Pulsars Tracing Black Holes in Globular Clusters

1、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 availa

2、ble d aamanuscriptno. (willbeinsertedbyhandlater) 6 991 tco 51 1v6010169/hp-o1.introduction rthubblespacetelescope(hst)observationsofglobularclus-stersprovideauniquepossibilityofrevealingthenatureoftheira:centralregions.doglobularclusterscontaincentralblackholesvorarewedealingwithpurelystellardynami

3、calphenomena?ixtheideaofblackholeswhichmightbesituatedatthecentersofglobularclustershasbeenseriouslydebatedsincethe rstraidenti cationofx-raysourceswithinglobularclusters(bah-callostriker1975,silkarons1975,newell,dacostagrindlay1976).groundbasedstudiesonsurfacebrightnessandvelocitydispersionpro lesw

4、erenotaccurateenoughformodelindependentanalysisoftheproblem(e.g.dubath,mey-lanmayor1993,meylan1994).recenthstobservationsofm15(yannyetal.1994),oneofthemostdenseclusters,sup-portthetheoreticallypredictedstardensityslope(bahcallwolf1976)forstarsinthepresenceofacentralmassiveblackholeandsupportthepossi

5、bilitythatthisblackholehasamassofmbh 103m.however,theobservedsurfacebrightnessdistributioncanalsobeexplainedviaakingmodelwithcoreradiusrc=2.2(phinney1993,gebhardtfischer1995). theaimofthepresentpaperistosuggestthepossibilityofusingmillisecondpulsarsasatraceofthecentralregionsofglobularclusterswithth

6、eparticularaimofrevealingtheexistenceofcentralblackholes.millisecondradio-pulsarswere g00 t.(1) whereg00=(1 rg/r),rgbeingthegravitationalradius.fromhere,onecaneasilyderivethatapulsarmovinginthevicinityofaschwarzschildblackholefromthedistancer1tor2withinthetimeinterval twillundergothefollowingap-pare

7、ntvariationofperiod p rg 2r, (2) with rr1 r2=v t,vthepulsarsvelocity,rthemeandistanceofthepulsarfromthecentralblackholeand r r.assumingv 15kms 1weobtainthecharacteristictimescaleforthegiven p/p: results of precise measurements of the periods of pulsars discovered in the central regions of globular c

8、lusters 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,manchesterlyne1993)andtwopulsarsin47tucanae(robinsonetal.1995). namepsrj r.a.(j2000) dec.(j2000

9、) 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)4.9 10 12 mbh p alp 4gr2 c results of precise measurements of the periods of pulsars discovered in the central regions of globular

10、 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,manchesterlyne1993). namer.a.dec.ppsrj (j2000) (j2000) (s) errorsintheestimationo

11、fdistancesofpulsarsfromthecenteroftheclusters.then,itwillbenecessarytotakeintoaccounttheaccuraciesinthealignmentoftheephemeridesdynamicalframewiththeopticalone,theaccuratede nitionoftheclus-tercenter,e.g.viatheluminositypro leorviathedynamicalproperties(cfcalzettietal.1993),andsoon.however,theconclu

12、sionmadeaboveform15isnotalteredevenifthepul-sarpositionwithrespecttotheclustercenterisknownwithanerroraslargeas0.5;inrealityerrorsareexpectedtobemuchless(meylan1994). theconditionswithinthecoreofm15seemtoprovidealsothepossibilityofexplainingtheaccelerationobservedforbothpulsarsasduetothe eldperturba

13、tionscausedbythesurroundingstars.thisallowsustomakethe rstpredictionconcerningthesinglepulsars,i.e.non-membersofbinarysys-tems:theaccelerationofpulsarsshouldbeobservedwithessen-tiallyhigherprobabilityinglobularclustersandinthegalacticcenter,than,say,inthediskofthegalaxy. thee ectofperturbationscause

14、dbythesurroundingstars,inprinciple,canbeempiricallydistinguishedfromtheperturbationcausedbytheregular eldoftheclustercoreconsideredbywolcszanetal.(1989),phinney(1991),nicethorsett(1992).thepointisthattheroleofthecoreshouldbecomemoreimportanttowardstheboundaryoftheclusterandwilltendtozeroapproachingt

15、hecenter,whilethestellarcontribution,viceversa,willincreasetowardsthecenter. thisleadstooursecondprediction:acceleratedpulsarsshouldbesituatedmainlyinthecentralregionsoftheglobu-larclusters,ratherthanintheirperipheralregions.obviously,someprobabilityremainsofthepulsarsbeingperturbedbyachanceencounte

16、rwithastar.theprojectione ectsshouldalsonotbeneglectedwhenconsideringthecorrespondingprobabil-ities.moreoversarswithp theexistenceofanomalouslyacceleratedpul-positivenot ttingthetypicalmagnetic eldac-tion,alsoshouldbeexpectedinthecentralregionofglobularclusters,duetothesamee ectofstellarperturbation

17、s. concerningtheroleofstellarperturbationsonpulsarsonecanpredictonemoree ect:thechangeoftheorientationoftheirrotationalaxes.thee ectofregularorchaoticvariationoftherotationalaxesisknownforthecaseoftheplanets(see,laskar1994;laskar1995andreferencestherein)andcanberepresentedasaproblemofasystemwithpert

18、urbedhamilto-nian: h(i, , )=h0(i)+ h1(i, , ). (6) sincethecorrespondingproblemisintegrableonlyinthecaseofasingleperiodicperturbationterm(colombo,1966),onecanconcludethatstellarperturbationsintheformrep-resentedbychandrasekharandvonneumann(1943)havetoleadtochaoticvariationsofthepulsaraxes. thus,pulsa

19、rscannotavoidthise ect,evenforthelow-estvaluesoftheiroblateness.thenumericalestimationofthe p dmindmax(10 17) (kpc) (kpc) obliquityvariation,timescales,etc.,canvarywithinextremelybroadranges,sinceitcrucially(non-linearly)dependsuponnumerousparametersoftheproblem;thecorrespondingmod-ellingisatopicofc

20、omprehensivestudiesandisoutofthescopeofourpaper.weonlynotethatempiricalstudiescanthemselvesprovideinformationonthise ectaswell. ourthirdpredictionthereforereads:pulsarslocatedinthecentralregionsofglobularclusters,inprinciple,shouldundergochaoticvariationsoftheirspinaxesand,asaresult,canre-vealsponta

21、neousappearancesanddisappearancesduringtheirobservations. theseexamplesindicate: a)theexistenceofaspecialsubclassofpulsars,i.e.thosesit-uatedinglobularclusterswithpropertiesdi erentfromthosesituatedinthegalacticdiskorinthehalo; b)theimportanceofthesearchofpulsarsinthecentralre-gionsofglobularcluster

22、sandofthegalaxyinrevealingthedynamicalstructureofthosesystems,includingthepresenceofmassiveblackholes.acknowledgement wearegratefultoa.lyneandm.tavaniforexplanationofobservationaldetailsandvaluablecomments.oneofus(v.g.)skarforvaluablediscussions.thisworkhasbeeninpartsupportedbyinfn,agenziaspazialeit

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