,....

NATUREVOL.33125FEBRUARY1988 687LETTERSTONATUREWethankLauraKayforassistanceintheobservationsandW.Burkefordiscussions.Thisresearchwassupportedinpartby NSF.

Received 29 October; accepted 23 November 1987.

1.Lynds,R.&Petrosian,V.Bu!LAm.astroSoe.18,1014(1986).2.Paczynski,B.Nalure325,572-573(1987).

3. Robinson, L. B. el aL OpIo Engng 26, 795-805 (1987).

4.Soucail,G.,Fort,B.,Mellier,Y.&Picat,J.P.Astr.Astrophys.172,Ll4-Ll6(1987).5.Stone,R.P.S.Astrophys.J.218,767-769(1977).6.Home,K.PubisastroSoe.Paci{.98,609-617(1986).7.Soucail,G.,Mellier,Y.,Fort,B.,Matbez,G.&d'Odorico,S.IAUCire.No.4456(1987).8.Dressfer.A.&Gunn.J.E.Aslrophys.J.270,7-19(1983).9.Soucaif,G.elal.IAUCire.No.4482(1987).

Hyper-velocity and tidal starsfrom binaries disruptedby a massive Galactic black boJe

J.G.HilIsTheoreticalDivision,LosAlamosNationalLaboratory,LosAlamos,NewMexico,USAAclosebutnewtonianencounterbetweenatightlyboundbinaryanda106M0blackbotecausesORebinarycomponenttobecomebound to the black bote and the other to beejected at up to4,000kmS-l.ThediscoveryofevenOResuchhyper-velocitystarcoming from the Galactic centre would be nearly definitive evidenceforamassiveblackbote.Thenewcompanionoftheblackbotehas a high orbital velocity which increases further as its orbitshrinks by tidal dissipation. The gravitational energy released bythe orbit shrinkage of a such a tidal star can be comparable toits total nuclear energy release.ThedynamicsofgasintheGalacticcentre(GC)suggestthatitmayhavea106M0blackholel.Suchamassiveblackbalewould, by capturing the debris of stars that pass within its Rocheradius,growinlessthan109yrto108M0,whichisthemassofblackholesexpectedinluminousquasars2,3.AGCblackbalemoremassivethan4x104M0ispredictedtoemitmorenon-stellarradiationthanisobservedfromtheGC,duetocapture of stellar tidal debris2, Although this is asevere problem,itdoesnottotallyruleouta106M0GCblackbale.

Simulations of clase encounters between binaries and stellar

intruders4 have shown that in exchange collisions, in which' amassive intruder replaces one binary component, the averagegravitationalbindingenergyofthebinaryincreaseswiththemass, MI, of the captured intruder. The increase is fivefold ifMIis100timesthemassofthebinarycomponents.Ishowherethatthistrendcontinuesforencounterswithmuchmoremassiveintruders.ThecomputationsweredonewiththeShampine-Gordon5variable-arder,variable-step-sizeintegrator.Themeanfractional change in the energy of the system due to integration

errors was 10-7, so the high ejection velocities found in thesesimulations are not numerical artefacts. I used newtonian

mechanics. Most encounters occurred well beyond the last stablecircular orbit at three Schwarzschild radii.Inthesesimulationseachbinarycomponentisof1M0andtheblackbalemassesareMbb=104,lOs,106and107M0'Thesemi-majar axis of the binary is ao =0.01AV,exceptfortwoseriesofrunswithao=0.02and0.1AVforMbb=106M0'Only'hard'binaries,withorbitalvelocitieslargerthanthemeanvelocityinthestellarsystem,surviveencounterswith

I

fellow stars of approximately the same mass6-8. The maximum

semi-majar axes of hard binaries in galactic nuclei, where stellarvelocitiesaretypically80-300kms-\areintherangeao=10.01-0.1AV.ThevelocitydispersionintheGCisalgointhisrange9.Theaveragemassdensitywithin0.25pcoftheGC

0.8

o 10: M", '.0 =0.01o 106M", ;.0=0.02. 10 M",'.0 -0.1

0.6

w

"-

0.4

~10:M",

. 107M",. 10M",0.2

25 50 75 100Dmln

125 150

Fig. 1 Probability of an exchange collision in which the blackbale replaces one of the original binary components, plotted as afunctionofthedimensionlessclosestapproachparameterDminofthebinarytotheblackbale.Thecurvesarelabelledbythemassoftheblackbaleandthesemi-majaraxisofthebinaryorbit.ThesmallestDminplottedforeachofthetwomostmassiveblackholes

is just inside the last stable circular orbit.exceeds107M0pc-3(ref.9),soclaseencountersbetweenstarsare common. '

I simulated encounters having a wide range of impact para-meters.Ateachimpactparameter,250runsweremadeusingdifierentbinaryorientationsrandom)ychosenwithrespecttothe approaching intruder, whlich has a velocity at infinity ofV=250kmS-l.Atthisvelocity,thetotalenergyofthethree-body system (binary plus black ~ole) is positive even for ao =0.01AV(bydesign,sotheencountersaretlybys).Itisthusenergetically possible for the encounter to dissociate the binary,but in almost every case the encounter left behind either theoriginal binary or one in which the black bale had replaced onestar.BecauseVismuchlessthaneitherthevelocityofthebinarywithrespecttotheblackbaleatclosestapproachortherecoil velocity of the ejected binary component, the resultsshouldnotbesensitivetothechosenvalueofV.Thebinaryis1,500timesitssemi-majaraxisfromtheblackbale at the beginning of each computation, far enough awayfor the tidal field of the black bale to be small but clase enoughsothebinarycomestopericentrewiththeblackbaleafterrelatively few integration steps. I treat the stars as point masses,

but they are broken apart if they pass within their Roche radiusof the black bale. While tidal breakup is not a problem forneutron stars and white dwarfs, it is serious for main-sequencestarsbecauseoftheirrelativelylowdensities.A1M0main-sequencestaristoroapartbya106M0blackbaleifitpasseswithin Rmin =150R0=0.70AVoftheblackbale(W.BenzandJ.G.Hills,inpreparation).Becauselowermain-sequencestarsare denser than the Sun, they can pass significantly closer totheblackbalebeforetidalbreakup.Amain-sequencestarof0.1M0hasone-fourththeRocheradiusofa1M0star.Fora1M0main-sequencestar,theRocheradiusexceedstheSchwarzschild radius if the black bale is less massive than3x108M0(rer.2),sosuchastarismuchmorelikelytobetidally toro apart by the black bale than to be swallowed whole.Figure1showstheprobabilityPEofanexchangecollisionas a function of the dimensionless closest approach parameterDmin=(Rmin/ao)[2Mbh/1O6(MI+ M2)]-1/3,whereRministheclosestapproachofabinarywithsemi-majaraxisaoandcom-ponentmassesMIandM2toablackbaleofmassMbh'Thefactor in the square bracket compensates for the increase in theiidalinteractionradiusoftheblackbaleasMbhincreases.Exchange collisions occur in nearly 90'% of the closest encoun-tersoWenotethatPEisnearlythesameata'givenvalueof

NATUREVOL.33125FEBRUARY1988LElTERSTONATURE5

o10:Me'.0-0.01o106Me'.0-0.02.10Me'.0-0.150 75

Dmln

100 125Fig.2Theincreaseinthedimensionlessbinding-energypara-meter of the binary as the result of an exchange collision with a

black bale.DminforvariousvaluesofMbhandao,sowecanuseFig.1tofiadPEforarbitraryvaluesofao,RminandMbh'Figure2showsEbind,thenormalized(dimensionless)increaseintheaveragebindingenergyofthosebinarieswhichBufferexchange collisions. Here

(Increase in binding energy)(2Mbh

)

-1/3

Ebind '= Original binding energy 106(MI + Mz) .WenotethattheresultsareagainnearlyindependentofaoandMbhwhengivenasafunctionofDmin'Figure 3 shows the ejection velocity parameter

( 2Mbh )

-1/6

Vejection'= Voo 106(MI+Mz)

x [(O.O::U)(~I:~z)rl/zfortheejectedstarintheseexchangecollisions.HereV00isther.m.s. velocity at infinity of the ejected star as found in thenumerical experiments. Figure 3 shows that Vejectionis well-behaved,soitiseasytodetermineV00forarbitraryvaluesofMbhandao.ForablackholewithMbh=106Mo,c.m.s.ejectionvelocitiesatinfinityareaboutV00=4,000,3,000and1,400kmS-Iforao=0.01,0.02and0.1AVrespectively.Thesevelocitiesgreatly exceed that of any known star in the Galaxy, and thetwohigheronesaremuchlargerthantheescapevelocityfromthe Galaxy.

The high ejection velocities occur because Vbreak, the centre-of-mass velocity of the binary at the point where the tidal fieldof the black hole pulls it apart, is much greater than the internalorbital velocity,Vor\"of the binary components. Ir each binarycomponentexperiencesanaveragechangeinitsvelocitywithrespect to the black hole on the arder of Vorbbecause of theperturbation of its companion, the corresponding change in itsspecifickineticenergyisi>KE=VorbVbreak'ForMbh=106Mo,Vbreak=0.14c=lOzVorbforao=0.01AV,sothechangeinthespecific kinetic energy of the binary components with respecttotheblackholeismorethantwoordersofmagnitudelargerthan their original orbital binding energy.Forabinarytohaveanexchangeprobabilityof50%ormoreinanencounterwitha106Moblackbalerequiresittopasswithinabout100aooftheblackhole,orwithinRmin=1and10AVforao=O.Oland0.1AVrespectively.ForastellarmassdensityattheGCof107MopC-3,astarpasseswithin1AVofa106Moblackbaleaboutevery100yrandwithin10AVevery10 y?3. (Here gravitational focusing is important, so the cross-sectionforpassingwithindistanceRmin0[.theblackholeis

4.5

o.10:Me'.0'0.01'o106Me'.0=0.02.10Me'.0=0.1'j..E...oo~ 4

f,. ~104Me.105Me.107Me3.5

15ó 25 15050 75Dmln

IDO 125

Fig. 3 The ejection velocity parameter of the unbound binarycomponentafteranexchangecollisionwiththeblackbale.proportionaltoRminratherthantoR;"in')If1%ofthestarsinvolvedintheseclaseencountersarebinarieswithao=0.01AU,andanother1%arebinarieswithao=0.1AU,thenoneofthecloser binaries suffers an exchange collision about every 104yrand one of the more distant binaries every 103yr. (Ir the binarycomponentsare1Momain-sequencestars,thenabouthalfofthe encounters which are clase enough to produce an exchangecollision for ao =0.01AVleadtotidalbreakupoftheindividualstars by the black hole, but the fraction of stars broken up isnegligible in exchange collisions in which ao=0.1 AV.)FromFig.3weseethatthetypicalejectionvelocity,Voo,ofthediscardedbinarycomponentis-4,000kmS-Iforao=0.01AV,and1,400kmS-Iforao=0.1AU,ifMbh=106Mo.Becauseittakeshyper-velocitystarswithVoo=4,000kmS-Iabout2x106yrtoreachtheSun'sdistanceof-8kpcfromtheGC,thereareabout200ofthembetweentheGCandthesolarcircle if one is produced every 104 yr. Hyper-velocity stars withVoo=1,400kmS-Itakeatleast6x106yrtotraversethisdistanceevenifweignoretheirgravitationaldeceleration,sotherearemore than 6,000 ofthem inside the solar circle if one is producedevery 103 yr.

The average space density of hyper-velocity stars decreaseswiththeinversesquareoftheirdistancefromtheGC,withtheclosestonetotheGCbeingwithin40pcforVoo=4,000kmS-1andwithin1pcforVoo=1,400kmS-l.PropermotionsurveyfieldsneartheGCbutabovetheGalacticplaneshouldbebeBífor detecting hyper-velocity stars.

For Voo=4,OOOkms-I=800AV yr-\ the maximum propermotionofahyper-velocitystarat8kpcis0.1arcsyr-I.Asolar-luminosity star at this distance would be at magnitud e 19

in the absence of interstellar extinction. Many other hyper-velocitystarswillbecloser,brighter,andhavelargerpropermotions. If hyper-velocity stars exist, Borne may be included inexisting proper motion surveys. The simplest explanation fortheirnotbeingreportedisthattheydonotexist,whichimpliesthatthemassoftheGCblackholeismuchlessthan106Mo.Alternatively,observersmayhavedisbelievedtheoutlandishvelocities implied by a facile interpretation of their propermotions and assumed these stars to be peculiar and much closerto us than they actually are. Hyper-velocity stars should algohave large radial velocities which are hard to rationalize away.Butradialvelocitiesaremuchmoreexpensivetodeterminethanproper motions, so relatively few proper motion stars haveknown radial velocities.Hyper-velocitystarsmaywellbepeculiarcomparedtostarsin the solar neighborhood. Because they originate in the core

jof the Galaxy, their metal abundances may actually be severaltimes greater than solar, and because they reach the solar

#

688

275

250

225

200:¡;

...

175

f 104 Me

150 . 105 Me

. 107 Me

125

10025

-ri

NATUREVOL.33125FEBRUARY1988 689LETTERSTONATUREdistancefromtheGCinmuchlessthanthesolarKelvintime,theymaynothaveretumedtothemainsequenceiftheywerestronglyperturbedbythetidalfieldoftheblackbale.AstrongI tidal perturbation would algo cause them to be in rapid rotation(W.BenzandJ.G.Hills,inpreparation).AIIactivegalacticnuclei(AGNs)ejecthyper-velocitystarswhichbecomeintergalactictramps.Theexpansionoftheuni-versegraduallyslowsthemdownwithrespecttotheHubbleflowuntiltheyarecapturedbygalaxies.Hyper-velocitystarsfromAGNsmayconstituteaminarimpurityofmetal-richstars

in the Galactic halo.If hyper-velocity stárs are not found, it may still be possibletoretainthehypothesisofamassiveGCblackbalebyarguingthatmyestímateofthebinaryfrequencyintheGCistoaoptimistic,thatmostGCstarsarelessmassive,sofainter,than

the Son, or that exchange collisions between binaries and stellarremnants(whitedwarfs,neutronstars,andsmallblackbotes)haveallowedthesehard-to-detectobjectstoreplacesomanymain-sequencestarsinGCbinariesthatfewmain-sequencestarsareleftinthemlO.Butthedetectionofevenonehyper-velocitySIalcomingfromtheGCwouldbenearlydefinitiveproof of its having a massive black bale.Afteranexchagnecollisionwitha106M0blackbale,thesemi-majaraxisofthebinaryistypically50AVforao=0.01AVand500AVforao=0.1AV.Ther.m.s.orbitalvelocity,VorbitaboftheSIalabouttheblackbaleisnearlythesameastheejectionvelocity, Veo, of its Corroer companion, or about 4,000 and1,400kmS-1respectivelyforthesetwobinaries.ThevelocityofanunboundSIalwhichcollideswithoneoftheseboundstarsexceedsthelocalparabolicspeedwhichis,on average, about J2Vorbital,sothetwostarscollideatanaveragespeed of about J3Vorbital =6,900and2,400kmS-1forthetwocases.Theminimumcollisionvelocityrequiredtobreakuptwoequallymassivemain-sequencestarsisonlyabout2.3timestheescapevelocityfromtheirsurface,orabout1,400kmS-1(ref.11).Mostofthedebrisfromthecollidingstarsshouldremainbound to the black bale and eventually be accreted by it.TheorbitoftheboundSIalaroundtheblackbaleisveryeccentric,buttidalenergydissipationatpericentremaybeableto circularize it before the SIal is destroyed in a stellar collision.Because of angular momentum conservation, the final semi-majaraxisofthecircularizedorbitwillbeaboutaf=2Rmin'Many.tidal stars can accumulate in these clase orbits becausethehighvelocitiesinthemmakethemvery'stiff',soitisverydifficultforstarsinotherboundorbitstoperturbthemgravita-tionally.

The tidal energy dissipated in circularizing the orbits of starscapturedinanexchangecollisionwitha106M0blackbaleis-0.1-1%oftheirrest-massenergy,or1051-52ergfora1M0SIal. (Comparable energy is released in one final supemova-classcataclysm when a tidal SIal in a nearly circularized orbit collideswithanunboundstar.)TheradiosofthecapturedtidalSIalincreases, eventually following its Hayashi track, until its lumi-nosity matches its Tale of tidal energy dissipation. If each tidalSIalemits1051ergbeforeitsdestructioninacollisionandoneis captured every 104 yr, the total integrated luminosity of the

: tidal stars orbiting the GC black bale is -106 L0' The maximum

luminosity of an individual SIal is its Eddington value, so atleast 30 solar-mass stars are needed to produce the integratedIluminosity.TheintegratedspectrumofthesestarsshouldmimicthatofagiantwithitsabsorptionliDeswashedoutbytheextreme differential Doppler moliDo resulting from the high

orbital velocities (0.03-0.1 e), ofthe individual tidal giants. TheGCblackbalemayhaveaccumulatedalargenumberoftheselow-mass tidal giants in orbits with semi-majar axes, at, on the.arderoffewtimesRmin'ItistemptingtoidentifyatwithradiusoftheGCradiosource,-10AV.StellarwindsandRoche

I overflow from the tidal giants may terminate any accretion disk

lbeyond at.

I Ste"" "IDn,n', ,ooh " no""nn ""', 'ID'" h1,,' hn1", ,nd

whitedwarfsdonotBufferappreciabletidaldissipation,sotheytendtoremainintheiroriginalpost-exchangeorbits.TheGCblack bale can accumulate a large number of these stellarremnantsinorbitswithsemi-majaraxiesof50-500AVandorbitalvelocitiesof1,000-4,000kmS-l.Theyare'IDealgrinders'which help pro vide fuel for their master, the central black bale,by tearing material from main-sequence stars and giants thatpassnearthem.Received18August;accepted18November1987.1.Oort,J.H.ARev.Asir.Aslrvphy.15.295-362(1977).2.Hills,J.G.Nature254.295-298(1975).3.Hills,J.G.Mon.Nat.R.asir.SocoSoco

182.517-536 (1978).

4.Hills,J.G.&Fullerton,L.W.Asir.J.85,1281-1291(1980).5.Shampine,L.F&Gordon,M.K.ComputerSolutionoiOrdinaryDifferentialEquations:TheInitia!ValueProblem(Freeman,SanFrancisco,1975).6.Aarseth,S.J.&Hills,J.G.Asir.Aslrophy.21,255-263(1972).7.Heggie,O.C.Mon.Nat.R.asir.Soco

173,729-788 (1975).

8.Hills,J.G.AsIr.1.80,809-825(1975).9.Sellgren,K.,Hall,O.N.B.,Kleinmann,S.G.&Scoville,N.Z.Astrophys.J.317,881-891

(1987).

10.Hills,J.G.Mon.Nat.R.asIr.Soco 175, ]p-4p (1976).

11.Benz,W.&Hills,J.G.Astrophys.J.323,6]4-628(1987).

Laboratory simulation of Jupiter's GreatRed SpotJoelSommeria*,StevenD.Meyers&HarryL.SwinneyCenterforNonlinearDynamicsandtheDepartmentofPhysics,TheUniversityofTexas,Austin,Texas78712,USAIsolated large stable vortices have long been observed in the jovianatmosphereandmorerecentlyonSaturo.Theexistenceofsuchstable vortices in strongly turbulentplanetary atmospheres is achallenging problem in fluid mechanics. In a numerical simulationMarcus1 found that a single stable vortex developed for a widevariety of conditions in a turbulent shear flow in a rotating annulus.Totestthisweconductedanexperimentonarotatingannulusfilledwithfluidpumpedintheradialdirection.Theannulusrotatesrigidly (there is no differential rotation), but the action of theCoriolis force on the radially pumped fIuid produces a counter-rotating jet. Coherent vortices spontaneously forro in this turbulentjet, and for a wide range of rotation and pumping rates the flowevolves unti) only one large vortex remains.Figure1showstheannulartankusedintheexperiments.Thetankisrotatedrapidlytoachieveanessentiallygeostrophicflow(atwo-dimensionalfIowinwhichtheCoriolisforceisbalancedbypressuregradients2).InsuchafIowtheinertialforceissmallcomparedwiththeCoriolisforce,thatis,theRossbynumberissmal!.InOuTsystemtheRossbynumberis-0.1,asestimatedfromtheratioofthecharacteristictimefortheinertialforce(thetumovertimeforavortex)tothecharacteristictimeforthe Coriolis force (the rotation period of the tank).OnJupitertheGreatRedSpotandotherpersistentcoherentvortices lie in latitudinal zones of strong shear3. Marcus'snumericalsimulationindicatesthatinaquasi-geostrophicflowthe existence of a strong shear can lead to the formation of asinglepersistentcoherentvortex.InOUTexperimentthereisastrong shear on the outer edge of the counter-rotating jet (seeFig.2).

Dissipation appears to play little Tole in the dynamics of thejovianatmosphere4,andmesimulationbyMarcuswasdoneforaninviscidfluidoOUTexperimentisunusualinthatthedynamical timescales of interest are typically an arder of magni-tudeshorterIbantheviscoustimescale.Forexample,theEkmanspin-downtimetEistypically20swhilethevortextumovertimeisonly2s,(MeasurementsoftEagreewellwiththecalcu-latedvalue,tE=ho/2(fl/1)1/2,where/1isthekinematicviscosity,flistheangularvelocityofthetank,andhoistheIDeandepth

*Permanentaddress:Madylam,ENSHMG,BP95,38402StMartinO'HéresCedex,France.