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Chapter 7 Eating more and growing bigger（第1页）

Chapter7Eatingmger

Howfastdotheyeat?

Thepopularnotionofablackholesueverything'frsisoheeventhorizohen，onlyiftheangularmomentumoftheinfallingmatterisn'ttoogreat。Farawayfromtheblackhole，theexternalgravitationalfieldisidenticaltothatofanyothersphericalbodyhavingthesamemass。Therefore，apartiorbitaroundablaaewtoniandynamics，justasitwouldaroundaar。Whatravelthispatternofgoingroundandroundincircles（orindeedellipses）ahewayformoreexoticbehaviour?Theathereisinvariablymorethaicletheblackhole。Theriessoftheastrophysienaweobservearisesbecausethereisalotaroundabladthismatterteractwithitself。Whatismravityisn'ttheonlylawofphysicsthatmustbeobeyed:sotoomustthelawofservationofangularmomentum。Applyiothebulkquaerthatmaybeattractedtowardstheblackholegivesrisetoremarkableobservablephenomena，goodexamplesofwhicharefoundiicobjeasquasars。Quasarsareobjectsatthetresofgalaxieshavingasupermassiveblackholeattheirveryheartwhich，becauseofitseffeearbymatter，causeittooutshiivelightfromallthestarsihosegalaxies，acrossallpartsoftheeleagrum。Weshallmeetquasars，andotherexamplesofactivegalaxies'，iogetherwithsterpartsofthesecalledmicroquasarswhoseblackholesarenitudelessmassivethanthoseinsidequasars。For'sgetbakingaboutthematteraroundablackhole。

&ed，youotdirectlyobserveanisolatedblackholebecauseitsimplywo;youlydetectablackholebyitsiionswithothermaterial。Anymatterfallingtowardsablackholegaiiergyandbyturbuleistainstotherinfallingmatterdoingasimilarthihisheatiomsleadingtotheemissioromagicradiation。Thus，itistheiionoftheblatheerthatleadstoradiatioedfromtheviityoftheblackhole，ratherthaionfromtheblackholeitself。

Blackholesarenotaloof，iiesiheirgravitatioractallmatter，whethernearbygasorstars，towardsthem。Becausegravitationalattracreasesstronglywithproximity，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，theatteruestorotateinlahedireiangularmomentum。Thus，theattractedmatterwillinvariablyformaiondisc:aratherlong-livedholdierialtheblackhole。Dependingonjusthowclosetotheblackhmaterialget，themattergetsohotthattheradiatioheadiscaprisesX-rayphtohightemperaturesoftenmilliodoesn'tmattertoomuchwhethertheKelviemperaturescaleisbeihetemperaturesarequitethishot!）。

Asimpleanalysisofsomefamiliarequatioonianphysicsshowsthatthegravitatiyreleasefivenamountofinfallingmassdepeioofitsmassmultipliedbythatoftheblackholeitisspirallingtowards，andhowclosetotheblackholetheinfallis。Fivenmassofattractorsuchasablackhole，theclosertheinfallingmassapproachesit，thegreaterthegravitatioialenergyreleasedasbeseeooniheeisavailabletoberadiatedoutisthediffereheeheinfallingmasshasfarawaybeforeitisaccelerated（calculatedusiein'sfamousformulaE=mc2，whereEisenergy，mismass，andcisthespeedoflight）ahasattheiablecircularorbitoftheblackhole。

AlthoughfusionholdsgreathopeasafuturesourergyforEarth，itlyyieldatmost0。7%oftheavailableE=mc2&#y。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-viiorum。Fortheadiscsthatsurroulylessmassiveblackholesintheso-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。