(1968) 139, 425-459. Photometry, Kinematics And

Home , Barred spiral galaxy, NGC 1313, NGC 3504, NGC 4027, NGC 55

Mon, Not, R, astr. Soc, (1968) 139, 425-459.

PHOTOMETRY, KINEMATICS AND DYNAMICS OF THE MAGELLANIC-TYPE BARRED SPIRAL GALAXY NGC 4027*

Gerard de Vaucouleurs, Antoinette de Vaucouleurs and Kenneth C, Freeman

(Received 1967 December 27)f

Summary Photometric and spectroscopic observations with the 36-in. and 82-in. reflectors are analysed to derive a mean rotation curve, total mass and mass- luminosity ratio of the Magellanic-type barred spiral NGC 4027. For an estimated distance A = 12*5 Mpc the adopted values are T = (13 ±3) x I°9»/b = 1*85 ±0*4 with By = ii*7o±o-o5, (B-V)t = +0*54, {U-B)t = —0-03. The mass is close to that of the Large Magellanic Cloud, but the mass- luminosity ratio is lower because of the relatively higher surface brightness of NGC 4027. The rotation curve is asymmetric with respect to the centre of the bar as previously observed in galaxies of the same type (LMC, NGC 55, 4631). A model consisting of a prolate spheroid (bar) offset from the centre of a larger oblate spheroid is described; it accounts qualitatively and quantita- tively for the residual velocity pattern (non-circular motions) observed in NGC 4027 and the Large Cloud. Detailed isophotometry of emission and absorption lines in the bar confirms the previously reported evidence for large scale gas streaming away from the centre and along the major axis of the bar, but it also reveals that, as theoreti- cally predicted, the mean motion of the stars near the minor axis of the bar is in a direction opposite to that of the gas and of the figure of the bar.

i. Introduction, Several late-type barred spiral galaxies similar to the Large Magellanic Cloud have been observed in detail with the B-spectrograph at the prime-focus of the 82-in. Struve reflector since i960. The initial objective was to determine whether the peculiar, asymmetric rotation curve first observed in the Large Cloud (Kerr & de Vaucouleurs 1955, 1956; de Vaucouleurs 1960a; Feast, Thackeray & Wesselink 1961 ; McGee & Milton 1966) and later in NGC 55 (de Vaucouleurs 1961; Epstein 1964; Robinson & van Damme 1964, 1966) is a general phenomenon, characteristic of this galaxy type and reflecting its structural asymmetry (de Vaucouleurs 1954, 1955, 1960a). The second objective was to obtain additional information on the large-scale gas streaming motions in the bars first detected in NGC 4631 (de Vaucouleurs & de Vaucouleurs 1963a) and later in NGC 4027 and NGC 7741 (de Vaucouleurs & de Vaucouleurs 1963b; de Vaucouleurs 1964). The final objective is to provide tests for the dynamical models of barred spiral galaxies developed in recent years (Freeman 1966a, b), and in particular to check certain theoretical predictions on the relative peculiar motions of stars and gas (Freeman & de Vaucouleurs 1966). We report here on our analysis of NGC 4027 which, as explained previously (de Vaucouleurs 1964), is one of the very few objects suitably orientated and large * Contributions from the McDonald Observatory, University of Texas, No. 424. f Received in original form 1967 September 16.

© Royal Astronomical Society • Provided by the NASA Astrophysics Data System 19 68MNRAS.139. .425D o # well-known interactingpairNGC4038-39(Burbidgeetal.1966)at41'andhasa 426 GerarddeVaucouleursetahVol.139 Appendix II).Fig.1isaphotographtaken(inpoorseeing)attheCassegrainfocus faint dwarfMagellanicirregularcompanionNGC4027-Aat4'oinp.a.190(see isophotometer (deVaucouleurs,Griboval&White1965)areshowninFig.2. bar. Uncalibrateddensitycontoursofthe82-in.platetracedwithGriboval of thisgalaxyarelistedinTableI.Itformsaprobablyphysicaltripletwiththe enough tobeobservedinsomedetailwiththe82-in.reflector.Themainelements of the82-in.reflectorandshowsinnerregions,inparticularshortbright A betterphotograph(Fig.3)takenbyH.D.AbieswiththeKron-Lallemand faint outerwhorl.Onbothphotographstheasymmetricspiralstructure,dominated Vaucouleurs 1960a,1961,1964)isclearlyinevidence. However,itsstageisslightly by themajortrailingarmandcharacteristicofmagellanic-typespirals(de Electronic camera(Kron&Papiashvili1966)attachedtothe40-in.reflectorof was investigatedphotographicallyin1940by F. S.Patterson(nowMrsJones) in anunpublishedRadcliffeCollegeDissertation (1941).Throughthecourtesyof assign toNGC4027theclassificationSB{s)dor dminagreementwiththeReference U.S. NavalObservatoryFlagstaffStationshowsdetailsofthespiralpatternand grid (Patterson1940); isophotes werederivedbylinearinterpolation between Mrs Joneswewereabletouseherdataconsisting ofmagnitudedifferences ‘ earlier’thantheLargeCloud.Fromastudy ofmorphologyandcolours,we Catalogue (deVaucouleurs&deVaucoulers1964). smoothing andplotting programfortheCDC1604computerwasprepared by adjacent squareswithout smoothingandwitha9-pointgaussiansmoothing. The Fig. 4.Themagnitudes weremeasuredatregularintervalsof9"7ina rectangular ÙM =m—m§,(mocentral magnitude)topreparetheisophotemap shownin © Royal Astronomical Society • Provided by theNASA Astrophysics Data System * ReferenceCatalogueofBrightGalaxies(1964). 2. Integratedmagnitudeandcolours.Theluminosity distributioninNGC4027 Apparent photographicmodulus New galacticcoordinates* Equatorial coordinates(1950)* Average surfacebrightness* Photographic axisratio* Revised type* Distance inmegaparsecs Apparent colourindices Microphotometric diameter Reduced (faceon)diameter* Corrected modulus Group membership Supergalactic coordinates* Photometric effectiveaxes Microphotometric axisratio Standard photographicdiameter* Inclination Standard apparentmagnitude* Elements ofNGC4027 Table I (B-V)(o) =0*67(U-B)(o)-0*03 mo-M =30*5+0*5(A0*35mag.) dm!Dm -0*75 m —M=30*85 ,/ B\o) =13*44(wc'13-63) D{o) =2*35±oi8*5kpc B{6) —11*90(trie=12*09) d/D =0*775±0*05(m.e.) Dm -3*9=14kpc 11o0 2a =T*32bei'*o e Z =286*38b+41*94 hm0 D =2'*6±o'*2(m.e.)9*4kpc 0 L =i32°-8B—17°-9 A =i2*5±2*5 a =n57*o8—1859' i =40±2(m.e.) Pair withNGC4038-39 SB(s)dm 19 68MNRAS.139. .425D © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem [Facing page426

Fig. i. iVGC 4027 photographed at Cassegrainian focus of 8z-in. Struve reflector (77-in. diaphragm)y 1963 March 1 exposure 2 h 24 m, 103 a-O, no filter, poor seeing. Fig. 3. NGC 4.027 electronograph by H. D. Abies with the Kron-Lallemand camera attached to the 40-in. Ritchey-Chretien reflector of the U.S. Naval Observatory, Flagstaff Station. U.S. Navy Photograph.

© Royal Astronomical Society • Provided by the NASA Astrophysics Data System 19 68MNRAS.139. .425D © Royal Astronomical Society No. 4,1968 Fig. 2.Uncalibrateddensity contoursof82-in.photographNGC4027traced withthe Griboval isophotometer. The barredspiralgalaxyNGC4027 Provided bythe NASA Astrophysics Data System 427 19 68MNRAS.139. .425D 428 GerarddeVaucouleursetal.Vol.139 effective axesare2^=zbi'o. derived inrelativeunitsbyplanimetryoftheisophotesisshownFig.6.The The integratedluminositydistribution Mr D.Wells.Themeanluminosityprofiles1(a),1(b),I(r*)aregiveninFig.5. for whichV=14*22,B-V =+0*63,U-B—0*03(in). e 2 function shownininsetcorrespondtoabout15"resolution. Patter son-Jones.InnermostisophoteisforlogI=—o-6,outercontour—2-7, level spacingAlogI=o-i;unitof19*12(B)magsec~.Weightssmoothing Fig. 4.SmoothedisophotesofNGC4027fromthephotographicphotometryF.S. © Royal Astronomical Society • Provided by theNASA Astrophysics Data System * Magnitudesandcolours in threelargestaperturesarecorrectedfortheeffect ofstarA A =zr o'*20 0*50 0*52 2*68* 2*50* 2*30* i *08 i *07 00 Magnitudes andcoloursofNGC4027 L(Am) =Jio-o-4AmdS(Am) 11*92 12*87 II-I5 ii •10 11*87 12*78 14*06 II *21 11*37 V (•Am Table II 0*497 0*525 0*527 o*54 0*539 0*501 0*533 0*528 0*542 B-V — 0*129 + 0*023 -0*074 + 0*030 -0*03 — 0*011 + 0*005 — 0*030 — 0*062 U-B 19 68MNRAS.139. .425D photographic magnitudescaleisgivenby where BisthemagnitudemeasuredthroughanapertureA=ar.Thethree the McDonald36-inchreflectorandlistedinTableII.ThezeropointKof with No. 4,1968ThebarredspiralgalaxyNGC429 total (asymptotic)magnitude11*69.Allowingfortheeffectofasecondfieldstar larger aperturesgiveB(A=a'5)1179forwhichA(r*T25)0*915anda oí 16(notmeasured)weadopt comparison withphotoelectricmagnitudesinthe£/,fi,Vsystemmeasured brightness withinthis circle isp,/*=(¿^+075)—5logD*—2*5 tt=13*4 colours. galactic extinctionand internal absorptionadduptoabout—o*o8mag. inboth and asymmetryaremore consistentwithSdorSm.Correctionsfor redshift, The colour-colourrelationshipisconsistentwith typeScorSd,butthestructure r e 2 9 photometry, a,alongmajoraods\b>minoraxis,(r*)equivalent profile.UnitofI=19*12 (jB) magsec~. Fig. 5.MeanphotographicluminosityprofilesofNGC 4027derivedfromF.S.Jones © Royal Astronomical Society • Provided by theNASA Astrophysics Data System The zero-pointcalibrationofthephotographicisophoteswasderivedby The effectiveequivalent diameterisD*=1T3andtheaverage surface e ,4Am B =K—z-$log(ztt)Jio“°rdr r Bt =1170±0*05(m.e.) (B-V)t =+0-54 (U-B)t =—0*03. 19 68MNRAS.139. .425D -2 4027 itselfaspossible distance indicators.Fromanunpublishedstudy ofthe Vaucouleurs 1958,1966). Thisleavesonlythemagnitudeanddiameter ofNGC the non-linearityand anisotropy ofthevelocityfieldatsmallvelocities (de magnitudes anddiametersofthefivedominant members(N4038-39excluded). survey ofnearbygroups wederivefxo=30-53fromD{6)andfi 30-84 from grouping andNGC4038-39istoopeculiar an objecttobeusedfordistance list. Forthepresentweregardonlytriplet NGC4027,4038-39asaphysical of thisgroupingdidnotappearsubstantiated and itwasrejectedfromthefinal a fewotherswasconsideredandtentativemodulus /x=30-3derivedfromapparent because itisnotamemberofanyrecognizedgroup.Duringthepreparation estimates. Norcanwetrusttheradialvelocities asdistanceindicatorsbecauseof However, upondetailedanalysisofthepresumed membershipthephysicalreality group possiblyincludingNGC3956,3981,4027, 4038-39,4050,4094andperhaps systematic surveyofnearbygroups(deVaucouleurs 1967)ahypotheticalNGC4038 43ô GerarddeVaucouleursetal.Vol.139 distances ofallgalaxies intheReferenceCatalogueandonsame scale asthe mag. min.CorrespondingvaluesforNGC1313,typeSB(s)d,andtheLarge Cloud, SB(s)m,arefie=12-50and13-80respectively(deVaucouleurs1960b, 1963)- 2 within theeffectiveequivalentradiusr*=o'56. and surfacebrightnesslevel¡¿{magsec*).Halfthetotalphotographicluminosityisemitted Fig. 6.IntegratedequivalentluminosityprofilesofNGC4027vsradiusr* e © Royal Astronomical Society • Provided by theNASA Astrophysics Data System 3. Distancemodulus.ItisdifficulttoestimatethedistancemodulusofNGC4027 19 68MNRAS.139. .425D # ma-2 öor 12 n 0 40-in. and82-in.photographstheapproximateseeing-correcteddiameteris the correspondingfigureforLargeCloud,viz.i)=5°-85*5kpcif/xo187 plane; B\o) —13*44g*min.isaboveaverageforitstype(14*5)and,inparticular, (de Vaucouleurs1960a). with anestimateduncertaintyof±0-5mag.WewilladopthereA=12*52-5Mpc very nearlyalongtheminoraxisofimage and thereisnovelocitycomponent the baraxiswehaveadoptedforitsposition angle Z>i/=75°(iftheexactvalue (¿Wra —3/4)>to15kpcattheadopteddistance;correspondingfiguresare B(o), mandJ5'(o).Thegalacticextinctioncomputedthroughtheformulagiven the tangentplane,andpositionangle^>2/ofbaraxis; Vaucouleurs 1964): system oftheMagellanic-typethreeanglesshowninFig.7mustbeknown(de exceeds thatoftheLargeCloud(14*2). luminosity ofNGC4027isconsistentwiththefactthatitsmeansurfacebrightness agreement withthevaluesforNGC1313{Mt=—187if/x28-5).Thehigher (i960) dataforthisgalaxytype. d~2\ thecorrespondinglineardiameterof120pcisconsistentwithSersic’s and 1"=60pc,buttheneedforabetterdistancedeterminationisobvious. tion laneintheconcavity ofthemainspiralarmandanotherseenin projection galaxy. Ifsoweshould expect andobservationsconfirmthatthemain armorthe in thelineofsightduetopurerotation;any radialvelocityresidualfromthe is different,pQwillbechangedbythesameamount, butnotQq=py—po)- normal tothebaraxisYY'.Theprojectionofthisangleintangentplaneis Large Cloud. in (deVaucouleurs1967)is=i*4X0*250*35mag.;thus No. 4,1968ThebarredspiralgalaxyNGC4027431 against theeastendof bar,weconcludethattheeastsideisnear sideofthe systemic velocitymustbeduetoradialstreaming ornon-circularmotions. and 0^90°,i.e.thelineofnodesisperpendicular tothebaraxis.Thus,is North sideisrecedingin therotation. #o withtan6=0oseci. io' to14'=1218kpcforNGC1313,and15the e c © Royal Astronomical Society • Provided by theNASA Astrophysics Data System 0 As acheckwenotethat: 4. Spaceorientation.Inordertointerprettherotationcurveofanasymmetric (1) ThelargestH11regionsinthemainspiralarmsarebarelyresolvedon (3) Themaximumdetectablediameteronthephotographsis2tf~3'5to4' (4) TheabsolutemagnitudeMt{B)=117—30-85—19*15isalsoinfair (2) TheeffectivediameterZV*=47kpcagreesverywellwith (3) theazimuthalangledbetweenplaneofvisionZCOandXCZ (2) thepositionangle^>0oflinenodesequatorialplaneXCYwith (1) theinclinationitolineofsight,CO,normal,CZ,equatorial The veryfavourableorientationofNGC4027 results fromthefactthat¿—45 From measurementsofphotographsandsettings ofthespectrographslitalong From thepatternofdark matter(Figs1and3),inparticularthestrong absorp- m /x =30-85and/xo30-5, 19 68MNRAS.139. .425D o 0l o o o0 0 (P~Po) givespo=346 ±5(m.e.)or0=py-po-9* the linearpartofvelocitycurve(Section6). Aleast-squaresfitofthegradients the axisratiob¡a=0*777ori40°. the lineofnodeswithrespecttobaraxis0o =84or086°,andthesecond the principalaxesandradiiofgyrationarederived. Thefirstgivethedirectionof moments ofthebrightnessdistributionin outer regions(/9O9o ±2°, i=40. 0 z 19 68MNRAS.139. .425D velocity, foreachplatefromHaandÀ6584onlyarealsogiveninthetable.These lines inthebar;however,Haand[N11]À6584arealmostalwayspresent. graph andthe‘red’gratingforanaggregateexposuretimeof45h.AKodak common zeropointinthecentreCofbar.ThevaluesF,systemic mapped inFig.8,wherealldifferentialvelocitiesAFo=V—Varereducedtoa velocity ofthenightskylines.Additionaldetailsreductionprocedurewill the rangeÀÀ3611-6717;appropriatecorrectionsarefinallymadeforanyresidual so severalspectraareunderexposedandonlyafewshowmeasurableabsorption of NGC4027weresecuredineightdifferentpositionangleswiththeBSpectro- Peak Observatoryequippedwithaspeciallybuiltupperstagefilmholderproviding Figs 2and8. at 68°Ffor6-7min.toachievemaximumefficiencywasusedthroughout.Even No. 4,1968ThebarredspiralgalaxyNGC\oz^]433 only ontheweightedmeanvelocitiesofHaandÀ6584asfistedinTableIV width wasabout13Â.Theoverallangularresolutionlimitintheplaneofimage be foundinourlistofabout100newredshiftsmeasuredwiththeBspectrograph means ofaspecialcomputerprogramwrittenbyMrG.MalikfortheCDC1604 precise ordinatesalongthelines.Thereadingswerereducedtowavelengthsby Hy; theGbandwasnotmeasurable.Therotationanalysiswas,therefore,based in absorption,areweakorill-defined.Theemissionlines[O11]À3727,Hß, is 7"x5"asshowninFig.8. in bothwavelengthandangulardistancesalongtheslit,readingsweretakenevery and 6600computersoftheUniversityTexas.Thisprogramallowsforalinear Ha, [Nil]ÀÀ6548,6584,[S11]6717,6731.TheabsorptionfinesareK,H,HS, a widthof25ncorrespondingtoabout8ÂatHa.Theprojectedspectrographslit (de Vaucouleurs&de1967). dispersion formulaisafifthorderpolynomialfitofthe28comparisonlinescovering dependence vswavelengthofthelineinclinationandcurvaturecoefficients; 50 fxalongthespectrumlineswithaprojectedmeasuringslitlengthof¡jland i03a-F emulsiongenerallypre-flashedtooptimumdensityanddevelopedinD19 c c 28 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System All filmsweremeasuredwiththedigitizedGrantprofilecomparatorofKitt Table IIIliststheobservationaldataandlocationsofslitareshownin The measuredvelocitiesaregiveninAppendixI.Manyofthelines,especially 5. Radialvelocities.Atotalofeightlong-slitandfourshort-slitspectrograms In ordertopreservethemaximumdetailcompatiblewithresolutionlimits Film No. B 972 1366 1365 1361 1358 1356 1354 980 989 978 976 974 1966 March28 1966 March27 1966 March20 1966 March17 1966 March15 1962 May 1966 March18 1962 May 1962 May 1962 May 1962 May 1962 April Date (U.T.) 29 ii 4 5 3 2 Spectrograms Table III (hm) Exp. 4 00 4 55 2 00 2 15 3 o° 5 00 4 iS 5 00 5 30 6 00 i 00 1 53 (deg) p.a. 145 no no 130 165 60 75 60 60 75 30 o Slit length (sec) 290 290 290 290 290 290 290 290 103 103 103 103 19 68MNRAS.139. .425D -1 434 GerarddeVaucouleursetal.Vol.139 Vaucouleurs 1962)based ononeplate(threeabsorptionlines)onlyisF = +1844± may becomparedwiththeweightedmeansystemic velocityfromallplatesand lines (includingabsorptionlines) 88 (m.e.). The onlypreviousMcDonald velocityofNGC4027,V=+2000km s, (Struve 1940) wasapreliminary estimateoflowweight.Anothervelocity(Mayall &de © Royal Astronomical Society • Provided by theNASA Astrophysics Data System centre ofbar.Resolutionrectangledefinedbyspectrograph andmeasuringslitsiss'ix Fig. 8.Meanobserveddifferentialradialvelocities AVo =V—V(Ha,A6584)from c =+1671±10(m.e.)(12plates). C N. 19 68MNRAS.139. .425D No. 4,1968ThebarredspiralgalaxyNGC4027 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System * Includesalso A6717-6731, N +43**5 NE +36"-2 SW C o NE +6o"-9 S - SW -26-1 C o W o B 976,P=75°,1598* B 1358,£=60°,1583 C B 972,p= B 978,p=30,1689 C + 36"-3 — 29*0 x -36-3 21 *8 21 *8 29*0 29*0 21 *8 21 ’8 29*0 21*8 14*5 24*7 i4*5 39*i 54*3 i4*5 14*5 18*9 21-8 14*5 ii -6 10*2 17*4 i4*5 7*3 o 7*3 7*3 7*3 4*4 o 7*3 4*4 7*3 Weighted meandifferentialvelocitiesfromHaandA6584 =1779 +112 + 179 + 131 + XI3 +196 — IOI -113 AF + 57 + 13 — 21 + 80 + 92 + 98 -84 -87 + 77 + 45 + 46 + 44 “53 “94 -64 +10 + 17 + 67 + 38 + 54 + 83 “53 + 29 + 14 + 31 + 90 + 30 -9 -8 + 4 o o o o 2 2 2i 2Í li li li 2Í 1 li I 2 li 2 li I li li li I ii I I li li li ii if w i i ! * i i I i i I i Table IV >/ NW —36*3 0 C o W -21*8 NW ~39*5 SE +6*3 C o E +36^3 SE N o 3 B 1356,£=no,1695 C B 974,p=165,1672 B 980,p=130°,1725 C C B 989,£=75 + 43**5 + 55"*o X “65*3 29*0 21*8 29*0 21 ’8 36*3 21 *8 14*5 47*8 29*0 40*5 14*5 21 *8 29*0 21 »8 24*6 26*1 29*0 14*5 33*3 43*5 14*5 36*3 14*5 14*5 17*4 IO-I ii *6 i8*8 50-8 7*3 7*3 7*3 7*3 o 7*3 7*3 4*3 2*9 =1565 C + 146 + 200 + 147 -131 + 128 + 142 + 235 + 121 “137 -158 + 172 “44 “39 “74 -46 “55 + 93 AF “43 + 39 + 21 -30 + 43 -70 — 62 “25 + 73 + 45 “56 + 69 “49 + 93 “3i -84 -15 + 86 + 19 “48 “25 + 90 + 43 “3i + 43 -8 + 8 + 8 o o o o I ii ii li ii li li li I ii ii li li li li ii ii li I i ii I ii I I li ii ii ii li X li w i i i i i i i i i 4 i i i f i i i 435 19 68MNRAS.139. .425D 0 _1-1 6 -1_1 -1 -1 436 GerarddeVaucouleursetal.Vol.139 where 7*0isinsecondsofarcarelistedTableVtogetherwithther.m.s.residual analysed forgeneralrotation,i.e.neglectingthedeparturesfromcircularmotions in theequation seven positionanglesusingonlythethreepointsnearestcentreoneitherside discussed inSections8and9. to findthedirectionoflinenodespo=166±5alongwhichmaximum of thebar,andexcludingcentralpointinbar.ThecoefficientsAB gradient isSi=5*15+o*6okmsarcsec.For¿=40°thecorresponding figure forthecentralregionsofLargeCloud(deVaucouleurs1960a;Feast the rotationperiodisP=47X10years.Thisabouthalfcorresponding angular velocityisil=Bi/sini8*okmsarcsec130kpcand for unitweightcri.Theaverageplateresidual<|^41>=35*okmscorrespondsto 2*3 /xonthefilm.ThegradientBwasthenfittedthroughequation et al.1961). the velocityatcentreofbar,Fo(ro=°)-However,thissinglevalueFo(o) is subjecttoaccidentalerror(ontheorderof±50kms)anddoesnotconstitute We have,therefore,referredthedifferentialvelocities inagivenpositionangleto be biasedbytheeffectsofnon-circularmotions farfromthebar(Sections8and9). a well-definedzeropoint.Ontheotherhand,constantAinequation(1)may measured pointsinthatpositionangle,excluding thecenterofbar;thus the centralvelocityderivedbylinearinterpolation betweenthetwoinnermost component intheequatorialplanethrough relations(Kerr&deVaucouleurs AF =AFo—. where 7*0,0o>AFoarethe observedquantitiesandr,0,Fthecorresponding variables in theequatorialplaneof thegalaxy,and/=sec0coseci. ^ss)- r r © Royal Astronomical Society • Provided by theNASA Astrophysics Data System 6. Rotationcurve.ThedifferentialvelocitiesAFomappedinFig.8werefirst The slopeofthelinearpartrotationcurvewasdeterminedforeach The observeddifferentialvelocitiesAFoare,asexplainedabove,relativeto Each reduceddifferentialvelocityAFwasthen transformedtoarotational r — o o 0 110 °44*3 o 165 +8-5 130 +27-7 p.a. A 75° +37*0 60 +75*3 30 -40*6 o° —ii*5 tan d=doseci (3) F =AFosec9coseci = AFo/.(5) r r =rosec0/sec6q, (4) 0 B =5*15cos(£—166) B =cos(p—po) 1 0 23*9 -5*94i 27*8 2*818 m.e. B 10*7 -3*713 13*8 1-093 10-i 4*684 19-0 3*231 AFo =^+5r(1) 0 ± o•605 7*2 -4*342 Linear gradients Table V 0*462 17*9 0*728 28*7 o*66i 52*7 0*882 26*2 1*302 32*4 1*128 47*4 i*779 55*7 m.e. ai (2) 19 68MNRAS.139. .425D to arotationcurveasymmetricaboutthecentreofbarasobservedpreviously but conspicuous‘irregularities’arepresentonthenorthside,i.e.sideof p. 270)arelistedinTableVI.Theoverlappingweightedmeansofgroupsfive No. 4,1968ThebarredspiralgalaxyNGC4027437 in theLargeCloud(Kerr&deVaucouleurs1955,1956;Feastetal.1961), main spiralarm.Further,themaximumvelocityislargeronnorthside,leading of thebar(75<0o<255).Therotationcurveisfairlyregularonsouthside, successive pointsaregiveninTableVIIandshownFig.9;risnegativesouth 4631 (deVaucouleurs&de1963a;Roberts1968). NGC 55(deVaucouleurs1961;Robinson&vanDamme1964,1966)and N +S-I53°'S the so-called‘radiocentre’in21cmanalysis oftheLargeCloud),mean points inTableVIIwerefittedthroughacubic The centreofsymmetryC'thiscurveisat in thesamesense. (i*5 kpc)andNGC4631 (0*85kpc),butisstillofthesameordermagnitude and - © Royal Astronomical Society • Provided by theNASA Astrophysics Data System +14-8 340-7 + 14-5o-o + 12*053*5 + 21*70*0 + 20-753-5 +16-i 42-4 + 24*142*4 + 22*2340*7 + 29*00*0 + 32-242-4 + 29-253-5 Differential velocitiesprojectedontoequatorialplaneontheassumptionofcircularorbits + 43-5o-o + 40-242-4 + 36-2o-o + 46-5S35 + 50*70*0 + 64-5S3'5 + 65*20*0 + 72*453*5 The valuesofr,6,VandtotalweightW=wjf(cf.deVaucouleurs1960a, r + 7*20-0 + 7*4340-7 + 8-042*4 r" d To determineacentreofsymmetrytherotation curve(correspondingto The displacementisapparently lessthanintheLargeCloud(o*8kpc), NGC 55 23 V =6*029r+o-0229r—o*ooi58r(r") r _1 V(C') =+29kms. + 2060*910+117 + 2270*287+154 + 3270*287+206 + 1330*474+37 + 1070*607—i16 + 2210*321+95 + 2470*237+110 1 + 1880*096—32 + 3580*237+193 + 2450*237+69 + 2510*096+80 + 2330*765(+172) + 1780*191(221) + 2680*321(215) r(C') =+4"*8±2"*8(m.e.)0*29±0*17kpc. + 130*574-18 + 670*964+23 + 700*964—17 + 190*712—30 + 660*455+2 + 670*321—89 V WO-C + 120*964—161 + 120*964—163 + 67o•643—92 r ±o-88o ±0*0198±0*00062(m.e.) (6) Table VI 0 S -5*1233*5 -13-8 233*5 — 14*8160*7 — 14*5i8o*o — 2i*7i8o*o —i6*i 222*4 — 24*1222*4 — 22*2160*7 — 29*0i8o*o -31-0 233-5 — 29*7160*7 — 32*2i8o*o — 36*2222*4 — 40*2222*4 -43*5 i8o*o — 8*o222*4 — 7*4160*7 — 7*2i8o*o r" 6 22 *5233-5 -120 0*574“45 — 1260*712—42 — 2110*712—101 -144 0*382-56 — 115o•964+2 -181 0*593-63 -167 0*593-65 -16 0*574+Ï4 + 640*607+143 — 190*237+27 -64 0*303-21 -67 0*964-25 — 860*964+18 — 720*482+6 — 870*910+18 -59 0*910+58 + 130*382+131 -68 0*321+45 — 610*321+27 Vr WO-C 19 68MNRAS.139. .425D 200 100 100- 43« © Royal Astronomical Society ■60' spirals. Largewaveonnorthsidereflectsnon-circularmotionsdiscussedinSection8. a pointC'displacedfromcentreCofbartowardmajorarminmannertypicalMagellanic Fig. 9.MeanrotationvelocitiesofNGC4027.Thebestfittingcubicissymmetricabout South NGC 4027 5-point runningmeans Rotation velocities /?=0^30°, 130°,165° N +7-5+6040 8 4-6o*i +181 55 + 56*8+178 54 4-51*2 +109 63 4-45*5 +82 56 + 12*0+10953 + 40*7+59 58 4-39*7 +79 77 + 15-2+16355 + 13*2+11952 4-38*8 +7480 +18*3 +18545 + 16-2+16354 4-34*6 +10585 4-32*5 +1055 + 26*0+16669 + 24*2+14846 + 23*3+17562 + 20*6+18253 r' p.e. r + 9*9+7135 \ I v—«V -30' Mean rotationvelocitiesinequatorialplane • Geratd deVaucouleursetaL i o (5-point runningmeans) Provided bythe NASA Astrophysics Data System Table VII / C / / / S -8*3-6325 •/ -36*4 -115 53 ““33 *4-1035° — 29*0—i1748 —18*7 —6741 -14*3 -6151 — 12*7—4048 -io*i -7519 -30*8 -9139 — 24*1—12131 -19*6 -7545 -16*9 -7145 — 27*6—10946 — 26*0—11635 ~2i*3 -12432 r* p.e. r / / •• J \IL / +30 / • / • 3 kpc Vol. 139 \ r +60 Nor^h 19 68MNRAS.139. .425D au2ear_1 4 9 -1 #9 42-3 -1 2 15-16 o2 curve givethefollowingvaluesofr.m.s.errorforunitweight No. 4,1968ThebarredspiralgalaxyNGC4027439 or inpracticalunitsof^>0 =*^0(*0(y) momentum ofaflatgalaxy by numericalintegrationasimpleapproximate expressionforthetotalangular formula hasbeenderivedbyBrandt(i960)and fromitBrosche(1963)computed Here (r,Vm)arethecoordinates ofthemaximumrotationcurve givenby southern halfalonegivesa=4*9x10,b1*95, and^=8*8x10solarmasses. because oftheirregularitiesnorthernhalf oftherotationcurve.Afit regions, butthisvalueisaffectedbythenorth-sideirregularity. The slope3*9isonlyhalfthevaluecosec¿=8*ofoundaboveforinner linear fitofthepointsinFig.9wasmadeasfollows of ±45kmsasindicatedbypointsonthesouthside. on thenorthsideofgalaxyinadditiontoobservationalerrorsorder ajbG =(65±i*o)x10solarmasses.However, thefitisratherpoormainly and givesa=(2*9±1*3)xio(km/s)(kpc),b=1*4+0*4J( about itscentreofsymmetryC'(Fig.10)maybefittedbytheformula(Lohmann where F^150kms,give with thecorrespondingamplitudesforNGC55,4631,andLarge probably abetterapproximationtotheangularvelocityofbar,£í=2tt¡P implies thatconst.,oradensitypceP~. (de Vaucouleurs1959): 3'24X 10“s,correspondingtotherotationperiodP=6ox10years. Cloud if¿=27.Since,foragivenmodel,themassis^ocFP,thisresult 1954) w r 2z -1 19 = 3(vmlrm),bzlr orr~i-ikpc,v120kmsandp/po-5x 10. m m _1 -1 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System The residualsoftheindividualpoints(TableVI)fromthissmoothinterpolation We concludethatnon-circularmotionsoftheorder±65kmsarepresent Because auniformlyrotatingframeofreferencewillbeneededlater,simple Angular momentum.Themass-distributionfunction correspondingtotheL-B (2) Lohmann-Bottlingerapproximation.Themeanrotationcurvereflected The totalamplitudeofthevelocitycurve,about300kms,agreesclosely The intermediatevalue6*ogivenbytheslopeofcubicatoriginis (1) Pointmassapproximation.Theoutermostmeanpointsnearkpc, 7. Rotationalmass.Asusualthemassmaybecomputedbyvariousmethods 132 3-1 pjpo =2-3xiorz% (rinkpc,vkms)(9b) w m 29 M =rVIGi6x10solarmasses.(8) r 1 -1 north side:cri(N)=81kms”. south side:^(S)=46kms # V =—i*o-f39r(r")(7) 2 p =2-yVrr^lG(9a) m F2 =ar^i+br^)(9) r ±7*o ±2*8(m.e.) 440 Gerard de Vaucouleurs et al. Vol. 139

Fig. 10. Mean rotation velocities of NGC 402J reflected about the centre of symmetry C'. A and B are the two overall mean points used to fit the thin disk and oblate spheroid models. The theoretical rotation curves computed for the various models discussed in text are shown. The straight line has the slope Ü = 5*3 km s-1 arcsec-1 used as reference in Fig. 13.

This is only one half to one quarter of the values for M33, NGC 3504 or the Large Cloud computed by Brosche from a variety of sources. However, p depends critically on rm and both of which are poorly determined as indicated by the computed mean errors in a and b. We can only conclude that/>/po is of the expected order of magnitude 1020). (3) Thin disk model. A simple thin disk model (Wyse & Mayall 1942) is one in which the superficial mass density a(r) is everywhere proportional to the pro- jected light density /(r), i.e. the mass-luminosity ratio / = o(r)II(r) is assumed to be a constant independent of r (Schwarzschild 1954). If, then, the observed mean luminosity distribution I{r) is represented by

I{r) = ^an(i-^ (10) and the mass density by

An a(r) = YJ (ï-^j (11)

where An = fani the thin disk model gives for a linear density law cjn = 1— r/Rn,

2 Vo (r) = 59-0 ¿ r £ ang(rlRn) (12)

© Royal Astronomical Society • Provided by the NASA Astrophysics Data System 19 68MNRAS.139. .425D 10 2 2 where isthefunctionM(a),m(ß)ofWyse&Mayall.Afitobserved in solarunitsifA,Rareparsecsanda,Apersquareparsec. mean rotationcurvethroughequation(12)gives/andthetotalmass luminosity profilearegiveninTableVIII.Ther.m.s.deviationofthefitis±o*oi No. 4,1968ThebarredspiralgalaxyNGC4027441 or 4-2percent(26points). per squareminute(observed)or2*iixiocorrectedforgalacticextinction {Ab =0-35mag.).Thefollowingtwomeanpointsoftherotationcurvewereused and thefitthroughequation(12)gave,forA=12*5Mpc, n The relativemeanerrors€fjfderivedfromthe(AV/V)invelocities (A, i,/,etc.).Theadoptedmeanmass-luminosityratioisfß=M/S^b1*89 (1 ±0*31)andgivesthroughequation(13) only correspondtotheweights£zvanddonotincludeerrorsfromothersources where m=(x+y)lazlc.Followingaprocedure usedearlierfortheLarge of theform with n=iandc/aJ.Theprecisionofthe data andthepresenceofdepartures from purerotation(Sections8and9)doesnot warrantmoreelaboratemodels. several inhomogeneousoblatespheroids(Perek1948,1962)havingdensitylaws Each ofthemeanpointsgivesanequation form. (de Vaucouleurs&de1963a)weadopt asimple,two-spheroidmodel Cloud (Kerr&deVaucouleurs1956; 1960a)andNGC4631 where 01,02aretheequatorial radiiofthespheroidsandpic,p2ctheir central densities. Then 4 ioö 3700319012403904809020430820045153 w R o'-io'•2o'*4o'-6o'-8i'-oi'*2i'*4i'*6i'-82'*i9 10 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System n n 12345678910ii The coefficientsofanapproximationby11linearcomponentsthemean The unitofIdefinedby/=1atrocorrespondsto1*53x10solarunits (4) Compositeoblatespheroidmodel.Amorerealisticmodelinvolvesoneor c -1w = 111-1w = (B) (Vf)=102*9kms(Y,8*26)ato'*69 (A) (Vf)=123*5ks(Yj10*00)ato'*33 / Y ag(r/Rn)0-2073o•1160 tflf n Coefficients oflinearcomponentsluminosityprofile 10 Jt =(1*28±0*40)x10solarmasses. 2 Vlr =ßociaipic+oiza2p2c (14) r 3 J( =(«lpic+ß2P2c). (15) 2n p =(i-m) c 0-35 2-31 aR2 = W'En(X3) 8tt 75 Table VIII A B 0-52 1-38 1 Mean 0-3- 1*89 19 68MNRAS.139. .425D ea 44^ GerarddeVaucouleursetalVol.139 values ofaâi=\and£wereused(values#2/^1>ldtonegativedensities from equation(14)whentwomeanvelocitypointsonlyareavailable,trial torial plane;itcanbecomputedfromPerek’stables(1948,1950)(seealsograph points aregiveninTableIX. in onecomponent).Elementsoftwospheroidmodelsfittingthesamemeanvelocity in deVaucouleurs1960a).Since02/^1isnotknownaprioriandcannotbederived The coefficientadependsonlyon(r/a)forgivennandc/apointsintheequa- within aneffectiveradiusrô'y+oTincloseagreementwiththephotometric that theSchwarzschildapproximationofaconstantmass-luminosityratioisnot value (TableI)a—o'65.Thisresultandthesmallrangeof<7//inFig.12suggest of thetotalmassinsideradiusrshowthathalfmodelsis following wewillusesymmetricmodelsmainly asaframeofreferenceagainst with theobservedmeanvelocitycurve.Itis ofinterestthatbothmodelsgive mass assummarizedin Table X. which thedeparturesfrompurerotationcanbe analysed. a badone.AsimilarconclusionwasreachedpreviouslyfortheLargeMagellanic and the observedmean(folded)rotationcurvecarries muchsignificanceandinthe curves withavelocityminimumnearr=o'6 toi'osomewhatsimilarthe Magellanic irregulars. 01+ 0-2,andprojectedmass-luminosityratioo-//areshowninFigs1112. comparison oftherotationcurvecomputedfor circularlysymmetricmodelswith observed curveontheNorthside.Nevertheless, wedonotbelievethatadetailed Cloud (deVaucouleurs1960a)anditmaybetypicaloflate-typespirals e (I) (II) © Royal Astronomical Society • Provided by theNASA Astrophysics Data System * cja=0*2 The relativeintegratedmassdistributions,i.e.thefractionsK{r)=[^]o/^ The correspondingmassdistributions,projecteddensitydistributions<7= The mainpurposeofthepresentsectionwas to deriveestimatesofthetotal The adoptedvaluesare The theoreticalrotationvelocitycurvesfortwo modelsarecomparedinFig.10 Spheroid Í f JC Jt a a Pc Pc Elements oftwo-spheroidscompositemodels* 2 *0=7*29 2 -o=7-29 0*70 0*1264 0*0538 3-66 8*59 i *64 9 /b =I-8510-4(/o1-35). Ji =(13±3)xioO Table IX o *25=0*91 o'*5 =1*82 872 139*2 12*85 0-33 0*41 2*052 Total 2*91 i*97 1*65 i *ii 243 24-3 10 kpc kpc io~ gcm“ io“ gcm io G 10 10 Unit O pc 3 O pc~ 19 68MNRAS.139. .425D 0 0-35 (B)and/o^/ß/i-38î-35. precepts ofHolmberg(1958)whoestimatedthephotographictotalself-absorption No. 4,1968ThebarredspiralgalaxyNGC4027443 in face-on,late-typespiralsat0*28mag.Thecorrespondingvaluefor/=40is spheroid models. Halfthemassiswithin o'7 =2*5kpcfromthecentre. Fig. ii.Relativeintegrated massdistributionK{f)=J({r)IJtforthetwocomposite oblate 9 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System * Unit=10solarmasses, f ForA=12*5Mpc. In parenthesisisthevalueof/correctedforinternalabsorptionfollowing Adoptedf Perek Lohmann-Bottlinger Kepler Schwarzschild Method Estimates oftotalmassNGC4027* ii -ito19*7 6 •5or8 Mass 13 12*8 16 Table X Mean error 4*o 3 i *o i *65to2*91 / =Jil# i *85 i -89 19 68MNRAS.139. .425D 444 GerarddeVaucouleursetahVol.139 in particulartheLargeCloud, but themass-luminosityratioissignificantly lower, aresultconsistentwiththe velocity appearstodecrease fromabout180km/satr=20"to70 atr=40" fact notedinSection3thatthesurfacebrightness ofNGC4027isabout1mag. above average. curve intheNorth(the majorarmside)showsalarge-scalewave;the rotational about thebarcentre;this isusualforsystemsofthiskind.Further, the rotation and thenincreasesagain to180km/satr=60".Thisprobablyindicates the two compositeoblatespheroidmodels. Fig. 12.Mass-luminosityratioo/Iandsurfacedensityoprojectedtoequatorialplanefor © Royal Astronomical Society • Provided by theNASA Astrophysics Data System The massagreeswellwithcorrespondingvalues forotherMagellanicspirals, 8. Non-circularmotions. TherotationcurveforNGC4027isnotsymmetrical 9 9 9 NGC 55Ji=2$x10,/7-2(2-9:) NGC4631 J(—(2414)xio,/=5-6(2*25) LMC ^=(14±3)x10,/4-9(3-65) 19 68MNRAS.139. .425D No. 4,1968ThebarredspiralgalaxyNGC4027445 motions inasystemwhichsoclearlylackscircularsymmetry).Wehave,therefore presence ofnon-circularmotions(notthatonewouldexpecttofindonlycircular s investigated thespatialdistributionovergalaxyofresidualsobserved velocities fromapurerotationfield,toseeifthereemergesanypatternoflarge- scale non-circularmotions.cut. the rotationcurveissoasymmetricandirregular,wehavetakenresidualsfrom than arotationperiod,thenitisplausiblethattheyareinanapproximatelysteady if weassumethatgalaxiesofthiskindpreservetheirappearanceovertuneslonger a solidbodyrotation.Thereissometheoreticaljustificationforthistreatment; state, referredtosomeuniformlyrotatingframe.Sincethestructureofthese systems ispresumablydeterminedbythebackgroundgravitationalfieldoftheir We mustthendeterminetheangularvelocityofbar. stellar component,itislikelythatthisuniformlyrotatingframefixedinthebar. velocity ofthebar.Thebeststraightlinefit(equation(7))topointsin rotation curvepassesalmostthroughtheoriginwithaslopeÎÎ=3'9 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System 1 It isnotatallclearwhatshouldbetakenasthereferencerotationfield.Because The orientationofNGC4027makesitdifficulttodeterminedirectlytheangular velocity 'ofthe barO.=5‘3kms"arcsec^ =86kms^kpc~KCompare withFig.15. Fig 13Line-of-sightvelocity residualsfromasolidbodyrotationhavingthe angular N 19 68MNRAS.139. .425D 1 -1 1 0 velocity ofthebartoprepareamap(Fig.13)residualsSV(ro,do)=AF— the origin,bestcubicfittorotationcurve(equation(6))hasaslopeQ=6*o. that northofthebarandwithinabout30"centrealmostallresiduals We haveadopted=5-3kms“arcsec"86kpc“astheangular the residualsarelargeandnegative.Itisthisfeaturethatcauseswavein patterns shouldbelookedfor. standard errorforunitweightis50kms).Thismeansthatonlylarge-scale arcsec”, whilethemaximumgradientfit(equation(2))gaveQ=8*oand,near 446 GerarddeVaucouleursetal.Vol.139 photometry ofMagellanicsystems(deVaucouleurs1957,1960b,1961)(seealso properties ofthegravitationalfieldarotatingbarredsystem.Thesurface north halfoftherotationcurve. only onespectrogramineachpositionangle(exceptforp.a.75wheretwoplates computed forauniformrotation.Theobservedvelocitiescomeingeneralfrom are available),sothereisconsiderableuncertaintyinindividualresiduals(the spheroid S2isimmersed.Thecentresofthespheroidsneednotcoincidebutmay gravitational fieldinthesesystemsisanoblatespheroidSiwhichaprolate are positiveinallsixpositionangles,whereasatgreaterdistancefromthecentre model oftheLargeMagellanicCloud(Freeman&Harrington1967),semimajor be displacedinlate-typesystemsbyadistanceA(seeFig.14).Forexample, AFc oftheobservedvelocitiesAVat(ro,do)fromvalues=Qrocosdosint Figs 2and4)suggeststhatthemostappropriatesimplemodelforbackground r rC Niy ÍV2.Brokenarrowsindicate thedirectionofgradi. equipotentials ofthecentrifugal+gravitational field(f>iareshownwiththeneutral points Fig. 14.Asimplemodelof asymmetricbarredspiredcomposedofasmallprolate spheroid (par) displacedbyAfrom the centreC'ofalargeroblatespheroid{mainbody). Some © Royal Astronomical Society • Provided by theNASA Astrophysics Data System It islikelythatthisphenomenonmaybeunderstoodbyconsideringthe South ofthebarthereisnoobviouspatterninresiduals.However,wesee 19 68MNRAS.139. .425D 9 1-115 2 2 with A=075kpc.ThemassesofS\and8%are15x10i*2Xsolar masses, andtheangularvelocityQofbaris35kms“kpc=1*ixio~. axis andtheaxialratioare8kpc1to5for-54£2, field. where m=-n+Tn-h-nand82rotatessynchronouslyinequilibriumaboutthe gravitational fieldofthefollowingsimplemodel.ThespheroidsSiand82are Magellanic-type spirals(deVaucouleurs&Freeman1968). The sourcesfortheseparameterswillbefoundinaforthcomingreviewpaperon No. 4,1968ThebarredspiralgalaxyNGC4027 centre ofSi.AnobserverrotatingwithS2thenseesatime-independentgravitational inhomogeneous, eachwithaspecifieddensitylaw(Perek1962)p=(i—m) degree ofrealism(Freeman1966a,b).Becausethis,wehaveinvestigatedthe that force=+gradO);therearealsotwosaddle-typeneutralpoints,Nsand shown inFig.14fortheLargeCloudmodeldescribedabove.Twoneutralpoints N4 say,neartheendsofbar.TheeffectSi,forthismodel,istoforceN2, Ns andN4intocoincidenceatN2;theresultisaminimuminOiN± are atNiandÍV2.ItisofinterestthatintheabsenceSi,N±N2equi- saddle pointatN2. distant fromthebarcentreandarebothtrueminimainOi(withconvention case) andthatorbitsaboutsaddlepointsareunstable.Thismeansstars c 01 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System NGC 4027.Compare withFig.13. residuals (dashedcontours, unites kms-)forasystemhavingthesameorientation as rotating framehavingangular velocity£2ofbarandcorrespondingline-of-sight velocity Fig. 15.Somestableorbits aboutthelibrationpointNi(closedcontours)inuniformly It isdifficulttoconstructself-consistentbar-likestellarsystemswithany The equipotentialsofthecombinedgravitationalandcentrifugalfieldOiare It iswellknownthatorbitsaboutextremain®canbestable(theyarethis t ^>2 /y2 a ¿ b c 447 19 68MNRAS.139. .425D _1 0 -1 448 GerarddeVaucouleursetahVol.139 some computedstableperiodicorbitsaboutiViareshowninFig.15;these gas cloudscanbetrappedinstableorbitsaboutiVibutnotTheformof the observedresidualsofFig.13withthosein15.The15 velocities fromthesolid-bodyrotationofbar,asitwouldappeartoanobserver unit isabout50kmsintheLargeMagellanicCloudandalsoNGC4027). in theYOZplane.ThiscorrespondstoaspectofNGC4027,sowemaycompare are inunitssuchthattheproductofsemimajoraxis8%byiiisunity(this are retrogradeaswewouldexpectandformakindof‘whirlpool’about bar isseeninbothFig.13and15;thetheoreticalresidualsarealsoof The patternofpositiveresidualsnearthebarandnegativefarfrom Fig. 15alsoshowstheline-of-sightvelocityfieldofresidualsorbital present inthe21cmvelocityfieldofLargeCloud(McGee&Milton1966). observed residualpatterninNGC4027.Asimilarphenomenonappearstobe correct orderofmagnitude. were purelycircular.Thisphenomenonindicatesthepresenceoflargescale velocities AFo(referred tothecentreofbar)alongmajoraxis of thebarin measurements (deVaucouleurs1964).These isophotes weredrawnonalarge the baraxisinFig.17,whichmaybecompared withearliervisualmicrometer liminary reports(deVaucouleurs&de1963b)thattheHalineis scale sothatthe‘centreofgravity’line couldbemeasuredwithadequate were measuredat0*05mmintervals(5ju,onoriginal film)intheregionofHawith tive toallowusingverysmallscanningspotsindensepartsofthefilms.Thefollow- with conventionalmeasuringinstrumentswhicharegenerallyinsufficientlysensi- independent. Furthermore,inthebarregionHaisdifficulttomeasureaccurately the natureandpatternofradialmotions. streaming motionsinthebar(deVaucouleurs1964).Wehave,therefore,made (Fig. 16)aswewouldexpectfromtheorientationofgalaxyifgasmotions not straightonthespectrogramstakenwithslitalongbarin/>o=75 Further detailsofthistheorywillappearelsewhere(Freeman&Harrington1967). position angled=75°. associated witheachdifferentialvelocitymeasurement isoforder1/xî5to accuracy inseveralcross-sectionsalongtheline. Thetypicalinternalstandarderror local smoothingbymeansoftheCDC1604computer. Examplesareshownfor on original).Isophotesofthespectrallinewere thenobtainedwithorwithout ing specialmeasuringtechniquewas,then,devised:glasspositiveenlargements detailed measurementsofthevelocityfieldinbar,anattempttodetermine 20 km/s,whichismuch lessthantheplateerrorsforabsolutemeasurements by a precisiontwo-coordinatemicrodensitometer using a130/xscanningspot(13 ( x10)ofdifferentdensitiesweremadetheoriginalspectrograms.Thesepositives and soanydetailedmeasurementsthataremadeinsuchasmallbarwillnotallbe conventional techniques. 145" mm.Thismeansthatspatialfeaturessmallerthanabout3"arenotresolved, © Royal Astronomical Society • Provided by theNASA Astrophysics Data System We suggestthatsuchwhirlpoolsaboutthestablelibrationpointiVicause (1) Themotionofionizedgasinthebar.Wehavealreadypointedoutpre- The imageofthebarisonly8"x20",whileplatescalealongslit Fig. 18showstheline-of-sight velocityresidualsoftheobserveddifferential 10. Thevelocityfieldinthebar 19 68MNRAS.139. .425D -1 -1 No. 4,1968ThebarredspiralgalaxyNGC4027449 the baraxisYY'(Fig.7)atmaximumvelocities oftheorder100kms(70to limits ofthedata,patternconstitutesclearevidenceforanoutflowgasalong We canonlyconcludethatresidualvelocitiesof the orderof50kmsareindicated, the endsofbar. insufficient fordefiniteresults(thebarisonly8" wideorlessthan50p,onthefilms). by thesametechniques,butprecisionand resolutionofourspectrogramsis but noconsistentpictureoftheflowpatterncould beobtained.Newobservations 80 inthelineofsight),comparabletorotational velocitycomponentAFat investigate someproperties ofbarredgalaxies. self-consistent, rotating, ellipsoidalmodelsofstellarsystems,whichwere usedto at higherdispersionandlargerplatescaleareneeded fordefiniteresults. orbit within auniformellipsoidisthe vectorsumofthedirect driftwithfrequency r with slitalongbarinp=75°.Systematicdistortionsindicatedeparturesfromcircular motions yi.e.gasstreamingalongthebar.ComparewithFigs17and18.Xisasmalldefect Fig. 16.Highly-magnifiedisophotesofHaandA6584fromspectrogramB989taken not presentonoriginalfilm. © Royal Astronomical Society • Provided by theNASA Astrophysics Data System 29 Although thedifferentialvelocitiesareclosetoprecisionandresolution We haveattemptedtostudyresidualvelocities neartheminoraxisofbar We areinterestedhere in themeanstellarmotionssuchsystems. A stellar (2) Themotionofstars in thebar.Oneofus(Freeman1966b)hasconstructed 19 68MNRAS.139. .425D bar. to beinthesenseoffi.However,nearminoraxisbar,c>Qrand mean motionappearstobeintheoppositesenserotationoffigure streaming velocitycandthemeanmotionappears,tonon-rotatingobserver, the meanmotionreferredtorotatingframeandrotationof 450 GerarddeVaucouleursetal.Vol.139 itself. Neartheendsofbar,rotationalvelocityfirisgreaterthan the meanmotionofstars.Thestreamlinesthisstellarare shown inFig.19(b).Anobserveranon-rotatingframeseesthevectorsumof gyration whichisretrograde,referredtotherotatingframeofbar,dominates frequency ß(seeFig.19(a)).Fortypicalgalacticparameters,ol.Whenwetake an assemblyofsuchorbitstomakeaself-consistentellipsoidalsystem,therapid to seewhetherthisretrograde meanstellarmotionispresentinareal system. velocity equalbutopposite tothatofthefigurebar. a, ofaguidingcentrearoundthebarandretrogradeepicyclicgyrationwith field neartheminoraxis ofthebarappearstobeinuniformrotationwith angular the minoraxisofbar. Itturnsoutthat,tothenon-rotatingobserver, thestar slit alongmajoraxisofbar.CompareFigs16,18and 20. meter measurementsofenlargedpositivesspectrograms B976and989takenwith © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Fig. 17.Computer-processedandsmoothedisophotesof HaandA6584/rowmicrodensito- We haveexaminedthestellar absorptionlinesinthespectrogramsofNGC 4027 Consider amodelgalaxyorientedlikeNGC4027 withthelineofnodesalong 19 68MNRAS.139. .425D No. 4,1968ThebarredspiralgalaxyÍVGC4027451 -1 centre. ComparewithFigs16and17. large scalestreamingmotionswithvelocitiesoftheorder50to100kmsawayfrom Fig. 18.Line-of-sightvelocityresidualsofemissionlinesalongmajoraxisbarindicating stars inbar. Fig. 19(a)Epicyclicmotion ofastarinuniformbar.(b)Streamlinesmeanmotion of © Royal Astronomical Society • Provided by theNASA Astrophysics Data System (a) 19 68MNRAS.139. .425D _1-1 -1 lines ineachpositionangleareshownFig.21.Weseethattheabsorption squares solution.Theinclinationofalineistakentobepositiveifitinthesense of thelinesaregiveninTableXItogetherwithprobableerrorleast of therotationgalaxyasawhole.Themeaninclinationsabsorption as anull-test,isophotesoftheairglowlineÀ5577arealsoshown.Theinclinations absorption lines.Fig.20showsanexampleofisophotesHandK;forcomparison, mined fromtheisophotes.InsomepositionanglesitwaspossibletomeasureH8 general rotationofthegalaxy,aspredicted,butmaximumtiltabout30km do appeartobeinclinedintheoppositesenseemissionlinesand and Hyaswell.Ineachofthefourpositionanglesthereareatleasttwomeasurable s arcsec=0*5kmpcissurprisinglylargecomparedwith5*3 methods describedintheprevioussection,andslopeoflineswasdeter- arcsec fortheadoptedangularvelocityofbar. 452 GerarddeVaucouleursetal.Vol.139 Isophotes oftheHandKlinesineachspectrogramwereobtained,using systems areatleastmoving inthecorrectdirection. it isfoundtobegenerallypresentinSBgalaxies, then For example,let(#,y, z) bethevelocityofastarreferredtoaxes shownin o _1 of barfromspectrogramB974takenwithslitalong minoraxis(p=165).Inclination of airglowlineA5577areshownforcomparison.Slope isinkmsper100pc. of linesisindirectionoppositetothatO.Isophotes emissionlinesHaandÀ6584 Fig. ao.Computer-processedandsmoothedisophotesof theHandKlinesinstellarspectrum © Royal Astronomical Society • Provided by theNASA Astrophysics Data System (2) Itmayprovideasevere constraintontheoreticalmodelsofbarred systems. (1) Itsuggeststhatpresent rudimentaryideasonthestellardynamics ofSB Other suitablyorientedsystemsshouldbeexamined forthiseffectbecauseif NGC 4027 B 974 p =165° 19 68MNRAS.139. .425D that thereisanotherintegral,probablylikethe‘thirdintegral’ingalaxy;this through theisolatingintegralsofmotion.If/=f(J)thentherecanbeno star-streaming relativetotherotatingbarbecause,forexample (the integralisoverallvelocities),bythesymmetryof/in(¿,j>,z).Thissuggests The distributionfunction/(#,3;,2:;#,j),z)dependson(x>y,z;x,only orbit; thisistheJacobiintegral, from theslopeofabsorptionlineswithoutdetailedallowancefororientation is discussedfurtherbyFreeman&Harrington(1967). of thesystem. No. 4,1968ThebarredspiralgalaxyiVGC4027453 Fig. 19.Ingeneral,thereisonlyoneisolatingintegralassociatedwiththestar’s y o Inclination ofabsorptionlinesisindirectionoppositeto Onearminoraxisofbar{p=165 in stellarspectrumofbarversuspositionangle.Emission lines{opencircles)arealsoshown. ando°). Fig. 21.Meanresidualgradientofabsorptionlines{filled circleswithprobableerrorsshown) © Royal Astronomical Society • Provided by theNASA Astrophysics Data System n =numberoflines.The inclinationisinkm/sperparsec. (3) Itindicatesthatthecentraldensityinbarredsystemscannotbederived o 0 o B 980130 B 97830 B 972o° B 974165 Plate p Mean inclinationsoflinesinspectrabar 2 J =!(i+j>£)—íh* — 0*52±0*043 + o*i6±o*o52 — 0-42±0*042 — o•07±o•042 Absorption n J xfdxdydz=o. Table XI + 0-I3±0-022 + 0*28±0*02I Emission n 19 68MNRAS.139. .425D on later. We alsothankMrsF.S.Jonesforpermissiontouseherunpublishedphotometry, expedited bytheableprogrammingandcomputationalassistanceofMrsC. Naval ResearchundercontractwiththeUniversityofTexas.Ourworkwasgreatly NGC 4027.Theanalysisoftheseobservationsisinprogressandwillbereported (NGC 4258,7640,7741)inordertochecksomeofthephenomenadetected 454 GerarddeVaucouleursetahVol.139 and DrG.E.KronMrH.D.Abiesforcommunicationofthefineelectron Robertson andofMessrsR.S.Harrington,G.M.Malik,E.H.ScottD.Wells. camera photographusedinFig.3.Oneofus(K.C.F.)wassupportedbyaMcDonald Post-Doctoral Fellowshipduringthefinalyearofthisstudy. Arp, H.,1966.AtlasofPeculiarGalaxies,CaliforniaInstituteTechnology,Pasadena. Brandt, J.C.,i960.Astrophys.131,293,553. Burbidge, E.M.&G.R.,1966.Astrophys.J,,145,661. Brosche, P.,1963.Z,Astrophys,,57,143. Epstein, E.E.,1964.Astr.J.,69,490. Freeman, K.C.,1966a.Mon.Not.R.astr.Soc.,134,1. Feast, M.W.,Thackeray,A.D.&Wesselink,J.,1961.Mon.Not.R.astr.Soc.,122,433. Freeman, K.C.,1966b.Mon.Not.R.astr.Soc.,134,15. Freeman, K.C.&deVaucouleurs,G.,1966.Astr.J.,71,855(Abstract). Freeman, K.C.&Harrington,R.S.,1967.Unpublished. Holmberg, E.,1958.Medd.Lund.Obs.,BE,No.136. y Kerr, F.J.&deVaucouleurs,G.,1955.Aust.Phys.,8,508;1956.9,90. Kron, G.E.&Papiashvili,I.I.,1966.Pubisastr.Soc.Pacif.,78,445(Abstract). Lohmann, W.,1954.Z.Astrophys.,35,159. Mayall, N.U.&deVaucouleurs,A.,1962.Astr.J.,67,363. Patterson, F.S.,1940.HarvardObs.Bull.,No.913,13. McGee, R.X.&Milton,J.A.,1966.Aust.Phys.,19,343. Patterson, F.S.,1941.RadcliffeCollegeDissertationUnpublished. de Vaucouleurs,G.,1960b. Astrophys.J.,131,574. Perek, L.,1948.Contr.astr.Inst.MasarykUniv.,1,No.6. de Vaucouleurs,G.,1960a. Astrophys.J.,131,265. Perek, L.,1962.Distributionofmassinoblatestellar systems,inAdvancesAstronomy Perek, L.,1950.Bull.astr.InstsCsh,2,75. de Vaucouleurs,G.,1959* Handb.Phys.,53,348. Roberts, M.S.1968.Astrophys.J.,151,117. de Vaucouleurs,G.,1958. Astr. J.,63,253. de Vaucouleurs,G.,1957. Astr. J.,62,69. Robinson, B.J.&vanDamme,K.J.,1964.TheGalaxy andtheMagellanicClouds,p.276, de Vaucouleurs,G.,1955. Astr.J., 60,126. de Vaucouleurs,G.,1954.Observatory,74,23. de Vaucouleurs,A.&G.,1967.Astr. J.,72,730. Sersic, J.L.,i960.Z.Astrophys.,50,168. Struve, O.,1940.Pubisastr.Soc.Pacif.,52,140. Schwarzschild, M.,1954.Astr.J.,59,273. © Royal Astronomical Society • Provided by theNASA Astrophysics Data System McDonald Observatory AcJmowledgments. ThisresearchwassponsoredbytheU.S.NavyOfficeof We havemadedetailedspectralobservationsofseveralotherbarredspirals, y 1967 December, University ofTexas y and Astrophysics,Vol.I,AcademicPress,NewYork. I.A.U. SymposiumNo.20,Canberra,Australia;1966. Aust.J.Phys.,19,in. Austin, Texas, References 19 68MNRAS.139. .425D lines inTableAll;weights=1,or|(:),J(::). No. 4,1968ThebarredspiralgalaxyNGC4027 Wyse, A.B.&Mayall,N.U.,1942.Astrophys.J.95,24. de Vaucouleurs,G.,1967.Astr.J.72,325(Abstract), (de Vaucouleurs&de1967).EmissionlinesareinTableAI,absorption de Vaucouleurs,G.,Griboval,P.&White,Th.,1965.Puhlsastr.Soc.Pacif.,77,115. de Vaucouleurs,G.&A.,1963b.Astr.J.68,278(Abstract), de Vaucouleurs,G.&A.,1963a.Astrophys.J.137,363. de Vaucouleurs,G.,1966.TheVelocityDistanceRelationforBrightGalaxies,inAttidel de Vaucouleurs,G.,1964.TheGalaxyandtheMagellanicClouds,I.A.U.Symp.No.20, de Vaucouleurs,G.,1963.Astrophys.J.137,720. de Vaucouleurs,G.,1961.Astrophys.J.133,405. between theHandKlines.Foradiscussionofadoptedrestwavelengthssee all cases.The‘absorptionline’designatedH-Kreferstothecontinuumpeak de Vaucouleurs,G.&Freeman,K.C.,1968.VistasinAstronomy,ed.byA.Beer,press, de Vaucouleurs,G.&A.,1964.ReferenceCatalogueofBrightGalaxies, and plate.Abscissaexaremeasuredinsecondsofarcfromthecentrebar point themeasuredheliocentricradialvelocitiesandrelativeweightsforeachline y y y y y y P =165 p =o' B 974 B 972 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Plates Measured radialvelocitiesinNGC4027.Thefollowingtablesgivepoint-by- p. 269,Canberra,Australia. Convegno SullaCosmología,Firenze, University ofTexasPress,Austin. N 65*3 N 43*5 s 43-5 S 29-0 0 x‘ 43*5 21*8 29-0 21 *8 29-0 5‘8 7*3 36-3 36-3 21 *8 21 *8 14-5 14*5 14*5 14*5 7*3 o 7*3 7*3 o 1636 1557 3727 APPENDIX I Hß 6548Ha Emission lines Table AI 1698 I72O 1817: 1631: 1581 1635 1614: 1652 1675 I718: 1693 1718 1636: 1683 1847: 169I I668: 1827: I772 1704 1746 I755 l8S2 180O: 1583 1653 1585 1669 1751 1713 1635 1656: 1676 1625 1702 1826 1657 1863 6548 1514: 1450:: 1507: 1711: 1709: 6717 6731 455 19 68MNRAS.139. .425D 456 P =75 B 976 P =30 B 978 P =130' B 980 B 989 p =no' B 1354 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Plates = 75 W NE 60-9 NW 36•3 SW 26*1 SE NW 21•8 W SE 50*8 " 39*i X 21 *8 29*0 36-3 21 *8 29*0 14-5 36*3 14*5 24*7 54*3 17*4 29-0 10*2 21 *8 il -6 18*9 29*0 14*5 21 *8 363 14*5 29*0 36-3 21*8 14*5 7*3 21 *8 O 7-3 14*5 21 -8 43*5 29*0 14*5 36-2 4*4 4*4 14*5 o 7*3 o 7*3 7*3 o 7*3 7*3 7*3 o : 1630: 1536:1781::1667 1711: 1665:1727::1614 i557 1790*^12 2109: 1992: 3727 Hß6548Ha Gerard eleVaucouleursetal. Table AI{continued) 1642: 1758::1659 1585: 1560: 1722 1754 1651 1733 1642 1704: 1678 1669: 1727 1734: 1706: 1710: 1712: 1730: 1658 1657 1696 1583 1597 1643 1925: 1871 : 1818 1872: 1779 1725 1746: 1669 1680 1705 1673 1657 1653 1436: 1611 1567 1574 1650 1537 1695: 1551: 1697: 1539 1632 1503: 1414: 1565 1565 1685 1753: 1732: 1635 *• 1658: 1671: 1710: 1658: 1662: 1843: 1695: 1676: 1594: 1562: 1593: 1734: 1725: 1605: 1670: 1675: 1689: 1645: 1678: 1560 1522: 6584 1613 1545 1637: 1610: 1616: 1640: 1558: 1647: 1589: 1526: 1535: 1666: 1644: 1607: 1637: 1782: 1646 1652 6717 1474 : 1540: Vol. 139 1622: : 1601 : 1610: : 1654*. 1589: 1442: : 1516: 1598: 1590: 1677: 1639: 6731 19 68MNRAS.139. .425D No. 4,1968 0 p =IIO° p =6o° P =145° B 1356 B 1358 p =(yo° B 1361 p =60 B 1365 B 1366 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Plates NW39-5 NE 36*2 SE 55-0 NE 25*4 SW 29*0 NE 7*3 SW 29*0 x" 3727Hß6548 24*6 40*5 47*8 33*3 26-1 17- 4 21*8 29-0 io* i 21 *8 18- 8 il *6 14-5 21 *8 14*5 io*9 i4‘5 i8*i 25*4 21 *8 io*9 18 •i 14*5 4*3 o 2*9 o 7*3 7*3 7*3 o 7*3 3-6 3-6 The barredspiralgalaxyNGC4027457 Table AI(continued) 1769 1797: 1911 : 1544 1839:: 1620 1752: 1636: 1724: 1548 1562:: 1695 1614: : 1661 : 1547 1517:: 1637 1740: 1592 1756: 1692 1700: 1759 1676 1733: 1687 1816:: 1786: 1763:: 1629 1530: 1528 1627: 1580 1588: 1645 1820:: 1642 1637: 1660: 1711 1640 1681 1705: 1761 : 1800: 1539 1733 1710 1732 1667 1691 1579 1752 1567 1658: 1648: 1526: Ha 658467176731 19 68MNRAS.139. .425D # 458 was measuredbyoneofus(G.V.)andJ.E.SolheiminMarch1967withatwo- the systemDoxdo=i'*oo'*5asmeasuredonFig.22ofArp’sAtlas(1966).The total magnitudeandcoloursare The colourshavealargeuncertaintyduetothefaintnessofobjectbutare apertures used(i'iand2'*7)werelargeenoughtoincludeallthevisibleextentof channel pulsecountingphotometerattachedtothe36-in.reflector.Thetwo consistent withtheImclassification. that onemaywonderwhetherthedatabevitiatedbysystematicerrors,and the streamingmotionsnearminoraxisofbarindicatedbyobservations if not,whethersuchmotionscanbecontrolled gravitationallybythebar. where cisreferredto the rotatingframeofangularvelocity£2,ais the velocity grainy spectrograms.Itisratherunlikely,however, thatsuchdistortionswill (Fig. 21)isfarinexcessof£2.Thecorrespondingcentrifugalforcesaresolarge account. Themeanstellarmotioncmustsatisfy themomentumtransferequation The nulltestaffordedbytheairglowline(Fig. 20)wassatisfactoryinallcases. affect consistentlythewholelengthoftwobroad absorptionlines,suchasHand K, onthetwocriticalspectrogramstakenatdifferent timesandnoneoftheothers. and occasionallydodistortshortsectionsofan emissionlineonlow-dispersion, dispersion, pthedensity, thegravitationalpotential,andris component ( p =o° P =i6s' P =130 P =30° P =75° B 974 B 972 B 978 B 976 B 980 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Magnitude andcoloursofNGC4027-ÆTheirregularcompanion4027-A Remarks oncentrifugalandCoriolisforces.Therotationalangularvelocityof On thetheoreticalsideweremarkthatCoriolis forcesmustbetakeninto Concerning possiblesystematicerrors,wenote thatlocalemulsiondefectscan Plates NE 4*4 W 7*3 NW 7*3 SW 4-4 SE 7*3 x‘ o o o 2 c-Vc =—iV(pc7)—2ßx c+^+£2r Gerard deVaucouleursetal. 2014: : 1775: 1873: 1590: K B-V =+0*5±o*i: U-B =—0-2±0*2: APPENDIX III B =15-05±0-05 APPENDIX II t P dr Absorption Unes Table AU 1404: : 1843: : 1952: : 1628: : 1626: : 1604: : 1521: : H-K 2119: 1805: 1819: 1862: 1627: 1919: 1422: 1872: 1381: 1370: H 1613: 1395: 1384: HS 1487: : Vol. 139 Hy 19 68MNRAS.139. .425D forces. Inrealsystems,especiallywhensomecentralcondensationispresent,the perpendicular toSIofthepositionvectorreferredrotatingframe.Fora retrograde circulationinthemeanstellarmotionoutward-directedcentrifugal streamline isi?iandthestreamingvelocityVi;nearextremitiesofbar as inFig.19(b).Neartheminoraxisofbarradiuscurvature and pressureforcesarebalancedbytheinward-directedgravitationalCoriolis No. 4,1968ThebarredspiralgalaxyNGC4027459 so thatneartheminoraxisVi~2Q.R1greatlyexceedsrotationalvelocity£2r, retrograde circulation,wehave Coriolis forceisdominant. (R2