NewResult!Anoninteractinglow-massblackhole–giantstarbinarysystemScience01Nov2019:Vol.366,Issue6465,pp.637-640ToddA.Thompsonetal•  Almostallblackholesarediscoveredbytheirx-rayemission.•  Thompsonetal.observedlightfromagiantstarthatisDoppler

shifted,indicatinganorbitaroundabinarycompanion.•  Thecompanionobjectmustweighmorethan2.6solarmasses,butit

emitsnolight,includingx-rays.•  Thisindicatesthepresenceofablackholethatisnotcurrently

consuminganymaterial.•  Theremaybeapopulationofsimilarlyhiddenblackholesthathave

beenmissedbyx-rayobservations.

Theopticalspectraexhibitonlyasinglesetofabsorptionlines,i.e.,asingle-linedspectroscopicbinary.•  ThesystemhasanearlycircularorbitwithorbitalperiodPorb�83.2±0.06days,•  radialvelocitysemi-amplitudeK�44.6±0.1kms−1,andeccentricity

e�0.0048±0.0026.•  Themassfunction

Thus J05215658 likely consists of a M�3.2+/-1.0 M giant star and a noninteracting low-mass black hole companion with MCO�3.3 (+2.8,-0.7) M

CompactObjectMassesDeterminedviaDynamics

NS in black BHs in red is there a gap between�2-5 M¤ the most massive black holes (�15 M¤) are found in HMXBs. J. Casares, P.G. Jonker, and G. Israelian 1701.07450.pdf

Max mass of NS

HomeworkCommonErrors•  Inproblem4veryfewstudentsmentionedthatoneneedstoobservethelinesof

highlyionizedelementstodeterminetheabundanceAlsomanystudentssaidthistechniquecouldfailsincethex-rayemissionisrelativelyshortlived�whilethisisnottotallywrong,the'lifetime'oftheSNRinthex-raysisnotmuchshorterthanthatinradiooropticalandthusisnota'bestanswer'Twobetteranswersare1)iftheremnantisaplerion(synchrotrondominatedremnant)andthushadeitherweakorabsentlinesor2)ifthesweptupmaterialdominatesthex-rayemissionreducingtheimpactoftheejectaonthex-rayemissionlinesAnotheranswer(notasgood,butcorrect)isthattheremnantmayshowstrongspatialvariationsinemissionlines(e.g.Cas-A)andthusonemaydrawawrongconclusioniflookingatjustonespot.5)Thisproblemshouldhavebeenwrittenmoreclearly-Ishouldhavesaid'observationalevidence'The'lifetime'ofCRis,ofcourse,energydependent;ignoringthisthe'confinementtime'ofCRintheMW(1407.5223.pdf)is~τesc=15.0±1.6Myr(comparedtothe5MyrIgaveintheproblem).Thepaperarguesforatimescaleof~5Myr

RecentReviews•  NatureAstronomyJan082019Cosmiccelebritieswithgravitas

Blackholeshavethedistincthonorofbeingthemostpopularandpotentiallytheleastwell-understoodobjectsintheUniverse.Thisissue’sInsightexploreshowfarblackholeresearchhascomesinceitsinception,thoughitstillhasalongwaytogo.•  Observingblackholesspin:ChristopherS.ReynoldsaXiv:1903.11704•  Observationalconstraintsonthefeedingofsupermassiveblackholes

ThaisaStorchi-BergmannarXiv:1904.03338•  Themanydefinitionsofablackhole:ErikCurielarXiv:1808.01507ReviewsforScienceSpecialIssueonblackholes•  StellarMassBlackHolesandUltraluminousX-RaySourcesRobFender&TomasoBelloniarXiv:1208.1138•  TheFormationandEvolutionofMassiveBlackHolesM.Volonteri

Science03Aug2012:Vol.337,Issue6094,pp.544-547

GravitationalWaves

•  SeeClassicalBlackHoles:TheNonlinearDynamicsofCurvedSpacetimeKipS.ThorneScience03Aug2012:Vol.337,Issue6094,pp.536-538

•  andBlackholes,gravitationalwavesandfundamentalphysics:aroadmap1806.05195.pdf

blackholesareobjectsmadewhollyandsolelyfromcurvedspacetime,objectswhosecurvatureisgeneratedbytheenergystoredinthecurvature.Generalrelativity,predictsthatblackholescanspinandoscillate.

Thegravitationalwaveformsfromamergingblack-holebinaryinprinciplecarrydetailedinformationabouttheinitialblackholes(theirmasses,spins,andorbit),thefinalmergedblackhole(itsmassandspin),andthebinaryorbitalplaneorientation,theeccentricity,thedistancetothesourceandtheskylocation

NewtonianConceptIn1783attheRoyalSocietyofLondonin,JohnMichellnotedthat,•  ifastarweresufficientlymassive,theescapevelocityfromitssurface

wouldexceedthespeedoflightandsolightwouldnotescapefromit(Michell,1784).

•  Inclassicalterms,theescapevelocityfromthesurfaceofastarofmassMandradiusrisv=(2GM/r)1/2.

•  Settingvequaltothespeedoflightc,theradiusofsuchastarwouldberg=2GM/c2.

exactlythesameastheSchwarzschildradiusofablackholeofmassMingeneralrelativity,

althoughthecoordinaterhasadifferentmeaningfromtheNewtoniandefinitionofdistance.Thissphericalsurfaceplaystheroleofthesurfaceoftheblackhole.

Basicanatomyofablackhole•  Completegravitationalcollapseinevitablyleadstoablackhole(Hawking)

•  Space-timesingularity– Wherethemass-energyresides

– PlacewhereGRbreaksdownandthe(unknown)lawsofquantumgravitymustbeapplied

Event horizon Point of no return for light or matter Events inside horizon can have no causal effect on universe outside of the horizon

PropertiesofBlackHoles

•  1.Onceonefallsintothesphereofinfluenceofanblackhole,thereisnoescape.

•  2.Theregionofspacetimeblackholesencompassonlyeverincreases.

•  3.Itisimpossible,byanyphysicalprocess,toreducetheeffectofblackholestozero

•  .4.Allblackholesareessentiallythesameontheoutside,nomatterthefinedetailsoftheirinnerconstitution.

•  5.Onecannotmakeanblackholenotbeanblackhole.•  6.Onceanblackholegetsholdofinformation,itisforeverlost

ATinyHistory(ErikCuriel)

•  Hawkingshowedthatwhenquantumeffectsaretakenintoaccount,blackholesshouldemitthermalizedradiationlikeanordinaryblackbody.Thisappearstopointtoadeepconnectionamongourthreemostfundamental,theories,generalrelativity,quantumfieldtheory,andthermodynamics.

•  ....thecommunityachievedsomethinglikeunanimousagreementontheexistenceandrelevanceofblackholesonlyintheearly2000s,withthedemonstrationthatSgrA�,thecenteroftheMilkyWay,holdsasupermassiveblackhole,

AFewDefinitions(E.Curel)

Basicanatomyofablackhole•  Completegravitationalcollapse

inevitablyleadstoablackhole(Hawking)

•  Space-timesingularity–  Wherethemass-energyresides–  PlacewhereGRbreaksdownand

lawsofquantumgravitymustbeapplied

•  Eventhorizon–  Pointofnoreturnforlightor

matter–  Eventsinsidehorizoncanhaveno

causaleffectonuniverseoutsideofthehorizon

–  Analogoustothepointofnoreturninawaterfall

*blackholeshavenohair

3 parameters mass, angular momentum, and electric charge completely characterize black holes Everything else (quadrupole terms, magnetic moments, weak forces, etc.) decays away*.

R. Fender 2007

ISCO=innermost stable orbit-disk terminates there

SchwarzschildRadius-AKAtheEventHorizonforaNon-SpinningBlackHoles-Longair19.1

•  Rs=2GM/c2;3(M/M!)km

•  TheSchwarzschildradiusistheradiusof'noreturn'foranon-rotatingblackhole-itisnotthesingularity.Itsapparentsingularityisaduetoachoiceofcoordinates(Longairpg433).

SchwarzschildRadius-AKAtheEventHorizonforaNon-SpinningBlackHoles-Longair19.1

•  Eventsinsidethathorizoncannotbeseenbyanyexternalobserver•  insidetheeventhorizontheradiusbecomesatimelikecoordinate,

andthetimebecomesaspacelikecoordinate.Specifically,thatmeansthatonceinsideRs,youmustgotosmallerradii,justasnowyoumustgoforwardintime

•  onceyou�reinsidetheeventhorizononecannotavoidthesingularityatr=0

•  Thesearethe'simplest'macroscopicobjects-theonlyinstanceofanexactdescriptionofamacroscopicobject...,almostbydefinition,themostperfectmacroscopicobjectsthereareintheuniverse

•  TimescalesareVERYsortT~Rs/c=2GM/c3≈10−5(M/M!)sec

11/5/19 32

MorefeaturesofSchwarzschildblackhole–  Eventsinsidetheeventhorizonarecausally-disconnectedfromeventsoutsideoftheeventhorizon(i.e.noinformationcanbesentfrominsidetooutsidethehorizon)

–  Observerwhoenterseventhorizonwouldonly"feel"�strange�gravitationaleffectsiftheblackholemassissmall,sothatRsiscomparabletoobserver�ssize

–  Onceinsidetheeventhorizon,futurelightconealwayspointstowardsingularity(anymotionmustbeinward)

–  Stable,circularorbitsarenotpossibleinside3Rs:insidethisradius,orbitmusteitherbeinwardoroutwardbutnotsteady

–  LightraypassingBHtangentiallyatdistance1.5Rswouldbebentaroundintoacircle

–  Thusblackholewouldproduce�shadow�onsky

'The'Singularity•  Atr=0,thereisarealphysical

singularityand,accordingtoclassicalgeneralrelativity,theinfallingmattercollapsestoasingularpoint.

•  HowevertheSchwarzschildsingularityisunobservablebecausenoinformationcanarrivetotheexternalobserverfromwithintheSchwarzschildradiusRs.

•  seediscussiononpg433ofLongair

FortheMathematicallyInclinedseesec13.11.1•  TheSchwarzschildsolutionforthemetricaroundapointmass

insphericalcoordinatesis•  ds2=-(1-2GM/c2r)c2dt2+(1-2GM/c2r)-1dr2+r2(dθ2+sin2θdφ2)eq

13.52sisthelengthelement

–  Noticesingularityatr=2GM/c2(canbegottenridofinacoordinatetransformation)

•  Astaticobservermeasurespropertimec2dτ2=-ds2=-(1-2GM/c2r)c2dt2

FortheMathematicallyInclinedseesec13.11.1timeissloweddownina gravitationalfield

•  δτ=sqrt(1-2GM/c2r)) δt=1+zgrav-(thetimeintervalδτ correspondstothe

periodofthewavesemittedatthepointr,theobservedperiodofthewaveatinfinityisδt)

Thefrequencyofradiationemittedfromradiusrasseenbyadistantobserverisν∞whereν0istheemittedfrequencyν∞=ν0sqrt(1-2GM/c2r))-ifr=2GM/c2iszero�e.g.redshiftingofradiationinagravitationalfield.Pictureisthefrequencyoflightemittingbyanaccretiondisk-redisredshift,blueisblueshift(Quiz-howdowegetblueshifts??)

Gravitationalredshift-Longair19.21•  Thoughtexperiment:

–  Sendphotonupwardsinagravitationalfield

–  Convertthatenergyintomassanddropthemass

–  Convertmassbackintophoton•  Conservationofenergy⇒photonmustlose

energyasitclimbsinthegravitationalfield•  Anotherwayofthinkingaboutthis-theescape

speedfromtheobjecthastobelessthanthespeedoflight(assuming,incorrectluy,thatlightcouldslowdownandfall).

•  InNewtonmechanicstheescapespeedisv2=2GM/r,sov2=c2atr=2GM/c2•  RedshiftoflightZ=(λ0-λe)/λe;λ0=wavelength

asmeasuredbytheobserver,λeasemitted

•  Gravitationalredshiftisreallyaformofrelativistictimedilation•  Asobservedfrominfinity,timeneara(non-spinning,non-charged)blackholeruns

slowbyafactorof

•  Theeventhorizonisthe�infiniteredshift�surfacewhere(asobservedfrom

infinity)timeappearstostop!•  But…afreefallingobservingwouldfallthroughtheeventhorizonwithoutnoticing

anythingunusual.•  Thewavelengthoflightisredshifted(Z=(λ0-λe)/λe;λ0=wavelengthasmeasuredby

theobserver,λeas emitted at radius r • 

Gravitationalredshiftsnearablackhole

Longair13.58infrequencyunitsν∞=νemsqrt(1-2GM/rc2)

Whatarethepossibleenergysources?•  Accretion?

–  Releaseofgravitationalpotentialenergyasmatterfallsintoblackhole

–  YES!Thoughttobeprimarypowersourceofallsystemsjustdiscussed

•  Rotationalenergyofblackhole?Spinning(Kerr)BHsseeLongair13.11.2–  Tappingtherotationalenergyofaspinningblackhole1/2IΩ2canbeverylarge

– Maybeimportantinsomesettings…butcanonlybetappedifaccretionoccurring!

Examplemetrics•  Normal(flat)3-dspaceincartesiancoordinates

•  FlatspacetimeofSpecialRelativityincartesiancoordinates

•  Non-spinning,unchargedblackhole(Schwarzschildmetric)in�Schwarzschildcoordinates�

WhatistheEventHorizon

•  Theeventhorizonisthe�infiniteredshift�surfacewhere(asobservedfrominfinity)–  theradiusatwhichthegravitationalredshift(z)isinfinite–  z=Δλ/λ;1+z=1/sqrt(1-Rs/R);Rs=2GM/c2

•  But…afreefallingobservingwouldfallthroughtheeventhorizonwithoutnoticinganythingunusual.

•  Asobservedfrominfinity,timeneara(non-spinning,non-charged)blackholerunslowbyafactorof

• Also time appears to stop !

R. Fender 2007

ISCO=innermost stable orbit-disk terminates there

If the specific angular momentum of a particle is l ≤ 2rgc , it inevitably falls into r = 0, where rg is the Schwarzschild radius, rg = 2GM/c2 . There is a last stable circular orbit about a mass with radius r = 3rg . There do not exist circular orbits with radii less than this value, particles rapidly spiral into r = 0. This is why the black hole is called a ‘hole’ – matter inevitably collapses in to r = 0 if it comes too close to the point mass.

Why is it a Black Hole-Longair pg 433

ABitMore-Longair13.11.2,19.6.2•  Foranon-rotatingBHthelast

stableorbitisat3Rs;thisisduetotheformofthepotentialwhichisNOT1/r

•  ParticlesonthelaststableorbitaboutaSchwarzschildblackholemoveathalfthespeedoflight.

ForthoseinterestedthepotentialcanbeexpressedasU(r)eff= (1−rS/r)(mc2+l2/mr2)wherelistheangularmomentum(K.Griest)

For a Schwarzschild black hole, the maximum energy which can be released corresponds to the binding energy of the matter on the last stable circular orbit at r = 3 Rs= 6GM/c2. A fraction [1 − (8/9)1/2] = 0.0572 of the rest mass energy can thus be released

Question for class- what is the redshift from the surface of a NS?

•  M~Msun;R=10km(setbynuclearphysics)

Redshifted absorption lines from a neutron star surface Cottam, Paerels & Mendez (2002)

Assuming M>1.4Msun, z=0.35 gives -β<9 (DeDeo & Psaltis 2003)

Emission of line radiation from highly ionized atoms of Fe And O from near the surface of a NS

11/5/19 46

Rotatingblackholes-remembertheextraspecialnatureofacceleratedframes

•  RoyKerr(1963)–  DiscoveredsolutiontoEinstein�sequationscorrespondingtoarotatingblackhole

–  Kerrsolutiondescribesallblackholesfoundinnature•  FeaturesoftheKerrsolution

–  BlackHolecompletelycharacterizedbyitsmassandspinrate(nootherfeatures[exceptcharge];no-hairtheorem)

–  Hasspace-timesingularityandeventhorizon(likeSchwarzschildsolution)

–  Alsohas�staticsurface�insideofwhichnothingcanremainmotionlesswithrespecttodistantfixedcoordinates

–  Space-timenearrotatingblackholeisdraggedaroundinthedirectionofrotation:�framedragging�.

–  Ergosphere–regionwherespace-timedraggingissointensethatitsimpossibletoresistrotationofblackhole.

SpinningBH-Longairsec13.11.2•  AblackholewithangularmomentumJhasametricds2=(1-2GMr/ρc2)dr2-{(1/c2)[4GMrasin2 θ/ρc]drdφ}+(ρ/Δ)dr2+ρdθ2+(r2+a2+2GMra2 sin2θ/ρ c2) sin2θ dφ2]--Longaireq13.63r,θ,φ� usual polar coordinates wherea=(J/Mc)istheangularmomentumperunitmass(dimensionsof

distance)andΔ=r2-(2GMr/c2)+a2 ; ρ=r2+a2cos2θ

•  Iftheblackholeisnon-rotating,J=a=0andtheKerrmetricreducestotheSchwarzschildmetric

SpinningBH-Longairsec13.11.2

Just like Schwarschild metric it becomes singular but at a radius where

Δ=r2-(2GMr/c2)+a2=0;

the larger root is r+=GM/c2 +[(GM/c2 )2- (J/Mc)2]1/2Longair13.65

forJ>0thisissmallerthantheSchwarschildradiusthereisamaximumangularmomentumJ=GM2/c;forthisvalueofJthe

horizonisatr+=GM/c;1/2oftheSchwarzschildradius•  Iftheblackholeisnotrotating(a=J/M=0),theKerrlineelement

reducestotheSchwarzschildlineelement