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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=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-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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