ARlogo Annu. Rev. Astron. Astrophys. 2012. 50:531-608
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4.1. Outline of low-mass star formation

The formation of low-mass stars can be studied in greatest detail because it occurs in relatively nearby clouds and sometimes in isolation from other forming stars. The established paradigm provides a point of comparison for more massive, distant, and clustered star formation.

Physically, an individual star forming event, which may produce a single star or a small number multiple system, proceeds from a prestellar core, which is a gravitationally bound starless core (see § 2.2, di Francesco et al. 2007 for definitions), a dense region, usually within a larger molecular cloud. Prestellar cores are centrally condensed, and can be modeled as Bonnor-Ebert spheres (Ward-Thompson et al. 1999; Evans et al. 2001; Kirk et al. 2005), which have nearly power-law (n(r) ∝ r-2) envelopes around a core with nearly constant density.

Collapse leads to the formation of a first hydrostatic core in a small region where the dust continuum emission becomes optically thick; this short-lived core is still molecular and grows in mass by continued infall from the outer layers (Larson 1969; Boss & Yorke 1995; Omukai 2007; Stahler & Palla 2005). When the temperature reaches 2000 K, the molecules in the first hydrostatic core collisionally dissociate, leading to a further collapse to the true protostar, still surrounded by the bulk of the core, often referred to as the envelope. Rotation leads to flattening and a centrifugally supported disk (Terebey et al. 1984). Magnetic fields plus rotation lead to winds and jets (Shang et al. 2007; Pudritz et al. 2007), which drive molecular outflows from young stars of essentially all masses (Arce et al. 2007; Wu et al. 2004).

Stage 0 sources have protostars, disks, jets, and envelopes with more mass in the envelope than in the star plus disk (Andre et al. 1993). Stage I sources are similar to Stage 0, but with less mass in the envelope than in star plus disk. Stage II sources lack an envelope, but have a disk, while Stage III sources have little or no disk left. There are several alternative quantitative definitions of the qualitative terms used here (Robitaille et al. 2006; Crapsi et al. 2008).

Stages I through III are usually associated with SED Classes I through III defined by SED slopes rising, falling slowly, and falling more rapidly from 2 to 25 µm (Lada & Wilking 1984). A class intermediate between I and II, with a slope near zero (Flat SED) was added by Greene et al. (1994). In fact, orientation effects in the earlier stages can confuse the connection between class and stage; without detailed studies of each source, one cannot observationally determine the stage without ambiguity. For this reason, most of the subsequent discussion will use classes despite their questionable correspondence to physical configurations. Evans et al. (2009) give a historical account of the development of the class and stage nomenclature.

For our present purposes, the main point is to establish time scales for the changing observational signatures, so the classes are useful. Using the boundaries between classes from Greene et al. (1994), Evans et al. (2009) found that the combined Class 0/I phases last ~ 0.5 Myr, with a similar duration for Flat SEDs, assuming a continuous flow through the classes for at least the Class II duration of 2± 1 Myr (e.g., Mamajek 2009), which is essentially the age when about half the stars in a dated cluster lack infrared excesses; hence all durations can be thought of as half-lives.

To summarize, we would expect a single star-forming core to be dominated by emission at far-infrared and submillimeter wavelengths for about 0.5 Myr, near-infrared and mid-infrared radiation for about 1.5 Myr and near-infrared to visible light thereafter. However, the duration of emission at longer wavelengths can be substantially lengthened by material in surrounding clumps or clouds not directly associated with the forming star.

The star formation rates and efficiencies can be calculated for a set of 20 nearby clouds (⟨d⟩ = 275 pc) with uniform data from Spitzer. The star formation rate was calculated from equation 9 and the assumptions in § 3.1 by Heiderman et al. (2010), who found a wide range of values for dot{M}*, with a mean value for the 20 clouds of dot{M}* = 39 ± 18 M Myr-1. The star formation efficiency (є = M* / (M* + Mgas)) can only be calculated over the last 2 Myr because surveys are incomplete at larger ages; averaging over all 20 clouds, only 2.6% of the cloud mass has turned into YSOs in that period and ⟨Σ(SFR)⟩ = 1.2 M yr-1kpc-2 (Heiderman et al. 2010). For individual clouds, є ranges from 2% to 8% (Evans et al. 2009; Peterson et al. 2011). The final efficiency will depend on how long the cloud continues to form stars before being disrupted; cloud lifetimes are poorly constrained (McKee & Ostriker 2007; Bergin & Tafalla 2007), and they may differ for clouds where massive stars form.

For comparison to extragalactic usage, the mean tdep = 1 / є (§ 1.2) is about 82 Myr for seven local clouds, longer than most estimates of cloud lifetime, and much longer than either ⟨tff⟩ (1.4 Myr) or ⟨tcross⟩ (5.5 Myr) (Evans et al. 2009). The ⟨tdep⟩ for local clouds is, on the other hand, about 10% of the tdep for the MW molecular gas as a whole (§ 5.1).

4.2. Formation of Clusters and High-mass Stars

The study of young clusters provides some distinct opportunities. By averaging over many stars, a characteristic age can be assigned, with perhaps more reliability than can be achieved for a single star. As noted (§ 4.1), the set point for ages of all SED classes is determined by the fraction of mid-infrared excesses in clusters. This approach does implicitly assume that the cluster forms "coevally", by which one really means that the spread in times of formation is small compared to the age of the cluster. Because objects ranging from prestellar cores to Class III objects often coexist (Rebull et al. 2007), this assumption is of dubious reliability for clusters with ages less than about 5 Myr, exactly the ones used to set the timescales for earlier classes. Note also that assuming coeval formation in this sense directly contradicts the assumption of continuous flow through the classes. We live with these contradictions.

Most nearby clusters do not sample very far up the IMF. The nearest young cluster that has formed O stars is 415-430 pc away in Orion (Menten et al. 2007; Hirota et al. 2007), and most lie at much larger distances, making study of the entire IMF difficult.

Theoretically, the birthplace of a cluster is a clump (Williams et al. 2000). The clumps identified by 13CO maps in nearby clouds are dubious candidates for the reasons given in § 2.5. The structures identified by Kainulainen et al. (2009) in the power-law tail of the probability distribution function are better candidates, but most are still unbound. Objects found in some surveys of dust continuum emission (§ 2.3) appear to be still better candidates. For example, analysis (Schlingman et al. 2011; Dunham et al. 2011b) of the sources found in millimeter-wave continuum emission surveys of the MW (§ 2.3) indicates typical volume densities of a few × 103 cm-3, compared to about 200 cm-3 for 13CO structures. Mean surface densities are about 180 M pc-2, higher than those of gas in the the power-law tail (Σgas ~ 40-80 M pc-2). These structures have a wide range of sizes, with a median of 0.75 to 1 pc.

Studies of regions with signposts of massive star formation, using tracers requiring higher densities (e.g., Plume et al. 1992; Beuther et al. 2002) or millimeter continuum emission from dust (e.g., Beuther et al. 2002; Mueller et al. 2002) have identified slightly smaller structures (r ~ 0.5 pc) that are much denser, indeed denser on average than cores in nearby clouds. In addition to having a mass distribution consistent with that of clusters (§ 2.5), many have far-infrared luminosities consistent with the formation of clusters of stars with masses ranging up to those of O stars. The properties of the Plume et al. (1992) sample have been studied in a series of papers (Plume et al. 1997; Mueller et al. 2002; Shirley et al. 2003), with the most recent summary in Wu et al. (2010a). The properties of the clumps depend on the tracer used. Since the HCN J = 1 → 0 line is used in many extragalactic studies, we will give the properties as measured in that line. The mean and median FWHM are 1.13 and 0.71 pc; the mean and median infrared luminosities are 4.7 × 105 and 1.06 × 105 L; the mean and median virial mass are 5300 and 2700 M; the mean and median surface densities are 0.29 and 0.28 gm cm-2; and the mean and median of the average volume densities (n) are 3.2 × 104 and 1.6 × 104 cm-3. As lines tracing higher densities are used, the sizes and masses decrease, while the surface densities and volume densities increase, as expected for centrally condensed regions. Very similar results were obtained from studies of millimeter continuum emission from dust (Faúndez et al. 2004) toward a sample of southern hemisphere sources surveyed in CS J = 2 → 1 (Bronfman et al. 1996).

Embedded clusters provide important testing grounds for theories of star formation. Using criteria of 35 members with a stellar density of 1 Mpc-3 for a cluster, Lada & Lada (2003) argue that most stars form in clusters, and 90% of those are in rich clusters with more than 100 stars, but that almost all clusters (> 93%) dissipate as the gas is removed, a process they call "infant mortality." With more complete surveys enabled by Spitzer, the distributions of numbers of stars in clusters and stellar densities are being clarified. Allen et al. (2007) found that about 60% of young stars within 1 kpc of the Sun are in clusters with more than 100 members, but this number is heavily dominated by the Orion Nebula cluster. Drawing on the samples from Spitzer surveys of nearly all clouds within 0.5 kpc, Bressert et al. (2010) found a continuous distribution of surface densities and no evidence for a bimodal distribution, with distinct "clustered" and "distributed" modes. They found that the fraction of stars that form in clusters ranged from 0.4 to 0.9, depending on which definition of "clustered" was used. Even regions of low-mass star formation, often described as distributed star formation, are quite clustered and the youngest objects (Class I and Flat SED sources, see § 4.1) are very strongly concentrated to regions of high extinction, especially after the samples have been culled of interlopers (Fig. 4, § 6.4). Similarly, studies of three clouds found that 75% of prestellar cores lay above thresholds in AV of 8, 15, and 20 mag, while most of the cloud mass was at much lower extinction levels (Enoch et al. 2007).

Figure 4

Figure 4. Example of the strong concentration of star formation in regions of high extinction, or mass surface density in the Perseus molecular cloud. The gray-scale with black contours is the extinction map ranging from 2 to 29 mag in intervals of 4.5 mag. The yellow filled circles are Flat SED sources and the red filled circles are Class I sources. Sources with an open star were not detected in HCO+ J = 3 → 2 emission and are either older sources that may have moved from their birthplace or background galaxies. Essentially all truly young objects lie within contours of AV ≥ 8 mag. Taken from Heiderman et al. (2010); reproduced by permission of the AAS.

A Spitzer study (Gutermuth et al. 2009) of 2548 YSOs in 39 nearby (d < 1.7 kpc), previously known (primarily from the compilation by Porras et al. (2003)) young clusters, but excluding Orion and NGC 2264, found the following median properties: 26 members, core radius of 0.39 pc, stellar surface density of 60 pc-2, and embedded in a clump with AK = 0.8 mag, which corresponds to AV = 7.1 mag. Translating to mass surface density using ⟨M*⟩ = 0.5 M, the median stellar mass surface density would be 30 M pc-2 and the gas surface density would be 107 M pc-2. The distributions are often elongated, with a median aspect ratio of 1.82. The median spacing between YSOs, averaged over all 39 clusters, is 0.072 ± 0.006 pc, comparable to the size of individual cores, and a plausible scale for Jeans fragmentation. The distributions are all skewed toward low values, with a tail to higher values.

While various definitions of "clustered" have been used, one physically meaningful measure is a surface density of ~ 200 YSOs pc-2 (Gutermuth et al. 2005), below which individual cores are likely to evolve in relative isolation (i.e., the timescale for infall is less than the timescale for core collisions). With their sample, Bressert et al. (2010) found that only 26% were likely to interact faster than they collapse. However, that statistic did not include the Orion cluster, which exceeds that criterion.

The fact that the Orion cluster dominates the local star formation warns us that our local sample may be unrepresentative of the Galaxy as a whole. Leaving aside globular clusters, there are young clusters that are much more massive than Orion. Portegies Zwart et al. (2010) have cataloged massive (M* ≥ 104 M), young (age ≤ 100 Myr) clusters (12) and associations (13), but none of these are more distant than the Galactic Center, so they are clearly undercounted. The mean half-light radius of the 12 clusters is 1.7 ± 1.3 pc compared to 11.2 ± 6.4 pc for the associations. For the clusters, ⟨log M*(M)⟩ = 4.2 ± 0.3. Three of the massive dense clumps from the Wu et al. (2010a) study have masses above 104 M and are plausible precursors of this class of clusters. Still more massive clusters can be found in other galaxies, and a possible precursor (Mcloud > 1 × 105 M within a 2.8 p radius) has recently been identified near the center of the MW (Longmore et al. 2012).

The topic of clusters is connected to the topic of massive stars because 70% of O stars reside in young clusters or associations (Gies 1987). Furthermore, most of the field population can be identified as runaways (de Wit et al. 2005), with no more than 4% with no evidence of having formed in a cluster. While there may be exceptions (see Zinnecker & Yorke 2007 for discussion), the vast majority of massive stars form in clusters. The most massive star with a dynamical mass (NGC 3603-A1) weighs in at 116 ± 31 M and is a 3.77 day binary with a companion at 89 ± 16 M (Schnurr et al. 2008). Still higher initial masses (105-170 M) for the stars in NGC 3603 and even higher in R136 (165-320 M) have been suggested (Crowther et al. 2010). Many of the most massive stars exist in tight (orbital periods of a few days) binaries (Zinnecker & Yorke 2007). For a recent update on massive binary properties, see Sana & Evans (2011).

There is some evidence, summarized by Zinnecker & Yorke (2007), that massive stars form only in the most massive molecular clouds, with max(M*) ∝ Mcloud0.43 suggested by Larson (1982). Roughly speaking, it takes Mcloud = 105 M to make a 50 M star. Recognizing that clumps are the birthplaces of clusters and that efficiencies are not unity could make the formation of massive stars even less likely. The question (§ 2.5) is whether the absence of massive stars in clumps or clusters of modest total mass is purely a sampling effect (Fumagalli et al. 2011; Calzetti et al. 2010a and references therein) or a causal relation (Weidner & Kroupa 2006). If causal, differences in the upper mass limit to clouds or clumps (§ 2.5) in a galaxy could limit the formation of the most massive stars. Larson (1982) concluded that his correlation could be due to sampling. As a concrete example, is the formation of a 50 M star as likely in an ensemble of 100 clouds, each with 103 M, as it is in a single 105 M cloud? Unbiased surveys of the MW for clumps and massive stars (§ 5.1) could allow a fresh look at this question, with due regard for the difficulty of distinguishing "very rarely" from "never."

4.3. Theoretical Aspects

The fundamental problem presented to modern theorists of star formation has been to explain the low efficiency of star formation on the scale of molecular clouds. Early studies of molecular clouds concluded that they were gravitationally bound and should be collapsing at free fall (e.g., Goldreich & Kwan 1974). Zuckerman & Palmer 1974 pointed out that such a picture would produce stars at 30 times the accepted average recent rate of star formation in the Milky Way (§ 5.1) if stars formed with high efficiency. Furthermore, Zuckerman & Evans (1974) found no observational evidence for large scale collapse and suggested that turbulence, perhaps aided by magnetic fields, prevented overall collapse. This suggestion led eventually to a picture of magnetically subcritical clouds that formed stars only via a redistribution of magnetic flux, commonly referred to as ambipolar diffusion (Shu et al. 1987; Mouschovias 1991), which resulted in cloud lifetimes about 10 times the free-fall time. If, in addition, only 10% of the cloud became supercritical, a factor of 100 decrease in star formation rate could be achieved.

Studies of the Zeeman effect in OH have now provided enough measurements of the line-of-sight strength of the magnetic field to test that picture. While there are still controversies, the data indicate that most clouds (or, more precisely, the parts of clouds with Zeeman measurements) are supercritical or close to critical, but not strongly subcritical (Crutcher et al. 2010). Pictures of static clouds supported by magnetic fields are currently out of fashion (McKee & Ostriker 2007), but magnetic fields are almost certain to play a role in some way (for a current review, see Crutcher 2012, this volume). Simulations of turbulence indicate a fairly rapid decay, even when magnetic fields are included (Stone et al. 1998). As a result, there is growing support for a more dynamical picture in which clouds evolve on a crossing time (Elmegreen 2000). However, this picture must still deal with the Zuckerman-Palmer problem.

There are two main approaches to solving this problem at the level of clouds, and they are essentially extensions of the two original ideas, magnetic fields and turbulence, into larger scales. One approach, exemplified by Vázquez-Semadeni et al. (2011) argues that clouds are formed in colliding flows of the warm, neutral medium. They simulate the outcome of these flows with magnetic fields, but without feedback from star formation. Much of the mass is magnetically subcritical and star formation happens only in the supercritical parts of the cloud. A continued flow of material balances the mass lost to star formation so that the star formation efficiency approaches a steady value, in rough agreement with the observations.

A second picture, exemplified by Dobbs et al. (2011), is that most clouds and most parts of clouds are not gravitationally bound but are transient objects. Their simulations include feedback from star formation, but not magnetic fields. During cloud collisions, material is redistributed, clouds may be shredded, and feedback removes gas. Except for a few very massive clouds, most clouds lose their identity on the timescales of a few Myr. In this picture, the low efficiency simply reflects the fraction of molecular gas that is in bound structures.

It is not straightforward to determine observationally if clouds are bound, especially when they have complex and filamentary boundaries. Heyer et al. (2001) argued that most clouds in the outer galaxy with M > 104 M were bound, but clumps and clouds with M < 103 M were often not bound. Heyer et al. (2009) address the issues associated with determining accurate masses for molecular clouds. In a study on the inner Galaxy, Roman-Duval et al. (2010) concluded that 70% of molecular clouds (both in mass and number) were bound.

If molecular clouds are bound and last longer than a few crossing times, feedback or turbulence resulting from feedback is invoked. For low-mass stars, outflows provide the primary feedback (e.g., Li & Nakamura 2006) while high-mass stars add radiation pressure and expanding HII regions (e.g., Murray (2011)). In addition, the efficiency is not much higher in most clumps, so the problem persists to scales smaller than that of clouds.

Another longstanding problem of star formation theory has been to explain the IMF (§ 2.5). This topic has been covered by many reviews, so we emphasize only two aspects. The basic issue is that the typical conditions in star forming regions suggest a characteristic mass, either the Jeans mass or the Bonnor-Ebert mass, around 1 M (e.g., Bonnell et al. 2007). Recently, Krumholz (2011) has derived a very general expression for a characteristic mass of 0.15 M, with only a very weak dependence on pressure. However, we see stars down to the hydrogen-burning limit and a continuous distribution of brown dwarfs below that, extending down even to masses lower than those seen in extrasolar planets (Allers et al. 2006). An extraordinarily high density would be required to make such a low mass region unstable.

On the other end, making a star with mass over 100 times the characteristic mass is challenging. Beuther et al. (2007a) provide a nice review of both observations and theory of massive star formation. While dense clumps with mass much greater than 100 M are seen, they are likely to fragment into smaller cores. Fragmentation can solve the problem of forming low mass objects, but it makes it hard to form massive objects. Simulations of unstable large clumps in fact tend to fragment so strongly as the mean density increases that they overproduce brown dwarfs, but no massive stars (e.g., Klessen et al. 1998; Martel et al. 2006). This effect is caused by the assumed isothermality of the gas, because the Jeans mass is proportional to (TK3 / n)0.5. Simulations including radiative feedback, acting on a global scale, have shown that fragmentation can be suppressed and massive stars formed (e.g., Bate 2009; Urban et al. 2010; Krumholz et al. 2010). Krumholz & McKee 2008 have argued that a threshold clump surface density of 1 gm cm-2 is needed to suppress fragmentation, allowing the formation of massive stars.

The radiative feedback, acting locally, can in principle also limit the mass of the massive stars through radiation pressure. This can be a serious issue for the formation of massive stars in spherical geometries, but more realistic, aspherical simulations show that the radiation is channeled out along the rotation axis, allowing continued accretion through a disk (Yorke & Sonnhalter 2002; Krumholz et al. 2009a; Kuiper et al. 2011).

The picture discussed so far is basically a scaled-up version of the formation of low mass stars by accretion of material from a single core (sometimes called Core Accretion). An alternative picture, called Competitive Accretion, developed by Klessen et al. (1998), Bate et al. (2003), and Bonnell et al. (2003), builds massive stars from the initial low-mass fragments. The pros and cons of these two models are discussed in a joint paper by the leading protagonists (Krumholz & Bonnell 2009). They agree that the primary distinction between the two is the original location of the matter that winds up in the star: in Core Accretion models, the star gains the bulk of its mass from the local dense core, continuing the connection of the core mass function to the initial stellar mass function to massive stars; in Competitive Accretion models, the more massive stars collect most of their mass from the larger clump by out-competing other, initially low mass, fragments. A hybrid picture, in which a star forms initially from its parent core, but then continues to accrete from the surrounding clump, has been advanced (Myers 2009; Myers 2011), with some observational support (e.g., Longmore et al. 2011).

Observational tests of these ideas are difficult. The Core Accretion model requires that clumps contain a core mass function extending to massive cores. Some observations of massive dense clumps have found substructure on the scale of cores (Beuther et al. 2007b; Brogan et al. 2009), but the most massive cores identified in these works are 50-75 M. Discussions in those references illustrate the difficulties in doing this with current capabilities. ALMA will make this kind of study much more viable, but interpretation will always be tricky. The Competitive Accretion model relies on a continuous flow of material to the densest parts of the clump to feed the growing oligarchs. Evidence for overall inward flow in clumps is difficult; evidence for it is found in some surveys (Wu & Evans 2003; Fuller et al. 2005; Reiter et al. 2011a), but not in others (Purcell et al. 2006). Since special conditions are required to produce an inflow signature, the detection rates may underestimate the fraction with inflow. The dense clumps are generally found to be centrally condensed (Beuther et al. 2002; Mueller et al. 2002; van der Tak et al. 2000), which can also suppress over-fragmentation.

Other possible tests include the coherence of outflows in clusters, as these should be distorted by sufficiently rapid motions. The kinematics of stars in forming clusters, which should show more velocity dispersion in the competitive accretion models, provide another test. Astrometric studies are beginning to be able to constrain these motions (Rochau et al. 2010), along with cleaner separation of cluster members from field objects. Relative motions of cores within clumps appear to be very low (< 0.1 /kms), challenging the Competitive Accretion model (Walsh et al. 2004).

Theoretical studies include evolutionary tracks of pre-main-sequence stars (e.g., Chabrier & Baraffe 2000 for low mass stars and substellar objects). These evolutionary calculations are critical for determining the ages of stars and clusters. For more massive stars, it is essential to include accretion in the evolutionary calculations (Palla & Stahler 1992) and high accretion rates strongly affect the star's evolution (Zinnecker & Yorke 2007; Hosokawa & Omukai 2009). Assumptions about accretion and initial conditions may also have substantial consequences for the usual methods of determining ages of young stars (Baraffe et al. 2009; Baraffe & Chabrier 2010; Hosokawa et al. 2011).

4.4. Summary Points from the Local Perspective

The main lessons to retain from local studies of star formation as we move to the scale of galaxies are summarized here.

  1. Star formation is not distributed smoothly over molecular clouds but is instead highly concentrated into regions of high extinction or mass surface density, plausibly associated with the theoretical idea of a cluster-forming clump. This is particularly apparent when prestellar cores or the youngest protostars are considered (e.g., Figure 4). In contrast, most of the mass in nearby molecular clouds is in regions of lower extinction.
  2. By counting YSOs in nearby clouds, one can obtain reasonably accurate measures of star formation rate and efficiency without the uncertainties of extrapolation from the high-mass tail of the IMF. The main source of uncertainty is the ages of YSOs.
  3. There is no obvious bimodality between "distributed" and "clustered" star formation, but dense clusters with massive stars tend to form in regions of higher mean density and turbulence, which are centrally condensed. Plausible precursors of quite massive (up to 104 or perhaps 105 M) clusters can be found in the MW.
  4. Despite much theoretical progress, the challenge of explaining the low efficiency of star formation, even in regions forming only low-mass stars, remains. Similarly, an understanding of the full IMF, from brown dwarfs to the most massive stars, remains elusive.

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