sign in sign up
<<
Home , Bipolar outflow

19 94ApJS. . .92. .189B globally averaged,uniformdensity distributionofgasexpand- ing-shell model.Initssimplest form,thismodelassumes(1)a able starstypicallyareinterpreted inthecontextofanexpand- © 1994.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. The AstrophysicalJournalSupplementSeries,92:189-218,1994May 1 Data pertainingtocircumstellar outflowsoflong-periodvari- WorkperformedatNRLundercontract numberN00014-89-C-2398. -1 -761 -1 -1 _1 Subject headings:ISM:jetsandoutflows—masersstars: variables:other(long-period,semiregular) of increasingoutflowvelocitywithmasershellradius. Itisproposedthattheoutflowweaklybipolar. problems ofinterpretation,thewell-knowncaseVXSgr isreexamined.Thedatadonotsupportasimplemodel direction fromthestar.Fromangulardistributionsand velocityranges,thereisgoodevidencethatatleast outflow atp^10-15AU;somegasprobablyisfullyaccelerated atradiilessthan10AU.Toillustratethe some parcelsofgasareacceleratedtotheterminaloutflow velocityatp>20AUandthatthereisacomponentof and achieveuniqueinterpretation.Aplausiblemodelisclumps orfilamentsdistributedatradiiwhichvarywith within afewkilometerspersecondofF,anddoublypeakedcurves,wherethemaximumradiusoccursat sphericity, andanisotropiesinthevelocityfield,butitis difficult todisentangletheeffectsofthesephenomena Comparison ofOHandH0distributionsshowspointssimilarityforseveralstars.Plotsshellradiusasa appears tooccuroveraradialintervallessthanorequalone-thirdoftheshellradius.Theangulardistributions by aboutafactor<2duringthelightcycle,withstatisticallylargestradius((p)^25AU)at0.2<00.4.The function ofradialvelocityexhibittwoformscurves:singlypeakedcurves,wheretheradiusincreasesrapidly strongest componentsnearVareconfinednortheastandsouthwestofthestar,suggestiveaxialsymmetry. position. Forthreestars(RTVir,UHer,UXCyg),thin,asymmetricloopstructuresarefound.Ori, at agivenepochfrequentlyareelongatedandsometimesstronglyasymmetricrelativetotheestimatedstellar are likelytoreflectchangesinthepumpingconditions. observed atcomparablephasesofdifferentlightcurves,indicatingthatshort-termchanges(lessthanafewyears) morphology oftheangulardistributioncanchangestronglywith0,butsimilarmorphologiesaresometimes observations ofdifferentstarsandonrepeatedVLAspecificstars,theshellsizemayvarytypically larger velocityrange(V±9kms)at0.2<00.4,whentheintegratedHluminosityislargest.Basedon light-curve phase0,butthereisahigherprobabilityofdetectingmultiple(particularlyblueshifted)featuresand dent effects.Forthissampleofstars(ratesmasslossfromabout10toMyr),theaverageprofile yr) changesbutalsomayexhibitstabilityoffeaturesovertimescalesupto15yrafterallowanceforphase-depen- shape showsstrongestemissiongenerallywithin±2kmsofthestellarvelocityF,regardless cumstellar H0profilesandangulardistributions.Profilestructurescanexhibitdramatic,short-term(lessthan1 typically <0''15—animprovementoverpreviouscomparisonsbyafactorofabout2. with twodistinctmapmaximaatagivenvelocityoversignificantintervals. velocities symmetrictobutdisplacedfromV.Thelattertypeofcurvealsotendsbedouble-valued(X-shaped) . Comparisonofaccurateopticalpositionsthestarswithestimatesfrommasersyieldstotaldifferences (±35 mJybeam),andhour-anglecoverageisthebestyetobtainedforH0masersfromasignificantsampleof reported. Thecombinationofangularresolution(^70mas),spectral(0.3kms),rmssensitivity 0 2 0 02 0 0 2 0 2 There areindicationsofsomecombinationnonuniformitiesinthedensitydistribution,deviationsfrom The shellradiirangefrom>5toabout50AU,andtheregionofmaximalH0intensityatagivenepoch The homogeneous,high-qualitydatasetprovidesseveralnewinsightsintothetime-varyingstructureofcir- Results ofVLAobservations22GHzH0masersassociatedwith15Miraandsemiregularvariablesare 2 2 © American Astronomical Society • Provided by theNASA Astrophysics Data System VLA POSITIONSANDDISTRIBUTIONSOFH0MASERSASSOCIATEDWITH15MIRA 2 1. INTRODUCTION Remote SensingDivision,NavalResearchLaboratory,Washington,DC20375 SEA, Inc.,1401McCormickDrive,Landover,MD20785 Received 1993May27;acceptedOctober11 AND SEMIREGULARVARIABLES 1 K. J.Johnston P. F.Bowers ABSTRACT AND 189 the stellarradialvelocity.This modelpredictscircularringsof formed withthepeaksoccurring atK=L±,whereFis not extremelythin(Bowers1993a), adoublypeakedprofileis velocity Visconstantthroughout theshellandifis smaller thantheline-of-sight velocitygradient.Iftheoutflow For masers,amplificationoccursaslongthefinewidth is ing in(2)asphericalshellwith(3)anisotropicvelocityfield. 0p p 19 94ApJS. . .92. .189B 1 -5-1 tions orprofilesseverelylimit attemptstomodelindividual ables indicateshellradiiofabout 10-50AU(Laneetal.1987; tions canbequitecomplex.Modelsofaspherical(axiallysym- by thestandardmodel.Fromangulardistributionsthere sources. Collison &Fix1992),butasymmetries intheangulardistribu- data (Bowersetal.1989;Bowers 1991;Chapmanetal. metric) outflowscanaccountforsomeaspectsofthemaser component atradiiassmallabout50AU,butthedistribu- are indicationsthatradialexpansionisadominantkinematic profile shapesusuallytendtohavetwowell-separatedgroups de Vegt1989;Chapman,Cohen,&Saikia1991).The OH outflow, buttheydonotconformtotheclassicshapepredicted of features,asexpectedifthereisasignificantcomponent of radii rangingfromabout50to500AU(Bowers,Johnston, & bal, Gómez-González,&Planesas1989;Lucasetal.1992). which grainsarenotentirelyformedandthewindhas show arangeofdeviationsfromthestandardoutflowmodel at & Alcolea1991;Lucasetal.1992;SahaiBieging1993). appear tobeapproximatelycircularmorphologies(Bujarrabal (Planesas, Kenney,&Bachiller1990),butinothercasesthere For caseswherethethermaldistributionsarespatiallyre- the terminaloutflowvelocity(Bowers1993b).Thebrightness that theexpansionvelocityderivedfromhalf-velocitysepa- solved, thereissometimesevidenceforasymmetricoutflow attained itsterminalvelocity(Bujarrabaletal.1986;Bujarra- complex structureorkinematics(Bowers1990;Margulisetal. 0) SiOandCOhavebeenfoundfromanumberofMiravari- dard model.Evidenceforasymmetriesalsoisseenfrominfra- distributions arealwaysclumpy,however,andsometimes proximation tothelarge(p>1000AU)1612MHzOHmaser ables andhavebeeninterpretedtoarisefromoutflowswith complexities. SharplypeakedorGaussian-likeprofilesof(u= envelope structurestoabout1000-2000AUalsoshowmany yr“ ),theapproximationsofstandardoutflowmodelgen- ingly demonstratedbythedata(Efstathiou&Rowan-Robin- distributions oftenmustbefairlystronginordertoconvinc- Haniff etal.1992)andinthedustshells(e.g.,Johnson&Jones are knowntooccurclosethestars(Karovskaetal.1991; erally arelessadequate.Distortionsfromsphericalsymmetry son 1990;Collison&Fix1991;Bowers1991). cal effortsdemonstratethatasymmetriesindustorcoldgas aspherical dustdistributions(Jones&Gehrz1990).Theoreti- red polarizationmeasurements,suggestingclumpyand/or asymmetric relativetothestellarposition(Bowers&Johnston ration ofthepeaks(orhalf-profilewidth)isagoodmeasure essentially distributedinalldirectionsrelativetothestarand rates ofmasslossAf>10Myr,indicatingthattheOHis shells ofasymptoticgiantbranch(AGB)OH/IRstarswith velocity Vwhichisrelatedtotheshellradius6atby emission centeredaboutthestarwithanangularradius6at 1990) orfromanextendedinnerenvelope(p^100AU)in 190 1991) .Observationsofgaseousdistributionswhichtracethe 1990) ,indicatingdeparturesfromtheassumptionsofstan- 0 S0 -715 Interferometric observations of H0masersfromMiravari- Observations ofOHmasersfromMiravariablessimilarly The standardmodelusuallyprovidesagood,first-orderap- For classicalMiravariables(10Myr“

and 1990, but the angular distributions of the H20 masers are quite different (§ 6.1; Bowers et al. 1993). To obtain further insight into the statistical shape of the H20 profiles for Mira variables, selected averages of the profiles in U Lyn § 3 are presented in Figure 27. From a closely sampled (30 day) monitoring program of H20 masers associated with 22 Mira variables, Benson et al. (1993) find that the integrated 10 Jy emission is usually strongest near 0 = 0.3. Figures 21a and 21b respectively display the average profiles for the seven Mira vari- ables in this program which were observed at 0 ¥= 0.2-0.4 and the five Mira variables which were observed at 0 = 0.2-0.4 (Table 4). Prior to averaging, the area under each profile has been normalized to unity so that the average of the normalized profiles reflects the probability of emission as a function of >- H velocity. Both profiles show that the strongest emission gener- (/) Z LU Q X D ft j\ E = 1984.30 \Aj\ - = °-46 A 200 Jy

E = 1985.51 4» = 0.48

E = 1988.95 > <|) = 0.34 H (O z LU 100 Jy E = 1984.3 (|) = 0.03 -20 -10 0 Û X 3 V|_sr s1)

Fig. 25.—H20 profiles for U Lyn at three epochs (E) and light curve phases (0). The upper two profiles are taken from Engels et al. ( 1988), and the lower profile is taken from Fig. 7 of this paper. û clear, however, that such changes can occur for Mira variables as well as for OH/IR stars. Another case of interest is U Her (Fig. 26). The develop- ment of the blueshifted features between 1983.8 and 1984.3 probably reflects changes in the pumping conditions. The structures of the lower two profiles observed near light maxi- mum display more features over a larger velocity range than does that of the upper profile observed near light minimum. Inspection of published profiles indicates that the spectral fea- -1 tures at about -17.5 ± 0.5 and -14.5 ± 0.5 km s have been -20 -10 0 repeatedly detected from at least 1976 (Cox & Parker 1979; 1 Berulis et al. 1983) to 1990 (Menten & Melnick 1991), indi- VLSR (km s ) cating possible long-term (up to 15 yr) stability after allowance Fig. 26.—H20 profiles for U Her at three epochs {E) and light curve for phase-dependent changes. It is unclear whether this result phases ( 0 ). The upper profile is taken from Lane et al. ( 1987 ), the middle implies stability of the shell structure. For example, the profile profile is taken from Engels et al. ( 1988), and the lower profile is taken structures for W Hya are similar near light maxima in 1985 from Fig. 17 of this paper.

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1 1 V - V0 (km s- ) V - V0 (km s’ )

Fig. 27.—Selected averages of H20 maser profiles from § 3 of this paper, showing the probability of emission as a function of velocity for (û) the seven Mira variables observed at 0 ^ 0.2-0.4, (b) the five Mira variables observed at 0.2 < ^ 0.4, ( c) all 12 Mira variables, and ( d) the three semiregular variables.

ally occurs within about ±2 km s-1 of the stellar velocity. Both 6.3. Other Parameters profiles also are asymmetric, with systematically stronger emission at blueshifted velocities. Relative to V0, the velocity Figures 28-31 respectively display plots of the shell radii range increases from about -9 to +4 km s-1 in Figure 27a to measured at epoch 1988.95 as a function of light-curve phase, 1 ±9 km s“ in Figure 27b. Both profiles seem to be roughly the maximum velocity range Fmax of the H20 emission relative similar to the average for all 12 Mira variables (Fig. 27c). to F0, the integrated H20 luminosity, and the rate of mass loss. However, at = 0.2-0.4 there is a somewhat higher probabil- Figure 28 shows that the shell radii for Mira variables ity of detecting multiple ( >3 ) well-separated peaks and a larger observed near 0 = 0.2-0.4 are all greater than 15 AU ((p) == velocity range at redshifted velocities. The average profile for 26.6 ± 11.9 AU ), whereas radii determined at other phases are the three semiregulars is shown in Figure 27 d and is similar to usually (but not always) less than 15 AU ((p) = 12.1 ± 6.2 that in Figure 27b, except that there is no longer a clear ten- AU ). If the shell structures are generally asymmetric relative to dency for the strongest emission to be close to F0; instead, the stellar position, some of the estimated shell radii may be there is a roughly equal probability that the strongest feature too small (Table 4), so the average variation in shell size as a -1 can occur anywhere between F0 - 9 and F0 + 2 km s . The function of phase typically may be somewhat less than a factor trend in all these profiles for stronger emission to occur at of 2, consistent with repeated measurements of shell sizes for blueshifted rather than redshifted velocities may indicate that individual stars (§6.1). The threefold variation of shell size for there is amplification of photospheric emission by masers R Aql (§ 6.1 ) may thus be an extreme example. In any case, along the line of sight to the star in the near side of the shells these results give a crude measure of the radial thickness of the (e.g., § 3.4). Another contributing factor may be blocking by envelope over which H20 masers may occur at some phase of the of components at extreme redshifted veloci- the light cycle (also see § 7.3). ties, but this is probably secondary because of significant A plot of shell radius as a function of Fmax measured at angular offsets (greater than the stellar diameter) between the epoch 1988.95 is shown in Figure 29. Stars with larger values -1 extreme blue- and redshifted components (see R Crt, RT Vir, of Fmax (greater than 8 km s ) tend to have larger shell radii U Her). (p > 15 AU). Values of Fmax for U Her, U Orí, U Lyn, RT

© American Astronomical Society • Provided by the NASA Astrophysics Data System 19 94ApJS. . .92. .189B -1 42-1 _1 in thisstudy. range Vrelativetothestellarvelocity atepoch1988.95forthe15stars epoch 1988.95forthe12Miravariables. value ofL-foroCetmayberelatedtoitsbinarynature Figures 21aand21b(§6.2). (Lépine &PaesdeBarros1977;BowersHagen1984).IfS stars. ThesemiregularsandallfiveMiravariablesobservedat m¡iX The tendencyisconsistentwiththedifferentprofileshapesin km s)thanthoseobservedatotherphases((F=5.4± There isperhapsaweaktendencyforMiravariablesobserved 0 æ0.3havelargevaluesofL(>5X10s).Thesmall near 0^0.3tohavelargervaluesofV(F}=1.6±2.7 have attainedtheterminaloutflowvelocityforthesestars. and §3above).ItislikelythatsomeoftheH0components values derivedforOH,(p=0)SiO,orCO(Bowers1992 Vir, andRCrtarecomparabletoorslightlylargerthan 3.0 kms),buttherearenotableexceptions(e.g.,RRAql). mt 210 max int max 2 Fig. 29.—H0shellradiusasa function ofthemaximumvelocity Fig. 28.—H0shellradiusasafunctionofthelight-curvephase()at Figure 30displaysaplotoftheshellradiusasfunction 2 2 oc Cet RR Aql 4>=0.2 -0.4 4*0.2 -0.4 Semiregular R Tau• I R Cnc © T Y Cas _J *"s Crt 8 • RAql 6 810 Vmax ^ WXSer © • ZPup _L U Lyn © ©UXCyg © UHer _L T RT Vir + UOri 12 BOWERS &JOHNSTON R Crt + 14 al. (1987). 15 starsinthisstudy.Thesolidline showstherelationderivedbyLaneet distances tothesemiregularsarecomparablethosefor loss, wherethesolidlineisleast-squaresrelationdeter- ters, butthereisnonethelesssignificantscatterfortherangeof with comparabledistancesandmass-lossratestomini- mined byLaneetal.(1987).Thedataareconsistentwiththat of itsbinarynature),thetrendisnotapparent. with shellradius,butifonlyoCetisexcluded(possiblybecause Crt isarbitrarilyexcluded,thereatrendforLtoincrease ity forthe15starsinthisstudy. values forMiravariablesinthegroup1categories.Iftrue as pincreases(and0approaches0.3),averagevaluesof any particularparameter(Figs.29-31).Table5indicatesthat D <0.66kpcinanattempttoobtainahomogeneoussample ( Fax)andLarecomparabletoorslightlylargerthanthe mize anyselectioneffectonthedistance-dependentparame- AU). OnlyMiravariablesareconsideredforwhich0.20kpc< is nearlyidenticaltogroupsIp(p>15AU)and2p< ables observednearornot0=0.3.Thesample in Table5.Groups10and20respectivelyrepresentMiravari- pend onthephaseoflightcycleorshellradiusisgiven relation, butthereistoomuchscattertoconfirmit. F andLaremarginallylarger.Forthesemiregulars, int mint maxint Fig. 31.—H0shellradiusasafunction oftheratemasslossfor Figure 31showstheradiusasafunctionofratemass Fig. 30.—H0shellradiusasafunctionoftheintegratedHluminos- 2 An attempttosummarizehowthevariousparametersde- 2 < oc 5 3 < + Semiregular © <>=0.2-0.4 • (>#0.2-0.4 "T 421 L^tilO#-) R Aql WX Ser©4m+ m U Lyn Y Cas/ZPup €\j)RR Aqlpet RT Vlr. U Her® © SCrt UXCyg Vol. 92 19 94ApJS. . .92. .189B No. 1,1994H0MASERSASSOCIATEDWITH15LONG-PERIODVARIABLES211 between componentsatF.Inothercases, the loopofUXCyg.Inspectionmapsin§3reveals a components isreasonablywell determinedforsuchcases.The the 0(F)curvesrelativetoF indicatessymmetryintheveloc- the angulardistributions.Despitestronglyasymmetric angular separationoftheblue-andredshiftedcomponents in asymmetrically locatednearoneendoftheloop.ForUHer asymmetric ontheplaneofsky.Forthreestars(RTVir,U phase (Fig.24).Relativetotheestimatedstellarpositionde- this section. ten 1990).Propertiesofthedistributionsaresummarizedin tion ofthestarrelativetoH0masersisfairlycertainat possibility thattheposition of thestarrelativetomaser ity field(i.e.,organizedvelocity structure)andsupportsthe distributions (e.g.,RTVir;UX Cyg),thesymmetryofsome Ori, althoughstrongestcomponentsnearFarepreferentially are detectedatvelocitiesnearF(WHya;IKTau;possibly U ringlike structuresroughlycenteredaboutthestellarposition number ofotherexampleswherethereisanangularseparation shifted components,butnotexclusivelyso.Thereisaclear and RTVir,theloopsappeartoconsistprimarilyofblue- Her, UXCyg),thinloopstructuresareevident,withthestar shifted components,theH0distributionscanbestrongly rived fromthemeanpositionofextremeblue-andred- Cyg). Theshapecanbestronglydependentonthelight-curve a ratio^2:1(Table4)andsometimesmuchmore(e.g.,UX epoch oftheobservations.TheseincludeUOri,RCrt,RTVir, northeast andsouthwestoftheinferredstellarposition[Fig. 5 ]). (Bowers etal.1993);IKTauat1983(Lane1987)and U Her,andUXCyg,allatepoch1989(§3);RTVir1985 and Mforthesemiregularsalsoarecomparabletovalues 2 selected samplesofMiravariables(i.e.,(T>)^400pc),thenp for thegroup1Miravariables. 0 1985 (Bowersetal.1993);andWHyaat1990(Reid&Men- 0 2 0 0 2 7. CHARACTERISTICSOFTHEANGULARDISTRIBUTIONS There areaboutahalf-dozenAGBstarsforwhichtheposi- The 0(F)curvesprovideapartialbutusefuldescription of The overallshapesofthedistributionsoftenareelongatedby © American Astronomical Society • Provided by theNASA Astrophysics Data System 2p 410.6±3.44.6±0.83.5±5.72.72.00.380.22 20 513.3±6.85.8±2.73.1±5.02.51.80.350.20 SRs 312.2±5.19.5±3.723.98.21.1±0.30.26±0.14 and RTVir. 10 323.8±6.37.4±3.412.9±9.03.00.90.45±0.17 Ip 423.7±5.28.2±3.210.1±9.32.7±0.90.39±0.18 a!427 a Group Number(AU)(kms)(10^Myr(kpc) 0 Group:10:0=0.2-0.4;20:=£Ip:p>15AU;2p: (V^)(Tint)(D) TABLE 5 ble valuesofF(H0)andforothermolecularspecies given locusofpointsina0(F) plotovervelocityintervalssignif- brightness distributionatgivenFexhibitsmaximatwo dif- the maximum0(RTVirat1989;UHer;RCrt),i.e., the the doublypeakedtype,whereredshiftedcounterpart to tainty ofthestellarposition.The0(F)curveforRCrtmay be with F^typicallyhave015AU),components icantly largerthanthevelocity widthofamaserspot,thepeak- curves appeartobedistinctlydouble-valuedatvelocities near emission at0^150masismissing.Thedoublypeaked0(F) redshifted velocitiesmayreflectshellasymmetriesoruncer- doubly peakedtype;unequalvaluesof0attheblue- and displaced fromF•The0(F)curveforUHerappearstobe the bles theshapefoundforothersinglypeakedcurves,i.e.,thereis component ofoutflowatradii^10-15AU. Tau, ULyn,RCnc,Aql,RRAql;see§3),indicatinga suggest thatsomecomponentshaveattainedtheterminalout- maximum angularradiusatanyvelocity.Thisandcompara- nonetheless indicateevidenceforacomponentofoutflowin of equation(1),butlargervalues0nearthestellarvelocity shaped withtheintersectionatF^. ferent angularradiirelativetothestar.Fortwostars(RT Vir a rapidincreaseof0withinfewkilometerspersecondF. to O.20forcomponentsneartheextremeblue-andred- second ofF,thoughnotnecessarilyat(e.g.,YCas,oCet,R of thedistributiontobelargestwithinafewkilometersper masers isuncertain,therestillatendencyfortheangularsize other species,andwherethepositionofstarrelativeto resolved, whereF(H0)maybesignificantlylessthanfor smaller shellswheretheoveralldistributionisonlymarginally kilometers persecondofF.Withintheerrors,0=atFœ flow velocity(e.g.,UOri,RCrt,RTVir,Her,IKTau).For shifted velocitiesandrapidlyincreasesto0withinjustafew singly peakedcurves(RTVirat1985;UXCyg),0^0.1 [Fig. 15]andUHer19]),thecurvesareroughly X- 0(F) curvescandeviatesignificantlyfromtheparabolicform max2 1985), 0^atvelocitiessymmetrictobutsignificantly F. Theblueshiftedportionofthe0(F)curveforUOriresem- max 2 max 0 0 0 max 0 max2 0max max max max 0 For severalstarsthereisextremely smallscatterof0abouta For thedoublypeakedcurves(RTVirat1989;IKTau The curvesmaybesinglypeakedordoublypeaked.Forthe 7.3. ShellThickness 19 94ApJS. . .92. .189B -1 preferred directionsofmasslossoveratimescaleabout these resultsaretentative.Ifconfirmed,theycouldindicate blueshifted componentofeachspecies(FæV—10kms)is within theerrors.ForUOri[p(OH)^3p(H0],extreme ingly, thelarge-scaleangularseparationofblue-andredshifted located nearthecenterofoveralldistribution,whileemis- metries seenintheH0distributionsofRAqlandRR Aql not apparentintheH0distributions.Finally,certainasym- components seenintheOHdistributionsofthesetwostars is tion, anisotropicvelocityfield,andsaturatedemission. the calculationsofCooke&Elitzur(1985),butcomparisonis sion nearVislocatedinstructureswith6~0.Interest- H0 componentsatselectedvelocitiesarevirtuallyidentical 2p(H0)], forwhichtherelativepositionsofsomeOHand difficult becausetheyassumeauniform,sphericaldistribu- sity distribution,sphericalshell, isotropicvelocityfield),in- similarity insomecases.ThebestexampleisUHer[p(OH)^ [p(OH) ^10p(HO)]mayalsobepresentintheOH, but ginal usefulnessiftheemissiondistributionisstronglynonuni- regions ofmaximalintensityaresmallerthanissuggestedby but nonethelessprovidesomeobservationalconstraintfor potential H0emission(§6.3). probably thecase(Barvainis&Deguchi1989;ReidMenten intensity appearstooccuroveraradialintervalAp<0.3p^ loop structuresprojectedontotheplaneofsky.IfAp=p- to-peak scatterbeinglessthantherelativepositionalerrors 212 100 yr. form (e.g.,clumps)oraspherical.Theradialextentsofthe models. Theconceptofradialshellthicknessmaybemar- measure oftheradialintervaloverwhichemissionispresent, may belargerif,forexample,theemissionisunsaturated,as smaller thanthevalueof~2typicallyderivedfromOHmaser (50 mas/150mas;Reid&Menten1990).Thecorresponding ratio isfoundforUOri(30mas/100mas;Fig.6)andWHya of Ap/p=M/(d)<(20mas)/(70mas).Acomparable and p istheradialshellthicknessandcharacteristicradius (i.e., <20mas).Thesmallscatteralsoisapparentinthethin shells (cf.Bowers1991).ThustheregionofmaximalH0 “apparent” ratiooftheoutertoinnershellradiiispjp<1.4, Data forUHer,UXCyg,andRTVirindicateatypicalvalue of theemission[heredefinedas(p+p)/2],then 5-10 AU.Thetotalshellthicknessatagivenlight-curvephase 0 2 2 2 0max 2 2 2 1990). Integratedoverallphases,p/^2fortheregionof 2 c 0 cs tc 2 t 0/ 0z Comparison ofH0andOHdistributionsshowspoints With theassumptionsof standard model(uniformden- These estimatesoftheshellthicknessrepresentonlyacrude 2 8.1. OutflowVelocityasaFunction ofRadius © American Astronomical Society • Provided by theNASA Astrophysics Data System Pol Pi=(2+Ap/p)1(2-Ap/p.(6) c Ap =2p(1—p-/p)/+pi(5) cz0 7.4. H0versusOH 2 8. DISCUSSION BOWERS &JOHNSTON 1 -1_ _1 -1 £ to theterminaloutflowvelocity atradiiassmallthatofthe consistent withdatawhichindicate dustformationwithina though globalprofileaveragesobtainedforSiOmasers(Fig. 6 virtually equivalentforanumberofstarsandroughlyequal to models whichpredictacceleration essentiallytotheterminal few stellarradii(e.g.,Danchi etal.1992)andwithdynamical (t> =1)SiOmasers(p<10 AU forMiravariables).Thisis cluded thatsomeparcelsofgasmaybeacceleratedessentially clearly revealcomparablevaluesofF.Bowers(1992)con- quate torevealthefullextentoflow-levelemissionwhich oc- ues ofFforthe(i;=1)SiO,H0,andOHmasers are of Nyman&Olofsson1986)andH0masers(Fig.21c) curs atthemoreextremevelocities(e.g.,UOri;Fig.4¿z), al- quality COdata(Bowers1992;Bowersetal.1993;§3above). Previous dataforSiOandH0masersgenerallywereinade- tions, whereitisshownthatmanyaspectsofthedatacouldbe theoretical biases.Thesearediscussedinthefollowingsubsec- 80% oftheterminaloutflowvelocityinferredfromhigh- H0 masershells.Considerationofthewell-knowncaseVX equally wellexplainedwithoutanyradialaccelerationinthe masers], itisimportanttoexplorepossibleobservationaland 0(F) curves,comparablevaluesofFforSiO,H0,andOH are indicationsofsuchdepartures[asymmetries,complex bly isonlyalowerlimitbecauseeaveragedoverlargeradial centrally peakedprofilesuchasthatinFigure27c,butitproba- the radialaccelerationsuchthatF^/=(p7p)%acrudeesti- would indicateanincreaseofVfromabout5kms"atp^10 than attheextremevelocities(§7.2);2anapparentincrease Sgr isprovidedasaspecificexample. model canradicallychangetheinterpretation.Becausethere served averages. man &Cohen1985;Bowers1991)agreeroughlywiththeob- p'/p ^1.4(§7.3),thene>2,andcalculatedprofiles(Chap- in thecriticalregionwheregasisbeingaccelerated.Ifwetake interval, whereasitmaydecreaserapidlytozeroaspincreases mate ofefromFigure29is(10kms/5)=(20AU/ eration intheshell. in thestandardmodelifthereisrapidanduniformradialaccel- terminal velocity.Fromthepresentdataset,possiblesupport velocities intherangeF±5kmscanberoughlyproduced shape inFigure27c,forwhichthecentrallypeakedat AU to10kmsatp>20AU;and(3)theaverageprofile preacceleration regioninsidethecircumstellaroutflow, of FwiththeshellradiusMiravariables(Fig.29),which outflow inmanyH0shellsbasedonlargershellsizesnearF for suchaninterpretationis(1)evidenceacomponentof OH masersarelocatedinregionswherethegashasattainedits H0 masersarelocatedintheacceleratingportion,and cally hasbeenthoughtthattheSiOmasersarelocatedina mann 1977;Chapman&Cohen1986;Bowers1990).Ittypi- velocity Vwithlargershellradius(e.g.,Dickinson&Klein- in SiO,H0,andOHmaserprofilesimplyalargeroutflow creasingly largervelocityrangesforthestrongerfeaturesseen max max2 2 2 2 max2 p 0 max 20 2 p 2 10 AU),ore=1.0.Thisvalueistoosmalltoproducea Observations withhighspectralsensitivityindicatethatval- Assuming thestandardmodelandletting€beameasureof Small departuresfromtheassumptionsofstandard 8.1.1. ObservationalBias Vol. 92 19 94ApJS. . .92. .189B No. 1,1994H0MASERSASSOCIATEDWITH the shellthicknessvary(Fig.1ofBowers1993a). centrally peakedprofiles)ifonlythekinetictemperature and produce awiderangeofprofileshapesforgivenF(including velocity (Bowers1991).Evenforthestandardcaseofacon- quite differentprofileshapescanbeformed,dependingon lar profileshapescanbeproducedbycompletelydifferent the projectedpolaraxisin planeofthesky.Radius-velocity where x'isdirectedfromthe star totheEarthandz'represents stant isotropicoutflowinasphericalshell,itispossible to such fundamentalparametersastheDopplerwidthoroutflow dal shellswithavarietyofvelocityfieldsindicatethat(1)simi- cal modelsofmaseremissiondistributedthroughoutellipsoi- torial planeistilted45°tothelineofsightandouter di- velocity fields,and(2)foragivengeometry/velocityfield, of theunderlyinggasdistributionsorvelocityfields.Kinemati- tions inparticular(i.e.,FWHMDopplerwidth>10%of the standardmodelmayinfluenceprofileshapesandangular wing emission.Forexample,itappearsthatFfortheblue- because emissionneartheprofileedgesgenerallytendstobe and theannularregiondepicts thegeometryinjc'-z'plane, Calculations havebeenperformed inathree-dimensionalgrid, distributions indicatethatforwarm,complexgasconfigura- shifted velocityrangesinFigure27isessentiallyindependent dent oftheradius;strongeremissiondetectednearH0 mension oftheequatorialplaneistwicethatpolaraxis. radial shellthicknessinanoblatespheroidforwhichtheequa- excited) uniformlythroughoutanannularregionofconstant cold. Forbothmodelsthegasisassumedtobedistributed( and understand howsimpledeparturesfromtheassumptionsof of 0,aswouldbethecaseifVisindependentpand maximum mayincreasetheprobabilityofdetectinglow-level stronger when0.2<00.4thanitisnot(compareFigs. radii ofMiravariables,theresultmaybeaffectedbyvariability velocity rangesofthevibrationallyexcited1.6/¿mCOand ginning insidethedustcondensationradius(e.g.,Tsuji1988). While Figure29showsanincreaseofVwiththeH0shell other speciesforRAql(Fig.20). ever, italsoisconsistentwithaturbulence-drivenoutflowbe- shape canchange,dependingonwhetherthegasiswarm or a given(aspherical)geometryandvelocityfieldtheprofile Bowers 1991)orsimplyasrandommotions.Recenteffortsto rapid acceleration(cf.Chapman&Cohen1985;Fig.13of peaks. Centrallypeakedprofilescommonlyareinterpretedas peaked, Vistakentobeone-halfthevelocityseparationof small numberofstarsincludedineachprofileaverage. 21a and21b).ThetruevalueofFcouldthusbeindepen- Support forthelatterpossibilitymaybevirtuallyidentical outflow velocitywithin5-10stellarradii(Bowen1988).How- [ 0(F)]curvesandintensity[/(F)] curvesareshownforarela- model. Withthismodel,iftheprofileisessentiallydoubly are criticallydependentontheassumptionsinstandard (§6.2). Thisconclusionistentative,however,becauseofthe 2 extreme blueshiftedfeaturesareamplifyingstellaremission p max ^max) theshapesofmaserprofilescanbepoorindicators 2 max max2 p max ? Another possibleobservationalbiasisprofilevariability. Figure 32showstwooutflowmodelswhichillustratehowfor Estimates oftheoutflowvelocitybasedonprofileshape © American Astronomical Society • Provided by theNASA Astrophysics Data System 8.1.2. TheoreticalBias _1 -1 -1 -1 _1- _1 15 LONG-PERIODVARIABLES213 the shell,ifoutflowisentirely radial,andifthereisno be interpretedtoindicatetwoshellswithdifferentexpansion separation ofthestrongerpeaks orbyfittingequation(1)to (1991) indicatethatvalues of Fderivedfromthevelocity acceleration, Figure32and themodelprofilesofBowers context ofthestandardmodel. peaks wouldbesystematicallytoosmallifinterpretedin the rial plane.Thus,ifthereisanisotropicoutflowinthewarmer level wingemissionproducedathighlatitudesfromtheequato- bipolar) outflow.The/(F)curveforthewarmshellshows the but theresultwouldnotaccountforitsvariationwithdirection maser shells,valuesofFderivedfromthevelocities the inner peaksdominatingtheprofilewithavelocityseparation velocities, whereasitmaysimplyindicateanisotropic(weakly peaks. Withthestandardoutflowmodelsuchaprofilewould and wouldunderestimatethemaximumoutflowvelocity. the warmandcoldshells,0(F)curvesarenarrowerin much lessthanthetotalvelocityrangeindicatedby low- fitted tothe0(F)curvesobtainanapproximatevalueofF, departures fromtheexpectationsofstandardoutflow than isasphericityoftheshell(Bowers1991).Forexample, velocities isnotpositionallycoincident.Equation(1)couldbe model II,andemissionattheextremeblue-redshifted model aremoreapparentinIIthanI.Forboth for influencingtheprofilestructureandangulardistribution the polaraxisasinequatorialplane.Fvariesfrom5.7to locity isconstantinagivendirectionbutvariesinverse to thatinmodelIbutthevelocityfieldnowconsistsofamoder- to alesserextent,theshellthickness. proportion totheoutershellradius,beingtwiceaslargealong ate (weaklybipolar),anisotropicoutflow;i.e.,theoutflowve- is asensitivefunctionoftheDopplerwidth,ellipticity,and, the lineofsighttostarifDopplerwidthissufficiently large. Theratioofthestrengthsinnertoouterpeaks emission neartheequatorialplaneiscomparabletothatalong warm-shell case,aquadruplypeakedprofileisevident.The inner peaksformbecausethevelocity-coherentpathlengthfor distribution atvelocitiesnearFwouldbenecessarytodeter- dicted inthestandardoutflowmodel.Mapsofangular times themaximumatanyvelocity.Detailsofmodeling where theminimumvelocity-coherentpathlengthis0.25 mine theshellgeometry(e.g.,Fig.2ofBowers1991).For Thus modelIillustratestheinfluenceofanasphericalshell and 15kmsforthecold-shellcase(typicalofOH/IRstars). procedure arediscussedbyBowers(1991). effects ofaminimumcolumndensityforsaturatedemission, width (0.35kms)moreappropriateforOHmasersfrom 0(F) and/(F)curvesareessentiallyidenticaltothosepre- structure withanisotropicoutflow.Forthecold-shellcase, OH/IR stars.Dashedcurvesinthe/(F)profilesillustrate tively largeDopplerwidth(FWHM=2.0kms),asmightbe appropriate forSiOorH0masers,andasmallDoppler p p p 17.1 kmsforF=15(coldshell). 11.4 kmsforF=10(warmshell)andfrom8.6to p 10 kmsforthewarm-shellcase(typicalofMiravariables) 0 2 max max In summary,evenifgasisuniformly distributedthroughout The /(F)profileinmodelIIforthecoldshellmayhavefour Anisotropy inthevelocityfieldisgenerallymoreimportant Model IIshowsthecasewhereshellgeometryisidentical In modelI,Fisconstantinalldirectionsandtakentobe p 19 94ApJS. . .92. .189B _1- been proposedbyNetzer(1989) andbyPijpers(1990).An- which showedincreasinglylarger velocityrangesfortheSiO, giant VXSgr.ChapmanScCohen(1986)published data acceleration toaverylargedistance fromthestar(greaterthan H0, andOHmaserssuggested thatthereiscontinued increasing outflowvelocitywithradiusisthesuper- tive totheequatorialplane)canalsocontributethiseffect gas distributionforwhichthedensityvarieswithlatituderela- is anisotropic.Thiseffect(i.e.,inferredV<)more the 6(V)curvecanbesignificantlysmallerthanmaximal 100 stellarradii).Modelstoaccount fortheaccelerationhave (§§ 8.1.3,8.2). cool shells.Anonuniformgasdistribution(e.g.,clumping ora easily producedinwarmermasershellsbutalsocanoccur in outflow velocityiftheshellisasphericalorfield velocity fieldisweaklybipolarwithanoutflowwhichinverselyproportionaltotheoutershellradius. the linelabeledE.P.Solidanddashedcontoursinannulirespectivelyindicatenegativepositiveradialvelocities;contourintervalsare 0.1V,where sky andisorientedalongtheprojectedpolaraxis.Theequatorialplaneedge-ontoofpage,itsorientationlinesight isindicatedby in alldirections.Theannularregionshowsthegeometryx'-z'plane,wherex'isdirectedalonglineofsighttoEarthandz'lies theplaneof distributed andexcitedthroughoutanannularregionwhichhastheshapeofoblatespheroidwithaxialratio2:1;outflowvelocity Fisconstant 2 V isthemaximumradialvelocity(10kmsforAV=2;15AK0.35).FormodelIIgeometry same,butthe pmax max p maxD 214 A frequentlycitedexampletosupportthecanonicalview of Fig. 32.—AsphericaloutflowmodelsshowingtheeffectofFWHMDopplerwidthAVon0(V)andI(V)curves.FormodelIgas isuniformly D © American Astronomical Society • Provided by theNASA Astrophysics Data System 8.1.3. VXSgr OBLATE (2=1) V/o =Constant MODEL I BOWERS &JOHNSTON _1 _1 to theoutflowvelocity(18.6 km s)derivedbyChapman& Cohen fortheOH(1612MHz) shell. absolute valuesofVareequivalent within1kmsforthe Cohen byfittingequation(1)tothe1612MHzdata.Table 6 indicates twicetheoutflowvelocityderivedbyChapman & inferred byChapman&Cohen(1986).ForOHthearrow SiO, H0,andOHmain-line masersandapproximatelyequal more recentlypublishedprofiles.Itisevidentthatthelargest measured fromtheprofilesofChapman&Cohenand summarizes thevelocityrangesforvariousmolecularspecies because ofadecreasingmass-lossrate. SiO andH0thehorizontalarrowsindicatevelocityranges of themasershells.ThisisshownexplicitlyinFigure33. For ple modelofincreasingoutflowvelocitywithradii velocity rangesthantheearlierdataanddonotsupportasim- ( 1993),isthattheoutflowvelocityhasdecreasedwithtime other interpretation,proposedrecentlybyNetzer&Elitzur max 2 2 It isbeyondthescopeofthis paper tocomputeamodelfor More sensitiveSiO(v=l)andH0profilesreveallarger 2 OBLATE (2=1) MODEL n yp «/>;' Vol. 92 19 94ApJS. . .92. .189B -1 the 1612MHzOHdataand thethermalSiOandCOdata and thelargervelocityrange indicated bythefullwidthof the valueofVderivedbyfittingequation(1)toOH data (1612 MHz)emission(Fig.33)andthediscrepancybetween account fortheroughlyquadruplypeakedprofile OH ity oftheH0andOHshells(Chapman&Cohen1986).Mod- erate anisotropyofthevelocityfield(i.e.,aweak,bipolar out- partially apply.Therearefairlygoodindicationsforaspheric- the envelopestructureofVXSgr,buttherearereasons to dashed lineindicatesthestellarvelocityof5.3kmsdeterminedbyChap- flow) alsomaybeindicated.Suchavelocityfieldcould suspect thatamodelsimilartoIIinFigure32 may larger latituderangethanisthe casefortheSiO,H0,andOH man &Cohen.Thehorizontalarrowsaredescribedinthetext. (Table 6)mayindicatethatthis emissionisdistributedovera Bowers etal.(1993),andJewell1991)forVXSgr.Thevertical SiO maseremission,respectivelypublishedbyChapman&Cohen(1986), 1612 MHzprofileinFigure33. ThelargervaluesofVfor p 2 2 max No. 1,1994H0MASERSASSOCIATEDWITH 2 Fig. 33.—Profilesofthe1612MHzOH,22GHzH0,and43 2 © American Astronomical Society • Provided by theNASA Astrophysics Data System VX Sgr ho 2 _1 Bowers etal.1993;(4)Knapp 1989. mates; ismeasuredrelativeto V=5.3kms. CO -24to+36 +30.74 OH (1612)-16to+29+23.72 SiO (v=0)-19to+29-24.31 OH (1665/67)-11to+23+17.72 H0 -11.5to+20.5-16.83 SiO (v=1)-6to+23+17.71 tions arenotmerelytheresultofchaoticvelocityfieldsbut pumping conditions.Thisalonecanexplainthestatisticalten- lar abundance,line-of-sightvelocitycoherence,andrequisite the outflowwhichprovideacombinationofsufficientmolecu- clumping. Themasersprobablytraceonlyselectedportionsof tive tothestellarposition,timevariabilityofprofilesand distributions duetoasymmetricmasslossand/orstrong point tononuniformitiesinthegasand(byinference)dust to varywithbothdirectionandradius.Anindependentcon- to anunderestimateofthetotalvelocityrangeemission distributions (§6),limitedspectralsensitivitywhichcanlead to disentanglethesefactorsbasedontheavailabledataand density distribution,deviationsfromsphericity,andmodest suggest thatstrongasymmetriesoftheoverallangulardistribu- in thelargerH0shells[byvirtueofsymmetric6(V)curves] scale couldbeveryuseful. dismiss aprioriphenomenawhichmaycausethevelocityfield achieve uniquemodelsforspecificcases.Modelingiscompli- We concludethatsomecombinationofnonuniformitiesinthe what modificationtothestandardmodelmaybenecessary general propertiesofthedistributionsinanattempttoexplore the data.Inthissectionweconsiderpossibleexplanationsfor because ofitssimplicity,butitdoesnotadequatelydescribe straint suchasthedustdistributionoveracomparableangular (§8.1.1), and,becauseofthesmallshellradii,inabilityto cated bystrongasymmetryoftheemissiondistributionsrela- anisotropies inthevelocityfieldislikely,butitverydifficult and tostimulatefurtherobservationaltheoreticalefforts. tion inthemasershellsofVXSgrorMiravariables,but above discussionillustratesthataquantitativemeasureofany the knownOHsupergiants(Bowersetal.1989;Bowers such accelerationcanbedifficulttoobtain. (Nedoluha &Bowers1992)andmaybeapplicabletomostof lar outflow)hasbeenusedtoapproximatethestructureof 0 OH shellsassociatedwiththesupergiantIRC+10420 main-line masers.AmodelsimilartoII(i.e.,weakbipo- 2 2 1993b). Wedonotruleoutthepossibilityofradialaccelera- 15 LONG-PERIODVARIABLES215 References.—(1) Jewelletal.1991; (2)Chapman&Cohen1986;(3) Notes.—Parenthetical valuesofvelocity rangerepresentsmalleresti- Indications thatthevelocityfieldsarereasonablyorganized The rapidaccelerationmodeloutlinedin§8.1isappealing J Species (kms)*)Reference 8.2. StructureoftheH0Shells 2 Velocity RangesforVXSgr Velocity RangeV max (-7 to+18)(+12.7)2 (—1 to+11)(-6.3)2 TABLE 6 19 94ApJS. . .92. .189B pic, thentheaccelerationis nonuniform withsomegasfully accelerated atp=0.2-0.4 2 the ,ed.G.Wallerstein(SanFrancisco: ASP),417 cal Masers,ed.A.W.Clegg&G.E.Nedoluha(Berlin:Springer-Verlag), 271 367, L27 Soviet Astron.,27,179 1990, A&A,232,258 VLA observationsof22GHzH0distributionshavebeen 3. ForthelargerH0shells(radii>15AU),thereisoften 2. Anaverageprofileshapeisconstructedforthestarsin 1. Shellradiirangefromabout5to50AU.ForM^3X 2 2 © American Astronomical Society • Provided by theNASA Astrophysics Data System 9. CONCLUSION H0 MASERSASSOCIATEDWITH15LONG-PERIODVARIABLES 2 REFERENCES -1 .1993b,inSub-arcsecondRadioAstronomy,ed.R.J.Davis& R. S. .1993a,inAstrophysicalMasers,ed.A.W.Clegg&G.E.Nedoluha .1990,ApJ,354,676 constructive comments. within 0''15—aboutafactorof2betterthanpreviouscompari- referee foraprompt,carefulreadingofthemanuscriptand for positions forULynandSCrt.Wealsothankananonymous the standardoutflowmodel(uniformity,sphericity,isotropy) tures, butthereareindicationsthatnoneoftheassumptions Bowers, P.F.1992,ApJ,390,L27 sons. Furtherimprovementappearstobepossible. sitions inferredfromthemasersindicatesagreementtypically is strictlyvalidintheregionofH0masers. ently precludeauniquedescriptionofindividualshellstruc- tributed asymmetricallyinellipsoidalgeometriescouldex- tive totheinferredstellarposition,probablyindicatingthat emission distributionsgenerallyarestronglyasymmetricrela- the lightcycle,butthereareindicationsthatmorphology Bowers, P.F.,&Hagen,W.1984,ApJ,285,637 Bowers, P.F.,Claussen,M.J.,&Johnston,K.J.1993,AJ,105,284 ity, asymmetries,andlackofindependentconstraintspres- and high-velocitycomponents.TheH0distributionforUOri plain manyaspectsofthedata,includingshapes0(V) density distributionisnonuniform.Clumpsorfilamentsdis- a timeintervalofjustfewyearsorless.Atgivenepoch,the Bujarrabal, V.,Gómez-González, J., &Planesas,P.1989,A&A,219,256 Bujarrabal, V.,Alcolea,J.,&Planesas, P.1992,A&A,257,701 Bujarrabal, V.,&Alcolea,J.1991, A&A,251,536 Bowers, P.F.,Johnston,K.J.,&Spencer, J.H.1983,ApJ,274,733 Bowers, P.F.,Johnston,K.J.,&de Vegt,C.1989,ApJ,340,479 Bowers, P.F.,&Johnston,K.J.1988,ApJ,330,339 supports anaxiallysymmetricoutflowmodel.Timevariabil- curves, thinloopstructures,andangularseparationoflow- may beroughlysimilaratphaseswhencomparedover Bowers, P.F.,&Knapp,G.R.1988, ApJ,332,299 the supergiantVXSgrarereexamined,anditisshownthat available datadonotsupportasimplemodelofincreasing large distancesfromthestarsmaybebiasedbydatawithlow vious suggestionsthatthereisgradualaccelerationtovery ated atp