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Astron. Astrophys. 342, 257-270 (1999)

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6. Discussion

What is the explanation for the decrease of the abundance ratio [FORMULA]/[FORMULA] with extinction (Fig. 11c, Eq. 7) for the mapped region and also, though less pronounced, (Fig. 12c, Eq. 9) for the background stars? In our opinion, the simplest interpretation is that in the central portions of the IC 5146 cloud and in other parts of the Northern Streamer, CO and hence [FORMULA] are underabundant by a factor of at least 3 because a large fraction, i.e. at least 70%, of the available carbon is frozen out on dust grain surfaces. In addition, we infer that the degree of depletion in the inner, central regions may be higher since the surface regions appear to contain undepleted CO. Our [FORMULA] observations discussed earlier make it appear unlikely that the discrepancy with the canonical abundance ratio (Eq. 5) can be explained by optical depth effects. The fact that we observed two [FORMULA] transitions has allowed us to account for excitation. Anomalies in the gas phase chemistry seem unlikely because CO is under almost all circumstances the main repository of gas phase carbon. We thus conclude that the reduction of [FORMULA]/[FORMULA] observed by us at high extinctions is due to a reduction of the total amount of gas phase carbon.

Depletion of CO is consistent with the observation of CO ice features in quiescent dark clouds (Chiar et al. 1995) at visual extinctions of more than 6 mag. These absorption measurements towards background stars and embedded stars indicate that up to [FORMULA]% of the CO is depleted onto dust grains. In general, the observations of solid CO do not suggest solid phase CO column densities higher than seen in the gas phase (Whittet & Duley 1991, Sandford & Allamandola 1993). However, observations of the deuterium fractionation indicate that depletion of CO by a factor of order 5 are common in dense cores (Caselli et al. 1998).

Chemical models of developing protostellar cores (Bergin et al. 1995, Bergin & Langer 1997), similar to the one described here indicate, that the molecular abundances of species like NH3,CS, HCO+, etc. are very sensitive functions of the density for [FORMULA] cm-3 and grain mantle composition (CO or H2O ices). There are observational evidences (Chiar et al. 1995) that CO resides predominantly in nonpolar ices where H2O is not the main constituent. At densities below [FORMULA] cm-3, NH3, being a minor species, does not deplete (see e.g. Pineau des Forêts 1991, Bergin & Langer 1997). This is consistent with observations of ammonia that often show smaller line widths and spatial extents than observed in [FORMULA] (e.g. Myers et al. 1991). Also, the deuterium fractionation is expected to depend upon the depletion (Dalgarno & Lepp 1984). It will thus be useful to study correlations, e.g. between [CO]/[H2], [DCO+]/[HCO+], and [CS]/[NH3].

6.1. Mapped region

6.1.1. Core masses

It is of interest to know to what extent depletion onto grain surfaces might cause us to underestimate cloud masses when using [FORMULA] as a tracer. We consider first the mapped region used to derive [FORMULA] LVG column densities (Figs. 9, 11). The gas mass derived from the NIR extinction measurements is [FORMULA] while [FORMULA] LVG column densities show [FORMULA] and thus miss [FORMULA]. Considering only the region with [FORMULA][FORMULA] mag, the difference is already a factor of more than 2: [FORMULA], [FORMULA]. We can use the NIR observations to estimate the mass in the high density core where CO is nearly absent by subtracting a background of [FORMULA]= 10 mag from our NIR map and integrating over the residual high density core. We find in this way that the NIR core has a mass of [FORMULA], exactly the mass missed by [FORMULA], and half-power diameters of [FORMULA] ([FORMULA] pc2). The latter is hardly resolved in our NIR map and it will be useful to obtain maps of the core in high density molecular line tracers. The average volume density of this core is [FORMULA] cm-3.

6.1.2. Depletion factor and dust temperature

In Paper I, we analyzed the variation of the ratio of observed 1.2mm dust flux per beam divided by [FORMULA] (Fig. 2 therein) over the mapped region in IC 5146. We argued that the most plausible explanation of these data is a dust temperature gradient from 8 K in the core interior ([FORMULA][FORMULA] mag) to 20 K in the regions of low (5 mag) extinction. The inner central regions might be colder than 8 K, since dust temperatures are, like depletion factors, averages along each line of sight, and the exterior regions appear to be warmer.

In Fig. 13 we plot dust temperature (Paper I) and depletion factor (derived in Sect. 4) at the positions within the mapped region shown in Fig. 9. The highest depletion values [FORMULA] (Eq. 8) are reached in the coldest ([FORMULA] K) and densest ([FORMULA] = 28 mag) part of the region. CO is depleted by a factor of about 2 when the dust temperature falls from 15 K to 10 K, and there is practically no depletion at [FORMULA] K. These two findings are in good agreement with the model calulations of Bergin et al. (1995).

[FIGURE] Fig. 13. Depletion factors [FORMULA] and dust temperatures [FORMULA] within the mapped region. Depletion factors were derived from [FORMULA] data and a comparison with the extinctions [FORMULA] found by Lada et al. (1998). Dust temperatures had been derived in Paper I from the ratio of 1.2 mm flux and [FORMULA]. We fitted an exponential function to the data (full curve).

The depletion factor [FORMULA] shown in Fig. 13 appears to depend exponentially on the dust temperature: [FORMULA]. A linear least squares fit to the linearized data of Fig. 13 results in


and a high correlation coefficient of 0.92. The fitted temperature, [FORMULA] K, is an average temperature of the observed positions and along the lines of sight, describing the region as a whole. [FORMULA] might reflect the desorption processes at work on the grain surfaces. Thermal evaporation cannot be the dominant process at these dust temperatures, since the binding energy of CO on CO ices is about 1000 K (e.g. Bergin et al. 1995). Other desorption processes, like e.g. cosmic ray induced desorption (Bergin & Langer 1997) or spot heating by H2 formation on grain surfaces may be dominant at low temperatures and may, moreover, depend on the dust temperature.

The large scatter of the abundance ratios shown in Fig. 11c for [FORMULA][FORMULA] mag is naturally explained by a variation of dust temperatures between [FORMULA] and 20 K at depletion factors close to the canonical ratio (Fig. 13), given the exponential dependence of [FORMULA] on [FORMULA].

6.2. The pointed observations towards background stars

It seems reasonable to believe that the dispersion in integrated [FORMULA] intensity plotted against [FORMULA] by factors of 7 relative to the observational uncertainty, at [FORMULA][FORMULA] mag (Fig. 12), is due to dispersion in the fraction of CO depleted onto dust grains. If we consider the dust temperatures to be constant, one explanation might be that we are observing a set of clumps with a wide dispersion of ages. The fraction of CO in the gas phase will decrease with time at a rate which depends upon the local density but in general a large value for [FORMULA]([FORMULA])/[FORMULA] should be a mark of youth.

The large scatter of optical extinctions [FORMULA] in the direction of background stars for a given integrated [FORMULA] intensity (Fig. 12) may also be explained by clumping on size scales smaller than 0.05 pc. This is because the [FORMULA] measurements average over the size of the beam ([FORMULA]) while the resolution of the extinction measurements is that of a pencil beam. This argument will be analyzed in Lada et al. (1998) by comparing the scatter of individual [FORMULA] values within the averaged [FORMULA] optical extinctions, similar to what LLCB94 did - but at a higher resolution of [FORMULA]. Clumpiness at scales beyond 0.05 pc is e.g. consistent with recent observations of nearby non-star forming clouds at high resolutions (Heithausen et al. 1998, Kramer et al. 1998). These show substructure down to sizes of about 0.01 pc or 2000 a.u..

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Online publication: December 22, 1998