Hypervelocity Collisions of Binary Stars at the Galactic Centre

0.21 MB·English

by  Idan Ginsburg

Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed5February2008 (MNLATEXstylefilev2.2)
Hypervelocity Collisions of Binary Stars at the Galactic
Centre
⋆
Idan Ginsburg & Abraham Loeb†
Harvard-Smithsonian Centerfor Astrophysics, 60 Garden St., MS51, Cambridge, MA 02138, USA
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5February2008

n
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J ABSTRACT

1
1 Recent surveys have identified seven hypervelocity stars (HVSs) in the halo of

the Milky Way. Most of these stars may have originated from the breakup of binary
2
star systems by the nuclear black hole SgrA*. In some instances, the breakup of the
v
binary may lead to a collision between its member stars. We examine the dynamical
0
propertiesofthesecollisionsbysimulatingthousandsofdifferentbinaryorbitsaround
4
4 SgrA* with a direct N-body integration code. For some orbital parameters, the two
9 starscollidewithanimpactvelocitylowerthantheirescapevelocityandmaytherefore
0 coalesce. It is possible for a coalescing binary to have sufficient velocity to escape the
6 galaxy. Furthermore, some of the massive S-stars near Sgr A* might be the merger
0 remnantsofbinarysystems,howeverthisproductionmethodcannotaccountformost
/ of the S-stars.
h
p Key words: black hole physics-Galaxy:center-Galaxy:kinematics and dynamics-
-
stellar dynamics
o
r
t
s
a
:
v 1 INTRODUCTION tence is robustly supported by data (e.g. Ghez et al. 2005;
i Reid & Brunthaler 2004; Sch¨odelet al. 2003).
X First theorized by Hills (1988), a hypervelocity star (HVS)
r hassufficientvelocitytoescapethegravitationalpullofthe
a MilkyWaygalaxy.ThefirstHVS,SDSSJ090745.0+024507,
was recently discovered in the Galactic halo (Brown et al. SimulationsshowthattightbinariescanproduceHVSs
2005; Fuenteset al. 2005). This HVS is located at a helio- with velocities comparable to the observed HVSs (e.g.
centric distance of ∼ 110 kpc and has radial velocity 853 Ginsburg & Loeb 2006 (hereafter Paper I); Bromley et al.
± 12 kms−1, over twice that needed to escape the gravita- 2006). In Paper I, we show that the companion to the hy-
tional pull of the Milky Way. Since that initial discovery, pervelocitystarwillbeleftinahighlyeccentricorbit,which
six other HVSshavebeen identified (Edelmann et al. 2005; agrees with the known orbits of a number of S-stars orbit-
Hirsch et al.2005;Brown et al.2006a;Brown et al.2006b). ing Sgr A* (e.g. Eckart & Genzel 1997, Sch¨odel et al. 2003,
Hills(1988)suggestedthataHVSmightresultfromaclose andGhez et al.2005).Therefore,wesuggestedthatsomeof
encounter between a tightly bound binary star system and thesestars areformercompanions ofHVSs.Furthermore,a
theblackholeattheGalacticcenter,SgrA*.Yu& Tremaine small fraction (∼10%) ofthebinarysystems werefound to
(2003) refined Hills’ argument and noted that HVSs might collide. Hereweexamine in detail thedynamical properties
also beproduced bythree-bodyinteractions between a star ofsuchcollisions,andcheckwhethersomeofthesecollisions
and a binary black hole system. Because the existence of a may end in coalescence.
second(intermediate-mass)blackholeintheGalacticcenter
(Hansen & Milosavljevi´c 2003) is only ahypotheticalpossi-
bility (Sch¨odel et al. 2003), we focus here on the disruption In §2 we describe the N-body code and the simulation
of a tightly bound binary by a single supermassive black parameters that were used. In §3 we discuss our numerical
hole (SMBH) with a mass of ∼ 4 × 106M⊙ whose exis- results for the collisions, and in §4 we discuss the outcome
ofbinarymergersattheGalacticCentre.Ourgoalisnotto
cover the entire range of binaries that could produce HVSs
or end in collisions, but rather to determine whether some
⋆ E-mail:[email protected] tightbinarieswithmassessimilartotheHVSsobservedthus
† E-mail:[email protected] far could coalesce.
2 Idan Ginsburg & Abraham Loeb
2 COMPUTATIONAL METHOD radial velocity but a tangential velocity with an amplitude
in the range between 5 and 25 km s−1 at the distance of
In our study we have used the N-body code written by
2000AU. In total, we ran 2000 simulations.
Aarseth(Aarseth1999)whosedetailsweredescribedinPa-
per I. We treat the stars as point particles and ignore tidal
andgeneralrelativisticeffectsontheirorbits,sincetheseef-
3 PROPERTIES OF HYPERVELOCITY
fects are small at the distance (∼ 10AU) where the binary
COLLISIONS
is tidally disrupted by the SMBH. We have set the mass of
the SMBH to M = 4×106M⊙. The masses of the binary Givenabinarysystemwithstarsofequalmassmseparated
members are set to either 3M⊙ & 3M⊙ [since 3M⊙ is the byadistanceaandaSMBHofmassM ≫matadistanceb
estimated mass of SDSS J090745.0+024507 (Fuenteset al. fromthebinary,tidaldisruptionwouldoccurifb.bt where
2005)],orto3M⊙&10M⊙[as10M⊙iscomparabletothees-
m M
timated mass of HE0437-5439 (Edelmann et al. 2005)].All ∼ (1)
a3 b3
runsstartwiththecenterofthecircularbinarylocated2000 t
AU (=10−2pc) away from theSMBH along the positive y- Thedistanceof closest approach intheinitial plungeof the
axis.Thisdistanceiscomparabletotheinnerscaleoftheob- binary towards the SMBH can be obtained by angular mo-
serveddistributionofstarsaroundSgrA*(Eckart & Genzel mentumconservationfromitsinitialtransversespeedv⊥ at
1997;Sch¨odel et al.2003;Ghezet al.2005),allowingthere- its initial distance from the SMBH,d,
mainingstartopopulatethisregion aftertheejection ofits
companion. This radiusis also muchlarger than thebinary GM 1/2
v⊥d= b. (2)
size or the distance of closest approach necessary to obtain b
„ «
therelevantejectionvelocityofHVSs,makingthesimulated
The binary will be tidally disrupted if its initial transverse
orbits nearly parabolic.
speed is lower than some critical value,
Werantwosetsofdata.Thefirsthadthebinarysystem
rzotpalatinneg. aWloengustehdetxh–eysapmlaeneinaitnidaltdhiestsaenccoendfoarloanllgruthnesyto– v⊥ .v⊥,crit ≡ (GMda)1/2 „Mm«1/6 =102m10a/.1−56/d123.3 km s−1,
make thecomparison among them easier to interpret as we (3)
varied thedistance ofclosest approach totheSMBHor the where a−1 ≡ (a/0.1 AU), d3.3 = (d/2000 AU), m0.5 ≡
relative positions of the two stars within the binary. We (m/3M⊙).Ifv⊥ .v⊥,crit,oneofthestarsreceivessufficient
choseinitialbinaryseparationsbetweena=0.05and0.2AU kineticenergy to become unbound,while thesecond star is
becausesucharangeislikelytoproduceHVSsfortheabove kicked into a tighter orbit around the SMBH. The ejection
parameters(seePaperI).Significantlywiderbinarieswould speedvejoftheunboundstarcanbeobtainedbyconsidering
givelowerejectionvelocities(Gualandris et al.2005).Much the change in its kinetic energy ∼ vδv as it acquires a ve-
tighter binaries would not be easily disrupted by the black locity shift of order the binary orbital speed δv ∼ Gm/a
hole,ormaycoalescetomakeasinglestarbeforeinteracting during the disruption process of the binary at a distance
p
withtheSMBH.Theradiusofamainsequencestarofafew ∼b from theSMBH when thebinary center-of-mass speed
t
solarmassesis∼0.01AU,andthatofa10solarmassstaris isv∼ GM/b (Hills1988;Yu& Tremaine2003).Atlater
t
∼0.03AU(see,e.g.Fig.4inFreitag&Benz2005).Binaries times, the binary stars separate and move independently
p
tighter than ∼0.02AU are precluded because the two stars relativetotheSMBH,eachwithitsown orbitalenergy.For
will develop a common envelopeand eventually coalesce. v.v⊥,crit, we therefore expect
IntheGalactic disk,aboutone-thirdtohalfofallstars
form in binaries or small multiple systems (see e.g. Lada Gm 1/2 GM 1/2 1/2
vej ∼
2006;Duquennoy& Mayor1991),with roughlyequalprob- "„ a « „ bt « #
ability perlogarithmic intervalofseparations, dP/dln(a)=
=1.7×103m1/3a−1/2 km s−1. (4)
const (e.g. Abt 1983; Heacox 1998; Larson 2003). In the 0.5 −1
Galactic center environment, the maximum binary separa- Under some circumstances, the binary is disrupted in
tion is limited by the tidal force of SgrA* at the distance d such a way that the two stars collide. Assuming that the
where the binary is formed (for conditions that enable star impulsive kick is given by theSMBH towards a random di-
formation near the SMBH, see Milosavljevi´c & Loeb 2004). rection within the orbital plane and ignoring gravitational
Since the mass of the black hole is ∼106 times larger than focusing(whichisimportantatlowspeeds),theprobability
that of a star, this implies a maximum binary separation foracollision inacasethatotherwisewould haveproduced
less than (10−6)1/3 = 10−2 of the initial distance d. For a HVS is four time the radius of a star divided by the cir-
d = 2×103AU, the upper limit on the binary separation cumference of a circle with a radius equal to the binary
would be 20AU (or smaller if the tidal restriction applies separation. The likelihood for a collision is expected to be
during the formation process of the binary). If we assume smaller in the more general case where the binary lies in a
a constant probability per ln(a) for 0.02<a<20AU, then differentplanethanitsorbitaroundtheSMBH,unlessgrav-
theprobabilityoffindingabinaryintherangeofa=0.05– itationalfocusingdominates.Table1summarizestheactual
0.2AU is substantial, ∼20%. statistical results from our runs.
AsshowninPaperI,theinitialphaseofthebinaryorbit The two stars would merge as a result of the collision
plays a crucial role in the outcome. Therefore, we sampled if their relative speed is lower than the escape speed from
caseswithinitialphasevaluesof0-360degreesinincrements their surface (∼ 500 km s−1). In our runs 22% of all col-
of 15◦. As initial conditions, we gave the binary system no lisions have impact velocities low enough to allow the two
Hypervelocity Collisions of Binary Stars at the Galactic Centre 3
60 60
a = 0.05 AU a = 0.1 AU a = 0.15 AU a = 0.2 AU Sum a = 0.10 AU a = 0.15 AU a = 0.20 AU Sum
40 40
20 20
600 600
40 40
20 20
0 0
0 1000 2000 0 1000 2000
Relative Velocity upon Impact (km/s) Relative Velocity upon Impact (km/s)
Figure 1. Fraction of all collisions (in percent per 100 kms−1 bin) versus relative velocity upon impact (in kms−1). The left section
is for amin = 0.02 AU and the right section is for amin = 0.04 AU. The label of the lower left panel corresponds to all panels. The
dashed vertical line shows the impact velocity that would have resulted from free fall starting at the binary separation (see equation
6). The solid line is the median velocity of all runs. (We choose to use the median rather than the average value because outliers bias
thedataotherwise.)Theminimumimpactparameter foracollisionisexpected tobeamin=(R1+R2)=0.02AUfora3M⊙ &3M⊙
binary, but amin = 0.04 AU for a 10M⊙ & 3M⊙ binary. We show results inother cases for pedagogical purposes, namely to illustrate
thedependence oftheresultsonthebinarymassesandamin separately.Ifthe10M⊙ companionisablackholethen amin∼0.01AU.
orbital separation. Conservation of energy
a(AU) P(3M⊙) P(10M⊙)
0.05 0.11±0.02 0.21±0.05 E = 1 m1m2 r˙2− Gm1m2 =const, (5)
0.10 0.11±0.02 0.13±0.04 2m1+m2 r
0.15 0.06±0.01 0.12±0.03 yields therelative velocity upon impact,
0.20 0.03±0.01 0.04±0.02
1 1 1/2
0.05 0.09 0.27 vf = 2G(m1+m2)(a − a) . (6)
0.10 0.06 0.13 » min –
0.15 0.03 0.09 The actual impact speed would vary around this value due
0.20 0.02 0.07 to the additional velocity induced by the SMBH tidal force
along the axis connecting the stars. Nevertheless, Equation
Table1.Collisionprobabilitywithdifferentvaluesofaforbina- 6 agrees well with the median of the distribution of impact
riesof3M⊙&3M⊙(secondcolumn)and10M⊙&3M⊙(thirdcol- speeds in our runs (see Figure 1). Collisions always occur
umn).Thetopfourrowsshowthevaluesobtainedfromoursim- shortlyaftertidaldisruption,asseenfromtheseparationof
ulationswiththeircorrespondingPoissonerrors.Forcomparison, theblack and filled circles in Figure 2.
the bottom rows show the expected probability from a simplis-
tic“billiardball”model(withoutgravitationalfocusing)inwhich
the probability of acollisionis 2(R1+R2)/2πa. Here {Ri}i=1,2 4 FATE OF THE COALESCING BINARY
aretheradiiofthetwostarsand athebinaryseparation.
Stellar collisions are likely the main assembly line of blue
stragglers (see e.g. Leonard 1989; Bailyn & Pinsonneault
1995; Lombardi et al. 2002), and ultracompact X-ray bina-
ries(e.g.Ivanovaet al.2005;Lombardi et al. 2006)in glob-
stars to coalesce (see Table 2). Also of note is the fact that ular clusters. The Galactic Centre of the Milky Way is an-
many collisions involve hypervelocities of v > 1000 kms−1 otherplacewherecollisionsarelikelytooccur.Tidaldisrup-
upon impact. The typical impact velocity of the two stars tionsofabinarybytheSMBHwillproduce∼0.1collisions
canbecrudelyestimated from amodelinwhich theSMBH per HVS (see Paper I). The ultimate fate of the binary de-
removestheangularmomentumfromthebinaryandcauses pends on the velocity of its member stars upon impact. As
the two stars to fall toward each other from their initial evident from Figure 1, the impact velocity vimp can vary
4 Idan Ginsburg & Abraham Loeb
100 100
00..0044
0.1
50 50
00..0022
0 (a) 00 0 (d) 0
--00..0022
-50 -50
-0.1
--00..0044
-100 -100
-4 -2 0 2 4 --00..0055 00 00..0055 -4 -2 0 2 4 -0.1 0 0.1
100 0.1 100
0.1
50 0.05 50
0 (b) 0 0 (e) 0
-50 -0.05 -50
-0.1
-100 -0.1 -100
-4 -2 0 2 4 -0.1 0 0.1 -4 -2 0 2 4 -0.1 0 0.1
100 600
00..11 0.1
50
400
0 (c) 00 (f) 0
200
-50
--00..11 -0.1
0
-100
-4 -2 0 2 4 --00..11 00 00..11 -20-10 0 10 20 -0.1 0 0.1
Figure2.Orbitsofstars(inunitsofAU)priortocollisionforbinariesof3M⊙ &3M⊙ inpanels(a)−(c)andbinariesof10M⊙ &3M⊙
inpanels (d)−(f). For all panels, the graphs on the left arethe orbits of the stars as they pass near the SMBH located at the origin.
For panels (a)−(c), the graphs on the right areplotted at the center of mass frame. For panels (d)−(f), the graphs on the rightare
plottedattherestframeofthe10M⊙ star.Theredfilledcircledenotes thecollisioninstantandtheblackfilledcircledenotes thetime
when the stars started to move towards each other as a result of the SMBH tidal force. Note that before the binary is disrupted, the
3M⊙ star makes many revolutions as denoted by the blue circles. After the binary is disrupted, the approaching stars are denoted by
blacktrianglesforclarity.Panelsaanddbothhaveaninitialseparationofa=0.05AU.Panelsbandehavea=0.10AU,andpanels
candf havea=0.15AU.
coremerger,whereasahead-oncollisionmightresultincore
a(AU) P(3M⊙) P(10M⊙)
merger, and thus form a more massive star (Dale & Davies
0.05 0.46 0.13 2006).Theresultsofsmoothedparticlehydrodynamicssim-
0.10 0.19 0.05 ulations of blue stragglers (Sills et al. 2005) show that off-
0.15 0.08 0.00 axis collisions initially have large angular momentum but
0.20 0.00 0.00
eventually lose it to allow the merger to contract down to
0.05 N/A N/A themainsequence.Off-axiscollisions,whicharemoreproba-
0.10 0.81 0.33 blethanhead-oncollisions,couldneverthelessleadtoHVSs
0.15 0.93 0.05 which are rapidly spinning (Alexander& Kumar 2001). Fi-
0.20 0.25 0.03 nally,amergerbetweenalowermassstarwithahighermass
star may extend the massive star’s main-sequence phase
Table 2. Probability of coalescence upon collision for different (Dale & Davies 2006).
values of a for binaries of 3M⊙ & 3M⊙ (second column) and
Edelmann et al. (2005) notes that HVS HE 0437-5439
10M⊙ & 3M⊙ (third column). The top four rows show the val-
ues obtained fromour simulations for amin = 0.02 AU,and the might be the merger of two 4M⊙ stars, and that such a
bottom rowsfor amin = 0.04AU. Herewe assumethat the two mergeris consistent with theage of theHVS.Furthermore,
starswillmergeifvimp.500kms−1. Hirsch et al. (2005) suggests that HVS US 708, a sublumi-
nous O star, might be the merger of two helium-core white
dwarfs. After losing mass, some of the coalescing binaries
in our runs might end up with sufficient velocity to escape
over a wide range of values. A star with v > v ≡
imp esc
[2G(m1 +m2)/(R1 +R2)]1/2 will likely pass through the thegalaxy.Unfortunately,oursimulationscannottreatmass
lossaswellasthelargeamountofthermalenergydeposited
other star, even during a head-on collision (Freitag & Benz
in each collision (see Leonard & Livio 1995). Coalescing bi-
2005). However, in any collision there certainly will be in-
narysystemsthatremainboundtotheSMBHcouldendup
teractions where the smaller star may gain mass and the
as massive S-stars.
larger star will likely lose mass (Freitag & Benz2005).Fur-
thermore, a collision where the impact velocity is less than Aside from stellar collisions of main-sequence stars, it
theescapevelocityv willnotnecessarilyendasamerger. ispossible forcollisions toinvolvecompact objects. Aslong
esc
A grazing collision might result in envelope-ejection but no as the colliding objects are gravitationally bound, thecom-
Hypervelocity Collisions of Binary Stars at the Galactic Centre 5
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ACKNOWLEDGMENTS ThispaperhasbeentypesetfromaTEX/LATEXfileprepared
bythe author.
We thank Avery Broderick, Warren Brown, Yosi Gelfand,
andLorenHoffmanfortheirtimeandusefuldiscussions,and
ourrefereeforhelpfulsuggestions.Thisworkwassupported
in part by Harvard Universityfunds.
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