Stellar dynamics in young clusters: the formation of massive runaways and very massive runaway mergers

0.16 MB·English

by  D. Vanbeveren

AstrophysicsandSpaceScience
DOI10.1007/s•••••-•••-••••-•
Stellar dynamics in young clusters: the formation of
massive runaways and very massive runaway mergers
D. Vanbeveren1,2, H. Belkus1, J. Van Bever3, N.
Mennekens1
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(cid:13)c Springer-Verlag••••
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Abstract InthepresentpaperwecombineanN-body Keywords Clusterstellardynamics,massivestarevo-
7
code that simulates the dynamics of young dense stel- lution, massive star winds

] lar systems with a massive star evolution handler that
h
accountsinarealisticwayfortheeffectsofstellarwind
p
mass loss. We discuss two topics: 1 Introduction
-
o 1. The formation and the evolution of very massive
r
t stars (with a mass > 120 M⊙) is followed in detail. The temporal evolution of the population of differ-
s
a These verymassive starsare formedin the cluster core ent types of massive stars in starbursts has been the
[ asa consequenceofthe successive(physical)collisonof subject of numerous research topics in the last two

3 10-20 most massive stars of the cluster (the process is decades. We can distinguish studies dealing with OB-
v known as runaway merging). The further evolution is type stars, Wolf-Rayet (WR) type stars and compact
3 governed by stellar wind mass loss during core hydro- objects. Some of them have only been concerned with
4 gen burning and during core helium burning (the WR
single stars (e.g. Arnault et al. 1989; Maeder 1991;
3
phase of very massive stars). Our simulations reveal
Mas-Hesse & Kunth 1991; Cervino & Mas-Hesse 1994;
3
that as a consequence of runaway merging in clusters
. Meynet1995;Leithereretal. 1999). Theeffectsofclose
2 with solar and supersolar values, massive black holes
binaries were investigated by Dalton & Sarazin(1995);
1
7 can be formed but with a maximum mass ≈ 70 M⊙. Schaerer& Vacca(1998);Polsetal. (1991);VanBever
In small metallicity clusters however, it cannot be ex-
0 & Vanbeveren (1997, 2000, 2003); Vanbeveren et al.
: cludedthattherunawaymergingprocessisresponsible
v (1997, 1998a, b, c); Belczynski et al. (2002). However,
for pair instability supernovae or for the formation of
i none of the papers listed above account for the effects
X intermediate mass black holes with a mass of several
of stellar dynamics, although young massive starbursts
r 100 M⊙.
a may be very dense. Attempts to include dynamics in
2. Massive runaways can be formed via the supernova
ordertofollowtheearlyevolutionofmassivestarbursts
explosion of one of the components in a binary (the
have been presented by Portegies Zwart et al. (1999),
Blaauw scenario)or via dynamical interactionof a sin-
Ebisuzaki et al. (2001); Portegies Zwart & McMillan
gle star and a binary or between two binaries in a star
(2002); Gu¨rkan et al. (2004); Freitag et al. (2006).
cluster. We explore the possibility that the most mas-
sive runaways (e.g., ζ Pup, λ Cep, BD+43o3654) are These papers investigate the starburst conditions to
initiate a runaway collision (runaway merger), which
the product of the collision and merger of 2 or 3 mas-
may lead to the formation of a very massive object at
sive stars.
the centre of the cluster, and the possible formation
of an intermediate mass black hole (IMBH). IMBHs
D.Vanbeveren, H.Belkus,J.VanBever,N.Mennekens
and their formation became a hot topic soon after the
1AstrophysicalInstitute,VrijeUniversiteitBrussel,Brussels,Bel-
ROSAT and Einstein X-ray surveys of galaxies, when
gium,
[email protected], [email protected],[email protected] it was realised that the high-luminosity sources (with
2GroepT,AssociationK.U.Leuven,Leuven,Belgium luminosity up to ∼1042 erg/s) were linked to regions
3InstituteofComputationalAstrophysics,St.-Mary’sUniversity, of intense star formation activity, starbursts. Despite
Halifax,Canada, the limited sensitivity and spatial resolution of both
[email protected] telescopes, the images of nearby galaxiessuggestedthe
2
presenceofhighlysuper-Eddingtonstellar-masssources section 2 we present our N-body code, whereas section
with luminosities as high as ∼1040 erg/s. The X-ray 3 summarizes the massive star evolution handler. In
telescope on boardof Chandra confirmedthe existence section 4 we present simulations of the dynamical evo-
of these sources, but it also revealed the existence of lution of a cluster combined with the massive and very
individual sources with a luminosity ∼1041-1042 erg/s massive evolution handler, and we discuss the results
(Ptak &Colbert,2004for areviewofgalaxieswithUl- in relation to the cluster MGG 11.
tra Luminous X-ray sources, ULXs). Many models to Massive star runaways are defined as massive stars
explain ULXs have been proposed in literature (e.g., with a peculiar space velocity ≥ 30-40 km/s. At least
Fabbiano, 1989; Colbert & Mushotsky, 1999; Perna & 10% of the O-type stars are classified as runaways
Stella, 2004, and references therein) and IMBHs is one (Gies & Bolton, 1986). They can form either by the
ofthem. MGG11isayoungdensestarcluster∼200pc dynamical ejection from a cluster due to single star-
fromthecentreofthestarburstgalaxyM82,whosepa- binary or binary-binary interactions (Poveda et al.,
rameters have been studied by McCrady et al. (2003). 1967;Leonard& Duncan,1988,1990),orbythe explo-
A ULX associated with the cluster, the runaway col- sionas asupernova(SN) ofamember of aclose binary
lision process and formation of an IMBH in order to (Blaauw, 1961). A word of caution: it is not because
explain this source was promoted by Portegies Zwart a runawayis observedclose to a dense cluster that one
etal. (2004). The questionwhether ornotanIMBH is should favor the dynamical formation mechanism. If
needed in order to explain ULXs was addressed in de- mostofthestarsareformedinclusters,alsobinary-SN
tail by Soria (2007), who concluded that most of them formed runaways will come out of a cluster. On the
canbe explained with a 50-100M⊙ BH accretingmass other hand, it is not because there is no O-type cluster
at super-Eddington rates. observed in the neighbourhood of an O-type runaway
At the center of the Galactic bulge lies a supermas- that one should favor the binary-SN mechanism. Dy-
siveblackhole(SMBHwithamass∼3-4.106M⊙,Ghez namically formed runaways are in many cases rejuve-
etal.,1998,2000). Severalyoung(≤10Myr)densestar nated collision products (stellar mergers of 2-3 stars,
clusters were observed within ∼100 pc of this SMBH see section 5) and the other O-type stars of the parent
(Arches, Figer et al., 2002; Quintuplet, Figer et al., cluster of the runaway may have disappeared already.
1999; IRS 13E, Maillard et al., 2004; IRS 16SW, Lu et ζ Pup, λ Cep and BD+43o3654 are 3 most massive
al.,2005). TheformationofIMBHsinbulgeclustersof runawayswitharunawayvelocitybetween40km/sand
this type has been investigated by Portegies Zwart et 70 km/s (Vanbeveren et al., 1998b, c; Hoogerwerf et
al. (2006). TheauthorsconcludedthatIMBHsthatare al., 2001; Comeron & Pasquali, 2007). In section 5
formed as a consequence of core collapse accompanied we explore the dynamical ejection process in order to
by runaway star collisions in dense clusters with the explain their properties.
propertiesofbulgeclusters,maybethebuildingblocks
of SMBHs, a model that was originally proposed by
2 The dynamical N-body code for young dense
Ebisuzaki et al. (2001).
stellar systems
Therunawaymergerprocessindensestellarsystems
as a model to explain IMBHs contains two major un-
Afull descriptionofourN-body code willbe presented
certainties: first, the core collapse and the formation
elsewhere (Van Bever et al., 2008). Summarizing, our
of a runaway merger can be considered as facts, but it
code (written in C++) contains three main compo-
is as yet unclear whether or not a very massive object
nents. There is the standard scheme for integrating
like this will ever become a star, and, secondly, when
single stars and the centers of mass of stellar hierar-
this object becomes a very massive star, what the ef-
chies (e.g., binaries), for which we use the fourth order
fect of stellar wind mass loss is on its evolution and on
HermiteschemedescribedbyMakino&Aarseth(1992).
the finalmass the momentthat the star collapses. The
The treatment of compact subsystems requires special
evolution of very massive stars has been discussed re-
techniques that deal with the extremely small inter-
centlybyBelkusetal. (2007)anditwasconcludedthat
particle distances that occur in these cases. We distin-
stellar wind mass losses during core hydrogen burning
guish between two-body motion, which is handled by
and during core helium burning are very important. A
theKustaanheimo-Stiefelregularisationtechnique,and
convenient evolutionary recipe for such very massive
more complex encounters between more than 2 stars.
stars was presented, a recipe that can easily be imple-
The latter is treated by the so-called chain regulariza-
mented in a N-body dynamical code. In the present
tion(Mikkola&Aarseth,1993,andreferencestherein),
paper we first investigate the formation and evolution
whichallowstheaccurateintegrationofacompactsub-
ofverymassivestarsinadenseclusterenvironment. In
system with arbitrary membership.
Stellardynamicsinyoungclusters: theformationofmassiverunawaysandverymassiverunawaymergers 3
The code generates a zero age massive single star formalism (e.g., Meynet & Maeder, 2003; Eldridge
populationaccordingto apredefinedIMFandaprede- & Vink, 2006). Vanbeveren (1995) and Vanbeveren
fined spatialcluster distribution. We use a Kingmodel et al. (2007)illustratedthat an update may be nec-
with various concentrations, parametrized by the di- essary,that affects the evolution of single stars with
mensionless central potential, W0. We do not account an initial mass between 20 M⊙ and 40 M⊙. Our
for the presence of a primordial binary population in evolutionary handler accounts for this update.
the cluster simulations of the present paper. 3. Since 1998 we use core helium burning WR mass
lossratesinourevolutionarycode,whichcorrespond
to empirical rates determined by accounting for the
3 The massive single star evolution handler effects of clumping. The WR rates are assumed to
be Z-dependent (Vanbeveren et al., 1998b, c; Van
Our preferred evolutionary model for massive single Bever & Vanbeveren, 2003). Notice that the WR-
stars has been described in a number of papers (Van- mass loss rate formalism critically affects the pre-
beveren et al. 1998a, b, c; Van Bever & Vanbeveren, supernovamassofa massivestar,thus alsothe final
1997, 2000, 2003 and references therein). It is summa- fate (neutron star or black hole) and, in case of a
rized here together with a few updates. black hole, the mass of this compact object.
4. Realistic dynamical simulations of young dense sys-
1. Stars with an initial mass larger than 40 M⊙ evolve
tems of massive stars reveal the existence of what
according to the LBV scenario as it was introduced
can be considered as one of the most spectacular
byVanbeveren(1991). Summarizing: duetothefact
events in astrophysics: the gravitational encounter
that no yellow or red supergiants (YSG and RSG)
of two objects (single star-single star), (single star-
are observed brighter than Mbol = -9.5, we use as
binary) or (binary-binary) resulting in many cases
a working hypothesis in our evolutionary computa-
tions that the M˙ during the LBV phase of a star in a physical collision of two stars. A collision of
twomassivestarsindense stellarenvironmentsmay
with Mbol ≤ -9.5 must be sufficiently large to sup-
initiateachainreactionwherethesamecollisionob-
pressalargeexpansion,hencetoprohibittheredward
ject merges with other massive stars: the term run-
evolution in the HR-diagram. When this criterion
away merger is used. In many cases, this runaway
is implemented into a stellar evolutionary code, the
code calculates the mass loss rates that are needed merger may become as massive as 1000 M⊙ or even
larger (Portugies Zwart et al., 2006, and references
at any time in order to prohibit the redward evolu-
therein, see also section 4) and to investigate the
tion. Since we do not observe RSGs with Mbol ≤
consequences of this process it is indispensable to
-9.5 in the LMC or SMC either, we consider this as
know how such an object further evolves. Using 3D
evidence thatthe LBVscenarioisindependent from
smoothed-particle-hydrodynamics (SPH) Suzuki et
the initial metallicity.
al. (2007) simulated the collision and merging of
2. The RSG evolutionary phase of massive single stars
2 massive stars. The evolution during merging de-
withaninitialmass<40M⊙ iscomputedinmostof
pends on the mass ratio of the two colliding stars,
the present single star evolutionary codes by using
butafterthethermaladjustment(Kelvin-Helmholtz
thedeJageretal. (1988)stellarwindmasslossrate
contraction) the merger is nearly homogenized. In
our N-body simulations we therefore assume that
500 similarity theory massive collision objects are homogenized and be-
Eggleton code
come ZAMS stars (with the appropriate chemical
400
composition)onatimescalewhichisshortcompared
300 to the stellar evolutionarytimescale. Obviously,the
M (Msun) evolution of this new massive star will be critically
200 affected by stellar wind mass loss.
100
INTERMEZZO: Suzuki et al. (2007) simulated the
0 0 0.5 1 1.5 2 2.5 collision of a star with a mass = 88 M⊙ with a star
t(Myr)
with the same mass and one with a mass = 28 M⊙.
Fig.1 Thetemporalevolutionduringcorehydrogenburn- The merging process is very short (of the order of
ing of the total mass and of the core mass of a 500 M⊙ days)and,interestingly,during the mergingthe col-
star calculated with the Eggleton stellar evolutionary code
lision object loses ∼ 10 M⊙. It is tempting to link
(black color) and with the very massive star evolutionary
this collision and merging process to the η Car out-
recipe discussed by Belkus et al. (2007) (red color).
4
burst in the 19th century. Note that a collision be- TheBHs inoursimulationhaveamassnotlargerthan
tweenasinglestarandabinarymayalsoexplainthe 75 M⊙ (see also Belkus et al., 2007). Notice that this
observedanomalouseccentricityoftheη Carbinary. may be sufficient in order to explain the presence of a
ULX in MGG 11, provided that we accept the X-ray
Withourevolutionarylibraryofmassivesinglestars,
formation scenario of Soria (2007).
it is straightforward to estimate the evolution of a
In order to investigate the effect of the metallicity
merger with a mass smaller than 120 M⊙, given its
on the formation and evolution of runaway mergers
chemical composition after homogenization. However,
(through the effect of Z on the stellar wind mass loss),
what about mergers with a mass larger than 120 M⊙,
we followed the dynamical evolution of the same clus-
upto1000M⊙ (verymassivestars=VMSs)? Theevo-
ter as the one discussed above, but for Z = 0.001. The
lutionofVMSshasbeenstudiedbyBelkusetal. (2007)
results are shown in figure 2 as well. The final mass is
where it was demonstrated that stellar wind mass loss
of the order of 200 M⊙ and we conclude that the for-
plays a crucial role. At solar metallicity and larger,
mation of an IMBH is possible in dense clusters with
VMSs lose most of their mass on a timescale of the or-
small Z. When small Z globular clusters are preceded
der of 2 million years and end their life as a black hole
by a massive supercluster phase, it can thus not be ex-
with a mass less than 75 M⊙. We extended these cal-
cluded that during this early phase an IMBH formed.
culations for stars with an initial mass up to 3000M⊙.
Notice that pair instability supernovae are expected
Stars with a larger mass have a larger luminosity and
to happen when the final mass after core helium burn-
thus a larger stellar wind mass loss. Our computations
revealthata3000M⊙ starhasa masslossofthe order ing is between ∼ 65 M⊙ and ∼ 130 M⊙ (Heger &
of 10−2 M⊙/yr. As a consequence, the final mass at Woosley,2002). Theresultswhicharedepictedinfigure
2 illustrate that in dense clusters with subsolar metal-
the endofcoreheliumburningislessthan∼75M⊙ as
licity pair instability supernovae may happen.
well. AtZ=0.001(andsmaller),thefinalmassmaybe
More details of the N-body simulations discussed
a factor 2-3 larger and the formation of an IMBH with
above are given in Belkus et al. (2008).
a mass of a few hundred M⊙ is a possibility. We pre-
sentedaconvenientevolutionrecipeforVMSsthatcan
easilybe implementedinadynamical-populationcode.
5 The formation of massive runaways
To illustrate the validity of our recipe, figure 1 com-
pares evolutionary results of a galactic 500 M⊙ VMS ζ Pup, λ Cep and BD+43o3654 are 3 massive run-
calculated with the Eggleton code with the evolution
aways with a runaway velocity between 40 km/s and
predicted by the recipe. As can be noticed, the overall
70 km/s. Their location in the HR diagram suggests
evolutionary results that are important in order to fol-
that they belong to the most massive star sample of
low the evolution of this object in a dense cluster are
the solar neighborhood (Vanbeveren et al., 1998b, c;
very similar.
Hoogerwerf et al., 2001; Comeron & Pasquali, 2007).
Runaways can be formed by the binary-SN scenario
(Blaauw,1961)wheretheoriginalmassiveprimary(the
4 The formation and evolution of runaway
mass loser when the Roche lobe overflow process hap-
mergers in dense stellar systems
pens)explodesandeventuallydisruptsthebinary,leav-
ing a neutron star remnant and a runaway secondary
Wesimulatedtheearlyevolutionofadenseclustercore
(the mass gainer when the Roche lobe overflow hap-
containing 3000 massive single stars (with a mass be-
pens). Such a scenario for ζ Pup was presented by
tween10M⊙ and120M⊙ satisfyingtheSalpeterinitial
Vanbeverenetal. (1998b,c). Toexplainthesignificant
mass function) distributed according to a King model
surfaceheliumenrichmentofthestar,itsrapidrotation
(Wo = 9). We adopt a half-mass radius = 0.5 pc. In
anditsrunawayvelocity(=70km/s),themasstransfer
figure2weshowthegrowthinmassofthecollisionrun-
phase and the accretion process must be accompanied
awaystarwithtime. Ourchoiceofthehalfmassradius
by spinning-up and quasi-homogenization of the mass
was motivated by the fact that, with the stellar wind
gainer (the full mixing model as it was introduced by
masslossformalismastheoneusedbyPortegiesZwart
Vanbeveren and De Loore, 1994) whereas the overall
et al. (2004, 2006), we confirm the mass evolution of
evolutionshould have resultedin a pre-SN binary with
the runaway merger and the possible formation of an
aperiodoftheorderof4days. Thelatterrequiressome
IMBHwithamassaslargeas1000M⊙. However,with
fine-tunning.
a more realistic mass loss rate formalism, the figure il-
To illustratethatthe dynamicalejectionmechanism
lustrates that if a dense cluster has solar or supersolar
isaveryvaluablealternative,theFEWBODYsoftware
metallicitytheformationofanIMBHisratherunlikely.
Stellardynamicsinyoungclusters: theformationofmassiverunawaysandverymassiverunawaymergers 5
1400
1200
1000
800
s
s
a
M
600
400
200
0
0 1 2 3 4 5
t/10^6
Fig. 2 The effect of stellar wind mass loss on the temporal evolution of the runaway merger during core hydrogen and
core helium burning. The blue curve corresponds to a very massive star stellar wind mass loss rate formalism as the one
used by Portegies Zwart et al., theblack illustrates theevolution with theformalism discussed in Belkus et al. (2007) and
metallicity Z = 0.02; the red curveis similar as theblack one but for Z = 0.001.
of Fregeau et al. (2004) was used to reproduce the ob- favourofthedynamicalejectionscenarioinordertoex-
servedpropertiesofζ Pup. Weperformedover1million plaintherunaways(spacevelocitylargerthan30km/s)
single star-binary and binary-binary scattering experi- with a mass larger than 40 M⊙, like ζ Pup, λ Cep and
o
ments. The details of these experiments are givenelse- BD+43 3654. We conclude:
where (Belkus et al., 2008). We explored the effects of
1. Inclusterswithsolarorsupersolarmetallicity,black
differentmassesanddifferentbinaryperiodsandeccen-
holes form with a mass smaller than 70-75 M⊙, but
tricities and, obviously, many experiments reproduce ζ
the formation of an intermediate mass black hole
Pup, but to obtain a runaway velocity as observed the
with a mass of several 100 M⊙ is less likely.
binaries participating in the scattering process always
2. Duetothemetallicitydependenceofthestellarwind
have to be very close (periods smaller than 100 days).
mass loss, the occurence of pair instability super-
Most interestingly, in all our experiments, ζ Pup turns
novaeortheformationofanintermediatemassblack
out to be a merger of 2 or 3 stars.
hole in dense clusters becomes more probable for
smaller metallicities.
3. Itisplausiblethatatleastsomeofthemostmassive
6 Conclusions
runaways, like ζ Pup, λ Cep and BD+43o3654, are
formed during a dynamical encounter of a massive
Inthe presentpaper wefirstdiscussthe dynamicalfor-
single star and a massive close binary, or by two
mation(duetorunawaymerging)andevolutionofvery
massive close binaries. In this case, the runaway is
massivestars(withmassesupto1000M⊙ andmore)in
the merger of 2 or 3 massive stars.
the cores of young dense clusters. To predict whether
suchaverymassiveobjectbecomesastellarmassblack
hole, an intermediate mass black hole or explodes as a Ackowledgement
pair instability supernova, one has to combine a dy- WethankDr. LevYungelsonwhocalculatedtheevolu-
namical N-body code with a massive and very massive tionofthe500M⊙ starwithhisversionoftheEggleton
star evolutionary library, that considers in detail the code but with our preferred stellar wind mass loss for-
importance of stellar winds and of the metallicity de- malism.
pendence of these winds on the core hydrogen burning
and core helium burning evolution of the massive and
very massive stars. Secondly we present arguments in
6
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