1946ApJ. . .104 . . 290M 1 0 ities oftheglobularstarclustersisrepresentedby thepioneerworkofV.M.Slipher, A.A.S., 3,331,1918. is concludedthatthemostprobablevalueforsolarmotion,withallowanceclustersofunknown bility ofasmallamountflatteningthesystemforreasonablevaluesspaceabsorption.Theelliptical their radialvelocities,provideacheckonFo*Severalsolar-motionsolutionsyieldtheroundnumber taining theapexandantapexfromadiscussionofdegreecompletenessintwogroups,it ciable deviationofthecomputedapexfromonegenerallyassumedatgalacticlongitude55°andlati- presented orallyatthededicationofMexicanNational AstrophysicalObservatoryatTonanzintla, for theclustersinthatspiralasprobablymostdirectmeans forfurtherinvestigationofthedynamics cluster systemmaybeappreciablyflattened.Thiscircumstance suggestsradial-velocitydeterminations clusters, butespeciallythelargedispersionsinvelocityanddistancefromgalacticplane.Neverthe- ing the50velocities,isF©=175±25km/sec,butthisvalueprobablytoosmallbecauseofob- is introducedintothesolutionbasedonfiftyclusters,K=—1.9±18.8km/sec;(2)therenoappre- Puebla, Mexico,February20,1942. outline oftheprojecteddistributionclustersinAndromeda nebulaindicatesthataglobular- less, thephotometricdistancesformanyclustersarestilltooimperfectlyknowntoruleoutpossi- system haveledtoinconclusiveresults.Thereasonsarepartlytheinaccuratedistancesforanumberof most obviousinterpretationofthedifferenceisthatclustersystempartakesingeneralgalactic between thesun’smotionwithrespecttogalacticcenterandsystemofglobularclusters.The rotation andthatitmay,fordynamicalreasons,beappreciablyflattened. from valuesheretoforegenerallyadopted.Thelocalgroupofnebulae,withcertainqualificationsbecause most recentmaterialforgalacticobjects,itisconcludedthatF©=280±40km/sec,i.e.,unchanged of asystemglobularclusters. of thepossibilityred-shiftsandacomponentmotiongalaxyaswholebeingincludedin suggests re-examinationofthequestionsun’sorbitalvelocity,Vq.Fromaconsideration velocity, isF©=200±25km/sec.Themeanresidualmotionwithoutregardtosign101 servational selection;(4)fromseparatesolutionsforthetwogroupsofclustersinhemispherescon- tude 0°;(3)thesolarmotionwithrespecttoclusters,F©,averagedfromfourdifferentwaysoftreat- electrically measuredcolorclassesshowslittlevariationofwithspectralclass,aftertheeffect selection, forthemajorityofobservedclustersarelocatedingalacticlongitudes(145-325°),where space reddeningisremovedbythecosecantlawpreviouslydeducedfromcolorobservations. spectra, appeartorangefromA5G5,withanaverageofF7.6,butthereisapreponderantnumber the solar-motioncomponentisnegative. however, indicatethatthefinalvelocitiesmaybeuncertainby15-20km/sec,especiallyforclustersob- four satisfactoryspectrogramswereobtainedforeachcluster;theresidualsfrommeanvelocity the previouslyknownrangefrom+291to—360km/sec.Theexcessofnegativevelocitiesisdue served onlywithlowdispersion. eral, thesystematicerrorsaresmall,onlyseveralkm/sec.Theaveragedifferenceswithoutregardtosign, 36-inch refractorandfromacomparisonwithvelocitiesdeterminedelsewhere,itisfoundthat,ingen- pendent seriesofhigher-dispersionspectra(130A/mmatHy)fifteenclustersobservedwiththe the 36-inchCrossleyreflectorarereportedforfiftyglobularclusters.Thelistissubstantiallycompleteto (thirty) includedinthesmallerintervalfromF8toG5.ComparisonwithStebbinsandWhitford’sphoto- each clusterindicateanaverageinternalprobableerrorforasingleplateof±22km/sec.Frominde- 5 =—40°fortheequipmentused.Allvelocitiesareintegratedlightofclusters.Atleast F© =300±25km/sec,sothattherenowseemstobearealdifferenceof—80-100km/sec 1 © American Astronomical Society The onlyextensiveseriesofobservationshitherto made todeterminetheradialveloc- Pop.Asir.,26,8,1918;30,11,1922;32,622,1924.Apreliminary announcementwasmadeinPub. * ContributionsfromtheLickObservatory,Ser.II,No.15. The principalresultsofthispaperwere Attempts tofind,inthepeculiarvelocities,evidenceofageneralordifferentialrotationcluster A clustersolarmotionsmallerbyabout75km/secthanhithertoobtainedfromhalfasmuchdata The spectraltypes,althoughdifficulttoestimatebecauseofthecompositeandpeculiarnature On thebasisofanumbersolar-motionsolutionsitisfoundthat(1)noiT-termindicated;ifone Of thefiftyvelocitiesmeasured,nineteenarepositiveandthirty-onenegative;allofthemfallwithin Radial velocitiesdeterminedwithalow-dispersion(430A/mmatHy)spectrographattachedto THE RADIALVELOCITIESOFFIFTYGLOBULARSTARCLUSTERS* I. PREVIOUSWORK Received July15,1946 Lick Observatory N. U.Mayall Provided bytheNASA Astrophysics DataSystem ABSTRACT 290 1946ApJ. . .104 . . 290M 9 56 2 10 78 34 published thevelocitiesforthreeclusters,buttwoofthemhadalreadybeenobservedby lem forseveralreasons,whichmeritabriefdiscussionbecausetheyshedlightonthe recently as1935,whenthepresentworkwasundertaken,radialvelocitieswereavailable published measuresbyHumasonandtwoonspectrogramsobtainedSlipher.Thus,as Edmondson reportedvelocitiesoffourmoreclusters,twowhichwerebasedonun- for onlytwenty-sixclusters.Sincethisnumberrepresentsbutone-fourthoftheknown Strömberg, andMoore,buttheyrefertoobjectspreviouslyobservedbySlipher.In Slipher; withthisexception,therearenovelocitiesreportedforadditionalclustersfrom who publishedthevelocitiesforseventeenclustersfrom1918to1924.In1919,Sanford bright---their averagephotographicmagnitude,accordingtoChristie,is9.5,witha so considerableforthelastfewclustersobservedthatprogramseemedtohave under existingconditions,onlybytheexpenditureofadisproportionateamounttime. reached thepointatwhichlawofdiminishingreturnsbecameoperative. The exposuretimesweresolongandthedifficultiesofworkingatverylowaltitudes globular clustersandsincetheseobjectsplayauniqueimportantroleinthestruc- spectrographs. Forthemajorityofclusterslightisdistributedoveranareamuch sufficiently concentratedtowardthecentertopermitobservationswithordinarystellar closely approachesthepracticablelimitforinstrumentalequipmentemployed. as couldbeobservedatMountHamiltonwithinareasonabletime. ture anddynamicsofthegalaxy,itwasapparentthatfurtherradial-velocitymeasures 1934, HumasonpublishedvelocitiesforthreeclustersandBaadeone.Ayearlater this number,forty-seven,or65percent,liebetweendeclination—10°and—40°; temperate zone.Thereareapproximatelyseventyclustersnorthofdeclination—40°; mean thatexposures,evenoftheorderseveralhourswithordinarystellarspectro- larger thanthatoftheslit.Consequently,afairlybrighttotalmagnitudedoesnotalways the distributioninskyofclustersisunfavorableforanobservernorth range from4.6to12.9—thereisonlyarathersmallnumberoftheminwhichthelight causes fortheslowaccumulationofdata.First,althoughtheseobjectsarerelatively were desirable.Itisthepurposeofthispapertogivesuchmeasuresforasmanyclusters thirty-four, or72percentofthem,fallbetweenrightascensions16and19hours.Be- graphs, willrecordthespectraofglobularclusters. While itwouldbepossibletoaddafewmoreobjectsthelist,couldaccomplished, clusters) ;8,63,1936(23platesof8globular8,162, 1936(1plateofNGC1851,4104); 1918 to1934.WithinthisintervalthereareafewnewmeasuresreportedbyPease, observations: Pub.A.A.S.,7,165,193,1932(24plateswith asmallspectrograph,mostlyofglobular published. Thefollowinglistofreferencesappearstobethe only informationavailableonsuchimportant reflector, foranumberofsouthernclusters;but,sofarasthe writer>knows,thevelocitieshavenotbeen 8, 271,1936(10platesof3globularclusters). 6 2 ú 3 4 7 9 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem A seconddifficultyinthedeterminationofradialvelocitiesglobularclustersisthat The determinationofradialvelocitiesglobularclustersisacuriouslydifficultprob- During 1935-42,radialvelocitieswereobtainedforfiftyclusters,andthisnumber * Pub.LickObs.,18,217,1932. Ap./.,61,353,1925;Mt.W.Contr.,No.292. Ann.Rep.DirectorMt.W.Obs.,1919. Ap. /.,91,8,1940;MLW. Contr., No.620. *Ap. /.,82,410,1935;MLW. Contr.,No.529. C.D.Perrinehasreportedthatspectrogramshavebeen obtainedatCórdoba,withthe30-inch Pw6. A.S.P.,40,342,1928. Pw&. 4.S.P.,46,357,1934. LowellObs.Bull.,3,No.88, 143, 1935. II. DIFFICULTIESAFFECTINGSPECTROSCOPICOBSERVATION GLOBULAR CLUSTERS 291 1946ApJ. . .104 . . 290M 11 12 292 cause ofthisremarkablyhighconcentrationinarelativelysmallarea,itisnotpossible year. Theconsequenceisthatanumberofyearsrequiredtoaccumulatespectroscopic electric measuresofcolorbyStebbinsandWhitfordhaveshown.Theobscurationis to observethemajorityofglobulai/clustersformorethanafewmonthsduring observations foraconsiderablenumberofclusters. that manyoftheseclustersarepartiallyobscuredbyinterstellarmatter,asthephoto- blend andbroaden,respectively,thespectrumlines.Theresultisthatonlyafewlinesof ' Finally,thecompositenatureofspectraandvelocitydispersionineachcluster more pronouncedforbluelightthanred,asiswellshownonphotographstakenby rather poorvisibilityareavailableforradial-velocitymeasurement. show thatmanyclustersareabnormallyweakinactiniclight;andthiscircumstance a consequence,theradialvelocitiesofglobularclustersnotonlyaredifficulttodetermine for mostclsters,spectrographsgivinglowdispersion,oftheorder300-500A/mm.As Baade withthe100-inchreflectoronMountWilson.PicturessuchasBaade’sclearly as inthepresentinvestigation,aimwastogetvelocitiesfromintegratedlightof but are,forthemostpart,unobtainablewithhighaccuracy.Thiswasespeciallytruewhen, nary photographicregion. combines withtheaveragelowaltitudeofclusterstomakeworkdifficultinordi- too faintfortheavailableequipment.Inmakingobservationsclusterswerein- the clusters.Thequestionofspectraandvelocitiesindividualstars,however because experiencedemonstratedthatmostofthe errorofalow-dispersionradial-veloc- prime focusofthe36-inchCrossleyreflector.Theopticalpartsthisspectrographcon- tion ofdispersion,wereobtained. important andinterestingitmaybe,hadtobepassedoverbecausetheclusterstarsare integrated light,ofsatisfactorywidth,anduniformdensityperpendiculartothedirec- tentionally placedoutoffocusandallowedtodriftontheslit.Inthiswayspectra cluster—one takeninbluelight andtheotherinredlight—arereproducedbyB.J. P.F.Bokin sist oftwo60°UVglassprismsandan//l.3cameralens,withthecombinationgivinga ity determinationisinherentinthespectrograms, i.e., theerrorofmeasurementissmall spectrograms obtainedwithbothtelescopes. telescope ;withthisapparatustheeffectivesouthernlimitforexposuresofseveralhours each clusterandthatplatewasmeasuredonly once.Thisprocedurewasadopted cerning thevelocitiesobtainedwithCrossleylow-dispersion spectrograph.Itmaybe is reachedataboutdéchnation—38°.Sincethereabrightandconcentratedcluster dispersion atHyof430A/mm.PlateXIIshowsthespectrographasitismountedin noted that,ingeneral,fourandoccasionallyfivelow-dispersion plateswereobtainedfor ters aspossible,theaimbeingtoobtainacheckonvelocitiesdeterminedwith inch refractor.Thislatterequipmentwasalsousedtoobserveasmanyoftheotherclus- ness totheantapexofsolarmotion,itwasnecessaryobserveit,fiftiethcluster, Crossley low-dispersionapparatus.Table1liststhe radialvelocitiesfortheindividual with thelowest-dispersion(130A/mmatHy)stellarspectrographattachedto36- The MilkyWay,p.145,Philadelphia: Blakiston,1941. (NGC 1851)locatedatô=—40°,whichitwasimportanttoobservebecauseofitsnear- 11 13 12 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem A thirdfactorwhichincreasesthedifficultiesofspectroscopicobservationisfact The combinationoftheseseveraldifficultiesmeansthattheobserverisobligedtouse, Ap.84,132,1936;Mt.W.Conir.,No.547. vPub.A.S.P.,& 14,1936. Forty-nine oftheclusterswereobservedwithnebularspectrographusedin Pub.A.A.S.,9,31,1937;Trans.I.A.U.,6,452,1938.Two ofBaade’sphotographsareddened While thedatainTable1areself-explanatory,a fewremarksshouldbemadecon- ) in. OBSERVATIONALMATERIAL N. U.MAYALL 1946ApJ. . .104 . . 290M © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem
Nebular Spectrograph Mounted at the Primary Focus oe the Crossley 36-Inch Reflector 1946ApJ. . .104 . . 290M © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 6266 6723 M62 M80 6093 5272 M92 6341 M30 7099 M3 E1IH1I11I tIII'llI in rih Linear dispersionoforiginalnegatives,430A/mmatH;enlargement, X8.9 ililllllll HIHI iiiiiiiiii Typical SpectraofGlobularStarClusters III liUN Í PLATE XIII I «in itnitnimi! «ini limiTTSm miniII MVMMl linn itmiin mill liiiiiii,i,uji ■iM miliimi iiiiiili milimi 11 ilhmitiii I M69 6637 6356 6229 M22 6656 5694 7006 CT) O CM OÏ o
TABLE 1 © American Astronomical Society Radial Velocities of Globular Clusters from Individual Spectrograms > K W S W £ > w u ^ 5 O O ^ a >N 9, X £ « O 7777 © O^ 00 OnQ Tfl i-HCSCO cq -thi-i © i-l * A plus sign (+) after the date indicates that the exposure extended over several nights. O^i O CM OÏ o s TABLE 1—Continued © American Astronomical Society Provided bytheNASA Astrophysics DataSystem 294 t The spectrograms of 6205 (M 13) and of 7078 (M 15), taken in 1914, were obtained by W. H. Wright. O^i O CM OÏ o s TABLE 1—Continued © American Astronomical Society Z ~ s* ^ S > M W S Ji CJ ^ ^ I > M pH to H-l O H ^ Q ^ U V P o ^ £ U « CJ ai n aJ in ® Ö « O U C. !>-00 CO TÍTpTfHTÍ» On no © 353 tí T^ lOCNCO CO © SIO ©'tH I—j<î i—i*—i 00 CN»O + On ^ (Uo0) bOr*> I Tfl ^H tí CN IO u + NO LO CO co t-H CS © On00 On © CO t-H co T*00 NO co1000 sO NOiO10 Il II CS tHCSJ(N J>> OOoo + CO OnCN^ O 00 pB 33 On ©O' CO >N bb>» t-H T-H CN TABLE 1—Continued W ^ > w •3 6* w S > M 'o £ O o| $ % . J>.00 O © + rvrscc W reflprtnr nhotoerranhs taken in red light leave little doubt that NGC 6544 is a globular cluster; a similar conclusion, for different reasons, has also been reached by P. Collinder O^i O CM OÏ o s TABLE 1—Continued © American Astronomical Society 2 u ^ 2 s 1 a H S > M “ CO u ^ .2 H ^ > M £ CJ a X £ >> y a ö h •- Ö x^x^ VO CO Os O' i-H 03 © VO00 vO X>.00 00 COVO© VO 3>-00 IO VO VO 03x>. Os O'© CO 00 VOOS vo rhtJh 03 CNtH tí< 0\CNVO Si^S Il II MM 1-H co03 ©© Os ^r—4 tHi—< CN 0300 tí tí ' 03 VO vo ©CO co + vo 1-HVOOs O' co00 lO VOO»o»o« CO Os Q\ 03 CO^ CO vOQ\VO 03 OlOVOvO I MM i—i O' covOCO O VO O O-03 + CO CJ Provided bytheNASA Astrophysics DataSystem Os co ^. 1-H C3i-H03 03 i-H00 © + +++1 vO J>- 1-.00 VO 00 vo1-11" iO O'co VO O Os CO 03 CO 03 CO 00 ©O 00 -^-1COVO ^-h íOO' B vo 297 MM T-I CO 03 + O' VO vOt"-O- 's ^'o3 VO ©vo 1-H 03 O' CO co © 00CO VO 3^00 03 i—ii-H OO CO©1-H 00 ©1-H OO coOs vO CO03 CO co © Os 03 CO Os O'O03 VO 03^ >•0 bbk*> Il II Mil Ov 0003 o x^. x^oo XT' 00OO 00 03 O' Os co CO 1-H coCO03 00 ©vo © vo VO ^ 00 03VO -»-i i-i03 00 co CO CO coOsO' >0 O'O»*0 O' Os CO VO0003 VO ti bb>> 17 il MM f IT—I 03 3 * >> u § Although Shapley (Star Clusters, p. 233) includes NGC 6838 (M 71) in his catalogue of galactic clusters, it is here considered to be a globular cluster, for the following reasons: (1) J. Guffey (Pub. A.A.S., 10, 122, 1941), from star counts on 36-inch reflector plates, found a diameter of 23 minutes of arc and a population of between three and four thousand stars. (2) Crossley reflector plates suggest the presence of a rich background of faint stars, typical of globular clusters. (3) R. J. Trumpler (Lick Obs. Bull., 14 No. 420, 175, 1930) did not in- clude M 71 in his preliminary catalogue of open-star clusters because of its exceptional richness, which would set it apart from all the other known galactic? clusters. 1946ApJ. . .104 . . 290M © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem O ^ s > M H S ^ s > ^ u ^ W S S ë U ^ ^ O ^ £ O ^ a « o ^ a « O « •- 0-2 O Ç_) d + ÏÏ77 00 ooi>- 0\ On co CO Tt CM OO O <î ►—> O0 ^ O vo lO00 y-* CO rf vO On + MO •t'~ bh>i 17 •t— Spectral Gass Fig. 1.—Comparison of color and spectral classes of globular clusters. A, observed photoelectric color classes. B, color classes corrected for space reddening according to cosecant relation. #, clusters in fields with nebulae. O, clusters in without nebulae. 1946ApJ. . .104 . . 290M tioned abovehavebeenomittedfromtheaverages(figuresinparenthesesdenotenum- vard pole),is,ofcourse,extremelysensitivetoacosecantcorrection,anditsdeparture bers ofclusters). appears tobetoosmall.NGC6440,withthelowestlatitude(+2?4referredHar- 6293 and6779,forwhichthecorrectionseemstobetoolarge,NGC6171,which,it dening seemstohaveworkedsatisfactorilyinastatisticalsense,ifnotwithoutfailure from theothersishardlysignificant.Onwhole,useofcosecantlawred- velocities ingalacticlongitudeisshownFigure 2.Thefirstpointtobenotedisthe tively broughtoutintheaccompanyingtabulation,whichexceptionalcasesmen- a fewindividualcases is theapparentlackofvelocitiesbetweengalactic longitudes 40°and190°,againbe- velocity axisfallsat—58km/sec.Athirdcharacteristic inthedistributionofmotions spread inthevelocities;theyrangefrom—360to +291km/sec,andinthisrespectthe spectral types“normal”colorindicesandtousethelatterobtainexcessesfrom photoelectric scaleofC2.Itwouldthereforebeunprofitabletoobtainfromtheintegrated new materialagreeswithwhatwaspreviouslyknown. Asecondfairlyevidentfeatureis lar clusters.Inotherwords,theintegratedspectralclassprobablycannotbeinferred class; thedifference,3.1±4.0,clearlyhaslittlesignificance. class isf4.5±1.8(p.e.),whichmaybecomparedtoF7.6±3.6fortheaveragespectral that therearemorenegativethanpositivevelocities; infact,thecenterofgravityon cedure fordeterminingcolorexcessesoftheglobularclustersisonealreadyfollowed tween longitudes230°and300°.Thefirstofthese gaps, inthegeneraldirectionopposite color excessesasderivedbyStebbinsandWhitfordfortheglobularclusters. above, thereisgoodreason,asfartheclusterspectraareconcerned,toaccept class F6,whichispreciselythemeanofaveragecolorandspectralclassesfound by StebbinsandWhitfordinderivingtheircosecantlawofreddening,namely,toassume the measuredcolorindices.Theevidenceathandsuggeststhatprobablybestpro- no closerelationshipbetweencolorandspectraltypeoftheintegratedlightglobu- class, itcanscarcelyberegardedasestablishedwiththeavailabledata.Theaveragecolor tions ofthesolarmotionreferredtoglobular clusters, thedistributionofradial with safetyfromthecolorclass,atleastwhenlatterisbasedonverycompressed Obscured clusters.. the factthatmostof globularclustersinthisregioncannotbeobserved fromthe the sameintrinsiccolorforallclusters.Sincetheyusedacorrespondingtospectral north temperatezone. a regionincludingmorethan one-thirdofthesky.Thesecondvacancyissimply dueto to thatofthegalacticcenter,isquitereal;there but asingleclusterknownthroughout Unobscured clusters. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The lackofappreciablechangeincolorclasswithspectralmaybemorequantita- The foregoingcomparisonsupportstheworkinghypothesisthatthereappearstobe While theremaybeaslightsuggestionofincreasingcolorwithadvancingspectral In ordertoshowataglancethenatureofbasic datanowavailablefordetermina- All, Spectral Class AVERAGE COLORCLASSESCORRECTEDFORSPACEREDDENING vm. SOLUTIONSFORTHESOLARMOTION £3.0(4) £3.0(4) A 5-A9 GLOBULAR CLUSTERS £3.5(2) £3.2 (4) £3.3 (6) F0-F4 £6.0(2) £5.6 (8) £5.5(6) F5-F9 £4.7 (21) £4.7(16) £4.8 (5) G0-G5 £4.5 (39) £4.7 (20) £4.3 (19) (Total) A5-G5 309 1946ApJ. . .104 . . 290M © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 1946ApJ. . .104 . . 290M 21 209 lie inthehemispherescenteredonassumedapex andthosecenteredonthecorre- the solarmotionhavebeencorrected hereforthelocalmotionofsun. the velocities.Theresultquoted hereisfromthesolutionwithK—0andwithoutgrouping, sinceStröm- sponding antapex;thesixthgroupofforty-seven clustersomitsthreewhosevelocities members, respectively,havealreadybeendescribed;thethirdgroupoffiftyclustersin- longitude 55°,latitude0°.Thefirsttwogroupsofclusterswitheighteenandtwenty-six listed inTable4;(3)co-ordinatesoftheapexincludedasunknowns;(4)assumedat may appearratherdiscouragingtoattemptfindthesolarmotionreferredsystem moves inacircularorbitaroundgalacticcenterlocatednearlongitude325°.Viewed berg obtainediT-termswithprobable errorsaslargeK.BothStrömberg’sandEdmondson’s valuesfor that theapexcouldhaveanappreciablenortherly latitude,thelatterisduealmosten- apex atlongitude55°andlatitude0°.Whileitmight appearfromthevaluesincolumn6 cludes allthoseforwhichvelocitiesarenowavailable;thefourthgroupofthirty-four fifty velocities,iffornootherreasonthanthatanumberofreferencesaretobefoundin tirely totheinfluenceoftwoclustersNGC5272 (M3)andNGC620513).These the probableerrorsinvolvedthatthereishardly anyappreciabledeviationfroman may haveundulydecreasedthesolarmotion: clusters andthefifthgroupofsixteencontain, respectively,thoseclusterswhich —Strömberg’s andEdmondson’ssolar-motionsolutionswererepeatedwiththenewer sideration oftheresultsobtainedfromanumbersolar-motionsolutionsbasedonthese based onthisbodyofmaterialcanhardlybeexpectedtoyieldresultshighprecision. from thenorthgalacticpole,motionisclockwise;apexthereforeatlongitude of theglobularclusters,hereafterdenotedbyFe.Accordingtocurrentideas,sun corrected velocitiesarenowavailableforsomeoftheclustersusedinearlierwork these resultscomparablewiththosededucedfromtheadditionaldata—improvedor respectively. Strömberg’sresultwasF©=272±45km/sectowardanapex Principles ofStellarDynamics,p.3[“AstrophysicalMonographs”],UniversityChica- responds totheaveragemotionofnear-bystars. Moreover, theproblemisnotmadeeasierbylargevelocitydispersioninmotions of theseplacesbut,instead,arehighlyconcentratedaroundapointhalfwaybetween, 55°, theantapexat235°.Sinceglobularclustersarenotfoundinabundanceeither since afirstsolutionbaseduponfiftyvelocitiesyieldedX-termof—7.9±18.8km/sec. are giveninTable6.Inthistablealltheresultsdependuponassumptionthat=0, solutions weremade:(1)velocitiesgivenequalweight;(2)assignedtheweights data. Theresultsfromthesesolutionsandanumberofothersnowtobediscussed of StrömbergandEdmondson,whousedeighteentwenty-sixvelocities, go Press,1942),itbecameapparentthatthesolarmotionfromincreasedmaterialwas of theclusters.Nevertheless,despitethesenaturaldifficulties,weshallproceedtoacon- where thesolar-motioncomponentissmall,itevidentthatasolution in galacticlongitude70°±7°andlatitude+13°7°;whileEdmondson’swas going tobenearly100km/secsmallerthanthatobtainedfromtheearlierinvestigations to amovingco-ordinatesystemwhoserotationalvelocityaboutthegalacticcentercor- for alocalsolarmotionof20km/sectowardtheconventionalapexat=271°and8 the literaturetosimilarsolutionsbasedononlyeighteentwenty-sixvelocities. +28°; bythisprocedureanysolarmotiondeducedfromtheclustervelocitiesisreferred F© =261±40km/sectoward67°6°and+1°8°.Inordertomake 20 21 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 61,353,1925;MLW.Contr.,No.292. Strömbergactuallymadefour solutions,withandwithoutaiUterm grouping To consider,first,thesolutionsforfirstthree groups, itisevidentonthebasisof With thispictureofthedistributionglobularclusterradialvelocitiesbeforeus,it As thefirststepinsolar-motionsolutions,velocitiesTable4werecorrected From preliminarysolutionsmadewithaboutfortyvelocities(seeS.Chandrasekhar, For eachofthesixgroupsclustersnotedincolumn1Table6,foursolar-motion GLOBULAR CLUSTERS 311 1946ApJ. . .104 . . 290M values intherangefrom168to180km/sec.Theseresultsmaybecontrastedwith from thefiftyequallyweightedvelocitiesThevaluesofapexlongitudeincolumns3 each giventheaverageweightof7,amodifiedsolutionwithweightedvelocitiesgave assigned weightsof24and16,respectively,contributednearly20percenttotheweight km/sec canbeaccepted;thisquestionistakenup inthefollowingsection. tions basedonfiftyvelocitiesisF©=174±23km/sec,withthefoursolutionsgiving km/sec. Thecomparisonclearlyshowsthat,forasmallgroupofeighteentotwenty-six average ofthoseobtainedforthetwosmallergroupsinvestigatedearlierbyStrömberg 5. Antapexgroup 4. Apexgroup... found inthethirdlineofcolumns7,8,9,and10Table6.Theaveragefoursolu- there isnolargedeviationofthesolarmotionfromadirectionatrightanglestocenter tained fromfewervelocitiesarenotsubstantiatedbytheincreaseddata.Onwhole, and 4shownosignificantdeviationfrom55°;thesomewhatlargervaluespreviouslyob- two objectsatthehighlatitudesof+78°and+40°withvelocitieshaving 312 it maybeconcludedonthebasisofthesefiftyglobular-clustervelocitiesthatprobably of thesolar-motioncomponentperpendiculartogalacticplane.WithM3and13 known globularclusters,itbecomesimportantto try toestimatetheprobableeffecton al selection,whichhastobefullyinvestigatedbefore asolarmotionassmallF©=175 than thatforthegroupoffiftyclusters.Suchresults suggesttheinfluenceofobservation- weights; infact,therangefromF©=264to198 km/sec isfiveandahalftimesgreater and byEdmondson.Withtheco-ordinatesofapexincludedasunknowns,anaverage 3. Mayall clusters, thesolarmotionisquitesensitivetopositionofapexandassigned weights orassignedareused;fortheassumedapex,F©=226±3319829 6. NGC2298, of thegalaxyorfromgalacticplane. 2. Edmondson. +9?2 ±8?1fortheapexlatitude;thisvalueagreescloselywith+8?2+8?8obtained longitude 55°andlatitude 0°.Thenew,thepreviouslyknownbutredetermined, andthe the solarmotionofthoseclusterswhich,because oftheirpositions,contributemost weight tosolar-motionsolutions.Inordershow graphicallyhowdifferentgroupsof shown plottedagainstthe cosineoftheangulardistancefromanapexassumed tobeat clusters, orevenindividualmayaffect the solarmotion,adiagramsuchas Figure 3isuseful.Inthis figure theknownvelocities,correctedforlocalsolar motion,are 1. Strömberg.. Fe =264±38km/secor21036isobtained,dependingonwhetherequal omitted 4590, 5694 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The evidenceforasolarmotionconsiderablysmallerthanheretoforederivedistobe Since radialvelocitieshavebeendeterminedfor only slightlymorethanhalfofthe Solution (1) Cl. No. (2) OF 47 Solar-Motion SolutionsC£=0)forGlobularClusters 57.1± 4.8 26.1+18.1 64.5± 4.0 51.3± 6.8 61.8± 5.3 69?9± 6?1 Equal Wt. (3) Galactic Co-ordinatesofApex(Harv.Pole) Longitude 27.4+11.1 54.4+ 5.3 63.6± 5.4 50.1± 5.5 54.8± 7.0 60?9± 8?5 Weighted IX. OBSERVATIONALSELECTION (4) N. U.MAYALL +27.3± 16.1 + 1.3±6.5 + 8.2±8.8 + 8?5±7?0 - 6.7±7.4 Equal Wt. TABLE 6 0.0± 6.3 (5) Latitude + 11.6±6.4 + 12.2±5.6 + 6.7±6.2 + 16.4±6.6 + 19?1±7?7 +29.2 ±9.7 Weighted (6) 248 ±35 Eq. Wt. 219± 24 264 ±34 264± 42 133± 30 168± 23 Apex fromSol. (7) Solar Motion(Km/Sec),Vq 224± 31 205 ±22 214± 31 205± 37 179± 19 172± 25 Wtd. (8) Apex ¿=55°,b=0° 205 ±29 Eq. Wt. 219± 37 213±26 237 ±29 171 ±26 86 ±50 (9) 201± 27 192 ±23 135± 50 178± 26 180± 23 194± 31 Wtd. (10) 1946ApJ. . .104 . . 290M © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem O O + ro O O + o o o fO 1 Antapex -0.8 -0.6 -0.4 -0.2 Cos A +0.2 +0.4 +0.6 +0.8 Apex Fig. 3.—Distribution of radial velocities of globular clusters with respect to cosine of apical distance, .4. Velocities are corrected for local solar motion, and the apex is assumed to be at / = 55°, ô = 0°. #, velocities previously known but redetermined. Q, new velocities. O, corrected earlier velocities. 1946ApJ. . .104 . . 290M 2324 25 reddened toencourageradial-velocityobservations intheordinaryphotographicregion. tion fortheequipmentemployed.Twoofthese clusters—NGC 6121(M4)and6809 in themannerdescribedSectionIII;buteventhey arenearthethresholdofobserva- encountered eventherebecauseoftheveryfewand faintlinesavailableformeasurement; for radial-velocitydeterminations,andatelescope ofconsiderablylargeraperturethan velocities areunknown.Thepercentagesofcompletenessforvelocityobservations H andK.Thethirdgroupincludesonlyfourclusters, whichprobablycouldbeobserved with lowdispersion,itisdoubtfulwhetheranylines willhavevisibilitiescomparableto graphs designedforworkinthevisualandredspectral regions,althoughdifficultymaybe twelve clusters,whiletheirlightisnotnearlysospread out,itisstilltoofaintand unknown. Thetabulationseparatestheclustersverticallyaccordingtoapexandantapex corrected earliervelocitiesaredenotedbydifferentsymbols.Fortheassumedapex,any 314 faint thatslitspectraoftheirintegratedlightwillbeextremelydifficult,ifnotimpossible, limit fortheradial-velocityobservationsmadeatMountHamilton.Inadditionto For theseclustersthebestmeansforvelocitydeterminations wouldseemtobespectro- 36 incheswillbeneededtomaketheobservations. Inthecaseofsecondgroup clusters containsthoseofleastcentralconcentration.Theyaresolittlecondensedand columnar segregation,theclustersnorthof5=—40°arearrangedinthreegroupsac- group, withthelattersubdividedatÔ=—40°,whichisnearpracticablesouthern because theydonotshowhowtheclustersaredistributedasregardsapicaldistance.In centages, however,donotfairlyindicatetheeffectivecompletenessintwogroups, therefore 65and36percentfortheapexantapexgroups,respectively.Theseper- eighteen clustersintheapexgroupandtwenty-nineantapexforwhich six additionsgivearevisedtotalofninety-sevenglobularclusters.Ofthese,theapex ters thenbecomeseparatedintotwogoups,oneincludinglongitudesfrom325°to145° km/sec. Inthelowerpartoffigurepositionsonahorizontalaxisareshownfor in thefigurebyastraightlinethroughorigin.Theslopeofisequaltosolar solar-motion solutionofthekindlistedincolumns9and10Table6mayberepresented observations, Table7hasbeenprepared. order toexaminethispointandestimatethepossibilitiesforfurtherradial-velocity four clustersintheapexgroupandforsixteenantapexgroup.Thusthereremain group includesfifty-two,theantapexforty-five.Radialvelocitiesareavailableforthirty- to obtain.Forsuchclusters,observationsofindividualstarsprobablywillberequired cording totheestimateddifficultyofspectroscopicobservation.Thefirstgroupeight are NGC5694,discoveredbyLamplandandTombaughinvestigatedBaade, the radial-velocityobservationsforclusterslocatedintwohemispherescontaining tion. number ofclustersunknownvelocity;theyaremorefullydiscussedlaterinthissec- motion, andthediagramshowsalinecorrespondingtosolutiongivingF©=200 and NGC1841,reportedbyShapleyParaskevopoulos.Thetworejectionsthe tainly aretobeaddedthelistofglobularclusters.Othernewlyfoundclusters not globular,andthatfourotherclusters—NGC6355,6401,6544,6838—almostcer- the assumedapexandantapex.Withvaluesof/=55°b0°,clus- Crossley photographsitappearsthattwoclusters—NGC6235and6535—probablyare (apex group)andtheother,145°to325°(antapexgroup). 22 24: 2 2 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Star Clusters,Appen.A,1930. Pub.A.S.P.,46,52,1934. M.A, 246,171,1932. 26 ffdBull,,No.914,1941. In Table7,cosinesofapicaldistancesaregivenfortheclusterswhosevelocities There areninety-threeentriesinShapley’scatalogueofglobularclusters.From For reasonssoontobecomeapparent,weshallconsiderthedegreeofcompleteness arvar APEX ANDANTAPEXGROUPS N. U.MAYALL 1946ApJ. . .104 . . 290M values ofcosA(smallapicaldistances)toaffectseriouslythesolar-motionsolution. scale thantheCrossley. 0.5, andthree(NGC6366,6539,7492)withcosAbetween0.30.4.Underthese There isonlyonecluster(NGC6760)withcosA=0.6,6426) in Table7thattheapexgroupthereareveryfewclusterswhichhavelargeenough taining theapexmaybeexpectedtohavelittleeffectonfuturesolar-motionsolutions. circumstances, additionalradial-velocityobservationsforclustersinthehemispherecon- (M 55)—aresolargethattheyprobablyshouldbeobservedwithatelescopeofsmaller Faint andinsufficient- Sufficiently con- served forradialvelocity.Fromthepublisheddescriptions, however,itwouldappear how manyofthese,far-southernclusterswithsuitably largevaluesofcos+couldbeob- would beveryvaluabletohavevelocitiesforadefinitive solar-motionsolution Sufficiently bright Figure 3.Theotherclusters forwhichvelocitiesarenotavailableomitted, because that atleastsixclusters(thoseinparentheses)might bedifficultobjectsforspectro- out directphotographsonascalecomparablewith Crossleyplates,itisdifficulttotell number oflargevaluescos+,whichoccurinthe polarcapsouthofô=—40°.With- scopic study.Exclusionofthesedoubtfulcases leaves thirteenclustersforwhichit which have|cosA\>0.3 areshownplottedonahorizontalaxisinthelowe* partof ly condensed [8 clusters] dened and greatlyred- densed butfaint [12 clusters] and condensed [4 clusters] © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Turning, now,tothedistributionofapicaldistances,weseefromvaluescosA The caseisquitedifferentfortheclustersin antapexgroup,forherewefinda To summarizegraphically theforegoingdiscussion,thoseclustersofunknown velocity Character op Clusters Distribution ofValuescosAforClustersUnknownVelocity {A =AngularDistancefromAssumedApexat/55°,b—0°) 6366 5466 6426 NGC 6324 6287 6522 6517 6401 6355 7492 6553 6539 6528 6809 6342 6316 6760 6569 Apex Group ô >—40° + .498 + .346 + .205 + .035 +.368^ + .044 + .051 + .061 + .052 + .101 + .614 + .129 + .389 + .155 + .009 + .051 + .138 + .173 cos A GLOBULAR CLUSTERS 6144 5897 5053 NGC 6453 6121 288 TABLE 7 5> —40° -.056 -.014 -.100 -.197 -.044 -.100 cos A Antapex Group (IC 4499) (4372) (5946) (5927) (6352) (6496) NGC 4833 3201 2808 5286 5139 6362 6101 1261 6752 6584 6397 6388 6139 1841 6541 362 104 5 <—40° -.758 -.572 -.564 -.817 -.976 -.952 -.621 -.800 -.491 -.720 -.696 -.717 -.342 -.206 -.504 -.273 -.257 -.624 -.491 -.336 -.255 -.136 -.171 cos A Southern Hemi- (Parentheses denote [23 clusters] . centration) insufficient con- ful nature,orof sphere objects objects ofdoubt- Character op Clusters 315 1946ApJ. . .104 . . 290M portance thereductionin velocityrangearoundtheantapexproducedby the omission velocity betweenNGC7089and6934,353km/sec, neartheapex,issimilarto velocity rangebetweenNGC1851and4590,390 km/sec,neartheantapex.Theprin- the antapexgroupdistributionofresidualvelocities isasymmetrical:therearenearly average radialvelocityof —58km/secforallfiftyclusters,probablyoutweigh inim- as thosewhichhelptoincrease it.Thislattercircumstance,andthestrongly negative cipal differenceinthecharacterofvelocitydispersions inthetwogroupsisthat plausibly correctedforobservationalselection. because ofobservationalselection.(5)Forforty-sevenclusters/F©=207+24km/sec, velocities dependentirelyuponlow-dispersionCrossleyspectrograms,andtherefore twice asmanyclusterswhichtendtodecreaseasolar motionoftheorder175km/sec that aroundtheapexwhenallvelocitiesare included.Forexample,therangein the useofconsiderablejudgment,andomission ofthreevelocitiesmaybeobjected much weightistobeattachedthelargervalue? It resultedfromaprocedureinvolving for thefourdifferentwaysoftreatingdata;co-ordinatescomputedapex they maybeundersuspicion.Withthesethreevelocitiesomitted,thesolarmotion, to foratleastonereason:thevelocitydispersionaround theantapexiscomparablewith for thesolarmotion:{a)Forfiftyclusters,F©=174±23km/sec,probablytoosmall agree closelywiththoseoftheassumedapex. based onforty-sevenvelocities,averages207±24km/sec,witharangeof27km/sec from theassumedapexandasmallersolarmotioncanresultlackofvelocities 5694) whosevelocitiescanappreciablydecreasethesolarmotion.Moreover,thesethree clusters ofunknownvelocityintheantapexgroup,seriessolutionslastline for thosethirteenclustersintheantapexgroupwhichhavebeendesignatedTable7 cated inFigure3,itmaybeseenthattherearethreeclusters(NGC2298,4590,and of Table6weremade.Fromaninspectionthedistributionnewvelocitiesindi- represents aforcedandunwarrantedtreatmentoftheobservations,asisevidentfrom and inFigure3. in theoppositesense.Thecomparisonsuggestsconclusionthatappreciabledeviation group, whiletheyshownearlythesamerange,donotreachsuchlowvaluesasin the exceptionallysmallsolarmotionsandlargeprobableerrorslistedinline5 other group;also,thelongitudeofcomputedapexdeviatesfromassumed columns 9and10ofTable6.Thecorrespondingsolarmotionsinline4fortheapex velocities derivedfromtheirintegratedlight.Theotherthree,asindicatedinTable7, velocity observationsintheapexgrouparesubstantiallycompleteforsolar-motionsolu- so differentfromtheassumedapexthatuseoflattertocalculatesolarmotion solar motion.Infact,theco-ordinatesofapexcomputedfromsmallergroupare points onthehorizontalaxissuggestsaseriousdeficiency,whoseinfluencewenowat- velocities ofenoughindividualstarsinthemareobtainedtogivesatisfactoryradial the longitudeofapex,(b)increaseslatitudeand(c)decreases velocities fortheseclusters.Intheantapexgroup,onotherhand,distributionof are amongtheleastconcentratedandfaintestclusters,itmaybesometimebefore 5, Table6)indicatesthatthedeficiencyofvelocitiesinantapexgroup{a)decreases comparison ofthesolar-motionsolutionsforapexandantapexgroups(seelines4 tempt toestimatebyconsideringthesolutionsinlastthreelinesofTable6. are mainlyofvaluefordeterminationsthemeanpeculiarvelocity. clusters with|cos<0.3contributebutlittleweighttosolar-motionsolutions;they 316 tions. Ofthefiveclustersindicated,onlytwo(NGC6760and6539)arelikelytoprovide © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The questionwhichhastobeconsideredbefore a finalvaluecanbegivenis:How From theforegoingdiscussion,wehaveatthispointfollowingalternativevalues With theaimofallowingquantitativelyforeffectonsolarmotion Since theradialvelocitiesforclustersinapexgrouparesubstantiallycomplete, It isevidentfromthedistributionofpointsonhorizontalaxisthatradial- N. U.MAYALL 1946ApJ. . .104 . . 290M , 101km/sec. : Indiscussionsofgalacticrotationthesun’sorbitalvelocityoftenhasbeenconsidered 26 27 28 give asthemostreliablevalueforsolarmotionreferredtoglobularclusters: of thethreeclustersinquestion.Atallevents,untilfurtherdatabecomeavailable,we from V©. circular velocityofrotation,whichhereafterwillbedesignatedbyFotodistinguishit tion isprobable;andhencetheresomereasontore-examinethequestionofsun’s clusters. Itappearsfromfiftyvelocities,however,thatasignificantlysmallersolarmo- as thesolarmotionderivedfromradialvelocitiesofeighteentotwenty-sixglobular circular velocityatthedistanceRofromgalacticcenter,asfollows: gests twoalternativeinterpretations:either(1)nosignificantgeneralrotationofa rotation. Accordingly,asmallersolarmotionofF®=200km/secfortheclusterssug- that itwouldthereforebeexpected,fordynamicalreasons,tohavelittleifanygeneral to beoftheorder275-300km/sec;andbasisforthisfigureusuallyhasbeengiven The averageoftheresidualmotionswithoutregardtosign(meanpeculiarmotion)is sources, discussedbelow. cluster systemandasolarorbitalvelocityashithertoassumed(Fo=275-300km/sec). spherical clustersystemandasmallercircularvelocity(Fo=200km/sec)forthesun as thesun’sorbitalvelocityhasbeenthatclustersystemisessentiallysphericaland velocity anddistancefromthegalacticcenterarethereforeconnectedasinaccom- and Baresimplyrelatedtothetotalangularvelocity,Vo/Ro,whereFoissun’s The secondalternativeappearstobemoreprobableonthebasisofdatafromother or (2)anappreciableamount(75-100km/sec)ofsystematicrotationforaflattened panying tabulation.Thesimpletheoryofgalactic rotationthusleadsessentiallytoa for ^4andjBare-f-0.0177and—0.0128km/sec/parsec,respectively.Thesun’sorbital for thestudyofgalacticrotation,R.E.Wilsonconcludedthatmostprobablevalues In themostrecentdiscussionofradial-velocityandproper-motionmaterialsuitable numerical dependenceofFouponRo,orviceversa, andamoreprecisespecificationof Lundmark’s earlydiscussionof theproblem{Mon.Not.R.A.S.,84,749,1924). one requirestheevaluationofotherbysome other means. of therotationlocalstellarsystemaroundadistant galacticcentergoesbackatleastasfar 26 27 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The underlyingsuppositionintheinterpretationofglobularclustersolarmotion Theideathatthesolarmotionwithrespecttoglobular clustersmaybeprincipallyareflection a) InthetheoryofgalacticrotationasformulatedbyOort,hisdynamicalconstantsA B.Lindblad,UpsalaMedd., No.3,1925;Ark.f.math.,ast.ochfys.,19,A,21,1925. ™ Ap./.,92,170,1940;Mt.W. Contr.,No.631. X. GALACTICROTATIONANDTHEGLOBULARCLUSTERSYSTEM F© =200±25km/sec,toward¿55°,0°. 350. 300. 250. 200. GLOBULAR CLUSTERS sun’s ORBITALVELOCITY (Km/Sec) Vo/R® =A—B. vo (Kpc) 11.5 RQ 9.8 8.2 6.6 317 1946ApJ. . .104 . . 290M • formityofdistributionisanextremeconditionprobablynotrealizedinthegalaxy,it 30 3132 29 26 33 82 38 35,36,37 318 velocity measuresofthegalacticCepheids.Byusingmoregeneralformulaederived formulae forgalacticrotation,withobservationsofobjectsatgreaterdistancesfromthe by MissHayfordandBottlinger,JoyobtainedRo—10.0kpcFo=296 sun. ArecentexampleofthisprocedureisJoy’sdiscussionhisextensiveradial- km/sec. Bothofthesevalues,however,maybesubjecttorevisionbecause(1)the adopted constantofinterstellarabsorption,a—0.85mag/kpc,probablyistoolarge represented withamorenearlyuniformdistributionofmassandconcludedthat mass ofthegalaxyisconcentratedatcenter.Infirstcase,R.E.Wilsonfound and (2)Bottlinger’sformulausedtoobtainVorestedontheassumptionthatentire spirals—M 31andM33—foundthattherotationalvelocitiesinthesesystemscouldbe for Roshouldbeincreasedby10percent,toaboutRo=11kpc.Inthesecondcase, body ofradial-velocityobservationsCepheidsandotherstars,sothatJoy’svalue that a=0.65mag/kpcbroughtintoagreementthedeterminationsofAfromlarge similar distributioninthegalaxycouldnotberuledoutbyavailabledata.If Wyse andMayallinaninvestigationofthedistributionmasstwonearest would seembettermerelytogivetherevisedresultas240