Astron. Astrophys. 359, 113-130 (2000)

6. The unknown Class III source population

In this section, we seek to characterize the suspected unknown Class III source population, which is likely to exist on the basis of the Class II source findings by ISOCAM and other IR observations. We will use (i) the spatial distribution of all known Class II sources, and (ii) the extinction map derived from C¹⁸O observations.

6.1. Compared spatial distributions of the Class II and Class III sources

The conventional wisdom is that Class III sources are descendants of Class II sources after dispersion of their disks (e.g., Lada 1987; AM). As cloud cores have an internal velocity dispersion, stars form with an initial mean velocity distribution, implying that they drift away from their formation site (e.g., Feigelson 1996). This is the usual explanation for the increase with distance from cloud cores of the Class III/Class II source ratio (or equivalently at that stage the WTTS/CTTS ratio), which is within the core region (e.g., CMFA), and reaches values far from the cores (e.g., Martín et al. 1998). This implies a larger spread of the spatial distribution of the Class III source population compared to that of the Class II source population.

Let us first study the spatial distribution of the Class II source population within the HRI /ISOCAM area. We analyze the source surface density by using a 2-D Gaussian filter of a given FWHM on source position. The choice of the FWHM is optimized to enhance the contrast between regions of low and high source density, and thus reveal any clustering. Fig. 8 shows the resulting density map, in the form of dashed contours obtained with FWHM=6´. The Class II sources show three strong density peaks well centered on DCO⁺ cores A, B and F, which is consistent with the idea that most of these sources were born in these cores. However, in spite of its comparable DCO⁺ line-of-sight density, core C appears much poorer in Class II sources; the weaker star-forming activity of this core is confirmed by the presence of only one Class I source (see Bontemps et al. 2000).

Fig. 8. Spatial distribution of Class II sources in the Ophiuchi Cloud. Black dots show the position of Class II sources. The dot size gives information on the source visual extinction. The dashed contour map is an estimate of the local Class II source surface density (in linear arbitray units) obtained using a sum of Gaussians (FWHM=6´) centered on each Class II source position; crosses show the maxima of these peaks. The letters show the location of DCO+(J=2-1) dense cores A, B, C, E, F (see Fig. 2). The contour map shows the visual extinction (=36, 54, 72, 90) derived from C18O column density (Wilking & Lada 1983). A scale of 0.5 pc is shown for pc.

One can go one step further by comparing the source distribution with the matter distribution along the line-of-sight, i.e., with the extinction map. The DCO⁺ radical is a good indicator of large densities (- cm^-3) in cold cores, but the relevant regions occupy a relatively small volume; by contrast, C¹⁸O, which is generally optically thin and sensitive to smaller densities, is a good column-density tracer. Using this molecule, Wilking & Lada (1983) derived an extinction map of the  Oph cloud center, showing that the denser regions have an equivalent visual extinction between and .

Fig. 8 displays the C¹⁸O contours, labeled in by steps of , starting at , from Wilking & Lada (1983). Correspondingly, the Class II sources are represented by black dots of size decreasing with , from low extinctions () to high extinctions (), by steps of . A large majority of these sources are seen to have moderate extinctions (), even in the areas overlapping regions of high extinctions traced by C¹⁸O. This implies that such sources are actually only moderately embedded in the cloud, in front of the densest regions traced by C¹⁸O and DCO⁺, rather than within them. The spatial distribution of the Class II sources can thus be more appropriately described as gaussian-like three-dimensional overlapping "haloes" around the DCO⁺ cores A, B and F. This also implies that at least a fraction of the Class II sources with high extinctions are not necessarily really embedded in the densest regions, but may be part of these haloes behind the dense cores.

In the very same fashion, Fig. 9 displays the distribution of the known Class III sources, this time using FWHM=8´. ¹⁴ This distribution is different from that of Class II sources in Fig 8. With respect to the DCO⁺ cores, there is a strong density peak  SW of the location of core F, and no peak associated with cores A and B: in contrast with the distribution of Class II sources, there is a deficiency of Class III sources in the cloud center regions with high extinction.

Fig. 9. Spatial distribution of Class III sources in the Ophiuchi Cloud. White dots show the position of Class III sources excluding the early-type star S1. Crosses show X-ray detected Class III sources (Montmerle et al. 1983; CMFA; Koyama et al. 1994; Kamata et al. 1997; this article). The dashed contour map is an estimate of the Class III source surface density (in arbitrary linear units) obtained using a sum of Gaussians (FWHM=8´) centered on each Class III source position. Plus signs show the positions of the density peaks of Class II sources (see Fig. 8). Class III sources with known spectral types are labeled, and put in an H-R diagram in Fig. 10.

The explanation for this apparent absence may be as follows. Whether they lie on the line-of-sight to regions of moderate extinction, or of high extinction, moderate-extinction Class II sources are found essentially everywhere. Therefore we also expect to have low-extinction Class III sources everywhere , in a 1:1 proportion. If they are not detected with the HRI , it can thus only mean that they are too faint in X-rays, hence have a small stellar luminosity. In addition, as for Class II sources, we must expect along the line-of-sight to the densest regions of the cloud to also have moderately embedded Class III sources at the back of the cloud. Their spatial density should be roughly comparable to that of the unseen Class III sources in the front, i.e., yield a small absolute number given the compact size of the C¹⁸O cores.

There is also the possibility of having genuinely embedded (hence very young) Class III sources in these cores: we have no information about the Class III/Class II source ratio there, so it is impossible to estimate their number. Should this number be large (such that Class III/Class II for instance), this would be a problem for the earliest stages of YSO evolution; one rather expects to have Class III/Class II if all stars form with a disk taking at least yr to dissipate. However, a disk stage is perhaps not necessary for very low-mass stars, which would increase the number of very young Class III sources.

6.2. Constraints on the nature of the unknown Class III sources

Let us construct the H-R diagram of the 12 Class III sources in HRI /ISOCAM area for which we know the spectral types from the optical observations of Bouvier & Appenzeller (1992), and from the K-band observations of Luhman & Rieke (1999), using the stellar luminosities determined by Bontemps et al. (2000). ¹⁵ Fig. 10 displays the result, along with the birthline and pre-main sequence evolutionary tracks of Palla & Stahler (1999). According to these evolutionary tracks, the ages of the 12 Class III sources are found to be spread between and Myr.

Fig. 10. H-R diagram for the Class III source with a known spectral types. Dotted lines show Palla & Stahler (1999) pre-main sequence tracks, continuous lines show isochrones. The bold continuous line represents the birthline for the star build-up accretion rate ( yr-1). White dots show the position of Class III sources with known spectral type (Bouvier & Appenzeller 1992; Luhman & Rieke 1999; see also Greene & Meyer 1995), and using the Bontemps et al. (2000) luminosities. Crosses show X-ray detected Class III sources (Montmerle et al. 1983; CMFA; Koyama et al. 1994; Kamata et al. 1997; this article). We take pc. The error bar shows the systematic luminosity error corresponding to a distance error of pc.

It is reasonable to assume that the unknown Class III sources have the same age spread. These sources are not yet detected in X-rays either because their intrinsic X-ray luminosities are too low, and/or because they have high extinctions. In the first case they have stellar luminosities below 0.35 , and the isochrones imply that for the oldest ones, and for the youngest ones. In the second case, however, the unknown embedded Class III sources can have luminosities higher than , i.e., so that they are not necessarily very low-mass stars.

Unless the number of Class III sources embedded in the densest regions is very high, our conclusion is that the bulk of the Class III sources which are undetected by the HRIand unrecognized by ISOCAMshould be made of very low-mass stars .

© European Southern Observatory (ESO) 2000

Online publication: June 30, 2000
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