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

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1. Introduction

The determination of molecular cloud masses is of fundamental importance for star formation studies as well as for the related problem of the evolution of the interstellar medium. It is of necessity carried out by indirect means because molecular hydrogen, which is the most important constituent of molecular clouds, is not excited at the temperatures of around 10 K typical for dense dust clouds. One therefore has no direct measure of the hydrogen column density. Hence, mass estimates have traditionally used at least three different indirect approaches: First, one can use the dust emission as a surrogate for the gas and derive the hydrogen mass assuming a standard dust-to-gas ratio. Second, one can determine the visual extinction over the surface of the cloud using star counts or reddening measurements towards background stars and again derive the gas mass assuming standard dust properties. A third method, is to use CO isotopomers instead of dust as a hydrogen surrogate and to assume a "canonical" value for the [CO]/[H2] abundance ratio, which itself has been calibrated using dust extinction measurements (see below). This has probably been the most widespread method used to determine masses of dense cores in molecular clouds (e.g. Ladd et al. 1998) and it is thus of importance to test the assumptions used when applying it.

The emission from the main isotopic form of CO is optically thick in situations of interest but the isotopomers with 18O or 17O substituted for 16O usually show evidence for optically thin emission and hence determination of the column density is relatively straightforward. This presupposes knowledge of the true isotopic abundance ratios but there is now a considerable amount of information available (Wilson & Rood 1994) on these ratios. The main difficulty in fact is with the ratio [CO]/[H2] which has up to now only been directly determined in a dense cloud in one very special case (Lacy et al. 1994). The general practice has been to compare CO column densities with dust visual extinction measured along the same line of sight and then use the ratios between N([FORMULA]), H2, and [FORMULA] obtained e.g. by Frerking et al. (1982) and Bohlin et al. (1978) in order to convert dust extinction and CO column density into hydrogen column density. Thus, all three techniques for determining core masses depend on dust properties being standard in the dense gas. We have recently carried out a partial test of this hypothesis (Kramer et al. 1998a, hereafter Paper I) in which we showed that the millimeter wavelength emissivity of dust grains associated with a dense clump in the molecular cloud IC 5146 is consistent with theoretical expectations. In this paper, we use observations of the same dense core to examine the usefulness of [FORMULA] as a tracer of the dense gas distribution.

The work in this paper is motivated by the study of Lada et al. (1994, hereafter LLCB94) who used a JHK imaging survey to directly derive line-of-sight extinctions to more that 4000 field stars found in an area covering [FORMULA] towards the molecular cloud complex, called the Northern Streamer, presumably associated with the young cluster IC 5146 which lies in Cygnus. We adopt here a distance of 460 pc to the cloud (Lada et al. 1998). There is little evidence for star formation in the Northern Streamer. Only five candidate protostars were found by Dobashi et al. (1993) (Fig. 10). They were selected from the IRAS point source catalog and show a rising far infrared spectrum typical of young embedded protostellar objects. No such objects are found within the region mapped by us. The H II region S125 and its associated young open cluster are more than [FORMULA] to the east while the galactic plane lies [FORMULA] to the north-west.

LLCB94 also surveyed the molecular content of the Northern Streamer using the [FORMULA](1[FORMULA]0), [FORMULA](1[FORMULA]0) and CS(2[FORMULA]1) molecular-lines at millimeter-wavelengths. By spatially averaging the individual extinctions, [FORMULA], over boxes identical in width to the HPBW ([FORMULA]) of the molecular-line observations, LLCB94 were able to compare directly the molecular-line intensities and column densities with the spatially averaged extinction measurements, [FORMULA]. At low extinctions they found rough linear correlations between integrated intensities and extinction. However, the dispersions about these linear correlations were larger than could be accounted for by the observational errors. This led LLCB94 to suspect significant and perhaps random variations in the molecular abundances or excitation across the cloud complex. Perhaps related to this was the fact that LLCB94 also found that the measured dispersion of mean extinctions within a measurement cell was outside the measurement error and increased with mean extinction, [FORMULA]. This suggested that structure on scales smaller than their cell size ([FORMULA]) was influencing their results. In addition, LLCB94 found that the relation between integrated intensities and extinctions significantly flattened at large extinctions for all molecular tracers. For [FORMULA] the relation became flat at extinctions [FORMULA] 3-5 mag while for the [FORMULA] and CS lines, this occurred at [FORMULA] 15 magnitudes. Because of its relatively high abundance, the flattening of [FORMULA] integrated intensity with extinction likely results from high opacity in the observed transition leading to saturation at high column densities. However, for the much less abundant species of [FORMULA] and CS a decrease in molecular abundance with extinction could also be the cause of the depressed intensities of the lines at high extinctions (LLCB94). A decrease in abundance or depletion of molecules at high extinction would have interesting consequences for cloud chemistry. To distinguish between opacity and depletion as the cause of this effect we need a determination of the opacities of the lines in question.

The data presented by LLCB94 prompted us to use the IRAM 30m telescope to observe the transitions of [FORMULA] and [FORMULA] in the 1[FORMULA]0 and 2[FORMULA]1 lines to both examine the small scale structure of the cloud and investigate the behavior of [FORMULA] emission at high extinction. With the 30m telescope we reach an angular resolution of 0.05 pc ([FORMULA]) in the 1[FORMULA]0 line and 0.025 pc ([FORMULA]) in the 2[FORMULA]1 line. We obtained maps of both the [FORMULA]1[FORMULA]0 and 2[FORMULA]1 transitions of [FORMULA] in a [FORMULA] core region of the dark cloud selected for both its high mean extinction and lack of star formation activity. To check the optical depth of these lines we obtained [FORMULA] observations at 24 positions in the core region. In this way we were able to examine the small scale structure of the [FORMULA] emission, its excitation, and abundance over an area of [FORMULA] pc2. The high extinction stars observed by LLCB94 extend over a much larger area than our map and so we have also made pointed observations of [FORMULA] (1[FORMULA]0) and (2[FORMULA]1) towards 94 stars with visual extinction [FORMULA] greater than 10 magnitudes from the list of LLCB94. This enables us to compare directly the visual extinction derived from the results of LLCB94 with the [FORMULA] (1[FORMULA]0) and (2[FORMULA]1) integrated intensity within our relatively small beam.

In a parallel study to improve the angular resolution and depth of the extinction measurements, Lada et al. (1998) obtained a new and significantly more sensitive infrared imaging survey of the Northern Streamer. This deep infrared survey includes the core region observed here and allowed the construction of a new map of mean extinction, [FORMULA], at an effective resolution of [FORMULA]1 In Paper I we compared this data with observations of the [FORMULA] 1.2mm dust emission of the core region mapped here at the same resolution. The data indicates a gradient in dust temperature from 8 K in the interior to 20 K in regions of low extinction and suggests that the 1.2mm intensity is by itself not a good tracer of mass in this core. In this paper we directly compare the new CO and extinction measurements by convolving our CO observations to the same angular resolution as the extinction measurements. In this way we are able to investigate the relation between CO and hydrogen abundances at higher resolution and extinction than possible in the earlier LLCB94 study and thus to assess the questions of CO depletion and the ability of [FORMULA] emission to trace cloud mass.

In Sect. 2 of this paper we describe our observational method and in Sect. 3.1.-3.6. we present our [FORMULA] maps and column density estimates. In Sect. 4 we compare our findings with the NIR extinction data. In Sect. 5 we present our [FORMULA] pointed measurements towards background stars and compare them with extinctions. Sect. 6 discusses the results and Sect. 7 gives a summary.

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© European Southern Observatory (ESO) 1999

Online publication: December 22, 1998