Astron. Astrophys. 358, 257-275 (2000)

2. Observational results, subsequent data processing, and analysis

The source coordinates are, together with distance estimates, catalogued in Table 1 of Paper I. Moreover, the observational procedures, data reduction, and observational results have been described in Paper I. The observing strategy was to map the SO() line until the signal disappeared and subsequently make CS(2-1) maps. We also observed C³⁴S(2-1) and ³⁴SO() in strategic positions. We mapped the C³⁴S(2-1) and ³⁴SO() lines in the very clear case of variations in NGC 1333.

2.1. Integrated intensity ratio maps

The SO() and CS(2-1) integrated intensities and 1 errors were calculated and tabulated for all positions where both lines had been observed. As a measure of the uncertainty of the ratio we use

where and are the errors in A and B, respectively. Our acceptance criterion for a "reliable" ratio was set to (). However, this strong criterion could not be applied to the NGC 1333 rare isotopomer data for which a limit was used. The ratios are presented as ratio maps in Figs. 1a-1v. Here we have also included physical size scales together with selected objects from the SIMBAD database. The SIMBAD objects presented in Figs. 1a-1v are X-ray and IR sources, masers, HII regions and HH-objects (see Table 1 for symbol explanations). The contour maps in Figs. 1a-1v have been displayed using bicubic interpolation of the contour lines.

Fig. 1a. The SO/CS integrated intensity ratio in DR 21(OH). Observed positions are marked with a cross (+). Various objects from the SIMBAD database have been entered, see Table 1

Fig. 1b. The SO/CS integrated intensity ratio in G 34.3+0.2

Fig. 1c. The SO/CS integrated intensity ratio in IRAS 21391+5802

Fig. 1d. The SO/CS integrated intensity ratio in NGC 1333

Fig. 1e. The 34SO/C34S integrated intensity ratio in NGC 1333

Fig. 1f. The SO/CS integrated intensity ratio in Mon R2

Fig. 1g. The SO/CS integrated intensity ratio in NGC 2023

Fig. 1h. The SO/CS integrated intensity ratio in NGC 2024

Fig. 1i. The SO/CS integrated intensity ratio in NGC 2068

Fig. 1j. The SO/CS integrated intensity ratio in NGC 2071, outflow component included

Fig. 1k. The SO/CS integrated intensity ratio in NGC 2071, with a gaussian outflow component removed

Fig. 1l. The SO/CS integrated intensity ratio in NGC 2264IR

Fig. 1m. The SO/CS integrated intensity ratio in NGC 7538

Fig. 1n. The SO/CS integrated intensity ratio in Orion A (outflow component included)

Fig. 1o. The SO/CS integrated intensity ratio in Orion A, with outflow and hot core components removed

Fig. 1p. The SO/CS integrated intensity ratio in OMC-2

Fig. 1q. The SO/CS integrated intensity ratio in OMC-3

Fig. 1r. The SO/CS integrated intensity ratio in S 140

Fig. 1s. The SO/CS integrated intensity ratio in W3(IRS4)

Fig. 1t. The SO/CS integrated intensity ratio in W3(OH)

Fig. 1u. The SO/CS integrated intensity ratio in W 49N

Fig. 1v. The SO/CS integrated intensity ratio in W 51N

Considerable variations in the SO/CS integrated intensity ratio have been found within as well as between the sources. In some sources this ratio exhibits very large variations while in others the variations are small. The maximum and minimum ratios have been tabulated for each map in Table 2.

Table 2. Maxima and minima of SO/CS integrated intensity ratios

As explained in Paper I, we have removed a broad gaussian outflow component from the CS(2-1) and SO() line profile maps of NGC 2071 and Orion A. In Orion A an additional component due to the hot core emission was removed. In the integrated intensity ratio maps (Figs. 1j-1k and Figs. 1n-1o) and in Table 2, we present results for both these sources with as well as without removal of an outflow component.

2.1.1. NGC 1333

In NGC 1333 we observe a highly varying SO/CS ratio. In the main isotopomer ratio map (Fig. 1d) we found a very low ratio of about 0.25 at the driving source of the HH 7-11 outflow SVS 13 (Liseau et al. 1988), while the position of the highest ratio of 1.3 coincides with the strong far infrared source IRAS 4 (Jennings et al. 1987). We also see an elevated ratio in an extended region north of IRAS 4. In the ³⁴SO/C³⁴S isotopomer ratio map we confirm, within the current error limits, the main features of the main isotopomer ratio map, using optically thin lines. No kinematical outflow evidence in terms of line-wings is apparent in the observed SO() and CS(2-1) lines. Hence, the strong enhancement of the SO/CS abundance ratio is intrinsic to the quiescent gas although the probable reason for this enhancement is compression caused by the outflow from SVS 13, as will be argued in our subsequent discussion (Sect. 4.1.1). Chernin et al. (1994) have noted that the SO() transition does not (easily) probe the outflowing gas, while the higher excitation SO() line is a useful outflow tracer.

2.1.2. NGC 2068

The (0,0) position in our map (Fig. 1i) coincides with the Herbig Haro object HH 24 and the area mapped contains two molecular outflows (Snell & Edwards 1982; Edwards & Snell 1984). The SO/CS ratio maximum of about 1.3 is located in the outflow area between HH 24 and HH 27. Our observed SO and CS distributions are rather clumpy (see Paper I), but the SO and CS "brightness clumps" do not coincide and no kinematic evidence of outflows is apparent in our data. It may well be that the SO/CS ratio maximum in the quiescent gas coincides with a compressed region caused by the "CO outflows". We will return to an analysis of this source in Paper III.

2.1.3. NGC 2071

In NGC 2071 (Fig. 1k) the lowest SO/CS ratio (0.25) appears close to the origin of a very extended outflow source oriented in the NE/SW direction (Snell et al. 1984b; Chernin et al. 1994). The maximum SO/CS ratio (1.6) appears NW of the outflow and results from an increase of the SO emission together with a decrease of the CS emission (see Paper I). This does not indicate a compression by the outflow and we see at present no obvious physical reason for the increased SO/CS ratio. We will return to this question in Paper III.

2.1.4. Orion A

Orion A contains a well-known outflow in our map centre position (e.g. Olofsson et al. 1982; Friberg 1984; Sutton et al. 1995). The SO emission is extremely enhanced in the outflow (see Paper I and Friberg 1984). The broad gaussian outflow component has an SO/CS integrated intensity ratio of about 6 in the centre position. The quiescent cloud (the remaining emission when the outflow and hot core components have been removed, Fig. 1o) has a very low SO/CS integrated intensity ratio (0.03-0.34) - among the lowest found in our sample of molecular clouds.

2.1.5. IRAS 21391+5802

In IRAS 21391+5802 we observe an elevated SO/CS ratio north of map centre position (Fig. 1c). This source contains two outflows (Patel et al. 1995), which are both located near the SO/CS ratio peak.

2.2. Correlation with SIMBAD objects

In Figs. 1a-1v we have displayed a number of SO/CS integrated intensity ratio maps, where also selected objects from the SIMBAD database have been entered (see Table 1 for symbol explanations). However, unfortunately we see no obvious correlation between the SIMBAD objects and the observed variations in the SO/CS ratio.

2.3. From intensity to abundance ratios

Table 3 contains a number of relevant ratios at positions where we have at least three observed lines. The integrated intensity isotopomer ratios (SO/³⁴SO and CS/C³⁴S) provide information about the optical depth. Fig. 2 displays the main line optical depth as a function of the main line to isotopomer intensity ratio, assuming a ³²S/³⁴S abundance ratio of 22 (Wilson & Rood 1994; Lucas & Liszt 1998) and the same excitation temperature for both isotopomers. SO/³⁴SO or CS/C³⁴S ratios well below 22 are indicative of optically thick main isotopomer lines. The SO/CS ratio has been included in Table 3 for comparison, with the ratio of the optically thin lines ³⁴SO and C³⁴S. The latter lines will lead to a more reliable estimate of the abundance ratio. In the penultimate column of Table 3 we have entered the ratio considered to be the most reliable ratio, i.e. the ratio derived from the observational data after an optical depth correction. We have here compensated for the assumed isotopic ratio ³²S/³⁴S = 22. See the footnotes of Table 3 for further explanations.

Fig. 2. SO or CS main line optical depth as function of main line to isotopomer ratio (assuming the same for both isotopomers and a 32S/34S ratio of 22)

Table 3. Integrated intensity ratios (A-E) and estimated abundance ratios (F) at certain positions.
Notes:
a(b) denotes value( error) where an error of (0.00) means error Ratio A: SO()/³⁴SO(), Ratio B: CS(2-1)/C³⁴S(2-1), Ratio C: SO()/CS(2-1) Ratio D: ³⁴SO()/C³⁴S(2-1), Ratio E: adopted SO/CS ratio, calculated for optically thin lines, T = 20 K (see text). Explanations of the adopted SO/CS ratio: : ³⁴SO()/C³⁴S(2-1), b): SO()/(C³⁴S(2-1)), c): SO()/CS(2-1), d): SO()/CS(2-1)

Table 3. (continued)
Notes:
a(b) denotes value( error) where an error of (0.00) means error Ratio A: SO()/³⁴SO(), Ratio B: CS(2-1)/C³⁴S(2-1), Ratio C: SO()/CS(2-1) Ratio D: ³⁴SO()/C³⁴S(2-1), Ratio E: adopted SO/CS ratio, calculated for optically thin lines, T = 20 K (see text). Explanations of the adopted SO/CS ratio: : ³⁴SO()/C³⁴S(2-1), b): SO()/(C³⁴S(2-1)), c): SO()/CS(2-1), d): SO()/CS(2-1)

Following Irvine et al. (1987) we have subsequently calculated the [SO]/[CS] ratios assuming optically thin lines as stated below, and entered the results in the last column of Table 3.

Using the relationship between the observed intensity integrated across the spectral line, , and the upper state column density of the transition, , derived by Irvine et al. (1987), for optically thin emission and ignoring the background brightness, we arrive at the following expression for the ratio between the upper state column densities

where and A are the frequencies and spontaneous emission rates of the observed transitions. Here all quantities have been properly identified as belonging to SO or CS. The above relationship may be understood as the ratio between the number of photons spontaneously emitted from the upper to the lower SO and CS states in question, and will remain a good approximation if the SO and CS excitation temperatures are similarly large (cf. Irvine et al. 1987). Excitation temperatures of similar size would be expected from the SO() and CS(2-1) transitions because of their very similar upper state energies ( 9.23 and 7.05 K, respectively) and A-coefficients ( and s^-1). The relatively large A-coefficients imply that both transitions are mainly probing gas of high H₂ density, (Snell et al. 1984a; Mundy et al. 1986).

Since the total molecular column density N may be related to the upper state column density via

we may now proceed to calculate the ratio of the total SO and CS column densities. Here the is the statistical weight of the upper state whose energy is and whose total angular momentum quantum number is J, k is the Boltzmann constant, T is the population distribution ("rotation") temperature and is the molecular partition function evaluated at temperature T. The partition function for a linear molecule may (for not too low T) be approximated by

where h is Planck's constant and B is the molecular rotation constant. Here for CS and for SO [accounting for the threefold multiplicity of its ground state, cf. Turner (1991)]. Using the approximate partition function, Eq. (6), together with Eqs. (4) and (5), we finally arrive at the following useful measure of the SO to CS abundance ratio,

If we assume the same excitation temperature, T, for both species this relation simplifies to

where the proper molecular parameters have been entered. We note that according to Eq. (7) the conversion factor determining from only varies from 4.5 to 3.9 if the common excitation temperature changes from 10 K to 30 K. The SO/CS abundance ratios entered in the last column of Table 3 are calculated for 20 K. We will now proceed to motivate our simplified analytical approach by some exploratory Monte Carlo simulations.

2.4. Monte Carlo simulations

In order to verify that the above estimate of the SO/CS abundance ratio is not severely affected by non-LTE excitation effects we have performed Monte Carlo simulations (cf. Bernes 1979) using a spherical model cloud of radius (divided into 19 concentrical shells of equal volume) exposed to the cosmic background radiation (T=2.73 K). The abundance, H₂ density, and kinetic temperature, , were all kept constant throughout the cloud. For CS and SO we included all levels with excitation energies below 400 K. Collisional rate coefficients for SO-H₂ were taken from Green (1994) and for CS-H₂ we used those reported by Turner et al. (1992). The modelled line intensities were obtained by numerically integrating the intensity along rays at different offsets from the model cloud center and adding together the contributions from each ray with a proper weight corresponding to a gaussian beam of width 39". The model cloud was assumed to be at a distance of 1 kpc.

We have performed Monte Carlo simulations for CS and SO at four different abundances in the range at several H₂ densites in the range . The kinetic temperature was 30 K in all simulations. The results are presented in Fig. 3, where the SO()/CS(2-1) integrated intensity ratio is plotted as a function of molecular column density through the center of the model cloud. The displayed intensity ratio reflects the case when the molecular column density is the same for both species. The CS and SO lines start to become optically thick at column densities . At lower column densites (and low H₂ densities since the cloud size is constant) the excitation is highly subthermal, and at high column densities (also high H₂ densities) the ratio approaches 1 when both lines are very optically thick. The reason why the limit ratio is slightly below 1 is that the optical depth broadening is somewhat larger for the CS line as compared to the SO line. Judging from the Monte Carlo results shown in Fig. 3 we find that the variation of the SO/CS integrated intensity ratio is fairly small for a large range of H₂ densities and abundances, and that the variations that do occur are mainly due to optical depth effects. Here the lowest abundance () should be representative of ³⁴SO/C³⁴S data. We conclude that the simplified analysis presented in Sect. 2.3 is sufficiently accurate for our purposes.

Fig. 3. The SO()/CS(2-1) integrated intensity ratio as function of molecular column density () for a Monte Carlo model cloud of radius .

© European Southern Observatory (ESO) 2000

Online publication: June 26, 2000
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