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Chapter7Eatingmger
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Howfastdotheyeat?
Thepopularnotionofablackholesueverything'frsisoheeventhorizohen,onlyiftheangularmomentumoftheinfallingmatterisn'ttoogreat.Farawayfromtheblackhole,theexternalgravitationalfieldisidenticaltothatofanyothersphericalbodyhavingthesamemass.Therefore,apartiorbitaroundablaaewtoniandynamics,justasitwouldaroundaar.Whatravelthispatternofgoingroundandroundincircles(orindeedellipses)ahewayformoreexoticbehaviour?Theathereisinvariablymorethaicletheblackhole.Theriessoftheastrophysienaweobservearisesbecausethereisalotaroundabladthismatterteractwithitself.Whatismravityisn'ttheonlylawofphysicsthatmustbeobeyed:sotoomustthelawofservationofangularmomentuApplyiothebulkquaerthatmaybeattractedtowardstheblackholegivesrisetoremarkableobservablephenomena,goodexamplesofwhicharefoundiicobjeasquasars.Quasarsareobjectsatthetresofgalaxieshavingasupermassiveblackholeattheirveryheartwhich,becauseofitseffeearbymatter,causeittooutshiivelightfromallthestarsihosegalaxies,acrossallpartsoftheeleagruWeshallmeetquasars,andotherexamplesofactivegalaxies',iogetherwithsterpartsofthesecalledmicroquasarswhoseblackholesarenitudelessmassivethanthoseinsidequasars.For'sgetbakingaboutthematteraroundablackhole.
&ed,youotdirectlyobserveanisolatedblackholebecauseitsimplywo;youlydetectablackholebyitsiionswithothermaterial.Anymatterfallingtowardsablackholegaiiergyandbyturbuleistainstotherinfallingmatterdoingasimilarthihisheatiomsleadingtotheemissioromagicradiation.Thus,itistheiionoftheblatheerthatleadstoradiatioedfromtheviityoftheblackhole,ratherthaionfromtheblackholeitself.
Blackholesarenotaloof,iiesiheirgravitatioractallmatter,whethernearbygasorstars,towardstheBecausegravitationalattracreasesstronglywithproximity,starsarerippedapartiftheyareuohaveaterwithablackhole;auredinFigure15.Afraoftheattractedmatterwillbeentirelyswallowedoraccretedbytheblaatterdoesn'tjustaccelerateintotheblackholewhohtheeventhorizohereissomethiecourtshipritualasthegravitationally-attractedmatterdrawsheblackhole.Veryoftenitisfoundthatapartietrycharacterizesagmatter:thatofadisc.Ifthegravitationalfieldweresphericallysymmetric,theblackholewouldplayerminingtheplahinwhichthegaswouldsettletoformaiondisc-thedisewouldbedetermiureofthegasflowfarfromtheblackhole.If,however,theblackholehasspiedgaswilleveotheplaneperpendiculartoitsspinaxis,regardlessofhowitfleradii.Ifthereisanyrotationatalliedmatter,thenthismustbethoughtofiheservationofangularmomentumthatwemetinChapter3whenwesideredtherotatioultimatelycollapsedtoformaspinningblackhole.Therotatiothematterwillbefollowing(fairlycircularbutactually)spiralling-inorbitsasitly.Closetotheblackhole,theLehirriwemetinChapter3meansthatatsmallradiitheaaybeealigheequatorialplahespinningblackhole.(Inthistext,thiseffeownastheBardeeerso.)
15.Artist'simpressionofaiondiswhichajetisshowe-seeChapter8)andadonorstarwhigrippedapartbythegravitationaltidalfortheblackholewhichisatthetreoftheadisc.
Ifgasisasignifipohegmatterthengasatomscollidewithaspartitheirownorbitsandthesesresultironsiomsbeiystates.Wheronsfallbacktystatestheyreleasephotonswhiesarepreciselythedifferehehighereheeledthelylevelithasfallento.Thereleaseofphotoradiativeeheggasdsothisly.Whileenergyisreleasedintheseprocesses,bulkangularmomentumisnot.Begularmomentumremaiem,theatteruestorotateinlahedireiangularmomentuThus,theattractedmatterwillinvariablyformaiondisc:aratherlong-livedholdierialtheblackhole.Dependingonjusthowclosetotheblackhmaterialget,themattergetsohotthattheradiatioheadiscaprisesX-rayphtohightemperaturesoftenmilliodoesn'tmattertoomuchwhethertheKelviemperaturescaleisbeihetemperaturesarequitethishot!).
Asimpleanalysisofsomefamiliarequatioonianphysicsshowsthatthegravitatiyreleasefivenamountofinfallingmassdepeioofitsmassmultipliedbythatoftheblackholeitisspirallingtowards,andhowclosetotheblackholetheinfallis.Fivenmassofattractorsuchasablackhole,theclosertheinfallingmassapproachesit,thegreaterthegravitatioialenergyreleasedasbeseeooniheeisavailabletoberadiatedoutisthediffereheeheinfallingmasshasfarawaybeforeitisaccelerated(calculatedusiein'sfamousformulaE=mc2,whereEisenergy,mismass,andcisthespeedoflight)ahasattheiablecircularorbitoftheblackhole.
AlthoughfusionholdsgreathopeasafuturesourergyforEarth,itlyyieldatmost0.7%oftheavailableE=mc2y.Intrast,signifitlymoreoftheavailablerestmassbereleasedasenergyfrmaterial,viaeleagherradiation.Quitehowclosetoablackholetheagmaterialgetdepends,asdesChapter4,onhowfasttheblackholeisspinning.Iftheblackholeisspinningfast,theholdihematerialuch,onmuchsmallerorbits.Infact,aassontoaspinningblackholeisthemosteffitwayknownofusingmassty.Thisprocessisthoughttobethemeismbywhichquasarsarefuelled.QuasarsarethesitesofthemostpowerfulsustainedeheUniverseandarediscussedfurtherinChapter8.
16.Diagramshowiialenergyofamass(atestparticle)decreaseswithdegdistaoablackhole.
I'vealreadymehereisaweenmassandenergyandforaSchwarzs-rotating)blaountyequivalentto6%inalmasspried,andthatRoyKerr'ssolutioeiionsshowthatthelaststablecircularorbithasamuchsmallerradiusfromthespinningblackholethanwouldanblaemass.InprilymorerotatiybeextraaKerrblackhole,butonlyiftheinfallingmatterisinthesameseheblackholeitself.Ifmatterisiediretothewaytheblackholeisspiisradeorbit,thenherestenergycouldbereleasedaseleagicradiation.If,however,thematterinfallingtowardsamaximallyspinningblackholewereinthesameseheblackholewerespinning,theninprinciplearemarkable42%ycouldbereleasedasradiatioercouldlosesuffigularmomentumthatitcouldorbittheblackholeascloseastheiableprogradecircularorbit.
Howfastdotheyeat?
&ioheblackholeatthetrealaxy,inSagittariusA*,whosedisetinChapter6,is100-millionthofthemassoftheSuhisdoesn'tsoundverymutilyourealizethatthisdstoaeof300Earthmassesperyear.Toatforthetypiseluminositiesofquasars,matter-iihemassofourSuneachyeararerequired.Toatforthetypiositiesofthesmaller-scalemicroquasarsthatweshallalsomeetiherequiredmatter-ibeohofthisvalue.
Ainwhichasimilareionprocessmaybetakingplagamma-raybursts,usuallyreferredtoasGRBs.ThesearesuddeensebeamsofgammaraysthatseemtobeassociatedwithviolentexplosionsindistaheywerefirstobservedbyUSsatellitesie1960sandthereceivedsigiallysuspeSovietnuclear>
&heubiquityofmatterspirallingintoablackholeviaadisc,physidithelpfultomakesimpleandiioahahemagnitudesofsomeoftheimportantphysitities:if'onesidersaspherietryratherthanadisetrytheinglimitsemerge.Aparticularlyillustrativeexampletheworldofstars,whicharemuchbetterapproximationstospheresofplasmathaiondiscs.SirArthurEddingtohattheradiatioheexcitedelesgwithotheriogasofastarwillexertaradiationpressureonasubseques.Photonsscatter'(whichsimplymeansgiveenergyao')eletaiionizedplasmawithieriorofastar.Thisoutressureisunicatedviaelectrostaticforces(theelectrically-alogueofthegravitatiohepositivelychargedionssuchasthenucleien(alsoknorotons)andthenuandotherheavierelementsthatarepresent.
Iar,theionheadsradiallyoutwardsaingoutressureactsoppositelytothegravitatiopullsmatterinwardtowardstheore-or-lessspherietryofastar,thereisamaximumlimittotheamountofoutressurebeforeitoverwhelmstheinwardgravitationalpullaarsimplyblowsitselfapart.Thismaximumradiationpressureisknowonlimit.Higherradiatioablyfherluminosityofradiation,andtheluminosityofabeestimatedfrhthedista.Therefore,lifyingassumptionsingapproximatingaiondisctoasphere,theamountofradiationpressureinsideaferred.Thissimplemethodissometimesusedtomakeanieofthemassoftheblatheobservedluminosityoftheradiatiefrplasma,ifitisdeemedtobeatthemaximallimitiheEddingtonluminosity'(abovewhichhigherluminositywouldgivesuffitlyhighradiatiowouldexceedthegravityfromthemasswithinaselfapart)thenthemassbeestimated.
ThisEddingtonluminositybethoughtofintermsofamaximumrateatwhichmatteraccrete,forsuitableassumptionsabouthoweffittheprocessofais.ThisgivesaquantitycalledtheEddingtonratewhich(fortheassumedefficy)isamaximalvalue.Therearewaysthisparticularmaximumlimit,ofwhichistherejeoftheassumptionofsphericalsymmetry(thisisfiarbutmalydoesn'tapplytothedisetryofadiscsthatweosideriouandhowblackholesgrow).
Howtomeasurethespeedofrotationwithiiondisc
Becauseofadvaronomiologyitisnowpossibletomeasurethespeedatwhichmaterialisablackhole,atleastforexamplesthatarerelativelyclosetoEarth.Ohebiggesisthatitisdifficulttoobtaininformationonasuffitlyfineangularscale.Thespatialresolutioobeatleastoohousahanthatroutiaiicaltelespriheroutetoagfiionewouldbetoobserveatshthsandtobuildalargertelesparticulartoreducetheratioofthewavelengthofobservatioerofthetelesgused.Uhelattergetshideouslyexpensiveveryquicklywhiletheformertakestheusualvisiblewavelengthsira-viime,towhichtheatmosphereoftheEarthisratheropaque.Theroutetoagasmallerratiwavelengthtoteleseteris,tuitively,toobserveatradiowavelengths(mugerwavelengthsthahervisibleorultra-violet)forwhichtheatmosphereandionosphereareusuallytraotakethetelesetertobemostoftheEarth'sdiameter.
Thereareafewteicalissuesaboutthisapproaeedalittledis:itturnsoutthatthankstosomeveryusefulmathematicsdevelopedbytheFreiBaptisteJosephFourier,itispossibletoreuchofthesignalthatafulltelescopeaperturewouldobserve,eveualgareaosiofthefullaperturethatonerefer.Ifthesignalsfromdistennas(eaglikeanindividualtelescope-seeFigure17showingtheVeryLongBaselineArray,knownastheVLBA)arecorrelatedtogether,itispossibletesiohavedetailasfiwhichwouldbeobtainedifah-sizedtelescopecouldhavebeenfullybuilt.Justtogiveanideaofhowfiionis,supposethatIwasstandingontopoftheEmpireStateBuildinginNewYork,andyouwereinSanFrancisco.Withthisamouionyouwouldbeabletoresolvedetailthatisseparatedbythesizeofmylittlefingernail.
17.Artist'simpressionBaselineArray(VLBA)ofacollectivelygiveimageswitharesolutiohatwhichwouldbeobtaielescopeertureasignifitfraofthediameteroftheEarth.
18.TheVLBAhasmeasuredthedistributionofdiscretemaserswithiiondiscofthegalaxyNGC4258(alsoknownasMessier106)arouralblackholewhosemassis40milliohemassofourSun.
(IamglossihefactthattheEarthisaspheresothereislibetweenSanFrandtheEmpireStateBuilding,butyougettheidea.)ThismeansthatwithisliketheVLBAwedividualfeatureslessthanalight-monthapartinalaxies.
Highresolutionaageinaspatialsense,aioralsehatonedisverypreciselywhatthewavelengthsofparticularfeaturesareirum)isaverypowerfulakiheDopplereffect,ateamledbyJimMoranofHarvardUyusedtheVLBAtomakeobservatioiondisdiralblackholealaxyknownasNGC4258.Theymeasuredthevariatiohofaparticularspectrosal(awatermaser')acradisdusedthisredshiftingaing,asthemasiowardsandawayfromtheEarth,todetectthevariationihwhichmatteratagivesaroundtheblackhole.TheseexquisitelybeautifuldatathatthematterorbitsaroundtheblackholejustasKepler'slawswoulddesdtheseorbitsaredepiFigure18.
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Iableorbitofablackholewhosemassis100milliohemassofourSun,theangularmomentumisover10,000timessmallerthantheangularmomentuminatypicalgalaxy.Itisclearthatformattertobeaccretedbytheblackhole,thisrequirestheremovalofthevastmajorityofthisangularmomentum,andthisisaplishedbyprocesseswithiiondisc.Theorbitsiiondiscmayberegardedasagoodapproximationthinfacttheyaresubtlyandgraduallyspirallingin.Kepler'slawssaythatthematteronthesmallerradiiwillbemovihematteronslightlylargerorbits.Thisdifferentialrotationallowsablackholetoabsorbtheplasmathatprisestheadisc:therapidlyrotatisfriagainsttheneighbmaterialonorbitswithslightlylargerradii.Thisdiffereywillmeaeronslightlylargerorbitswill,byviscousturbules,bedraggedalongalittlefasterandslythematteroswillbeslightlyslowed.Therefore,beotionhasiherout,angularmomentumhasbeeheoutermaterialfromtheierial,heatingasitdoesso.
ularmomentumisserved,andtheierialsystematicallyloseangularmomentum,makiobeswallowedbytheblaotethatifablmatterhastoomugularmomentum,itwillstayfurtherawayfromtheassaboutwhichitis:itwouldbemovingtoofasttogetakindofviscouseffectsmightberelevanttotheplasmawithiiondister-atomicvisbesmallinthissituation-thegaseousplasmaofwhichtheadisprisedisveryfarremovedfromthecyoftreafaeticfieldsmaybeveryimportantintransferringangularmomentumoutihemagicfields?Theplasmaiiondiscisveryhot,aomsarepartiallyiooeledpositivelyus.Therefore,therearefloartidmesprodueticfields,asdescribedbytheequationsofJamesClerkMaxwell.Onveryweakmag,theybestretdamplifiedbydifferentialrotationaheturbuleheplasma,uptolevelsatwhichtheygivetherequiredviscosity.Thisisthebasisofwhatisknoworotationalinstability.TheimportahismethistextwasfirstrealizedbySteveBalbusandJohheearly1990swhenwattheUyinia.
Byviscousturbulendprobablyothermeans,plasmatuallyloseangularmomentumandorbitatsmallerradiiclosertotheblackhole.Ohegaseousplasmareachestheiableorbit,iotoslipdownintotheblackhole,afterwhichitwillneverbeseenagain,butitwillhaveaugmehemassandspinoftheblackhole.
Whatdoadiscslooklike,andhowhotarethey?
Wehaveseenthatvisdturbulesplayasignifiovingangularmomentumfrmaterialsothatitorecloselytothebladbeswallowedbyit.Aceoftheviscousa,however,isthatthebulkorbitalspirallingmotiosvertedintoraiohematterheatsup.Thegreatertheraiohemoreheatehasandthehigheritstemperature.AsmentionedinChapter5,whereverthereisheat,therewillbethermaleleagicradiation.Everybodyemitsthermalradiatioisatabsolutezero.
Sugisohehighlyluminousradiationweobservefromadiscs.Fortheadiscsthatsurroundthesupermassiveblackholesthatareattheheartsofquasars,thecharacteristicsizeofaiondiscisabillioresandthebulkoftheradiatioiondistheoptidtheultra-viioruFortheadiscsthatsurroulylessmassiveblackholesintheso-calledmicroquasars(thataredisChapter8),theadiscsareamilliontimessmalleriheradiationisdominatedbyX-rays.Themoremassiveablackholeis,thelargertheiablecircularorbitisahecoolerthesurroundiiondiscwillbe.
ThemaximumtemperatureiiondisdasupermassiveblaesthemassofourSunwillbearound1millionKelvinwhileforadisdastellar-massblackhole,itbeuptoafactorof100higher.
Howdoyoumeasurehowfastablackholeisspinning?
Givenyou'tactuallydirectlyseeblackholes,you'tseethemspiher.Buttherearewomaihowfastablackholeisspinning.AsdisChapter4,whenblackholesspi,itispossibleformattertobeiaroundtheblauchthanwouldbepossibleiftheywerenotspinning.Itturnsoutthatmatteriorbitsisheatedbystroandviscouseffectsasitswirlsin,andthisimmeleadtemitted,dependingonhowclosetotheblaatterhasswirledinbefs.Geypredictsthattheshapeofthespeesisaffectedbythedistaingmatterisfromtheblackhfromthegravitatio)inawaythathasacharacteristiature.ThissignaturearisesfrironatomswithinthismatterahinformationfrhtioneeredbyAndrewFabianeUy.
Thesearegmeasurementstoi,beaors,suchastheinoftheadiscwithrespecttoEarth,aureofwindandoutflowihesurfaceoftheadistheviityof(alongourlito)itsinnerrimwhosecharacteristicsholdthekeytounloationabouttheblackholethatisotherwiseinaccessible.OthermethodsfthespinofstellarmassblackholesinvnifigeoftheX-rayspedagforthediffereuresoftheinnerregioiondisc(whicharehotter)andtheregiohatbeegraduallycooler).ItispossibletoestimatefromtheshapeoftheX-rayspectrumtheinofthedisthehighesttemperature(assumingyouknowthemassoftheblackhole,anditsdistaoinferhowfarfromtheblackholetheierialis.AnalogousmethodstomeasurethespinofsupermassiveblackholesattheheartsofquasarsarebeingdevelopedbyeDoDurhamUy.Howatterisabletoorbit(befswallowedbytheblackhole)tellsyouhowfasttheblackholeitselfmustbespinning.
Blackholesareverymessyeaters
Ittraonlyafraatedtobe10%,thoughitbeverysignifitlyhigher)ofthematterthatgetsattratowardsablackholegetsasfarastheeventhorizonandactuallygetsswalloter8siderseerinfallingtowardsablackholethatdoesn'tactuallygetsithihorizon.Fromacrosstheadiscitself,matterblowoffasawind;fromwithiradiioftheadiscveryrapidjetsofplasmasquirtoutatspeedsthatarereallyquiteclosetothespeedoflight.AsChapter8shows,whatdoesn'tgeteatenbytheblackholegetsspunoutandspatoutratherspectacularly.
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