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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）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.
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