Is Dark Matter in Spiral Galaxies Cold Gas II. Fra

astro-ph/931104418NOV93A&Amanuscriptno.(willbeinsertedbyhandlater)Yourthesauruscodesare:11(12.04.01;11.09.4;09.19.1;08.06.2;11.05.02)ASTRONOMYANDASTROPHYSICS16.11.1993Isdarkmatterinspiralgalaxiescoldgas?II.Fractalmodelsandstarnon-formationDanielPfenniger1,Fran¸coiseCombes21ObservatoiredeGen`eve,CH-1290Sauverny,Switzerland2DEMIRM,ObservatoiredeMeudon,92190Meudon,FranceReceivedJune3,1993;acceptedNovember8,1993Abstract.Inacompanionpaper(PaperI)wehaveproposedanewcandidatetoaccountforthedarkmatteraroundspiralgalaxies:coldH2gasinafractalstructure,supportedbyrota-tion,andconcomitantwiththeHIdisc.Wehaveshownthatthishypothesisiscompatiblewithdynamicalandobservationalconstraintsaboutdiscgalaxies,andexplainsseveralconspira-ciesandparadoxes,sincethedarkmatteristheninaformoffreshgasabletoproducestars.Inthispaperweattempttode-scribethephysicalconditionsleadingtoafractalstateofcoldgasinoutergalaxydiscs.Gascloudmodelstakingintoaccounttherecentlydisclosedfractalstructureofcoldgasaresetup,showingthatlargeerrorsintheclassicalgasmassdeterminationbasedonsmoothcloudmodelscaneasilyfollowifthegasisinrealityfractal.Indeedtherangeofpossiblecolumndensitiesisthenmuchlarger,including5ormoredecadesofsurfacedensities,insteadof2forsmoothcloudmodels.Thusfractalcloudsmustpresentbothopticallythinandopticallythickclumpsinanysinglewavelengthobservations.TheobservedfractaldimensionofthecoldISMsuggeststhatmassunderestimatesbyafactor10ormorearetypical.Duetoitslowtemperature(around3K),anditscondensedfractalstructure,togetherwithitslowmetallicity,theoutergaswouldbealmostinvisibleforusualdetectors.WeconsidertheparadoxofthepersistenceofcoldJeansunstablegasinouterdiscs,farfromimportantheatingsources,yetnotformingstarsorJupiters.FollowingRees(1976),wedeterminethesmallestclumpdistributionthatcanpersistinacollisionalandalmostisothermalfragmentingcoldgas.At3Ktheseelementarycloudletsarepredictedtohavearadiusofabout30AU,andhaveamassoftheorderofaJupiter.Theiraveragedensityandcolumndensityare109cm3and1024cm2.Theyaregravitationallybound,andtheirlineofsightthermalwidthisabout0:1kms1.Theirfrequentcolli-sionspreventthemfromformingJupitersorstarsandthenearisothermalityofthefractalnearlysuppressesenergydissipa-tion.Athighertemperature,especiallyaboveH2dissociation,Sendoffprintrequeststo:D.Pfennigerthecollisionrateinthefractaldecreases,favouringstarforma-tion.Itturnsoutthatthesmallestdensitycondensations,called“clumpuscules”offerfavourableconditionsforcontainingH2inbothvapourandsolidphases.HoweveritisunknownwhetherenoughcondensationssitessuchasdustexistintheouterdiscstopermitthefreezingofH2.Itisexpectedthatthelargesubli-mationenergypreventsmuchH2tobecomesolid,butasmallamountofH2icegrainsisacrucialfactorforagoodcouplingbetweengasandthe3Kbackground.Manyofthegeneralargumentspresentedhereaboutfractalscanbeappliedtootherinhomogeneousstructures,suchasthehotgasingalaxyclusters.Theclumpusculespresentedheremightbetheformofmatterinwhichcoolingflowsinclustersseemtodisappear.Keywords:darkmatter–galaxies:ISM–ISM:structure–stars:formation1.IntroductionInordertounderstandbettertheproblemsandconspiraciesdiscussedinPaperI(Pfennigeretal.1994),weconsiderinmoredepthitsmainhypothesis:darkmatterinspiralgalaxieswouldbemadeessentiallyofaformofhydrogensufficientlydiffusetobestillabletoformstars,andatthesameplacethanHI,mainlyoutsidetheopticaldiscs.Itshouldbeprefer-entiallyincoldmoleculargasform,sincethewarmandhotdiffusephasesfillmostofthevolumeatatoolowdensitytocontributesignificantlytodarkmatter.Indeedtheexistenceofacold,dense,self-shieldedandverylowvolume-fillinggasiscompatiblewithobservations.Thisistheonlygaseousformwherealargeamountofmasscanbehidden.Inthenumerousconferencesdedicatedtothedarkmatterproblem,extremelylittlecriticalattentionhasbeendevotedtothispossibility.Thispapercontainsinmoredetailaworkpresentedelsewhereasafirstaccount(Pfenniger1993).2D.Pfenniger&F.Combes:Isdarkmatterinspiralgalaxiescoldgas?II.Firstofall,thefactthathydrogenatlowtemperaturehasveryshortcoolingtimes(106yr),isJeansunstable,butmanagestosurviveintheouterdiscsofgalaxiesforseveralGyrremotefromimportantheatingsourcesandwithoutcol-lapsingintostarsorJupiters,isafactnotproperlyunderstood.Apparently,coldandclumpygaswithsupersonicturbulencevelocities(10kms1)dissipatesverylittle.Thisproblemhasbeenmentionedseveraltimesinthecontextofmolecularcloudsintheopticalpartofgalaxies(seee.g.Scalo1985),butsincestarsarethenpossibleimportantenergyinputsources,thelongmolecularcloudlifetimethereisnotaproblemasobviousasforHIinoutergalacticdiscs.Thephysicalstateofthisgasmustbehighdensityandlowtemperature.Sincenosignificantheatingsourcesintheoutergalacticdiscspresumablyexist,wecanassumethatthegasisonlybathinginthecosmologicalbackground,andthatitstemperatureisabout3K.Inthesenearlyisothermalconditions,cloudscanfragment(Hoyle1953)untiltheyreachsmallclumpunits,inwhichthecoolingtimebecomescomparabletothefree-falltime(Rees1976).Theaveragetypicaldensityoftheseelementarycloudlets,called“clumpuscules”,is109cm3,col-umndensity1024cm2,size30AU,andmass