A hypervelocity star from the Large Magellanic Cloud

0.32 MB·English

by  Alessia Gualandris

Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed5February2008 (MNLATEXstylefilev2.2)
A hypervelocity star from the Large Magellanic Cloud
Alessia Gualandris 1⋆ and Simon Portegies Zwart1
1 Astronomical Institute ’Anton Pannekoek’ and SectionComputational Science, Universityof Amsterdam, the Netherlands
7
0
5February2008
0
2

n ABSTRACT
a We study the acceleration of the star HE0437–5439 to hypervelocity and discuss its
J
possibleoriginintheLargeMagellanicCloud(LMC).Thestarhasaradialvelocityof
5 723kms−1 and is located at a distance of 61kpc fromthe Sun. With a mass of about
1
8M⊙, the traveltime fromthe Galactic centre is of about 100Myr, much longerthan

its main sequence lifetime. Given the relatively small distance to the LMC (18kpc),
2
we consider it likely that HE0437–5439 originated in the cloud rather than in the
v
3 Galactic centre, like the other hypervelocity stars. The minimum ejection velocity
7 required to travel from the LMC to its current location within its lifetime is about
6 500kms−1.Suchahighvelocitycanonlybeobtainedinadynamicalencounterwitha
2 massiveblackhole.Weperform3-bodyscatteringsimulationsinwhichastellarbinary
1 encountersa massiveblackhole andfind thata blackhole moremassivethan103M⊙
6 is necessaryto explainthe highvelocityofHE0437–5439.We lookforpossible parent
0 clusters for HE0437–5439 and find that NGC2100 and NGC2004 are young enough
/
h to host stars coeval to HE0437–5439 and dense enough to produce an intermediate
p mass black hole able to eject an 8M⊙ star with hypervelocity.
-
o Keywords: Stars:black-holes–Stars:individual(HE0437-5439)–Methods:N-body
r simulations – Binaries: dynamics.
t
s
a
:
v
i
X 1 INTRODUCTION (Brown et al. 2006), it seems likely that they were ejected
r inacontinuousprocess.For6oftheobservedHVSs,infact,
Recent radial velocity measurements of young stars in the
a the travel time from the Galactic centre and the estimated
Galactic halo has led to the discovery of a new class of
age are consistent and, by assuming a suitable proper mo-
stars, the so-called hypervelocity stars (HVS), which travel
tion, it is possible to calculate a realistic trajectory.
with velocities exceeding the escape speed of the Galaxy
ForHE0437–5439,however,anejectionfromtheGalac-
(Brown et al. 2005, 2006). A total of 7 HVSs has been dis-
ticcentreappearsproblematicasthetimerequiredtotravel
covered so far, of which six are consistent with an ejection
from the centre to its observed location exceeds the maxi-
from the centreof theMilky Way.
mumlifetime of thestar. HE0437–5439 is amain-sequence
The existence of a population of HVSs was first pro-
posed by Hills (1988), who considered hypervelocity ejec- star with spectral typeBand amass of about 8.4M⊙ for a
tions as a natural consequence of galaxies hosting super- solar metallicity orof about 8M⊙ for a Z =0.008 metallic-
ity,which corresponds to main-sequencelifetimes of 25 and
massive black holes (SMBHs). The interaction between a
35Myr,respectively.Adoptingadistanceof61kpcfromthe
SMBH and a stellar binary can result in the dynamical
Sun (Edelmann et al. 2005) and considering a total space
capture of one of the binary components at the expense of
velocityequaltotheradialvelocityonly,thetraveltimefor
the high velocity ejection of its companion star (Hills 1988;
astraightorbitfromtheGalacticcentreisofabout80Myr,
Yu& Tremaine 2003; Gualandris et al. 2005). Later an al-
much longer than the main-sequence lifetime of the star.
ternativewasproposedbyBaumgardt et al.(2006),whoar-
Theestimatedpropermotionforwhichtheorbitofthestar
guethatan intermediate-massblackhole(IMBH)can eject comeswithin10pcfromthecentreisofabout0.55masyr−1
stars with extremely high velocities as it spirals in towards
(Edelmann et al.2005).Thisresultsinatangentialvelocity
the Galactic centre. The latter mechanism tends to pro- of about 160kms−1 and hence in a total space velocity of
duceHVSsinburstswhichlastafewMyr(Baumgardt et al. 740kms−1, which corresponds to a travel time of 100Myr
2006).Sincethereconstructedejectiontimesoftheobserved
for a realistic orbit.
HVSs are roughly evenly distributed over about 100Myr
Wediscard thepossibility thatHE0437–5439 isablue
straggleroriginatedintheGalactic centresince,eveninthe
⋆ E-mail:[email protected] caseofamergerbetweentwoless massivestars,themerger
2 Gualandris and Portegies Zwart
product would not surviveas an 8M⊙ star for muchlonger the relative velocity at infinity between the binary’s centre
than themain-sequence lifetime of such a star. of mass and the single star. The phase of the encounter-
Given the fact that HE0437–5439 is much closer to ing binary is randomly drawn from a uniform distribution
the LMC galaxy than to the Milky Way, Edelmann et al. (Hut& Bahcall 1983) and the orbital eccentricity is taken
(2005) suggest that HE0437–5439 might havebeen ejected randomlybetweencircularandhyperbolicfromthethermal
from the LMC. Considering a total distance of 18kpc from distribution.Theimpactparameterbisrandomisedaccord-
theLMC centre, theminimum ejection velocity required to ingtob2 intherange[0−bmax]toguaranteethattheprob-
travel to the current position is about 500kms−1. (Here ability distribution is homogeneously sampled. The maxi-
we adopted a travel time of 35Myr, which is equal to mum value bmax is determined automatically for each set
the main-sequence lifetime in a low metallicity environ- of experiments (see Gualandris et al. (2004) for a descrip-
ment.) The radial velocity of HE0437–5439 relative to the tion).Energy conservation is typically betterthan onepart
LMC is 461kms−1, and the required tangential velocity is in 106 and, in case the error exceeds 10−5, the encounter is
then 160kms−1, which in turns implies a proper motion of rejected. The accuracy in theintegrator is chosen in such a
1.9masyr−1. Avelocity of theorder of500kms−1 can only way that at most 5% of the encounters are rejected. Dur-
beobtainedinadynamicalinteractionwithamassiveblack ingthesimulationsweallowforphysicalcollisionswhenthe
hole (see Gualandris et al. (2005)). distance between any two stars is smaller than the sum of
IfHE0437–5439 wasejectedbyanIMBHandifitcame their radii. The black hole is assumed to be a point mass,
from the LMC, the natural consequence is that there must while for the stars we adopt zero-age main-sequence radii,
then be an IMBH in theLMC. We investigate this hypoth- taken from Eggleton et al. (1989).
esis by studying the dynamical ejection of an 8M⊙ main-
sequence star in an interaction with a massive black hole.
We simulate the encounter between a stellar binary and a 2.1 Encounters between a stellar binary and a
black hole to study the minimum mass of the black hole massive black hole
requiredtoaccelerateoneoftheinteractingstarstoaveloc-
We consider encounters between a binary consisting of two
ity of at least 500kms−1. Wethen investigate where in the
main-sequence stars with masses m1 and m2 and a single
LMC such an interaction could havetaken place.
We find that a black hole of ∼> 103M⊙ is re- nbelanctkishofilxeewdittoh8mMas⊙s wMhbihle. Tthheemmaassssoofftohneecboimnapraynicoonmsptaor-
quired to explain the velocity of HE0437–5439. Such an
hasvaluesof2M⊙,4M⊙,8M⊙ and16M⊙.Foreachchoice
IMBH could form in a young and dense star cluster
of stellar masses, the semi-major axis a is varied between
(Portegies Zwart et al.2004)andwouldhelpdrivingthefre-
a minimum value, which is set by the physical radii of the
quentstrongencounterswith massive stars neededto make
stars so that the two components do not touch at the first
high-velocity ejections likely (Baumgardt et al. 2006). The
pericentre passage, and a maximum of 1AU. We consider
IMBH must still be present in a star cluster which con- blackholesofmasses102M⊙,103 and104M⊙.Therelative
tains stars as massive as HE0437–5439. In addition, the
velocity at infinity between the black hole and the binary’s
parent star cluster must have been massive enough and centreof mass is set equal to 20kms−1.
with a short enough relaxation time to produce an IMBH
In Fig.1 we present the probability of different out-
(Portegies Zwart et al. 2004). The most likely clusters are
comes(branchingratios) in thesimulationsofan encounter
NGC2100 and NGC2004.
between an equal mass binary (m1 = m2 = 8M⊙) and a
103M⊙ black hole. For each of the initial semi-major axes
weperformatotalof1500scatteringexperiments,whichre-
2 THREE-BODY SCATTERINGS WITH A sulteitherinafly-by,anexchangeoramerger.Mergersoc-
MASSIVE BLACK HOLE IN THE LMC curpreferentially in thecase of tight binaries, leaving place
topreservationsandexchangesforwiderbinaries. Inanex-
In this section we explore the hypothesis of a dynamical change interaction one of the main-sequence stars is cap-
ejectionfromtheLMCbymeansofnumericalsimulationsof tured by theblack hole while the other star is ejected, pos-
three-bodyscatteringswithamassiveblackhole.In§2.1we sibly with high velocity. If the velocity exceeds 500kms−1,
focus on interactions in which a binary containing a young weregardthestarasapossiblecandidateforHE0437–5439.
8M⊙ main-sequence star (representing HE0437–5439) en- This occurs in about 10% or less of all encountersfor semi-
counters a single black hole of 102M⊙ to 104M⊙, whereas major axes in the range 0.1−1.0AU.
in §2.2 a single 8M⊙ main-sequence star encounters a bi- InFig.2weshowthebranchingratios forhighvelocity
nary black hole. In the first case, an exchange interaction ejections for binaries with a 8M⊙ star and a companion
can lead to the high velocity ejection of one of the binary withmassintherange2.0−16.0M⊙.Whilethe8M⊙ main-
components while in the latter case the main-sequence star sequence star is ejected, the companion star is captured by
can beaccelerated in a fly-by. the IMBH. As in the previous plot, the black hole mass is
Thesimulationsarecarried outusingthesigma3pack- of103M⊙.Exchangeencounterswithfastescapersaremore
age, which is part of the STARLAB1 software environment likely in the case of binaries with larger companion masses
(McMillan & Hut1996; Portegies Zwart et al. 2001). and/or shorter orbital periods.
For each simulation we select the masses of the three Analytical estimates by Yu& Tremaine (2003) for the
stars,thesemi-majoraxisandeccentricityofthebinaryand case of tidal breakuppredict an ejection velocity at infinity
′ Mbh 1/6 0.1AU m 1/2
1 http://www.manybody.org/manybody/starlab.html V∞ =v (cid:16) m (cid:17) (cid:18) a 1M⊙(cid:19) , (1)
A hypervelocity star from the LMC 3
′
where v is a function of the distance of closest approach
Rmin. If we define a dimensionless closest approach param-
eter Rm′ in = Rmain Mmbh −1/3 , v′ varies in the range 130–
160kms−1 forRm′ i(cid:0)n=0(cid:1)−1.Form=8M⊙ anda=0.1AU
Eq.1 yields v∞ ≈560kms−1 for Mbh =102M⊙; a 100M⊙
IMBH would in principle be sufficient to explain the origin
of HE0437–5439.
In Fig.3 we show the velocity distributions of the es-
caping single star in the case of equal mass binaries (m1 =
m2=8M⊙).Thedifferentpanelsrefertodifferentvaluesof
theblackholemass,from 102M⊙ (left) to103M⊙ (middle)
and 104M⊙ (right). In each panel, the different distribu-
tionsrefertothreedifferentvaluesof theinitialsemi-major
axis. While it appears possible to reach the required recoil
velocity in thecase of Mbh =102M⊙, thesmallest possible
semi-major axis is needed (a= 0.1AU) for this to happen,
andonlyinabout10%ofexchangeencounters,whichcorre-
spondstoabout3%ofallsimulatedscatterings. Inthecase
of the 104M⊙ black hole it is possible to achieve such high
velocitiesevenforratherwidebinaries.Basedonthesedata
we conclude that a 100M⊙ black hole is unlikely to have
Figure1.Branchingratiofortheoutcomeofencountersbetween resulted in the ejection of HE0437–5439 and a black hole
a stellar binary and a single 103M⊙ black hole as a function of mass ∼> 103M⊙ is favoured for typical valuesof a.
the initial binary semi-major axis. The two binary components
Wenotethatthevelocitydistributionsarenotsensitive
areassumed to be 8M⊙ main-sequence stars. The different out-
totheinitialvelocitybetweenthebinaryandthesinglestar
comes are: merger (stars), preservation (triangles) and exchange
asthetotalenergy of thesystem is dominated bythebind-
(squares). The subset of exchanges with a high velocity escaper
(V∞>500kms−1)isindicatedwithbullets.Theerrorbarsrepre- ingenergyofthebinaryratherthanbythekineticenergyof
senttheformal(1σ)Poissonianuncertaintyofthemeasurement. the incoming star. Additional experiments performed with
initialvelocitiesof5kms−1 and10kms−1 showednoappre-
ciable difference in theejection velocities.
Wealsonotethatfordetachedbinariesthebinarytidal
radiusisalwayslargerthanthetidalradiusofthesinglestars
and therefore tidal breakup and ejection occur before the
starscanbedisruptedbytheblackhole.For(near)contact
binaries, instead, it is possible to disrupt a star before an
ejectioncantakeplace.Thisprocessdoesnotdependonthe
black hole mass but on the size of the binary compared to
thesize of thestars. Oursimulations only include detached
binaries as the proper treatment of contact binaries would
requirehydrodynamical simulations.
TheanalyticalestimatesobtainedwithEq.1areconsid-
erablylargerthantheresultsofoursimulations(seeFig.3).
This discrepancy is probably caused by the assumption of
Yu& Tremaine (2003) that the binary is disrupted well
′
within the tidal radius, i.e. Rmin ∼< 1, whereas in 10% to
′
20%ofoursimulatedencountersRmin >1.Forexample,for
′
Rmin≃3−4,acapturecanoccurwhicheventuallyleadsto
theejection of onestar. Since theejection velocity depends
largely on the Keplerian velocity of the binary at the posi-
tion of tidal breakup, we expect a dependence of the final
′
velocityofescapersontheparameterRmin.Fig.4showsthe
Figure 2.Fractionofexchange encounters between astellarbi-
velocity atinfinityoftheejected starversusthedimension-
nary and a 103M⊙ black hole that results in the ejection of a
main-sequence stars with a velocity ∼> 500kms−1. The bullets lessdistanceofclosestapproach.Inthisexampleweconsider
indicatetherelativeprobabilityforanincomingbinarywithtwo equalmassbinarieswithm=8M⊙ andablackholeofmass
8M⊙ stars(seeFig.1).Theothercurves arecomputed withdif- 103M⊙. The figure shows that the highest ejection veloci-
ferentcompanion masses to an8M⊙ star: 2M⊙ (crosses), 4M⊙ ties are preferentially achieved in close encounters. The ne-
(squares), 16M⊙ (triangles). In the latter case, the ejected star glectofrelativelywideencountersbyYu & Tremaine(2003)
isthesecondary. mightthereforebetheoriginoftheapparentdiscrepancyin
thevelocities.Theagreementbetweenournumericalsimula-
tionsandtheanalytical estimatesofYu & Tremaine(2003)
4 Gualandris and Portegies Zwart
Figure3.VelocitydistributionsfordifferentvaluesoftheblackholemassMbh=102M⊙ (left),103M⊙ (middle),104M⊙ (right),and
oftheinitialsemi-majoraxisa=0.1,0.3,1.0AU.
Figure 4. Velocity of the ejected star after an exchange inter- Figure 5. Velocity distribution for the ejected star after an in-
action witha103M⊙ blackholeas afunction of the distance of teractionbetweenanequalmass(m=8M⊙)binaryandablack
closestapproachtotheblackhole.Thedifferentsymbolsindicate hole of 102M⊙ (black), 103M⊙ (blue)and 104M⊙ (red). These
differentinitialvaluesofthebinarysemi-majoraxis. velocity distributions are integrated over the entire range of or-
bitalseparations fortheinitialbinary.
improves for higher black hole masses, and is very good for
2.2 Encounters between a single star and a binary
encounterswith a SMBH (see Gualandris et al. 2005).
black hole
Inoursystematicstudyoftheeffectoftheinitialsemi-
major axis of the interacting binary we adopted a homoge- We now consider encounters between a single star and a
neous sampling in loga. Furthermore, the number of scat- binary black hole. In a recent study Gu¨rkan et al. (2006)
tering experiments performed per initial selection of a are argue that it is possible to form a black hole binary as a
weighted with equal cross section. If the distribution of or- result of two collision runaways in a star cluster. The bi-
bital separations in a star cluster is flat in loga, like in the nary eventuallymerges duetotheemission of gravitational
case of young star clusters (Kouwenhoven et al. 2005), we waveradiation(Peters1964)but,beforecoalescing,thetwo
can superpose the results of these experiments in order to blackholesexperiencefrequentinteractionswithotherclus-
acquire a total velocity distribution of the ejected star. In terstars, possibly accelerating them to larger velocities.
Fig.5 we present thissuperposed velocity distribution for a Wesimulatetheseencountersandstudytheprobability
binaryconsistingoftwo8M⊙ stars.Thethreehistogramsin ofhighvelocityejectionsasafunctionofthebinaryparam-
thisfiguregivethevelocitydistribution fora100M⊙ (left), eters: the masses of the two black holes MBh1 and MBh2
103M⊙ (middle) and 104M⊙ (right) black hole. and the initial semi-major axis a. The mass of the single
A hypervelocity star from the LMC 5
sotfaHrEis0fi4x3e7d–5t4o389.MW⊙e, icnonascicdoerrdbalnaccekwhiotlhetmhaesosebsseorfv1e0d2mMa⊙ss, aTnabelsetim1a.tedLisintitoifalyroeulnaxgat(iaognetim∼<e3s5mMayllre)rLthManC1c0lu0sMteyrsr.wTihthe
103M⊙ and 104M⊙ in both equal mass and unequal mass columns give the name of the cluster, the mass, the core radius,
binaries. For each choice of black hole masses, the semi- the ratio of the core radius to the half-massradius, the age, the
major axis is varied between a minimum value of 1AU and currenttwo-bodyrelaxationtime,theinitialtwo-bodyrelaxation
a maximum value of 1000AU. The minimum value is cho- time (computed using Eq.1 of PortegiesZwart&Chen (2006)
seninordertoguaranteethatthebinaryremainsunaffected with κ = 0.1) and the black hole mass based on Heggieetal.
by the emission of gravitational wave radiation during the (2006). For estimating the relaxation time we adopted a mean
period over which the encountertakesplace2. mass hmi = 1 and a Coulomb logarithm parameter γ = 0.4 for
thelowerlimit,andhmi=0.65andγ=0.01fortheupperlimit.
Except forafew mergers (about1-2% of all cases), the
The core and half-mass radius for R136 are from Brandletal.
vast majority of the encounters result in a fly-by. The ve-
(1996).
locity at infinityof theescapingstar dependssensitively on
the impact parameter of the encounter. Only in encounters
forwhichtheimpactparameteriscomparabletothebinary name M rc rc/rh age Trlx Tr0lx Mbh
M⊙ pc Myr Myr Myr M⊙
separationarehighvelocityejectionsrealized.Mostofthese
encountersareresonant,allowingtheincomingstartocome R136 35000 0.32 0.29 3 7–17 6–14 1000
as close to one the black holes as a fraction of the orbital NGC2004 27000 1.57 0.50 20 71–170 41–98 1600
separation.Onlyafew%oftheencountersresultinejection NGC2100 30200 1.22 0.62 16 51–120 31–73 2200
velocitiesashighas500kms−1andwearguethatthismech-
anism is unlikely to have produced theobserved velocity of
for themass of theIMBH using thisrelation. Wefindthat,
HE0437–5439.
given the structure of the observed clusters, a 1600M⊙ to
2200M⊙ IMBH could bepresent.
WearguethatNGC2100andNGC2004formthemost
3 AN IMBH IN THE LMC? promising birth places for HE0437–5439. If this were the
case, the travel time from the parent cluster to the cur-
Theanalysiscarriedoutintheprevioussectionssuggestthe
rentlocation wouldbelessthanabout20Myr.Suchashort
intriguing idea that HE0437–5439 was ejected by an en- traveltimewouldrequireanejectionvelocity ∼> 800kms−1
counter with an IMBH of ∼> 103M⊙ in the LMC. Such for the adopted total distance to the LMC of 18kpc. This
an IMBH would most likely be found in a young dense
large velocity could only be obtained with a black hole of
cluster containing stars coeval to HE0437–5439. Recently several 103M⊙, somewhat higher than the estimated mass
Mackey & Gilmore (2003) measured the structural param-
of a possible black hole in these clusters.
eters for 53 LMC clusters. A total of nine clusters in this
We now compute the rate for ejection of hyperveloc-
database are younger than 35Myr. Three of these clusters,
ity stars from NGC2100 and NGC2004 using the param-
NGC1818, NGC1847 and NGC1850, have the appropriate
eters listed in Tab.1 and a dimensionless cross-section for
age to be the host of HE0437–5439 but their current den- exchange encountersσ˜ ≃5000, as derived from the scatter-
sities are much smaller than what is required to produce ingexperiments.Adoptingacentraldensityof2×104pc−3
an IMBH (Portegies Zwart et al. 2004; Miller & Hamilton (consistentwith aKingW0=9initial profile),avelocityof
2002). Of the six remaining clusters, three (NGC1805, 10kms−1 andasemi-majoraxisof0.2AU,weobtainanen-
NGC1984, NGC2011) haveamass below 5000M⊙ and are counterrateofaboutoneper2Myrforbothclusters.Since
therefore unlikely to have produced an IMBH. Also, the
only one in about ten exchange encounters produces a fast
presence of an IMBH in these clusters would havebeen no-
escaper (see Fig.2), we derive a production rate of one per
ticed easily (Baumgardt et al. 2005).
20Myr.Thisvaluerepresentsalowerlimit aswedon’ttake
The remaining three clusters are listed in Tab.1. For
into account the effects of a mass function in the core and
these clusters we reconstruct the initial relaxation time via
thesemi-major distribution.Itistherefore conceivablethat
themethoddescribedbyPortegies Zwart & Chen(2006).In
NGC2100 or NGC2004 has produced one high velocity es-
thisrelativelysimplemodel,thecurrentrelaxationtimehas
caper, in which case an IMBH must be present in one of
aone-parameterrelationwiththecluster’sinitialrelaxation
theseclusters.
time. Of the three clusters listed in Tab.1, one (R136) is
tooyoungtoproduceanIMBHandexperienceastrongen-
counter with a binary. The best candidate clusters to host
4 ACKNOWLEDGMENTS
an IMBH are then NGC2100 and NGC2004. We can es-
timate the mass of a possible black hole in these clusters We are grateful to Jesu´s Ma´ız Apell´aniz for interesting
by adopting the relation between the cluster structural pa- comments on the manuscript. This work was supported by
rameters and the mass of a central black hole presented by theNetherlandsOrganizationforScientificResearch(NWO
Heggie et al. (2006). The authors performed direct N-body under grant No. 635.000.001 and 643.200.503), the Royal
simulations to quantify the relation between the mass of a Netherlands Academy of Arts and Sciences (KNAW) and
central IMBH and the ratio of the core radius to the half- theNetherlandsResearch School for Astronomy (NOVA).
massradius.ThelastcolumninTab.1providesanestimate
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