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

Abstract

In the present paper we combine an N-body code that simulates the dynamics of young dense stellar systems with a massive star evolution handler that accounts
in a realistic way for the effects of stellar wind mass loss. We discuss two topics.

1.

The formation and the evolution of very massive stars (with masses >120 M⊙) is followed in detail. These very massive stars are formed in the cluster core as a consequence of the successive (physical)
collisions of the 10–20 most massive stars in the cluster (this process is known as ‘runaway merging’). The further evolution
is governed by stellar wind mass loss during core hydrogen and core helium burning (the WR phase of very massive stars). Our
simulations reveal that, as a consequence of runaway merging in clusters with solar and supersolar values, massive black holes
can be formed, but with a maximum mass ≈70 M⊙. In low-metallicity clusters, however, it cannot be excluded that the runaway-merging process is responsible for pair-instability
supernovae or for the formation of intermediate-mass black holes with a mass of several 100M⊙.

2.

Massive runaways can be formed via the supernova explosion of one of the components in a binary system (the Blaauw scenario),
or via dynamical interaction of a single star and a binary or between two binaries in a star cluster. We explore the possibility
that the most massive runaways (e.g. ζ Pup, λ Cep, BD+43°3654) are the product of the collision and merger of two or three massive stars.

KeywordsCluster stellar dynamics-Massive star evolution-Massive star winds

Full text

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arXiv:0712.3343v3 [astro-ph] 7 Jan 2008
Astrophysics and Space Science
DOI 10.1007/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
c ? Springer-Verlag ••••
Abstract In the present paper we combine an N-body
code that simulates the dynamics of young dense stel-
lar systems with a massive star evolution handler that
accounts in a realistic way for the effects of stellar wind
mass loss. We discuss two topics:
1. The formation and the evolution of very massive
stars (with a mass > 120 M⊙) is followed in detail.
These very massive stars are formed in the cluster core
as a consequence of the successive (physical) collison of
10-20 most massive stars of the cluster (the process is
known as runaway merging). The further evolution is
governed by stellar wind mass loss during core hydro-
gen burning and during core helium burning (the WR
phase of very massive stars). Our simulations reveal
that as a consequence of runaway merging in clusters
with solar and supersolar values, massive black holes
can be formed but with a maximum mass ≈ 70 M⊙.
In small metallicity clusters however, it cannot be ex-
cluded that the runaway merging process is responsible
for pair instability supernovae or for the formation of
intermediate mass black holes with a mass of several
100 M⊙.
2. Massive runaways can be formed via the supernova
explosion of one of the components in a binary (the
Blaauw scenario) or via dynamical interaction of a sin-
gle star and a binary or between two binaries in a star
cluster. We explore the possibility that the most mas-
sive runaways (e.g., ζ Pup, λ Cep, BD+43o3654) are
the product of the collision and merger of 2 or 3 mas-
sive stars.
D. Vanbeveren, H. Belkus, J. Van Bever, N. Mennekens
1Astrophysical Institute, Vrije Universiteit Brussel, Brussels, Bel-
gium,
dvbevere@vub.ac.be, hbelkus@vub.ac.be, nmenneke@vub.ac.be
2Groep T, Association K.U.Leuven, Leuven, Belgium
3Institute of Computational Astrophysics, St.-Mary’s University,
Halifax, Canada,
vanbever@penguin.stmarys.ca
Keywords Cluster stellar dynamics, massive star evo-
lution, massive star winds
1 Introduction
The temporal evolution of the population of differ-
ent types of massive stars in starbursts has been the
subject of numerous research topics in the last two
decades. We can distinguish studies dealing with OB-
type stars, Wolf-Rayet (WR) type stars and compact
objects. Some of them have only been concerned with
single stars (e.g. Arnault et al. 1989; Maeder 1991;
Mas-Hesse & Kunth 1991; Cervino & Mas-Hesse 1994;
Meynet 1995; Leitherer et al. 1999). The effects of close
binaries were investigated by Dalton & Sarazin (1995);
Schaerer & Vacca (1998); Pols et al. (1991); Van Bever
& Vanbeveren (1997, 2000, 2003); Vanbeveren et al.
(1997, 1998a, b, c); Belczynski et al. (2002). However,
none of the papers listed above account for the effects
of stellar dynamics, although young massive starbursts
may be very dense. Attempts to include dynamics in
order to follow the early evolution of massive starbursts
have been presented by Portegies Zwart et al. (1999),
Ebisuzaki et al. (2001); Portegies Zwart & McMillan
(2002); G¨ urkan et al. (2004); Freitag et al. (2006).
These papers investigate the starburst conditions to
initiate a runaway collision (runaway merger), which
may lead to the formation of a very massive object at
the centre of the cluster, and the possible formation
of an intermediate mass black hole (IMBH). IMBHs
and their formation became a hot topic soon after the
ROSAT and Einstein X-ray surveys of galaxies, when
it was realised that the high-luminosity sources (with
luminosity up to ∼1042erg/s) were linked to regions
of intense star formation activity, starbursts. Despite
the limited sensitivity and spatial resolution of both
telescopes, the images of nearby galaxies suggested the

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presence of highly super-Eddington stellar-mass sources
with luminosities as high as ∼1040erg/s. The X-ray
telescope on board of Chandra confirmed the existence
of these sources, but it also revealed the existence of
individual sources with a luminosity ∼1041-1042erg/s
(Ptak & Colbert, 2004 for a review of galaxies with Ul-
tra Luminous X-ray sources, ULXs). Many models to
explain ULXs have been proposed in literature (e.g.,
Fabbiano, 1989; Colbert & Mushotsky, 1999; Perna &
Stella, 2004, and references therein) and IMBHs is one
of them. MGG 11 is a young dense star cluster ∼200 pc
from the centre of the starburst galaxy M 82, whose pa-
rameters have been studied by McCrady et al. (2003).
A ULX associated with the cluster, the runaway col-
lision process and formation of an IMBH in order to
explain this source was promoted by Portegies Zwart
et al. (2004). The question whether or not an IMBH is
needed in order to explain ULXs was addressed in de-
tail by Soria (2007), who concluded that most of them
can be explained with a 50-100 M⊙BH accreting mass
at super-Eddington rates.
At the center of the Galactic bulge lies a supermas-
sive black hole (SMBH with a mass ∼3-4.106M⊙, Ghez
et al., 1998, 2000). Several young (≤ 10 Myr) dense star
clusters were observed within ∼100 pc of this SMBH
(Arches, Figer et al., 2002; Quintuplet, Figer et al.,
1999; IRS 13E, Maillard et al., 2004; IRS 16SW, Lu et
al., 2005). The formation of IMBHs in bulge clusters of
this type has been investigated by Portegies Zwart et
al. (2006). The authors concluded that IMBHs that are
formed as a consequence of core collapse accompanied
by runaway star collisions in dense clusters with the
properties of bulge clusters, may be the building blocks
of SMBHs, a model that was originally proposed by
Ebisuzaki et al. (2001).
The runaway merger process in dense stellar systems
as a model to explain IMBHs contains two major un-
certainties: first, the core collapse and the formation
of a runaway merger can be considered as facts, but it
is as yet unclear whether or not a very massive object
like this will ever become a star, and, secondly, when
this object becomes a very massive star, what the ef-
fect of stellar wind mass loss is on its evolution and on
the final mass the moment that the star collapses. The
evolution of very massive stars has been discussed re-
cently by Belkus et al. (2007) and it was concluded that
stellar wind mass losses during core hydrogen burning
and during core helium burning are very important. A
convenient evolutionary recipe for such very massive
stars was presented, a recipe that can easily be imple-
mented in a N-body dynamical code. In the present
paper we first investigate the formation and evolution
of very massive stars in a dense cluster environment. In
section 2 we present our N-body code, whereas section
3 summarizes the massive star evolution handler. In
section 4 we present simulations of the dynamical evo-
lution of a cluster combined with the massive and very
massive evolution handler, and we discuss the results
in relation to the cluster MGG 11.
Massive star runaways are defined as massive stars
with a peculiar space velocity ≥ 30-40 km/s. At least
10% of the O-type stars are classified as runaways
(Gies & Bolton, 1986). They can form either by the
dynamical ejection from a cluster due to single star-
binary or binary-binary interactions (Poveda et al.,
1967; Leonard & Duncan, 1988, 1990), or by the explo-
sion as a supernova (SN) of a member of a close binary
(Blaauw, 1961). A word of caution: it is not because
a runaway is observed close to a dense cluster that one
should favor the dynamical formation mechanism. If
most of the stars are formed in clusters, also binary-SN
formed runaways will come out of a cluster. On the
other hand, it is not because there is no O-type cluster
observed in the neighbourhood of an O-type runaway
that one should favor the binary-SN mechanism. Dy-
namically formed runaways are in many cases rejuve-
nated collision products (stellar mergers of 2-3 stars,
see section 5) and the other O-type stars of the parent
cluster of the runaway may have disappeared already.
ζ Pup, λ Cep and BD+43o3654 are 3 most massive
runaways with a runaway velocity between 40 km/s and
70 km/s (Vanbeveren et al., 1998b, c; Hoogerwerf et
al., 2001; Comeron & Pasquali, 2007). In section 5
we explore the dynamical ejection process in order to
explain their properties.
2 The dynamical N-body code for young dense
stellar systems
A full description of our N-body code will be presented
elsewhere (Van Bever et al., 2008). Summarizing, our
code (written in C++) contains three main compo-
nents. There is the standard scheme for integrating
single stars and the centers of mass of stellar hierar-
chies (e.g., binaries), for which we use the fourth order
Hermite scheme described by Makino & Aarseth (1992).
The treatment of compact subsystems requires special
techniques that deal with the extremely small inter-
particle distances that occur in these cases. We distin-
guish between two-body motion, which is handled by
the Kustaanheimo-Stiefel regularisation technique, and
more complex encounters between more than 2 stars.
The latter is treated by the so-called chain regulariza-
tion (Mikkola & Aarseth, 1993, and references therein),
which allows the accurate integration of a compact sub-
system with arbitrary membership.

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Stellar dynamics in young clusters: the formation of massive runaways and very massive runaway mergers3
The code generates a zero age massive single star
population according to a predefined IMF and a prede-
fined spatial cluster distribution. We use a King model
with various concentrations, parametrized by the di-
mensionless central potential, W0. We do not account
for the presence of a primordial binary population in
the cluster simulations of the present paper.
3 The massive single star evolution handler
Our preferred evolutionary model for massive single
stars has been described in a number of papers (Van-
beveren et al. 1998a, b, c; Van Bever & Vanbeveren,
1997, 2000, 2003 and references therein). It is summa-
rized here together with a few updates.
1. Stars with an initial mass larger than 40 M⊙evolve
according to the LBV scenario as it was introduced
by Vanbeveren (1991). Summarizing: due to the fact
that no yellow or red supergiants (YSG and RSG)
are observed brighter than Mbol = -9.5, we use as
a working hypothesis in our evolutionary computa-
tions that the
˙M during the LBV phase of a star
with Mbol ≤ -9.5 must be sufficiently large to sup-
press a large expansion, hence to prohibit the redward
evolution in the HR-diagram. When this criterion
is implemented into a stellar evolutionary code, the
code calculates the mass loss rates that are needed
at any time in order to prohibit the redward evolu-
tion. Since we do not observe RSGs with Mbol ≤
-9.5 in the LMC or SMC either, we consider this as
evidence that the LBV scenario is independent from
the initial metallicity.
2. The RSG evolutionary phase of massive single stars
with an initial mass < 40 M⊙is computed in most of
the present single star evolutionary codes by using
the de Jager et al. (1988) stellar wind mass loss rate
0
100
200
300
400
500
0 0.5 1 1.5 2 2.5
M (Msun)
t(Myr)
similarity theory
Eggleton code
Fig. 1 The temporal evolution during core hydrogen burn-
ing of the total mass and of the core mass of a 500 M⊙
star calculated with the Eggleton stellar evolutionary code
(black color) and with the very massive star evolutionary
recipe discussed by Belkus et al. (2007) (red color).
formalism (e.g., Meynet & Maeder, 2003; Eldridge
& Vink, 2006). Vanbeveren (1995) and Vanbeveren
et al. (2007) illustrated that an update may be nec-
essary, that affects the evolution of single stars with
an initial mass between 20 M⊙ and 40 M⊙. Our
evolutionary handler accounts for this update.
3. Since 1998 we use core helium burning WR mass
loss rates in our evolutionary code, which correspond
to empirical rates determined by accounting for the
effects of clumping. The WR rates are assumed to
be Z-dependent (Vanbeveren et al., 1998b, c; Van
Bever & Vanbeveren, 2003). Notice that the WR-
mass loss rate formalism critically affects the pre-
supernova mass of a massive star, thus also the final
fate (neutron star or black hole) and, in case of a
black hole, the mass of this compact object.
4. Realistic dynamical simulations of young dense sys-
tems of massive stars reveal the existence of what
can be considered as one of the most spectacular
events in astrophysics: the gravitational encounter
of two objects (single star-single star), (single star-
binary) or (binary-binary) resulting in many cases
in a physical collision of two stars. A collision of
two massive stars in dense stellar environments may
initiate a chain reaction where the same collision ob-
ject merges with other massive stars: the term run-
away merger is used. In many cases, this runaway
merger may become as massive as 1000 M⊙or even
larger (Portugies Zwart et al., 2006, and references
therein, see also section 4) and to investigate the
consequences of this process it is indispensable to
know how such an object further evolves. Using 3D
smoothed-particle-hydrodynamics (SPH) Suzuki et
al. (2007) simulated the collision and merging of
2 massive stars. The evolution during merging de-
pends on the mass ratio of the two colliding stars,
but after the thermal adjustment (Kelvin-Helmholtz
contraction) the merger is nearly homogenized. In
our N-body simulations we therefore assume that
massive collision objects are homogenized and be-
come ZAMS stars (with the appropriate chemical
composition) on a timescale which is short compared
to the stellar evolutionary timescale. Obviously, the
evolution of this new massive star will be critically
affected by stellar wind mass loss.
INTERMEZZO: Suzuki et al. (2007) simulated the
collision of a star with a mass = 88 M⊙with a star
with the same mass and one with a mass = 28 M⊙.
The merging process is very short (of the order of
days) and, interestingly, during the merging the col-
lision object loses ∼ 10 M⊙. It is tempting to link
this collision and merging process to the η Car out-

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4
burst in the 19th century. Note that a collision be-
tween a single star and a binary may also explain the
observed anomalous eccentricity of the η Car binary.
With our evolutionary library of massive single stars,
it is straightforward to estimate the evolution of a
merger with a mass smaller than 120 M⊙, given its
chemical composition after homogenization. However,
what about mergers with a mass larger than 120 M⊙,
up to 1000 M⊙(very massive stars = VMSs)? The evo-
lution of VMSs has been studied by Belkus et al. (2007)
where it was demonstrated that stellar wind mass loss
plays a crucial role. At solar metallicity and larger,
VMSs lose most of their mass on a timescale of the or-
der of 2 million years and end their life as a black hole
with a mass less than 75 M⊙. We extended these cal-
culations for stars with an initial mass up to 3000 M⊙.
Stars with a larger mass have a larger luminosity and
thus a larger stellar wind mass loss. Our computations
reveal that a 3000 M⊙star has a mass loss of the order
of 10−2M⊙/yr. As a consequence, the final mass at
the end of core helium burning is less than ∼ 75 M⊙as
well. At Z = 0.001 (and smaller), the final mass may be
a factor 2-3 larger and the formation of an IMBH with
a mass of a few hundred M⊙is a possibility. We pre-
sented a convenient evolution recipe for VMSs that can
easily be implemented in a dynamical-population code.
To illustrate the validity of our recipe, figure 1 com-
pares evolutionary results of a galactic 500 M⊙ VMS
calculated with the Eggleton code with the evolution
predicted by the recipe. As can be noticed, the overall
evolutionary results that are important in order to fol-
low the evolution of this object in a dense cluster are
very similar.
4 The formation and evolution of runaway
mergers in dense stellar systems
We simulated the early evolution of a dense cluster core
containing 3000 massive single stars (with a mass be-
tween 10 M⊙and 120 M⊙satisfying the Salpeter initial
mass function) distributed according to a King model
(Wo = 9). We adopt a half-mass radius = 0.5 pc. In
figure 2 we show the growth in mass of the collision run-
away star with time. Our choice of the half mass radius
was motivated by the fact that, with the stellar wind
mass loss formalism as the one used by Portegies Zwart
et al. (2004, 2006), we confirm the mass evolution of
the runaway merger and the possible formation of an
IMBH with a mass as large as 1000 M⊙. However, with
a more realistic mass loss rate formalism, the figure il-
lustrates that if a dense cluster has solar or supersolar
metallicity the formation of an IMBH is rather unlikely.
The BHs in our simulation have a mass not larger than
75 M⊙(see also Belkus et al., 2007). Notice that this
may be sufficient in order to explain the presence of a
ULX in MGG 11, provided that we accept the X-ray
formation scenario of Soria (2007).
In order to investigate the effect of the metallicity
on the formation and evolution of runaway mergers
(through the effect of Z on the stellar wind mass loss),
we followed the dynamical evolution of the same clus-
ter as the one discussed above, but for Z = 0.001. The
results are shown in figure 2 as well. The final mass is
of the order of 200 M⊙and we conclude that the for-
mation of an IMBH is possible in dense clusters with
small Z. When small Z globular clusters are preceded
by a massive supercluster phase, it can thus not be ex-
cluded that during this early phase an IMBH formed.
Notice that pair instability supernovae are expected
to happen when the final mass after core helium burn-
ing is between ∼ 65 M⊙ and ∼ 130 M⊙ (Heger &
Woosley, 2002). The results which are depicted in figure
2 illustrate that in dense clusters with subsolar metal-
licity pair instability supernovae may happen.
More details of the N-body simulations discussed
above are given in Belkus et al. (2008).
5 The formation of massive runaways
ζ Pup, λ Cep and BD+43o3654 are 3 massive run-
aways with a runaway velocity between 40 km/s and
70 km/s. Their location in the HR diagram suggests
that they belong to the most massive star sample of
the solar neighborhood (Vanbeveren et al., 1998b, c;
Hoogerwerf et al., 2001; Comeron & Pasquali, 2007).
Runaways can be formed by the binary-SN scenario
(Blaauw, 1961) where the original massive primary (the
mass loser when the Roche lobe overflow process hap-
pens) explodes and eventually disrupts the binary, leav-
ing a neutron star remnant and a runaway secondary
(the mass gainer when the Roche lobe overflow hap-
pens).Such a scenario for ζ Pup was presented by
Vanbeveren et al. (1998b, c). To explain the significant
surface helium enrichment of the star, its rapid rotation
and its runaway velocity (= 70 km/s), the mass transfer
phase and the accretion process must be accompanied
by spinning-up and quasi-homogenization of the mass
gainer (the full mixing model as it was introduced by
Vanbeveren and De Loore, 1994) whereas the overall
evolution should have resulted in a pre-SN binary with
a period of the order of 4 days. The latter requires some
fine-tunning.
To illustrate that the dynamical ejection mechanism
is a very valuable alternative, the FEWBODY software

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Stellar dynamics in young clusters: the formation of massive runaways and very massive runaway mergers5
0
200
400
600
800
1000
1200
1400
0 1 2 3 4 5
Mass
t/10^6
Fig. 2
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., the black illustrates the evolution with the formalism discussed in Belkus et al. (2007) and
metallicity Z = 0.02; the red curve is similar as the black one but for Z = 0.001.
The effect of stellar wind mass loss on the temporal evolution of the runaway merger during core hydrogen and
of Fregeau et al. (2004) was used to reproduce the ob-
served properties of ζ Pup. We performed over 1 million
single star-binary and binary-binary scattering experi-
ments. The details of these experiments are given else-
where (Belkus et al., 2008). We explored the effects of
different masses and different binary periods and eccen-
tricities and, obviously, many experiments reproduce ζ
Pup, but to obtain a runaway velocity as observed the
binaries participating in the scattering process always
have to be very close (periods smaller than 100 days).
Most interestingly, in all our experiments, ζ Pup turns
out to be a merger of 2 or 3 stars.
6 Conclusions
In the present paper we first discuss the dynamical for-
mation (due to runaway merging) and evolution of very
massive stars (with masses up to 1000 M⊙and more) in
the cores of young dense clusters. To predict whether
such a very massive object becomes a stellar mass black
hole, an intermediate mass black hole or explodes as a
pair instability supernova, one has to combine a dy-
namical N-body code with a massive and very massive
star evolutionary library, that considers in detail the
importance of stellar winds and of the metallicity de-
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
favour of the dynamical ejection scenario in order to ex-
plain the runaways (space velocity larger than 30 km/s)
with a mass larger than 40 M⊙, like ζ Pup, λ Cep and
BD+43o3654. We conclude:
1. In clusters with solar or supersolar metallicity, black
holes form with a mass smaller than 70-75 M⊙, but
the formation of an intermediate mass black hole
with a mass of several 100 M⊙is less likely.
2. Due to the metallicity dependence of the stellar wind
mass loss, the occurence of pair instability super-
novae or the formation of an intermediate mass black
hole in dense clusters becomes more probable for
smaller metallicities.
3. It is plausible that at least some of the most massive
runaways, like ζ Pup, λ Cep and BD+43o3654, are
formed during a dynamical encounter of a massive
single star and a massive close binary, or by two
massive close binaries. In this case, the runaway is
the merger of 2 or 3 massive stars.
Ackowledgement
We thank Dr. Lev Yungelson who calculated the evolu-
tion of the 500 M⊙star with his version of the Eggleton
code but with our preferred stellar wind mass loss for-
malism.