NEARBY PROTOCLUSTERS AS LABORATORIES FORUNDERSTANDING STAR FORMATION ON GALACTIC SCALES

PHILIPPE ANDRÉCEA Saclay, Service d’Astrophysique, F-91191 Gif-sur-Yvette, France

Abstract. Detailed studies of nearby cluster-forming molecular clouds can help us understand thephysical processes by which most stars form in galaxies. I review recent advances made on thissubject. Submillimeter observations of nearby protoclusters suggest that stars are generally built fromfinite, detached reservoirs of mass inside molecular cloud cores, and point to a cloud fragmentationorigin for the IMF. Much progress in this field will come from future large submillimeter instrumentssuch as Herschel and ALMA.

Keywords: molecular clouds, star formation, star clusters, protostars, initial mass function, dustemission

1. Introduction

The formation of isolated low-mass stars is now reasonably well understood inoutline (e.g. Shu, Adams, Lizano, 1987; Mannings, Boss and Russell, 2000; seeSection 1.1 below). By contrast, while most stars are believed to be born in clusters(cf. Section 1.2), the formation of young stellar clusters is still poorly known (cf.Pudritz, 2001). Improving our understanding of the clustered mode of star form-ation is crucial if we are to explain the origin of the stellar initial mass function(IMF) and the birth of massive stars, two major building blocks of the evolution ofgalaxies.

1.1. MAIN CONCEPTUAL PHASES OF INDIVIDUAL STAR FORMATION

At the individual level, the formation of low-mass (M�<∼ 8M�) stars is believed to

involve a series of three, conceptually different phases (e.g. Larson, 1969; Moucho-vias, 1991; Shu et al., 1987). The first phase corresponds to the formation of one(or more) gravitationally-bound core(s)/condensation(s) inside a molecular cloudby pre-collapse fragmentation. At some point, a given pre-stellar condensation be-comes gravitationally unstable and quickly collapses to form a (possibly multiple)hydrostatic protostellar object in the center (e.g. Bate, 1998). One then enters themain protostellar accretion phase during which the central object builds up its mass(M�) from a surrounding infalling envelope (of mass Menv) and accretion disk. Theyoungest accreting protostars, corresponding observationally to Class 0 submilli-meter objects (André, Ward-Thompson, Barsony, 1993), have Menv > M�, while

Astrophysics and Space Science 281: 51–66, 2002.© 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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more evolved protostars (Class I infrared objects – Lada, 1987) have Menv < M�.These protostars radiate the accretion luminosity Lacc ≈ GM�Macc/R�. Obser-vations have shown that the main accretion phase is always accompanied by apowerful ejection of a small (∼ 10%) fraction of the accreted material in theform of prominent bipolar flows (e.g. Bachiller, 1996). These flows are believed tocarry away the excess angular momentum of the infalling matter (e.g. Königl andPudritz, 2000; Lery, this volume). The accretion/ejection rate declines with timefrom Macc ∼ 10−5 M� yr−1 at the Class 0 stage to Macc

<∼ 10−6 M� yr−1 at theClass I stage (Bontemps et al., 1996), supporting the idea that protostellar collapseis initiated in finite-sized Bonnor-Ebert cloudlets (cf. Foster and Chevalier, 1993)rather than singular isothermal spheroids (as in the ‘standard’ picture of Shu et al.,1987).

When the central object has accumulated most ( >∼ 90%) of its main-sequencemass, it becomes a pre-main sequence (PMS) star (corresponding to a Class II orClass III near-IR source – Lada, 1987), which evolves approximately at fixed masson the Kelvin-Helmholtz contraction timescale (e.g. Stahler and Walter, 1993).There is no PMS phase for stars more massive than ∼ 8M� since they begin toburn hydrogen during the protostellar accretion phase (see Palla and Stahler, 1991).

1.2. GMCS AND THE IMPORTANCE OF THE CLUSTERED MODE

On larger, galactic scales, star formation is known to occur primarily in GiantMolecular Clouds (GMCs). With M > 105 M� and R ∼ 50 pc, GMCs containmost of the mass of the molecular interstellar medium and, in spiral galaxies, arewell confined to the arms. They follow a well-defined power-law mass spectrumdN/dM ∝ M−1.6 (e.g. Blitz, 1993) and have a typical lifetime ∼ 2 × 107–108 yr. GMCs are gravitationally bound, supported against global free-fall collapseby MHD turbulence, and as a result have a hierarchical or fractal structure (cf.Williams, Blitz and McKee, 2000 for a recent review). One manifestation of theself-similar character of the structure is that the mass spectrum of the clumpsidentified within a given GMC is a universal power law, dN/dM ∝ M−1.7±0.1

(e.g. Kramer et al., 1998), essentially identical to the mass distribution of GMCsthemselves. This spectrum is such that there are many more low-mass clumps thanhigh-mass clumps, but most of the molecular mass is in the few massive clumps.By contrast, the stellar IMF follows a steeper power law above ∼ 0.5 − 1M�, i.e.,dN�/dM� ∝ M−2.5±0.2 (e.g. Salpeter, 1955, Scalo, 1998), implying that most ofthe stellar mass in galaxies is in low-mass (M�

<∼ 1M�) stars.Most of the star formation activity in a GMC is expected to take place within

its few most massive clumps since these contain the majority of the molecular gas.Direct confirmation of this came with the advent of near-IR arrays >∼ 10 years ago,which made wide-field imaging surveys of star-forming clouds possible around∼ 2µm. A good example is provided by the extensive study of L1630 (Orion B),the nearest GMC (at d ∼ 400 pc), by E. Lada and co-workers. A major portion

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of Orion B was surveyed for both dense gas in CS(2–1) (Lada et al., 1991a) andembedded young stars at 2.2 µm (Lada et al., 1991b; Li et al., 1997). Remarkably,over a spatial extent of ∼ 200 pc2 (∼ 4 deg2), the vast majority (∼ 96%) ofyoung stars were found to be concentrated within three rich clusters associatedwith three of the five most massive (M > 200M�) CS clumps, corresponding toonly 30% of the total mass of dense gas and only ∼ 1 − 2% of the cloud’s totalarea. Similar findings have been reported for other cloud complexes (e.g. Carpenter,2000). These results suggest that star formation is an inefficient, highly localizedprocess, producing most stars in compact embedded clusters, from only a smallfraction of the total gas mass available in a GMC.

That the clustered mode of star formation dominates is also demonstrated by thediscovery of near-IR aggregates of low-mass young stars (with n�

>∼ 100 stars/pc3)around PMS (Herbig Be) stars of spectral type earlier than B5 (i.e. M�

>∼ 4M�)(Testi, Palla and Natta, 1999). While most stars appear to form in groups or clusters,the majority of embedded clusters do not survive as bound open clusters, butquickly disperse in the field once their gas content has been removed (e.g. Adams,2000). Accordingly, less than ∼ 10% of all stars in the Galaxy belong to long-livedopen clusters (e.g. Adams and Myers, 2001).

Leaving aside the formation of molecular clouds (cf. Inutsuka, this volume),understanding the formation and evolution of embedded star clusters within GMCswould be a fundamental step toward explaining star formation on global, galaxyscales. Here, I first summarize two contrasted views on clustered star formation(Section 2) and then discuss the results of recent observational tests (Section 3 andSection 4).

2. Theoretical Ideas on the Formation of Protoclusters

In order for a nearly coeval cluster of stars to form, it appears that the parent cloudmust contain a large number of Jeans masses (e.g. Clarke et al., 2000). Initiallythe protocluster cloud is most likely stabilized against global free-fall collapse byinterstellar turbulence, but this support is quickly removed on small spatial scales asa result of, e.g., an external trigger or the internal dissipation of short wavelengthMHD waves (e.g. Elmegreen et al., 2000; Nakano, 1998). This leads to almostsimultaneous collapse onto a large number of gravitating centers (e.g. Bonnell etal., 1997).

2.1. THE JEANS OR KERNEL MODEL

According to one school of thought, a given protocluster condensation correspondsto the fragmentation/decoupling of one local Jeans mass in the parent cloud core(e.g. Larson, 1985; Padoan, Nordlund and Jones, 1997; Myers, 1998). Modelsbased on this idea account quite naturally for the typical mass and spacing of

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stars in embedded clusters, but have more difficulty explaining the overall dis-tribution of stellar masses. As pointed out by Larson (1999), the mass MBE =1.18 a4 G−3/2 P

−1/2ext of a critical ‘Bonnor-Ebert’ self-gravitating isothermal sphere

with sound speed a and ambient boundary pressure Pext is ∼ 0.7M� for Pext/k ∼3 × 105 cm−3 K and a cloud temperature of 10 K. Such a characteristic massagrees well with the flattening observed in the IMF of field stars below ∼ 0.5–1M� (e.g. Kroupa, Tout and Gilmore, 1993; Scalo, 1998). An attractive physicalexplanation for the required value of the external core pressure, Pext , was pro-posed by Myers (1998). In his model, protocluster condensations develop onlywithin massive, turbulent cloud cores and correspond to self-gravitating Bonnor-Ebert spheroids or ‘kernels’ of size comparable to the cutoff wavelength λA forMHD waves (see Mouschovias, 1991). The idea is that MHD (e.g. Alfvén) wavesprovide the turbulent pressure necessary to support a (cosmic-ray ionized) cluster-forming core against global collapse but cannot propagate on scales smaller thanλA ∼ 0.03 pc × ( B

30µG) × (nH2

104cm−3 )−1 because collisions are not frequent enough

to make the neutrals move with the ions. (The typical ionization degree is onlyni/nH2 ∼ 10−8 − 10−6 – e.g. Caselli et al., 1998.) Such an effect can initiate thedecoupling of several fragments or kernels of size ∼ λA providing the mediumis dense enough to be self-gravitating on that scale. This type of fragmentationcannot occur in low-pressure, low-mass cores (such as those observed in the Tauruscloud) because their self-gravitating size is larger than the cutoff Alfvén scale λA.More precisely, Myers (1998) showed that critically stable kernels exist only forambient pressures Pext

>∼ (5–10) × 105 cm−3 K, corresponding to turbulent coreswith ‘supercritical’ nonthermal linewidths �vNT

>∼ 3.5 a ∼ 0.7 − 1.0 km/s fortypical core densities ∼ 104 cm−3 and core temperatures ∼ 10 − 20 K. Sincethe cores are themselves assumed to be close to gravitational virial equilibrium,a core with critical kernels must also be ‘massive’, with a mean column densityNH2 > 1022 cm−2. Thus, Myers’ model predicts that only turbulent, massive densecores should be cluster-forming and that protocluster condensations should havemuch narrower linewidths (by a factor >∼ 2 − 3) than their parent cores.

In this picture, a whole spectrum of protostellar masses can emerge if the con-densations are allowed to grow by Bondi-type accretion before collapsing (Myers,2000), or if there is an initial spectrum of density (or pressure) fluctuations suchas in the supersonic random flow model of Padoan et al. (1997). It is also possiblethat the IMF ultimately results from the fractal nature of turbulent molecular cloudsthrough random sampling of self-gravitating gas (Elmegreen, 1999). At any rate, inthis class of models, the stellar masses are already determined prior to individualprotostellar collapse.

2.2. THE DYNAMICAL, COMPETITIVE ACCRETION PICTURE

An alternative scenario (e.g. Bonnell et al., 1997, 2001a) views a protocluster asmade up of gas and protostars, the latter traveling in the (gas-dominated) gravita-

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tional potential of the system and accreting mass at the rate Macc ∼ π ρ vrel R2acc

as they execute many orbits (ρ is the gas density, vrel the relative gas-star velocity,and Racc the accretion radius). In this view, competitive accretion and dynamicalinteractions between individual protostars play a key role in shaping the final spec-trum of stellar masses. The accretion radius is well approximated by the localtidal-lobe radius: Racc ∼ Rtidal ∼ 0.5 ( M�

Menc)1/3R�, where Menc is the mass en-

closed within the protocluster at the protostar’s position R� (Bonnell et al., 2001b).The radius Rtidal simply expresses the fact that the tidal forces exerted by thegravitational potential of the ambient protocluster limit the zone of influence ofa given protostar. The process of competitive gas accretion is highly non-uniformand depends primarily on the initial stellar position R� within the protocluster.The few protostars initially located near the center of the cluster potential accreterapidly from the start and become massive stars, while protostars in the low-densityouter regions accrete much more slowly and become low-mass stars (see Bonnellet al., 2001a for a quantitative toy model consistent with the observed IMF). Suchan effect also provides an elegant explanation for the mass segregation generallyobserved in revealed young star clusters such as the ONC in Orion (e.g. Hillenbrandand Hartmann, 1998).

As an illustration (see Figure 1), recent numerical SPH simulations show thata molecular cloud containing N Jeans masses and a spectrum of random initialdensity fluctuations (with most structure on large scales) quickly fragments andevolves (through, e.g., competitive accretion) into a filamentary network of ∼ N

interacting protostars whose mass spectrum is reminiscent of the IMF (Klessen andBurkert, 2000). In this picture, the trajectories of individual objects in the proto-cluster are highly stochastic in nature and feature close encounters, merging and/ordynamical ejections. Relatively large relative motions should thus exist betweenobjects compared to the kernel scenario of Section 2.1. Another important charac-teristic of the dynamics of a gas-dominated protocluster is that the entire system isexpected to undergo global collapse/contraction, resulting in a centrally-condensedoverall structure much like a self-gravitating isothermal sphere (cf. Adams, 2000and Bonnell et al., 2001a). Both the gas accretion and the protocluster evolutionoccur on the global dynamical timescale (cf. Figure 1).

Such a dynamical scenario has the advantage of providing potential explana-tions for the formation of both massive stars and brown dwarfs. According to Bon-nell et al. (1998), massive stars may form by collision/coalescence of intermediate-mass protostars in the central cores of rich protoclusters, where the initial stellardensity exceeds 104 stars/pc3 and the initial crossing time is much less than 106 yr.(In this case, gas accretion can make the cores contract to the point where, atn� ∼ 108 stars/pc3, protostellar collisions become very significant.) Brown dwarfs,on the other hand, might be aborted stellar embryos that were dynamically ejectedfrom multiple systems in their parent protocluster before they could accrete enoughmass to become true stars (Reipurth and Clarke, 2001).

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Figure 1. Numerical simulations of the collapse and fragmentation of a molecular cloud containing>∼ 200 Jeans masses and a Gaussian random field of density fluctuations with P(k) ∝ k−2 initially.

Protostars form in ∼ 1 − 2 global free-fall times, stream toward each other along filaments, andmerge at the intersections of filaments. (From Klessen and Burkert, 2000.)

In the original form of the competitive accretion model, the stellar mass isprimarily determined during the protostellar accretion/ejection phase, correspond-ing observationally to Class 0/Class I objects (see Section 1.1). We will see inSection 3 and Section 4 below that there are observational arguments to believethe IMF is actually fixed earlier than that. In a variant of the model, however,competitive accretion already operates at earlier stages and governs the growth ofpre-stellar condensations within a cluster-forming cloud (cf. Bonnell et al., 2001a).

3. Submillimeter Surveys of Cluster-Forming Clouds

To test the ideas outlined in Section 2 above, nearby (d <∼ 1 kpc) Galactic proto-clusters provide ideal laboratories since the sensitivity and resolution of present

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Figure 2. Cumulative mass distributions of the pre-stellar condensations found by MAN98 and Motteet al. (2001) in the ρ Oph (a) and NGC 2068/2071 (b) protoclusters (histograms with error bars).For comparison, the dotted and dashed lines show power-laws of the form N(> m) ∝ m−0.5

(typical mass distribution of CO clumps, see Blitz, 1993) and N(> m) ∝ m−1.35 (Salpeter’s IMF),respectively. The solid curve in (a) shows the shape of the field star IMF (Kroupa et al., 1993), andthe star markers represent the mass function of ρ Oph PMS objects derived from a mid-IR surveywith ISOCAM (Bontemps et al., 2001).

infrared/submillimeter instruments are such that one can study the structure andkinematics of individual objects in detail.

At d ≈ 150 pc, the ρ Oph cloud harbors the nearest example of a rich embeddedinfrared cluster, with ∼ 200 − 300 PMS objects which have a mass distributioncompatible with the field-star IMF (e.g. Luhman et al., 2000, Bontemps et al., 2001– see Figure 2a). With a stellar volume density approaching n� ∼ 103 stars/pc3, theρ Oph cluster is still >∼ 80% gas-dominated and can potentially form many morestars in the future. There is evidence that the formation of this cluster was induced

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by the passage of a compression wavefront coming from the Sco OB2 association(e.g. MAN98, Preibisch and Zinnecker, 1999). More generally, the narrow spreadin stellar ages observed in the clustered star-forming clouds of the solar neigh-borhood points to rapid star formation resulting from large-scale triggering (cf.Hartmann et al., 2001).

A complete 1.3 mm dust continuum mosaic of the ρ Oph central cloud (∼480 arcmin2) was obtained by Motte, André and Neri (1998 – MAN98) with theMPIfR bolometer array on the IRAM 30 m telescope. Wide-field (sub)mm dust mo-saics are powerful tools to characterize the column-density structure of molecularcloud cores. Based on a multi-resolution wavelet analysis (cf. Starck et al., 1998),a total of 58 starless condensations (undetected by ISOCAM in the mid-IR – cf.Bontemps et al., 2001) can be identified in the 1.3 mm mosaic of MAN98 on thesame spatial scales as protostellar envelopes (i.e., ∼ 2500–5000 AU or ∼ 15′′−30′′in ρ Oph). These starless condensations have estimated peak H2 densities rangingfrom ∼ 4 × 105 cm−3 and 2 × 108 cm−3. Their column-density profiles are re-miniscent of finite-sized Bonnor-Ebert spheroids with Rout

<∼ 5000 AU (cf. Fig 4cof MAN98). The typical pre-collapse fragmentation lengthscale derived from theaverage projected separation between condensations is ∼ 6000 AU ∼ 0.03 pc.The mass distribution of these 58 compact starless condensations, complete downto ∼ 0.1M�, is remarkable in that it mimics the shape of the stellar IMF (seeFigure 2a). In particular, it is very similar in shape to the stellar mass spectrumdetermined for the Class II PMS objects of the ρ Oph cluster from ISOCAM7/15 µm observations (Bontemps et al., 2001). Both mass spectra show a breakat ∼ 0.3–0.5 M�, indicative of a characteristic stellar/pre-stellar mass of order∼ 0.3 M�, comparable to the typical Jeans mass in the dense (nH2 ∼ 105 cm−3)DCO+ cores of the cloud (cf. Loren et al., 1990). This suggests that the starlesscondensations identified at 1.3 mm are about to form stars on a one-to-one basis,with a high ( >∼ 50%) local efficiency.

The results of MAN98 have been essentially confirmed by an independent 850µm SCUBA study of the same region with JCMT (Johnstone et al., 2000), using adifferent algorithm for analyzing cloud structure (Clumpfind – cf. Williams et al.,1994).

Other studies have found pre-stellar mass spectra consistent with the IMF. Usingthe OVRO interferometer at 3 mm to mosaic the inner 5.5′ × 5.5′ region of theSerpens cloud core, Testi and Sargent (1998) detected 26 starless condensationsabove ∼ 0.5M� and measured their mass spectrum to be dN/dM ∝ M−2.1, closeto the Salpeter IMF. More recently, Motte et al. (2001) used SCUBA to image a32′ × 18′ field at 450 µm and 850 µm around the NGC 2068/2071 protoclustersin Orion B (see Figure 3). Their images reveal a total of ∼ 70 compact starlesscondensations whose mass spectrum is again reminiscent of the IMF between∼ 0.3M� and ∼ 5M� (see Figure 2b).

By contrast, the clump mass spectrum found by large-scale CO studies of mo-lecular clouds (dN/dM ∝ M−1.7 – cf. Section 1 and Kramer et al., 1998) is much

NEARBY PROTOCLUSTERS 59

JCMTNGC2068: Dust

Figure 3. SCUBA 850 µm dust continuum map of the NGC 2068 protocluster extracted from themosaic of NGC 2068/2071 by Motte et al. (2001). A total of 30 compact starless condensations (cf.crosses), with masses between ∼ 0.4M� and ∼ 4.5M�, are detected in this ∼ 1 pc × 0.7 pc field.Note some morphological similarity with the simulations shown in Figure 1.

shallower than the IMF above ∼ 0.5M�. The difference presumably arises becauseCO clumps are primarily structured by turbulence (e.g. Elmegreen and Falgarone,1996) while submm condensations are clearly shaped by self-gravity (cf. Motte etal., 2001).

4. Kinematics of Protocluster Condensations

Investigating the dynamics of the pre-stellar condensations identified in submilli-meter dust continuum surveys is of great interest to discriminate between possibletheoretical scenarios. Interesting results have emerged from recent spectroscopicstudies using molecules such as NH3, N2H+, N2D+, and DCO+, which do notdeplete onto dust grains until fairly high densities (e.g. Bergin and Langer, 1997;Tafalla et al., 2002). As an example, Figure 4 shows an N2H+(1–0) map of theNGC 2068 protocluster obtained at the IRAM 30 m telescope (Belloche, André,Motte, in prep.). Such observations set valuable constraints on the kinematics ofprotocluster condensations (Section 4.1 and Section 4.2 below).

4.1. INTERNAL MOTIONS

First, it appears that the small-scale (∼ 0.03 pc) pre-stellar condensations ob-served in the Ophiuchus, Serpens, Perseus, and Orion cluster-forming regions arecharacterized by fairly narrow (�VFWHM

<∼ 0.5 km s−1) N2H+(1-0) line widths(e.g. Belloche et al., 2001, Myers, 2001 – see also Figure 5). For instance, the

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NGC2068: N H (1-0)2+

IRAM 30m

Figure 4. N2H+(1–0) integrated intensity map of the NGC2068 protocluster taken at the IRAM 30mtelescope in the on-the-fly scanning mode (Belloche, Andre, Motte, in prep.). Most of the protoclustercondensations identified in the 850 µm map (Figure 3) show up in N2H+(1–0), despite a factor of∼ 2 lower angular resolution.

nonthermal velocity dispersion toward the starless condensations of the ρ Ophprotocluster is about half the thermal velocity dispersion of H2 (σNT /σT ∼ 0.7– Belloche et al., 2001). This indicates that the initial conditions of individualprotostellar collapse are ‘coherent’ (cf. Goodman et al., 1998) and essentially freeof turbulence (σNT < σT ∼ 0.2 km s−1), even when the parent cluster-formingclouds/cores have relatively high levels of turbulence (σNT

>∼ 0.4 km s−1 – cf.Loren et al., 1990; Jijina et al., 1999). In some cases, the condensations are ob-served to have significantly narrower lines (by a factor ∼ 2) than their parent cores(e.g. Williams and Myers, 2000). These findings are in qualitative agreement withthe ‘kernel’ picture described in Section 2.1. At variance with the model, however,some cluster-forming cores such as Oph-E exhibit narrow, ‘subcritical’ linewidths(cf. Section 2.1), comparable to those of their own condensations, suggesting thedissipation of MHD turbulence is not the only mechanism responsible for corefragmentation. As an aside, the narrow N2H+ linewidths of the condensationsimply virial masses (Mvir ∼ 3 − 5 × Rσ 2

G) which generally agree well with the

mass estimates derived from the dust continuum. This confirms that most of thestarless submm continuum condensations are gravitationally bound and very likelypre-stellar in nature.

Second, some starless condensations show evidence of collapse motions in op-tically thick line tracers such as HCO+(3–2). As an example, toward OphE-MM2in the ρ Oph protocluster, the HCO+(3–2) line exhibits a self-absorbed, double-peaked profile with a blue peak stronger than the red peak, while small opticaldepth lines such as N2H+(101–012) are single-peaked and peak in the absorption

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Figure 5. HCO+(3–2) and N2H+(101-012) spectra observed at the IRAM 30 m telescope toward thestarless 1.3 mm continuum condensation E-MM2 identified by MAN98 in the ρ Oph protocluster.The optically thick HCO+ line is self-absorbed and skewed to the blue, which is the classical signa-ture of collapse (e.g. Evans, 1999), while the optically thin N2H+ line is narrow (�V <∼ 0.3 km s−1)indicating small levels of turbulence. (From Belloche et al., 2001.)

dip of HCO+(3–2) (see Figure 5 and Belloche et al., 2001). This type of blueasymmetry is expected in optically thick lines when a gradient in excitation tem-perature toward the center is combined with inward motions, and is now acceptedas a classical spectral signature of collapse (cf. Evans, 1999). The infall speedsderived from radiative transfer modeling are ∼ 0.1 − 0.3 km s−1 (e.g. Bellocheet al., 2001; Williams and Myers, 2000), consistent with a typical condensationlifetime ∼ 105 yr. The detection of infall motions further supports the idea that theprotocluster condensations identified in the submm dust continuum are the directprogenitors of individual Class 0 protostars or systems.

4.2. OVERALL PROTOCLUSTER KINEMATICS

Line observations can also provide information on the relative motions betweencondensations, as well as on possible global, large-scale motions in the parentprotoclusters.

For instance, Belloche et al. (2001) have analyzed the distribution of line-of-sight velocities among 45 condensations of the ρ Oph protocluster, based on Gaus-sian fits to the observed N2H+(1–0) lines. The results, illustrated in Figure 6,indicate a global, one-dimensional velocity dispersion σ1D ∼ 0.37 km s−1 aboutthe ρ Oph mean systemic velocity. Assuming isotropic relative motions, this cor-responds to a three-dimensional velocity dispersion σ3D ∼ 0.64 km s−1. With a ρOph central cloud diameter of ∼ 1.1 pc, such a small velocity dispersion implies

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Figure 6. Line-of-sight systemic velocities of the pre-stellar condensations of the ρ Oph protoclusteroverlaid on the lowest contours of the 1.3mm continuum mosaic of Motte et al. (1998). The velocit-ies were derived from hyperfine fits to N2H+(1–0) spectra. Each condensation is represented by afilled circle whose size increases with VLSR and the grey scale varies from light grey to black withincreasing Doppler shift. (From Belloche et al., 2001.)

a typical crossing time D/σ3D ∼ 1.7 × 106 yr. The crossing times determinedfor individual cores are only slightly shorter (∼ 0.6 × 106 yr). Since neither theage of the embedded IR cluster nor the lifetime of the 1.3 mm condensations canbe much larger than 106 yr (cf. Bontemps et al. 2001 and Section 4.1 above),it appears that the pre-stellar condensations do not have time to orbit throughthe protocluster gas and collide with one another (even inside individual cores)before evolving into young stars. (This would require several crossing times – cf.Elmegreen, 2001.) Similar results have been obtained for 25 condensations in theNGC 2068 protocluster (Belloche et al., in prep.). As the estimated tidal-lobe radius(cf. Section 2.2) of the ρ Oph condensations is comparable to their observed radius<∼ 5000 AU (cf. MAN98), competitive accretion may nevertheless play a role in

limiting the condensation masses.The above estimate of the velocity dispersion σ1D among the ρ Oph protocluster

condensations corresponds to a virial mass ≈ 3 × Rσ 21D/G ∼ 50 M�, which is

much less than the total gas mass ∼ 550 M� of the associated C18O cloud (cf. Wilk-

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ing and Lada, 1983) and even less than the total stellar mass of the present infraredembedded cluster (Mstars ∼ 100 M�, Bontemps et al., 2001). Since the magneticfield does not seem to be strong enough to support the cloud, this comparisonsuggests that the ρ Oph system is gravitationally unstable and possibly in a stateof large-scale, global contraction (e.g. Troland et al., 1996). Interestingly, the COand 13CO lines observed toward the ρ Oph cloud exhibit the classical signature ofcollapse (see Section 4.1 above) over most of the protocluster extent (cf. Encrenazet al., 1975), indicating a global infall speed of order ∼ 0.5 km s−1 and a contrac-tion timescale ∼ 106 yr. Evidence for large-scale collapse motions has also beenreported recently in more massive protoclusters such as NGC 2264 (Williams andGarland, 2002) and W43 (Motte, Lis, Schilke, in prep.). Such collapsing systemswill most likely form bound star clusters even if all their gas is suddenly removed(cf. Adams, 2000).

5. Conclusions and Future Prospects

Most stars in our Galaxy (and presumably other galaxies) appear to form in embed-ded clusters/aggregates of density n�

<∼ 103 objects/pc3. The study of the nearest(d <∼ 500 pc) cluster-forming clouds is thus of great interest to shed light on thephysics of the dominant mode of star formation. Recent (sub)millimeter dust con-tinuum surveys of nearby protoclusters have discovered starless condensations thatseem to be the direct pre-stellar precursors of individual (proto-)stars: their massspectrum resembles the stellar IMF. These condensations are gravitationally-bound,essentially devoid of turbulence, and sometimes already collapsing. Their observedrelative motions do not seem to be consistent with strong dynamical interactions.In qualitative agreement with the theoretical picture outlined in Section 2.1 (e.g.Myers, 1998; Padoan et al., 2001), current observations suggest the following scen-ario for the formation of low- to intermediate-mass stars in clusters. First, externalcompression and/or MHD turbulence generate a field of density fluctuations insidea molecular cloud, a fraction of them corresponding to self-gravitating fragments.Second, these fragments (or ‘kernels’) decouple from their turbulent environmentand collapse to protostars with little interaction with their surroundings. In thisview, the IMF up to ∼ 10M� is primarily determined by ‘turbulent fragmentation’at the pre-stellar stage of star formation.

The jury is still out, however, concerning the formation of stars more massivethan ∼ 10M�. While they could form in a way similar to low-mass stars, i.e.,via collapse and accretion (with a higher Macc ∼ 10−3 M� yr−1 – Maeder, thisvolume), the finding of global collapse signatures in several regions (cf. Section4.2) leaves open the possibility that some protoclusters may shrink to high enoughcentral densities (n� ∼ 104 − 108 stars/pc3) for significant collisional build-up ofmassive stars to occur (cf. Bonnell et al., 1998).

64 P. ANDRE

To fully understand how the IMF comes about, it is crucial to further investigatethe processes by which pre-stellar condensations form and evolve in molecularclouds. With present submillimeter instrumentation, however, detailed studies arelimited by small-number statistics and restricted to the nearest regions. The ad-vent of major new facilities at the end of the present decade should yield severalbreakthroughs in this area. With an angular resolution at 75–300 µm comparable to(or better than) the largest ground-based millimeter radiotelescopes, Herschel, theFar InfraRed and Submillimeter Telescope to be launched by ESA in 2007 (cf. Pil-bratt et al., 2001 and references therein), will make possible complete surveys forprotocluster condensations in the cloud complexes of the Gould Belt (d <∼ 1 kpc).

High-resolution ( <∼ 0.1′′) observations with the ‘Atacama Large Millimeter Ar-ray’ (ALMA, available around 2008 – cf. Wootten, 2001) at ∼ 450 µm–8.5 mmwill beat source confusion and allow us to probe individual condensations in dis-tant, massive protoclusters, all the way to the Galactic center and the Magellanicclouds.

Complementing each other nicely, Herschel and ALMA will tremendouslyimprove our global understanding of the initial stages of star formation in theGalaxy.

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