Massive star formation: Nurture, not nature

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by  I. A. Bonnell

Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed2February2008 (MNLaTEXstylefilev2.2)
Massive star formation: Nurture, not nature
Ian A. Bonnell1⋆, Stephen G. Vine1 & Matthew R. Bate2
1 School of Physicsand Astronomy, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS.
2 School of Physics, University of Exeter, Stocker Road, ExeterEX4 4QL
4
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0 2February2008
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n
a ABSTRACT
J We investigate the physical processes which lead to the formation of massive stars.
Using a numerical simulation of the formation of a stellar cluster from a turbulent
6
molecular cloud, we evaluate the relevant contributions of fragmentation and com-

1 petitive accretion in determining the masses of the more massive stars. We find no
v correlationbetween the final mass of a massive star, and the mass of the clump from
9 whichitforms.Instead,wefindthatthe bulkofthe massofmassivestarscomesfrom
5 subsequent competitive accretion in a clustered environment. In fact, the majority of
0 this mass infalls ontoa pre-existingstellarcluster.Furthermore,the massofthe most
1
massivestarinasystemincreasesasthesystemgrowsinnumbersofstarsandintotal
0
mass. This arises as the infalling gas is accompaniedby newly formed stars, resulting
4
in a larger cluster around a more massive star. High-mass stars gain mass as they
0
gain companions, implying a direct causal relationship between the cluster formation
/
h process, and the formation of higher-mass stars therein.
p
- Key words: stars: formation – stars: luminosity function, mass function – globular
o
clusters and associations: general.
r
t
s
a
:
v
i 1 INTRODUCTION fluenced, if not determined, by the stellar environment, a
X
stellar cluster. Individual stars compete for the reservoir of
There are currentlytwo competing ideas as to how massive
r gas(Zinnecker1982; Larson 1992), withthosesittingin the
a stars form. Do they form as essentially a scaled-up version
bottom of the potential winning the competition and thus
of low-mass stars (e.g. Shu, Adams & Lizano 1987), where
accreting more gas and attaining higher masses (Bonnell et
the star’s mass is determined by the mass in the molecular
al.1997;2001a).Inthiscase,thefinalmassesneedhavelittle
core that collapses due to its self-gravity? Alternatively, is
correlation with their initial masses, the accretion can ex-
thefinalmassofmassivestarsdeterminedthroughenviron-
plain thefullrange and distribution of stellar masses (Bon-
mental processes such as competitive accretion or mergers
nelletal.2001b).AsimilarprocesswasdiscussedbyMurray
in clusters? In the first scenario, the stellar environment is
& Lin (1996) where gas parcels were evolved under purely
unimportantandthemassisdecidedbytheamountofmass
dynamical forces until they collided and merged. Parcels
which is necessary to be self-gravitating considering either
that become gravitationally unstable collapse to form stars
thermal or turbulent support (Yorke & Kruegel 1977; Mc-
and grow in mass through further collisions with other gas
Kee & Tan 2002, 2003). Thus, high-mass clumps in molec-
parcels.
ular clouds, if they are just self-gravitating, lead directly
In both cases, the massive star grows through ac-
to high-mass stars (Padoan & Nordlund 2002). This is an
cretion onto a lower-mass protostellar core (Behrend &
attractive possibility as the high-mass tail of the clump-
Maeder 2001). One potential difficulty with accretion is
mass spectrum resembles the stellar initial mass function
that feedback in the form of radiation pressure may limit
(eg., ρ Ophiuchus; Motte, Andr´e & Neri 1998). McKee &
the mass accumulation process to masses of order ∼ 10
Tan (2003) envision that the pre-massive star clumps are
located in the high pressure regions in the centre of clus- M⊙(Wolfire&Cassinelli1987;Yorke&Kruegel1977;Edgar
& Clarke 2003), although a rapid rotation may sufficently
ters, although such a spatial segregation of massive clumps
reducethestar’sluminosityintheequatorialplane(Yorke&
is not found in the ρ Ophiuchus and Serpens protoclusters
Sonnhalter2002).Thus,moreexoticprocessessuchasstellar
(Elmegreen & Krakowski 2001).
mergersmay bepotentially requiredinordertoexplain the
In the second scenario, the star’s mass is strongly in-
formationofmassivestars(Bonnell,Bate&Zinnecker1998).
Observationally, there are a number of circumstantial
⋆ E-mail:[email protected] clues that support an environmental influence on massive
2 I. A. Bonnell et al.
starformation.Massivestarsareevenmorelikelythantheir HeitschandMacLow2000andKlessen&Burkert2001).In
low-masscounterpartstobefoundinstellarclusters(Clarke, three dimensions, this matches the observed variation with
Bonnell & Hillenbrand 2000; Lada & Lada 2003). Young size of the velocity dispersion found in molecular clouds
clusters are generally mass segregated with the most mas- (Larson 1981). The velocities are normalised to make the
sive stars found in their cores. Additionally, there is an ob- kinetic energy equal to the absolute magnitude of the po-
servationalcorrelationofthemassofintermediateandhigh- tentialenergysothatthecloudismarginallybound.Incon-
massstarswiththestellardensityofthesurroundingcluster trast, the thermal energy is initially only 1 per cent of the
(Testi, Palla & Natta 1999; Hillenbrand 1995, see Clarke et kinetic energy. The Jeans mass of the cloud is then 1M⊙,
al. 2000). For example, Testi et al. (1997, 1999) surveyed andthecloudcontains1000thermalJeansmasses.Thetur-
the environments of pre-main sequence Herbig AeBe stars bulenceleadstothegeneration ofshocks,structureandthe
and found that stars more massive than ≈ 6M⊙ are gen- dissipation ofkineticenergy(MacLow etal. 1998, Ostriker
erally surrounded by a cluster of lower-mass stars and that et al. 2001). We do not include any feedback (radiative or
the number of stars in the cluster increases with increasing kinematic) from the newly formed stars, which is a limita-
mass. This implies a potential causal relationship between tionasfeedbackfrommassivestarscanbedynamicalimpor-
thenumberofstarsin theclusterandthemassof themost tant (radiation pressure, HII regions etc). Osorio, Lizano &
massive star. The Herbig AeBe data is also consistent with D’Alessio(1999)discusshowtheincipientHIIregionfroma
random pairing from an initial mass function (IMF) (Bon- youngmassivestarcanbechokedoffthroughhighaccretion
nell & Clarke 1999) although this would not explain the rates. The simulation was carried out on the United King-
observed mass segregation in larger clusters. dom’s Astrophysical Fluids Facility (UKAFF), a 128 CPU
In this paper, we investigate the formation of massive SGI Origin 3800 supercomputer.
stars that occur in a numerical simulation of the fragmen- Dense protostellar fragments are replaced by sink-
tation of a turbulent molecular cloud and the subsequent particlesinordertofollowtheevolutionfurther(Bate,Bon-
formation of a stellar cluster (Bonnell, Bate & Vine 2003). nell&Price1995).Thesesink-particlesaccreteinfalling gas
This simulation showed that the stellar cluster, containing thatfallswithinasink-radiusof200 AUiftheyareboundto
approximately400stars,formedthroughahierarchicalfrag- thesink-particle,whereasallgasparticlesthatfallwithin40
mentationandmergingprocess.Theturbulenceleadstosev- AUare accreted,regardless oftheirproperties. Thesimula-
eralsitesofstarformation.Individualstarsforminfilamen- tionused5×105 particles,implyingaminimumprotostellar
tary structures and then fall towards their local potential massof 0.1 M⊙(e.g. Bate &Burkert1997). Fragmentswith
minima.Thisformssmall-Nsubclusterswhichgrowthrough lower-massesarenotresolvableinthissimulation.Thegrav-
accretinginfalling starsandgas.Thesubclusterseventually itational accelerations between sink-particles are smoothed
merge, aided by the dissipation of kinetic energies by the within distances of 160 AU. Stellar collisions are not in-
gas, to form one large cluster. The simulation formed six cluded in thesimulation.
stars with masses greater than 10 M⊙ with a maximum
stellar mass of ≈ 27 M⊙, ignoring any radiative feedback
(e.g. Yorke & Kruegel 1977; Yorke & Sonnhalter 2002). In
3 THE ORIGIN OF MASSIVE STARS
section 2 we detail the calculations. Section 3 investigates
theorigin, in thesimulation, ofthemassive stars.Section 4 Oneofthemajor resultsof thesimulation reported inBon-
relates the massive star formation to the process of cluster nell et al. (2003) is that the cluster formation process nat-
formation and the resultant cluster properties. We discuss urally results in a distribution of stellar masses from 0.1 to
the implications of this work for massive star formation in ≈27M⊙,withamedianmassof≈0.43M⊙,andthatagrees
Section 5 while our conclusions are given in Section 6. broadlywithobservedinitialmassfunctions.Figure1shows
the evolution of the number of stars present in the cluster
as well as the maximum and median stellar masses. The
medianmassisapproximatelyconstantthroughouttheevo-
2 CALCULATIONS
lution while both the number of stars, and the maximum
Theresultspresentedinthispaperarebasedonanumerical stellar mass, increase.
simulationperformedwiththeSmoothedParticleHydrody- Thisresult couldbemisinterpretedasbeingduetothe
namics (SPH) method (Monaghan 1992, Benz et al. 1991). random sampling from an IMF such that when more stars
Thedetailsofthissimulationhavealreadybeenpresentedin are present, the chance of having a more massive star in-
Bonnelletal.(2003),andwesummarisetherelevantdetails creases. This neglects the fact that the individual stars ac-
here.Thesimulation followed thefragmentation ofaturbu- cretemassthroughouttheevolution.Thusforexample,the
lent molecular cloud containing 1000 M⊙ in a region of 0.5 star that is the most massive star (at 5 M⊙) when ≈ 50
pc radius for 2.5t or 4.75×105 years. The gas is isother- stars are present, is the same star that ultimately is the
ff
mal at 10 K as expected for densities <∼10−13 g cm−3 (eg., mostmassivestar(at≈30M⊙)inthefinalclusterof≈400
Larson1969;Masunaga,Miyama&Inutsuka1998).Thesu- stars.
personic turbulence is modelled by including a divergence- It is not always the same star which is the most mas-
free random Gaussian velocity field with a power spectrum sive star in the system. The discontinuities in the maxi-
P(k) ∝ k−4 where k is the wavenumber of the velocity mum stellar mass indicates where different stars take over
perturbations (Ostriker, Stone & Gammie 2001). The de- being the most massive star present. We thus have a self-
pendenceof the fragmentation and resultant IMF has been consistent star formation laboratory with which to study
shown to be rather insensitive to the slope of the power massive star formation, and how individual stellar masses
spectrum(Delgado-Donate,Clarke&Bate2004;cfKlessen, aredetermined.Forexample,wecaninvestigatetheclump-
Massive star formation 3
10 clump envelope accrete
1
0.1
0.1 1 10 0.1 1 10 0.1 1 10
Figure 2. Three potential sources for the stellar masses, the clump structures in the cloud (left panel), the surrounding envelopes
(middle panel) and subsequent accretion (right panel), are plotted against the final stellar masses (all in M⊙). The clump masses and
envelopemasses(seetext) aredeterminedatthetimeofprotostar formation.Weseenocorrelationbetweentheclumpmassesandthe
finalmasses.Instead,themassesoflower-mass(m<∼M⊙)starsarelargelyduetotheenvelopemassesatthetimeofprotostarformation.
Incontrast,theformationofhigher-massstars(withm>∼M⊙)requiressubsequentaccretioninordertoexplaintheirmasses.Thesolid
linesinthemiddleandrightpanelindicateaonetoonerelationwiththefinalmass.
We estimate the clump-mass from which each star
forms,atthetimeofformation,asthemasscontainedwithin
aspherical radiuswhere thelocal gas densityis continually
decreasing. Theend of a clump is thendefinedas when the
local gas density starts to rise, or when another star is en-
countered. We see in figure 2 that there is no correlation
between these clump masses and the final stellar masses.
The clump masses extend from above our resolution limit
of 0.1M⊙ to ≈ 1M⊙. The most massive stars originate
from clumps that are near the median of the distribution
at ≈0.4M⊙, which is itself approximately the final median
stellarmassof≈0.43M⊙.Someofthemoremassiveclumps
actuallyresultinlower-massstarssuggestingeithermultiple
fragmentation or that a significant fraction of the clump is
accreted by anotherstar.
Asmentionedabove,wecanusetheLagrangiannature
of SPH to reconstruct the mass accretion history for each
star and determine where the mass originated. The middle
panel of figure 2 plots the relation between the final stellar
masses and the mass contained within an initial envelope
aroundtheformingstar.Thisenvelopeisdefinedasaspher-
Figure 1. Theevolution of the number of stars (solidline), the
maximumstellarmass(long-dashedline)andmedianstellarmass icalregioninwhichatleast99percentofthegasultimately
(short-dashed line) are plotted as a function of time in units of ends up on the star concerned. This envelope represents a
thefree-falltime(tff =1.9×105 years). ThemassesareinM⊙ mass reservoir from which the star accretes unimpeded by
and shouldbe readagainst the axis on the rightside. Note that thepresenceofotherstars.Thus,althoughit includesmass
thesamestarisnotalwaysthemostmassivestarpresent. added through accretion after protostar formation, it ex-
cludes any mass added through competitive accretion in a
cluster environment. This envelope mass can account for
masses from which the stars form and thus whether the someofthelower-mass starsbutfails torecoverthemasses
physical conditions of the pre-collapse clumps determines of themore massive stars (>∼2M⊙).Even thoughone of the
the stellar masses. Furthermore, SPH being a Lagrangian more massive stars has the most massive envelope, this en-
method,wecan traceback wherethemass, that ultimately veloperepresentsonly≈10percentofthefinalmass.There
comprises themore massive stars, originates in themolecu- is a definite trend that higher-mass stars originated within
lar cloud. moremassiveenvelopes.Aninitiallyhigher-massaidsinthe
4 I. A. Bonnell et al.
Figure 3. The cumulative mass distributionof the gas that ultimately accretes onto the most massive star is plotted as a function of
itsdistancefromthestaratthetimeofformation(solidline)inthelefthandpanel.Thedistributionwhenthisstarhas10lower-mass
companionswithin0.1parsecsisalsoplotted(dashedline).Thesamedistributionisplottedintheright-handpanelagainstthemaximum
number ofother starscontained withinthis gas (closer tothe targetstar). Thus,littlegas isabletoaccrete beforeadditional starsare
presenttocompeteforthemassreservoir.
subsequent accretion process. The right-hand panel of fig- 19 M⊙ is still veryextended,even though manyotherstars
ure 2 plots the remaining mass that therefore is accreted have since formed which make up the cluster as a whole
from regions outside this envelope and therefore from re- (Bonnell et al. 2003).
gions which contribute mass to more than one star. This The right-panelof figure3 plotsthedistribution of the
accretion accountsforthebulkofthemassofmoremassive accreted mass against the maximum number of stars that
stars. Thus we see the role played by competitive accretion lie within this gas and its target star. We can see from this
faroutweighsthatofthestructureinthemolecularcloudin figurethatthevastmajorityofthegascomesfromoutsidea
determining themasses of higher-mass stars. significant group of stars and could in principle beaccreted
Wegainabetterunderstandingofwherethemassofthe byanyof them. That thisone staris able toaccrete such a
more massive stars comes from in figure 3 which plots the significant fraction of the infalling gas is due to the nature
cumulative distribution of themass, which ultimately com- of competitive accretion in clusters. The accretion rate is
prisesthemostmassivestar,atthetimeofprotostarforma- then determined by a combination of the star’s mass and
tion. The mass distribution extends throughout the cloud, kinematics such that more massive stars, which generally
withonlyaboutathirdofthetotalmassinitiallycontained move slower, accrete at significantly higher rates than do
within 0.1 parsecs. Figure 3 also plots the cumulative mass lower-mass stars (Bonnell et al. 2001a).
distributionatatimewhenithas10otherstarsascompan- In general, the stars that eventually attain higher
ions within 0.1 parsecs, the typical size of the sublcusters masses form earlier in the simulation. This provides more
thatforminthesimulation.Evenoncethestarhas10other time for them to accrete, but more importantly, they have
starsinitssubcluster,thebulkofthestar’smassisatlarge less competition initially such that they are already more
distances and has to be accreted from outside the system. massive than the average star by the time they have many
This can be seen from Figure 4 that shows the spatial dis- companions. They are then more likely to accrete enough
tributionofthemassthatultimatelyisaccretedbythisstar gas to become massive stars. Thus, five of the six highest
at four different epochs, protostar formation (t = 0.66tff, massstars(withm>∼10M⊙)formoutoftheinitial50stars,
t =1.9×105 years), when the star has 10 and 25 neigh- but thereremain many low-mass stars amongst these50.
ff
bourswithin0.1parsecs(attimes1and1.15t andmasses
ff
of 4.42 and 5.86M⊙), and when the star attains a mass of
≈8M⊙ (at t=1.3tff). 4 MASSIVE STARS AND CLUSTER
At the time of protostar formation (upper-left panel),
FORMATION
thereisonly oneotherstar presentin thesystem and there
is a well defined clump around the forming star. The gas is In the previous section we have seen that massive stars ac-
extendedovermuchofthevolumefromwhichtheclusteras cretethemajority oftheirmasscompetitively,thatiswhen
awholeultimatelyforms.Themassdistributionisstillvery other stars are present in a clustered environment and the
extended when 10 and 25 companion stars are contained gas infalls from outside the cluster (Figs. 3 and 4). Shock
within 0.1 parsecs. By the time the star has accreted up to dissipation results in a decrease in theturbulentsupport in
≈8M⊙,thegas distributionwhichmakesuptheremaining the cloud (Mac Low et al. 1998; Ostriker et al. 2001), al-
Massive star formation 5
Figure 4.Thespatialdistributionofthecolumndensity ofthegas that accretes onto themostmassivestar isshownatfourdifferent
times. Each panel shows a region 0.8 parsecs on a side centred on the star concerned. The upper-left panel shows the distribution at
the time the star forms (t = 0.66tff = 1.26×105 years). Note there is only one pre-existing star. The upper-right panel shows the
distributionwhenthestarhas10companionswithin0.1parsecsandamassof4.42M⊙ (t=1tff =1.9×105 years)whilethelower-left
panelshowsthedistributionwhenthestarhas25companionswithin0.1parsecsandamassof5.86M⊙ (t=1.15tff =2.19×105 years).
The lower-right panel shows the distribution once the star has accreted up to 8M⊙ and is now part of a rich cluster containing many
tensofstars(t=1.3tff =2.46×105 years).
lowing the gas to infall into the potential wells formed by linkedtotheformationofthemassivestarstheclusterscon-
the stellar clusters. This gas accretion into the cluster, and tain.Figure5showsthesubclusteringat t=1.4tff,roughly
ultimately ontothemost massivestar, mustalso beaccom- half-way through the simulation and at a time where 244
panied by any stars that form in this infalling gas (Fig 4). stars have formed. We see that the system is highly sub-
This then links the formation of the stellar cluster and the clustered and that there is a relatively massive star (m≥5
formation of themassive stars therein. M⊙)inthecentreofeachsubcluster.Inthissection,weex-
plore the interelation between massive star formation and
AsreportedinBonnelletal.(2003),thesimulationpro- theformation of a stellar cluster.
ducedanumberofsubclusterswhichevolvedindependently
beforemerging toform thefinalcluster.This providesmul- For what follows, we definea cluster size of 0.1 parsecs
tiple sites to assess how the formation of a stellar cluster is radius. We then evaluate, for each star, how many other
6 I. A. Bonnell et al.
Figure 5. The positions of the stars formed by t=1.4tff areplotted in the leftpanel, whiletheir local stellar densities, as a function
of their radius from the centre of mass, are shown at the same time in the right panel. The local stellar density is calculated as the
regionrequiredtohave10neighbours.Starsmoremassivethan5M⊙ aredenotedbythesolidtriangles.Weseefromthisthatthemore
massivestarsarelocatedinthecentreofindividualsubclusters.
stars are in this region and whether the star considered is
themost massiveofallitscompanions.InFigure6,weplot
theevolutionoffivestarswhichspendsignificantamountsof
timeasthemostmassivestarintheirsubcluster.Thenum-
berofcompanion stars within0.1 parsecsisplottedagainst
themassofthismostmassivestar.Starsstartoutwithlow
masses and evolve to higher masses due to gas accretion.
Whennew,lower-masscompanionsenterwithin0.1parsecs,
thestarmovesupwardstowardshavingmorecompanions.If
ahigher-masscompanionentersthisvolume,thentheorigi-
nalstarbeingconsidered isnolongerthemostmassivestar
in its group and is then no longer plotted.
Weseethatthegeneralevolutionisfromlow-massstars
with few companions towards high-mass stars with a hun-
dred or more companions. This tells us that as the most
massivestargrowsbyaccretingthegasthatinfallsontothe
cluster(Fig.3),thesub-clustergrowsbygainingmorestars.
Figure6showsanearlylinearrelation(M ∝N )be-
max comp
tween the numberof companions and themass of the most
massive star. Thus, lower-mass stars are not the most mas-
sivestarsinrichclusters,norarehigher-massstarsgenerally Figure 6.Theevolutionoffivedifferent stars,that areeach, at
found in isolation orin sparsely populated clusters. Indeed, leasttemporarily,themostmassivestarintheirsubclusterofsize
no stars more massive than ≈ 5M⊙ are found in relative 0.1 parsecs, is shown in the plane of the number of companions
isolation ( <0.1 parsecs of another star) in the simulation. vsthemassofthemostmassivestar.
There are a number of stars that form in relative isolation,
but they neverattain a significantly high mass.
The underlying explanation for the correlation evident
in Figure 6 between the number of stars in the cluster and numbers.Some starsactually form insideournominal clus-
the mass of the most massive star is simply that both are ter radius from the infalling gas. The infalling and newly
due to the same process. Gas infalls onto the local poten- formed stars are generally lower-mass stars maintaining a
tial minimum, which is the stellar cluster. This gas forms low median stellar mass (≈ 0.5 M⊙). The correlation must
a reservoir of mass from which the stars accrete competi- then arise as the star formation is inefficient but converts
tively.Themost massive star’wins’ thecompetition dueto anapproximatelyconstantmass-fractionoftheinfallinggas
itsmassandlocationinthecentreofthesubcluster(Bonnell into stars. The remaining mass provides the gas reservoir
etal.2001a).Atthesametime,thegasisformingadditional from which the individual stars accrete allowing some to
stars,whichtheninfallintothecluster,increasingthecluster attain high masses.
Massive star formation 7
Eachsubclusterevolvesbyaccretingstarsandgasfrom
thesurroundingcloud.Thestarsaretypicallylow-massstars
ofmedianmass≈0.5M⊙,similartotheclumpmassesfrom
which they form. Along with thestars, gas also infalls onto
the system. Competitive accretion will occur such that the
more massive, slower moving, and more centrally located
stars benefit and accrete mass at higher rates (Bonnell et
al.1997,2001a).Competitiveaccretioninthevirialisedcores
of clusters naturally yields a Salpeter-like IMF for higher
mass stars while subvirial infall into thecluster yields shal-
lowerIMFforlower-massstars(Bonnelletal.2001b).That
thisprocessoccursapproximatelyindependentofthesizeof
the system explains the general evolution found in figure 7
for the individual subclusters. We thus find a direct rela-
tionship between the process which builds clusters and the
mass accretion which forms themost massive star.
Inordertoexplainthehigh-massendofthemassspec-
trum, the infalling gas must comprise a sufficient reservoir
toproduceameanstellar massapproximatelytwicethatof
the median stellar mass. This implies that at most half of
the infalling mass can be in gravitationally bound and col-
Figure7.Thetotalmassincompanions(within0.1pc)isplotted
lapsingclumps.Thisthenleavesatleasthalfofthemassto
as a function of the most massive star in this subcluster for the
same five stars as in Figure 6. Note that the companion mass beaccreted by theindividual stars of thecluster.
doesnotincludethemassofthemostmassivestaritself.Theline
showsacorrelationofthemostmassivestar’smassasafunction
ofthemassincompanionstarsasM∗∝Ms2t/a3rs.
5 DISCUSSION
In this paper we have investigated how massive star for-
4.1 Cluster properties and the IMF
mation occurs in the context of one numerical simulation.
Inthissectionweinvestigatehowthemassofthemostmas- Thisisundoubtablynottheonlyenvironmentinwhichone
sive star grows relative to the total mass in stars in each couldimage massivestarformation occurring. Theprimary
system. Observed stellar clusters show a clear correlation assumptionsofthesimulationarethemeanJeansmass[the
of total mass as a function of the mass of the most mas- minimum mass to be gravitationally bound] in the cloud,
sive star in the system (e.g. Larson 2003). This correlation the total number (1000) of such Jeans masses in the cloud,
couldevenextendouttomuchhighermasssystemscontain- andthatthecloudisglobally supportedbyturbulencewith
ingintermediateandsupermassiveblackholes(Larson2003; thepowerspectrumprescribedin§2.Thefirsttwowerecho-
Clarke2003).Itisalsoofinterestasoneexpectsthatacom- sen in order that the mean stellar mass be similar to that
petitive accretion model naturally results in a similar mass found in the field and star forming regions as well as the
spectrum independent of thesize of the cluster. Galaxy as a whole. The second assumption is a requisite in
Foreachsubcluster,weevaluatethetotalmassincom- order for fragmentation to form sufficient numbers of stars
panion stars within 0.1 parsecs of the most massive star tobeastellarcluster.Theexactnatureoftheturbulenceis
therein.Weexcludethemassofthemostmassivestarinthis a more difficult manner, although its justification is due to
total. The evolution of the total companion mass is plotted theobservedline-widthsizerelationshipofmolecularclouds
against themostmassivestar’smassinfigure7,forthefive (Larson1981). Changingthepowerspectrumcanaffect the
most massive stars that spend significant amounts of time fractionofgasinclumpsandhencetheamountleft-overfor
as the most massive in theirsystems. competitive accretion (Klessen, Heitsch & Mac Low 2000).
Once again we see a strong correlation between these Thus,although this could increase themaximum mass pro-
two quantities with the general evolution of an increasing duced by the fragmentation, it would most likely be at the
mass in companion stars as the maximum stellar mass in- costofthelower-massmassspectrum.Wecanthereforecon-
creases. The five systems evolve along similar slopes in the cludethatcompetitiveaccretionmustplayaroleinthefor-
diagram even though one of thesystems is significantly un- mation of massive stars unless they form in isolation (away
derpopulated in numbers of companion stars, and in their from low-mass stars).
total mass. The rapid rise in companion mass in the up- It is worth noting here that we have not included any
per right-hand part of the diagram occurs near the end of radiativefeedbackfromthemassivestars(Yorke&Sonnhal-
the evolution when the systems merge. Otherwise, the gen- ter 2002; Edgar & Clarke 2003), nor have we investigated
eral evolution is along a slope given by M ∝ M3/2 the likelihood of direct collisions in massive star formation
stars max
or M ∝ M2/3 . Interestingly, this result is basically (Bonnell, Bate & Zinnecker 1998; Bonnell & Bate 2002).
max stars
what one expects for the relation between the mass of a Radiation pressure on dust could halt infall for stars more
systemanditsmostmassivecomponentwhentheyfollow a massive than 10M⊙, limiting the masses of the most mas-
Salpeter-type IMF (Larson 2003, Clarke 2003). Thus, each sivestars. Wewould still get thesame trend found herefor
individual system is evolving in a manner consistent with intermediate-mass stars. Furthermore, even with the gravi-
populating a Salpeter-like IMF. tationalsoftenningused,stellardensitiesreachedmaximum
8 I. A. Bonnell et al.
values of ≈ 107 stars/pc−3, which is near the threshold for EdgarR.,ClarkeC.,2003, MNRAS,338,962
collisions. Thus it is conceivable that stellar mergers may ElmegreenB.G.,KrakowskiA.,2001,ApJ,562,433
play a role in massive star formation. HillenbrandL.A.,1995,PhDthesis,UniversityofMassachusetts,
Amherst.
KlessenR.S.,BurkertA.,2001,ApJ,549,386
KlessenR.S.,HeitschF.,MacLowM.,2000, ApJ,535,887
6 CONCLUSIONS
LadaC.J.,LadaE.A.,2003,ARA&A,inpress
LarsonR.B.,1969,MNRAS,145,271
The formation of massive stars is intricately linked to the
LarsonR.B.,1981,MNRAS,194,809.
formation of stellar clusters. Using a numerical simulation
LarsonR.B.,1992,MNRAS,256,641
of the formation of a stellar cluster from the fragmentation
LarsonR.B.,2003,inGalacticStarformationAcrosstheStellar
of a turbulent molecular cloud, we show that massive stars
MassSpectrum,ASPConferenceSeries,ed.J.M.DeBuizer,
do not owe their masses to the pre-collapse clump masses. p.65
Massive star formation is not just a scaled-up version of Mac Low M., Klessen R. S., Burkert A., Smith M. D., 1998,
low-mass star formation. Instead, their masses are due to PhRvL,80,2754
subsequent infall from outside the subcluster in which the MasunagaH.,MiyamaS.M.;Inutsuka, S.,1998,ApJ,495,346
massive star resides. The mass of the most massive stars is McKeeC.,TanJ.,2002,Nature,416,59
thereforeprimarilyduetocompetitiveaccretioninacluster McKeeC.F.,TanJ.C.,2003,ApJ,585,850
MonaghanJ.J.,1992,ARA&A,30,543.
environment(Bonnelletal.2001a).Evenrelativelylow-mass
stars(withm>∼0.5M⊙derivethemajorityoftheirmassfrom MMoutrtreayFS.,.ADn.,drL´einP.D,.NNer.iCR.,.,11999968,,AAp&J,A4,6373,67,21850
competitive accretion.
OsorioM.,LizanoS.,D’AlessioP.,1999, ApJ,525,808
The infalling gas is accompanied into the subcluster
OstrikerE.C.,StoneJ.M.,GammieC.F.,2001,ApJ,546,980.
by newly formed stars. Thus, an individual cluster grows PadoanP.,Nordlund˚A.,2002,ApJ,576,870
in numbers of stars as the most massive star increases in ShuF.H.,AdamsF.C.,LizanoS.,1987, ARA&A,25,23
mass. Thisresultsinadirect correlation similar tothatob- TestiL.,PallaF.,PrustiT.,NattaA.,MaltagliatiS.,1997, A&A,
servedinHerbigAeBestars(Testietal.1997, 1999; Hillen- 320,159.
brand1995, see Clarkeet al.2000), and providesaphysical TestiL.,SargetA.I.,OlmiL.,OnelloJ.S.,2000,ApJL,540,L53
alternative to a probabilistic sampling from an IMF (Bon- WolfireM.G.,CassinelliJ.P.,1987, ApJ,319,850
YorkeH.W.,Sonnhalter C.,2002, ApJ,569,846
nell & Clarke 1999). Lastly, we find that the mass of the
YorkeH.W.,KruegelE.,1977,A&A,54,183
most massive star in each subsystem is linked to the total
ZinneckerH.,1982,inSymposiumontheOrionNebulatoHonour
mass in stars that the system contains. This is due to the
HenryDraper,edsA.E.Glassgoldetal.,NewYorkAcademy
natureofcompetitiveaccretion inproducingaSalpeter-like
ofSciences, p.226
IMF in individual systems.
ACKNOWLEDGMENTS
The computations reported here were performed using the
U.K.Astrophysical Fluids Facility (UKAFF).
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