5.1. Connection between SEDs, outflows, and dense cores
The presence or absence of dense cores which are a prerequisite for star formation can be tested by the thermal dust emission as well as by molecular line transitions which require high densities to be excited. We found a clear correlation (77%) between the probabilities to detect a source at 1.3 mm continuum and in the CS (2-1) line emission. Out of 35 globules, 17 objects were detected in both tracers (16 of group 1, one of group 2), 10 objects were detected in none of the tracers (3 of group 1, 6 of group 2, one not classified), 7 objects were detected in CS only, and one object was detected at 1.3 mm continuum only.
It was shown in Fig. 6 that there is a clear correlation between the mm continuum flux densities and the CS line peak temperatures of the detected cores. The only (southern) object which deviates considerably from this correlation is DC 267.2-7.2 (group 2, local source). The relatively high CS line temperature (1.5 K) together with the non-detection in the continuum indicate that this globule has a higher density than the other group 2 sources, but a lower column density than the group 1 sources, i.e., it is less centrally condensed than those. This object is a good candidate of a pre-protostellar core being in quasi-static contraction phase prior to collapse (Ward-Thompson et al. 1994).
We found also a clear correlation between the probability to detect a source at 1.3 mm continuum and its position in the IRAS colour-colour diagram (Fig. 8; cf. Sect. 2.1, Fig. 1) which characterizes the spectral slope of the SEDs in two different wavelength ranges . We would like to mention in passing that the SEDs are not only a function of age, but may also depend on the "outer" radiation field and the inclination angle. Nevertheless, it can be clearly seen that the sources of group 1, which have steadily rising SEDs from 12 to 100m (see Fig. 2) and FIR colour temperatures of 25 K, have in general much higher millimetre fluxes than the colder group 2 sources. This looks, at first sight, somewhat surprising since one usually expects the coldest IRAS sources (here group 2) to be the youngest ones and the ones with the most massive dust envelopes. However, as mentioned above, the group 1 sources are "self-embedded" protostars with high column densities (cf. Sects. 4.2.2and 5.4). The low mm continuum fluxes of the colder group 2 sources indicate that these objects are much less condensed than the group 1 sources and, thus, cannot be representative of the isothermal protostellar phase. Such "isothermal protostars" would appear as compact mm continuum sources (core-envelope) without or with extremely cold and weak FIR counterparts (e.g., VLA 1623; André et al. 1993). Hence, the group 2 sources are either of pre-protostellar nature (cf. Ward-thompson et al. 1994) or they do not form stars at all (cf. discussion in Sect. 5.5).
The results of this survey show that the 1.3 mm dust continuum emission and the CS line emission are equivalent tracers of dense, star-forming molecular cloud cores. The high mm continuum and CS detection rates for the group 1 sources (local globules: 78% in the continuum and 89% in CS) together with the high outflow rate (67%, Sect. 4.3.3) show that these globules harbour dense cores which are in an early stage of star formation. The significantly lower detection rates for the group 2 sources (local globules: 22% in the continuum and 44% in CS) indicate that these globules don't have such dense cores or that their cores are much less dense and compact, respectively.
The far Carina sources ( kpc) are completely excluded from the above discussion. Due to their large distance and, consequently, the large projected beam size, it is very likely that several individual objects contribute to the IRAS fluxes and we see only effective SEDs (cf. Sect. 5.6). The SEDs and the frequency of dense cores of the far Carina sources are, however, not systematically different from those of the local globules.
5.2. Properties of the dense cores
In order to check the significance of the difference in the detection rates and masses between the two globule goups, we performed a two-sample survival test with the local globules. The test results in a probability of 12% for the assumption that both source groups follow the same mass distribution, i.e., the mass distributions are NOT similar at the 5% confidence level. This is demonstrated in Fig. 9 by means of the cumulative Kaplan-Meier estimator of the mass distributions. For the sake of comparison, we perfomed the same test for a subsample of northern globules (Paper I) which was selected with the same distance restriction. The result is very similar to that of the southern globules, i.e. the mass distributions of group 1 and 2 sources differ significantly from each other and the mass distributions of the northern and southern globule cores (circumstellar envelope masses) are similar at the 75% confidence level. Fig. 9 shows the cumulative mass distributions for the local group 1 and 2 sources in the southern, northern, and combined samples. We use the cumulative form because the differential form does not have a simple analytic error analysis.
The group 1 sources (combined sample) span a wide range of envelope masses from 0.04 to 2.3 /beam with a mean mass of 0.50.15 . The two most promising Class 0 candidates within our sample (DC 253.3-1.6 and 297.7-2.8; see Sect. 5.4) occupy the upper end of this mass range ( = 2.3 and 1.3 ). This result corresponds well to the circumstellar envelope masses derived by André & Montmerle (1994) for Class I and 0 sources in the Oph cloud ( = 0.03 - 2.3 = 0.30.15 ). The Class 0 candidates in their sample cover again the upper end of this range. In contrast, more than 90% of the group 2 sources have masses below 0.1 /beam.
The best (logarithmic) fit to the mass distribution of the (local) group 1 sources results in a mass function of the form: with = 1.8 (differential form). Note, that only 17 data points, of which two are upper limits, were used for this analysis. Although there is some indication that there is a gap in the mass distribution function between 0.3 and 0.7 and that the slope is steeper for masses larger than 0.7 , the total mass range covered can be fitted with a single slope. The number of sources investigated here is too small to discriminate between different power laws (cf. Motte et al. 1998). Note that although the method takes upper limits into account, our sample is sensitivity-limited for masses below 0.15 /beam. The mass spectrum obtained in this way may be, of course, affected by the fact that the measured fluxes and, thus, the masses, refer to the beam area only and, therefore, depend on the distances. For the upper part of the mass range, we will check the mass distribution with the complete mm continuum maps of 23 globule cores (Launhardt et al. 1998b).
The power law slope of the mass spectrum for circum-protostellar envelopes in Bok globules agrees perfectly with the slope derived for envelope masses of the Oph Class I/0 sources (André & Montmerle 1994). The slope of the envelope mass spectrum agrees also very well with the single-slope clump mass spectrum found in several molecular clouds ( = 1.51.8; see Kramer et al. 1998 and references therein). The mass spectra obtained by these authors were derived from molecular line maps by Gaussian clump decompositions and span a range in masses of several orders of magnitudes. The similarity in the slopes of the mass distributions of molecular cloud cores and circum-protostellar envelopes in low-mass star-forming regions is remarkable. It suggests that there is a close connection between the fragmentation law in molecular clouds and the stellar initial mass function (IMF). Remember that the IMF for low-mass stars is known to have a slope of 1.5 (e.g., Miller & Scalo 1979). In order to reveal this connection in more detail, a large number of complete maps of well-established protostars with infalling envelopes is required. The fact that the mass spectrum of circum-protostellar envelopes in Bok globules is similar to the envelope mass spectrum as well as to the clump mass spectrum in other dark clouds supports further the assumption that Bok globules are former cloud cores which remain when the thin gas of a molecular cloud dissipates (e.g., by stellar winds or supernova explosions).
The group 1 sources have not only higher masses per beam than the group 2 sources, but also higher bolometric luminosities (6.72 vs. 1.50.4 , local globules).
A typical, opaque globule receives 1 to 50 from the interstellar radiation field (ISRF; e.g., Mathis et al. 1983), depending on the size of the globule and the strength of the radiation field. Since the penetration depth of the radiation field strongly depends on the grain properties, the density profile, and the clumpiness, one can, in general, not discriminate between the contributions from internal and external heating to the total luminosity of the IRAS source without having spatially resolved MIR/FIR maps. In case of the group 1 sources where we see at shorter wavelengths IR sources smaller than the 100 µm IRAS beam of , it is clear that a considerable fraction of the total luminosity of the IRAS point source must come from an internal heating source. A quantitative analysis of the luminosity of these sources will be undertaken in Sect. 5.4.
In case of the group 2 sources, this question remains open. The lower luminosities of these sources together with their extremely "cold" SEDs give, however, further evidence that these globules are not yet heated by embedded protostars with their high accretion luminosities (cf. Sect. 5.4). A luminosity of 1 is much higher than the expected intrinsic "thermal" luminosity (due to gravitational forces, cf. Ward-Thompson et al. 1994) of such a cloud core, but is consistent with external heating by the ISRF. The average luminosity of the group 2 globule sources (1.50.4 ) is somewhat higher than the value of 0.90.8 derived for a sample of pre-protostellar cores by Ward-Thompson et al. (1994), but agrees within the uncertainty limit. Since the isolated globules are much more exposed to the ISRF than dense cores in larger dark clouds, they must receive more luminosity from the ISRF. This might explain the slightly higher luminosities compared to the pre-protostellar cores studied by Ward-Thompson et al..
The kinetic gas temperatures derived from 12CO and NH3 (9 - 13 K) are much lower than the dust temperatures of the dense cores derived from the broad-band SEDs ( 26 K for group 1 and 20 K for group 2). One reason for this discrepancy may be that gas and dust get in thermal equilibrium only at densities higher than cm-3. The beam-averaged hydrogen densities of the globule cores lie, however, just in this range or are below this value (cf. Sect. 4.2.3). In addition, we already mentioned in Sect. 2.1that the FIR colour temperature may overestimate the true effective dust temperature of the globule cores.
The more important reason for this discrepancy in gas and colour (dust) temperatures is probably that internally heated cores have a temperature gradient. The relatively "high" colour temperatures and the higher bolometric luminosities of the group 1 sources (together with the presence of molecular outflows) compared to the group 2 sources suggest that these cores are indeed heated by embedded YSOs (cf. discussion in Sect. 5.4). While the optically thin dust continuum emission is dominated by the warm inner region close to the protostar, the optically thick CO line traces only the cooler envelopes in which the gas and dust are de-coupled due to the lower densities. The ammonia observations (Bourke et al. 1995b; Lemme et al. 1996) were performed with relatively large beam sizes and are, therefore, also more sensitive to the cold and extended gas of intermediate density than to the high-density protostellar cores.
No evidence for internal heating was found for the group 2 sources. These objects are probably externally heated (cf. Sects. 5.2.2and 5.5) and the difference in gas and dust temperatures may be real.
5.3. Outflow energetics
Outflows of low-mass YSOs are closely connected (causal and temporal) to the accretion of mass. Recently, Bontemps et al. (1996) found that the outflow activity declines during the protostellar accretion phase. This means that the youngest protostellar objects being in their main accretion phase ("Class 0" sources) have not only exceptional high / ratios (see Sect. 5.4), but lie also an order of magnitude above the well-known correlation between outflow momentum flux and bolometric luminosity observed for embedded YSOs which have passed the main accretion phase (Class I).
Since important outflow parameters such as the flow extent, velocity structure, mass distribution, or inclination angle cannot be derived from one-point measurements of a single line, it is difficult to compare the energetics and evolutionary stages of the outflows. Outflows from low-mass YSOs are generally thought to be momentum-driven (e.g. Masson & Chernin 1993). The effective momentum flux (where P is the momentum and T is the time the flow needs to cross the observed region) can, therefore, be assumed to be conserved along the flow direction. Under this assumption, the momentum flux measured within the beam area at the central position should be a characteristic quantity of the outflow which does not depend, at first order, on the projected beam area (distance). Here, we follow the approach of Bontemps et al. (1996) (cf. also Cabrit & Bertout 1992) and compute the momentum flux from:
where is the total gas mass contained in the wings within the observed area, is the "characteristic" flow velocity, is the radius of the observed area, and is the inclination correction factor. As the characteristic flow velocity we took the maximum velocity extent from the line center (average of red and blue wing) at the 0.2 K level (). The HPBW of projected at the distance of the object was taken as 2 . Both the observed flow velocity and the projected radius along the flow direction depend on the inclination angle i of the outflow (, ). Since we have no information on individual inclination angles, we assume a random distribution of outflow orientations resulting in a mean inclination angle of corresponding to a mean correction factor of (Bontemps et al. 1996).
The largest uncertainty is introduced by the conversion from CO wing emission to the gas mass contained in the outflow wings. It was shown by other authors that the 12CO(2-1) wing emission from outflows in low-mass YSOs is moderately optically thick (e.g. Cabrit & Bertout 1992; Bourke et al. 1997) and that the CO optical depth seems to be constant over the outflow (e.g. Wilking et al. 1990). Therefore, the derivation of the total flow mass from the integrated 12CO(2-1) wing intensity in the optically thin approximation together with an opacity correction gives reasonable results (see Cabrit & Bertout 1990 for a detailed discussion of uncertainties in deriving outflow parameters). For the sake of comparison we adopt the same mean opacity correction factor of 3.5 as Bontemps et al. (1996) did in their investigation of outflow activity around low-mass embedded YSOs. This correction factor is consistent with the CO(1-0) optical depth of 2 - 3 measured in the outflow wings of DC 297.7-2.8 by Bourke et al. (1997).
With the method described above we derive momentum fluxes between (DC 297.7-2.8) and km s-1 yr-1 (DC 356.5-4.5), with a mean value of km s-1 yr-1 for the local group 1 sources (d 500 pc) and a value of km s-1 yr-1 for the only group 2 source with an outflow detected.
Fig. 10 shows the correlation of the CO momentum flux with the envelope mass (per beam) as derived from the 1.3 mm continuum emission and with the bolometric luminosity of the central IR sources. There is a clear positive correlation (%) between and the circumstellar envelope mass . The correlation between and the bolometric luminosity is less clear (%, only group 1 sources considered), but is still present. The best linear fits for both correlations are:
The / correlation compares well to the results obtained for a sample of 45 embedded YSOs by Bontemps et al. (1996). The / correlation for our sample lies between the correlations derived by Cabrit & Bertout (1991) and by Bontemps et al. (1996). This shows that the link between the outflow energetics and the properties of the protostellar cores cannot be significantly different for Bok globules than for other embedded YSO's in larger molecular clouds. Note, however, that due to the small number of objects in our sample the uncertainty of the fitted correlations is too high to recognize smaller deviations from other source samples.
The high CO momentum flux and envelope mass of DC 297.7-2.8 clearly resembles the properties of the Class 0 sources in the sample of embedded YSOs analysed by Bontemps et al. (1996) (cf. Bourke et al. 1997). The properties of DC 253.3-1.6 and 267.4-7.4 are intermediate to that of Class 0 and Class I sources while the lower CO momentum fluxes of DC267.7-7.4, 275.9+1.9, and 303.8-14.2 give evidence that these objects have passed their main accretion phase. The same holds for the two sources in the near Carina arm (DC 295.0+1.3 and 344.6-4.3). The only group 2 source with a CO line wing (DC 356.5-4.5) has lower values of , , and than the group 1 sources. It is not clear whether this source is distinguished from the group 1 outflow sources only by its lower mass or whether it is already more evolved than those. Another explanation could be that the weak line wing in this source is not caused by an outflow at all (cf. Sect. 4.3.3).
5.4. Evolutionary stage of the group 1 sources
In this paragraph, the evolutionary stage of the local group 1 sources will be discussed together with the mass-luminosity diagram for protostellar systems. The circumstellar masses and the luminosities of the embedded sources will be used in the same way as in Paper I to characterize the evolutionary stage of the (proto-)star-envelope systems (cf. André & Montmerle 1994). Fig. 11 shows the mass-luminosity diagram for our target sources. In the diagram, the observed objects are indicated by their circumstellar mass and their bolometric luminosity , while different theoretical mass-luminosity relations for protostars are indicated by the stellar mass and the appropriate luminosity (see below).
The masses of the circumstellar envelopes are measured by their optically thin thermal dust emission at mm wavelengths. The masses of the embedded protostars can be derived from the bolometric luminosities under the assumption that the luminosity originates mainly from the accretion shock on the stellar surface. This accretion luminosity (for spherical infall) is given by = , where is the mass of the central star, is the mass accretion rate, and is the stellar radius. Here, we use the mass-radius relation for accreting protostars given by Stahler (1988) and Palla & Stahler (1990). For the mass accretion rate, we use the conservative (low) value of yr-1 (see Paper I). This relation is indicated by the upper dashed line in Fig. 11. The internal luminosity of a star of mass and appropriate radius at the stellar birthline (Fletcher & Stahler 1994) is indicated by the lower dashed line in Fig. 11. During the main accretion phase, is about one order of magnitude smaller than . The total luminosity of the protostellar system is then given by the sum of the accretion luminosity and the internal luminosity , as indicated by the solid curve in Fig. 11. Due to several uncertainties in the parameters and model assumptions, we consider the lowest ( vs. ) and uppermost (+ vs. ) curves as boundaries of the uncertainty region of the protostellar mass-luminosity relation.
Under the assumptions that the mass accretion rate and the total mass of the system remain constant during the main accretion phase, the circumstellar (envelope) mass is given by , where is the time since the onset of the collapse (see Paper I for a more detailed discussion of the derivation of these quantities). The expected evolutionary tracks of the / ratio of two protostellar systems of 0.3 and 1 are shown as dotted lines in Fig. 11 Similar evolutionary tracks were already derived by Saraceno et al. (1996).
An object with must be located on the (lower) right side of the protostellar / relation. Assuming that the entire envelope will be finally accreted onto the star, such objects have accreted less than 50% of their final mass hitherto and are, therefore, still in the main accretion phase. Such "Class 0" protostars (André et al. 1993) usually drive powerful outflows. Objects which have already accreted more than half of the total initial envelope mass and are, thus, more evolved, are located on the upper left side of this / relation (cf. Saraceno et al. 1996). For the sake of comparison, we show the locations of VLA 1623 ("Class 0") and L1551-IRS5 ("Class I") in the diagram.
The average mass-luminosity ratio of the local group 1 sources is / = 0.10.05 / (0.080.05 / for northern and southern objects). This value is somewhat smaller than the average / ratio of 0.30.2 derived for 9 Class 0 sources, but larger than the / ratio of 0.050.05 derived for a large number of Class I sources by Saraceno et al. 1996. For the sake of comparison, we applied the same dust temperature and opacity to their 1.3 mm fluxes as we did to our sources. Three objects in our sample have / ratios higher than 0.1 / (DC 253.3-1.6, 297.7-2.8, and 303.8-14.2). These objects lie very close to the lower boundary of the protostellar / relation and have, thus, very likely . All three sources drive molecular outflows and the first two of them have the most powerful outflows within our sample (see Sect. 4.3.3). These objects are the most promising candidates within our sample for being "Class 0" protostars.
The objects DC 267.4-7.5, 275.9+1.9, and 320.5-3.6 lie in the transition region between and . These objects are presumably very young, but no statement can be made here about their exact evolutionary stage. DC 267.7-7.4 is the outflow candidate with the lowest circumstellar mass ( ) and it is associated with a visible star at the IRAS position. It is also the most evolved source in the sense that it has the lowest / ratio (0.024). The near Carina objects resemble rather the properties of Class I than of Class 0 sources, although their larger distance (and projected beam size) does not allow a reliable interpretation.
The least massive one of the local group 1 sorces detected at 1.3 mm continuum is DC 320.5-3.6. In contrast to all other group 1 sources detected at 1.3 mm, no outflow was found in this source. It is not clear whether this object drives no or an extremely weak outflow due to its low mass or whether it is in an earlier (pre-protostellar) stage than the other group 1 sources.
Note that the circumstellar masses were derived from On-On measurements and refer to the beam area only. They are, therefore, lower limits of the total circumstellar masses. In contrast to this, the IRAS fluxes and, thus, the IR luminosities originate from the entire dense cores due to the large beam of IRAS. Therefore, the / ratios derived here are lower limits. For DC 297.7-2.8, a typical very young protostellar core (group 1, "Class 0"), the shift in the diagram when using the integrated circumstellar mass is shown by an arrow (data from Bourke et al. 1997).
Although the exact position of the objects in the / diagram and their evolutionary stage can only be derived from maps of the continuum emission and from complete SEDs, the diagram shows that the the globule cores of group 1 are in an early stage of star formation and reveal the properties of "Class 0" and "Class I" protostars. The youngest ones of these objects are still in their main accretion phase and must, therefore, have core masses which are of the same order as the masses of the stars which they will finally form. The average envelope mass of all local group 1 sources is 0.50.15 , while the average mass of the three Class 0 candidates (see above) is 1.30.8 . We conclude, therefore, that Bok globules form stars with typical masses of the order of 1 .
5.5. The nature of group 2 sources
In Paper I we speculated that the group 2 sources are mostly
pre-protostellar cores and that the less opaque ones could probably be
cirrus clouds since they match the FIR colours of cirrus clouds. There
are, however, two arguments against the cirrus hypothesis:
Hence, the group 2 globules are rather "real" dark clouds with cores just compact and dense enough to be detected by IRAS, probably only due to their isolated location. Comparable objects in larger dark clouds would not have enough contrast to the surrounding cloud to be detected by IRAS as point sources.
In Sect. 5.2.2we pointed out that the bolometric luminosities of these objects could be completely due to external heating by the ISRF, so that no statement can be made about the contribution of a possible internal heating source, except that it must have a lower luminosity than the total luminosity ( ). Although the beam-averaged densities of these sources (Sect. 4.2.3) are about five times lower than the values derived by Ward-Thompson et al. (1994) for a sample of pre-protostellar cores in dark clouds, we speculate that those group 2 globule cores which were detected in the CS line (DC 268.2-9.7, 267.2-7.2, and 319.9-4.8), or in the mm continuum (DC 249.4-5.1), or in both tracers (DC 289.3-2.8) are in a pre-protostellar stage. However, complete maps of the mm continuum and CS line emission are required to reveal the true nature of these sources.
The other group 2 sources which were not detected in the CS line nor in the mm continuum may have some kind of dense core (100 µm IRAS point source!). But, their cores are probably not massive and dense enough to form stars. Another explanation could be that they already formed very low-mass stars (or even brown dwarfs) which did not completely destroy the core. The group 2 is, thus, much less homogeneous than the group 1 and no easy classification criterion seems to exist which can be used to distinguish between the different alternative explanations.
5.6. The nature of the Carina sources
The sources in the near Carina arm ( kpc) are not significantly different than the local globules. The CO and CS linewidths as well as the CO line temperatures (and, hence, the kinetic gas temperatures) are comparable to that of the local globules. Due to the selection effect, their avearge size and mass are somewhat larger than those of the local globules. Their bolometric luminosities are by about one order of magnitude higher than those of the local globules, which is also a selection effect. As a result, the objects in the near Carina arm are, on average, more evolved than the local group 1 globules in the sense that they have lower envelope mass to bolometric luminosity ratios. However, they still resemble the typical properties of globules with embedded low-mass YSOs of mainly "Class I".
The sources in the far Carina arm ( kpc) are not typical of "classical" globules. While the typical size of a globule is 0.5 pc, these clouds have sizes of 5 to 10 pc which is larger than, e.g., the Oph cloud core. These clouds are, very likely, more complex structured than globules and they have probably more than one star-forming core. Such clouds would not have been identified as Bok globules if they were located at shorter distances. According to their masses and luminosities, they are, however, also low-mass (or intermediate-mass) star-forming regions and do not form high-mass stars. When putting the Oph cloud at a distance of 3 kpc, its central part would appear like a diffuse globule, and its star-forming cores, which harbour rhich clusters of YSOs (e.g., L 1689, Wilking & Lada 1983), would appear as unresolved IR sources in the IRAS beam with a total luminosity of the order of 1000 . Therefore, we propose that the sources in the far Carina arm are cores of dark cloud complexes with embedded clusters of low-mass YSOs. The higher kinetic gas temperature compared to the local globules (cf. Sect. 4.3.2) also suggests the presence of additional heating sources like, e.g., embedded clusters of YSOs. High-resolution imaging of the infrared sources and of the mm dust continuum and molecular line emission (e.g., 13CO and CS) is required to reveal the true nature of these objects.
© European Southern Observatory (ESO) 1998
Online publication: September 8, 1998