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Modes of Star Formation and the Origin of Field Populations
ASP Conference Series, Vol. XXXX, 2001
E. K. Grebel and W. Brandner, eds.
Star Formation in Clusters: Subclustering, Cloud
Fragmentation and the Origin of the Stellar IMF
Leonardo Testi
Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I­50125 Firenze,
Italy
Abstract. We review recent high spatial resolution millimeter contin­
uum and spectral line observations of (proto­)cluster regions. These ob­
servations reveal that the mass distribution of prestellar cores is consistent
with the initial mass function for field stars suggesting that the IMF is
connected to the molecular clouds structure or the cloud fragmentation
processes, rather than the details of the star formation mechanism. We
discuss the evidence for at­birth subclustering independently obtained for
two separate protoclusters. The presence of subclustering within coher­
ent subclumps suggests that the fragmentation process is hierarchical and
that young stellar clusters are assembled by independent substructures.
The local (proto­)stellar density and star formation efficiency within the
subclusters are much higher than the average values for the entire star
forming cloud. Unfortunately, current observations are sparse and limited
to the nearest star forming regions, for spatial resolution and sensitivity
considerations, the future millimeter wave arrays, especially ALMA, will
allow to expand considerably the sample of observed regions.
1. Introduction
There is now a fairly robust theory of how isolated, low­mass stars form (e.g.
Shu et al. 1987; 1993). One notable omission, is the failure to predict the
resulting stellar masses. Stars in the field are known to be distributed according
to a well defined mass function (e.g. Salpeter 1955; Kroupa et al. 1993), and
a complete theory of star formation should explain this mass distribution, the
Initial Mass Function (IMF). Since it now seems very likely that most stars form
in clusters rather than in isolation (Clarke et al. 2000), the way in which the IMF
originates must be closely related to the way stars form in clusters. Indeed, young
embedded clusters appear to be populated by stars with a mass distribution very
close to that observed in the solar neighbourhood (Hillenbrand 1997).
The different theories of the IMF have been recently reviewed by several
authors (e.g. Elmegreen 2001), two different phylosophies are generally consid­
ered: i) the observed distribution of stellar masses may result naturally from the
protostellar accretion process, such as due to feedback effects (e.g. Fatuzzo &
Adams 1996) or competitive accretion (Bonnell et al. 1997), alternatively, ii) it
may be related to the molecular clouds structure and fragmentation processes
(Elmegreen 2000; Myers 2000; Padoan & Nordlund 2001). If the fragmentation
1

2
hypothesis is correct, the mass distribution of prestellar condensations in cluster­
forming molecular cores should follow the IMF of the stars in young embedded
clusters and in the field. Millimeter wavelength interferometry offers both a high
spatial resolution and high sensitivity that are critical to shredding light on this
problem. At 3 mm the thermal emission from dust in the condensations is prob­
ably optically thin, allowing a reasonable estimate of clump masses, and thus
an insight into the clump mass spectrum. High resolution imaging of extended
areas of the sky at millimeter wavelengths can be performed by means of the
multi­field interferometric imaging technique (see Testi & Sargent 2000 for its
implementation at the OVRO array). In addition, an interferometer provides
simultaneous observations of molecular line and broad band continuum emis­
sion. Any contamination of the continuum flux by molecular line radiation can
therefore be eliminated. Finally, thanks to the interferometric filtering capa­
bility, smooth, extended emission from the molecular cloud in which cores are
embedded is resolved out.
Using the Owens Valley Radio Observatory millimeter wave array, we have
begun a program of high resolution, millimeter­wave mapping of molecular cloud
cores with a view to establishing whether the prestellar clump mass function and
the IMF are in general similar. Here we review our results for the Serpens star­
forming core (Testi & Sargent 1998, Testi et al. 2000). The results of other
surveys towards other regions as well as the promise of the next generation of
millimeter arrays (ALMA) are also discussed.
2. The Serpens core
At a distance of 310 pc (de Lara et al. 1991), and with an angular extent of few
arcmin (Loren etal. 1979), the Serpens molecular core is an ideal target to search
for compact prestellar and protostellar condensations. Inside the 500­1500 M fi
core is a young stellar cluster of approximate mass 15­40 M fi (Giovannetti et
al. 1998), while far­infrared and submillimeter observations reveal the presence of
a new generation of embedded objects (Casali et al. 1993; Hurt & Barsony 1996).
At low spatial resolution (¸ 50 00 ) the Serpens core appears as a massive
rotating molecular clump which is fragmented in two main sub­clumps with
size­sclae of ¸0.2 pc, each with a remarkable internal velocity coherence (Testi
et al. 2000; Olmi et al. 2001). Our millimeter interferometric observations in
the 99 GHz continuum and CS(2--1) line cover the inner regions of the clump
and encompass all the sub­clumps structures seen at low spatial resolution. The
details of the observations are given elsewhere and will not be reviewed here (see
Testi & Sargent 1998; 2000).
The 3 mm continuum high resolution mosaic (Fig 1) further resolve the
structure of the clump in a large number (¸30) of cores. The mass of each
of the dust condensations in Figure 1 can be calculated, assuming reasonable
values for the parameters of the emitting dust (see Testi & Sargent 1998 for de­
tails). Using existing near­ and far­infrared observations (Givannetti et al. 1998;
Hurt & Barsony 1996), the few condensations associated with already formed
stars were eliminated from our list of candidate prestellar and protostellar can­
didates. Figure 2 displays the cumulative mass spectrum for the remaining 26
continuum sources above a the ¸4.5oe peak threshold of 4 mJy/beam. This mass

3
Figure 1. The 3 mm continuum hybrid mosaic of the Serpens core
(Testi & Sargent 1998). The rms in the map is ¸ 0:9 mJy/beam, and
the synthesised beam, indicated by a black ellipse in the lower right
corner, is 5:5 00 \Theta 4:3 00 FWHM. Submillimeter and far­infrared sources
from Casali et al. (1993) and Hurt & Barsony (1996) are indicated.
distribution is well fitted by a power law dN=dM ¸ M \Gamma2:1 , significantly steeper
than the mass spectrum of larger­scale gaseous clumps in molecular clouds
dN=dM ¸ M \Gamma1:7 (Williams et al. 2000), which is rejected by the Kolmogorov­
Smirnov test at the 98% confidence level. Our power law exponent, \Gamma2.1, is
close to the Salpeter (1955) IMF value, \Gamma2.35, and very similar to that sug­
gested recently by Kroupa et al. (1993, see also his review in this volume) for
solar and slightly subsolar stellar masses. The inferred masses and sizes of the
cores suggest that these are self gravitating and are going to be the progenitors
of individual stellar systems (single or multiple stars). Our result are supported
by the findings by Motte et al. (1998), their IRAM­30m 1.3 mm continuum
maps of ae­Ophiuchi, another cluster forming core, show that the mass spectrum
of the prestellar and protostellar clumps within the core appear consistent with
the IMF. Taken together these observations provide compelling evidence for a
``clump fragmentation'' origin for the stellar IMF.
3. Hierarchical fragmentation and sub­clustering
In Figure 3 we show the OVRO CS(2--1) integrated intensity and first moment
mosaics for the Serpens core. Most of the extended emission seen in the single
dish maps (McMullin et al. 1994; 2000; Olmi et al. 2001) is missing, probably
because the optically thick, extended, molecular line emission is resolved out by
the interferometer. Most of the CS(2--1) emission we detect appears to be due

4
Figure 2. Cumulative mass spectrum of the protostellar and prestel­
lar cores found in the 3 mm continuum mosaic shown in Figure 1.
The dotted line is the best fitting power law dN=dM ¸ M \Gamma2:1 , the
dashed line shows the Salpeter IMF, and the dot­dashed line depicts
the power law typical of gaseous clumps in molecular clouds, rejected
by the Kolmogorov­Smirnov test at the 98% confidence level (Testi &
Sargent 1998).
Figure 3. a) The OVRO CS(2--1) integrated intensity contour map at
5 00 :5 \Theta 4 00 :3 resolution, superposed on the millimeter continuum mosaic.
b) CS(2--1) first moment map, the direction of optical and near infrared
outflows are marked (adapted from Testi et al. 2000).

5
to the known outflow sources. This interpretation is confirmed by the coinci­
dence of the CS features with emission of molecular tracers enhanced in outflow
regions. In Figure 3 we indicate these outflows along with their approximate
orientations (Testi et al. 2000; Olmi et al. 2001; but see also Wolf­Chase et
al. 1998; Hogerheijde et al. 1999).
We find that the millimeter continuum cores are mostly confined within the
two subclumps detected in the large scale molecular line emission. Moreover,
the direction of the flows from the protostars within a single subclump are well
aligned (Figure 3). These findings together with the internal velocity coherence
of the subclumps suggest a hierarchical picture for the fragmentation of the
molecular cloud, in which coherent velocity structures (the sub­clumps) fragment
to form the millimeter continuum cores, which are the progenitors of single stellar
systems. Thus, within each of the sub­clumps an independent sub­cluster of
protostars is being assembled. A similar behaviour is also observed in the ae­Oph
cluster, where Johnstone et al. (2001) noted a sub­clustering of the prestellar
cores over the same scale length observed in Serpens, ¸ 0:2 pc. It is interesting
to note that this scale­length is of the same order as the scale­length of the
externally driven shear flow turbulence in non star­forming clouds, i.e. clouds
without an internal perturbance (LaRosa et al. 1999). It is, however, premature
at this point to argue if and how this process may affect star formation in
molecular clouds.
The picture that comes out is that of a stellar cluster being assembled in
denser subclusters that eventually will merge during the dynamical evolution
of the (proto­)cluster on a timescale of a few million years (Testi et al. 2000;
Clarke et al. 2000). An important consequence of this view is that even though
the average (proto­)stellar density of the (proto­)cluster and the total star for­
mation efficiency of the parent cloud are both rather low, the local density and
star formation efficiency are expected to be much higher. In the case of the
Serpens, while the average (proto­)stellar density and star fromation efficiency
are ¸400 ?/pc 3 and Ÿ 2 \Gamma 5%, both are a factor of ¸10 higher in the sub­clusters
(Testi et al. 2000).
The conclusions, although consistently supported by independent observa­
tions of two different regions, are, however, preliminary, since the results of the
surveys may be vitiated by small number statistics. Combined millimeter and
infrared surveys of a larger number of cluster forming cores are necessary to en­
sure the required statistical significance. We note that in this respect the next
generation millimeter arrays will be the ideal instruments to attain the required
resolution and sensitivity. In fact, at the low resolution attainable with single
dish instruments, it is not possible to resolve the parent cores of each individual
star, and the mass distribution of the large scale gaseous clumps in molecular
clouds is recovered (e.g. Tothill & White 2000). A tremendous advance is ex­
pected from the next generation millimeter array (ALMA). At the sensitivity,
frequency coverage and spatial resolution of the ALMA baseline array, it will
be possible to map at the same linear resolution and mass sensitivity than the
Serpens OVRO mosaic the giant star forming regions (e.g. 30 Doradus) in the
Large Magellanic Cloud, it will thus be possible to probe the initial conditions
for star formation beyond our own galaxy.

6
Acknowledgments. The Owens Valley millimeter­wave array is supported
by NSF grant AST­96­13717. Research on the formation of young stars and
planets is also supported by the Norris Planetary Origins Project. Funding
from the C.N.R.--N.A.T.O. Advanced Fellowship program and from NASA's
Origins of Solar Systems program (through grant NAGW--4030) is also gratefully
acknowledged.
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