In the 
range 
was scanned for the three W 3
sources, compared with 
in the 
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(
). 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
JPL
(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 
lines in this frequency range became available at
the end of 1994, while some frequencies for 
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 
and
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 
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(
) is picked
up by our 15 and 21
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(
). 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(
) (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.
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(
). On the
other hand, asymmetric rotors, like 
and 
, 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 
, 
, 
and 
.
They are shown in Fig. 2 (click here). It should be noted that these organics are
found primarily toward W 3(
).
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 
also have transitions which are very
sensitive to the kinetic temperature. In Paper I, the densities were
constrained to be 
, 
and 
for
IRS4, IRS5 and W 3(
), respectively, and the temperatures
, 
and 
from the ratios
of 
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 
, 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 
345 GHz beam, unless otherwise
stated.
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
10
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(
)
(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 
column density is needed. In
this study the total column density is determined from observations of
an optically thin 
line. The uncertainty in the
abundance introduces a factor of 2-3 uncertainty in
derived 
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.
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 
, whereas the 
isotopomer is written 
etc.
The following solar abundance ratios are used (Wilson & Rood 1994):
[
; [
;
[
; [
;
[
; [
and
[
. For deuterium no ratio is given, since
deuterium fractionation is highly variable in dense molecular clouds.