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4. Analysis

4.1. Line identification and profile fits

In the tex2html_wrap_inline3901 range tex2html_wrap_inline3903 was scanned for the three W 3 sources, compared with tex2html_wrap_inline3905 in the tex2html_wrap_inline3907 range. In total 100 lines of 14 different molecules (24 including isotopic species) were detected in W 3 IRS4, 187 of 18 molecules (31 isotopes) in IRS5, and 354 of 22 molecules (41 isotopes) in W 3(tex2html_wrap_inline3909). After calibration, base line subtraction, smoothing and line identification, the lines were fit with single Gaussians using the IRAM CLASS software. The line frequencies were obtained mainly from the JPLgif (Pickett 1991) and Lovas catalog (see Groesbeck 1994). A detailed list with frequencies for methanol, methyl formate and dimethyl ether is given in Anderson et al. (1990, and by Herbst (private communication). A complete list of tex2html_wrap_inline3911 lines in this frequency range became available at the end of 1994, while some frequencies for tex2html_wrap_inline3913 were taken from Sutton et al. (1991, 1995). Most of this information was incorporated into the SIMCAT software at the California Institute of Technology (Groesbeck 1994), and was heavily used during this study. The results can be found in Tables 7 (click here)-14 (click here). Only a handful of lines remain unidentified, which are summarized in Table 4 (click here) at the end of the paper.

Although in general good single Gaussian fits were readily obtained, the widths of the lines were found to vary considerably. Explanations for this behavior can be blending with other lines; blending with a line in the other sideband; outflowing gas (e.g., CO); saturation of the line (e.g., SO), blending of hyper-fine components; and in some cases problems in the determination of the base line (some tex2html_wrap_inline3915 and tex2html_wrap_inline3917 lines). In cases where the line widths varied substantially this is indicated in the discussion per molecule. In Tables 7 (click here)-14 (click here) the listed values are generally those from the Gaussian fits, but in a few complicated cases the integrals over the line are given. Footnotes indicate blending, absorption, or problems encountered. No attempt has been made to disentangle the individual contributions to the integrated line strength in case of blended components. In the subsequent analysis, error bars on high S/N lines are taken to be 30%, whereas 60% is adopted for marginal cases. If upper limits are used in the analysis their integrated line strength was calculated using the tex2html_wrap_inline3919 noise temperature together with the characteristic velocity width of the source given in Sect. 3.

As discussed in Paper I, not only emission from W 3(tex2html_wrap_inline3921) is picked up by our 15 and 21tex2html_wrap3929 beams, but also from the compact HII region W 3(OH). In the analysis of the data it turned out that this confusion is very small and that most emission is indeed from W 3(tex2html_wrap_inline3925). This is strengthened by interferometric observations (Wink et al. 1994; Wilner et al. 1995; Turner & Welch 1984) which show that compact line emission is concentrated at W 3(tex2html_wrap_inline3927) (the Turner-Welch object), whereas W 3(OH) dominates the continuum maps. Most of the extended emission stems from the core surrounding the two objects.

4.2. Excitation analysis

As was done in Paper I, rotation diagrams were constructed for those species for which a sufficient number of lines are available. The rotation diagram method (e.g., Blake et al. 1987; Sutton et al. 1985; Turner 1991; Sutton et al. 1995) is a powerful tool to determine the rotational excitation temperature and the beam-averaged column density. It requires the lines to be optically thin and the level populations to be thermalised, but even deviations provide very useful information about optical thickness and/or non-thermal excitation (cf. Blake et al. 1994; Sutton et al. 1995). The method only works well, however, if a sufficient number of lines of the same molecule have been detected. Especially linear molecules often have only two or three transitions in the scanned frequency range, which limits the usefulness of the derived rotational temperature. An exception is OCS, which is heavy enough that several lines are covered in the survey and detected toward W 3(tex2html_wrap_inline3931). On the other hand, asymmetric rotors, like tex2html_wrap_inline3933 and tex2html_wrap_inline3935, have a large number of transitions in the scanned frequency range which are easily observed. Other species for which rotation diagrams could be constructed are tex2html_wrap_inline3937, tex2html_wrap_inline3939, tex2html_wrap_inline3941 and tex2html_wrap_inline3943. They are shown in Fig. 2 (click here). It should be noted that these organics are found primarily toward W 3(tex2html_wrap_inline3945).

A better method to analyze the data is through statistical equilibrium calculations. This has not been done with earlier survey data (e.g. Blake et al. 1995; Schilke et al. 1996), but provides direct constraints on the physical parameters, in particular kinetic temperature and density. The adopted method, described in detail in Jansen et al. (1994), van Dishoeck et al. (1993b) and Jansen (1995), solves the level populations of a molecule by balancing the collisional and radiative upward and downward rates. The necessary decoupling of radiative transfer and level populations is done by means of an escape probability formalism. The adopted collisional rate coefficients are summarized in Jansen et al. (1994) and Jansen (1995). Linear rotors are particularly useful in determining the density, whereas (near-) symmetric rotors like tex2html_wrap_inline3947 also have transitions which are very sensitive to the kinetic temperature. In Paper I, the densities were constrained to be tex2html_wrap_inline3949, tex2html_wrap_inline3951 and tex2html_wrap_inline3953 for IRS4, IRS5 and W 3(tex2html_wrap_inline3955), respectively, and the temperatures tex2html_wrap_inline3957, tex2html_wrap_inline3959 and tex2html_wrap_inline3961 from the ratios of tex2html_wrap_inline3963 lines. These values will be adopted in this work for those molecules that do not provide constraints themselves (e.g. single lines).

The statistical equilibrium calculations have been applied mostly to the optically thin (isotopomer) lines present in the survey, although the code can handle moderately optically thick transitions as well. The optically thick lines are useful for a different purpose: once their excitation temperature has been obtained from the isotopomers, they give valuable information about the area-filling factor of the beam, or equivalently, about the source size. Two different methods have been used. For species for which rotation diagrams have been constructed, the inferred excitation temperature for the optically thin isotope has been used in conjunction with the observed main beam temperature of the most optically thick line observed. For other molecules, excitation calculations have been performed using the physical conditions and column density derived from the optically thin isotope. The predicted radiation temperature of the main species has then been compared with the observed value to derive the area-filling factor. Although the results are not very accurate, they give a useful indication of the distribution of the species in the source. The main uncertainty in the first method is caused by the fact that often the main lines have optical depths of tex2html_wrap_inline3965, i.e., somewhat optically thick but not very thick.

For consistency, it is assumed throughout this paper in the excitation analysis that the emission fills the beams, thereby implying that the inferred beam-averaged column densities are lower limits to the ``true'' column densities (see Sect. 4.3). The beam-averaged column densities refer to the tex2html_wrap_inline3967 345 GHz beam, unless otherwise stated.

4.3. Discussion of uncertainties

As mentioned in Sect. 2, the absolute calibration of sub-millimeter lines is accurate to about 30%. The rotation diagram method gives a formal error in rotation temperature and column density, but optical depth and non-LTE conditions can introduce additional uncertainty. In particular, if the lines are optically thick, this will lead to an overestimate of the rotational temperature. Subthermal excitation, on the other hand, implies that the rotational temperature is an underestimate of the kinetic temperature. These effects are better taken into account in the statistical equilibrium calculations, but these depend on the relative and absolute accuracy of the collisional rate coefficients, which can vary from species to species. Altogether, we estimate that the beam-averaged column densities obtained in this study are accurate to better than a factor of two.

A much larger uncertainty in the eventual chemical analysis is introduced by the unknown coupling between telescope beam and source. It is difficult to estimate this influence, since it will vary from molecule to molecule, or even from line to line. A source size of 10tex2html_wrap3983 implies that lines in the 345 GHz window are diluted by a factor of 3, and lines in the 230 GHz window by a factor of 5. For source sizes of 1-2'', as may apply to some species in W 3(tex2html_wrap_inline3973) (Wink et al. 1994), the correction to the column density can be more than two orders of magnitude.

The analysis of the physical parameters is much less affected by the unknown source size. The ratio of a 230 and a 345 GHz line intensity is off by at most a factor of two, if the emission comes from a point source. The excitation effects are often much larger than a factor of two over a narrow density range (cf. Jansen 1995), so that the physical parameters can still be determined quite accurately. For small source sizes, the density will tend to be overestimated, and the beam-averaged column densities underestimated.

In order to determine abundances which can be compared directly with chemical models, information on the tex2html_wrap_inline3975 column density is needed. In this study the total column density is determined from observations of an optically thin tex2html_wrap_inline3977 line. The uncertainty in the tex2html_wrap_inline3979 abundance introduces a factor of 2-3 uncertainty in derived tex2html_wrap_inline3981 column density. This value is again beam-averaged; because CO may be more broadly distributed than some other molecules, the correction factors for source structure are not necessarily the same. Thus, local abundances may differ considerably from the beam-averaged integrated abundances along the line of sight presented here.

4.4. Isotopic abundances

The determination of column densities from optically thin lines of isotopic species requires information on the overall isotopic abundances. As a convention, the main isotopomer is given without atomic weight numbers throughout this paper. Thus CO stands for tex2html_wrap_inline3985, whereas the tex2html_wrap_inline3987 isotopomer is written tex2html_wrap_inline3989 etc. The following solar abundance ratios are used (Wilson & Rood 1994): [tex2html_wrap_inline3991; [tex2html_wrap_inline3993; [tex2html_wrap_inline3995; [tex2html_wrap_inline3997; [tex2html_wrap_inline3999; [tex2html_wrap_inline4001 and [tex2html_wrap_inline4003. For deuterium no ratio is given, since deuterium fractionation is highly variable in dense molecular clouds.

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