4 Discussion

4.1 Clustering

In Papers I and II, SED's were derived for all selected YSO's based on IRAS fluxes (within beams of $\sim\!1'$) and single channel NIR photometry (with an aperture of $15 \hbox{$^{\prime\prime}$}$). These SED's were then used to determine the luminosity function (LF) of Class I sources in the VMR. Yet, source clustering may have affected significantly both SED's and the LF, therefore making compelling to assess the degree of source multiplicity (and extendedness) using NIR images. The way in which clustering may have acted is threefold: first, uncorrect identifications of NIR counterparts may have caused errors in the SED's at NIR wavelengths; second, if FIR fluxes (whose resolution is somewhat low) generally resulted from the contribution of two or more close-by sources, the true LF might differ both in the shape and in the luminosity range. Third, the IRAS Class I sources may "conceal'' fainter Class I sources whose presence, anyway, should be accounted for in the LF (shadowing).

As for SED's, we found that NIR fluxes need to be revised (downward) in 6 cases (namely, IRS 18, IRS 20, IRS 21, IRS 62, IRS 63 and IRS 71). Yet, previous estimates of the NIR contribution to the bolometric luminosity are < 0.5% of the whole emitted energy for all sources but IRS 62, where it amounted to 17.4% (see Papers I and II). Hence, given that NIR fluxes were found to be % of the total flux throughout the catalogue of VMR Class I sources (see Table 5 of Paper I and Table 3 of Paper II), and considering that any change due to misidentifications of NIR counterparts is likely downward, these changes barely affect the bolometric luminosities and, hence, the LF.

Instead, it is much more important to check the possibility that IRAS fluxes may result from the contribution of two or more extremely close-by objects. Although clustering is well evident in our images at size scales (see Fig. 2, and our paper in preparation for an in-depth discussion), IRAS Class I sources do seem to have well defined NIR counterparts which begin to dominate the emission in the K band. Generally, many objects lie within or near the IRAS uncertainty ellipse, but they are well resolved (see, e.g., Fig. 4c), and often much fainter than the Class I source main candidates (see, e.g., Fig. 5c). A few images show in fact that the identified counterparts stand out even more noticeably in the L' band with respect to all other NIR sources (IRS 13, IRS 14, IRS 17 and IRS 19). However, in some cases (IRS 18, IRS 62, IRS 63) Mid-Infrared observations at comparable spatial resolution are compulsory in order to confirm the predominance of a single source.

Once excluded the possibility that more sources contribute to the IRAS fluxes, shadowing remains the major concern, since in many fields there are more than one object with typical colours of Class I sources. Some of the "shadowed'' sources (i.e., possible Class I sources discarded as IRAS counterparts) have greater K luminosities with respect to other IRAS counterparts (e.g., IRS 17 # 40 and IRS 13 # 25); unfortunately, it is not possible to infer a bolometric luminosity from the NIR brightness only, since, as we have already shown, there is no correlation between NIR and IRAS fluxes. However, there are indications that these sources, if their protostellar nature was confirmed, have to be accounted for probably only in the $L_{\hbox{$\odot$}}$ part of the LF. In fact, let us first examine the case of IRS 62 # 27: though we have not considered it as the NIR counterpart of the IRAS source, it is one of the NIR brightest Class I (-like) sources we have found. Nevertheless, certainly it has a small bolometric luminosity ($< 120~L_{\hbox{$\odot$}}$; see Table 3). Similarly, IRS 13 is the less luminous of the IRAS sources with F₁₂>2.5 Jy (excluding IRS 14) and one of the brightest in the K band (# 29); in this field, two objects have typical colours of Class I sources (# 25 and 29), but only one seems to dominate in the FIR, so the other cannot affect the upper luminosity end of the LF.

Then, if bright Class I sources are accompanied by other YSO's of the same kind, these latter should have somewhat smaller bolometric luminosities (however, a conclusive assessment in this sense requires Mid-Infrared observations). Therefore, the LF given in Paper II should be well established for $L_{\hbox{$\odot$}}$, unless clustering at a size scale of , a conservative estimate of the K image resolution, occurs. Assuming a distance of 700 pc, this would indicate that multiple stars form within 0.007 pc of each others (i.e., $\sim 1500$ AU). But this size is roughly less than typical diameters of circumstellar envelopes, so this scenario appears unrealistic. Actually, we cannot rule out the possibility that a few NIR counterparts of the IRAS sources are close binaries; anyway, even in the worst case of companions with the same bolometric luminosity of the main object the inferred protostar masses would not be greatly changed. At the high luminosity end, the true LF should not be significantly different from that found by Lorenzetti et al. (1993), if roughly the same fraction of sources in each luminosity bin is composed of close binaries of identical mass. Also a wider mass spectrum for the companions of protostars would probably reflect on basically the low luminosity end of the LF. However, this issue cannot be settled by our observations.

4.2 Reflection nebulae

Remarkably, we found extended nebulosities in a number of fields; these probably represent reflection nebulae and further confirm the youthness of the objects in the region. The NIR counterparts of 5 IRAS sources (namely IRS 13, IRS 14, IRS 17, IRS 18 and IRS 19) appear embedded in nebulosities. Furthermore, within the fields of IRS 20, IRS 21 and IRS 62, small nebulae lie close to the IRAS source and, in the remaining fields, the NIR counterparts may be embedded in faint patches of diffuse emission (e.g. IRS 71). The nebulosities are well evident in K images and, sometimes, less evident in the J band, because of either the increase in bulk extinction or/and the SED of the illuminating sources (usually extremely red). Note also that the majority of nebulosities (IRS 13, IRS 14, IRS 17, IRS 18, IRS 19 and IRS 62) host multiple stars separated by a few arcseconds from each other.

It is interesting to examine in closer detail the morphology of IRS 20 and IRS 21, where apparently the NIR counterparts are not embedded in the local nebulosities. In IRS 20 (see Fig. 8c) three nebulosities are projected around source # 98; although we have found sources within the diffuse emission (# 82, 96 and 109), they are probably only small nebular peaks. In fact, the colours of sources # 82 and # 96 are very similar to those obtained from the integrated brightnesses of the corresponding nebulae (indicated by asterisks in Fig. 8a), but note that, since these sources are somewhat fainter than the whole nebulae (see Table 4), they do not significantly contribute to the integrated fluxes. Conversely, although the colours of # 109 are quite different from those of the corresponding nebula (see Table 4), morphologically, it resembles a blob of nebular emission rather than a star-like object, as well (Fig. 8c).

As a result, it is tempting to interpret the structure towards IRS 20 as a single reflection nebula illuminated by source # 98, in a region of highly variable extinction, which could make up dark lanes splitting the extended emission into three parts. In this case, the colours of the nebulae must be consistent with those of the illuminating source. To check this circumstance we assume a $\lambda ^{-4}$ dust isotropic scattering; hence, the received flux from a reflecting nebula is roughly given by:

$$F_{\lambda} = \frac{f_{\lambda} \Omega_{\rm s} L_{0}(\lambda... ...\pi d^{2}}\bigg[ 1- \exp(-\frac{\tau_{0}}{\lambda^{4}}) \bigg ]$$ (2)

where $L_{0}(\lambda)$ is the luminosity of the illuminating source in the $\lambda$ band, $f_{\lambda}$ a factor accounting for atmospheric transmission, filter bandpass and detector sensitivity, $\Omega_{\rm s}$the fraction of solid angle subtended by the nebula (with respect to the illuminating source), d the distance from the observer, $\lambda$ the effective wavelength and $\tau_{0}$ a factor depending on the density and geometry of the nebula. Assuming $\tau_{0}$ does not depend on $\lambda$, the colour of a reflection nebula is given by:

$$\begin{eqnarray} m_{\lambda_2}-m_{\lambda_1} = &-2.5& \log \Bigg[\frac{f_{\lam... ...^4}) \bigg ]}{ \bigg[ 1-\exp(-\frac{\tau_0} {\lambda_1^4})\bigg ]}\end{eqnarray}$$ (3)

where $m_{\lambda}$ is the flux in magnitudes and we have considered no extinction. Note that the first term on the right-hand side is the intrinsic colour of the illuminating source.

The isotropic scattering law (applied to # 98) has been drawn in Fig. 8a by varying $\tau_{0}$;both the illuminating source and the reflection nebulae must be individually reddened according to the extinction towards them. Since the brightest nebula exceeds in K luminosity # 98 by 3 mag, the extinction A_V towards # 98 must be at least $\sim 30$mag greater than towards the nebula (assuming A_K =0.11 A_V; see Rieke & Lebofsky 1985), if the former illuminates the latter (since a reflection nebula cannot be intrinsically brighter than its illuminating source). As indicated in the colour-colour diagram of Fig. 8a (where, as said, nebulae are indicated by asterisks), the given value of J-H for source # 98 is a lower limit, suggesting that # 98 might have a sufficiently large J-H to account both for the colours and for the K flux difference of the nebulae. Namely, the position of # 98 in Fig. 8a is allowed to be moved in the upper right corner of the plot in such a way that the scattering law is compatible with the obscured colours of the nebula, once the extinction is accounted for. Similarly, it is possible to find combinations of $\tau_{0}$, $\Omega_{\rm s}$ and extinction which account for both colours and K flux differences of the three individual nebulae. Other star-like objects close to the smallest nebulae (# 113, 96, 99, 102) cannot account for the nebular colours since lying to the left in the colour-colour diagram, with the possible exception of # 103.

A small extended nebulosity (source # 43) appears to the south of the NIR counterpart (source # 50) of IRS 21 (see Fig. 9c). The isotropic scattering law (applied to # 50) has been drawn in Fig. 9a and, as can be seen, the colours of # 43 are, in principle, compatible with those of a reflection nebula illuminated by # 50, if the latter is more extincted than the former of A_V $\sim 12$ mag (according to the colour-colour diagram of Fig. 9a, where the nebula is indicated by the asterisk). Source # 43 is as bright as source # 50 in the K band, so, considering an extinction difference between the object and the nebula A_K $\sim 0.11\times 12=1.3$ mag, it would be $\sim 1.3$mag fainter, whereas its small apparent size would indicate a difference of at least $K=-2.5 \log (\Omega_{\rm s}) \sim 2.0$ mag, in rough agreement considering the oversimplification of our model. In conclusion, both in the case of IRS 20 and IRS 21 the NIR counterparts of the IRAS objects may be the illuminating sources of nearby nebulosities.

As shown in Fig. 7a, also the colours of the nebular emission (indicated by the asterisk) south of source # 49, towards IRS 19, are compatible with isotropic scattering of NIR radiation from # 49 itself. It must be more extincted than the nebula, since it is $\sim\!1$ mag fainter in the J band; this means A_V> 3.5 mag (using the reddening law of Rieke & Lebofsky 1985) which is plausible as can be checked in the colour-colour diagram of Fig. 7a. Conversely, the colours of # 43 (an object found within the nebula) are very similar to those obtained from the integrated magnitudes of the nebula itself, but since it is much fainter than the latter, # 43 is probably only part of the nebular emission.

In conclusion, if the NIR counterparts of IRS 19, 20 and 21 are the illuminating sources of the nearby nebulosities, they must be heavily extincted (more than A_V $\sim 30$ mag in one case), confirming their nature of embedded Class I sources.

The large number of (possible) reflection nebulae is not unexpected; e.g., Yun et al. (1994) found evidence of embedded nebulosities in 11 out of 34 Bok globules imaged in the JHK bands. Nebulae which appear brighter in the K band than in the J band are found by these authors to be associated with IRAS sources displaying a 12/25 $\mu$m spectral index $\alpha={\rm d}\log (\nu B_{\nu})/{\rm d} \log \nu <0$, and are attributed to objects deeply embedded in the clouds. According to these authors, they represent an earlier evolutionary state with respect to similar regions associated with nebulae which are brighter in the J band. According to our observations, most of the Class I source candidates in VMR-D would be in this stage.

  

Table 4: JHK photometry and positions of found K sources towards IRS 63, given as an example of the whole list in electronic form. Due to the presence of bad pixels or the closeness to the image edge, a few JHK entries are not given and marked as "unav'' (unavailable)