planetary nebulae kinematics in m94 · planetary nebulae kinematics in m94 originally published as...

5Planetarynebulaekinematicsin M94

Originally publishedasN.G. Douglas,J. Gerssen,K. Kuijk en,M.R. Merrifield,MNRAS in press(2000)

Theplanetarynebulapopulationsof relatively nearbygalaxiescanbeeasilyobservedandprovide botha distanceestimateanda tool with whichdynamicalinformationcanbeob-tained. Usually the requisiteradial velocitiesareobtainedby multi-objectspectroscopyoncethe planetarynebulae have beenlocatedby direct imaging. Herewe reporton atechniquefor measuringplanetarynebula kinematicsusingthe double-beamISIS spec-trographat the William HerschelTelescopein a novel slitlessmode,which enablesthedetectionandradialvelocitymeasurementsto becombinedinto asinglestep.Theresultson our first target,theSabgalaxyNGC 4736,allow thevelocity dispersionof thestellarpopulationin a diskgalaxyto betracedout to four scalelengthsfor thefirst time andareconsistentwith a simpleisothermalsheetmodel.

THE he outerkinematicsof galaxieshave playeda crucial role in our understandingoftheirstructure.Thedarkmatterhalosaremostimportantthere,sothatconclusionsabout

their shape,massand extent may be drawn that are lessdependenton assumedmass-to-light ratiosof theobservedstars.Most of theangularmomentumresidesat largeradii, andrelaxationtimesare longestthere,possiblyenablingechosof the formationprocessto beobserved directly. However, the requiredobservationsare ratherdifficult. The integratedstellar light of a galaxyrapidly becomestoo weakat large radii to do spectroscopy. In thecaseof elliptical galaxies,theold stellarpopulationshavenow in a few casesbeenprobedasfarastwo effectiveradii (e.g.,Carolloet al. 1995;Gerhardetal. 1997).

Sometracers,suchasglobular clustersandHI emission,canbeobservedat largerradii,but neitherprovidesa reliabletracerof thekinematicsof therelaxed,old stellarpopulation.Moreover systemslike S0sandellipticals generallylack an extensive gaseousdisk. Fortu-natelyanalternative tracerof thekinematicsout to largeradii hasbeenidentifiedby Hui etal. (1993),who showed that the radial velocitiesof a galaxy’s planetarynebula (PN) pop-ulation constitutea suitablediagnostic. Planetarynebulae (PNe) appearin the post-mainsequencephaseof starsin therange0.8 - 8 M � . Fortunately, in all but thevery youngestofsystemsthe PN populationis stronglycorrelatedwith the older, andthereforedynamically

49

50 CHAPTER5 PLANETARY NEBULAE KINEMATICSIN M94

relaxed,populationof low-massstars.This statementis truenot only becauseof thestatis-tics of stellar formationandevolution, but alsobecausethe PN lifetime is itself a stronglydecreasingfunctionof progenitormass(Vassiliadis& Wood1994).

PNeemit almostall of their light in a few bright emissionlines, particularlythe O[III]line at5007A. Thereis evidencethatthePNO[III] luminosityfunctionis essentiallyconstantwith galaxytypeandmetallicity (Jacobyet al 1992),sothat theobservedbright-endcut-offmagnitude�÷ö (Ciardulloetal 1989)representsa ‘standardcandle’with whichdistancescanbe determined.At a distanceof 10 Mpc, this cut-off correspondsto a flux of

J � iøÆ I i!� m�ùergcm� 6 s� m , makingPNewithin onedex of this limit easilydetectablein onenight with a4-m telescope.As a rule of thumb,approximately100suchPNearefoundto bepresentperI i ó L � of B-bandluminosity (Hui 1993),sothey areseenin sufficient numberto studythekinematicsof thestellarpopulationof thehostgalaxy.

Theusualapproachin makingsuchkinematicstudieshasbeento identify thePN popu-lation by narrow-bandimagingandthento re-observe thedetectedPN spectroscopicallytoobtainradial velocities. However, otherstrategiesexist that avoid the needfor several ob-servingruns. For example,Tremblayet al. (1995)usedFabry-Perotmeasurementsin a PNkinematicsstudyof theSB0galaxyNGC3384.In thispaper, wedescribeanovel alternative,basedonslitlessspectroscopy, anddiscussits applicationto theSabgalaxyM94.

5.1 SlitlessSpectroscopy

Our methodfor obtainingthekinematicsof PNeis outlinedin Figure5.1. Thegalaxyunderstudy is imagedthroughnarrow-bandfilters aroundthe two strongestemissionlines in atypical PN spectrum,H y andO[III]. TheH y imageis recordeddirectly, but theO[III] lightis dispersed.Comparisonof thedispersedandundispersedimagesthenallowsthekinematicsof thePNeto bemeasured,without prior knowledgeof thelocationof thePNe.Two modesof analysisarepossible:

Dispersed/UndispersedImaging (DUI): In thedispersedbluearmthePNewill bevis-ible throughtheir O[III] emissionaspoint sources,displacedfrom their ‘true’ positionsbyan amountrelatedto their radial velocity, againsta backgroundof dispersedgalacticlight.The red arm will detectthe PNe throughtheir H y emission,alongwith any otherobjectswith line or continuumemissionin the passbandof the filter. Assumingthat the PNecanbeunambiguouslyidentifiedin theH y image,their positionin theO[III] imagewill give theradialvelocity. We choseto dispersetheblueratherthantheredlight sincePNhaveahigherflux atO[III] thanat H y , andgratingsarelessefficient thanmirrors.

Counter-DispersedImaging (CDI): Themethodof counter-dispersedimagingwasde-scribedin anearlierpaper(Douglas& Taylor 1999). In this mode,pairsof dispersedO[III]imagesaremadewith theentirespectrographrotatedby 180degreesbetweenexposures.Thedifferencein thepositionof a givenPN in thetwo dispersedimagesagainreflectsits radialvelocity. In this casethe undispersedH y imagecanbe usedasa consistency checkon thederivedpositionsof thePNe.

We have implementedour methodon the ISIS medium-dispersionspectrographat theCassegrain (f/10.94) focusof the 4.2m William HerschelTelescope.The slit unit was re-moved during the observations,and the O[III] and H y light pathswere separatedwith adichroicbeforebeingpassedthroughappropriatenarrow-bandfilters. Thefilters ( ú 5026/47and ú 6581/50)werecustom-madefor this project in orderto exploit the full hÇÆ I arcmin

5.1 SlitlessSpectroscopy 51

Red Arm Blue Arm

α

mirr

or flat

1200l/mm

grating

αundispersed H image dispersed O[III] image

planetary nebulae

narrow-band H filter narrow-band O[III] filter

dichroic

FIGURE 5.1— Diagram showingschematicallyhow onecanusea dual-beamspectrographto study PN kinematics. Thenarrow-bandimagesin the two armsallowone to identify the PNe and measuretheirline intensitiesin both the [OIII]5007A andH û lines.Thedispersive elementin thebluearm shifts each PN image by an amountproportionalto its redshift. In the red armthegratinghasbeenreplacedby amirror.

field of the instrumentin slitlessmode,andto give adequatevelocity coverage.We useda1200g/mm(first order)gratingin thebluearm. Both armscontained1024

6-pixel Tek CCD

detectors.Thus,weobtaineddispersedimagesin theblue(calibrationshowedthedispersionto beabout24

± � 9 � m perpixel) andsimultaneousdirectimagesin thered.DUI observationsareaccomplishedin asingleexposure;CDI requirestwo exposures.

Theoverall efficiency of this setup,includingtelescope,instrument,filter andCCD,wasfoundfrom observationsof a standardstar(Feige34) to be14%in theblueand20%in theredfor air massof 0. We thereforeexpectedto detectp J � J O[III] photonspersecondfromthe brightestPN whenviewed at 6.6 Mpc. Dark sky (V=21.4) would produce p 2 countsper arcsec

6per second,andthe backgroundlight of the galaxy1–5 countsper arcsec

6. A

reasonablegoal is to obtaina 44

detectionover the top decade( üþýÿü ö > J � � ) of the PNpopulation,correspondingto p 4 hoursof integrationif theseeingconditionsareof theorderof onearcsec.The requiredintegrationtime is approximatelyproportionalto thesquareoftheseeing.


TABLE 5.1— Galaxyparameters

Name NGC4736(M94)Position(J2000) 12h50m53.061s

+41d07m13.65sHubbletype SA(r)abV �� 308 q 1 km/sB l� 8.99Angularsize

I|I � J Æ � � I arcminInclination � 35 jScalelength 57 q 10arcsecPositionangle 105j

5.2 ObservationsTheobservationswerecarriedout on 1997April 11 and12. For thispilot projectNGC4736(M94)waschosen.It hasalargeangularsizeandis atadistanceof 6 Mpc (Bosmaetal1977).Thegalaxyshowssomepeculiarmorphologicalfeatures,mostnotablyaninnerandanouteropticalring with radii of 1 and5.5arcminrespectively. Thestellarlight is too faint for directopticalspectroscopy outside1 arcmin,andour goalwasto measurePN kinematicsto threetimesthis radius.Key parametersof NGC4736arelistedin Table5.1,andtheobservinglogis givenin Table5.2.

Two fieldswereobserved,3 arcminwestof centreon themajoraxis,and3 arcminnorthof centreon theminor axis. Themajoraxiswasobservedat two orientations(allowing CDImode)while the minor axis wasobserved in oneorientationonly. We took the major axispositionangleto be 90j , aswould seemappropriatefrom the relevant isophotes(seeFig-ure5.3). Total integrationtimeswere6.0hrson theWesternfield (4.6hrsin oneorientation,and1.4hrswith thespectrographrotatedby 180degrees),and3hrsontheNorthernfield. Theobservingconditionswerecloseto photometicwith seeing,as judgedfrom stellar imagesin the red arm, lessthan1.1 arcsecat all times. We alsoobserved a flux standardstar forphotometryanda GalacticPN asa radialvelocity reference.A secondstarwasobservedasaspectralreference.

Thecustom-made[OIII] andH y filters hada centralwavelengthandpeaktransmissionof 5026A/0.823 and6581A/0.915, respectively. The nominal FWHM was 47A and50A,while theeffective photometicbandwidthwasevaluatedgraphicallyandfound to be38.7Aand45.7A, respectively.

5.3 Data Reduction5.3.1 Calibration

Thedispersionin thebluearmwasmeasuredby insertinga slit andusinganarc lamp,andfoundto be0.3992A/pixel. Thespectrumof thestarHD66637wasthenobservedthroughthesameslit andwavelength-calibrated.Subsequentobservationsof thesamestarat numerouspositionsin thefield (afterremoval of theslit) establishedthat thedispersioncouldbetakenasconstantover the field. The combinationof theseobservationswith the undispersedred

5.3 DataReduction 53

TAB�

LE 5.2— Log of our observationsat theWHT, La PalmaObservatory. PA is thepositionangleof thespec-trographandT thetotal integrationtime (wheretwo valuesaregiventhesereferto thered/bluearmsrespectively).

Field PA T UT AirmassApril 11

HD66637 90 60 20:35 1.06Feige34 90 2/10 21:15 1.07N4736- majoraxis 90 16,453 21:20- 2:13 1.35- 1.07PN 49+88.1 90 5 2:03 1.06N4736- majoraxis 270 4,868 2:36- 4:52 1.12- 1.54

April 12HD66637 90 0.1/10 20:29 1.06Feige34 90 3/60 20:57 1.09N4736- minoraxis 0 10,800 21:02- 0:08 1.42- 1.03

arm positionsof HD66637gave an unambiguoussolution for the transformationbetweenobjectsin the red(direct image)andblue (dispersedimage). (Note thatwith this techniquetheradialvelocityof thestardoesnot enterinto thecalculation.)

To checkthezeropoint of thevelocity scale,we movedthetelescopefrom thereferencestarto theGalacticplanetarynebulaPN 49.3+88.1,for which theheliocentricradialvelocityis listedas

L I h I ± � 9 � m (Schneideret. al 1983). In tenpointingsover thefield of thespec-trographwe measured

L I�� s � i�q � � J ± � 9 � m , in agreementwith the calculatedobservatoryframeredshiftof

L I��|� ± � 9 � m . Unfortunatelywe discoveredlater thatat certaintelescopeorientationsthe flexure is large enoughto causesignificantly larger errors. However, suchflexureonly introducesanoffsetin absolutevelocity, anddoesnotcompromiseourability tostudya galaxy’s internalkinematics.In orderto deriveanabsolutecalibrationfor theveloc-ity scale,we have alsoobtaineda long slit observationof two of theobjectsdetectedin thisanalysis(see

�5.4).

The spectrographfield of view with the slit unit removedconsistsof an approximatelyunvignettedareaof about4 arcmin Æ 1 arcmin, but we obtaineduseful dataoutsidethisregion. Correctingtheobservedfluxesfor the vignettingis only straightforwardfor the red(undispersed)arm. In thebluearm thecorrectionis complicatedby the fact that the imageis dispersed.The sky flat measuredin the blue arm wasfound to closelyapproximatetheaperturefunctionin theredarm,shiftedby asmallnumberof pixels,transformedto bluearmcoordinatesandthenconvolvedwith thefilter profile at theappropriatedispersion.

We thereforecarriedout thecompleteanalysisaftercorrectingonly for thepixel-to-pixelvariationof theCCDresponses,determinedin theusualway. OncethePNewereidentifieditwaspossibleto determinetheir wavelengthandtheir positionsin theapertureprior to beingshiftedby thespectrograph,sothattheO[III] magnitudescouldthenbecorrectedanalyticallybothfor thefilter response,whichwasfitted with a polynomial,andfor vignetting.

5.3.2 Object identification

Scriptsbasedon IRAF procedureswereusedfor all of thedatareduction.


Due to spectrographflexure, individual exposuresneededto be alignedbeforebeingadded. This wasaccomplishedby a simpleshift (at leastonePN was visible in eachin-dividual exposure).The imageswerethencombinedby computinga weightedandscaledmedian.A spatialmedianfilter wasappliedto thecombinedframe,andtheresultsubtractedfrom the original imageto yield a field of unresolved objectsagainsta backgroundwith ameanof zero.

The PNeandany otherpoint sourcesin the redandblue imageswereextractedby twomethods:(A) Blinking andhand-tagging,followedby a PSF-fittingstepto evaluatetheshapeandsizeparameters.For DUI modeobservingit wasusuallyfoundto beeasierto searchtherangeofpossible(red)coordinatescorrespondingto anobjectseenin theblue(seeFig. 5.2).(B) anautomatedprocedurebasedon objectlists generatedwith DAOPHOT. A 2D-gaussianfitto eachdetectedimagewasusedto selectPN candidates.The FWHM of a candidatewasrequiredto be within a small rangeof thatof the seeingdisk (PNeareunresolved)andtheaxialratiocloseto thevalue1.28expectedfrom ourinstrumentalconfiguration(theellipticityarisesfrom the anamorphiceffect of the grating). The object lists were thencorrelatedtosearchfor potentialPN imagepairs.

5.3.3 Comparing SpectralModes

WeidentifiedPNein NGC4736alongtheminoraxiswith DUI modeobservationsandalongthe major axis usingCDI (with DUI modedatabeingredundant).Although CDI requirestwo distinct integrations,we found thatdataobtainedfrom CDI resultsin a highernumberof detectedPN per unit integration time. For visual identificationusing blinking, CDI isconsiderablyeasiersincethe two imageshave the sameplatescaleandsimilar propertieswith respectto sky noiseandconfusion. Thereforeto illustrate the numericalsuperiorityof usingtwo dispersedO[III] imageswe rely on theautomatedsearchresultsfor themajoraxis observationsonly. 36 PNewereidentifiedin this field from matching2.5

4sourcesin

thecounterdispersedO[III] images.Thelimiting factorherewastheshorterintegrationtimewith one of the two spectrographorientations:had both integration times beenequalwewould presumablyhave found yet morePNe. By comparison,only 24 PNeweredetectedfrom the DUI modeanalysisof the samefield. Therefore,we concludethat a significantnumberof PNearetoo faint in H y for theDUI modeto detectthem.

5.4 Long-slit data

It hasbeenmentionedthat instrumentflexure, particularlybetweensetsof observationsinCDI mode,canleadto anuncertaintyin the absolutevelocity scale.To remove this uncer-tainty we attemptedto obtainthe velocity of at leastoneobject in the major axis field viatheWillian HerschelTelescopeservicedataprogram.As thePNearefaint,with effectiveV-bandmagnitudeof around25,theslit hadto bepositioned‘blind’ on thebasisof thepositioncomputedfrom thedisperseddata.Fortunatelytheastrometrydoesnot dependon velocity,but only oncorrectidentificationof PNpairs,andon thecentroidingof thedispersedimagesof starsin thefield.

We requesteda spectrumusingISIS in long-slit modeandwith theslit at a positionandPA chosensuchasto fall acrosstwoobjects.Thisprovidedagoodtestof theastrometry. Theserviceobservationwasattemptedon 1999July 28. Both objectswereacquired,andtheir

5.5 Results 55

FIGURE 5.2— An example of the‘postagestamp’ method for detectingredcounterparts.Theboxeson therighteachcontainonepoint sourceidentifiedin theblueframe.Theboxeson theleftsideshow thecorrespondingpartsof theredframe.Any redcounterpartmustbelocatedsomewherewithin theboxsincethe size of the box is such that it en-compassesthe velocity rangespannedby thefilter. The horizontallocationofthe counterpartis a measureof the ob-ject’s radial velocity. In the vertical di-rectionwe requirethe positionalagree-mentto bewithin onepixel.

separationalongtheslit agreedwith thatcalculated.Oneof theobjects,suspectedof beinganHII region,wasconfirmedassuch.Theradialvelocitiesobtainedhadaninternalerrorofabout10

± � 9 � m , asjudgedfrom thevaluesobtainedfrom differentlines,andwereusedtocalibratethemajoraxisdata(Table5.3).

5.5 Results

ThePNeidentifiedalongthemajoraxisarelistedin Table5.3andthosealongtheminoraxisin Table5.4. Their positionsarealsoshown in Fig 5.3. As suggestedby thesuccessfullong-slit experiment,thepositionaluncertaintyis of theorderof 1-2 arcsec.Theinternalerror inthevelocitiesis approximately10

± � 9 � m . Theminor axisvelocitieshave anoffset thathas


FIGURE 5.3— Digitised SkySurvey imageof NGC 4736(Northat top) with the observed fieldsmarked with boxes and the PNeshown asopencircles.

not beendetermined,but thevaluesaspresentedhave anaveragevelocity nearsystemic,aswould be expected.The derivationof velocitiesfrom DUI modedata,aswasusedfor theminor axis, is in factmuchlesssensitive to flexure. However, in orderto reducethenumberof candidateobjectsin the red image,only radial velocitiesbetween200 and500

± � 9 � mweresearchedfor, sothis tablehasto beusedwith caution.

5.5.1 Luminosity function

We placeda premiumon detectingasmany PNeaspossible,evenin thepartially vignettedregion of the instrument.Considerablecorrectionshave beenapplied,andthe magnitudesshouldthereforeonly betakenasindicative. Theluminosityfunctionof theobjectsdetectedis presentedin Fig. 5.4.The ü ö cutoff (24.4)for theassumeddistanceof 6 Mpc is indicated.At the faint endthe luminosity function is, of course,significantly incompletewhile at thebright endsomeobjectsarebrighterthanthecutoff. ThelatterareprobablyHII regionsandhavethereforenot beenincludedin theanalysisof thekinematics.

Thenumberof PNefoundin themajoraxisfield (CDI mode)is in roughagreementwithpredictions.From the basicdataon NGC 4736compiledby Mulder (1995)( üa � ã � � ã , � s � i Mpc) we have r � J � i � Æ I i m l � , andon the basisof the resultsof Hui et al(1993)the expectednumberof PN in the top decadeof the PNLF in M94 would thereforebearound2000.Mulder alsofoundthegalaxyto befairly well-fitted by anexponentialdisk

5.5 Results 57

RA (J2000) Dec(J2000) Rvel � �� FWHM12:50:49.46 41:07:09.5 459 23.44 3.5212:50:49.42 41:07:40.3 472 23.18 3.5912:50:49.35 41:07:17.5 463 23.48 3.3112:50:48.93 41:07:51.2 483 22.54 3.2912:50:48.62 41:07:22.9 444 23.18 3.3112:50:48.40 41:06:17.3 309 24.80 3.2412:50:48.53 41:07:45.8 450 24.63 3.5412:50:47.97 41:07:10.8 508 25.46 3.912:50:47.87 41:07:09.8 378 25.78 2.7912:50:47.73 41:06:33.2 296 24.56 3.912:50:47.61 41:07:00.2 345 24.45 3.6112:50:47.59 41:06:56.9 391 25.33 3.3812:50:47.50 41:06:26.2 525 25.52 3.512:50:47.17 41:06:27.4 429 25.34 3.5412:50:46.92 41:06:05.5 413 25.14 3.4512:50:46.93 41:06:35.3 378 25.41 3.4712:50:46.32 41:06:18.3 357 25.60 3.0512:50:46.40 41:07:46.8 466 24.95 4.3812:50:46.13 41:06:11.2 380 24.24 3.9412:50:46.17 41:08:13.6 491 24.34 3.5712:50:45.27 41:06:36.8 478 24.91 4.3712:50:45.11 41:06:27.8 308 25.30 3.7312:50:44.65 41:06:51.3 369 24.82 3.6612:50:44.26 41:07:39.2 432 25.78 2.6712:50:43.79 41:06:11.4 353 24.95 3.3312:50:43.76 41:06:48.3 348 25.18 2.7912:50:43.29 41:07:54.9 457 22.59 3.5212:50:43.03 41:06:07.7 485 24.91 3.1712:50:42.95 41:07:49.5 473 26.39 2.712:50:42.66 41:06:11.8 405 22.65 3.9212:50:42.58 41:06:36.6 428 25.00 4.3412:50:42.48 41:07:52.8 425 24.88 3.512:50:42.19 41:08:15.0 476 24.58 3.0712:50:41.40 41:07:01.5 433 24.98 3.512:50:41.17 41:06:21.0 413 25.21 3.4712:50:41.17 41:07:46.4 339 24.26 4.712:50:40.87 41:05:57.5 414 3.4712:50:40.74 41:06:11.7 410 25.53 4.3712:50:40.55 41:07:46.4 417 24.72 3.6112:50:40.26 41:08:00.7 400 25.33 4.0412:50:40.15 41:06:51.3 383 24.74 2.7712:50:38.62 41:07:04.9 409 25.41 3.7112:50:38.67 41:08:05.0 391 25.35 4.212:50:38.55 41:06:44.4 418 25.00 2.8912:50:38.02 41:06:20.9 423 25.54 3.6812:50:37.90 41:08:06.1 464 25.14 3.0512:50:36.34 41:06:48.0 430 25.65 3.0712:50:35.24 41:06:10.8 425 24.93 3.4512:50:34.75 41:06:18.3 408 24.87 3.3112:50:34.15 41:05:58.2 379 2.9112:50:25.18 41:06:16.4 415 25.50 4.312:50:48.71 41:06:32.7 378 25.18 5.4512:50:42.79 41:07:48.9 454 25.22 3.54

TABLE 5.3— Fifty-threepoint sourcesinthe major axis field. Rvel (heliocentric)isthe measuredrelative radial velocity fromtheslitlessspectroscopy plusanoffsetestab-lishedby anadditionalcalibration(see� 5.4).� �� = -2.5 log(� ) - 13.74 is the appar-entV-bandmagnitudeof theobjects,where� is the flux in ergcmÃ�� sÃÅÄ . The magni-tudeshave beencorrectedfor vignettingasdescribedearlier. The vignettingcorrectioncouldnot bereliably appliedfor two objectsas they were too close to the edgeof theaperture,andtheirmagnitudesarenotgiven.FWHM (in pixels)refersto themajoraxisofthegaussianfit.


TAB�

LE 5.4— Fourteenpointsourcesin theminoraxisfield. Thecoordinatesarederiveddirectlyfrom thepositionin the red image(seetext). �� givesthe ratio of thefluxes(in ergcmÃ � sÃÅÄ ) seenin the redandblue images.

Othersymbolsareasin Table5.3,exceptthattheradialvelocitieshavenotbeencheckedagainstanexternalreferenceandmayhave asmallcommonoffset.

RA (J2000) Dec(J2000) Rvel ! �� FWHM

12:50:52.02 41:11:22.3 330 26.26 1.26 3.3612:50:53.68 41:10:15.8 263 24.37 0.38 3.1712:50:50.03 41:09:22.2 341 26.56 1.11 3.7112:50:50.16 41:09:01.5 311 25.67 0.82 4.0412:50:51.57 41:08:58.3 270 24.74 0.62 3.112:50:56.25 41:08:42.6 265 25.54 0.65 4.7412:50:52.22 41:08:35.6 268 24.35 0.48 3.5412:50:48.81 41:08:25.3 367 26.21 1.57 2.7212:50:57.74 41:08:19.7 252 25.35 0.65 4.2512:50:46.14 41:08:13.2 408 3.6112:50:49.62 41:08:04.5 363 24.84 1.28 5.0212:50:52.93 41:08:02.5 496 25.63 2.47 4.4612:50:53.86 41:07:56.1 310 23.35 2.61 3.3112:50:51.57 41:07:52.1 367 23.62 8.87 3.76

with scalelength

d �57 arcsec.Theregion we examinedincludes0.029of thelight of such

anexponential,which shouldthereforeinclude59 PNein thebrightestdecade.This numbercompareswell with the53actuallyfound,thoughtheagreementmaybesomewhatfortuitousgiventheincompletenessat thefaint end.

5.5.2 Rotation curve

In Fig 5.5 the line-of-sightvelocitiesof the 53 objectsin the majoraxisfield areplottedasfunction of radius,after subtractionof the systemicvelocity. Flat rotationis seenuntil thelastmeasuredpointatalmost5 scalelengths.For comparisonweoverplottheHI/CO rotationcurveof Sofue(1997),projectedinto theplaneof thesky. Consideringobjectsnearadistanceof 1 armin alongthe major axis the meanvelocity is 98

± � 9 � m , in agreementwith the gasrotationvelocityof 103

± � 9 � m at thatpoint.Theuncorrectedminoraxisdatahaveavelocitymeanof 329

± � 9 � m , consistentwith thesystemicvelocity, anda dispersionof 68

± � 9 � m .5.5.3 Velocity dispersion

Generally, the vertical structurein disksof spiral galaxiesis reasonablywell describedbyan isothermalsheetapproximation(van der Kruit & Searle1982; Bottema1993). In thismodel,theverticalvelocity dispersionis foundto follow anexponentialdeclinewith radiuswith scalelengthtwice that of the surfacedensity. With the additionalassumptionthat thedispersionellipsoid hasconstantaxis ratiosthroughoutthe disk, onefinds that the line-of-sightvelocitydispersionfollows thesamedecline,independentof thegalaxy’s inclination.

Figure5.6 shows thevelocity dispersionin binsof distancealongthemajoraxis. Sevenobjectswereeliminatedfrom thekinematicanalysisastheirbrightnessessuggestedthatthey

5.5 Results 59

FIGURE 5.4— Theluminosityfunctionofthe 64 objectsfor which magnitudescouldbe determined.The cutoff peakfor PNeisclearly defined. The objectsbrighter thanthiscutoff areprobablybrightHII regions.

areHII regions.Thecurveis theleast-squaresexponentialfit with centralvelocitydispersion111

± � 9 � m andscalelength

d" = 130arcsec.Thesearecloseto thepublishedvaluefor the

centralstellarvelocity dispersion(I J i*q I � ± � 9 � m ) obtainedfrom absorption-linespectra

(Mulder andvanDriel, 1993)andto twice thephotometricscalelength(J d � ICI h arcsec),

suggestingthattheisothermalsheetapproximationis reasonable.

5.5.4 Combined Kinematic Model

The binning in Fig 5.6 effectively assumesthat the PNeall lie closeto the major axis. Infact, they are locatedup to onearcminutefrom the axis, at azimuthsup to 45j , so a moresophisticatedapproachis required.We thereforeprojectedthePNeon to a thin disk of fixedinclination(35j ), giving # ¬. coordinates.Thenebulae’s line-of-sightvelocitiescanthenbecomparedwith amodelconsistingof athree-dimensionalisothermalsheetwith aflat rotationcurve. This modelhasfive parameters,namelythethreecomponentsof thecentralvelocitydispersion

4 F 4 ? 4 8 , thescalelength

d" , andtherotationamplitude.A maximumlikelihood

methodwasthenusedto fit themodel.Weadded12PNefrom theminoraxisfield (Table5.4)to helpconstrainthefit (two wereexcludedfrom thefit asprobableHII regions).

In practicethedatawerenot adequateto constrainall five parameters.Usingthecanon-ical relationship

4 6? � 4 68 [ J from the epicyclic approximation(Binney & Merrifield 1998,eq.11.18)andallowing

4 F [ 4 8 to vary over the range0.2 to 2.0, we found a robust maxi-mumlikelihoodsolutionwith scalelength

d" � I h|hZq � i arcsec,centralvelocitydispersion4 ©=ª/« � I�J i�q � i ± � 9 � m , andcircular rotationspeed¢ U � I �|� q I|I ± � 9 � m . Theseresults

areconsistentwith theHI rotationspeedat 1 arcminradius(180± � 9 � m ) andwith (twice)

thephotometricscalelength(57arcsec).


FIGURE 5.5— Line-of-sightvelocitiesofthe 53 objectsin the major axis field plot-ted asa function of distancealongthe axis.Thedottedline shows thegasrotationcurve,from Sofue(1997.)

It wasnot possibleto constraintheshapeof thevelocity ellipsoidwith thesedata– suchananalysiswould requireamorecompleteazimuthalcoverageof thegalaxy. However if weassumei � �³ý 4 F [ 4 8 ý I � i thenwe infer � � ý 4 8 ý ICI i ± � 9 � m at onephotometricscalelength,consistentwith the trendbetweenrotationspeedanddisk velocity dispersionfoundby Bottema(1993).

Thusfarwehaveignoredmeasurementerrorin thevelocities,whichwill tendto increasethemeasuredvelocitydispersion.This turnsout to bea smalleffect: allowing for a 1

4error

of 10± � 9 � m , thefitted dispersionbecomesapproximately3% smallerandthescalelength

is unchanged.

5.6 Conclusions

In this paperwe have demonstratedhow the kinematicsof the PN populationin a galaxycanbemeasuredby slitlessspectroscopy throughnarrow-bandfilterswith adual-beamspec-trograph.We comparedtwo possiblemodes:dispersed/undispersedimaging,in which a dis-persedO[III] imageis comparedto anundispersedH y image;andcounterdispersedimaging,in which two O[III] images,dispersedin oppositedirections,areanalysed.It turnsout thatthelattermethodis moreeffective: evidently theH y fluxesof faintPNearenot reliablyhighenoughto allow bothspectrallinesto beused.

Ourpilot experimentwasperformedonthelargenearbySabgalaxyM94. It hasrevealed

5.6 Conclusions 61

0 2 4 60

20

40

60

80

100

120

FIGURE 5.6— The dispersionin radialvelocitiescomputedbybinningtheradialve-locity measurements,togetherwith thebest-fit exponentialcurve.

aPN populationin thediskwhoserotationcurveremainsflat, andwhosevelocitydispersiondeclinesradially exponentially, consistentwith the predictionsof a simpleisothermalsheetmodel. PNeweredetectedout to five exponentialscalelengths,well beyond the reachofkinematicmeasurementsbasedonintegrated-lightabsorption-linespectroscopy. Thenumberof PNedetectedwasconsistentwith expectations.

Thepresentexperimentwaslimited to two fieldsin this largegalaxy. Completecoverageof the galaxyshouldyield around2000PNe,andwould allow a detailedkinematicmodelto befitted, includinga determinationof theaxisratio of thevelocityellipsoidfollowing thetechniqueof Gerssenetal. (1997).Obtainingsuchdatafor asmallsampleof nearbygalaxiesin just a few nightsof 4-m telescopetime is a practicalproposition.

Acknowledgements

TheWHT is operatedon the islandof La Palmaby theIsaacNewton Groupin theSpanishObservatorio del Roquede los Muchachosof the Instituto de Astrofisica de Canarias.Wewish to acknowledgethe help andsupportof the ING staff. We arealsograteful for someexcellent additionaldataprovided by ING astronomersin servicemode. The IRAF datareductionpackageis writtenandsupportedby theIRAF programminggroupat theNationalOpticalAstronomyObservatories(NOAO) in Tucson,Arizona.


ReferencesBinney, J.,Merrifield, M.R., 1998,“GalacticAstronomy”,PrincetonUniversityPress.BosmaA., vanderHulst J.M.,SullivanW.T., 1977,A&A, 57,373Bottema,R., 1993,A&A, 275,16Carollo,C.M., deZeeuw, P.T., vanderMarel,R.P., Danziger, I.J.,1995,ApJL, 441,25CiardulloR., JacobyG.H.,FordH.C.,Neil J.D.,1989,ApJ,339,53DouglasN., TaylorK, 1999,MNRAS 307,190Gerhard,O., Jeske,G.,Saglia,R.P., Bender, R., 1998,MNRAS, 295,197GerssenJ.,KuijkenK., Merrifield M.R., 1997,MNRAS 288,618Hui X., 1993,PASP, 105,1011Hui X., etal., 1993,ApJ,414,463JacobyG.H.,BranchD., CiardulloR., DaviesR.L., HarrisW.E.,PierceM.J.,PritchetC.J.,Tonry J.L.,

WelchD.L., 1992,PASP, 104,599MulderP.S.,1995,Ph.D.Thesis,GroningenMulderP.S.,vanDriel W., 1993,A&A, 272,63SchneiderS.E.,TerzianY., PurgathoferA., PerinottoM., 1983,ApJSS52,399Sofue,Y., 1997,PASJ49,17TremblayB., Merrit D., Williams T.B., 1995,ApJ,443,L5VanderKruit, P.C.,Searle,L., 1982,A&A, 110,61Vassiliadis& Wood,1994,ApJS92,125

planetary nebulae kinematics in m94 · planetary nebulae kinematics in m94 originally published as...

Documents