Astron. Astrophys. 357, 637-650 (2000)

5. Discussion

The main results of the modelling are that a density distribution, plus in some cases a compact, high column density core, fits both SEDs and radial brightness distributions; and that the peaked sources which required compact cores in the modelling are also those identified as molecular line rich in our hot core survey (Hatchell et al. 1998a), as noted in Sect. 3. In this section we discuss the constraints which the models place on the source properties, compare the dust models with the molecular line data, and discuss the effect of grain opacity.

5.1. Source properties

We showed in Sect. 4 that the envelope density distribution is well constrained by the data: a distribution fits the radial intensity profiles of the non-peaked sources better than constant, or density distributions, and that the same envelope can be combined with a compact, optically thick core to produce the profiles for the peaked sources.

It is unclear what is setting the inner radius of the dust shells. Our models also require a low dust temperature of  K on the inner boundary, in agreement with the previous spherical dust models, in order to limit the short wavelength emission (CWW90; Faison et al. 1998). A boundary set by dust sublimation, expected at  K, appears to be ruled out by such low temperatures. Presumably the inner radius is set by either radiation pressure or stellar/disk winds.

The luminosity of the driving source(s) is constrained by the total flux emitted across all wavelengths. This can be estimated from the data by interpolation between the observed fluxes and integrating. Alternatively, the total flux can be taken from the combination of models used to fit the SED. For the sources observed here, Churchwell et al. (1990b) gave luminosities based on those produced by WC89 using the first method, corrected for revised distances. These flux estimates did not take into account the flux emitted outside the IRAS bands, which WC89 suggest may be as much as 50%. With the inclusion of the submm data, and using the models to fit the SED, we have revised luminosity estimates for G10.47, G12.21 and G43.89, which are listed in Table 5 along with the corresponding spectral type assuming a single driving source (although we cannot distinguish single sources from clusters).

Table 5. Revised luminosities and corresponding spectral types (from Panagia 1973).

As noted in Sect. 4.2, few of the core properties are well constrained. The cores must have size much less than the beamsize and a high optical depth. The radial distribution of the compact cores are poorly constrained; higher resolution observations would be of use here. Interferometric continuum observations of G10.47 and G31.41 suggest that these cores have diameters of and respectively (Cesaroni et al. 1994b; Olmi et al. 1996a), which is slightly smaller than our model cores. The relative contribution to the submm flux, which is constrained by the radial profile, determines the relative luminosity of core and envelope once SED models for each are chosen. In fact the cores may be flattened, or even disks.

Limits on core luminosities in the non-peaked sources G13.87 and G43.89 are 1-2% of the total; with any more flux in a core component the radial profile fails to fit the observations.

Our modelling assumes that the cores are heated independently from the UCHII regions, by internal sources, but external heating is also a possibility. Whether the UCHII driving sources can also provide enough flux to the cores can be settled by geometric arguments, if the relative positions of the star (in the UCHII region) and the cores are known. The cores provide - of the total flux; if they and the extended envelopes are heated by the same star then the cores must fill - of the solid angle surrounding the star. For a diameter core, the core has to be within of the star in order to capture sufficient flux. Higher angular resolution observations are required to determine the relative positions of UCHII driving source and dust core. Of the sources studied here, interferometric observations show that the G10.47 molecular core may satisfy this criterion, with the ammonia core surrounding the UCHII region at a distance of (assuming the line joining star and core lies within of the plane of the sky), but in G31.41 the molecular core is from the UCHII regions and must be separately powered (Cesaroni et al. 1998). Another argument against externally heated cores is that it is difficult to produce large amounts of hot gas (Kaufman et al. 1998). This does not conflict with the submm continuum observations, as enhanced emission at 450/850µm can be explained by dust at only a few tens of kelvin. But the detection of high column densities of highly excited molecular species such as methyl cyanide and ammonia (eg. Hatchell et al. 1998a; Cesaroni et al. 1992; Olmi et al. 1993) suggest that there are large amounts of hotter dust in the cores, which is naturally produced if the heating is internal rather than external. Such high-luminosity internally-heated cores without detectable UCHII regions are presumably massive protostars.

5.2. Comparison with molecular line data

The sources which required the addition of compact cores in order to model the radial density distributions were G10.47, G12.21 and G31.41, whereas G13.87 and G43.89 did not. In our molecular line survey towards UCHII regions (Hatchell et al. 1998a) we also differentiated between these groups of sources on the basis of their molecular line emission. G10.47, G12.21 and G31.41 were line-rich hot core sources, showing high abundances of grain ice evaporated species and their daughter products. The molecular lines showed evidence for a hot, dense core surrounded by a cooler envelope. Neither G13.87 nor G43.89 had a rich molecular line spectrum, and Hatchell et al. (1998a) concluded that neither contained a hot molecular core. The SCUBA results confirm the need for compact cores in G10.47, G12.21 and G31.41, but not G13.87 or G43.89. We identify the compact cores in the SCUBA dust continuum images with the hot molecular cores identified from their molecular line emission.

SCUBA is therefore an excellent instrument for identifying hot core sources, because the high sensitivity array results in high dynamic range images after short integrations (here just over a minute per source), and only basic removal of bad pixels is required to produce a radial distribution plot from which the sources with hot cores can be identified by their steep profiles.

Column densities and masses calculated from the models are given in Table 4. For both core and envelope these are consistent with molecular line data. The model masses of a few times correspond to a few times in a single 15- beam, consistent with measurements of from C¹⁷O/C¹⁸O and C³⁴S measurements (Hatchell et al. 1998a; Cesaroni et al. 1991). Column densities of agree well with what is measured in CO.

Another difference between sources with and without cores is apparent when considering just the envelopes. The envelopes of the sources with cores have higher column densities and higher masses than the coreless sources. There may be a mass cutoff of below which cores do not form.

Temperatures within the envelopes fall off rapidly. Only the inner of the envelopes remains at temperatures above 100 K, in the radiative transfer models; at a radius of the temperature has dropped to below 50 K. The temperatures at the outer edges of the envelopes are 10-20 K, typical of quiescent dense cloud material (envelope outer radii are 70-160" - see Table 4).

Core masses from the dust model, of a few times , are larger than virial mass estimates of a few hundred to from warm, dense gas tracers CH₃CN, CH₃OH and NH₃ (Hatchell et al. 1998a; Cesaroni et al. 1992), and from NH₃ interferometry in G10.47 and G31.41 (Cesaroni et al. 1994a), by a factor of a few. 3mm interferometry estimates for the cores are for G10.47 (Olmi et al. 1996a) and for G31.41 (Cesaroni et al. 1994b). Again the column densities of compare well with estimates from molecular lines. As mentioned above, the core model is only approximate as the parameters are not well constrained by the observations. Smaller cores could reduce the mass without reducing the column density, but also shift the spectrum to shorter wavelengths. It may be possible to reconcile this with the SED: the core emission is reduced at shorter wavelengths by the envelope optical depth (see Sect. 4.3), and a grain model with relatively high submm opacity could be used. A reduction in optical depth, or a simple increase in grain opacity (corresponding to icy or bare coagulates: see discussion of grain properties below) would reduce both mass and column density. Alternatively, the larger model masses may be explained if the cool,  K, outer parts of the cores are poorly traced by the high excitation molecular lines of CH₃OH and CH₃CN, or if the assumption of virial equilibrium is invalid.

The molecular line emission itself will contribute to the broad band submm flux. Although some molecular line survey data exists for the sources considered in this paper, the frequency coverage is such a small fraction of the total SCUBA bands that a source-by-source calculation of the line contribution is not possible. Sutton et al. (1984) estimate that as much as 45-60% of the 215-247 GHz flux in Orion, when measured with an beam, is due to line emission. The line contribution from the outer envelope will be small because the molecular lines are few and weak (Thompson et al. 1999) but the chemically active hot cores have rich molecular spectra and line emission will contribute significantly to the fluxes at the peaks. A comparison of the single-beam fluxes and map fluxes (Table 3) shows that 30-50% of the submm flux integrated over the map can be attributed to the cores. A possible enhancement in flux as measured with a large beam could therefore explain the appearance of peaked sources in the submm as wholly due to molecular line emission. In practice, the large column densities of molecular gas required to produce these line fluxes are likely to coexist with an equivalent quantity of dust: processes that destroy or remove the dust would also destroy or remove the molecules, and many of the molecular species observed rely on icy grain mantles for their production, indicating the presence of dust. Nevertheless, the core emission which we have modelled as due to dust alone may in fact be due to a combination of dust and molecular line emission.

5.3. Grain properties

The model SEDs depend on the dust opacities assumed, which are poorly known at long wavelength. The spectral index for the opacity above 100µm () is expected to lie in the range 1-2. Theory suggests for crystalline materials (Draine & Lee 1984; Ossenkopf et al. 1992) and for amorphous carbon (Hanner 1988; Jäger et al. 1998). As well as the spectral index, the actual value of the opacity at 100µm varies depending on the type of grain, including whether or not it has an ice mantle. The models here follow CWW90 in calculating the opacity assuming Mie scattering from the Draine & Lee (1984) optical properties for a mixture of graphite and silicon, giving for ice-free grains with .

Coagulated grains with or without ice increase (Ossenkopf & Henning 1994). Hence, masses and column densities could be reduced by a factor of a few for the same optical depths. Using a coagulated grain model would also affect the shape of the spectrum, producing more submm emission for the same infrared flux. This might enable the SEDs to be fitted with lower near- and mid-IR optical depths. Because the 1350/2000µm points are single-beam and therefore effectively lower limits, the mm/submm data is not sufficent to differentiate between and opacity models.

© European Southern Observatory (ESO) 2000

Online publication: June 5, 2000
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