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Chapter6Howdoyouweighablackhole?
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&heplaorbitaroundit,togetherlas(ofwhiostfamousexample),asteroids,ascolleprisetheSolarSysteTheSolarSystemitselforbitswithinthediscalaxyaroureofmassattheGalatre.ThespeedatwhichourSolarSystemtravelsarounditscircularpaththroughtheGalacticdiss,andtopleteaarouitreleofhundredmillionyears.Inadditiontothisorbitalmotion,thewholeSolarSystemmovesperpendiculartotheGalae.Thekindofmotiosiswellknowntophysicistsassimpleharmoniwiththerestforce,whichpullsourSolarSystembacktowardstheequilibriumpositionoftheplaheGalaxy,thegravitationalpullofthestarsandgasthatprisetheGalacticdisc.Atthemome45light-yearsabovethisequilibriumpoint.Inabout21millionyearsfromnowtheSolarSystemwillbeatitsextremepoint320light-yearsabovetheGalae.43millioerthat,theSolarSystemwillbebathemid-plaheGalaxy.WhentheSolarSystemliesiheGalaethehwillsuffermaximumexposuretotheicraysthatarewhizzingaroundintheplaheGalaxy,trappedalonglinesofmagravellingaroundthemonsomekindofacrossbetweeerandatramliherehavebeeionsthattheSun'smhtheGalaecouldhavebeenrespohemassexinofdinosaurs.Butthiskiionishardtoverifyorrefutebecausethetimescalesforthisorbitalmotionareofcourserathertrianobservers,whodon'ttehahisisaiionalastrotofollowsomeprocessthatescalesmugerthauriesoverwhichwe'vebeenmakingastronomicalobservationsofanyreasonableadthhness.
Thereare,however,orbitalmotionswithihataresignifitlyeasiertomeasure,atleastitherelevanttimescalesareeheattentionspansofhumaelescopes.OfpartiterestiofblackholesaretheorbitalmotioarsiregionsoftheMilkyearsinapartoftheskyknownasSagittariusA*.Lookingintion,mosteasilyseehernhemisphere,oneislookingtowardstheverytrealaxy,27,000light-yearsawayfromus.Thisisaparticularlydenselypionofspace,whichleadsustotwoproblemsanttostudytheGalatre.Thefirstisthatthereisarelativelyhighspasityofstarsahatthereislotsofdust.
&problemmeaouseameasuremehatenableshighresolutionimaging,i.e.fiailsbeseparatedfromohehotolensgivesfiailonagivehanawide-angleleusielesvariablyihis,buttherearevariousteiquesdevelliurbuleh'satmhwhievitablyviewallcelestialobjelessweputthetelesasatelliteabovetheatmosphere.Ofparticularimportaeotics.Thisteiquecorreosphericvariatioheblurringhtstar(calledaguidestar)aheprimarymirrorofthetelescopetoceloutthisvaryingblurring.Whenabrightstarisn'tavailableiofskythatisofi,apowerfulatedlaserbeambeshoomsimosphereamosphericsderivedfromthat.
Thesedissue,thepresequatalatre,isproblematicbecauseitishardtoseeopticallightthroughdust,justasitishardforultra-violetlightfromtheSuhroughtheopacityofasuiontothisproblemisthatooobserveatinfra-redwavelengthsratherthanvisiblewavelengths.
HowtomeasurethemassoftheblackholeattheGalatre
Sufra-redobservationshavebeenedbytwogroups,oneledbyAndreaGheziniaandoneledbyReinhardGeheworkofbothteamsilyprovidesawonderfullyclearmeasuremethetreoftheGalaxy.Figure14showsthedatafrhezaeaOverthelastfewyearstheyhavemaderepeatedobservatihtioftheGalatreahestarshavemovedsiimetheyobservedtheBecausethespectraltypesofthesestarsareknown,theirmassesareknown.Yearbyyear,astheorbitalpathofeachofthesestarsbeesapparent,thedyions(knoler'slaws,thesamelawsthatgoveriosaroundourSun)enableGhezaosolveforeachorbitilyahemassofthedarkionthatisattheonfocusofalltheseorbits.Theseiiohemassofthisdarkregionratherwell.Itisnowkover4milliohemassofourSun,withinaregionwhoseradiusishan6light-hours.Becausetheobjectisdarkbutextraordinarilymassive,theonlyisthatthereisamammothblackholeatthetrealaxy.
14.FigureshowingthesuccessivepositionsofstarsthatorbitarouralblaourMilky>
Thereisobelievethatalaxy,theMilkyWay,isuniqueinhavingablackholeatitsthetrary,itisstroallgalaxiesmaywellhaveablackholeattheirtres,atleastthemoremassiveohereasonforthisisbeinglyfualrelationship,discoveredbyJohnMagorriaheUyofDurham,andco-workers,betweenthemassofablackholeatthetreofagalaxyandthemassofthegalaxyitself.Ofcoursethebusihemassofabladthemassofagalaxyistricky.Theteiquethatworkssobeautifullyatthetrealaxyotbeappliedtalaxiesbecausetheyaresimplytoofara>
ThemassesofthetralblackholesattheheartsofellipticalgalaxiesexceedamilliohemassofourSuenduptoandbeyondabilliohemassofourSun.Forthisreasoentermedsupermassiveblackholes.
&hediffimeasuringthemassesofblackholesandthemassesofgalaxies,ithasbeenfoundforawiderangealaxiesthatthemassofthetralblackholescaleswiththemassofitshostgalaxy.Thisisthoughttosuggestthatboththetralbladthegalaxyitselfgrewaherae.
ManyblackhhouttheGalacticdisc
&hesiralsupermassiveblackholeattheheartofagalaxy,therearethoughttobemillionsofblackholesdistributedthroughouttheextentofeachgalaxy,andthesearebelievedtohaveformedinaverydifferentwayfromthegalatraloneswhichgrowbygradualaofinfallihesestellarmassblackholesareformerlymassivestars,ongverybrightly,withfusiawayihemkeepiandpressurized,andcruciallyabletravitationalcollapse.Whentheirnuclearfuelisallusedup,thereisnolongeranyradiatiooholdupthestar,andnothingtobalaheinwardfravity.ForastarwithasimilarmassasourSun,thecollapseuyultimatelyresultsinapactobjeasawhitedwarf.Theeinginastrophysihematterisdenseinawaythatisutterlydistinatter.Bythestandardsofnormalmatter,whitedactbecausethematterhasbeeremelypressed.Thismatterisiohatalltheelesareseparatefromtheirpareatterisohightemperature).Thepressurethatersistentinwardgravitationalpullarisesfromtheelesrefusingtobepressedintotooedaregion(aceoftheHeiseyprieameforthiseffectiseledegeneracypressure'.Hadthegstar,allitsfuel,beenmoremassive,theionalinfallwouldhavebeeillaroerpartprotonswouldhavefusedtogethertoformheseupactobjeawhitedwarf-aar.
But,ifweareiedinblackholes,theurntostarswhisiderablymoremassivethanthosewhitoproducewhitedwarfsorevears.Astarabovethismasswillbeverylumisfuellastsandnuclearfusioaihefuelisusedup,it'sgameoverforthestaraswillswitchoff.Thestarisnowsuffitlymassivethatthegravitationalforevereneracypressureandsothecollapseissopowerfulthateventhispressureotbalayandthecollapseleadsioablackhole.Theassivestarisoftenapaheexplosioacularsuper,leavingablackholeastheotheinalloenitorstar.Insuaicularlythoseheavierthanirohesized.
&blackholetobesecurelyidentifiedfromadeterminationofthemassesofthetwostarsinabinarystarsystemiscalledV404Cyg.JedPhildtheirco-workersobservedtheorbitsofthetwostarsverycarefullyaheiranalysisthatthisbinarypairincludesapactobjegamassatleastsixtimesgreaterthanthemassofourSun,andisthusablackhole.(ItsmasswaslaterfouimesthemassoftheSun.)
Itispossibletomakeplausibleestimatesofthearsiheirmasses.Weestimatetheellar-mass'blackholesinalaxybyghowmaarswouldhavefhinitshistorytohaveevolvedsuffitlybyheirnuclearfuelviafusion.Evenifonlyaverysmallproportionofstarsinoontoformblackholes,withmorethan1011objetheMilkyWaythatstillgivesusalotofblackholes.
Howeasurethemassesoftheseblackholesthatpervadegalaxies?Infaestellar-remnantblackholes,theteiqueisdynamicallyverysimilartothatusedfortheblackholeatthetrealaxy.Thereasonforthisisthataverysignifitfraofstarsinalaxy,aprobablyinalaxiesalso,einpairsthatformedbinarystarsystems.Itiseasytosurmisehowthismighteabout:gravitatioradmanytwo-bodyorbitsarestable,sooarseneanotheraionallybouheyarelikelytoremainso.Forabinarysystem,ifwemeasurethetimetakeodoapletelooparouher,atimeknowalperiod,ahedistahenwearewelloofindingtheirmasses.Ifthepactobjeorbitaroundanormal(fusioarofkypeandthereforeknownmass,thenthemassofthepactstarisstraightforwardtoderive.Ifapactobjectsuchasablackholeisasionandnotinabihelaieansthatthereisnomeasmassaerminingthatitisablackhole.ThesmallestblackholethatwemeasureisafewtimesthemassofourSustellar-massblackholesexdredtimesthemassofourSun.
Themeasurementofthemassofablackhole,giveeology,istractablealthoughitstillrequiresagoodmeasureofpatiey.Giventhatmassisoiallyonlythysicalpropertiesofablackholesuchstudiesgetushalf-waytocharagit!However,measuringthespinofablackholeisharder,andinChapter7Idescribetheheroiceffortsthatareryanddothis.
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