1981MNRAS.197..995M galaxies. Observationsgivelittleevidenceforappreciable amountsofgasorsignificantrates massive ellipticalsshowvariousindicationsofenergetic nuclearactivity(Collaetal.1975; stellar materialcanbeunderstoodifthereisan effective gasremovalmechanism,e.g.a An importantproblemofgalacticevolutionis the fateofstellarmasslossinelliptical not flowoutofthegalaxy butaccumulatesandflowsinwardstothecentre (Mathews& of starformationinmostthesesystems(Faber &Gallagher1976).Theabsenceofinter- Baker 1971;Bregman1978; Bailey1980). supernova-driven galacticwind(Mathews&Baker 1971)orram-pressurestripping(Gisler Condon &Dressei1978). Thissuggeststhatundersomecircumstancesstellar masslossdoes Osterbrock 1960;Gallagheretal.1977;Fosbury al.1978).Alsoasignificantfractionof standpoint, concentrating particularly ontheeffectsofhigher stellarmasslossrates 1 Introduction 1976). However,someellipticalgalaxiesdocontain gas(Minkowski&Osterbrock1959; This paperconsidersthe problem ofgasflowinellipticalgalaxiesfroman evolutionary © Royal Astronomical Society • Provided by theNASA Astrophysics Data System -1 Mon. Not.R.astr.Soc.(1981)197,995-1019 galaxies The evolutionofflowsstellarmasslossinactive lifetime ofmostgiantellipticalgalaxies,irrespectivetheirdetailedstructure. Received 1981April2;inoriginalformFebruary11 J. MacDonaldandM.E.BaileyAstronomyCentre, unable topreventtheinflowofstellarmasslossforalargeproportion Vaucouleurs modelsofNGC3379.Ourresultsshowthatsupernovaheatingis been calculatednumericallyforthreefiducialepochsusingbothKingandde University ofSussex,Falmer,Brighton,SussexBN19QH with meanline-of-sightvelocitydispersionä>a=*300kms.Atearlier At thepresentepoch,stellarmasslossflowsinwardsinthoseellipticalgalaxies Summary. Gasflowsinellipticalgalaxiesfuelledbystellarmasslosshave moving densityevolutionasobserved.Thisworkdemonstratestheimportance mass functionattherelevantmasses,thisleadstoarapidincreasewithred- evolution inthestellarmasslossrate.Becauseofsteepnessgalaxy ticals toretaintheirstellarmassloss.Evolutioninaiscausedprincipallyby epochs thetransitionvelocitydispersiona,dividinggalaxieswithinflow from thosewithtotalwinds(aalsoassumed t {^SNEsti+oc-aljjci. (4) due tobothsupernovaeand randomstellarmotions <* =a*+a. dp 1a T SN dt rdr SN 0 2 (dv dv\dp (bE bE\\b,! v\ © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Our calculationsdifferfromthoseofMathews&Baker(1971)inthatweusesomewhat The detailsofourmodelforthewindaregiveninSection2.Asimplepicturehow The totalspecificmasslossrateis The Euleriantime-dependentflowequationsforthewindare(Mathews&Baker1971) (2) (3) 1981MNRAS.197..995M 28 31 4 46 68 314 6 labelled ‘gas’. cooling curveofRaymond,Cox&Smith(1976)butwiththeFeabundancereducedtothat ment ofoutflowandalsothattheexternalpressurehasnosignificanteffectonanyoutflow. cooling curvefor graphitegrains. a waythatif(7)0asT^10K.Belowwetakei^=andaboveconsider where nandarethefreeelectrontotalhydrogen(i.e.ionizedneutral)number metric coolingrateisA=« «H-if (T)ergcm's"whereTisgastemperatureinKelvin. Alsoshownisthe Figure 1.Thecurvelabelled ‘gas’ isthecoolingcurveadoptedinnumericalcalculations. Thevolu- of Shapiro&Moore(1976).Below10Kweextrapolatethecurveinsuch of Cameron(1973).For10galaxy NGC3379.Twomodelsareconsidered:aKing(1966)modelandde law modelatthefittingradiusr,whichistakentobeKT*.Thismodificationaffects we modifythedensityprofilenearcentre.Wetake derived quantities,inTable1.Foreachtypeofmodelwecalculateself-consistentlythe The parametersadoptedinthisworkarebasedontheseandgiven,togetherwithsome 2.4 THEGALAXYSTRUCTURE Cameron (1973)abundances. Following Mathews&Baker(1971)webaseourgalaxymodelsonthewell-studiedEl observations ofSargentetal.(1978)toderivevaluesthefreeparametersthesemodels. Epoch (10yr) 10.0 3.0 Table 1.ParametersforthedeVaucouleursandKingmodels ofNGC3379asfunctionsepoch. P* =Pa-PbO'A’e) difficulties causedbythedensitysingularityatoriginofdeVaucouleurslawmodel, stellar density,p*,thegravity,g*,andvelocitydispersion,a*.Toavoidnumerical 998 J.MacDonaldandM.E.Bailey Core radius,r(100pc) 1.32 1.27 AX X(t)-X(t-kt) for Luminosity, L(1O) 1.33 2.81 2.5 METHODOFSOLUTION Specificsupernovamasslossrate, ú¡sn(10s)2.00 referring tothecentralsphericalzoneandn=Preferringoutermostshell.Timederiv- the nthshellbysubscriptsn—Viandn+Viatmidpointsubscriptn,with=l tities, e.g.r,v,g*,areevaluatedattheshellboundaries.Wedenoteevaluationedgesof quantities, e.g.p*,p,T,areevaluatedatthemidpointsofshellswhereas‘vector’quan- Equations (1),(2)and(3)aresolvedbytheHenyeymethod(Henyeyetal1959)normally Specific energyofsupernovaejecta, Sequence code A B finite difference atives arecalculatedimplicitly,i.e.thederivativeofaquantityXattimetisreplacedby fe c a x X t e x x0 Ai 18 -1 The calculationsofShapiro&Mooreshowthathydrogenremainsnearlycompletely ^SN (10ergg ) 2.00 2.00 Royal Astronomical Society •Provided bythe NASA Astrophysics Data System 22.6 13.3 4.58 5.86 2.00 2.00 1.0 1.21 1.99 1.74 1.72 1.09 (6) 1981MNRAS.197..995M v 3 rnn+1/2vn rv2 linear differenceequations issolvediterativelyusingaprogramkindlylent byDrPeter ture equaltotheinitial values. Thisfixesp/v+i,^v+in+3/2-Thecomplete setofnon- Material outsidetheouter edgeisassumedtoremainatrestandhavedensity andtempera- value. Wesetp=PiandE.Attimei0,we arefreetospecifytherunofp,Tand Eggleton. v intheflow.Sinceweareinteresteddevelopment oftheflowduetomasslossfrom Po andEwhichappearinequations(7)(9) appliedat«=1canbegivenanyfinite edge oftheflowistaken tobeatlargebutfixedradius(typically10 effectiveradii). take theinitialdensityandtemperaturetohave valuesgiveninSection2.2.Theouter initial conditionsarerequired.Atthecentreof flow(>1/2=0)wehaveu=0.Hence At stars weassumeanygasinitiallyinthegalaxyisat restandhaslowdensitypressure.We with theequationofstate,appliedtomeshpoints 1toNgive3Nequationsinvolving 3 (N+2)unknowns.Tocompletethesetofdifference equationsboundaryconditionsand mass exactly,momentumandenergyarenotconserved exactly.Truncationerrorsarekept and [X]=max(X,0.0)foranyX.Notethat,althoughtheformofequation(7)conserves small byusingalargenumber,typically270,ofshells. Equations(7),(8)and(9),together 5 01 0 where ~2^+^«-1/2)’n—(Pnl/2^«-1/2)?<^nl^« 1/2 Pn upstream differencestoensurenumericalstability.Shocksaretreatedbyaddingthe gas pressureapseudo-viscous Qn lPn[3OVî+1/2U«+i/2n-i/2n-i/2)(n+i/2~n-i/2)l(n+i/2~n-i/2)]> which spreadsshocksoveraboutthreemeshpoints.Thefulldifferenceschemeis where Aiisthetime-step.Advectiveterms,i.e.termsofformvdX/dr,arereplacedby where r?isadimensionlessconstantwhichdeterminestheshockthickness.Wetake=2.8 At 1 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System _ / jAr [ ^n+1/2](Pn+iPn)^P*in> n ^n-l)(^«+i~^«^,\s^rriir? v n + — (?n +iQ«+1—Pyi~Qn) 1^«+1/2J 7~^1^«+1/2J7"*"£*î«+1/2 r (^«+1 ~n) (^*«+1/2 ^«-1/2) [ ^«+1/2]^.¡^(P«>Tf^/En Pn Stellar masslossinactivegalaxies999 W+l/2 J 2 'n- 3r — r + 1/2 ^^*,«+1/2^«+1/2“0 n-1/2 [^«-1/2] (fin~Pn-\) r (n+3/2 —^«+1/2) (8) (7) 1981MNRAS.197..995M 1 lo 345 62 8lo 2 lo 1+ß m +dm),kisrelatedtoA/(0),theinitialtotalgalaxymassby(ß1) model galaxyisthenfoundtobeA/(0)=1.42x10 Af©. giveAi(m'). (De Young1976). the present-day(t=10yr)M/Lratioforgalaxy agreeswiththeobservationsofNGC as functionsoftime.Wenotethatifstellarmassloss isabletoflowinwardsandfuelnuclear 3379. Usingthemass—luminosityrelationforstars, L/L©=m(Allen1973)andA//L tion. Wetakeß=1.35(Salpeter1955)and50. Thelowerlimit,ra,ischosensothat and zerootherwise.(j)(m)dmisthenumberofstarswhichhavemassesininterval(m, efficiencies (0.7percent) theenergyreleasedisinexcessof2x10erg.This suggeststhat activity, theamountoffuel madeavailableintheinterval10 =0.19(i/o/55kms"Mpc")(LT/10L®)(100yr)" ec an ejectionvelocityof2x10kms'(Searle1974), correspondingtoi^N=2xlO^ergg”, 0 SN SN SN xT T sn eoT sn A furtherconsequenceofmasslossfromthegalaxyisthatitbecomeslesstightlybound © Royal Astronomical Society • Provided by theNASA Astrophysics Data System In viewoftheabove-mentioned uncertainties,wemakethesimplestassumption thataN S Figure 2.Specificstellarmasslossrate,a,andfractionalgalaxymass,/,asfunctionofepoch,t. Stellar masslossinactivegalaxies1001 1981MNRAS.197..995M lo 6 1 e 2 2 and massinellipticalgalaxies.However,theirresultdependscruciallyonthefractionof ratio a/thatdetermineswhetherornotinflowoccurs.Hence,provideddoes companion (Whelan&Iben1973),amayincreasewithtimebecauseofthelongevolu- tionary time-scaleofthecompanion.Innextsectionweshowthatitisessentially than dM2areactive.Kunkel(1975)givesstrongevidencethatthedurationofflare bourhood stars,Coleman&Worden(1976)concludedthatabout50percentofstarslater decrease asrapidlya,inflowwilloccuratsomeepochearlierthanthepresent. (Kunkel 1975).However,evenifweassume50percentofMstarsareinbinariesandhence The situationiscomplicatedbythefactthatstarsinbinarieshaveaprolongedactivestage estimated theimportanceofflarestarsasanenergysourceinellipticalgalaxiesatlateepochs. spectral type(Kunkel1973),Coleman&Worden(1976)mayhavesubstantiallyover- elliptical galaxy,inwhichnostarformationhasbeengoingon,onlytheverylowluminosity and iscomparabletotheageofGalaxyforstarsfainterthan7k/=15.Henceinan active stageofalowmassstarismonotonicallyincreasingfunctionabsolutemagnitude dwarf Mstarsthatareactiveflarestars.UsingthedataofJoy&Abt(1974)forsolarneigh- stars ofspectraltypelaterthanM7willbeflareactiveafter10yr.Sincethefraction are active,andthat=0.003wefindaflarestarenergyinputrateof3.8x10L©for of stellarenergyexpendedinflareactivityisbetween0.1and1percent,irrespective sidered indetailbyColeman&Worden(1977). our modelsanenergysourcetermduetoflarestars.Flare-star-drivenwindshavebeencon- 1002 J.MacDonaldandM.E.Bailey SN SN lO^/© galaxy,afactor5lessthanoursupernovaheatingrate.Hencewedonotincludein v 4 Approximateanalyticresults point’, atwhichu=0,intheflowradiusr.Fromequations(1),(2)and(3)steady worth consideringtheglobalenergybalanceofasteadyflow.Supposethereis‘stagnation To getsomeinsightintotheconditionsunderwhichatotalorpartialwindispossible,it state energyfluxequationcanbederived a [My-m* <*sn SN[M-m.Jr)]/a >~+—r|(p*aj) 4nr andintegratingfromrtoinfinitygivesaglobalenergyequationfortheflowoutside Using thefactthatgalaxyisinhydrostaticequilibrium,multiplyingequation(15)by s within r.SinceZ,>0,weseethatanecessarycondition fortheexistenceofasteadystate where L(r)istheluminosityofgasoutside radiusrandm^.^)isthemassofstars r dr solution withstagnationradiusris ts s gas gas s 1 d Coleman &Worden(1976)havesuggestedthatflarestarsareamajorsourceofenergy © Royal Astronomical Society • Provided by theNASA Astrophysics Data System “J m "M's) t Gm^dm*2ir 2 + -v 2 Mr = -h-vpg*+cip*E. + m*(r) T 3 rïGm*dm*2tt s 2J, r3 r m(rs) s Gml(r) s ar¡(p*ol) + a ¿gasOs)SN^SNWt -af— 0 •Vc ' J r f Gm 00 Gm±dr L r Gml(r) s - ™*0s)] (17) (16) (15) 1981MNRAS.197..995M 1 2 4 0í0l> 2 line-of-sight velocitydispersionofthegalaxy,ñ,by values ofa,Fandthepresentepochvaluea,wefindthatinflowwillbegoingonin wind calculations. s =r/rçforboththeKingand deVaucouleursgalaxymodels. nearby galaxieswithmeanline-of-sightvelocitydispersiongreaterthan300kms".Alsothe both typesofmodel.FortheKingmodelwehavetakenA*/r=187,valueusedin galaxy, s=r/rforaKingmodel).ThefunctionFisshownplottedagainstinFig.3 where Fisadimensionlessfunctionofradius,s(e.g.=r/rfordeVaucouleurs galaxies withhighötobemoreactivethanlowö.Since,aspointedoutby greater thevalueofä,willbea*,andhenceinflowrate.Hencewemightexpect Hence galaxieswitha>2aFsN/9awillhaveinflowofstellarmassloss.Usingour Figure 3.ThefunctionFthat appearsinthepartialwindcriterionplottedagainstdimensionless radius radio emissionandopticalluminosityofellipticalgalaxiesasfoundbyEkers&(1973) roughly asLF(s), where Visthepotentialenergyofgalaxy. Faber &Gallagher(1976),theopticalluminosityofellipticalgalaxiesiscorrelatedwitha, becomes condition (17)canthenbewritten sn^sn^tI ~\ A caseofparticularinterestisthatatotalwindforwhichr=0.Thecondition(17)then SN 7 =-«SN^SN^T/a|L|, tc ce e s SN T \V\ =3Mo.(20) s t © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Since thegalaxyisinhydrostaticequilibriumpotentialenergyrelatedtomean Let 2 M 3 fxGm^dm* 2Jo r Stellar masslossinactivegalaxies1003 (19) (18) 1981MNRAS.197..995M 2 6537 292o6-3_1 128/135_1 1/2 to radiosourcenumberdensityevolutioncanbefoundinBailey&MacDonald(1981b). and Collaetal.(1975).Adetaileddiscussionoftherelevanceenergybalancecriterion 1004 J.MacDonaldandM.E.Bailey (r =0)canoccurbeobtainedbyconsideringthecasey>1(formallyequivalenttoG-► 0). Firstsupposethatcoolingisnegligible.Theflowequationscanthenbereducedtothe x =Inr. single windequation The centralgastemperatureis (4w —1)—=—w(4w+1)2w(l,(21) where u and can beapproximatedby The sonicpoint,a=V2,occurswhere d\nm* For typicalvaluesofq&nE^jawefindT~10*K.Thecoolingratefor<'K Comparing thiswiththetotalsupernovaheatingwe seethatcoolingisimportantif s gives thetotalgasluminosityforKingmodel Similarly forthedeVaucouleurslawgalaxywefind thecondition Solving equation(21)numericallyandintegratingtheapproximation(23)overflow A= 1.33x10pr"‘ergcms.(23) asN ^sn<6.78x10a(M/r)ergg's. (26) T = whole galaxy with theevolutionarytrack ofNGC3379.Themeanline-of-sightvelocitydispersion forthe equivalent. 3 Since r=16.4forourmodelsofNGC3379, conditions (25)and(26)areessentially c a =0.335(GM /r) Te r ec Te 2 _ dx Some ideaofwhencoolingisanimportantfactorindeterminingwhethertotaloutflow © Royal Astronomical Society • Provided by theNASA Astrophysics Data System In Fig.4weplottheconditions (18)and(26)inthe(logA///e—loga)plane, together 128/13 T ^sn <2.44x10c* asN 2E W = 1.20x10 2 m^sn^sn a = 74. du „dlnra*. dx a 27 r ttSN^SN cT { or M% 1 0.6 ergs erg g^ -1 (25) (22) (24) 1981MNRAS.197..995M 4_11 =-1 1 1 9 lo 9 3O and gravitypreventtotaloutflow,inwhichoutflowcanoccur,accordingtotheanalyticresults of Section4.ag^^SN=4X10"erggs"hasbeenassumed. Figure 4.TheevolutionarytrackofourmodelforNGC3379inthe(loga—logAfx/r)plane.filled circles arelabelledbylogt,wheretisepochinyr.Alsoshowntheregionswhichradiativecooling is alsoshown,oísn^sn4xlO^ergg^shasbeenassumed.WeseefromFig.4,thatfor Vaucouleurs galaxymodelandsequenceKAfortheKingmodel),then Vaucouleurs modelsofNGC3379atthethreeepochsgiveninTable1.Wediscussfirst We havefollowednumericallythedevelopmentofgasflowinbothKingandde total outflowoccurs.Formoretightlyboundgalaxiesitisthebalancebetweengravityand galaxies withö^75kms",coolingisthemajorfactorindeterminingwhetherinflowor velocities ofsequenceDA atradiilessthan100pc.Thisisduetothemuch highercentral parameters ofthesteadyoutflowsaregiveninTable 2. in parsecsatdifferenttimesafterthestartof calculation.Somephysicallyinteresting ture inKelvinandgasvelocityunitsof100km s",respectivelyareplottedagainstradius models fortheearlierepochs(sequencesDB,KBati=3x10yrandsequencesDC,KC As predictedbycondition(18),steadystateoutflow developsinbothsequenceDAand present epoch(t=1x10yr)models(hereafterreferredtoassequenceDAforthede 5 Resultsofthenumericalcalculations supernova heatingthatdecidestheissue. e (1971); thedifferencesin thevelocityprofileatearlytimesaredueto differentchoice sequence KA.Theevolutiontowardsthesteadystates isshowninFigs5(a)—(c)(sequence rate withinthe inner100pcofthegalaxy, andalsoasmallerdynamical time-scale. star densityofthedeVaucouleurs galaxymodelwhichresultsinamuchlarger massinput of initialconditions.The major differencebetweensequencesDAandKAis themuchlarger 5.1 PRESENTEPOCHMODELS t= lx10yr). KA) and6(a)—(c)(sequenceDA)inwhichgasdensity inunitsof10‘gcm',gastempera- © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Sequence KAisqualitativelysimilartothesteady outflowmodelofMathews&Baker Stellar masslossinactivegalaxies1005 Log er 1981MNRAS.197..995M 1 303 in kms"andr is radiusinpc.Thecurvesare labelledwithlogf,wheretis thetimeinyr. various times,pisthegasdensity inunitsof10"gcm',TisgastemperatureKelvin, Visgasvelocity Figure 5.Plotsof(a)gasdensity, (b)temperatureand(c)velocityagainstradiusfor sequenceKAat 30 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System 5 (a) (b) (c) 1981MNRAS.197..995M © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Figure 6.(a)-(c) AsFig.5(a)-(c)butforsequence DA. Log r (a) 1981MNRAS.197..995M 3 7 r. Thetimetoreachequilibriumwillalsobe~tfandhencep,thecentralgasdensity, 1008 be ~ap*tfevaluatedatthecentre.Thevaluesfoundinnumericalcalculationsare Here Tisthemeantemperatureofinjectedgas,p*densitystarswithinr and f*isthegastemperaturecorrespondingtomeanvelocitydispersionofstarswithin good agreementwiththisroughestimate. T = mate forthetotalluminosityofgas,L^4x10©whichagreessurprisinglywellwith who concludedthatsuchawindshouldbetotallyundetectableexceptpossiblyforinfrared ing inthehotoutflowinggasisnegligible.Hence, if afraction,/,ofthecarbonejectedby given inTable2arethemassesofgascontainedwithand20kpc. the valuesfoundinlastcomputedmodelforluminosityofoutflowinggas.Also c where Misthemassofahydrogenatomand is theradiusofatypicalgrain(Burke& is (forT<10K) emission fromdustgrainsejectedstars.Comparisonofflowtimeswithsputteringtime- in scales forgraphitegrains(Burke&Silk1974)indicatesthatdestructionofbysputter- The computedvaluesareslightlylessthanthisbecauseofthesmallamountcooling. cooling law, stars isintheformofgrains,coolingperunitvolume duetograin-gascollisions, Silk 1974).Taking/=1anda0.1pm,thiscan bewritteninthesameformasgas A.-7xl0-»/(^-) (^)(^)e, m-V', (29) c gas where g H ^grains “grains(T), (30) g Urai gc 23 In theabsenceofcoolinganexactexpressionforcentralgastemperatureis grains (7)-10|j erg CmS Equation (24),anditscounterpartforthedeVaucouleurslawgalaxy,givearoughesti- © Royal Astronomical Society • Provided by theNASA Astrophysics Data System The observabilityofahottotaloutflowhasbeendiscussedbyMathews&Baker(1971) The characteristictimefordevelopmentofoutflowatradiusrisadynamicaltime-scale 2pE 5 á? t 6 5 263 4 7 7 Afgas (20kpc)(10M) M (2kpc)(lOAf) L /. MacDonaldandM.E.Bailey ap* p (10-gcm-) Table 2.Parametersoftotaloutflows. Sequence if (10yr,centre) Tjn (10K,centre) T (10K) o gas0 c c gas ^o) _263 t (10gcm") f 3/2 / T\ KA 30 2.301 9.11 3 3.80 3.98 1.980 1.378 DA 10.73 18 0.2 8.05 3.63 1.988 1.190 3.93 (28) (27) (31) 1981MNRAS.197..995M 4 6 6 s _24_3 4 6 6 / 4x10L©forbothsequencesDAandKA.Thisismuchlessthanthesupernovaheating however, bedetectedindirectlybytheirinteractionwiththeintergalacticmedium(IGM). gas coolingandweneedtocheckthatitisnegligiblecomparedthesupernovaheating. galaxies (Malin&Carter1980). As thewindevolves,ashockfrontdevelops,sweepingupIGMtoformhot,denseshell The graintemperature,-15K,issuchthattheIRdustemissionpeaksatawavelengthof Integrating thegraincoolingoversteadystateoutflowwefindaluminosity^ g (see Figs5aand6a).Suchshellsmayhavealreadybeendetectedaroundgiantelliptical that ofthestarsandhenceisprobablyundetectable. As predictedbycondition(18),steadytotaloutflowdevelopsinnoneoftheearlyepoch ^grains (T)isshowninFig.1.Hence,forT>3x10K,graincoolingmaybegreaterthan for thegastocoolrapidly.Thedecreaseinpressureresultsinflowofmaterial.In Instead materialaccumulatesinthecentralregionsuntildensitybecomeshighenough energy toejectmatterfromthedeeppotentialwellofcentralregionsgalaxy. sequences, DB,KB,DCandKC.Thisissimplybecausesupernovaedonotprovideenough 5.2 EARLYEPOCHMODELS ^ 250/¿m.Weestimatethat,atthiswavelength,thedustemissionisonlyabout10times drive gasoutandhenceapartialwinddevelops. outer, lesstightlyboundpartsofthegalaxysupernovaecanstillsupplyenoughenergyto similar. sequences KCandDCrespectively.TheoveralldevelopmentofKBDBis For sequencesKBandKC,withinonecoreradiusofthecentre,T^8x10K5x ture oftheinjectedgas adiabatic expansionisunimportantandhencethegastemperatureremainsneartempera- is compressedandpressure forcesagainbecomenon-negiigible.Ashock develops atthe moves towardsthecentre.Whengastemperature is~3x10K,i.e.nearthepeakof which givesp-10gcmforbothsequences. outflow beginsatthecentre.However,velocitiesdonotbecomelargeenoughtosetupa within 1.3pc ofthecentreforsequence KBandwithin1.2pcfor sequenceKC. wards. Itisthispressuregradientthatresponsible formostoftheaccelerationasgas A (Tin)~asEp* (33) steady-state densitydistribution,andsothecontinuestoincrease.Coolingby cooling curve,thegascoolsrapidlyto~10K. This leadstoanoutwardmovingcooling situation developsinwhich,althoughdensitydecreases outwards,thepressureincreasesout- centre andslowlymoves outward.Fortheextentofcalculationsthis shockremains and thegassupersonically freefallsforashortperiod.Asthegascontinues to fallinwardsit Tv front (seeFigs7b,8b). Immediately aftertherapidcooling,pressureforces arenegligible 10K respectively.Coolingbecomesimportantwhen thedensityissuchthat 1.1 x10yrforsequencesKBandKC,respectively. Becausethedensergascoolsfastera in NSN in 7 6 We concludethatsteadyoutflowingwindsarenotdirectlyobservable.Theymay, © Royal Astronomical Society • Provided by theNASA Astrophysics Data System The earlyevolutionofsequencesKBandKCissimilartothatsequenceKAin Figs 7and8showtheevolutionofdensity,temperaturevelocitygasfor 2 x1OL)andhencecoolingbygrain—gascollisionsdoesnotupsetthesteadyoutflow. Since thisdensityisattainedfirstatthecentre,inflow beginsthereattimes8.4x10and 0 Stellar masslossinactivegalaxies1009 (32) 1981MNRAS.197..995M 1 1010 J.MacDonaldandM.E.Bailey Figure 7.(a)—(c) AsFig.5(a)—(c)butforsequence KC,Fisthegasvelocity inunitsof100kms". 10 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System 1981MNRAS.197..995M © Royal Astronomical Society • Provided by theNASA Astrophysics Data System 15 10 0 5 0 12345 Stellar masslossinactivegalaxies (a) Log r 1011 1981MNRAS.197..995M 7 5 7 aree 7 6 7 4 6 7 7 7 1 7 Mgas isthemassofgasinsidestagnationradiusrandF(=am(A‘)totalinflow limit onrof169pc.However,thisisforasteadyflowandobtainedbyneglecting will continuetomoveoutwardsonatime-scale10yr,i.e.aboutoneflowtime. the instabilityonflow. traverse theunstableregion,~10yr.Henceitisnotunreasonabletoneglecteffectsof equal tothedensityscaleheightisatleastafactorof2greaterthantimecompletely at 1.08x10yr.Asthedensityincentralregionsfurtherincreases.rcontinuestomove the numericalcalculationaresomewhathigherthangivenbycondition(19).Itisclearfrom cooling whichisnecessaryfortheretobeanyinflowatall.Hencethevaluesrfoundin Rayleigh—Taylor instability.However,thegrowthtimeforperturbationsofwavelength rate. A/and£ga,tthtotdXmassluminosityofthegasinsidegalaxy. taken arbitrarilytobeat1.76x10yr.Thisislongerthanthetimewhichnatureof the numericalcalculationsthatasdensityincentralregionscontinuestoincrease,r calculations. reaching 536pcat4.23x10yr,butthenslowsdown,1.59kpctheendof specific masslossrateandhencelowerenergyoftheinjectedmaterial,inflow the flowwillbechangedbyself-gravitationofgasbecomingimportantatcentre. outwards butmoreslowly,reaching300pcat1.76x10yr.Condition(19)givesalower S)sHî 1012 J.MacDonaldandM.E.Bailey starts earlierandinvolvesagreaterpartofthegalaxy.Againrmovesoutrapidlyatfirst, increasing randcoolingbecomesmoreeffective.Againimportantwhen away fromthecentre.Thisisbecauseveryhighcentralstardensityresultsina unstable. Hencetheshellmaybreakupintocoldblobsthatsinktowardscentre,with increases thecooling.Thusacool,densegasshellformsabovehotter,lessinterior A ~aifp*.Theresultantlocaldropinpressurecausesmaterialtoflowintothe supernova heatingratethatdominatesthegascooling.Thestellardensitydropsrapidlywith which triestosupportitagainstgravity.ThisisagainasituationthatmayresultinRayleigh- cooling regionfrombothsides.Thisresultsinasharpincreasedensitywhichfurther s Taylor instability.Thegrowthtimeforperturbationsofwavelengthequaltothedensity scale height,~10yr,isnowmuchlessthanthetimeforwhichshellRayleigh—Taylor the hotinteriorgasmovingoutwardsaroundthem.Wehavenottriedtomodelbehaviour s that ofsequenceKB,themaindifferencebeing that, atcomparabletimes,thestagnation By i=4.80x10yrtheshellhasfallentocentre. Thesubsequentevolutionissimilarto Rayleigh—Taylor instability. of thistwo-componentmediumbutinsteadhave continuedtheevolution,ignoring s gaS)tS s -^gas,tot (10Af©) ^gas,s(103f) s ^gas^ot (10¿ o) ^sd^oyr') r (1kpc) SN Table 3.Parametersofpartialinflowsatr=1.76X10yr. Sequence o s 6 In sequenceKBthestagnationradius,r,atfirstmovesrapidlyoutwardsreaching209pc Another consequenceofthepressureincreasingoutwardsisthatgasproneto The evolutionofsequenceKCissimilartothatKB.Becausethehigher In Table3wegivesomeparametersoftheinflowmodelsatendcalculations, © Royal Astronomical Society • Provided by theNASA Astrophysics Data System The evolutionofsequencesDBandDCdiffersfromtheKingmodelsinthatinflowbegins In sequenceDBthehigh-density,coldshellforms atr=4.2pcwheni2.78x10yr. s 0.38 4.4 0.10 1.5 0.12 2.4 KB KC 2.3 8.1 0.30 1.6 DB DC 0.064 1.7 0.071 2.7 0.23 6.7 0.23 1.7 2.6 8.3 1981MNRAS.197..995M 4 5 5O 54 25-3203 4,/111711 = = 1 5/6 5/731/73 heating andtheglobalpropertiesofgalaxy,e.g.itspotentialenergy. to theGalacticCentre.Againhighermasslossrateisresponsibleasitgivesalowermean (19), forsteadyflows. is thenqualitativelysimilartosequenceKC.Thedifferenceinpositionsofthestagnation nova heatingisovercomeearlier.Inflowbeginsatr=1.37pcwhent7.22x10yr.Againa temperature fortheinjectedmaterialandafasterbuild-upofgasdensity,sothatsuper- structure oftheunderlyinggalaxyandisasexpectedfromanalyticcriterion,equation radius islargerfortheKingmodel.Thisdifferencecanbeattributedtoin radius is,however,notasmarkedforsequencesDBandKB. galaxy butareessentiallydeterminedbythevaluesofspecificmasslossrate,supernova e.g. thetotalinflowrate,donotdependcriticallyondetailedstructureofunderlying although therearedifferencesinthedetailsofflows,globalproperties dense coldshellformsandfallsinwards,reachingthecentreati=2.25x10yr.Theevolution heating tobe100percentefficientisthatSNRsintersectbeforeradiativecoolingbecomes the validityoftheseapproximations. tions, notallofwhichhavebeenstatedexplicitly,made.Inthissectionwecheck goes intoheatingtheinterstellarmedium(ISM).AspointedoutbyLarson(1974b),if In ourmodelforthegasflowinellipticalgalaxiesanumberofassumptionsandapproxima- important. Thetime-scaleforintersectionofSNRsis ISM issufficientlydense,radiativecoolingofsupernovaremnants(SNRs)canreducethe 5.3 VALIDITYOFASSUMPTIONSANDAPPROXIMATIONS efficiency ofsupernovaheatingbyanordermagnitude.Theconditionfor where Eisthekineticenergyofsupernovaejectainunits10erg,psISM the numberofsupernovaepersecond10grammesstars. density inunitsof10”gcm,p*oisthestellar10"cm"andR54 (Taylor 1950)andtheapproximatecoohnglawequation (23).Takingthevaluesusedfor These equationshavebeenderivedusingthesimilarity solutionfortheadiabaticblastwave the numericalcalculations,E=4and^541,we have have alsotocheckthatthe ISMpressuredoesnotconfinetheSNRsandprevent theminter- ijnt =8x10£5¿p|sRsiyr,(34) conclude thatradiativecooling oftheSNRsisnegligiblefortotaloutflow models,we the bulkofgalaxywealsofind¿hitAcooi0-07 inbothcases.However,beforewecan At thecentresofsequencesDAandKA,wefindijntAcool 0-01and0.07respectively.For W^coo^O^lp^^p-^o. (36) SQ2 secting. Theconditionfor thisisthattherampressureofpostshockmaterial begreater than thepressureofISM. Thisistruefortimeslessthan 2 so iconf =2.5x 10Vr r;yr, (37) icooi =10^Pyr. (35) 2 Sequence DCdiffersfromsequenceDBinthatinflowbeginsmuchearlierandcloser © Royal Astronomical Society • Provided by theNASA Astrophysics Data System By comparingtheflowsindeVaucouleursandKingmodelgalaxiesweseethat, Throughout thecalculationswehaveassumedthatallkineticenergyofsupernovae The time-scaleforonsetofradiativecoolingis Stellar masslossinactivegalaxies 1013 1981MNRAS.197..995M 7 = 17 2 3-1 41 16 1014 J,MacDonaldandM.E.Bailey indicate. Itseemslikelythatnon-intersectionofSNRswillresultinamultiphaseISM, more pressureconfinementoftheSNRsoccursinregionoutflow.Thereduction where TisthetemperatureofISMinunits10K.ForcentressequencesDA cantly reducedintheouterpartofgalaxy,makinginflowmorelikelythanourmodels ¿conf ^2.Hencethepossibilitymayarisethatefficiencyofsupernovaheatingissignifi- rather thanourassumedsingle-componentmodel.Theeffectsoftwoormorephasestothe and KA¿mtAconf0.070.7respectively.HoweverforthebulkofgalaxyP¡ met inmanygalaxies.However,beforewecandiscusstherelevanceofourmodelstonuclear models suggest. models ofram-pressurestrippingforsphericalgalaxieshavebeencomputedbyGisler(1976) pletely negligible.However,comparisonofelectronmeanfreepathandradiusgyration be usedtocalculatetheconductiveflux.Wefindthatluminosityisroughly efficiency ofsupernova-heatingwillleadtoagreaterregioninflowthanthenumerical reduction ofthesupernovaheatingefficiencyduetoradiativecoolingSNRs.Further- ISM inellipticalgalaxiesisanimportantproblemthatrequiresinvestigation. his numericalresults,wefindthatram-pressurestrippingwillbeeffectiveinsweepinginter- 20 percentofthesupernovaheatingrateforsequencesDAandKAhenceisnotcom- component perpendiculartothetemperaturegradient,equationsofBregman(1978)can retain theirinflowinggasandarenotstrippedbytheram-pressureofmotion.Numerical activity wehavetocheckthatgalaxiesmovingthroughtheintergalacticmedium(IGM)can shows thatmagneticfieldsoflessthan10"Garesufficienttosuppresselectronconduction. potentials ofthedarkandluminouscomponentsgalaxy.Thisquantityisuncertain tered inthecoldinflowingregionsresultagreatlyreducedconductioncoefficient. and Lea&DeYoung(1976).UsingananalyticapproximationderivedbyGisler(1976)from Conduction canalsobeignoredinthepartialwindsbecauselowtemperaturesencoun- stellar gasoutofanellipticalgalaxyif but theresultsofEinasto,Kaasik&Saar(1974)forellipticalsindicatethatitisprobablyless of ahaloinretardinganoutflowbybindinggastothegalaxyisratiobetweencentral for simplicitywehavenotincludedoneinourgalaxymodels.Ameasureoftheimportance Here ohasbeenexpressed intermsofMandrbytherelationfordeVaucouleurs galaxies than unity,andhenceourresultsarenotsignificantlyalteredbytheexistenceofhaloes. n (cf. Bailey& MacDonald1981a).Further progresscanbemade ifellipticalsareessentially a mt 10'cm" llOOOkms/ ~ \4x10'ergs'/lO^\1kpc/ larger thanatpresent.Asagalaxywithinflowing stellarmasslossevolvesitwillatsome heating. Weseefromtheinequalities(18)and(38) thatram-pressurestrippingwillbethe We seeimmediatelythatram-pressurestrippingis lesseffectiveatearlyepochswhenais initial causeofgaslossif Here PigmistfdensityoftheIGMandV velocity ofthegalaxyrelativetoIGM. pigm yg~ stage begintoloseitsISMeitherbecauseofram-pressure strippingorduetosupernova- Te G We haveshownthattheconditionsrequiredforoccurrenceofinflowarequitereadily In theearlyepochmodels,highgasdensityofinflowingmaterialalsoresultsin Thermal conductionbyelectronshasalsobeenneglected.Ifthereisnomagneticfield © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Although galaxiesundoubtedlyhavehaloesofdarkmatter(Faber&Gallagher1979), / VG\\(«SN^SN \/T/'e v (39) (38) 1981MNRAS.197..995M 1l -11 135 _1 31 9 -331 1 when allowanceismadeforthedependenceofaon/z, where hisHubble’sconstantHinunitsof100kmsMpc.Equation(59)thenbecomes, ratios typicalofellipticals(about30ifH=100kmsMpc',Tonry1980)wefind references therein)canbeusedtoderivearelationbetweenrandAf.Formass-to-light one-parameter family,e.g.ifweassumeellipticalshaveaconstantmass-to-lightratio,the massive ellipticals.Conditionsmostconducivetoefficientsweepingarefoundatthecentres ‘L-o*', lawrelatingluminositytoobservedvelocitydispersion(Terlevichetal1981and galaxies withmasses^lO/z4f.Thestrongdependenceonhmakesitdifficulttomake (Bahcall &Sarazin1977;StrimpelBinney1979)andV^1800kms(Roodetal Hence ram-pressurestrippingisofgreaterimportancethansupernovaheatingforthemore both theIGMdensityandvelocitydispersionarelower.Forexample,ram-pressure galaxies, notjustellipticals,atthecentresofgreatclusters.Awayfromclustercentre any hardandfastconclusionsuntilHisbetterdetermined.However,therestatistical of theX-rayemittingclusters.ForcentreComaclustern^2x1(Th'cm~ SN evidence (Gisler1978)thatsweepingisanimportantfactorindrivinggasoutofalltypes 0 0 ex ineffective comparedwithsupernovaheatingatallepochsforthemajorityofclusterellip- galaxies areoutside3coreradii,weseefromequation(61)thatram-pressurestrippingis drops toabout0.1ofitscentralvalueat^3clustercoreradii,theexactpositiondepending We haveshownthatatearlyepochssupernova-heating isincapableofdrivingatotalwindin cluster is~10yr,significantamountsofgascanbuildupeveninthoseoutlyinggalaxies on therunoftemperatureinX-rayemittinggas.Sinceover80percentcluster massive blackholeinourmodelsandhencesteady statesolutionswithaninflowingregion these galaxiesthatgivetailradiosources. that occasionallypassthroughthecentre(Roodetal1972argueagainstmajorityof persion abovewhichstellar masslossflowsinwardsandfuelsnuclearactivity inelliptical even themostenergeticradiosources.Wehave not includedanysinkssuchasacentral outlying galaxieshavingprimarilyradialmotions).Lea&DeYoung(1976)suggestthatitis ticals foranyplausiblevalueofH.Furthermore,sincethedynamicaltime-scale elliptical galaxies.Insteadmatterlostfromstarsflows inwardsinsufficientquantitiestofuel 6 Discussionandimplicationsfornuclearactivity 10cm' \1000kms'/W'mJ to totaloutflowdoesnotoccurearlierthanatime do notexist.HowevertheanalyticresultsofSection 4indicatethattransitionfrominflow 1972). Weseefromequation(41)thatram-pressuresweepingneedbeconsideredonlyin is expectedtobeoccurring atthepresentepochinellipticalgalaxieswith ä>300kms”. where öistheline-of-sight velocitydispersionaveragedoverthewholegalaxy. Henceinflow 0 G 0 e This conclusionisinfullagreement withtheresultsofnumericalcalculations. 0 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System There isalsoobservational evidencetosupporttheideathatthereisacritical velocitydis- n t Stellar masslossinactivegalaxies 11/4 1015 (41) 1981MNRAS.197..995M 1-1 1 _1 1-1 _1 lo v 7 1016 J.MacDonaldandM.E.Bailey has notbeenobservedatradiowavelengths.NGC1600isinthesurveyofEkers& velocity ~1800kms"(if=100Mpc). is orbitingitslessbright,butpossiblymoremassivecompanioncDgalaxy,NGC4874ata galaxies. Ofthe15ellipticalswithcentralvelocitydispersionknowntobegreaterthan sources (Heeschen1970;Ekers&1973;DresselCondon1978).Theremainingthree Mebold &Goss1978;Fosburyetal1978),NGC4278(BottinelliGouguenheim1977a; playing aroleindrivinggasoutofNGC4889(Cowie&Songaila1977).Itisalsointeresting at 21cm,wasadefiniteneutralhydrogencontentfound. to notethatinnoneofthefivehighvelocitydispersionradiosourceshavebeenobserved pressure strippedgalaxy.Thermalconductionfromthehotintergalacticgasmayalsobe probably movingwithit.ItthereforeseemslikelythatNGC4889isanexampleofaram- X-ray emittingComacluster.Ithasbeensuggested(Valtonen&Byrd1979)thatNGC4889 (1973) butwasnotdetectedandNGC4889,acDgalaxy,isthebrightestmemberof galaxies areNGC1573,1600andNGC4889.Asfarastheauthorsknow,1573 275 kms'(Schechter1980;Terlevichetal1981andreferencestherein),12areradio neutral hydrogen.Thefifthgalaxy,NGC7785,hasnotbeenobservedat21cm. Gallagher etal1977;Bieging1978),NGC4636(Bottinelli&Gouguenheim1977b;Knapp, Furthermore fourofthesefivegalaxies,NGC1052(Knapp,Gallagher&Faber1978;Reif, each case. active galaxieswitho>275kmssuggeststhattheradioemissionhasadifferentcausein Tammann &Wendker1977;BottinelliGouguenheim1979)containdetectableamountsof Faber &Gallagher1978;Knapp,KerrHenderson1979)andNGC5846(Huchtmeier, which theneutralhydrogenhascomeintogalaxyfromoutside.Furtherevidenceforthis external originofthegascomesfromlargedifference(~70°)betweendirection clusion canbealteredeither byinfallofgasfromoutside(seeabove)orif gas hasbeenleft Hence atthepresentepoch onlygalaxieswithAfmagnitude (Mg=19.8for^ 85kms"Mpc,Kirshner, Oemler&Schechter1979) by radiativeaccretionofgaslostfromtheclustergalaxies (Mathews&Bregman1978). case bySimkin(1979). galaxies witho^275kms.Iftheellipticalgalaxyhasawell-definedstellarrotationaxis, observations (Lo&Sargent1979;HaynesRoberts1979). proposal ofGunnthatitisinfallintergalacticHicloudshasbeenruledoutbyrecent the axisofneutralhydrogendiscandrotationstarsinNGC4278(Gunn over fromapreviousperiod ofactivity(Bailey1980).Ourlimitisbrighter than thecharac- (Terlevich etal1981)leadsto radio sources.ThecorrelationbetweenoandB magnitude,A/,forellipticalgalaxies from absorptionlinesandemissionshouldbe parallel.Thishasbeenshowntobethe the stellarmasslossshouldalsorotatearoundthisaxisandhencerotationaxesdetermined 1979). Theexactsourceoftheneutralgashasbecomeuncertainbecauseoriginal 10yr Ba B 1 1 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Of the38galaxieswithoknowntobelessthan275kms",onlyfiveareradiosources. Also recentX-rayobservationsindicatethatthehotgasiscentredonNGC4874and The presenceofHiinthoseactivegalaxieswitho<275kms'andthelackit Gunn (1979)hasoutlinedamodelforthecauseofactivityinNGC1052and4278 It isourcontentionthatinflowingstellarmasslossfuelsnuclearactivityinelliptical The dependenceoft^onöhasanimportantconsequence forthedensityevolutionof Slowly moving,massivegalaxiessuchasM87,atthe centresofclustersmayalsobefuelled 1o192M+2 - 0.5r10(B°). (43) 1981MNRAS.197..995M w 4 -1 12 6 3 8 inflowing gas.Inthenumericalmodelsnetangularmomentumofstarswasneglected. galaxies. Theevolutionoftheradiosourcedensityfunctionisdiscussedingreaterdepth material oflowerspecificangularmomentumandhencecentrifugalforceswillbelower, inflowing materialbreaksupintocloudsduetoRayleigh—Taylorinstability.Iftheflow NGC 3379atabout20arcsec(~700pc)fromthecentre.InsequencesKCandDCstagna- Davies 1981)thisisjustifiableinthecaseoftotaloutflow.However,becauselarge Bailey &MacDonald(1981b). decrease inülleadtoalargethecomovingnumberdensityofactive L =3xl0—^L. (45) from thecentre.Henceadiscofcoldgasdimension~100pcisexpectedtoform.The tion radiigreaterthanthisareattained.Ifgasflowsinwardsfromregion,conservingits injected gas.Thisagainhighlightstheimportanceofstudiesdealingwithmultiphase the discsmaller,thanforcaseinwhichinflowbreaksup(asitprobablydoes remains smooth(asitdoesintheKingmodels),infallinggasmixeswithfreshlyinjected angular momentum,thecentrifugalforceiscomparablewithgravitywhengas~100pc For example,theobservationsbyDavies(1981)givearotationvelocityof~SOkmsfor stagnation radiiencountered,angularmomentumcannotbeneglectedwheninflowoccurs. Since ellipticalgalaxiesare,ingeneral,slowrotators(Illingworth1977;Peterson1978; disc, onthestructureandrotationlawofgalaxyalsowhetherornotcooling, detailed structureandevolutionofthisdiscwilldependonthedegreedissipationin in thegalaxyluminosityfunctionofSchechter(1976)andhenceasmallevolutionary Z,=4xlOFZ-. (44) flows. de Vaucouleursmodels)intosmalldensecloudswhichhavelittleinteractionwithnewly evolution dependscriticallyonwhetherfurtherfragmentationoccurs,leadingtoordinary with time,ifstarformationoccurs,theratioofbluetoredellipticalgalaxiesinclusters supermassive star,low-massspinarorblackhole. star formationorwhethertheoriginalself-gravitatingobjectcollapsesasawholetoform forms inthenucleusofellipticalgalaxywhendiscmass~10M.Thesubsequent Bailey (1980)hasshownthataself-gravitatingobjectofmass~1OMandradius3pc F isadecreasingfunction oftimewhilstMincreaseswithtime.Hence accretion, which into energyatprodigiousrates.Lynden-Bell(1978) hasshownthatefficienciesof1/3are MBH^lOFAf. (46) (1978) whofoundthattwodistant(Z^0.4)clustershaveroughlyequalnumbersofblue should increasewithclusterredshift.SuchaneffecthasbeenobservedbyButcher&Oemler Hence accretionissupercritical if The Eddingtonlimitingluminosityforablackhole ofmassMis easily attainedfromdiscaccretionontoarotating blackhole.Atthisefficiency,anaccre- condensation tothedistantclusters,consistsentirelyofellipticalsandSOs. tion rate,producesanaccretionluminosity and redgalaxieswhereasthenearbyComacluster,ofcomparablerichnesscentral may besupercriticalatearly epochs,laterbecomessubcriticalandeventually ceaseswhen Ed0 acc0 o 0 BH 0 BH Under theassumptionthatmaterialarrivesatdiscincentrifugalequilibrium, The causeandformofnuclearactivityisintimatelyconnectedwiththefate © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Since, inourmodel,thefractionofellipticalswithinflowingstellarmasslossdecreases If thereisablackholeattheGalacticCentre,inflowing stellarmasslosscanbeconverted Stellar masslossinactivegalaxies 1017 1981MNRAS.197..995M galaxy willstillhaveabrightopticalcore(Ngalaxy?)whichfadewithtimeand tion ofdouble-loberadiosources(Lynden-Bell1978).Duringthesubcriticalphase total outflowbegins.Thesupercriticalphasecanbeassociatedwithquasarsandtheforma- underlying galaxy. 7 Conclusions disappear completelywhenthefuelsupplytoblackholeisfinallyturnedoff. galaxies ofhighervelocitydispersionandluminosity. 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