1987ApJ. . .316. .323H -1 (MMTO) operatedjointlybytheUniversity ofArizonaandtheSmithsonian form eitheraroundadense clumpofgasejectedintothe behind abowshock(Schwartz 1978).Thebowshockcould Institution. the emissionfromHHobjects arisefromthecoolingregion any plane-parallelmodel(Hartigan,Mundt,andStocke,1986). and Sii.Thisstructurecannotbeexplainedsatisfactorily by diameter? LineprofilesofHHobjectsinCepheusAand HH gan etal1986).Howcansuchlinewidthsbepresentin an object ofatmostafewEarthmassesthatisonly1500AU in 32 aredouble-peakedforthelowexcitationlinesofH,N n, objects canapproach500kmsforasingleknot(seeHarti- objects exhibitextraordinarylineprofiles.Linewidthsin HH single plane-parallelmodelfitstheobserveddata.Some HH nent low-excitationlineslikeSnandOi.Theresultisthat no lines ofhighlyionizedspecieslikeCivinadditiontopromi- line strengths.Themajorproblemisthepresenceofbright modeled theobservedemission-lineratiosfromHHobjects partially successfulinreproducingtheobservedUVandvisible using plane-parallelshocks.Theseattemptshaveonlybeen gas coolsbehindashock(seeSchwartz1983forreview). radiation fromtheseobjectsisthattheemissionlinesoccuras velocities (SchwartzandDopita1980)ofHHobjectsimply worth andHerbig1979;Jones1981)radial Several authors(e.g.,Dopita1978;Raymond1979)have supersonic motions,andthegeneralacceptedmodelfor sequence stars.Thelargepropermotions(Luyten1971;Cud- sources usuallylocatednearbipolarflowsfrompre-main- The AstrophysicalJournal,316:323-348,1987May1 © 1987.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. 1 One possibleresolutiontothesepuzzleswouldbehave ObservationsobtainedattheMultiple MirrorTelescopeObservatory Herbig-Haro (HH)objectsaresemistellaremission-line Subject headings:lineformation—profilesradiativetransfershockwaves formula thatcanbeusedtoestimatetheshockvelocityandboworientationfromasinglehigh- resolution observationofalow-excitationline. although oneobjectinparticularisbetterfittedwithashockedcloudletmodel.Wepresentsimpleanalytic Cepheus A.Ingeneral,analysisofmanybrightHHobjectsisconsistentwiththeinterstellarbulletmodel, can accountforthebulkofexistingobservations.Spectrallineprofilesexpectedfromstationarycloudlets model—a radiatingbowshockformedarounda“bullet”ofdensegasplowingintotheambientmedium— models. ThebowshockmodelsareusedtopredictthelineratiosandprofilesexpectedfromHHobjects, spectra, andthatsuchmodelsprovideanaturalexplanationforthespectraofHH32objectsin show thatforparticularbowshockorientationsdouble-peakedprofilesarepredictedinspatiallyunresolved and movingbulletsarediscussedforavarietyofshockvelocities,orientationangles,emissionlines.We and comparisonofthemodelwithfourdifferentregionscontainingHHobjectsindicatesthatasingleunifying © American Astronomical Society • Provided by the NASA Astrophysics Data System We haveconstructedbowshockmodelsofHHobjectsfromacollection43radiativeplanar I. INTRODUCTION 1 RADIATIVE BOWSHOCKMODELSOFHERBIG-HAROOBJECTS stars: pre-main-sequence Department ofPlanetarySciences,UniversityArizona Received 1986July17;acceptedOctober15 John RaymondandLeeHartmann Harvard-Smithsonian CenterforAstrophysics Patrick Hartigan ABSTRACT 323 AND 1 -1 shock velocities,andalsoto predict theemission-lineprofiles which sampleawiderangeofshockvelocities(20kms“ < models areconstructedfromasetof43planarshock used topredicttheemission-line ratiosexpectedforvarious models arepresentedin§III. In §IVthebowshockmodelsare bow shockmodelisdiscussed in§II,andtheplanarshock preshock densities,and ionizationconditions.The viewing thebowshockfromobliqueangles. from thecentralobstacle,producinglargelinewidthsa than thoseofHartmannandRaymond(1984).Thepresent small volume.Thedouble-peakedlineprofilesmightarisefrom agreement withobservations. velocity diagramsfrombowshocksandhavefoundfairlygood line ratiosthatagreedbetterwiththeobservationsthanplanar objects. Inaddition,abowshockwillsplattermaterialaway parallel modelstopredicttheobservedlineratiosfromHH line emission.Suchasenariocouldexplainthefailureofplane- shock models.Severalauthors(Choe,Böhm,andSolf1985; (1984) foundthatamodelbasedonapproximatingtheoblique (as inthe“shockedcloudlet”model;Schwartz1978).Thebow Raga andBöhm1985;1986)haveconstructedposition- shock modelswasabletoproducelargelinewidths,aswell as shock regionsofthebowbyaseriesplane-parallel reasoning couldbequitefruitful.HartmannandRaymond slowed, andthisperpendicularkineticenergyconvertedinto only thecomponentofmotionperpendiculartobowis shock geometryproducesamixtureofvelocitiesbecause sonic stellarwindimpinginguponaclumpofgasintheflow ambient cloud(asinthe“bullet”model;NormanandSilk V <400kms).Wealsoexplore avarietyofbowshapes, 1979 andTenorio-TagleRózyczka1984),orfromasuper- s In thisworkwepresentmorerefinedbowshockmodels Previous workonbowshocksindicatesthatthislineof 1987ApJ. . .316. .323H 5 4 jump conditions(byafactorof4forstrongshock).Thehot (Sandford andWhitaker1983;RózyczkaTenorio-Tagle needed tocomputeaccuratelineintensitiesandprofiles photoionization andtime-dependentionizationcalculations cooling included.Thisproblemhasbeensolved,butonlywith inside thevolumeboundedbybowshockwithradiative simplified radiativecoolingrates,andwithoutthedetailed velocity mustdecrease.Acompleteanalysiswouldrequire gas becomesdenserasitcools,andsincepvisconservedthe (>10 Kforshockvelocitiesofinterest)gasmustcoolto solving thetwo-dimensionalhydrodynamicflowproblem about 10Kbeforeopticallineradiationbecomesvisible.The perpendicular velocityVdiminishesaccordingtotheshock uous acrosstheshock,andimmediatelybehindshock The parallelcomponentV\\oftheincidentvelocityiscontin- the expectedemission-lineprofilesandratiosfromobject. models arediscussedin§III)weightedbytheareaof annulus. Co-additionoftheannulioverentirebowgives calculate thelineemissionbowshockisdividedinto200 from vertical.ThisangleisdeterminedonceabowshapeZ(R) to bethatfromaplane-parallelshockofvelocityV(theplanar annuli ofconstant£.Theemissionfromeachannulusistaken is chosen.Allmodelsassumeaxialsymmetry.Theobserver views thebowshockatananglefrombow’sapex.To at theshockvelocityVandentersbowshockanangle£ the bowshock,preshockmaterialisincidentfromleft know thepostshockvelocityVandangle6ofemittinggas to modelbowshocklineprofiles.Intheframeofreference 324 contexts (suchasgalacticjets). bow shockmodelswereconstructedwiththeintenttomodel existing high-resolutionspectraofHHobjects.Althoughthe in §V,wherewecomparethemodelpredictionswithnewand HH objects,theymightalsobeusefulinotherastrophysical are thenappliedtoindividualregionscontainingHHobjects a simpleanalyticformulawepresentin§IV.Thepredictions when thebowshockisviewedfromanarbitraryangle.Both the shockvelocityandboworientationcanbeestimatedfrom ± 1 s 2 Figure 1depictsthegeometryofabowshock.Onemust © American Astronomical Society • Provided by the NASA Astrophysics Data System a) GeometryandKinematics II. THEBOWSHOCKMODEL HARTIGAN, RAYMOND,ANDHARTMANN 4 peaks correspondingtotheextremeradialvelocitieson probability distributionisdouble-peaked(Fig.2),withthetwo where w=Vcos6,andsin00.The given radialvelocityP(V)isby velocity isproportionalto{d^ldV)^,sotheprobabilityofa an axiallysymmetricring,theprobabilitydistributionofradial the resonancelinesLya,CnA1335,andiv21550.Thus,for Emission fromHHobjectsisopticallythinexceptperhapsfor azimuthal anglei//isgivenby line intensityasobtainedfromtheplanarshockmodels. particle onanexpandingringofmaterial.Theprobabilitydis- lating aprobabilitydistributionfortheradialvelocityof tribution mustthenbeweightedbytheareaofringand from thermalmotionsoftheemittingionplusanyinstrumen- tal broadening. by smoothingthepointswithaGaussianwhosewidtharises profile consistsoftheco-additionaseriesexpandingrings of emittingmaterial(Fig.1).Thefinallineprofileiscalculated Taking Fytobeunchangedduringcoolingallowsthevelocity effect ofcooling(decreasebyanadditionalfactorabout10). (velocity decreasebyafactorof4forstrongshock)andthe 12 account boththejumpconditionsatshockinterface lines) andcalculatetheexpectedpostshockVtakinginto point). Guidedbytheplanarshockmodels,wechooseafixed r rdtV2 temperature forthelineofinterest(typically10Koptical narrow shellnexttothebow(see§IIIforadiscussionofthis models fortheemissionlines. the sizeofbowshock,sothatradiationoriginatesina the bowshockshapetomakefollowingapproximate V anddeflectionangle0tobecalculated.Hence,theline 1985a, b).Thereforeweuseexistingnumericalcalculationsof ± 2 We beginconstructionoftheoreticallineprofilesbycalcu- From Figure1,theradialvelocityofaparticleonringat We assumethecoolingdistancetobesmallcomparedwith V =F(cos6+sin0i¡/).(1) r2 21 P(V) =-lw-(Vr,(2) r2Wl b) LineProfiles Vol. 316 1987ApJ. . .316. .323H 21/ 1 we radial velocitiesareseen(atthefrontandbackofring). slit narrows,theexcludedregionwidensuntilonlyextreme tered atVcos0whichisnolongerseen(Fig.2).Asthe radial velocitiesofwidth2Vsin6[!—(D/d)]cen- to excludeemissionfronazimuthalanglesbetweeni¡jand positioned alongthez-axis.Theeffectofsuchaslitwillbe we wouldliketoknowhowthedistributionalterswhenaslitis expanding ringtobeincludedintheobservingaperture.Since and disthediameterofemissionring.Thus,thereaset sin “(D/d),Disthediameterofslitprojectedonsky, ti —i¡/,andalsobetweeni^tt+i/fwherei/^= spectroscopic observationsareusuallyobtainedthroughaslit, ring. Theprobabilitydistribution(2)assumestheentire (1986). Ragausedaninversemethodassumingpostshock ion- can writetheRagashapeas produced byasphericalobstacle. Normalizingthecoordinates ization equilibriumtodetermine thebowshapenearapex well asaclassofshapessimilartothatproposedbyRaga entire emissionfromthebowshock. No. 1,1987 R andZbytheobstacleradius R(z=[Z/R],r[R/R]) by DeYoungandAxford(1967)(hereaftertheDAshape) as bow shockmodels.Wehaveinvestigatedtheshapeproposed least. SincethisisontheorderofsizesmanyHHobjects, line profilesprobablyincludeemissionoverareas2"-3" at finite slit,andwehaveincludedthiscapabilityinourmodels. the lineprofilesreportedinthisworktypicallyinclude the seeing l"-2",andtelescopetrackingerrors~1",theobserved However, sincespectrographicslitwidthsaretypicallyl'/5, excluded whenthespectrographslitisnarrowerthanemittingring.TheparametersdandDareringdiameters,respectively. 2 2 c c 0 The bowshapeZ(R)isoneoftheinputparametersto The probabilityformalismeasilyaccountsfortheeffectsofa Fig. 2.—Probabilitydistributionofradialvelocitiesobservedfromtheexpandingringmaterialin1.Thebetweendashed linesare © American Astronomical Society • Provided by the NASA Astrophysics Data System Z r_21/ 3 [) 1+0.273(M—l)r c) BowShockShape 24 0.42r +0.136r RADIATIVE BOWSHOCKMODELSOFHHOBJECTS V2cos0cos4> 24 234 -1/2 24 constant R.Anytwoshapes withthesamevalueofßare therefore thesameformodeling purposes.Forexample,the the valueofadependsupon thechoiceofnormalization ß =ß.Hence,althoughisindependent ofthenormalization, where /cisaconstant.Then withz=Z/Rz/kandr importance tothefinalemissionlineprofile. that the incidentangle£isgivenbytan=(dzldr)-i2, so form z=Ar+Br.Tothisendweparameterizeaclassof R/R =r/kwefindz(r)(ka)r +(k(x)ßrsothatä=kotand exceeding £lieonthequarticcurveandhavelessrelative are ofequalmagnitudewhenr=a/?.Atthisvalue of r significance. Thequadraticandquartictermsinequation (4) With thisparameterizationßhasaclearlydefinedphysical bow shapesaccordingto we wouldliketobeableinvestigategeneralshapesofthe modified Ragashape(z=0.42r+0.136r)tomodelbow shape giveswaytothesteeperquarticshape.Incidentangles This criticalanglerepresentsthepointwherequadratic shock lineemission.Sincetheobstaclemaynotbespherical, at some(r,z)wherelineemissionmustcease.Wehaveusedthis axial solutionandachieveashapethatreachestheMachangle terminates. ceeds fromtheapex.Sinceshape(3)neverreaches angle £decreases,insteadofincreasinguniformlyasonepro- Z, sinceitdoesnotapproachtheMachangle,andincident Mach angle(V=Cssoundspeed),thebowshocknever Some difficultiesareencounteredwiththeshapeatlargeRand 0 0 cr=aLlß 0 c ± Suppose weweretonormalizetheshapeZ(R)byR=kR , If wedisregardthedenominatorterm,retainRaga’spar- 0 0 234 z(r) =ocr+a/?r,andßconstants.(4) -1/2 = tan(6/?).(5) 325 1987ApJ. . .316. .323H 24 -1 -1 2 4 is chosen,theabsolutefluxofHßasseenfromEarthcanbe values ofa.Inthemodels,Rischosentomakeangular bow shockflairsawayfromtheobstaclemoreforsmaller physical significanceisattachedtoR.Forinstance,if ratios. Theparameterahasphysicalsignificanceonlyif identical lineprofilesforeachemissionand always chosentobetheradiusofasphericalobstacle,then shapes z=O.Sr^+O.lrfandr0.8rproduce (Rózyczka andTenorio-Tagle1985b).Whiletransittimes importance ofthebowshockwings.Theyalsofindthatifone either the100or400kmsbowshocks,greatlyreducing calculated andcomparedwithobservedvalues. diameter oftheradiatingbowshockafewarcseconds,consis- medium attheendofcavityclearedbyoutflow,then exciting starstotheirpresentpositionsarehundredsofyears, inferred frompropermotionsofHHobjectknotsthe cloud islikelytobedisruptedbyRayleigh-Taylorinstabilities begins withasphericalobstacle,thecloudshockflattens the shapeofa200kmsbowshockmuchnarrowerthan hydrodynamics code.Theyfindthatradiativecoolingmakes shapes ofbowshocksusingatwo-dimensionalnumerical tent withtheobservedsizesofHHobjects.OnceavalueR obstacle andproducesaprogressivelymorebluntbowshock. times ofafewdecades(HerbigandJones1981).Ifweinterpret years fortypicalcloudparameters,andonthattimescalethe equation (6)inpowersofrnear=0wefinda0.25, where R=histhescaleheightfornormalization.Expanding polynomial, however.TheDAshapeisgivenby ness oftheassumptionasteadystatebowshockshape. However, suchshortlifetimescastsomedoubtonthecorrect- do notexpectsignificantflatteningordisruptionoftheclouds. the observedlifetimesofafewdecadesareappropriate,andwe similar velocityuntiltheyreachthehigh-densityambient this tomeanthattheseknotsmoveoutinalow-densityflowof some knotsareobservedtoturnonandfadeawaywithlife- Evolution intoamoreflattenedshaperequiresseveralhundred 326 (hereafter shapeA)reproducestheobservedlineprofilesfairly from theapex(r«n).Theshapez(r)=0.42r-I- l.Or like OinandCivascomparedtoH/?.Theproblemisthat the The oppositeisinfacttrue—DAmoreblunt-shaped than velocity shocksawayfromtheapexmorethanRagashape. ß =0.667,and<^82?3.Since£islargerforDAthan for thisshapethantheRagashape.Asothershapes, well andisusedextensivelyinthebowshockmodels.Shape A has acriticalangleof58?5,sothehighershockvelocities near DA shapecannotbeapproximatedbyaquarticpolynomial far Raga, givingrisetolargerfluxesinthehigh-excitation lines Raga (where4=77?3),wemightexpectDAtoemphasizelow the apexarerelativelymoreimportanttofinallineprofile the numericalintegrationterminateswhenshapeAreaches the Mach angle. 0 0 emission bydustintheobstacle. Wecanestimatetheamount 12 0 showed thatfory=5/3,the pressurePintheobstacleis of absorptionlikelytobepresent asfollows.Schwartz(1978) 0 c 0 Not allshapescanberepresentedaccuratelybyaquartic Rózyczka andTenorio-Tagle(1985a,b)havecomputedthe For simplicityweneglectabsorption offar-sidebowshock © American Astronomical Society • Provided by the NASA Astrophysics Data System d) TheObstacle HARTIGAN, RAYMOND,ANDHARTMANN _1 6-3 _1 21-2 5-3 -153 4-3 2 + -3 + 3 incident material,thenweshouldemployasetoffullypreion- expected tosurvivea100kmsshock.Hence,extinctiondue cially intheUV.ScabandShull(1983)showedthatabout50% (7), wefindrj<7x10cmandT<1K.Adopting large, andifthisradiationsucceedsinfullyionizingall the very hardUVradiationescapesneartheapexwhereV is were typicallycomputedevery20kmstofollowthevaria- velocity Vvariesmarkedlyacrossthebow.Ourplanarmodels detail byRaymond(1979)andCox(1985).A for theneutrallines.Theshockwilltakeabout600yrtotra- to postshockgrainscouldinprincipleaffectthelineprofiles, column densityfortheobstacleof2.2x10cm.Using tions infrontofabowshockarenoteasilydetermined.Some the linefluxesandratiosexpectedfromashock(seeCox and tion oflinefluxeswithshockvelocity. accurately modelbowshockemissionsincetheeffective grid ofshockmodelscloselyspacedinvelocityisneededto verse theobstacle,onorderofsoundcrossingtimefor although thecolumndensityofthismaterialshouldbeabout of silicategrainsandupto85%graphitecanbe obstacle couldhavesomeinfluenceonthelineprofiles,espe- A= 1.1alongthecenterofobstacle,suggestingthat an obstaclemassof160M,andamaximumhydrogen rio =10cm,and1500AUfortheobstaclediameteryields the ambientcloud’stemperature,about30K.Usingequation and Mannery1981).Thetemperatureoftheobstacleexceeds Raymond 1985).Unfortunately,thepreshockionizationcondi- should notaffectthelineprofilessignificantly,exceptperhaps this “cloudletshock”velocity.Thisisaveryweakand s, r}=10cmandrj100wefind6kmfor our calculations.FollowingSchwartz(1978),forV=200km obstacle. Spitzer’s (1978)relationbetweenNandE_=0.38,sothat find shocked wind,sowetakerj>3x10cm(Brugel,Böhm, number density(r})andtheshockvelocity(IQofwind.We temperature (T)intheobstacletermsofpreshock relation imposesaconstraintonthenumberdensity(rj)and related totheincidentrampressurebyP—0MrjV.This investigate thesetwocaseswe initiallycompiledasetoffully ionized attheapextoneutral neartheedgesofbow.To ized (H,He)planarmodelsinthebowshockcalculations. cm. Whenitbecameclear (see§IVb)thatequilibrium preionization shockmodelswith preshocknumberdensity100 preionized (H,He)shock modelsandasetofequilibrium preionization, wheretheionizedstateofpreshockgasis the preionization modelsfitthe data somewhatbetterthanthe such ascenario,thepreshockionizationcanvaryfrom fully same asthatinfrontofaplanarshockvelocityV.With On theotherhand,situationcouldresemble“equilibrium ” T =10K. 10 timeslessthanthemaximumcolumndensitythrough 0 ± ± v 0 0w w HBV 0 w 0 0 0ws ± o The ionizationstateofthepreshockgasgreatlyinfluences The planarshockmodelsusedinthisworkaredescribed We alsoignoretheshockpropagatingintocloudletin The numberdensityintheobstaclemustexceedthatof ^ T=2.1x10* 0 III. PLANARSHOCKMODELS - a) InputParameters 100 cm 200 kms cm K. (7) Vol. 316 198 7ApJ. . .316. .323H -1 4 + 1/2 -1 1 3 4 -3 1 -1 -1 realistic preshockionizationstateimpliesa15%increaseinthe described byCoxandRaymond(1985),wefindthatthismore ionized fractionpersistsevenforverysmalleffectiveshock No. 1,1987 absolute Hßflux,littlechangeinthe[Oin]/Hßratio,anda velocities inthebowshockwings.Basedonmethods entering a200kmsbowshockshowsthegastobe emission lines. (Cox 1972)wastakentobe1,avaluemoreappropriateforthe to determinetheimportanceofcollisionaldeexcitationfor fully chosentoadequatelysamplethetemperaturesnear10 K is animportantcoolant.Stepsizesintheprogramwerecare- correct valuefortheincidentfractionofHe,sincen2304 ionization problem.Itisespeciallyimportanttochoose the formed asomewhatmoredetailedanalysisofthepreshock each element.Thisinputradiationfieldwastakentobethe emission-line fluxeswasterminatedwhenthegastemperature (1985) areprincipallyduetothisparameter.Calculationof field wastakentobenegligible(0.1/iG)inallmodelsexcept effectively thanlow-velocityshocks.Thepreshockmagnetic model withabundancesofFeandSireducedby10togive continuum isroughlydoubled. 50% increasein[On]/H/?.Thestrengthofthetwophoton 50%-70% neutralforV=40-160kms,andasignificant Numerical difficultiesplaguethe shockmodelsforV>300km from theselinesareprobablyoverestimatedinthemodels. excitation infraredemission-linefluxesaccurately—the models, the20kms"resultscouldbesomewhatinaccurate. forbidden lines.Duetotheabsenceofmolecularcoolingin the continuum radiation.Undersamplingofthisregioncanlead to where thecoolinggasbecomesopticallythicktoLyman- values usingtheresultsofShullandMcKee(1979),whoper- Although theshockcodepredictspreshockionizationstate reached 10K. between fluxesreportedhereandthoseofCoxRaymond nonplanar geometryofabowshockthantheplanarvalue3. at 10Kforallmodels.AradiativetransferparameterR shock velocitysincehighershocksdestroygrainsmore shock flowhavedestroyedmostofthegrains(ScabandShull due todustcondensation.Thisdepletionissimilarwhat an indicationoftheeffectsdepletionrefractoryelements values, 12.0:10.93:8.52:7.96:8.82:8.12:7.52:7.62:7.20:6.90: preionized modelswithhigherpreshockdensity(1000cm) fully preionizedcase,wecompiledanothersetofequilibrium lines (OI,Ni,andCi).Moreover, shocksfasterthan200km predicted forlow-velocityshocks, especiallyfortheneutral Without molecularcoolingitisdifficulttopredictthe low- as muchafactorof2smallerfluxesforthebrightoptical of HandHe,fortheequilibriummodelswechosetofixthese output radiationfieldfromaplanarshockofsimilarvelocity. order tocalculatetheionizationstateofpreshockgasfor smaller valueofRmightbeappropriate.Differences For caseswherethecoolingdistanceapproachesR,aneven B100, whereB=10¿¿G.Thepreshocktemperaturewasfixed occurs aftersputteringandgrain-graincollisionsinthepost- 6.30:7.50:6.30 forallplanarmodelsexceptA100,a100kms~ 0:Ne:Mg:Si:S:Ar:Ca:Fe:Ni atthefollowing“cosmic” Innés, Giddings,andFalle1986). Effectsofthisinstabilityon s arethermallyunstable(McCray, Stein,andKafatos1975; s, andthesemodelfluxesare moreuncertainthanthefluxes 1983), althoughtheactualdepletionfactordependson ± s max max 0 An approximatecalculationoftheionizationstategas We fixedthelogarithmicabundanceratiosH:He:C:N: Planar shockmodelsrequireaninputradiationfieldin © American Astronomical Society • Provided by the NASA Astrophysics Data System RADIATIVE BOWSHOCKMODELSOFHHOBJECTS 4 -3 -1 -3 3 -3 forbidden lines(increasingthe ratiosof[Oi]/Hß,[Nn]/H/?, (lowering theIJV/Hßratiofor agivenUVline)andoptical cylindrical symmetryofHHobjectswillreducetheimportance remnants (Raymondetal.1981).Thelargelinewidthsand resonant linesofabundantions).Thisseverelyattenuatesthe interstellar gaswhentheisopticallythick(ascanoccurfor ing modelshockswithobservations.Resonancelinephotons model codesoccasionallydisagreebyasmuchafactorof3. etc.). Thisbehaviorapparently continuesatveryhighshock photons, andtheenergyisradiated awayintheBalmerlines increases. Recombininghydrogen at10Kabsorbsthese photons producedatthehigher postshocktemperaturesasV increases theUVlinesslowlydecreaseinintensityrelative to ion ofinterest,andthensuddenlybecomeprominant.As V enough tocollisionallydeexcitethelines.TheUVlines are ing shockvelocityuntilthepostshockdensitybecomeslarge increase monotonicallyinstrengthrelativetoHßwithincreas- cm to1000.RatiosofthepermittedUVlines Hß due tocollisionalquenchingwhenr¡isincreasedfrom 100 The [Oii]23727/H/?ratio,forexample,decreasesdramatically in theequilibriummodelsmakesalllinesbrighter(theHßflux cially fortheOiandnlines.Increasingpreshockdensity complete preionizationforshockvelocities>180kms. ized (Imodels)areshowninTable2.Equilibriummodelsreach cm (Emodels),andtheequilibriumpreionizationwith within agivensetofplanarshockmodels,ourresultsclarify ignores excitationfromthemetastablels2sSlevelofHei,so which occursinthehigh-temperatureregionjustbehind low temperaturesandvelocities,caseAforexcitation, interstellar Cnabsorptionlineisstrongenoughtoaffectthe of resonancelinescatteringwithintheemittingregion,but C ii21335andiv21550linesinthespectraofsupernova are scatteredwithintheemittinggasandinintervening predicted lineratiosof30%forthestronglines,though shop onNebulae(Péquinot1986)indicatedatypicalscatterin preshock conditionsandelementalabundancesattheWork- typically invisibleuntilVbecomeslargeenoughtocreate the are quiteinsensitivetorj. upon theimportanceofcollisionaldeexcitationforagiven line. scales linearlywithrj),butbydifferingamountsdepending preionized modelsatlowershockvelocities,however,espe- There aresignificantdifferencesbetweenequilibriumandfully rj =1000cm(Dmodels)appearinTable1.Thefullypreion- tion stateindividuallyinfluencetheemissionlinefluxes. how theshockvelocity,preshockdensity,andioniza- the intensityof210830lineisunderestimated(Raymond shock. Theseassumptionsintroduceaboutafactorof2uncer- assume caseBforrecombination,whichoccursprimarilyat H/?. Thesetrendsreflecttheincreasingamountofionizing tainty inthepredictedlineintensities.Thepresentmodelalso He iiLymanphotons,whichisnottreatedindetail.We the Hen21640,4686linesdependonradiativetransferof observed intensityofthe21335linesignificantly.Intensities Comparison ofvarioustheoreticalshockmodelswithsimilar an additionalturbulentcontributiontothelinewidthsislikely. the averageemission-linespectrumarenotyetunderstood,but Results oftheequilibriumpreionizationmodelswithr¡=100 1979). s s s -1 For >60kmstheopticalforbiddenlinestendto Several complicationsmustbekeptinmindwhencompar- Since theshockvelocitywasonlyparametervaried b) PlanarShockResults 327 a
TABLE 1 Predicted Energy Fluxes from Planar Shocks with Equilibrium Preionization W Û 3 M Q 8 § W Q 5 S Ed Q to o o 8S 0 co to o ©g O ©I © < © ( © g §8i2S © < © g M ©I © do' o d© © o ©d'HOOodd-Ht g 0>0)Ë CO ©O’-!00-H ©©-H©OO-H-H«-^Oe0H Z 8 00 00 05 -H © §© ooeo> -H ©(M< goot^oo^HOcocor^dd *H©»oeoco 05lo © ioeo< ©■^loococoeocoio -H .©*-H, O©©t^©C0OO©( 1 CO©©©rHCO-HCO^f'^<©«'^©'^©—l-H©COt^© 0©©rJl©000©05CO©'TfTfOO©COCO©CO© t-HW©t>.050©CO*-li i-H -H©’'T 1—Ir-l©©^Hi—(©©^Hi—IrHrH©©©©©©!— © ■ © t-3' © -H ooddo©oooo-Hdoooo©oooco' ©©©©©oooooooooggooooweo H,H I ©rHi-HCOTT I ©COCOCO^H-H©©^rH^^HeO© id^coddooooddddooooookot^ gQP~«Ç’~*d*^©©eo©©©©t-©r-»eoe< © 00p o z 3 3^ © »-H(M OO^H^Ht^»©©© © —< © © O rHhH rH hH© ^ rH© co eo Ir-IrHi-H©©-^^.^.^»^^ I rHCOCOTf'O'OOCOCOTyCO l©O©O©©©O©''fC0 I kO© © ■^ © CO C=l o Z -i“ <1- h«J3 ’ëS T»Ü -o 22«5 ca-â ■> ¡s ^ -o & c2h öo Œ «^ ^ § § ^ ■§ ^ ’S >H O o o a
TABLE 1—Continued tí Q W Q tí Q tí Û tí Û w a S W Q 8 00 o CO o eo ec o (M o W Q W Q O w S (M -CO^05iß005-^lßOiÄt^'WC5' OOOOOOOOOOOOOOOOOOOdeo^H'H^Hi 00000000000000000000e000505g05 0505000^coeo»Ok0^00^0000g5Codoa>CD05TP OOOOOOOOOOOOOOOOOOOOOOcoe0cOi002®5^228o58®^SS*Seo' ~ rHCM^05OIi—I ço 05i—(Tf00'tcoto^ coco^eooot^^O‘OOOiO'it>.t^-Hço‘00i»-it^ooeok005 © 05©©©©©-h©05-H©©©It.050©©© ©0©©t'-r'.©©©©Tp-H05©-H©©©t^^.-H©05©0 ©t^©©TPTP©©05O5©©©©©TP©©©©©-H©©©©05©©TP05©Ot^TP©^©©05^-H00-H©C0^C0 ©-H © ^W^©§©§^ -3^0000©©i-t^©-HT-.CO»H0005 ^Tp£©TP^©S ©*3«©©©©TPTP05©©©-H-H-H©-H05©—H©©©©-H©©05© ©©tP©0505-h©©© ©©t^O©t^©0îa>05 05©©CT>TPt^©©05©©©05©0>©©t'-OTP©©©©0î©©t^©a>CT>-H05TP05©©O©tT © O-HTp TP00OOO00t^05©-He0TH00 05©O05©00O©5ißTPiß © 05iß—HCO ©©05^©©©Tp-H-H©Tp©©0©©©Tp©l^-H-H-H-H©-H-Ht^TP©©©Ot^.©©©t^-H©r-05l^.0505©©05© © © r^ ; © American Astronomical Society • Provided by the NASA Astrophysics Data System iß t>>t»P©Tp0005»-ti—(^ !©^©©^© C0^©r-^^©Ä©©THiß-H-HO5©-H-H©©©©TPO5©©Tpiß-H-H©l>PO5(MO5-HO5-HO5 , ©^Q(>»t>,(>.HP—Htr*TPPt>-05t'*TpO*^H O Zü Lß iß ^ © Tptr. © ©©-H-H—H05CO ©t^ -hOlTp-H05 -*¿•5! OO05-H©-H-HTpC505© Tp -H05 CMfM —I©©—H05-H*-H©CO-H-H©-H05 > ^ iß© «-H05t>*tr»COTptHCO^Hi—l*-(05*—l TP 05© © -H o © Z. t'- t-© O COeo ~H 00 ^ tíOE p 00 CO 00TP «û. o CO O05p © Tp ^ SSSös’ö’k' -H ^ ^ 05_ 05 00 © © o -H —H050505-H-H©O-H-H-HTp © 05© 00 05CO © O-H '-H i-H05CO 05 TPTp—■-t—. iß 05^CO LO COißp © 05 j-H i—(lOCO50»HTp00p05-HtPO r-l 00TfCOpt''- o 329 © rpTP05 -H ©Tp tP 05TP 05 Tpkß 05 TP^ © COO05Tpß5iß00 00C0OOíO05OCOtPCOtPO’-h lO CO<—I0500i-l«-< f—( 1-H1—I05 CO tH 05 © Z O © iß© 0505t^^Ht^0005©^H r>.©©Tp©©i^©o5©-H „„_ ©05©©©t^ S Ol 05 © O Z 05 00 05 -H © p;o» © CO © "^ o Q © 05-H eo 05—it-ioo CO o CM 00
TABLE 1—Continued © American Astronomical Society • Provided by the NASA Astrophysics Data System 1987ApJ. . .316. .323H © American Astronomical Society W Q W Û -(t^O(M© ©COCO© Tfko co q.©>-Ht->. ^ COCM-H© .-l©D>D©©00(M cocot^c0'--i0©coeot''.co©00 C0C0t^iD(M-H©iDC000(MOOO 331 I t'»kDCO©O- (M IM oooooot^t^iaio i©©C0350km of bowshocksbothVand0 canbeestimatedfromasingle and enableonetopredictlineprofilespropermotions for orientation angleandshockvelocitydeterminetheflow’s age one toestimatethestellarmassoutflowrateaswellpredict outflowing material.Knowledgeoftheshockvelocityenables tionary medium,theshockvelocityrepresentsspeedof the shock since&Vonlyneartheapexofbow. unless Vislargeand//small.Evenfortheassumption s. Hence,theassumptionofsmallcoolingdistancesisvalid neutrals plusions,andVistheshockvelocity.Forrj=300 For astationarycloudletorforbulletcollidingwith sta- of smallcoolingdistanceswillbevalidovermostthebow point whereT=10K,rjisthepreshocknumberdensityof where disthedistancebetweenplanarshockand find results arefittedwellbyapowerlawwhen1^>60kms.We (typically 1500AU).Wecanusetheplane-parallelmodelsto and preshockdensity(Table1).Theequilibriumpreionization determine thecoolingdistanceasafunctionofshockvelocity in theextremeUVandfar-IRwhichmaybecomeobservable include predictionsforalargenumberofbrightemissionlines small comparedwiththesizeofemittingbowshock the nearfuturewithspace-borneinstruments. velocities (1000kms~;Binette,Dopita,andTouhy1985).We s s s s s c3 a) EstimatingtheShockVelocityandOrientationAngleofan Assume thatthecoolingdistance issmallcomparedwiththe The shockvelocityVandorientationangle0aretwoofthe Our bowshockmodelsassumethatthecoolingdistanceis s Arbitrary RadiatingBowShockfromaSingleObservation © American Astronomical Society • Provided by the NASA Astrophysics Data System = 12| 100 kms IV. BOWSHOCKRESULTS c) CoolingDistances He I10830 Table 1. 2 photon [S II]10289 [S II]10323 [N I]10402 [Ne II]12.8/i [Fe II]26.0// [Ne III]15.6/x [O I]63.2/2 [Si II]35.3/2 + 142 MODEL Note.—The incidentmaterialisfullyionized(H,He).Allvariablesaredefinedasfor Hßfluxinunitsof10“ergscm”s"outthefrontshock. 467- +10339 +10373 -/l0 cm RADIATIVE BOWSHOCKMODELSOFHHOBJECTS 1320 13001340 I 18016014012010080 351 214 166 35 39 28 53 18 11 313 132 193 33 30 45 28 16 AU, 8.9 227 263 100 126 27 24 42 15 6.4 TABLE 2—Continued (8) 276 205 133 20 48 90 19 16 4.3 and minimum atthebottom.Hence,tofindextremeradial § Ha),thisvelocityisnegligiblecomparedwithV,andwetake velocities ofthebowshockemissionitissufficienttosearch velocity reachesamaximumatthetopofring,and ver atangle0.Foragivenemittingring(Fig.1),theradial the fullwidthofanemissionline(FWZI)asseenbyobser- extreme maximumradialvelocityalongthetophalfof where the+and—signsrefertotopbottomhalvesof it tobezero,sothatV=Fy,and6(n/2)—Theradial diminishes byafactorof~40thetimegasradiates(see xz plane. frame ofreferencethebowshock,observedmaximum extreme radialvelocityoccurswhen(=0/2,sothatMN = can beperformedonthebottomhalfofbow,and this reached forallviewingangles0provided(rangesfromto value intoequation(9)wefindthemaximumradialvelocity bow. Thisoccurswhen(=(n/2)—(0/2),andsubstitutingthis the curve,respectively.NextsetdV/dÇ—0toobtain velocity oftheemittinggasinxzplaneisthen(cf.eq.[1]) along thecurvedefinedbyintersectionofbowand and minimumradialvelocitiesfromabowshockbecome A similarcalculationfortheminimumradialvelocityMN tion sincetheyexistonlyneartheapexwhereVislarge. shock. Thehighestexcitationlines(e.g.,Civ)violatethiscondi- tc/2, i.e.,thelineprofileofinterestradiatesoverentirebow MX =(VJ2){\-bcos0].Themaximumradialvelocitywillbe stationary mediumy=—Vcos0.Theobservedmaximum tionary cloudlety=0,whereasforabulletplowinginto a of thebowshockwithrespecttoexcitingstar.Fora sta- and minimumradialvelocitieswillshiftbythevelocity y 1390 s 2 r -(F/2)[1 -cos0]. L s s 282 140 117 55 75 13 14 16 The fullwidthofanemissionline isjust Since theperpendicularcomponentofincidentvelocity Since theformulaeforMXandMNwerederivedin 2.5 1470 1530 245 128 13 56 12 64 17 86 2.7 131 171 I 60 13 11 64 16 63 18 MN =-y(1cos0)+7 . (10) MX =y(1+cos0) FWZI =MX—MNV. (11) 2.8 s sin ((sin(cos±0),(9) 1420 238 141 I 40 50 11 17 63 9.7 2.6 6.9 V 1100 346 135 I 20 27 18 55 2.9 2.7 0.7 1.1 333 1987ApJ. . .316. .323H measured accuratelywhen<£æ90°(flowsapproximatelyinthe 334 in thenextsectionaltersanalyticalresultsonlyslightly. plane ofthesky),butallobliqueflows(0°<45°, cloudlet models,andthevelocityofexcitingsourcewith excitation line(e.g.,Ha).Ifoneinvokeseitherthebulletor estimated fromasinglehigh-resolutionlineprofileofanylow- ization stateandtemperatureoftheincidentgas,elemental modeling, suchaspreshockdensity,bowshockshape,theion- extremely usefuldiagnosticsandprovideastartingpointfor causing thebowshock.Therelations(10)and(11)are between MXandMN)is velocity. and MNdeterminethecosineof(eq.[10]),sothat0canbe However, suchestimatesof(j)arenotalwaysprecise,sinceMX velocity observedgivestheorientationangleofoutflow. respect totheobserverisknown(forexamplefromCS,NHor abundances, reddening,etc.Hence,theshockvelocitycanbe are independentofthemostuncertainaspectsbowshock Equations (10)and(11)areremarkablysimple,theresults broadening, andnonzeroFinthenumericalmodelsdiscussed any lineprofileanalysis.Includinginstrumentalandthermal since theradiatinggasmoveswithrespecttoobstacle so thatthisvelocityisnottheradialyofHH CO lineobservations),thenthemaximumorminimumradial object, ashasbeenwidelyassumedinthepast.Vandydiffer fixed. TheHalineprofileissymmetricalaboutzerovelocity when theHHobjectmovesinplaneofsky0«90°; varying orientationangleswhilekeepingtheothervariables theoretical lineprofiles.Figures3a-3gdisplaytheeffectof using thebowshockmodelin§II.Figure3presentsaseriesof 135° <(j)180°)havevaluesofMXorMNnearzeroradial expansion ofpostshockmaterialdistributesemissionover a ponent arisesfromnearthebowapex,andlowradial different areasonthebowshock;highradialvelocitycom- asymmetric, withtwodistinctpeaksappearingforviewing range ofradialvelocities(Figs.1and2).Thelinewidth at the distinctionbetweenpeaksisnolongerasclear,since the velocity fromthewings(forbulletmodel).When0= 45° angles lessthan45°.When0=thetwopeaksarisefrom Fig. (3a),butas(j)decreasestheprofilebecomesincreasingly from 180—0arereflectionsaboutzerooftheprofilesviewed velocities ofeachexpandingringmaterialsimplychange the symmetryaboutzeroradialvelocityforalllineswhen maximum radialvelocityissomewhat largerandtheminimum observed atangle0andthose180—0.Theradial analytic predictions(eqs.[10] and[11])duetotheinstrumen- radial velocitysomewhatmore negativeinthemodelthan sion lineremainsconstantas 0varies.Thiswidthexceedsthe at angle0(Figs.3gand3h). sign whenviewedat180—0(Fig.1).Hence,thelineprofiles 0 =butalsoensuresarelationshipbetweenprofiles 0 =90°arisessolelyfromthisexpansion. shock velocityslightlyforeach spectruminFigure3.The 3 ± c Using equation(10),thecentroidradialvelocity(average The lineprofilesdiscussedinthissectionweregenerated Axial symmetryofthebowshockmodelsnotonlydictates As theprevioussectionpredicts, theFWZIofHaemis- © American Astronomical Society • Provided by the NASA Astrophysics Data System K =2yCOS0+, „ MX+MNV s b) TheoreticalLineProfiles HARTIGAN, RAYMOND,ANDHARTMANN (12) -1 -1 1 and is small.Fromequation(10),thedifferencebetweenMXand points fortheanalysisofindividualregionscontainingHH can influencetheestimated0markedly. plowing intoamoving,insteadoffixed,medium,forexample) quite accurate,estimatesof0canbeuncertainwhentheangle Equations (10),(11),and(13)areusedin§Vasthestarting models inFigures3a-3h.Aswiththepreviousmodels,line files identicalineveryotherrespectwiththe200kms shift ofthelineprofile(whichmightbecausedbyabullet MAT for0=0°and30°isonly0.067Vsothatanysmall objects. Althoughestimatesof^obtainedinthismannerare more importantatlowerbowshockvelocities.The100kms flux increasesmorerapidlyatlowershockvelocities(Table1). widths slightlyexceedtheshockvelocityforallorientation ian beSM.Thiswidthcontainsbothinstrumentalandthermal measured asfollows.LettheFWHMofsmoothingGauss- profiles exhibitonlyasinglepeakatoblique0sincethehigh This behaviorcausestheapexemissiontobecomerelatively and 0foreachprofile.Whenplottedlogarithmically,theHa angles, andequations(10),(11),(13)successfullypredictF peak intensity.Set broadening terms.LetMXOAandMATO.1representthe tal andthermalbroadeningpresentinthemodels.Thebow component. Thesetrendsfollowfromtheremarksregarding line profile.Thehighradialvelocityemissionismorepro- profiles occuronlywhen1^>150kms~and0<45°. the lowradialvelocityemission.Ingeneral,double-peakHa radial velocityapexemissionhasincreasedandmergedwith observed maximumandminimumradialvelocitiesat0.1ofthe to estimateVand0providedthevaluesofMXMNare shock modelsshowthatrelations(10)and(11)canstillbeused (eqs. [10]and[12]),butthecloudletprofileismirrorimage will beblueshiftedwhen0>90°(eq.[12]),sotheorientation The Ragashape(Fig.3r)hastheweakesthighradialvelocity nounced fortheDAshape(Fig.3q)thanA3e). cloudlet withorientationangle0willmirrorthoseproduced The twoprofileshaveidenticalvelocitycentroidsandwidths shape in§lie. by abulletwithorientationangle180-0.Thisfollowsfrom tate comparisonwiththebulletmodelinFigure3e(0= 30°). angle ofthecloudletinFigure3sistakentobe150°facili- the axialsymmetryofproblem.FromFigure2,emis- of thebulletprofile.Ingeneral,lineprofilesfromastationary radial velocityW=—Vcos90.Ifthebulletisviewed at orientation angle180—0issymmetrical,anditcentered at sion fromasingleemittingringofmaterialbulletwith eq. [12]),thecentroidvelocity, sothattheemissionfroma to cloudletgeometryweobtainU=Vcos60+ 0 an angle0,theemissionshiftstoVcos9andcoverting cloudlet geometry. line profileconsistsoftheco-addition ofmanysuchrings,it as thecenter.Hence,average ofUandWissimplyV(cf. too isreflectedaboutVwhen onechangesfrombulletto single emittingringofmaterial isreflectedaboutV.Sincethe s9 s s 2 2 2 c c c _1 Figures 3i-3ppresent100kmsand400linepro- Figures 3qand3rillustratetheeffectofbowshapeon For astationarycloudlet,thecentroidofradiatinggas MN =MN0A+SM/2.(13) MX =MXOA-SM/2 Vol. 316 1987ApJ. . .316. .323H -1 1 -1 4 1 4 3-1 a mixtureof high-excitation andlow-excitation lines,as (see alsoTables1and2).Finally, Figure3vshowsthatthe Ha, since[Om]/15007forms only inregionswhereVislarge. high-excitation line[Oin]A5007 candiffersignificantlyfrom model inFigure3memphasizesthelowvelocityshocksmore velocities between—40and10kms.Thefullypreionized fraction oftheemissionfromwingsbow(radial the followingvariations:{b)(f)=75°.(c)60°.(d)=15°.(g)0°.(h)(f)180°.(z)V100kms“,090°.(j)K (normalized tounityatthepeak),(a)ShowsHafroma200kmsshock withequilibriumpreionization,bulletgeometry,orientationangle(cf.Fig.1)0=90°,bow be 0.4fortheprofileinFigure3i.Anarrowslitremovesalarge profiles alterradically.Theratioofslit/HHsizewastaken to [O in]A5007,0=30°,T3x10K. 0 =60°.{k)V100kms\30°.(/)s"\0°.(m) =400kms",090°.(n)Vs“60°.(o)30°.{p) shock shapeA,slitwiderthantheHHobject,T=10K,preshockdensity 300cm",andinstrumentalbroadening12kmsFWHM.Theremainingprofileshave V =400kms^00°.(4)30°,DAshape,(r)Raga (s)0=150°,cloudletgeometry,(t)30°,slit/HH0.4.(u)ófullypreionized,(r) L s s s s No. 1,1987 -1 Table 3listslineratiosforvarious bowshocks.Resultsshow Fig. 3.—Theoreticallineprofilesfromthebowshockmodels.Radial velocities inkmswithrespecttotheexcitingsourceareplottedvs.relativefluxes If theslitisnarrowerthanHHobjectpredictedline © American Astronomical Society • Provided by the NASA Astrophysics Data System c) TheoreticalLineRatios RADIATIVE BOWSHOCKMODELSOFHHOBJECTS -1 becomes important. Hß asshockvelocityincreases untilcollisionaldeexcitation ([O 1],[S11],[N11])generally increaseinstrengthrelativeto discussed in§IIIZ>,thelow-excitation opticalforbiddenlines it notfortheeffectofpreionization state.The[O11]lines are muchstrongerwhentheincident gasisfullypreionized.As density (thelinesaresensitive tocollisionaldeexcitation)were have strongerOmemission.Thestrengthofthe[O11]23726/ 3729 lineswouldbeareliablemeasureofthepreshocknumber also influencesthisline,however;morebluntshapes(like DA) cities. Thehigh-excitationline[Oin]A5007onlyappearswhen expected fromanobjectcontainingavarietyofshockvelo- V >100kms(Table1).Table3showsthatthebowshape s 335 1987ApJ. . .316. .323H 336 fact, HH2Histheonlyobject forwhichreliablereddening models ofHHobjects.Thereareadozenorsoobjects in ways constituteanideallaboratoryfortestingbowshock corrected fluxesexistintheultraviolet, andhenceistheonly this region,allintrinsically bright, makinghigh-resolution opposite sidesoftheexciting source (Pravdoetal1985;Strom ratios fromthebowshockmodels. SinceHH1and2lieon object thatcanbecompared directly againstthepredictedline optical observationsandUV fluxmeasurementsfeasible.In The groupofHHobjectscomprising1and2insome V. APPLICATIONOFTHEBOWSHOCKMODELTOREGIONS © American Astronomical Society • Provided by the NASA Astrophysics Data System CONTAINING HHOBJECTS a) TheHH1/2Region HARTIGAN, RAYMOND,ANDHARTMANN -1 flow mustbeorientednearlyintheplaneofsky.Thesource is lesssevere,sincetheHHobjects aremoredistinctforthat could representaradiatingbow shock.ThesituationforHH2 includes emissionfrommore thanoneclump,eachofwhich however. HerbigandJones(1981)haveshownthemorphology radial velocitiesmustbereferencedtothesourcevelocity. This informationisneededforthelineprofileanalysissince velocity isalsoknown(+9kmsk¡;Torrellesetal1985a). away fromtheexcitingsource(HerbigandJones1981), the et al1985)andtheHHobjectsshowlargepropermotions group. Extendedbackground emissionalsocomplicates the emissionfromHH1isclumpy, asingleapertureprobably of HH1tovarysubstantially ontimescalesofdecades.Since sr Some facetsofHH1and2complicatestudythisoutflow, Vol. 316 1987ApJ. . .316. .323H _ 1 No. 1,1987RADIATIVEBOWSHOCKMODELSOFHHOBJECTS337 effective apertureof1'.'5x2'.'5 onthesky.Positionsfor mined fromtheFWHMof calibrationThArlines,andan files arecenterednearzeroradialvelocityandroughly profiles ofHH1and2taken withthefacilityechelleon literature (Schwartz1981;HartmannandRaymond1984; will makeanyextendedlinewingsappearlesssignificant. affects estimatesofVand0(§IVa)sincebackgroundemission analysis ofHH1and2(BöhmSolf1985;Stromet al objects canbefoundinHerbig andJones(1981). shock modelsfor~90°.Figure 4presentsanumberofline symmetrical, preciselythebehaviorpredictedby bow Böhm andSolf1985).ForeachHHobjecttheobserved pro- MMT. Thisinstrumenthasa resolution of12kmsasdeter- 1985). Suchemissionalterstheobservedlineprofiles,and also s Several high-resolutionstudiesofHH1and2existinthe © American Astronomical Society • Provided by the NASA Astrophysics Data System may beaffectedbythelower signal-to-noise inspectraofthese slightly smallerthanHa,although thedifferencesaresmalland and [Nn].The[Sn] [O i]widthsarealsogenerally the sensethat[Om]line widths arealwayslargerthanHa tion (11)isnotpreciselyobeyed. Acleartrendisapparent,in However, thestrictequalityof linewidthspredictedbyequa- quite similar,inagreementwiththebowshockprediction. § IVh.ResultsappearinTable4.Inthistablewealsoinclude was measuredassumingthebulletmodelwithastationary ambient medium(y=—Vcosineq.[10]). as wellsomeunpublished[Oi]lineprofiles.Theangle spectra fromHartmannandRaymond(1984)forHa[N n] observed profileandcomputingVasprescribed in s s The velocitywidthsfordifferentlineswithinagivenknotare We begintheanalysisbyextractingMXandMNfromeach 1987ApJ. . .316. .323H in HH1(IA,1C,ID),provide noevidencefordoublepeaks. Choe, Böhm,andSolf(1985) wereforcedtoadoptverylarge (1985) andHartmannRaymond (1984)forotherpositions data, aswellthelineprofiles presentedbyBöhmandSolf line profileswouldbestrongly double-peaked.Thepresent case theobservingslitswould easilyresolvetheobject,and (1985) claimedHH1wasasinglebowshock.However,in this from thesimplebowshockmodel.Choe,Böhm,and Solf lack ofsymmetrymayhavesomethingtodowithdepartures relatively recently,soperhapstime-dependenteffectsaswell as Herbig andJones(1981)suggestedthatthisknothasappeared asymmetric (Fig.4;alsoHartmannandRaymond1984), and several bowshocks.ThelineprofileforHH2A'isstrongly that asingleaperturemightincludeemissionfromportions of knots quiteclosetogetherspatially(HerbigandJones1981), so tional complexities.HH1iscomposedofseveraldifferent (and emitting[Om]). deflected normaltothebowshockaxiswhilegasisstillhot more likelythatlongercoolingtimesnearthebowshock’s apex makeitpossibleforsomeofthevelocitythisgastobe enough toaffect[Om]proportionatelymorethanHa.Itis might createsubstantialturbulentvelocities,decayingrapidly Thermally unstablecoolingofthehighestvelocityshocks failure oftheassumptionthatemissionregioncanbe [O m]andHawidths,HHIF2A',mayreflectaddi- approximated byacombinationofindividualplanarshocks. emission components(Fig.4a). lines andpossiblecontaminationfromnarrowbackground 338 The twoknotsthathavethelargestdiscrepancybetween Differences inemissionwidthsaredirectindicationsofthe © American Astronomical Society • Provided by the NASA Astrophysics Data System HARTIGAN, RAYMOND,ANDHARTMANN 4 -3 _1 _1 the modelprofilesaresomewhat tooboxyinshape.These instrumental broadening,T= 10KforHa,andT=3x preionization, shapeA,preshock density500cm,bullet K for[Om]25007.Theoverall agreementisgood,although geometry, =75°,slitwider thantheHHobject,12kms profiles. Weuseda160km s bowshockwithequilibrium (1980). ate theoreticallineprofilesforHH2H.Theseareshown in plots ofRózyczkaandTenorio-Tagle(1985h),orthatthe flow Figures 4eand4/forHa[Om]25007alongwithobserved resembles thefocusedwindpredictedbyCantóandRodriguez up, perhapsbytheRayleigh-Taylorinstabilityshownin the angle canbetakentosuggesteitherthatabullethasbroken perhaps theobjectsmovewithinthiscone.Thewideopening comprising HH2seemtooutlineaconeofopeningangle within HH2ispeculiar,butitundeniablyreal.Sincethe exceptions (Table4).The45°dispersionoforientationangles opening angleapparentlyincreaseswithdistance.Theobjects objects onlysubtend~20°asseenfromthesource,flow’s HH 1and2arenegative,with2M,2E,2Ctheonly Centroid radialvelocitiesfornineofthe12knotsobservedin tion anglesareeasytoestimateaccuratelyforHH1and2. tive tosmallchangesinfor~90°(§IVh),sotheorienta- remarkably constantwithineachknot.MXandMNaresensi- more than3"-4"insize. simpler toassumethatthebowshockspresentmustbeno turbulent velocitiestoavoidthisproblem.Wefeelitismuch ~50° (seeHerbigandJones1981;orStrometal.1985), and -1 Using =75°and1^160kms(Table4)wecangener- Orientation anglespredictedfromthevariouslinesremain a
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