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Chapter 6 How do you weigh a black hole（第1页）

Chapter6Howdoyouweighablackhole?

&heplaorbitaroundit，togetherlas（ofwhiostfamousexample），asteroids，ascolleprisetheSolarSystem。TheSolarSystemitselforbitswithinthediscalaxyaroureofmassattheGalatre。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。Figure14showsthedatafrhezaeam。OverthelastfewyearstheyhavemaderepeatedobservatihtioftheGalatreahestarshavemovedsiimetheyobservedthem。Becausethespectraltypesofthesestarsareknown，theirmassesareknown。Yearbyyear，astheorbitalpathofeachofthesestarsbeesapparent，thedyions（knoler'slaws，thesamelawsthatgoveriosaroundourSun）enableGhezaosolveforeachorbitilyahemassofthedark&#ionthatisattheonfocusofalltheseorbits。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。