Evolution of Binaries in Dense Stellar Systems

0.14 MB·English

by  Natalia Ivanova

Evolution of Binaries in Dense Stellar Systems
Natalia Ivanova
UniversityofAlberta,Dept.ofPhysics,11322-89Ave,Edmonton,AB,T6G2E7,Canada
1
1
Abstract. In contrast to the field, the binaries in dense stellar systems are frequently not primordial, and could be either
0
dynamically formed or significantly altered from their primordial states. Destruction and formation of binaries occur in
2
parallel all thetime.The destruction, which constantly removes soft binariesfrom abinary pool, works asan energysink

n andcouldbeareasonforcluster enteringthebinary-burningphase. Thetruebinaryfractionisgreater thanobserved, asa
a result,theobservable binaryfractionevolvesdifferentlyfromthepredictions. Combinedmeasurements ofbinaryfractions
J in globular clusters suggest that most of the clusters arestill core-contracting. The formation, on other hand, affects most
themoreevolutionaryadvancedstars,whichsignificantlyenhancesthepopulationofX-raysourcesinglobularclusters.The
4
formationof binarieswithacompact objectsproceeds mainlythrough physical collisions,binary-binary and single-binary
1
encounters;however,itisthedynamicalformationoftriplesandmultipleencountersthatprincipallydeterminewhetherthe

formedbinarywillbecomeanX-raysource.
]
R
Keywords: binarystars–globularclusters–X-raybinaries–multiplestars–neutronstars–blackholes
S PACS: 97.80.-d,97.60.Gb,97.60.Lf,97.60.Jd,98.20.-d
.
h
p
BINARIESEVOLUTION:DESTRUCTION
-
o
r
t For low density environments, like solar neighborhoodand for solar-type stars, the binary fraction is known to be
s
50%(e.g.,[1]).Similarly,openclustersshowrelativelylargemeasuredbinaryfractions;aslargeas70%in some
a
∼
[ openclusters;aclearanti-correlationwiththeageoftheopenclusterhasbeenfound[2].Mostglobularclustershave

typicallysignificantlylowermeasuredbinaryfractionthanopenclusters,althoughforsomeitiscomparabletothatof
1
openclusters–e.g.,inacore-collapsedNGC6752,theupperlimitforthebinaryfractioncanbeashighas38%[3]
v
(althoughseealso[4]);inayoungandsparseglobularclusterinTer7,thebinaryfractionisestimatedtobe51%[5].
4
6 For globularclusters, the measured binaryfraction was foundto anti-correlatewith the total cluster luminosity [6];
8 the correlationwith the cluster collisionalparameter was foundto be only marginal.All together,measurementsof
2 binaryfractionsinopenandglobularclusterssuggestthatbinariesinclustersdepletewithtimeandithappensmore
.
1 efficientlyinmoremassiveclusters.
0 Thereis notheoreticalstudythatwouldsuggestthatthe initialbinaryfractionshouldbe significantlydifferentat
1 themomentofstarformationbetweenproto-openandproto-globularclusters1.Theconsistencybetweentheinitially
1 largebinaryfractionandcurrentlymeasuredlowbinaryfractioncanbeexplainedbytheefficientbinarydestruction
:
v thatcontinuesthroughouttheentireclusterevolution.
i Indeed,letusconsiderapopulationofprimordialbinarieswiththeinitialperiodsP=0.1 107andflatmassratio
X −
distribution,evolved for 10 Gyr using StarTrack [8]. By this age, significant fractionof initial binariesis destroyed
r
through evolution, mainly due to mergers, or, in case of massive stars, in supernovae (see Fig. 1). If we define the
a
hardness of a binary h as the ratio of the binary binding energy to the kinetic energy that a 0.5M object moving
with v=√3 10 km/s has (this energy is about an average kinetic energy of an object in a typic⊙al dense cluster
and is referre×d here to as kT), then it can be seen that by the age of 10 Gyr, almost all the hardest (h 100kT)
≥
binaries are destroyed via evolution. Now we place a population of these binaries – with primary masses drawn in
accordance to initial mass function (IMF) from [9], and with their initial eccentricities distributed thermally – in a
confined volume and keep the concentration of objects constant n =105 pc 3, constant velocity dispersion of 10
c −
km/sanddisallowtheobjectstoescapeformthistestvolume.Ifweletthesamestarsevolveforthesame10Gyr,but
allowthemtointeractdynamically,wefindthat-notsurprisingly-almostallthesoftbinaries(h 1kT)aredestroyed
≥
1 Recentstudiesshowedthattherecouldbemorethanoneperiodofstarformationinglobularclusters,anddifferentgenerationscouldhavebeen
formedwithdifferentbinaryfractions[7].
EvolutionofBinariesinDenseStellarSystems January17,2011 1
FIGURE1. Probabilitydensityforaprimordialbinarytosurvive10Gyrasabinary:theeffectoftheevolutiononly(left),the
effectofdynamics(right).Solidlinesshowsh ,binaryhardness,anddashedlinesshowt ,collisiontime.
coll
bydynamicalencounters,exceptthosewiththecollisiontime2t ofthesameorderastheclusterage(fortheFig.1,
coll
for t , an averageobjectis assumed to have mass of 0.5M ). Roughly,the binarieswith t morethan few Gyr,
coll coll
arenotperturbedbydynamicalencounters,andwitht less⊙thanfewGyr–onlythehardbinaries–didundergoa
coll
dynamicalencounterbutsurvived.
Clearlytheefficiencyofthedestructionofbinariesinrealisticdensestellarsystemsissomewhereinbetweenthese
limitingexamples,andalsostronglyaffectedbytheevaporationofbothbinariesandsinglestarsfromthecoredueto
highpost-encountervelocitiesorsupernovakicks,andbycontinuingsegregationofbinariesandsinglestarsfromless
densehalo,aswillbediscussedbelow.
Evolutionofhard binaries
TwomainapproachescurrentlyusedtomodelthedynamicsofadensestellarsystemaredirectN-body,themost
widelyknownrealizationisthefamilyofNBODY codeswrittenbyS.Aarseth3,withthemostrecentversionNBODY6;
and Monte Carlo (MC) methods,where encountersitself are usually treated with a directfew-bodyintegrator(e.g.,
[10,11]).MCmethodsaremorecapableoftreatinglargepopulationsandhavebeenalreadyusedtomakemodelsof
observedglobularclusters(e.g.,M4[12],NGC6397[13],47Tuc[14]),whiledirectN-bodyisusuallyusedtomodel
open clusters (e.g. NGC 188 [15], M76 [16]), but is starting to be also applied to globular cluster (e.g. NGC 6254
[17]).Here,wewillreferMCtothespecificrealizationsthatself-consistentlymodeltheglobalevolutionofacluster,
usingMCtechniquestosamplethestellardistributionfunctionwhenapplyingtheeffectsoftwo-bodyrelaxation[18].
This notto be confusedwith a simplified Monte Carlo methodwith a two-zone modelof a cluster as in [19]. In all
thecases,thedynamicalcodesassumeaswelltheuseofa(binary)stellarevolution(populationsynthesis)codeofa
differentcomplexity.
Due to still persisting computational power limitation, even with nowadays super-computers, including those
equipped with GPUs, the numerical N-body models of globular clusters are traditionally calculated either using
smallnumberofprimordialbinariesorsmallmassclusters(upto100,000stars,e.g.[20]),orratherverysparse.The
limitationsofarcomesnotfromthestellarevolution,whichiseitherparametrizedortabulated,butfromdynamics.
2 thisisthetime-scaleforabinarytoundergoastrongencounterwithanotherobject
3 Seehttp://www.ast.cam.ac.uk/ sverre/web/pages/nbody.htm
∼
EvolutionofBinariesinDenseStellarSystems January17,2011 2
ThemaximuminitialbinaryfractionusedforadirectN-bodymodelingis50%foran(open)clustermadeof12,000
single and 12,000 hard binary stars and with core density n =100 350 pc 3 [21]. For relatively more massive
c −
−
clusters, up to 100,000 stars (a factor of 10 short compared to observed massive and dense clusters) initial binary
fractionisusually5%.(e.g.[20]).
Withthesameinitialconditionsforhardbinaries(lowormediumdensityclusters,binaryfraction 50%),MCand
≤
directN-bodydo agree each otherqualitativelyand quantitatively:the core binaryfractionincreaseswith time (see
the comparisonmadein [18]).For largerinitial binaryfractions,MC shows the same behaviorfor almostall initial
binaryfractionsuptof =90%(here,allprimordialbinariesarehard).Thesimulationswereperformedforcluster
B
models with initially 105 objects and with IMF extends from 0.15 to only 18.5 M (MC is not designed to handle
subsystemsofrareobjects,likeblackholes(BHs),whichcouldbeproducebystars⊙moremassivethan18.5M );the
highestinitialcoredensity104.5pc 3. ⊙
−
Interestingenoughto notethattheincreaseofthecorebinaryfractionwithtimewasdueto thetworeasons.The
firstwastheoreticallyexpectedtoplaythemostsignificantrole–thesegregationofbinariesfromthehalotothecore.
However,especiallyinthecasewithbinaryfractionnobeingclosetoone,themainneteffectforthebinaryincrease
wasatlargeduesinglestarsevaporationfromthecore(infact,justafew%oforiginalcoresinglestarsremaininthe
core,therestisevaporateeithertothetheclustersoutskirts,orlostfromtheclustercompletely,thenforbinariesabout
ahalfoforiginalhardbinariesremainsinthecore).Bytheendofthecoremasswasdecreasedbyatleastanorderof
magnitudewithtime.
Comparisonwithobservations:is there a steady binary-burning phase?
In cases when MC models entered the binary-burning phase (not a common results among all models) before a
Hubble time, it was found that the core binary fraction in this phase steadily decreases with time. This behavior is
consistent with the results of simplified two-zone Monte Carlo model described in [19], where the binary-burning
phasewasimposedviaadoptedconstantwithtimeclustercoreproperties.Itislikelythenthatefficientthehardbinary
fractiondepletioncanproceedonlyinapost-collapsedcluster.Howcommoncanthisbe?
Asitwasmentioned,inmostofnumericalsimulationswithhardbinaries,thesteadybinary-burningregimeisnot
observed.AclusterevolutiontowardsthecorecollapsecantakeuptoaHubbletime.Oneotherhand,thetheoretical
predictions for a cluster in a binary-burning phase do not match well with observations. On Fig. 2 we show the
comparisonoftheclustercorespredictedbytheoryforclustersinabinary-burningmodeandoftheobservedcluster
cores.Itcanbeseen,thatthetheoreticalclustercoresaresignificantly(byanorderofmagnitude)aresmallerthanthe
observedones.ThislikelyindicatesthatthemostofglobularclustersinMilkyWayisnotinabinary-burningphase
[22].
Softbinaries: canthey stillbe neglected?
Thedescribedaboveresultswereobtainedusingonlyinitiallyhardbinaries,assoftbinarieshavebeentraditionally
ignoredin bothMonteCarloanddirectN-bodysimulations.Mainly,thisis becausesoftbinariesare expectedto be
destroyedon a very shorttime-scale and as such are notexpectedplay a role on the globularcluster dynamicsas a
whole. The other reason, specific for N-body, is that each wide (soft) binary requires enormous calculation power,
significantlyslowingdownthecluster’ssimulation.
However,largely unexpectedresult has been obtained in the modelthat included soft binaries, and had an initial
binaryfractionf =90%.Inthiscase,aftertherapidinitialcontractionofthecore,theclusterfairlyquickly(compared
B
to the modelswith onlyhardinitialbinaries,on thescale ofjusta fewMyr)entersintoa long-livedbinary-burning
phasekeepingalmostconstantbinaryfractionof40%[18].Theresultswereobtainedforaclustermodelwith5 105
×
stars.
The physical reason for a different behavior of a cluster with a substantial contain of initial soft binaries is that
thissoftcomponentacts, whilepresent,asa significantclusterenergysink.Softbinariesindeedareionizedquickly
throughencounters,absorbingclusters’energy.Assuch,ifthecorewasbornwithasignificantnumberofsoftbinaries,
itwillrapidlycontractonthetime-scaleofsoftbinariesdestruction.
EvolutionofBinariesinDenseStellarSystems January17,2011 3
FIGURE2. Thecomparisonofthetheoreticalrelationfortheclustercoresatbinary-burningphaseandtheobservedclustercores;
f isthecorebinaryfraction.CreditforthisfigureistoJohnFregeau,withthanktoCraigHeinkeforcompilingtheobservational
B
datawiththesameassumption(e.g.,flatmassratio)([4,19,23,24,25,26,27,28,29]).Thetheorycurvecomesfrom[30].
Whatis atrue binary fraction?
It is notwidely recognized,but theoreticallyobtained binaryfractionsare very differentfrom the observedones.
When describing simulations and its match to observed globular clusters, therefore, it is important to distinguish
betweena“true”theoreticalbinaryfraction–howmanybinaryobjectsarepresentinasimulation,independentlyon
theircharacteristics,suchasmassandluminosity,andan“observed”binaryfraction–howmanybinarieswouldbe
foundbyanobserverifthissimulationwouldbearealcluster.
Itcangoeitherdirections.Forinstance,whenobserversfindbinariesinaspecificperiodrange,anoverestimation
ofbinariesfractioncanbedoneifitisassumedthatthebirthperioddistributionhasbeenconservedforhardbinaries,
andonlysoftprimordialbinariesaredestroyed.In[19]itwasshownthatevenhardbinariesgetdestroyed,whenwider
hardbinariesaredestroyedbydynamicalencounters(asignificantfractionofbinariesupto10kT isveryvulnerable),
andtheevolutiontakesawayveryhardorintermediatelyhardbutmassivebinaries(seealsoFig.1).E.g.,in[23],the
observationallyderivedbinary fractionfor 47 Tuc was foundto be 13%, butif the changein periodsdistribution is
takenintoaccount,thentheextrapolationfromtheobservedbinariescangiveonlythebinaryfractionofabout6%.
Ontheotherhand,[18]haddemonstratedthateveninsimulationswithonlyhardbinaries,whentheoverall“true”
binaryfractioninthecoreincreases,the“observed”binaryfractiondecreasesforallsimulationswiththeinitialhard
binaryfractionabove40%.Forinstance,amediumdensityclusterwithinitialcoredensity103.5pc 3andinitialbinary
−
fraction 90%, evolvedto only 30% of observablebinaries in the core before the clusters was tidally disrupted. The
“true”binaryfractionthoughinthiscaseapproachedalmost100%.“Hiding”binarieshereincludebinarieswheretwo
mainsequence(MS)starswithalow-massratiowouldblendforanobserverintooneMSstar,orbinarieswithoneor
twodimcompactobjectasacompanion.
BINARIESEVOLUTION:FORMATIONOFCOMPACTBINARIES
Although most dynamicalinteractionsin dense cluster cores tend to destroy binaries, some can form binaries from
singlesstars,andmanymodifythem.Themostimportantprocessesarethosethatleadtoaformationofbinariesboth
haveacompactcompanionandarecompactenoughtostartmasstransfer.Suchbinariescanbedetectednotonlyin
ourMilkyWay,butinglobularclustersindistantgalaxiesaswell,givingusalinkbetweenthestatisticalproperties
of internalparameterof globular clustersand the efficiencyof dynamicalencounters.In particular,low-massX-ray
EvolutionofBinariesinDenseStellarSystems January17,2011 4
binaries(LMXBs)areformedinglobularclustersattherateof100timesexceedingthatofinthefield,perstellarmass
unit[31].Themostofbinarymillisecondpulsars(bMSPs)–thelikelyterminiofLMXBsevolution–detectedsofar
arelocatedinglobularclusters[32,33,34].ItwasevenproposedthatallLMXBsandbMSPsareformedinglobular
clusters [35]. The importance of dynamical encounters for LMXBs formation seems to be well established, as the
numberofLMXBswasfoundtocorrelatewellwiththeclusterdynamicalproperties[36]forallnon-core-collapsed
clusters.[37]explainedtheexceptionofcore-collapsedclustersbyourmisunderstandingofclusterscurrentdynamical
statesandsuggestedthatmostglobularclustersarestillintheprocessofcorecontraction.Morerecentobservations
showed that the overabundanceof LMXBs in core-collapsed clusters is statistically significant, and the number of
X-raysourcesinsuchclustersisalmostindependentonthecluster’sdynamicalproperties[38].TheonlyLMXBwith
aBHandawhitedwarf(WD)wasdetectedinaglobularcluster[39],althoughtheirtheoreticallypredictednumbers
in thefield shouldvastlyexceedthe numberofLMXBswith a MScompanion[40,41], and17LMXBswith a MS
companionintheMilkyWayareobserved.
There are several processes that lead to close binary formation: (1) binary companion exchange; (2) physical
collision; (3) tidal capture and (4) three-bodybinary formation. The evolution of a dynamically formed binary can
be further perturbed by dynamical encounters: a binary can be hardened and its eccentricity can be “pumped” via
multiple non-strong encounters; it also can become a member of a triple. The top channel to form a binary with a
neutron star (NS) or a WD is a binary companion exchange, if binary fraction is at least few % [42, 43]. A tidal
capture (TC) operates only within a narrow range of periastra during a single-single star encounter [42]; as such,
this channeldoesnotaccountformorethan a few %of all formedbinarieswith a compactcompanion.Ithasbeen
arguedthatTCscouldplayanimportantroleintheformationofultra-luminousX-raysources,withanintermediate-
mass BH (IMBH) acquiring a companion through a TC [44, 45]. However, in most of TCs events with an IMBH,
theenergydissipationrate inacapturedstargreatlyexceedsthestar’sEddingtonluminosity[45].Thefate ofsucha
binarydependsthenonwhereinsidethestartheenergywasdeposited,andcouldbeamerger[46].Three-bodybinary
formationis capable of creating a hard binary,but the formationrate of binaries which are hard enough to become
X-raysourcesissmall,evenformassiveblackholes[47].Hardening,throughmultipleencounters,canshrinkahard
binarytowardsitRochelobeoverflow,thoughafractionofthebinariesthatcansuccessfullysurvivethispathisnot
verylarge [47]. In the followingwe will review in more detailthe processes thatreceivedattentionin recentyears:
formationviaphysicalcollisionsandeffectofthetriplesformationoncompactbinaries.
Formationofclosebinaries viaphysicalcollisions
Theformationofbinariesviaaphysicalcollisionbetweenaredgiantandacompactobjecthasbeenproposedfirst
by[48],inordertoexplainultra-compactX-raybinaries(UCXBs)formation.Inthisscenario,acollisionleadstothe
formationofaboundsystemthatlatermightexperienceacommonenvelopeandformatightbinary(notethoughthat
forlow-massgiantremaininginglobularclustersatcurrentage,massratiofavorsadynamicallystablemasstransfer).
Smooth particle hydrodynamics(SPH) simulations showed later that the stellar envelope can be disrupted or fully
removedin close encounters,with an eccentric binary formedas a result [49, 50]. Later, consideringsubgiantsand
early giants obtained using a stellar evolution code, it was shown that (SPH) physicalcollisions between them and
NSs,withsmallimpactparameterr 1.5R whereR isagiantradius,alwaysleadtothecompleteexpulsionof
P RG RG
≤
theenvelopeduringacollision,resultinginatightandeccentricNS-WDbinary;thisbinaryshortlythereafterdecays
its orbitand starts mass transfer [51, 52]. Formationrate of UCXBs by these encountersis sufficientto explain the
observednumberofUCXBsinGalacticglobularclustersorLMXBsinglobularclustersnearothergalaxies[51].The
formationratesforUCXBs,beingconsistentwiththeobservednumber,atthesametimepredictthenumberofbMSPs
wellexceedingtheobservednumberofbMSPsinglobularclusters,anditwassuggestedthatthistypeofLMXBsdoes
notproducearadiobMSP[43].
WhenthefirstBH-WDLMXBswasdetected,itwasplausibletoconsiderasimilarformationmechanism.Detailed
SPH numerical simulation showed that even though in most of encounters with r up to 5R a bound system
P RG
∼
is formed, only a small fraction of them (with r up to R ) will lead to a formation of binaries that are tight
P RG
∼
enough and eccentric enough to start mass transfer in isolation [47]. A formation rate of BH-WD LMXBs through
onlyphysicalcollisionsisaboutorderofmagnitudelower thenrequiredto explainthe observedformationrate;the
binary exchange channel does not provide binaries compact enough to start the MT in isolation, so a sequence of
post-collisionaldynamicalencountersisnecessary.
EvolutionofBinariesinDenseStellarSystems January17,2011 5
Roleoftriples incompact binaries formation
One ofthe outcomesofa binary-binaryencounteris theformationof a triple system (e.g.[53]),andsome of the
formedtripleswill be hierarchically-stable[54]. In a typicaldense cluster with centraldensity 105 pc 3 and binary
−
fractionof 10%,at10Gyr,about5%ofallcorebinarieswouldhavesuccessfullyformedahierarchicallystabletriple
∼
during1Gyr[55];overwholelifeofthecluster,abouthalfofbinariescouldbecomeamemberofatriple.Atypical
formedtriplehaslargeratiooforbitalperiods,P /P 1000andverylargeoutereccentricity,e =0.95 0.05.
out in out
∼ ±
Aboutahalfofformedtriplesishard.
The effect of triples formation on the evolution of binaries population in globular clusters has just started to be
recognizedoverthelastseveralyears.Drivingforcebehindthetriples’effectonbinariesisthat,ifatriplehasalarge
enoughinclination,itssecularevolutionisaffectedbyKozaimechanism[56].Thismechanismcauseslargevariations
intheeccentricityandinclinationofthestarorbitsandcoulddrivetheinnerbinaryofthetriplesystemtoRochelobe
overflow,whenasresultofthestartingmasstransferabinaryeithermergesbeforethenextinteraction,orstartstable
masstransfer.Ifonecomponentoftheinnerbinaryisanon-degeneratestar,tidalinteractionscanbeimportantduring
the periastra,whenKozai-inducedeccentricityis at its maximum.Shrinkageof a binarybya combinationof Kozai
cyclingandtidalfriction(KCTF;[57,58,59,60])canberesponsibleforproductionofshort-periodactivestars,e.g.
BY-Dra-typebinaries[61].KCTFwouldoperateinaclusterifformedtriple’sKozaitime-scale[62]willbesmaller
thant .Astriplesformationprovidesratheruniformspacedistributionforinclinations,about1/3ofalltheformed
coll
triplesaffectedbyKozaimechanism.
Bluestragglers,whichareexoticstarswithmassesuptothreecluster’sturn-offmassbutpresumablystillburning
hydrogen, are detected both in globular and open clusters. They are believed to be either produced by collisions
between stars in clusters or stable or unstable mass transfer between the components of primordial short-period
binaries.UsingasimplifiedMonteCarlomethod,itwasfoundthatafractionofbluestragglerswhichcanbeprovided
byKCTFiscomparabletothatfromphysicalcollisionsandprimordialbinaries[55].KCTFalsohasbeenproposed
to have a dominant role in the formation of blue stragglers in open clusters and in the field [63]. Specifically, it
couldnaturallyexplainthelargebinaryfractionoflong-periodbluestragglersbinaries;theseresultsarebasedonan
assumptionofprimordialpopulationoftriplesratherthanonthepopulationofdynamicallyformedtriples.
Asastarevolves,theroleofthetripleintheformationofabinarywithsuchastarisincreasing,andtheprobability
that an inner binary would have a compact star as a companion is higher than for overall binary population [55].
E.g.,ifKCTFinatriplewithaninnerbinaryconsistingofaWDandaMSstarleadsnottoamergerbuttoastable
mass transfer,the numberofformedandpresentcataclysmicvariablescan be increasedby up to 50%,if compared
tosimulationswhereKCTFisnottakenintoaccount.IfKCTFistakenintoaccount,butleadstoamerger,thenthe
numberofCVscouldbedepletedbythird.
Ina47Tuctypecluster,5%ofallbinarieswithaNScompanionwouldbecomeamemberofahierarchicallystable
tripleina Gyr;inmoredensecluster,Ter5-type,15%ofallbinarieswitha NSwouldbea memberofatriple.In
simulations,itappearthat 50%ofallbMSPswereintriplesatsomepointintheirpast[43].
∼
Insimulationsofglobularclusters,sincethereisasyetno“triple”populationsynthesis,adynamicallyformedtriple
issimplybroken,andtheinnerbinaryisshrunktotheminimumperiastronitcouldhavethroughsimpleKozaicycle,
ifKozaitimescaleisshorterthant .Soincurrentclusterssimulations,themasstransfercouldbeinducedbytriple
coll
formation,butnotforcedbybeingcontinuouslyinatriple.
Thereis,however,anUCXB4U1820-303,locatedintheglobularclusterNGC6624,withtheorbitalperiodPof
685s [64, 65]. The stability value P˙/P= (3.5 1.5)10 8 yr 1 makes certain that 685s is the orbital period [66].
− −
− ±
SecondarystarisaHeWD 0.06 0.08M [67].NotethatstandardscenarioofRochelobemasstransferforasuch
otherwiseratherusualUCXBbin−aryimpli⊙espositiveperiodderivative.[66]foundthat,inaddition,4U1820-303has
theluminosityvariationbyafactorof2atasuper-orbitalperiodP 171d.Ithasbeensuggestthat,sinceX-raybusts
so
∼
takeplaceonlyatthefluxminimum,theobservedvariabilityisduetointrinsicluminosity/accretionratechangesand
notobscurationorchangesoftheprojectedareaofthesourceduetoprecession.Theratiobetweensuper-orbitaland
orbitalperiods(22000)istoohighforanykindofthediskprecessionatthemassratioofthesystem[68,69].
It has been suggested that this binary is part of a hierarchical triple [66], with the third body having a mass
<0.5MM (basedonthelackofitsopticaldetection)andwiththethirdbodyorbitalperiodP 1.1d(aseccentricity
out
modulatio⊙nisexpectedtobeonP P2 /P).[70]studiedthissystemindetailwiththeinclu∼sionofthefollowing:
so≃ out
perturbationfromathirdbodyonalongerperiodorbit;thequadrupolardistortionofstarsduetotheirintrinsicspins
andthefurtherquadrupolardistortionduetotheirmutualgravity;tidalfrictionintheequilibriumtideapproximation;
general relativity; mass transfer and gravitational radiation. They found that the long period naturally arises if the
systemislibratingaroundthestablefixedpointinaKozairesonance.Theobservedsystemincludingthelongperiod
EvolutionofBinariesinDenseStellarSystems January17,2011 6
foreccentricitymodulationcanbereproducedwithaNSwithmassof1.4M ,WDmassof0.067M andthirdbody
massof0.55M .Thesemi-majoraxesoftheinnerbinaryisa=1.32 1010⊙cm,oftheouterbinary⊙a =6.52aand
out
correspondingp⊙eriodofP =0.11d.Initialeccentricitye =0.002,×initialouterbinaryeccentricitye =0.0001
out 0 out,0
andinitialinclination65.66o.Theamplitudeoftheeccentricityoscillationswasfoundtobeof 3 10 3,whichis
−
∼ ×
sufficienttoenhancemasstransferenoughtoproducetheobservedluminosityoscillationsbyfactorof2[71].
AlthoughthereisnotyetadetectedtriplewithaBHasacompanionoftheinnerbinary,theroleofdynamicaltriple
formationforcompactbinarieswithaBHcouldbeevenhigherthanforcompactbinarieswithaNScompanion.For
binarieswithsimilarmassesandorbitalseparationa anda ,thefractionofbinary-binaryencountersthatresultina
1 2
hierarchicallystable tripleformationisabout25%forallencountersthathaveaperiastronwithin 7(a +a )(for
1 2
∼
detailssee [72]).Forbinarieswith highmassratiowherea moremassivebinaryalso ismorecompact,thisfraction
approaches30%forencounterswithaperiastronwithin 20(a +a ),essentially3.5timesmoreefficientthanequal
1 2
∼
mass binaries. For binaryfractionsof a few per cent, triple formationfor a binary with a BH is morefrequentthan
strongencounterswithsinglestars[47].IthasbeenshownthatforaseedBH-WDbinarywithaninitialseparationof
a 80R ,thetripleformationwithsubsequentKozaicyclecoupledwithgravitationalwaveemissionwillresultinan
LM≤XBf⊙ormationduringseveralGyr.
CONCLUSIONS
Instudiesofbinaryfractions,itiscrucialtodistinguishbetweenthe“observable”andthe“true”binaryfractions,they
havedifferentvaluesandhavedifferentevolution.Softbinariescannotbeignoredinsimulations:theyactasanenergy
sinkandcouldbethekeyinachievingsteadybinary-burningphase.Triplesplayveryimportantroleintheformation
ofcompactbinaries,specifically,X-raybinarieswithaNSoraBHaccretor.
ACKNOWLEDGMENTS
NIacknowledgessupportfromNSERCandCanadaResearchChairsProgram.
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