Pulsars Tracing Black Holes in Globular Clusters

Results of precise measurements of the periods of pulsars discovered in the central regions of globular clusters are shown to be approaching the capabilities of testing the existence of a central black hole. For example, in the case of M 15 the available d

A&Amanuscriptno.

(willbeinsertedbyhandlater)

6

991 tcO 51 1v6010169/hp-o1.Introduction

rtHubbleSpaceTelescope(HST)observationsofglobularclus-stersprovideauniquepossibilityofrevealingthenatureoftheira:centralregions.Doglobularclusterscontaincentralblackholesvorarewedealingwithpurelystellardynamicalphenomena?iXTheideaofblackholeswhichmightbesituatedatthecentersofglobularclustershasbeenseriouslydebatedsincethe rstraidenti cationofX-raysourceswithinglobularclusters(Bah-call&Ostriker1975,Silk&Arons1975,Newell,DaCosta&Grindlay1976).Groundbasedstudiesonsurfacebrightnessandvelocitydispersionpro leswerenotaccurateenoughformodelindependentanalysisoftheproblem(e.g.Dubath,Mey-lan&Mayor1993,Meylan1994).RecentHSTobservationsofM15(Yannyetal.1994),oneofthemostdenseclusters,sup-portthetheoreticallypredictedstardensityslope(Bahcall&Wolf1976)forstarsinthepresenceofacentralmassiveblackholeandsupportthepossibilitythatthisblackholehasamassofMbh 103M⊙.However,theobservedsurfacebrightnessdistributioncanalsobeexplainedviaaKingmodelwithcoreradiusrc=2.2′′(Phinney1993,Gebhardt&Fischer1995).

Theaimofthepresentpaperistosuggestthepossibilityofusingmillisecondpulsarsasatraceofthecentralregionsofglobularclusterswiththeparticularaimofrevealingtheexistenceofcentralblackholes.Millisecondradio-pulsarswere

g00 t.(1)

whereg00=(1 rg/r),rgbeingthegravitationalradius.Fromhere,onecaneasilyderivethatapulsarmovinginthevicinityofaSchwarzschildblackholefromthedistancer1tor2withinthetimeinterval Twillundergothefollowingap-parentvariationofperiod P

rg

2r,

(2)

with r≡r1 r2=v T,vthepulsar’svelocity,rthemeandistanceofthepulsarfromthecentralblackholeand r r.Assumingv 15kms 1weobtainthecharacteristictimescaleforthegiven P/P:

Results of precise measurements of the periods of pulsars discovered in the central regions of globular clusters are shown to be approaching the capabilities of testing the existence of a central black hole. For example, in the case of M 15 the available d

Table1.MainparametersoftwocentralpulsarsinM15(Taylor,Manchester&Lyne1993)andtwopulsarsin47Tucanae(Robinsonetal.1995).

NamePSRJ

R.A.(J2000)

Dec.(J2000)

P(s)

˙P

(10 17)

dmin(kpc)

dmax(kpc)

0024-72C0024-72D00:23:50.34300:24:13.877-72:04:31.46-72:04:43.820.00575678001161(±1)0.00535757328590(±1) 0.00498(±1) 0.00028(±2)4.14.14.94.9

10 12

Mbh

P

< alP

˙4πGr2

c

Results of precise measurements of the periods of pulsars discovered in the central regions of globular clusters are shown to be approaching the capabilities of testing the existence of a central black hole. For example, in the case of M 15 the available d

Table2.MainparametersoftwopulsarsclosetotheGalacticcenter(Taylor,Manchester&Lyne1993).

NameR.A.Dec.PPSRJ

(J2000)

(J2000)

(s)

errorsintheestimationofdistancesofpulsarsfromthecenteroftheclusters.Then,itwillbenecessarytotakeintoaccounttheaccuraciesinthealignmentoftheephemeridesdynamicalframewiththeopticalone,theaccuratede nitionoftheclus-tercenter,e.g.viatheluminositypro leorviathedynamicalproperties(cfCalzettietal.1993),andsoon.However,theconclusionmadeaboveforM15isnotalteredevenifthepul-sarpositionwithrespecttotheclustercenterisknownwithanerroraslargeas0.5′′;inrealityerrorsareexpectedtobemuchless(Meylan1994).

TheconditionswithinthecoreofM15seemtoprovidealsothepossibilityofexplainingtheaccelerationobservedforbothpulsarsasduetothe eldperturbationscausedbythesurroundingstars.Thisallowsustomakethe rstpredictionconcerningthesinglepulsars,i.e.non-membersofbinarysys-tems:theaccelerationofpulsarsshouldbeobservedwithessen-tiallyhigherprobabilityinglobularclustersandintheGalacticcenter,than,say,inthediskoftheGalaxy.

Thee ectofperturbationscausedbythesurroundingstars,inprinciple,canbeempiricallydistinguishedfromtheperturbationcausedbytheregular eldoftheclustercoreconsideredbyWolcszanetal.(1989),Phinney(1991),Nice&Thorsett(1992).Thepointisthattheroleofthecoreshouldbecomemoreimportanttowardstheboundaryoftheclusterandwilltendtozeroapproachingthecenter,whilethestellarcontribution,viceversa,willincreasetowardsthecenter.

Thisleadstooursecondprediction:acceleratedpulsarsshouldbesituatedmainlyinthecentralregionsoftheglobu-larclusters,ratherthanintheirperipheralregions.Obviously,someprobabilityremainsofthepulsarsbeingperturbedbyachanceencounterwithastar.Theprojectione ectsshouldalsonotbeneglectedwhenconsideringthecorrespondingprobabil-ities.MoreoversarswithP

˙theexistenceofanomalouslyacceleratedpul-positivenot ttingthetypicalmagnetic eldac-tion,alsoshouldbeexpectedinthecentralregionofglobularclusters,duetothesamee ectofstellarperturbations.

Concerningtheroleofstellarperturbationsonpulsarsonecanpredictonemoree ect:thechangeoftheorientationoftheirrotationalaxes.Thee ectofregularorchaoticvariationoftherotationalaxesisknownforthecaseoftheplanets(see,Laskar1994;Laskar1995andreferencestherein)andcanberepresentedasaproblemofasystemwithperturbedHamilto-nian:

H(I, , )=H0(I)+ H1(I, , ).

(6)

Sincethecorrespondingproblemisintegrableonlyinthecaseofasingleperiodicperturbationterm(Colombo,1966),onecanconcludethatstellarperturbationsintheformrep-resentedbyChandrasekharandvonNeumann(1943)havetoleadtochaoticvariationsofthepulsaraxes.

Thus,pulsarscannotavoidthise ect,evenforthelow-estvaluesoftheiroblateness.Thenumericalestimationofthe

P

˙dmindmax(10 17)

(kpc)

(kpc)

obliquityvariation,timescales,etc.,canvarywithinextremelybroadranges,sinceitcrucially(non-linearly)dependsuponnumerousparametersoftheproblem;thecorrespondingmod-ellingisatopicofcomprehensivestudiesandisoutofthescopeofourpaper.Weonlynotethatempiricalstudiescanthemselvesprovideinformationonthise ectaswell.

Ourthirdpredictionthereforereads:pulsarslocatedinthecentralregionsofglobularclusters,inprinciple,shouldundergochaoticvariationsoftheirspinaxesand,asaresult,canre-vealspontaneousappearancesanddisappearancesduringtheirobservations.

Theseexamplesindicate:

a)theexistenceofaspecialsubclassofpulsars,i.e.thosesit-uatedinglobularclusterswithpropertiesdi erentfromthosesituatedintheGalacticdiskorinthehalo;

b)theimportanceofthesearchofpulsarsinthecentralre-gionsofglobularclustersandoftheGalaxyinrevealingthedynamicalstructureofthosesystems,includingthepresenceofmassiveblackholes.ACKNOWLEDGEMENT

WearegratefultoA.LyneandM.Tavaniforexplanationofobservationaldetailsandvaluablecomments.Oneofus(V.G.)skarforvaluablediscussions.ThisworkhasbeeninpartsupportedbyINFN,AgenziaSpazialeItaliana(ASI)andTheRoyalSociety.References

BahcallJ.N.&OstrikerJ.P.1975,Nat256,23BahcallJ.N.&WolfR.A.1976,ApJ209,214

BlandfordR.D.,RomaniR.W.&ApplegateJ.H.1987,MN-RAS225,51P

CalzettiD.,DeMarchiG.,ParesceF.&SharaM.1993,ApJ,402,L1

ChandrasekharS.,vonNeumannJ.1943,ApJ97,1ColomboG.1966,A.J.71,891

DubathP.,MeylanG.&MayorM.1994,ApJ426,1922GebhardtK.&FischerP.1995,AJ109,209GenzelR.&TownesC.H.1987,ARAA25,377Gurzadyan,V.G.1982,AA114,71

LaskarJ.1994.in:ErgodicConceptsinStellarDynamics,(Eds.GurzadyanV.G.&PfennigerD.),LectureNotesinPhysics430,Springer-Verlag.

LaskarJ.1995,in:Proc.XIICMPMeeting(Paris,1994)

MeylanG.1994,in:ErgodicConceptsinStellarDynamics,(Eds.GurzadyanV.G.&PfennigerD.),LectureNotesinPhysics430,Springer-Verlag

NewellB.,DaCostaG.S.&GrindlayJ.E.1976,ApJ208,L55

NiceD.J.&ThorsettS.E.1992,ApJ397,249

Results of precise measurements of the periods of pulsars discovered in the central regions of globular clusters are shown to be approaching the capabilities of testing the existence of a central black hole. For example, in the case of M 15 the available d

PetersonR.C.,SeitzerP.&CudworthK.M.1989,ApJ347,351

PhinneyE.S.1993,in:ASPConferenceSeries30,(Eds.Djor-govskiS.G.&MeylanG.),pag.141

PhinneyE.S.&SigurdssonS.1991,Nat349,220

RobinsonC.,LyneA.G.,ManchesterR.N.,BailesM.,D’AmicoN.&JohnstonS.1995,MNRAS274,547SilkJ.&AronsJ.1975,ApJ200,L131

TaylorJ.H.,ManchesterR.N.&LyneA.G.1993,ApJ88,529

Wolszczanetal.1989,Nat337,531

YannyB.,GuhathakurtaP.,BahcallJ.N.&SchneiderD.P.1994,AJ107,1745

aTEXThisarticlewasprocessedbytheauthorusingSpringer-VerlagL

A&Astyle le1990.

本文来源：https://www.bwwdw.com/article/q844.html