195 9Apj. . .130. .629B the HERCULES CLUSTER OF

Home , 111 Herculis, Hercules (dwarf galaxy), Hercules Cluster, Hercules Superclusters, NGC 6041, NGC 6045

195 9ApJ. . .130. .629B 12 o 6 group ofabout75brightnebulaeandalargernumberfaintones,distributedoveranarea from thosecontainingveryfewnebulaeuptotherichclusterswithhundredsorthousands reflector, isshownanddescribed.Morethanthree-quartersofthebrightnebulaehavebeenclassified, are indeedaslargethis,thatthereisaamountofintergalacticmatter,andthecluster nebulae wereobtainedbyHumason,and10havebeenuswiththe82-inchreflector.The with alesssteepgradientofdensitywithinthecluster.Clearly,thisclusteringtendency of members.Richclustersmayhaveahighdegreecentralconcentration,orthey state, theaveragegalacticmassmustbe^10Mo.Threepossibilitiesarediscussed:thatmasses mated. Bymeasuringthedistancesbetweenallpairsona48-inchSchmidtenlargement,totalpoten- We shalldiscussresultswhichhavebeenobtainedinthiswaySectionIII.Sufficeit may containalargenumberofmembersspreadoverconsiderableareathesky expanding. ThedatafortheComaandVirgoclustersarealsoreviewed.Itisconcludedthatboth mean redshiftis10775km/sec.Fromthissample,thetotalkineticenergyofnebulaehasbeenesti- and, ofthese,69percentarespiralsorirregularsand31ellipticalSO.Radialvelocitiesfor7 highly symmetrical.Iftheseclustersarestationary,thenitispossibletousethevirial of thenebulaeinsomeclustersisthatanisothermalgravitationalgassphere Hydra, Cancer,andPegasusclusters.Zwickyhasshownthatthedensitydistribution by themethodofmakingcounts,Zwickyandhiscollaborators(1941,1942a,b, of nebulaeisthegreatestcosmologiesignificance,thoughonlyafewresultshave Coma cluster.Somediscussionoftheimplicationtheseresultsisgiven. Hercules andtheVirgoclustersareprobablyexpanding,butsituationisuncertainincaseof never acceptedanyoftherevisionsindistancescalesinceHubble’s(1936)value and thetotalmassofclusterhenceaveragemassesmembers. as yetbeenobtainedwhichbearatallonthefundamentalquestionsassociatedwith tial energyhasbeenestimated.Fromtheseresultsitisconcludedthat,iftheclustertobeinastationary the originandevolutionofthoseclusters. I X40'.Asetofplatespartsthiscluster,takenbyDr.WalterBaadewiththe200-inchHale been listedbyAbell(1958)(No.2151inhiscatalogue), andthereisanotherirregular irregular systemshave,toourknowledge,beenstudied indetail.TheHerculescluster, The firstlistofthesewasgivenbyShapley(1933). ThebestknownistheVirgocluster the red-shiftconstantof526km/secper10pc. to remarkherethatthevaluesobtainedbyZwickyareoftenunrealistic,sincehehas theorem todeterminetherelationbetweenvelocitydispersionofclustermembers which wasfirstbroughttoourattentionbyW.Baade, fallsintothiscategory.Ithas because itissonearandconspicuoustous. Apart fromthiscluster,noneofthe (with acutoff).Intheinnerpartsofsuchclustersdistributionnebulaeis 1951, 1957),ShaneandWirtanen(1954),Omer(1952).TheseincludetheComa, cluster, AbellNo.2152,1?3southofit.has putNo.2151inrichnesscategory © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The clusteringtendencyofnebulaeiswellestablished.Clustersareallsizes,ranging The northernoftwoclustersnebulaeinHercules,firstlistedbyShapley1933,isanirregular Of therichcompactclusters,anumberhavebeenstudiedinlasttwentyyears Besides therichcompactclusters,alargenumber of irregularclustersarealsoknown. * ContributionsfromtheMcDonaldObservatory,No.310. THE HERCULESCLUSTEROFNEBULAE* G. R.BurbidgeandE.Margaret Yerkes andMcDonaldObservatories Received March26,1959 I. INTRODUCTION ABSTRACT 629 195 9ApJ. . .130. .629B 1m 1m na o apparently significantlyhigher thanthecorrespondingproportioninVirgo cluster, both 200-inchplatestakenbyBaadeand attheprimefocusof82-inch and 31percentellipticalorSO.Thisremarkably highproportionofspirals,whichis have lowerresolution.Outofthe61galaxiesclassified, 69percentarespiralorirregular McDonald telescope.Thelatterplatescoveralarger areathanthe200-inchplatesbut such asthese.However,intheComacluster,of the 23membersforwhichredshifts are givenbyHumasonetal.,only1,orabout4per cent,hasbeenclassifiedasaspiral. of spiralandirregularnebulaeisverysmall(cf.Hubble, quotedbySpitzerandBaade concentrated clusters,suchastheComaandCorona Borealisclusters,theproportion fied asirregular.FromtheHumason,Mayall,andSandage(1956)catalogueofredshifts, percentages bytypesintheVirgoclusterdifferentapparentmagnituderanges. as spirals.Bycontrastwiththisitiswellknown thatinhighlycondensed,centrally cent; 49perISÔ-ld^,48140-149,32150- The percentagesofspiralsareasfollows:lOÔ-lO^,22percent;ll0-ll9,59per about 57percentarespirals.ShapleyandAmes(1930)(1950)havegiven which havepreviouslybeenobtainedfortheVirgocluster. but outsidetheregioncoveredby200-inchplates.Itismoreclearlyvisibleon reproduced inFigures1-5.2-5arefromplatestakenbyWalter 1951). Wehavenotbeenabletofindanygoodfigures basedoncountsbytypeinclusters 73 nebulaefromtheVirgoclusterarelisted,and,ofthese,27,or37percent,classified and SOnebulae.Beforediscussingtheseproportions,weshalldescribetheresults 159, 20percent.Ineachrangeasmallproportion—atmaximum,9cent—isclassi- 74 percentwerespirals.Ofthe400,about50belongtoVirgocluster,and,ofthose, system formed.Thereisatleastoneotherdoubleinthecluster,arelativelyfaintpair nebulae inthecluster,afactwhichmayhavesomebearingonway south andeast-westextentsareaboutI40',respectively. Baade withtheHale200-inchreflector.Thesystemisunsymmetrical,anditsnorth- nebulae hasbeenestimatedasthousands.Itisthisnumber,73,thatwillbeusedin a platetakenwiththe82-inchtelescope. of spiralsnearthenorthernboundary.ThisiswithinareacoveredinFigure1 Section III,wherethekineticandpotentialenergiesofHerculesclusterareobtained. bright nebulaeusedindiscussionsoftheComacluster,whichnumberfaint which appearinFigures2,3,and5.Themembersofthedoublesareamongbrightest that contributemostofthemass.Thusthese73nebulaeareequivalentto800 3-3J mag.fainterthanthebrightestnebula,wecounted73.Thesemustbenebulae which mostofthefaintonesmustbefieldnebulae.Downtoanestimatedlimitabout plate (red-sensitive)whichwasobtainedfortheSkySurvey.Thisisreproducedin be fainterthan17.4,butwehavenotestimatedbyhowmuch. graphic magnitude.Withthenecessaryrevisioninmagnitudescale,thislimitmust Figure 1.Downtothefaintestobjectthatcouldbeseen,wecounted242nebulae,of 2, whichmeansthatitcontainsbetween80and129membersdownto2mag.fainter 630 than thethirdbrightestmember.Shapley(1933)alsolistedaclusteratthisposition (No. 15)butgivesitsmembershipas256downtotheplatelimitof17.4apparentphoto- 1 0 1 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem We haveclassifiedasmanyofthemembers Herculesclusteraspossible,using 1950co-ordinatesofcenter: a =ôT1754'. Hubble (1926)discussedabout400nebulae,mostlyfieldandfoundthat The Herculesclusterisanextremelyinterestingone,aswillbeseenfromtheplates The secondnotablefeatureisthehighproportionofspiralsincomparisontoelliptical The firstfeaturethatonenoticesisthepresenceoffourconspicuousdoublesystems We havemadecountsonanenlargementfromtheoriginalPalomar48-inchSchmidt G. R.BURBIDGEANDE.MARGARET II. DESCRIPTIONANDOBSERVATIONS 195 9ApJ. . .130. . 62 9B Fig. 1.—Herculesclusterofnebulae.Reproducedfromoriginalred-sensitive48-inchSchmidt olatCjCourtesyNationalGeographicSociety-PalomarObservatorySkySurvey.Northisatthetop,eastleft © AmericanAstronomicalSociety•ProvidedbytheNASAAstrophysicsData System ■#* Fig. 2.—Part of Hercules cluster of nebulae. Plate obtained with 200-inch Hale reflector at Palomar Observatory by Dr. Walter Baade. Plate center (1950) : = ló^B, 5 = +17054'. Orientation Éià(Asi«iciimiTig^sêr!ôi»OHtiuidaSaH;ifièT;tl?aPtliL\^tdiJcÂ\iàklfâ.NthSi\ftV4tmïplws3tii.Data System Fig. 3.—Central part of Hercules cluster of nebulae. Plate obtained with 20(Mnch Hale reflector at Palomar Observatory by Dr. Walter Baade. Plate center (1950) : a = 16h2Ii19, ô = +17054/. Orienta0(îfî^lÂlÍPoB¡ábdcal Society • Provided by the NASA Astrophysics Data System 1959ApJ. . .130. .629B / a =8+17°54.Orientation andscaleasinFig.2. Fig. 4.—PartofHerculesclusternebulae.Plateobtainedwith200-irch HalereflectoratPalomarObservatorybyDr.WalterBaade.Platecenter(1950): © AmericanAstronomicalSociety •ProvidedbytheNASAAstrophysicsDataSystem h/ 195 9ApJ. . .130. .62 9B a =162“9,ô+17°39.Orientati@iAiri&îf^&F 10pcdistant,evenifonesystem in mindthat,forirregularclustersatsuchadistance, itisalwaysdifficulttoruleout position. table, buttheoutlyingmembersIC1173and 1186lienearerthemiddle.On is spoiledbycoma.However,thespectrumshowed,aswellH,K,andDlines well besmallerthanthe spreadinapparentmagnitudewithinacluster becauseof ment. Wehavesetanaverageprobableerrorof± 100 km/seconourmeasures.Theout- emission. Na I(themeanwavelengthwasused).Haemissionnotseeninmostofthenebulae general, thespectralfeaturesmeasuredwereHandKlinesofCan,Gband by Humason,withtheBspectrographatprimefocusof82-inchtelescope.In are physicallyunrelated,thoughinsomecases statistical argumentsmightbeused. observationally thepossibilitythatoneisseeinga superpositionofsmallgroupswhich and weshalldiscussthemonthatbasisinwhat follows. However,itshouldbeborne lying membersNGC6055,6061,andIC 1194 lietowardthehighendof and 10530km/secforNGC60411005899436045,inreasonableagree- corrected fortherotationofourGalaxy,aregiveninTable1.ForNGC6041and Although thereisstillsomeuncertainty,theemissionfeaturesmaybeidentifiedwith and theGbandinabsorption,whatisapparentlyasetofbroademissionfeatures. measured, althoughitwastheonlymeasurablefeatureinelongatedspiralNGC6045. the intrinsicspreadin absolutemagnitudesofnebulae. 6045 themeansofHumason’svaluesandoursaregiven;theywere,respectively,10592 covered bythe200-inchplatesandisnearedgeofan82-inchplate,whereitsimage It isperhapssurprisingthattheinvolveddoublesystemIC1181doesnotshowHa The nebulahasastringofbrightknots,togetherwithfaintermaterialextendingeast- points upasignificantdifferencefromthesituationinhighlyconcentratedclusters. of 8additionalnebulaehavebeenmeasuredbytheauthors,aswell2already Figure 5,aboutKEsouthofIC1182-1184. object butlistitasIC1181.Actually,1181istheconspicuousdoubleseenin ward inaroughlystraightline,andanS-shapedsweepoffaintmaterialextending [Fe vii]. to thenortheastandsoutheastofthisgrouparereallyphysicalmembers,radialvelocities central andeasternsubgroups.Inordertoattemptestablishwhetherthenebulae also asubgroupeastofthecentralsubgroup. northeast andthesoutheastdirectionthereappeartobe“chains”ofgalaxies;is 3, wheretheobjectappears51mmfromleft-handedgeand133bottom. in theHerculescluster. whole, thereisapparentlynosignificantpreferential groupingofradialvelocitywith the northwestdirection.AmbartsumianandSchachbazian(1957)havedescribedthis (using Humason’swavelengthforthisfeature),andtheblendoftwoDlines there maybeaconsiderablenumberoflow-luminositydwarfandirregularsystems analogy withthesituationinVirgocluster(Reaves1956),itistobeexpectedthat This matterwillbeexaminedfurtherinthediscussion. 1. Thereappearstobeasmallcentralsubgroup,whileemanatingfromitinboththe © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem There iseveryreasontosupposethatthenebulae in thisareaformaphysicalgroup, The radialvelocitiesforallthenebulaeobserved,bothbyHumasonandus, NGC 6055doesnotlookunusualonthe48-inchSchmidtplate.Itisoutsidearea A thirdnotablefeatureoftheclusterisitsconfiguration,whichshowninFigure A verycuriousstructureisseeninoneofthenebulae,IC1182-1184,shownFigure Many ofthefainternebulaeinthisclustercanbeseentoratherirregular.By Humason (Humasonetal.1956)hasmeasuredradialvelocitiesof7nebulaeinthe HERCULES CLUSTER 631 195 9ApJ. . .130. .629B 6 1/2 6 6 km/sec. Usingthered-shiftconstantof75km/secper10pcrecentlyderivedbySandage by afactor73/15,wefindthatthetotalkineticenergy is which are(^)=1010km/sec,v1749km/sec. These valuesmaybecomparedwiththoseobtained fortheComacluster(Oort1958), much smallersample. radial velocitiesequals3Af/22^,and,allowingfor therestofnebulaebymultiplying equal mass,Mgm.Thenthetotalkineticenergy ofthe15nebulaeforwhichwehave If wesupposethatthetotalaveragespacevelocityfornebulaeinacluster,v,isrelated et al.1956)hasvelocitiesforonly23nebulaeintheComacluster,orabout3percent a resultwhichisstrictlytrueonlyforspherical velocity distribution,then are thevelocityresiduals,whereVmeasuredrecessionvelocities,thenitisfound east-west extensionsoftheclustersareabout2.5X10and1.7pc,respectively.If to vbytherelation of thebrighternebulae,andusevirialtheoreminthatclusterrestsonthis 20 and25percentofthebrightmembership.OnotherhandHumason(Humason a smallclustersuchasthis,sincewehaveradialvelocitiesof15nebulae,orbetween nebulae iftheclusteristobeinastationarystate. 632 that kinetic energyoftheclustermembersandshalldeterminealsopotential of thecluster.Weshallthenusevirialtheoremtoobtainanaveragemass (1958), thedistanceofclusteris144X10pc.Inthiscasenorth-southand r r © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The meanrecessionvelocityobtainedfromthenebulaegiveninTable1is10775 As farasthekineticenergyisconcerned,thereclearlysomeadvantageinanalyzing To calculatethetotalkineticenergy,weshallsuppose thatallthenebulaehave In thissectionweshallusethemeasuredradialvelocitiestoestimatetotal NGC ngc NGC NGC IC 1C 1C 1C Velocities inHerculesCluster,CorrectedforRotationofOurGalaxy Nebula 6045. . 6044. . 6047. . 6041.. 1183. . 1181B. 1185. . 1181A. G. R.BURBIDGEANDE.MARGARET Observer H, B H, B III. APPLICATIONOPTHEVIRIALTHEOREM =Vr-{ Vr)—10775km/sec H H H H B B Vrr l7 ^ =yX8.7l6Xl0e rgs. 1//2 ( ^)=631km/sec. v =1093km/sec. M (km/sec) Velocity 10161 10813 10575 10561 10059 10001 10447 9593 zP =3< TABLE 1 NGC 6055.. NGC 6061.. NGC 6050A. NGC 6056.. IC 1194.. IC 1186. 1C 1173.. Nebula Observer B B H B B B B 11781 11765 11292 11179 11135 10963 11314 Velocity (km/sec) 195 9ApJ. . .130. .629B f 12 12 11 11 12 Here æ>1.Itisdifficulttoestimateavalueforæ,butitseemsprobablethatwill be nearto2.Thus,forthetimebeing,weshallputx= where rßisthetruedistance.Carryingoutsumoverallpairs,wefindthat projection factor,definedby Here risthedistancebetweennebulaeaandßmeasuredonprint^mean requires noconsideration,sinceitisfulfilledonly forM>10Mo.Thetotalenergy ulae mustbenotlessthanabout10Meiîthesystemistostationary.For,ifTf< pairs ofnebulaeonanenlargementthe48-inchSchmidtplatecluster.The The condition result, forthefollowingreason.Thesenebulae,iftheyareclustermembers,probably of thesystem,E,isgivenby is duetothefactthattheyarebackgroundobjects,itwouldbeincorrectincludethem. of muchsmallermassthantheaverage,inwhichcasetheywillmakeaninsignificant of thefaintestnebulaeinareaclustercanmakenoappreciablechange number ofmeasurementsrequiredforallpairsamong73nebulaeis2628.Theneglect therefore estimatedthepotentialenergybymeasuringdistancesbetweenall whether ornotthiscluster isinastateofdissolution.Itshouldbeemphasized thatin is fulfilledifTf=5X10Me.Thus,iîM< 10Me,then and thesystemisexpanding.Theconditionthat easily beapproximatedbyananalyticalexpression,asisthecaseinaclusterwhich contribution tothekineticandpotentialenergy.If,onotherhand,theirfaintness the nebulaehavedistributionofanisothermalgravitationalgassphere.We i.e., thesystemhaspositivetotalenergy. this calculationtheneglect ofanumberfaintnebulaewhichmaybepresent inthe 10 Me, a aß 12 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Now, iftheclusteristobestationary, For aclusterasdiffuseandunsymmetricalthis,thepotentialenergycannot The followingsectionwill bedevotedtoadiscussionofthisresult,try determine Solving forM,wefindthatM=1.03X1ÖTfo*Thustheaveragemassofneb- The totalpotentialenergy,0,isgivenby tt= -—X8.456X10 Q = HERCULES CLUSTER 2 x 1 M Z a, ß - - 2£^ fiU=0. 2Eji +Í2>0, E¿ +12>0, E =fi12. 2 2E +12<0 Efc -f-12—0 k GM V a, ßaß ‘ *Y' a, ßâß -28 erg . 633 195 9ApJ. . .130. .629B 14 12 14 6 14 15 11 14 6 12 14 Humason’s radialvelocities andadistancescaleinerrorbyfactorof7 as compared cluster isstationaryandusingtheradialvelocities givenbyHumason,hefounda of Zwicky(1951),Omer(1952),andShane Wirtanen (1954).Assumingthatthe metrical clusterfollowsthatofthemoleculesinan isothermalgravitationalgassphere. distance scale,andnowgetatotalmassof10.5X 10 Afo-Schwarzschildassumedthat nebulae isabout1.3X 10 Mo-Zwicky(1957),usinghisowndataon countsand the 800brightestmembers contributedthebulkofmass.Theaverage massofthe total massfortheclusterof3X10Mo-Wehave revisedthisvalue,usingSandage’s Schwarzschild (1954)hasanalyzedthedata,using acompromisebetweenthecounts earlier, Zwickylongagoshowedthatthedistribution ofthenebulaeinthishighlysym- in whichirregularclustersevolve.Thisisthefact,referredtobyZwicky(1957,p. pc. Thiswouldmeanthatallthemassesusedinthispapershouldbereducedbyafactor to bedistributedspatiallyinsubgroupsaccording tonebulartype. of theHubbleconstantassumed. the massesoffieldnebulaeandclusternebulae,thisratioisindependentvalue of about2.However,aswillbediscussedlater,theimportantfactorisratiobetween part ofasuperclusterwhichthelocalgroupisalsopart;thisboth ing thevirialtheoremandtotalmassofvisiblegalaxiesarisesfromfact 78) andothers,thatthereissometendencywithintheVirgoclusterformembers tion oftheHubbleconstantisrequired.Hesuggestsavalue140km/secper10 rotating andexpanding.IftheargumentofdeVaucouleursisvalid,afurthermodifica- Vaucouleurs (1958),inwhichitwasproposedthattheVirgoclusterformsmajor present intheformofdarkintergalacticmaterial. ferent interpretationonit.Hehasobtainedatotalmassof5X10Afoandstated are partofthephysicalgroup.Thefirstinvestigationusingearlyradialvelocities uniform distributionofnebulae,butoutsidethistherearemanysystemswhichalso the massofcluster.Suchanideaisimplicitinrecentlypublishedpaperde that thesystemisdissolvingandthusvirialcannotbeusedtodetermine sumian (1958).Hebelievesthatthediscrepancybetweentotalmassobtainedbyus- Mo- Thusiftheclusterisreallystationary,theremustbeabout30timesmoremass for theVirgocluster,wefindthattotalmassisnowabout10Mo,andaverage masses ofthegalaxieswerethen2XIQMo-IfweuseSandage’sdistancemodulus in circularorbits.Thetotalmasswasfoundtobeabout10Afo,andtheaverage Within adiameterofabout7°or1.9X10pc(Sandage1958"),thereisfairly Virgo clusterandhasobtainednearlythesameresult,althoughheputratheradif- nebular massisabout2X10Mo-Morerecently,Oort(1958)hasrediscussedthe tionary andobtainedatotalmassbysupposingthattheoutermostgalaxiesmoved to getatotalmasswasmadebySmith(1936).Heassumedthattheclustersta- that thecontributiontomassofvisiblegalaxiesisonlyabout0.18X10 by applyingthismethodtotheVirgoandComaclusters. cluster (cf.Sec.I)willmakeverylittledifferencetotheresult.Asbeshownlater, the situationwillnotbechangedunlesstherearehundredsofthousandsfaintnebulae. 634 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem We shallnowbrieflyreviewtheargumentsconcerning theComacluster.Aswasstated In passing,wenoteaninterestingpointwhichmusthavedirectbearingontheway An entirelydifferentinterpretationofthesameresulthasbeenmadebyAmbart- The VirgoclusterisafarmorepopulousirregulargroupthantheHerculescluster. It isofinterest,first,todiscusstheresultswhichhavepreviouslybeenobtained G. R.BURBIDGEANDE.MARGARET IV. DISCUSSIONANDCONCLUSIONS a) TheVirgoCluster b) TheComaCluster 195 9ApJ. . .130. .629B 10 8 11 12 12 10 8 9 11 12 11 11 13 12 1/2 for NGC5055,8X10Mo.] in proof:Twoadditionalmassesforspiralshaverecently beendeterminedbyBurbidge, M81 (Münch1957),andNGC4594(WyseMayall1942).UsingSandage’sdistance own Galaxy(Schmidt1956),M311957),M33(WyseandMayall1942), mined, withvaryingdegreesofprecision,fromtherotation-curves.Theseincludeour Poveda (1958)hasrecentlydeterminedamassof5 X10Mo,usingthevelocitydisper- nebulae forwhichwehavemassdeterminations aretheMagellanicClouds.From scale, theaveragemassderivedfromthesesystemsis1.5X10Mo.Theonlyirregular discuss eachofthesepossibilitiesinturn. is intheformofinvisibleintergalacticmatter;(3)systemsaredissolving,virial found thattheaveragemassofnebulaemustbeorder10Mo-Thus,al- These are(1)theaveragemassesofnebulae>10Moandclusterspres- sion ofthestarsinnuclearregion.Ifweput thenewdistancemodulusforM31, Burbidge, andPrendergast(unpublished).Theyare, forNGC2146,2X10Mo,and the resultsofBuscombe,Gascoigne,anddeVaucouleurs (1954),adjustedtothenew method clearlywasfraught withuncertainty.Ifisinterestingtonotein passing that, in thevelocity-curveof M31 wasduetogravitationalinteractionwith M32.This this massbecomes8X10Mo-Thisvaluewould appeartosupersedetheearlier distance modulus,thesemassesturnouttobe2X 10and1.5XMo-[Noteadded theorem isinvalid,andthereforethemassessoderivedarespurious.Weshallnow determination ofSchwarzschild,whichwasbased on thehypothesisthatanasymmetry ently inequilibrium;(2)aconsiderableproportionofthemasseachtheseclusters there appeartobethreepossiblewaysofinterpretingtheresultsforallclusters. Hercules andtheVirgoclustersfallintoonecategoryComaclusteranother, applying thevirialtheoremandtherebyassumingthatclusterisstationary,wehave are similartothosesummarizedabovefortheVirgoandComaclusters,i.e.,by also theclusterisinastateofexpansion. excess ofthemassourownGalaxy.Consequently,hebelievesthatinthiscase of thevirialtheoremisillegitimatebecauseitleadstoanaveragemasswhichfarin with thenewdetermination ofPoveda,themass-to-lightratioforM32is only3,i.e., though asfarthenebulartypesanddistributionofnebulaeareconcerned, with theobservedvalueof1010km/secobtainedbyhimfromHumason’smeasures. Mo forthebrightsystemsand0.5X10faintersystems.Withthesevalues, highly uncertainvaluesofaveragemassesnebulaebasedonguessesastothemass- as analyzedbyhimgiveanaveragemassnear1.5X10Mo. mass ofthebrightsystemsisnear6X10Mo.OtherwiseobservationsHumason culated velocitiescanbereducedbytheargumentssuggestedhim,thenaverage Oort believesthatthisisgoodagreement.Ifthedifferencebetweenobservedandcal- members, hehasputM/L=50.Fromthisdeducedaveragemassesof6X10 with Sandage’s,obtainedatotalmassof8X10Mo-Ifwecorrectthisforthedistance to-light ratio.FortheEandSOnebulae,whichformmajorityofcluster counts ofZwickyandthoseShaneWirtanen.However,hehastheninserted strong, highlycondensedcentralclusterfromwhichthesevalueswerederived. mass of1.0X10Mo.ItisalsointerestthatZwicky(1951,1957)haspointedout a radial-velocitydispersion,<^>,of583km/secispredicted.Thistobecompared that thereisamuchmorewidespreaddistributionoffaintergalaxiessurroundingthe scale andusethecountof670brightgalaxiesgivenbyZwicky,weobtainanaverage that ofanisothermalgravitationalgassphere.Hehasusedacompromisebetweenthe © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem For ellipticalorSOnebulaeveryfewdataareavailable. ForthedwarfsystemM32, The resultsderivedfortheHerculesclusterinprevioussectionsofthispaper 1. Forsinglespiralnebulaeinthegeneralfieldanumberofmasseshavebeendeter- Oort (1958)hasacceptedtheresultofZwickythatdistributionnebulaefollows Finally, forthisclusteralso,Ambartsumian(1958)hasarguedthattheapplication HERCULES CLUSTER 635 195 9ApJ. . .130. .629B a 14 12 11 n 10 11 luminous intergalacticmatter ofthiskindmaycontributealittletothe mass ofopen physically connectedpairs ofthistypearerareornon-existent.Weconclude that 10 cluster (Holmberg1937).Ontheotherhand,incompact clusterssuchastheComercluster knots andfaintermaterial.Therearealsoanumber ofpairsnebulaeintheVirgo NGC 4038-4039,4676(BurbidgeandBurbidge 19596),andNGC2444-2445 systems, aswellapeculiarsystemconsistingof anebulawithanextensionofbright 6771 (EvansandWayman1958),Stephan’squintet (BurbidgeandBurbidge1959tf), are Wild’striplesystem(Wild1953;Zwicky1957), thetriplesystemNGC6769,6770, with certainpeculiarsystems.Forexample,some systemsfallingintothesecategories in thecaseofComacluster.Itremainstodiscusspossibilities2and3. His argumentsarebasedontheexistenceofbridgesbetweengalaxies,onehand, references giventhere)thatthepresenceofintergalacticmatterhasbeenestablished. (Burbidge andBurbidge1959c). of whatVorontsov-Velyaminov(1958)hascalled aluminoushaze”inassociation of bridgesmaterialbetweenandaroundsome doubleandmultiplenebulae and onintergalacticabsorption,theother.Therecanbenodoubtofexistence of theclusterisratherdifficulttoanswer.IthasbeenclaimedbyZwicky(1957andother out, certainlyinthecaseofHerculesandVirgoclustersquiteprobably the ratiosgivenaboveareindependentofdistancescale. mass ofellipticalsandSOnebulae,theratiowillbe2or3,unlessoneispreparedtouse is 5X10/0.18^30.EveninthecaseofComacluster,withPage’saverage galaxies inclusterswillbe>10Tfo.Inparticular,theHerculescluster,since70per mass-to-light ratiosare1and31,respectively.Individualdeterminationsforspirals the specialargumentofOortpreviouslymentioned.Itisimportanttoemphasizethat derived byOortofthetotalmassclustertovisiblegalaxies,which virial theoremwasapplied.ThecorrespondingfactorfortheVirgoclusterisratio run almostashightheaverageforellipticals;mass-to-lightratioinM31isabout is 1.8X10Mo.Thislessbyafactorofabout6thanthevaluededucedwhen and SO,ifweusetheaveragemassesderivedbyPage,massofnebulae 20 (Schmidt1957).Thereisclearlynoevidencetosuggestthattheaveragemassesof These valueshavebeenadjustedtoSandage’sdistancescale.Thecorrespondingaverage for spiralandirregularnegulaetogether,5X10MoellipticalSOnebulae. in thisway,itisaveragesthatareneededtomakecomparisonswiththeaveragemasses recent yearsbyPage(1952,1959).Althoughonlyaveragemassescanbedetermined was firstdiscussedbyHubbleandHumason(1939)hasbeenactivelypursuedin cent ofitsmembersarespiralnebulaeandtheremaining30perellipticals of nebulaeinclusters.Page’smostrecentresultsgiveaveragemasses4X10Mo currently attemptingtousethismethod. velocity dispersionsinthenuclearregions.BothR.Minkowskiandauthorsare for theE5nebulaNGC720.Thoughresultsareincompleteanduncertain,acrude obtaining massesforsingleellipticalandSOnebulaeappearstobethatofthe estimate ofthemassobtainedfromthisworkis10Mo.Themostpromisingway nebula isveryuncertain.Theauthorshaverecentlyattemptedtoobtainarotation-curve and thenebulahasbeenreclassifiedSO.Furthermore,distancemodulusforthis it isassmallas,orsmallerthan,themass-to-lightratioformanyspirals.ForNGC observations ofMinkowskiandOorthavecastsomedoubtontheoriginalrotation-curve, 3115, whichwasoriginallyclassifiedE7,Schwarzschild(1954)obtainedamassof9X 636 10 MofromtheearlierworkofOort(1940).Thisvalueispreliminary,sincemorerecent © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Now intheHerculesclusterwehavealreadymentioned thattherearesomedouble 2. Thequestionofwhetherintergalacticmattercontributesappreciablytothemass Thus onthebasisofexistingevidenceweconcludethatpossibility1canberuled Another wayofdeterminingmassesistousephysicalpairsnebulae.Thismethod G. R.BURBIDGEANDE.MARGARET 195 9ApJ. . .130. .629B 96 87 10 12 between thebright,well-definednebulae,thereisaluminoushazewhichheargues Zwicky (1951)hasreportedthat,withinthewholeofinnerpartComacluster, more frequentinclustersofnebulaethantheyarethevicinityourownGalaxy, clusters suchastheComaclusterthereisnoevidenceforthistypeofintergalacticmatter. clusters liketheVirgoandHerculesgroups,butitwillclearlynotbesignificant.For they willcontributeverylittlemass(BurbidgeandSandage1958).Ontheotherhand, masses likethoseofglobularclustersaretocontributeanappreciablefractionthe should beinvestigatedfurtherwithphotoelectrictechniquesbeforeitcanassumed due toavastnumberoflow-luminositysystems.However,therealitythiseffect in theHerculesclusterwouldbe10and,respectively,situationseemsim- nebulae withmassesof^10Moarespecified,about10wouldhavetobepresent.Such mass intheComacluster,anumberoforder10mustbepresent.Ifdwarf plausible herealso. a situationseemshighlyimplausibleintheComacluster.Thecorrespondingnumbers that alargeamountofmasscanbecontributedbysuchsystems.Forifsystemswith in ouropinionthepresenceofintergalacticmattersufficientquantitiestocauseappre- is present.However,theargumentsofNeymann,Scott,andShane(1954)haveshown its presence(Zwicky1957)isapparentlybasedontheideathatobserveddistribution clustering withoutanyobscuringintergalacticmatter.Thoughthistopiciscontroversial, ciable absorptionhasnotbeenestablished. that theobserveddistributionofclustersiscompatiblewithassumptioncomplete of clustersgalaxiescannotbeunderstoodunlesssomeintergalacticobscuration condensed clusterssuchastheComacluster.Thisismatterwhichhasbeenswept out ofnebulaeincollisions.Theratecollisionsarichclusterwasoriginallyworked inelastic collisionprocessinwhichthekineticenergyhasbeentransformedtoheat the rateofcollisionsbelowthatcalculatedbySpitzerandBaade.Ifconditionsare out bySpitzerandBaade(1951).Thenewdistancescalewillhavetheeffectofreducing of thenormalpopulationnebulae.Ifnot,itwillcontributetomasscluster such thatmostofthematerialsweptouthasrecondensed,thenitwillnowformpart as intergalacticmatter.However,itisunlikelythatmaterialsweptoutinthiswaycan Hercules clusters,hasnotbeenconfirmedbyother 21-cmobservers.Theonlygood in whichhereporteditspresenceanumberofclusters,includingtheComaand contribute verymuchtothetotalmass.Ifitdid,then,sincehasallundergonean mass involvedisdifficulttoestimatebutmaybe oftheorder10Mo.Thiswould clusters fromtheobservationof21-cmline.TheworkHeeschen(1956,1957), energy, itmightbeexpectedthatthevelocitydispersioninclusterwouldsmaller hydrogen intherichclusterwhichradio source CygnusAlies.Herethetotal than itis,andtheclustertightlybound. be onlyasmallfractionofthemasscluster.Also, anattempttodetectintergalactic evidence appearstobethatofLilleyandMcClain (1956)forthepresenceofneutral neutral atomichydrogeninthegeneralfieldhasbeen unsuccessful(Field1959). be aconsiderabledensityofinvisiblematterinthe intergalactic medium.Ifthismaterial is distributeduniformlyinsideandoutsideclusters itwillnotaffecttheargumentscon- the Hubbleconstantandanyofreasonablecosmological modelsshowthattheremust cerning thestabilityofclusters. Onlyifitalsoisclusteredwilltheargument bechanged. If itwereconcentratedsufficiently tostabilizelooseclusters,therewould have tobea © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Another formofintergalacticmatterisstarclusters.Iftheseareno Dark intergalacticmatterisevenmoredifficulttoinvestigate.Zwicky’sargumentfor There isonetypeofintergalacticmatterwhichmustcertainlybepresentincentrally Finally, thereisverylittleevidenceforthepresenceofneutralatomichydrogenin Now, thevaluesofmeandensityinuniverse obtainedwiththecurrentvalueof HERCULES CLUSTER 637 195 9ApJ. . .130. .629B 10 9 9 10 nebulae arenear10years. ThereisnodiscrepancywiththeageofComa cluster, of thenebulaethemselves shouldbeconsideredinrelationtothetimescales fordisrup- or elsethattheywereformedalreadyinastateof expansion. and Burbidge1959a,d),itappearsthat2E+ Í2 >0.Nowmultiplesystemsofthis tion oftheclusters.Conventional argumentssuggestthattheagesofelliptical andS0- of amemberbeing^T0years.Thismeanseitherthat theywereinastateofequilibrium 2E +Í2>0meansthattheyarenowbreakingup morerapidly,thetimescaleforloss consist ofonemassiveandtwosatellitenebulae) andinStephan’sQuintet(Burbidge have comparablemasses(asdistinctfromsystems likeM31,M32,andNGC205,which when theyformedandhavenowprogressedto asituationinwhich2E+0> triple ormultiplesystems.Forexample,inonetwo triplesystemsinwhichthenebulae configurations. However,therearesomeindications thatthesituationisdifferentin spirals. Consequently,wehaveeveryreasontosupposethatdoublesystemsarestable derived byPagefromdoublenebulaeareinreasonableagreementwiththosesingle type, evenif2E+Œ=0,willeventuallydisrupt. Thefulfilmentofthecondition dimension ofthecluster,i.e.,about2X10years.Thepasttimescalemightbelonger time takenforanebulaofaveragevelocitytomovethroughdistanceequalthe in size. happen isthattheclusterorbitsofindividualmemberswilltendtoincreasegradually than this,iftheclusterwasmoretightlyboundinpast. cluster maybelong,sincethereisnearlyanenergybalance,andpresumablyallthatwill cantly fromanequilibriumconfiguration.ThetimescalefordisruptionoftheComa is anequilibriumconfiguration.Thismeansthatsuchclustershavebeeninexistence last fewyears. k a clusterhasonlyrecentlybeguntoexpandandthereforenotyetdepartedsignifi- distribution. Toavoidthecontradictionhere,itisnecessarytosupposethatsuch spherically symmetrical,itwillonlydepartslowlyfromtheisothermalgas-sphere years isindicated.IftheComaclusternowinastateofexpansion,then,sinceit long enoughforsuchadistributiontobesetup,i.e.,timescaleoftheorder10 the evidencethatsomestellarassociationsareexpanding(cf.Petrie1958;Woolley expanding (fromtheirtotalenergy)ispossiblymoreconvincingatthepresenttimethan case oftheirregularclusters,itisnothardtoseethattheymaybeexpanding.Insome k distributions fittingreasonablywellwiththeisothermalgravitationalgassphere,which and Eggen1958).Ontheotherhand,clusterssuchasComaclusterhavenebular that hasbeentakenbyAmbartsumian(1958andotherreferencesgiventhere)overthe k galactic magneticfieldsinclusters.Thoughthereissomeindirectevidenceforthese, strong probabilitythattheHerculesandVirgoclustersaredisrupting ways theycanbecomparedwithstellarassociations,thoughtheevidencethatare a cluster(Burbidge1958). it seemsimprobablethattheycouldcontributeappreciablytotheinternalenergyof k systems. would berequirediftheHercules,Virgo,andprobablyComaclustersarestationary servational evidenceforthepresenceoflargeamountsintergalacticmaterial,which (less probably)theComaclustermaybeunstablealso.Thisisexactlypointofview clusters. Thiswouldappeartobeimprobable. much higherdensityofintergalacticmatterinsidelooseclustersthancondensed 638 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Let usnowconsidertheequilibriumofsmallgroupsnebulae.Themassesspirals In discussingtheequilibriumoflargerclusters describedinthispaper,theages, In theHerculesclusterfuturetimescalefordisruptionmaybeoforder 3. Thediscussionscovering1and2haveledustotheconclusionthatthereisa It isofinteresttoconsiderthegeometricalconfigurationstheseclusters.In We haveneglectedthroughoutthisdiscussionthepossiblepresenceofweakinter- Thus weconcludefromthisdiscussionthatthereiscurrentlynogoodindependentob- G. R.BURBIDGEANDE.MARGARET 195 9ApJ. . .130. .629B 12 9 Lilley, A.E.,andMcClain,E.F.1956,Ap.J.,123,172. .1936,ibid.,84,270. .1940,Ap.J.,92,200. ———^ 1959,abstr.ofpaperreadattheGainesvillemeeting oftheA.A.S.,December,1958,AJ.,64,53, -.1958,paperreadattheSolvayConference,Brussels. Minkowski, R.1957,I.A.U.Symposium,Vol.4:RadioAstronomy (Cambridge:CambridgeUniversity Poveda, A.1958,Bol.Obs.Tonantzintla yTacubaya,No.17,p.3. Oort, J.H.1940,Ap.J.,91,273. Orner, G.1952,A.J.,57,22. Neymann, J.,Scott,E.L.,andShane,C.D.1954,Ap.J. Suppl, 1,269. Münch, G.1957,AJ.,62,28. Humason, M.L.,Mayall,N.U.,andSandage,A.R.1956, A.J., 61,97. Hubble, E.,andHumason,M.L.1939,AnnualReporttothe Director,MountWilsonObs.,p.20. Hubble, E.1926,Ap.J.,64,321. .1957,Pub.A.S.P.,69,350. Heeschen, D.S.1956,Ap.J.,124,660. ——■—. 19585,CapePhotographicAtlasofSouthernGalaxies,PI.21. •.1959d,inpreparation. .1959c,ibid.,p.12. Abell, G.O.1958,Ap.J.Suppl,3,211. Petrie, R.M.1958,M.N.,118, 80.. Holmberg, E.1937,Ann.Obs.Lund,No.6. Page, T.L.1952,Ap.J.,116,63. Field, G.1959,Ap.J.,129,525. Burbidge, E.M.,andSandage,A.R.1958,Ap.J.,128,527. .19595,ibid.,p.23. Ambartsumian, V.A.1958,paperreadattheSolvayConference,Brussels. Buscombe, W.,Gascoigne,S.C.B.,andVaucouleurs,G.de.1954.Suppl.AustralianJ.Sei.,Vol.17, Burbidge, G.R.1958,Ap.J.,128,1. Ambartsumian, V.A.,andShachbazian,R.K.1957,DokladyAkad.Nauk.ArmenianSSR,25,185. Evans, D.S.,andWayman,P.A.1958a,M.N.A.S.SA.,17,137. Burbidge, E.M.,andG.R.1959a,Ap.J130,15. for hisinterest,andlendingusplatesreproduction.Theirqualityhasbeen reports priortopublication. well broughtoutbytheskillofMr.W.C.Millerinphotographicreproduction.We universe. Thesequestionswillbeconsideredinafurtherpaper. Professors V.A.AmbartsumianandJ.H.OortkindlysentustheirSolvayConference also wishtoacknowledgemanyinterestingdiscussionswithDr.MiltonL.Humason. in whichthecondensationofnebulaeandclusterstakesplaceanexpanding overtones. Itisprobablyrelatedtothewell-knowndifficultyofunderstandingway universe, theproblemofevolutionthesedynamicalgroupshascosmological up. YettheComaclustermaybenowinastateofslowexpansion.EllipticalandSO is hardtoescapetheconclusionthatclusterswhicharenowexpandinghavepassed stationary universecouldthemultiplenebulaeandclustershavebeenformedthrough long agoshownbyHolmberg(1940)thatonlyintheframeworkofanon-expanding nebulae areintheminorityHerculescluster;yetsomepresent,whilefuture which mustbeofthisorderforanisothermalgas-spheredistributiontohavebeenset capture processes—undthisonatimescale^10yearstheolddistancescale—it through aperiodinwhichtheywerequasi-stationary. time scaleforexpansionofthissystemistheorder2X10years.Sinceitwas © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem and privatecommunicationto D.N.Limber. Press), p.107. No. 3. We aredeeplyindebtedtoDr.WalterBaadeforbringingthisclusterourattention, This workwassupportedinpartbyagrantfromtheNationalScienceFoundation. 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R.BURBIDGEANDE.MARGARET