Models of circumstellar molecular radio line emission: Mass loss rates for a sample of bright carbon stars

26 Pages·0.87 MB·English

by  F. L. Schoeier

A&Amanuscriptno. ASTRONOMY
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AND
Yourthesauruscodesare: ASTROPHYSICS
06(08.16.4;08.03.1;08.03.4;08.12.1;13.19.5)
⋆
Models of circumstellar molecular radio line emission
Mass loss rates for a sample of bright carbon stars
F.L.Scho¨ier1andH.Olofsson1
StockholmObservatory,SE-13336Saltsjo¨baden,Sweden
1
0
A&Ainpress
0
2

n
Abstract. Using a detailed radiative transfer analysis, com- ter) thestellar luminosity.Moreover,themass lossrate corre-
a
bined with an energy balance equation for the gas, we have latesweaklywiththestellareffectivetemperature,inthesense
J
performedextensivemodellingofcircumstellarCO radioline that the cooler stars tend to have higher mass loss rates, but
6
2 emission froma largesampleof opticallybrightcarbonstars, thereseemstobenocorrelationwiththestellarC/O-ratio.We
originallyobserved by Olofsson et al. (ApJS, 87, 267). Some concludethatthemasslossrateincreaseswithincreasedregu-

1 new observational results are presented here. We determine larpulsationand/orluminosity,andthattheexpansionvelocity
v
someofthebasicparametersthatcharacterizecircumstellaren- increasesasaneffectofincreasingmasslossrate(forlowmass
7
velopes(CSEs),e.g.,thestellarmasslossrate,thegasexpan- lossrates)andluminosity.
7
4 sionvelocity,andthekinetictemperaturestructureofthe gas. Five, of the remaining eight, sample stars have detached
1 AssumingasphericallysymmetricCSEwithasmoothgasden- CSEsintheformofgeometricallythinCOshells.Thepresent
0 sitydistribution,createdbyacontinuousmassloss,whichex- masslossratesandshellmassesofthesesourcesareestimated.
1
pandswithaconstantvelocityweareabletomodelreasonably Finally,inthreecasesweencounterproblemsusingourmodel.
0
well61ofour69samplestars.Thederivedmasslossratesde- Fortwoofthesesourcesthereareindicationsofsignificantde-
/
h pendcruciallyonthe assumptionsin the circumstellarmodel, parturesfromoverallsphericalsymmetryoftheCSEs.
p
ofwhichsomecanbeconstrainedifenoughobservationaldata CarbonstarsontheAGBareprobablyimportantinreturn-
-
o exist. Therefore, a reliable mass loss rate determination for ing processed gas to the ISM. We estimate that carbon stars
tr an individual star requires, in addition to a detailed radiative of the typeconsideredhere annuallyreturn 0.05M of gas
s transferanalysis,goodobservationalconstraintsintheformof to the Galaxy, but more extreme carbon sta∼rs may c⊙ontribute
a
: multi-line observations and radial brightness distributions. In an orderof magnitudemore.However,as for the totalcarbon
v ouranalysisweusetheresultsofamodelforthephotodissoci- budgetoftheGalaxy,carbonstarsappeartobeofonlyminor
i
X ationof circumstellarCO byMamonetal. (1988).Thisleads importance.
to modelfits to observedradialbrightnessprofilesthatare,in
r
a general,verygood,buttherearealsoafewcaseswithclearde-
Key words: Stars: AGB and post-AGB – Stars: carbon– cir-
viations, which suggestdeparturesfroma simple r−2 density
cumstellarmatter–Stars:late-type–Radiolines:stars
law.
Thederivedmasslossratesspanalmostfourordersofmag-
nitude, from 5 10−9M yr−1 up to 2 10−5M yr−1,
withthemedi∼anm×assloss⊙ratebeing2.8 ∼10×−7M yr⊙−1.We
1. Introduction
estimatethatthemasslossratesaretypica×llyaccura⊙teto 50%
∼
within the adopted circumstellar model. The physical condi- The carbon star phenomenon, i.e., the presence of stars for
tionsprevailingintheCSEsvaryconsiderablyoversuchalarge which the abundanceof carbonexceedsthatof oxygenin the
rangeofmasslossrates.Amongotherthings,itappearsthatthe atmospheres,occursduringthefinalevolutionarystageoflow
dust-to-gas mass ratio and/or the dust properties change with tointermediatemassstars( 1 10M ;Wallerstein&Knapp
themasslossrate.We findthatthe masslossrate andthegas 1998),anditisbelievedtob∼edu−etoad⊙redge-upprocessdriven
expansion velocity are well correlated, and that both of them byquasi-periodicHe-shellflashes(Stranieroetal.1997).These
clearlydependonthepulsationalperiodand(withlargerscat- stars,locatedontheasymptoticgiantbranch(AGB),losecopi-
ousamountsofmatter( 10−8 10−4M yr−1)inanintense
stellarwind.Infact,itis∼themas−slosstha⊙tdeterminestheAGB
Sendoffprintrequeststo:F.L.Scho¨ier([email protected])
⋆ Presented in this paper is observational data collected using the lifetimeandnotthenuclearburningprocesses.Hence,adeter-
Swedish-ESOsubmillimetretelescope,LaSilla,Chile,the20mtele- minationof the mass loss characteristics, i.e., the dependence
scope at Onsala Space Observatory, Chalmers Tekniska Ho¨gskola, ontime,mass,chemistry,metallicity,etc.,isofutmostimpor-
Sweden,andtheNRAO12mtelescopelocatedatKittPeak,USA. tanceforourunderstandingoflatestellarevolution.
2 F.L.Scho¨ier&H.Olofsson:Modelsofcircumstellarmolecularradiolineemission
Themasslosscreatesacircumstellarenvelope(CSE)ofgas Table1.Dataontelescopesandreceiversused.
anddustaroundthestar.Thelowtemperatureofthecentralstar
allowstheformationofawidevarietyofmolecularspeciesin Tel. Trans. ν Trec(SSB) θmb ηmb ηm∗
its atmosphere, and the expanding gas is therefore mainly in [GHz] [K] [′′]
molecular form. The chemistry in the CSE itself can be very
OSO CO(1−0) 115.271 100 33 0.5
rich,anditdependsontheC/O-ratio,thethicknessoftheenve- SEST CO(1−0) 115.271 110 45 0.7
lope,andthestrengthoftheambientultravioletradiationfield. CO(2−1) 230.538 110 23 0.5
Presently, 60differentmolecularspecieshavebeenidentified CO(3−2) 345.796 300 16 0.25
inCSEsar∼oundAGB-stars(Olofsson1997). NRAO CO(1−0) 115.271 80 55 0.55 0.84
ThestudyofAGB-CSEsisimportantfortheunderstanding CO(2−1) 230.538 200 27 0.30 0.45
ofthelatestagesofstellarevolutionasmentionedabove.Inad-
dition, an understandingof the atmospheric and circumstellar
chemistry is required to determine the elemental abundances Furthermore,themolecularexcitationisofaquasi-thermalna-
in these winds, which contributeto the chemical evolution of turewhichsimplifiesdetailedmodelling.
theinterstellarmedium(Bussoetal.1999).Finally,sinceAGB
starsaretheprogenitorsofplanetarynebulae(PNe),theCSEs
are very likely importantingredientsin the formationof PNe 2. Observations
(Kwok1993).
2.1. Thesample
Observations of molecular millimetre-wave line emission
haveproventobeoneofthebesttoolsforstudyingthestruc- We have selected a sample of 68 bright N- and J-type car-
ture,kinematics,andchemistryoftheCSEs, andCO andOH bon stars for which circumstellar CO emission was detected
observations have proven particularly useful for the determi- byOlofssonetal. (1993a).Theiroriginalsampleconsistedof
nation of accurate mass loss rates [see Olofsson (1996) and carbonstarsbrighterthanK=2mag.,intotal120sources.The
referencestherein]. detectionrate forall the carbonstars searchedforcircumstel-
WhiletheoverallpictureofmasslossontheAGBisfairly larCO wasashighas72%.Theoriginalsampleisthoughtto
wellunderstood,someoftheunderlyingphysicalprinciplesare be close to complete to distances below 1kpc [it is estimated
not.Theprevailingtheory,whichneedstobethoroughlytested that about a third of the carbon stars within this distance are
observationally,isthatthemasslossoccursinatwostagepro- missing,presumablytheoneswiththickanddustyCSEs, i.e.,
cess.Firstthepulsationsofthestardepositenergyintheatmo- thehighmasslossobjects(Olofssonetal.1993a)],andfordis-
sphere, leading to a considerably increased scale height, and tances below 500pc all sources (a total of 41) were detected
sufficientmatteratlowenoughtemperaturesforefficientdust inCO (notethatthedistancesusedinthispaperaregenerally
formation.Radiationpressureonthedustgrainsacceleratethe lowerthanthoseadoptedinOlofssonetal.1993a).Thesefacts
dustwindtoitsterminalexpansionvelocityinthesecondstage. taken togetherled to the conclusionthat the greatmajorityof
Thegasismomentumcoupled,throughcollisions,tothedust, all N-type carbon stars are losing mass at a rate higher than
anditwillbeeffectivelydraggedalong.Themechanismsthat about 10−8M yr−1. They do not, however, constitute a ho-
cause the mass loss to vary on a wide range of time scales mogeneousgro⊙upintermsofcircumstellarproperties.Instead
stillneedtobepinpointed.Eventually,thepossibilityofmass they show a wide rangeof gas expansionvelocities and mass
ejected in clumps has to be addressed, although in this paper lossrates,presumablyduetodifferencesinmass,evolutionary
wewillconsideronlyasmoothsphericallysymmetricwind. stage,etc..Inaddition,thereasonablywellstudied,highmass
This study of an essentially complete sample of visually loss rate carbon star, LP And (also known as IRC+40540), is
bright, relatively unobscured carbon stars will hopefully in- includedinouranalysis,sinceitprovidesagoodtestcasefor
creaseourknowledgeofthemodellingofcircumstellarmolec- theradiativetransfermodel.
ular radioline emission, the mass loss characteristics,the cir- The CO (J=1 0 and J=2 1) observations presented
→ →
cumstellar chemistry, the elemental abundances in the winds, in Olofsson et al. (1993a) were obtained using the 20m tele-
andpossiblytheevolutionarystatusoftheseobjects.Itwillalso scope atOnsala Space Observatory(OSO),Sweden,the 15m
provideus with the toolsrequiredto determinethe properties Swedish-ESO sub-millimetre telescope (SEST) at La Silla,
ofhighermasslossrateobjects,forwhichthecentralstarmay Chile,andtheIRAM30mtelescopeatPicoVeleta,Spain,dur-
becompletelyobscured. ingtheyears1986 1992.
−
InthispaperthebasicphysicalcharacteristicsoftheCSEs,
e.g., the stellar mass loss rate, the gas kinetic temperature,
2.2. Newobservations
and the gas expansion velocity, are determined using a ra-
diative transfer analysis of the observed 12CO (hereafter CO) WehavesupplementedtheoriginaldatawithnewCOobserva-
millimetre-wave line emission. The CO molecule is particu- tionsofsomeofthesamplestars.Inparticular,intheJ=3 2
→
larly well suited for this purpose, since it is difficult to pho- line using the SEST (August 1992). Also some J=1 0 and
→
todissociateandeasytoexcitethroughcollisions,andthusisa J=2 1 data were obtained at SEST (October 1998). A few
→
verygoodtracerofthemoleculargasdensityandtemperature. sourceswereobservedintheJ=1 0andJ=2 1lineswith
→ →
F.L.Scho¨ier&H.Olofsson:Modelsofcircumstellarmolecularradiolineemission 3
Fig.1.Newobservationsofcircumstellar12COlineemission.Thelineobservedandthetelescopeusedareshownintheupper
rightcornerofeachpanel.
4 F.L.Scho¨ier&H.Olofsson:Modelsofcircumstellarmolecularradiolineemission
Table2.Observationalresults(seetextfordetails).Theintensityscaleisthoughttobeaccuratetowithin 20%.
∼
Source Tel. Trans. Tmb Imb v∗ ve β
[K] [Kkms−1] [kms−1] [kms−1]
RFor SEST 3−2 0.70 17.9 −1.8 16.1 1.0
TWHor SEST 3−2 0.94 8.7 1.0 7.5 2.5
V384Per1 NRAO 1−0 0.37 7.8 −16.4 11.5 0.5
RLep SEST 3−2 0.48 12.9 12.4 19.5 1.7
WOri1 SEST 1−0 0.06 1.2 1.6 8.6 −0.7
SEST 2−1 0.27 4.9 0.0 10.0 0.4
SEST 3−2 0.27 4.8 −1.4 11.8 1.1
WPic SEST 3−2 0.24 6.3 20.7 13.9 0.4
RVol SEST 3−2 0.74 20.8 −10.6 16.9 0.8
XCnc NRAO 1−0 0.06 0.7 −10.3 7.6 1.3
SEST 1−0 0.12 1.7 −12.8 8.6 1.0
SEST 2−1 0.30 3.2 −14.3 7.5 1.7
CWLeo NRAO 1−0 7.1 170.8 −25.9 14.3 0.7
SZCar1 SEST 3−2 0.30 5.5 25.7 13.1 1.2
RWLMi NRAO 1−0 1.3 36.4 −1.6 15.8 0.7
XTrA SEST 3−2 1.2 15.3 −2.0 8.7 1.6
DRSer1 NRAO 2−1 0.26 11.3 11.6 24.1 1.1
VCyg NRAO 2−1 2.9 50.1 14.2 11.0 1.1
RVAqr SEST 3−2 0.83 18.6 1.2 14.5 1.1
PQCep1 NRAO 2−1 0.28 8.7 6.3 24.1 0.0
LPAnd OSO 1−0 2.6 57.0 −16.9 13.8 1.1
NRAO 2−1 3.1 60.7 −17.1 14.0 1.7
TXPsc2 SEST 3−2 1.0 7.0 1.0 7.5 2.0
1Contaminationbyinterstellarlines.2βwasfixed.
theNRAO12mtelescopeatKittPeak,USA(June1998),and of 512MHz (MUL A) and 64MHz (MUL B), were used.
someJ=1 0datawereobtainedusingOSO(1998to1999). The MUL A used 512 channels separated by 1MHz, and the
→
A summary of telescope and receiver data [the receiver MUL B filterbank used 256 channels with a separation of
temperatureT in single sidebandmode (SSB), the full half 250kHz.
rec
power main beam width θmb, the main beam efficiency ηmb, The SEST and OSO observations were made in a dual
andthecorrectedmainbeamefficiencyη∗]attheobservational beamswitchmode,wherethesourceisalternatelyplacedinthe
m
frequenciesaregiveninTable1. signal and the reference beam, using a beam throw of about
At SEST, a dual channel SIS mixer receiver was used to 12′ at SEST and 11′ at OSO. This method producesvery flat
simultaneously observe at 115GHz (the J=1 0 line) and baselines.Theintensityscalesaregiveninmainbeambright-
230GHz(theJ=2 1line).At345GHz(theJ=→3 2line),a nesstemperature,Tmb.Tmb=TA∗/ηmb,whereTA⋆istheantenna
singlepolarization→SiSmixerreceiverwasused.As→backends, temperature corrected for atmospheric attenuation using the
twoacousto-opticalspectrometers(AOS)wereused;onehigh chopper wheel method, and ηmb is the main beam efficiency,
resolution spectrometer (HRS) and one low resolution spec- seeTable1.
trometer (LRS). The wideband (1GHz) LRS had 1440 chan- AttheNRAO12mtelescopetheobservationswerecarried
nelsseparatedby0.7MHz,whereasthenarrowband(84MHz) out using a position switching mode,with the referenceposi-
HRSused2000channelsseparatedby42kHz. tionlocated+10′inazimuth.Thisisthepreferredobservation
FortheNRAO12mobservationsweusedadualpolariza- modeforspectrallineobservationsatthe12mtelescope.The
tion SISreceiver.As backendstwo filterbanks,each with 256 raw spectra,which arestored in the T∗ scale, were converted
R
channels and a channel separation of 1MHz, were used. The usingTmb=TR∗/ηm∗,whereηm∗ isthecorrectedmainbeameffi-
spectraobtainedateachofthepolarizationswereaddedtoin- ciencygiveninTable1.TheT∗ scaleisrelatedtoT⋆ through
R A
creasethesignal-to-noiseratio.Inaddition,forstrongsources, TR∗=TA⋆/ηfss,whereηfss istheforwardscatteringandspillover
amillimetreautocorrelator(MAC)wasusedinordertoobtain efficiency.
ahighervelocityresolution.TheMACwasusedinaconfigu- Regularpointingcheckswere madeonstrongSiO masers
rationwheretheusablebandwithwas300MHzandtheresolu- (OSO, SEST) and strong continuum sources (NRAO). The
tionwas98kHz. pointingwasusuallyconsistentwithin 3′′forSESTandOSO
At OSO, a single polarization SIS receiver was used for and 5′′ at NRAO. The uncertainties∼in the absolute inten-
∼
theobservations.Asbackendstwofilterbanks,withbandwidths sity scales at the varioustelescopes are estimated to be about
F.L.Scho¨ier&H.Olofsson:Modelsofcircumstellarmolecularradiolineemission 5
15 20%.However,duetothelowefficiencyoftheSESTat ered. These modelphotons,emitted bothlocally in the gasas
± −
345GHz, and the narrow beam, we consider these data to be wellasinjectedfromtheboundariesoftheCSE,arefollowed
particularlyuncertainintermsofcalibration. throughtheCSEandthenumberofabsorptionsarecalculated
The new observational results are summarized in Table 2 andstored.Photonsarespontaneouslyemittedinthegaswith
and the spectra are shown in Fig. 1. The line parameters,i.e., completeangularandfrequencyredistribution(CRD),i.e.,the
themainbeambrightnesstemperatureatthelinecentre(T ), localemissionisassumedtobeisotropicandthescatteringare
mb
thelinecentrevelocity(v∗),andhalfthefulllinewidth(ve),are assumed to be incoherent. The weight of a model photon is
obtainedbyfittingthefollowinglineprofiletothedata(Olofs- continuouslymodified,to take the absorptionsand stimulated
sonetal.1993a) emissions into account, as it travels through the CSE. When
all model photons are absorbed in, or have escaped, the CSE
2 β/2
v v∗ theSEaresolvedandthewholeprocessisthenrepeateduntil
T(v)=T 1 − , (1)
mb" −(cid:18) ve (cid:19) # somecriterionforconvergenceisfulfilled.Oncethemolecular
excitation, i.e., the level populations,is obtained the radiative
where β is a parameter describing the shape of the line (β=2 transferequationcanbesolvedexactly.
representsaparaboliclineshape,andβ<0meansaprofilewith ThemaindrawbackoftheMonteCarlomethodisitsslow
hornsattheextremevelocities).Theintegratedintensity(Imb) convergence( √Niter).Thisis,however,usuallyoutweighed
isobtainedbyintegratingtheemissionbetweenv∗ ve. by its great ad∼aptability.One of our motivationsfor choosing
±
Inaddition,wehaveobtainedpubliclyavailabledatafrom the Monte Carlo method was to be able to treat varyingmass
the James Clerk Maxwell Telescope (JCMT) at Mauna Kea, loss rates, departures from spherical symmetry, and the pos-
Hawaii.TheJCMTdataaretakenatfacevalue.However,inthe sibility of a highly clumped medium. These complicating is-
caseswheretherearemorethanoneobservationavailable,the sueswillbeinvestigatedinafutureversionofourMonteCarlo
derivedline intensities are generallyconsistentwithin 20%. code.
±
ThegoodagreementwithcorrespondingSESTintensitiesfur-
ther support the reliability of the JCMT public data. Further-
3.2. Thestandardmodel
more, interferometerobservationsof the CO(J=1 0) bright-
→
ness distribution around some of our carbon stars have been The numerical modelling of line emission from CSEs, where
obtainedbyNerietal.(1998)usingtheIRAMPlateaudeBure intricate interplays between physical and chemical processes
interferometer(PdBI).Thedataarepubliclyavailableandhave takeplace,isachallenge.Thisapplies,inparticular,totheim-
beenusedinthispaper. portant inner regions of the CSE model, where very few ob-
servationalconstraintsareavailableandourknowledgeisvery
3. Radiativetransfer limited. In this analysis, we will neglect many of these com-
plexitiesandassumearelativelysimple,yetreasonablyrealis-
3.1. TheMonteCarlomethod
tic, CSE model. By applying the model to a large sample we
Inordertomodelthecircumstellarmolecularlineemissionand will derive fairly reliable mass loss rates, and we will also be
to derivethe basic characteristicsof theCSEs we have devel- abletopickoutobjectsforwhichthereappearstobeclearde-
oped a non-LTE radiative transfer code based on the Monte viationsfromthesimplepicture.
Carlo method [Bernes (1979); see also Scho¨ier (2000), for Inwhatwillbereferredtoas”thestandardmodel”weas-
details]. An accurate treatment of the molecular excitation is sume a sphericallysymmetric CSE thatexpandsat a constant
needed for a correct description of the radiative transfer in velocity. In our data we see no evidence for gas acceleration
an expanding circumstellar envelope, e.g., the Sobolev ap- in the CO emitting region.The CSE is dividedinto a number
proximationhas beenshown to introducesignificanterrorsin ofdiscreteshells,eachwithitsownsetofphysicalparameters
thesecircumstances(e.g.,Scho¨nberg1985).TheMonteCarlo describingthestateofthemoleculargas.Thedensitystructure
method is well suited for the study of CSEs, since it is very (asafunctionofdistance,r,fromthecentralstar)canthenbe
flexibleandclosetothephysicsandyetsimpleinprinciple.For derivedfromtheconservationofmass
instance,onemayincludeverycomplexgeometriesandveloc- M˙
ity fields without being forced away from the physics of the ρH2 =nH2mH2 = 4πr2v , (2)
e
problem.Crosas&Menten1997haverecentlyusedtheMonte
Carlo method to model the circumstellar CO radio line emis- whereM˙ isthehydrogengasmasslossrate,andv isthegas
e
sion of the prominent carbon star IRC+10216 (from hereon expansionvelocitytakenfromthelineprofilefitsofOlofsson
calledCWLeo). etal.(1993a)orTable2.WeassumethatintheCSEsofinterest
Theaimoftheradiativetransferistoobtainthesteady-state herethehydrogenisinmolecularformintheregionprobedby
levelpopulations,ofthemoleculeunderstudy,usingthestatis- theCO emission(Glassgold& Huggins,1983).Theturbulent
tical equilibrium equations (SE). In the Monte Carlo method velocity is assumed to be equal to 0.5kms−1 throughoutthe
informationontheradiationfieldisobtainedbysimulatingthe entireCSE.
linephotonsusinganumberofmodelphotons,eachrepresent- The excitation of the CO molecules were calculated tak-
ingalargenumberofrealphotonsfromalltransitionsconsid- ingintoaccount30rotationallevelsineachofthegroundand
6 F.L.Scho¨ier&H.Olofsson:Modelsofcircumstellarmolecularradiolineemission
firstvibrationalstates.Theradiativetransitionprobabilitiesand where a and ρ are the average size and density of a dust
d d
energylevelsaretakenfromChandraetal.(1996),andthero- grain,respectively.
tationalcollisionalrate coefficients(CO-H ) are based on the Whensolvingtheenergybalanceequationfreeparameters
2
resultsinFlower&Launay(1985).Thesearefurtherextrapo- describingthedust,i.e.,viathedust-gascollisionalheating,are
latedforJ>11andfortemperatureshigherthan250K.Colli- introduced. These are highly uncertain, but affect the derived
sionaltransitionsbetweenvibrationallevelsarenotimportant lineintensities.HereweassumethattheQ-parameter,i.e.,the
duetothelowdensitiesandtheirshortradiativelifetimes. efficiency of momentum transfer, to be equal to 0.03 [for de-
The kinetic gas temperature is calculated after each itera- tailsseeHabingetal.(1994)],anddefineanewparameterthat
tion in a self-consistent way, using the derived level popula- containstheotherdustparameters,
tions, bysolvingthe energybalanceequation(e.g.,Goldreich
Ψ 2.0gcm−3 0.05µm
&Scoville1976), h= , (7)
0.01 ρ a
dT T γ 1 (cid:18) (cid:19)(cid:18) d (cid:19)(cid:18) d (cid:19)
=(2 2γ) + − (H C), (3) wherethenormalizedvaluesaretheonesweusedtofittheCO
dr − r n kv −
H2 e
line emission of CW Leo using our model, i.e., h=1 for this
where γ is the adiabatic index [assumed to be equal to 5/3, object.
buttheresultsarenotverysensitivetoitsexactvalue,seealso Additional heating is provided by the photoelectric effect
Groenewegen (1994) and Ryde et al. (1999)], k is the Boltz- (Hugginsetal.1988)
mannconstant,H isthetotalheatingrateperunitvolume,and
Cisthetotalcoolingrateperunitvolume.Thefirsttermonthe Hpe =kpenH2, (8)
righthandsideisthecoolingduetotheadiabaticexpansionof
where k is a constant that depends on the properties of
thegas.Additionalcoolingisprovidedbymolecularlineemis- pe
the dust grains. Following Huggins et al. (1988) we adopt
sion from CO and H . The molecular cooling due to CO is
2 k =1 10−26ergs−1. This heating mechanism is important
calculatedfromthederivedlevelpopulationsusingtheexpres- pe ×
inthecool,tenuous,outerpartsofCSEsaroundhighmassloss
sion of Crosas & Menten (1997). For the H cooling we use
2
ratestars.
the approach by Groenewegen (1994). HCN could be an im-
The spatial extent of the molecular envelope is generally
portantcoolantin the inner parts of the envelope(Cernicharo
an important input parameter, and the derived mass loss rate
etal. 1996),butGroenewegen(1994)demonstratesthatHCN
will dependon this. The radialdistributionof CO in the CSE
coolingisonlyofminorimportance.Inthepresentversionof
was estimated using the modellingpresentedin Mamonet al.
the code HCN cooling is therefore not included (in a forth-
(1988). It includes photodissociation, taking into account the
comingpaper,Scho¨ier & Olofsson in prep.,this issue will be
effectsofdust-,self-andH -shielding,andchemicalexchange
addressed). 2
reactions. Mamon et al. (1988)find that the radial abundance
The mechanism responsible for the observed mass loss is
distribution of CO with respectto H , f(r), can be described
probably(atleastforthestarsofinteresthere)radiationpres- 2
by
sure acting onsmall dustgrains,which in turn are coupledto
thegas(e.g.,Ho¨fner1999).Theradiationpressureonthedust α
r
grains will give them a drift velocity, vdr, relative to the gas f(r)=f0 exp −ln2 r , (9)
(Gilman1972;Goldreich&Scoville1976;Kwan&Hill1977) (cid:20) (cid:18) p(cid:19) (cid:21)
where f is the initial (photospheric) abundance, r is the
1/2 0 p
LveQ photodissociationradius(wheretheabundancehasdroppedto
v = , (4)
dr M˙ c f /2), and α is a parameter describing the rate at which the
(cid:18) (cid:19) 0
abundance declines. Both r and α depend on the mass loss
whereListheluminosity,Qistheaveragedmomentumtrans- p
rate(M˙ ),theexpansionvelocity(v ),andf .Inourmodelling
ferefficiency,andcisthespeedoflight[seeSahai(1990)fora e 0
weuseanalyticalfitstotheseresultsfromStaneketal.(1995)
moreelaboratetreatment].Asaresultofthedust-gasdrift,ki-
neticenergyoftheorderof 12mH2vd2r willbetransferedtothe M˙ 0.65 v −0.55 f 0.55
gaseach time a particle collideswith a dustgrain.This is as- r = 5.4 1016 e 0
sumedtoprovidethedominatingheatingofthegas(Goldreich p × 10−6! (cid:16)15(cid:17) (cid:18)8×10−4(cid:19)
&Scoville1976;Kwan&Hill1977), v
+7.5 1015 e cm (10)
× 15
1
H =(n σ v ) ρ v2 , (5) (cid:16) (cid:17)
dg d d dr 2 H2 dr andKwan&Webster(1993)
wherend isthenumberdensityofdustgrains,andσd thegeo- M˙ 0.09 15 0.09
metricalcrosssectionofadustgrain.Introducingthedust-to- α=2.79 , (11)
10−6 v
gasmassratioΨthisequationcanbewritten ! (cid:18) e(cid:19)
3 Ψ v3 wheretheunitsofM˙ andv areM yr−1andkms−1,respec-
H = m2 n2 dr , (6) e
dg 8 H2 H2adρd1+ vvder tively.Inwhatfollowswewillassu⊙mef0=1×10−3.Thisisan
F.L.Scho¨ier&H.Olofsson:Modelsofcircumstellarmolecularradiolineemission 7
average of the f :s estimated by Olofsson et al. (1993b) for
0
thissample of opticallybrightcarbonstars. The scatter in the
estimated f :s is about 40%. We note here that a somewhat
0
moresophisticatedphotodissociationmodelwasdevelopedby
Doty&Leung(1998)inwhichtheyincludescatteringbydust.
FortheCSEofCWLeotheyderiveaCOenvelopesizewhich
is 30% smaller than what is obtained using the Mamon et al.
model.Itishowevernotclearbyhowmuchtheenvelopesize
changesforanobjectwithasignificantlylowermasslossrate,
andhenceweusetheresultsofMamonetal.here.
In our models we include both a central source of radia-
tionandthecosmicmicrowavebackgroundradiationat2.7K.
Thecentralradiationemanatesfromthestar,andwasestimated
froma fittoits spectralenergydistribution(SED),usuallyby
assuming two blackbodies. This method is described in Ker-
schbaum (1999). A fit to the SED gives the two blackbody
temperatures, T∗ and Td, and the relative luminosities of the
twoblackbodies,Ld/L∗.Anydustpresentaroundthestarwill
absorb parts of the stellar light and re-emitit at longer wave-
lenghts.Thus,ofthetwoblackbodiesused,onerepresentsthe
Fig.2. Comparison between the distances derived from the
stellar contribution and one represents the dust. However, it
should be noted that, e.g., the stellar temperature T∗ derived lpaexreiosd(-Dlumin).oTsihtyeirrerleagtuiolanr(vDarPia−bLle)sawnhdetrheethHeilpupmairncoossitpyawraals-
in this manner is generally lower than the true temperature HIP
assumed to equal4000L are indicatedby open circles. The
of the star (Kerschbaum 1999). In any case, the two black-
dashedlineshowsthe1:1⊙correlation.
bodies used give a good description of the radiation that the
CSE is subjected to. The temperatures and luminosities used
in the modelling are presented in Table 3. Only in the cases
whereLd/L∗>0.1thedustcomponentwasretained.Theinner 4. Modelresults
boundary of the CSE, r, was set to reside outside the radius
i
of the central blackbody(s), but never lower than 1 1014cm
×
( 3R ), i.e., generallybeyondboththe sonic pointanddust
c∼onden⊙sationradius.
The distances, presented in Table 3, were estimated using
one of the following methods: the observed Hipparcos paral-
lax, a period-luminosity relation (Groenewegen & Whitelock
1996), or an assumed bolometric luminosity. In the two for-
mercasestheluminositieswereestimatedusingapparentbolo-
metric magnitudes and the distances. In the rare cases when
both the distance obtained from Hipparcos and the period-
luminosity relation result in extremely high or low luminosi-
ties,avalueof4000L wasadoptedastheluminosityandthe
distancewasestimated⊙usingthisvalue.Fortheirregularvari-
ables with no Hipparcos data we also assumed a luminosity
of 4000L . For a statistical study of a large sample of stars
thesedista⊙nceestimatesareadequate,althoughthedistancees-
timateforanindividualstarhasalargeuncertainty.Thereisno
apparent systematic difference between the distances derived
from the period-luminosity relation and the Hipparcos paral-
laxes,Fig.2.ThedistancesinOlofssonetal.(1993a)werees-
timatedfromanadoptedabsoluteK magnitude.Thedistances
presented here are systematically lower by, on the average, a
factorof1.4thanthoseusedinOlofssonetal.
Fig.3. The h-parameter derived from the radiative transfer
Thiswasasummaryoftheassumptionsusedin”thestan- analysis plotted against the adopted luminosity of the central
dard model”. In what follows, tests will be made to see how star. Note that the data points at L=4000L represent two
sensitivethemodelistothevariousassumptions. starseach. ⊙
8 F.L.Scho¨ier&H.Olofsson:Modelsofcircumstellarmolecularradiolineemission
Table3.InputparametersandCOmodellingresultsusingthestandardmodel(seetextfordetails)
Source Var.type P D L T∗ Td6 Ld/L6∗ M˙ ve rp h
[days] [pc] [L⊙] [K] [K] [M⊙yr−1] [kms−1] [cm]
VXAnd SRa 369 5602 5500 2000 4.0×10−8 11.5 1.4×1016 0.24
HVCas M 527 9702 7900 1800 900 0.54 9.0×10−7 18.5 6.1×1016 0.54
IRC+60041 6703 4000 1300 500 0.13 3.0×10−6 28.0 1.0×1017 0.24
ZPsc SRb 144 3201 3100 2600 2.5×10−8 3.5 1.4×1016 0.24
RFor M 389 6102 5800 1500 700 0.52 1.3×10−6 16.5 8.0×1016 0.7
TWHor SRb 158 4001 6700 2600 9.0×10−8 5.5 2.5×1016 0.5
V384Per M 535 5602 8100 1900 900 10 3.5×10−6 15.0 1.4×1017 0.4
V466Per SR 4503 4000 2200 1.3×10−7 9.0 2.6×1016 0.24
STCam SRb 300 3302 4400 1600 9.0×10−8 9.0 2.1×1016 0.24
TTTau SRb 167 3602 2400 2400 7.0×10−8 5.0 2.2×1016 0.24
RLep M 467 2501 4000 1900 800 0.14 7.0×10−7 18.0 5.3×1016 0.2
WOri SRb 212 2201 2600 2200 7.0×10−8 11.0 1.8×1016 0.3
SAur SR 590 8202 8900 1600 700 0.32 2.2×10−6 25.5 8.9×1016 0.54
WPic Lb 4903 4000 2000 3.0×10−7 16.0 3.5×1016 0.4
YTau SRb 242 3102 3500 2400 4.0×10−7 11.0 4.5×1016 0.1
TUGem SRb 230 3302 3400 2400 2.5×10−7 11.5 3.4×1016 0.24
BLOri Lb 3603 4000 2700 1.1×10−7 9.0 2.4×1016 0.24
UUAur SRb 234 2602 6900 2500 3.5×10−7 11.0 4.2×1016 0.1
NPPup Lb 4201 3500 2700 6.5×10−8 9.5 1.8×1016 0.24
CLMon M 497 7702 7500 2000 1100 1.4 2.2×10−6 25.0 8.9×1016 0.54
RYMon SRa 456 4561 3000 2000 3.5×10−7 11.0 4.2×1016 0.24
WCMa Lb 4503 4000 2500 3.0×10−7 10.5 3.9×1016 0.24
RVol M 454 7302 6800 1300 800 0.7 1.8×10−6 18.0 9.0×1016 1.0
XCnc SRb 195 2802 2800 2200 1.0×10−7 7.0 2.4×1016 0.1
CWLeo M 630 1202 9600 510 1.5×10−5 14.5 3.7×1017 1.0
YHya SRb 303 3501 4200 2600 1.9×10−7 9.0 3.2×1016 0.24
XVel SR 140 3102 2800 2200 1.8×10−7 10.0 3.0×1016 0.24
SZCar SRb 126 5803 4000 2400 2.0×10−6 14.0 1.1×1017 0.2
RWLMi SRa 640 4402 9700 1300 510 6.7 6.0×10−6 17.0 1.9×1017 1.4
XZVel 5303 4000 1900 6.0×10−7 14.0 5.2×1016 0.24
CZHya M 442 9602 6600 1800 9.0×10−7 12.0 7.0×1016 0.54
CCS2792 4803 4000 2000 6.5×10−7 17.0 5.2×1016 0.24
UHya SRb 450 1601 2500 2400 1.4×10−7 7.0 2.9×1016 0.24
VYUMa Lb 3303 4000 2700 7.0×10−8 6.0 2.1×1016 0.24
SSVir SRa 364 5402 5400 1800 2.0×10−7 12.5 3.0×1016 0.24
YCVn SRb 157 2201 4400 2200 1.5×10−7 8.5 2.9×1016 0.25
RYDra SRb: 200 4901 10000 2500 3.0×10−7 10.0 4.0×1016 1.25
HD121658 5303 4000 2400 1.0×10−7 6.5 2.5×1016 0.24
HD124268 3903 4000 2300 1.0×10−7 11.0 2.2×1016 0.24
XTrA Lb 4603 4000 2200 1.3×10−7 8.0 2.7×1016 0.4
VCrB M 358 6302 5300 1900 740 0.15 6.0×10−7 7.5 6.8×1016 0.2
TWOph SRb 185 2801 2700 2000 5.0×10−8 7.5 1.6×1016 0.24
TDra M 422 6102 6300 1600 650 0.28 1.2×10−6 13.5 8.0×1016 0.54
TLyr Lb 3403 4000 2000 7.0×10−8 11.5 1.8×1016 0.55
VAql SRb 353 3701 6500 2100 3.0×10−7 8.5 4.2×1016 0.2
V1942Sgr Lb 4303 4000 2600 1.6×10−7 10.0 2.8×1016 0.24
UXDra SRa: 168 3103 4000 2600 1.6×10−7 4.0 4.0×1016 0.24
AQSgr SRb 200 4203 4000 2700 2.5×10−7 10.0 3.6×1016 0.24
RTCap SRb 393 4502 5900 2200 1.0×10−7 8.0 2.3×1016 0.24
UCyg M 463 7102 6900 2200 9.0×10−7 13.0 6.8×1016 0.54
VCyg M 421 3702 6200 1500 860 0.84 1.2×10−6 11.5 8.5×1016 1.2
RVAqr M 454 6702 6800 1300 620 0.46 2.5×10−6 16.0 1.1×1017 0.5
TInd SRb 320 5701 8800 2600 9.0×10−8 6.0 2.4×1016 0.54
YPav SRb 233 3602 4100 2400 1.6×10−7 8.0 3.0×1016 0.24
V1426Cyg M 470 7802 7100 1200 580 0.5 1.0×10−5 14.0 2.9×1017 0.3
SCep M 487 3402 7300 1400 1.5×10−6 22.0 7.5×1016 0.4
F.L.Scho¨ier&H.Olofsson:Modelsofcircumstellarmolecularradiolineemission 9
Table3.continued.
Source Var.type P D L T∗ Td6 Ld/L6∗ M˙ ve rp h
[days] [pc] [L⊙] [K] [K] [M⊙yr−1] [kms−1] [cm]
V460Cyg SRb 180 2302 2600 2800 1.8×10−7 10.0 3.0×1016 0.24
RVCyg SRb 263 3102 3400 2100 4.5×10−7 13.5 4.5×1016 0.24
PQCep M 3902 4000 1700 840 0.13 1.4×10−6 19.5 7.6×1016 0.24
LPAnd M 620 6302 9400 1100 610 6.6 1.5×10−5 14.0 4.0×1017 0.7
WZCas SRb 186 2902 2700 2500 6.5×10−9 2.5 7.4×1015 0.24
1 Hipparcos;2 Period-luminosityrelation(Groenewegen&Whitelock1996);3 L=4000L⊙ assumed;4 Assumedh-parameter(seetextfor
details);5 J-typestar(onlyincluding12COcooling);6 InthecaseswhenLd/L∗<0.1thedustblackbodycomponentwasnotretainedanda
singleblackbodyrepresentingthestellarcomponentadequatelydescribestheSED.InthecaseofCWLeoasingledustblackbodyisusedto
representtheSED.
4.1. Thefittingstrategy luminositysourcesisunfortunate,sincethesearegenerallythe
sourceswherethederivedmasslossratesareparticularlysen-
With the assumptions made in the standard model there re-
sitive to the adopted value of h. For the majority of objects,
mains two principal free parameters, the mass loss rate (M˙ )
whereareliableestimateoftheh-parameterisnotpossible,we
and the h-parameter. These two parameters were allowed to
haveadopteda valueofh=0.2forthe lowluminosityobjects
varysimultaneously,M˙ instepsof 10%andhinsomewhat
∼ (below 6000L ) and h=0.5 for the high luminosity objects
largersteps,untilthemodelwiththesmallestdeviationsfrom
(above6000L⊙).
the observed intensities was found. The quality of a particu-
Theh-para⊙meterisrelatedtothedust-to-gasmassratio,Ψ
lar modelwith respect to the observationalconstraintscan be
(seeEq.7).Ifweassumethatthepropertiesofadustgrainare
quantifiedusingthechi-squarestatisticdefinedas
equaltothoseusedtofitthelineemissionfromCWLeo,and
N [I I )]2 thattheyarethesameforallstars,anh-parameterof0.2means
χ2 = mod,i− obs,i , (12) that Ψ=2 10−3. Groenewegen et al. (1998b) have modelled
i=1 σi2 the dust e×mission towards a large sample of carbon stars and
X
where I is the total integrated line intensity, σ is the uncer- find a value of Ψ which is fairly constant at 2.5 10−3 for
i ×
taintyinobservationi,andthesummationisdoneoverallin- stars with luminosities up to about 7900L , and which in-
dependent observations N. The errors in the observed inten- creasesdrasticallywithluminosityupto0.0⊙1andhigher.This
sitiesaregenerallydominatedbythecalibationuncertaintyof is in good agreement with our results and lends further sup-
20%. In some cases the line profiles were used to discrimi- porttoourdistinctionbetweenlow-andhigh-luminositystars
∼nate between models. For each new M˙ assigned, a consistent asregardsthevalueoftheh-parameter.Furthermore,Hiriart&
envelopesize(r )wascalculatedbasedupontheresultsofMa- Kwan (2000) derive, for 17 of our sample stars, on the aver-
p
monetal.(1988). age Ψ 7 10−4. The main reason for this discrepancy is the
∼ ×
It is found that the intensity ratios between the different difference in the adopted dust parameters. In fact, it can be
lines are sensitive to various parameters, and hence can be shownthatforh=0.2wegetessentiallythesameheatingterm
used to constrain them (Sec. 4.3). Therefore, in order to ac- (cf. Eq. 6) in the energy balance equation as Hiriart & Kwan
curately determine h, and ultimately M˙ , multi-transition ob- (2000).
servationsareneeded.Observedradialbrightnessprofilespro-
videadditionalimportantinformation.Foralimitednumberof
4.3. Themasslossrates
thesourcesinoursamplethereareenoughobservationalcon-
straints that a reliable h-parameter may be estimated. These Wehavemanagedtomodelreasonablywell61ofthe69sam-
sourceswerefirstmodelled,seeTable3. ple sources using our standard model and fitting strategy de-
finedabove.Thereducedχ2forthesemodelsisestimatedfrom
4.2. Theh-parameter χ2
χ2 = min , (13)
red N p
The derived h-parameters, as a function of the adopted lumi- −
nosity of the central source, are shown in Fig. 3. A division where χ2 is obtained from Eq. 12 for the best fit model,
min
between low luminosity objects and those with higher lumi- and p is the number of adjustable parameters(one or two) in
nosities is evident. For luminosities lower than 6000L the themodel.Typically,χ2 1 3assumingacalibrationuncer-
medianvalue of the estimated h-parameteris 0.2(based⊙on 9 tainty of 20%. The derrievde∼d m−ass loss rates and h-parameters
sources),whileforthehigherluminositiesitis0.5(12sources) arepresentedinTable3,wherealsothevelocitiesbywhichthe
(the J-type stars, i.e., stars with a highcontentof 13CO, were CSEsexpand,v ,andtheirspatialextents,r ,aregiven.
e p
notincludedin these estimatessince13CO line coolingis not The derived mass loss rates presented in Table 3 span
treated in the standard model). The large scatter for the high more than three orders of magnitude, 6.5 10−9M yr−1 to
× ⊙
10 F.L.Scho¨ier&H.Olofsson:Modelsofcircumstellarmolecularradiolineemission
Table4.COmodellingresultscomparedtosingledishobservations.
Source Tel. Trans. Iobs Imod Ref. Source Tel. Trans. Iobs Imod Ref.
[Kkms−1] [Kkms−1] [Kkms−1] [Kkms−1]
VXAnd OSO 1−0 <0.8 0.1 2 UUAur OSO 1−0 7.9 8.2 2
IRAM 1−0 <1.4 0.2 2 IRAM 1−0 18.8 16.9 2
IRAM 2−1 2.4 2.4 2 JCMT 2−1 16.8 14.8 4
HVCas OSO 1−0 <2.1 1.9 2 IRAM 2−1 39.0 46.2 2
IRAM 1−0 5.6 4.1 2 NPPup SEST 1−0 <0.5 0.3 2
IRAM 2−1 11.9 14.5 2 SEST 2−1 1.2 1.2 2
IRC+60041 IRAM 1−0 IS 4.7 2 CLMon SEST 1−0 3.2 3.3 2
IRAM 2−1 17.3 17.3 2 SEST 2−1 10.4 9.5 2
ZPsc OSO 1−0 1.0 0.7 2 IRAM 2−1 34.3 38.1 2
IRAM 1−0 2.1 1.6 2 RYMon IRAM 1−0 6.8 5.4 2
IRAM 2−1 4.6 6.0 2 IRAM 2−1 11.3 14.5 2
RFor SEST 1−0 4.8 4.9 2 WCMa SEST 1−0 1.3 1.3 2
SEST 2−1 11.0 14.5 2 SEST 2−1 4.6 3.9 2
JCMT 2−1 21.0 17.3 4 IRAM 2−1 11.7 16.0 2
SEST 3−2 18.0 19.9 1 RVol SEST 1−0 4.9 5.1 2
JCMT 3−2 27.4 25.6 4 SEST 2−1 15.3 14.7 2
TWHor SEST 1−0 1.0 0.9 2 SEST 3−2 21.0 22.2 1
SEST 2−1 3.3 3.8 2 XCnc NRAO 1−0 0.7 0.7 1
SEST 3−2 7.2 6.1 1 SEST 1−0 1.5 1.1 2
V384Per NRAO 1−0 7.8 10.1 1 OSO 1−0 1.7 2.0 2
OSO 1−0 25.5 25.1 2 SEST 2−1 3.2 2.9 2
IRAM 1−0 52.7 48.4 2 IRAM 2−1 11.1 11.8 2
JCMT 2−1 37.3 35.2 4 CWLeo NRAO 1−0 170.8 257.1 1
IRAM 2−1 83.6 102.0 2 SEST 1−0 288.1 305.3 2
JCMT 3−2 44.5 42.5 4 OSO 1−0 422.0 391.7 2
V466Per IRAM 1−0 3.6 2.5 2 SEST 2−1 487.3 580.5 2
IRAM 2−1 6.2 8.6 2 JCMT 2−1 731.8 632.2 4
STCam OSO 1−0 2.0 2.0 2 IRAM 2−1 1057.7 1116.1 2
JCMT 2−1 3.4 4.4 4 SEST 3−2 854.8 774.0 1
IRAM 2−1 15.2 14.8 2 JCMT 3−2 1066.3 883.7 4
TTTau IRAM 1−0 2.6 2.7 2 JCMT 4−3 1227.8 1052.0 4
IRAM 2−1 4.0 8.1 2 YHya SEST 1−0 1.6 1.6 2
RLep SEST 1−0 6.2 6.7 2 IRAM 2−1 18.7 19.4 2
IRAM 1−0 31.7 24.3 2 XVel SEST 1−0 1.4 1.5 2
SEST 2−1 18.1 17.4 2 SEST 2−1 4.3 4.4 2
IRAM 2−1 56.4 64.2 2 SZCar SEST 1−0 2.8 2.7 2
SEST 3−2 12.5 21.6 2 SEST 2−1 7.8 5.9 2
JCMT 3−2 28.1 27.9 4 SEST 3−2 5.9 6.2 1
WOri SEST 1−0 1.2 1.3 2 RWLMi NRAO 1−0 36.4 37.0 1
OSO 1−0 2.7 2.4 2 SEST 1−0 54.6 51.9 2
IRAM 1−0 5.0 5.1 2 OSO 1−0 87.0 83.8 2
SEST 2−1 4.9 4.3 2 SEST 2−1 105.4 128.4 2
IRAM 2−1 19.0 16.9 2 JCMT 2−1 163.2 147.4 4
SEST 3−2 4.8 5.4 1 JCMT 3−2 245.3 208.6 4
SAur OSO 1−0 6.7 5.5 2 JCMT 4−3 243.1 224.3 4
IRAM 1−0 10.9 11.9 2 XZVel SEST 1−0 1.8 1.4 2
IRAM 2−1 15.8 36.8 2 SEST 2−1 3.5 4.1 2
WPic SEST 1−0 0.9 0.9 2 CZHya SEST 1−0 1.5 1.5 2
SEST 2−1 2.6 3.1 2 SEST 2−1 4.2 4.5 2
SEST 3−2 6.1 4.5 1 CCS2792 SEST 1−0 1.9 1.8 2
YTau SEST 1−0 3.2 3.0 2 SEST 2−1 4.1 4.7 2
OSO 1−0 6.3 5.3 2 UHya SEST 1−0 5.4 5.4 2
IRAM 1−0 15.5 11.0 2 SEST 2−1 13.8 14.1 1
SEST 2−1 5.8 6.1 2 JCMT 2−1 20.2 16.6 4
IRAM 2−1 19.4 24.1 2 IRAM 2−1 48.8 48.7 4
TUGem OSO 1−0 3.4 3.4 2 VYUMa OSO 1−0 1.4 1.4 2
IRAM 1−0 6.5 21.1 2 IRAM 2−1 4.3 11.0 2
BLOri OSO 1−0 IS 1.2 2 SSVir OSO 1−0 <1.2 1.1 2
IRAM 1−0 IS 2.6 2 IRAM 1−0 7.9 8.5 2
IRAM 2−1 9.8 9.7 2