdatabase, oper-
2M⊙. atedatCDS,Strasbourg,France.Weacknowledgethevariablestarobservations
fromtheAAVSOInternationalDatabasethatwereusedinthisresearch.
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9
Klotzetal.:ConstrainingstellarparametersforTXPsc,OnlineMaterialp1
Table2.Propertiesofthecalibratortargets.
HD Name Sp.T.a F a θb
12
[Jy] [mas]
HD48915 Sirius A1 143.1±3 6.08±0.03
HD20720 τ04Eri M3/M4 162.7±6 10.14±0.04
HD224935 YYPsc M3 86.9±5 7.25±0.03
HD49161 17Mon K4 10.4±5 2.44±0.01
HD18884 αCet M1.5 234.7±3 12.28±0.05
HD45348 Canopus F0 154.8±3 6.87±0.03
Notes. (a)http://www.eso.org/observing/dfo/quality/MIDI/qc/
calibrators obs.html
(b) http://simbad.u-strasbg.fr/simbad/