5 Discussion of the results

5.1 Intensities and line widths

Figure 1 shows the distribution of the CS(2-1) line intensities of bipolar outflows and of Class I and Class II methanol masers. The distributions of the intensities are approximately the same for bipolar outflows and for Class II methanol masers: $\overline{T}^*_{\rm A}=0.95~\pm~$0.09 K and $\overline{T}^*_{\rm A}=1.38~\pm~$0.22 K, respectively. The Class I methanol masers are stronger in CS: $\overline{T}^*_{\rm A}=2.86~\pm~$0.41 K.

Figure 2 shows the distributions of the CS(2-1) line widths (main feature) for bipolar outflows and for Class I and Class II methanol masers. Methanol masers have, in general, wider main features:

$\Delta V_{\rm main}{\rm (CS)(BO)}=(2.33 \pm 0.15)~{\rm km~s}^{-1}$
$\Delta V_{\rm main}{\rm (CS)(MMI)}=(6.21 \pm 0.55)~{\rm km~s}^{-1}$
$\Delta V_{\rm main}{\rm (CS)(MMII)}=(4.80 \pm 0.34)~{\rm km~s}^{-1}$.

  

Figure 2: Distributions of the CS(2-1) line widths (main feature) for bipolar outflows (BO), for Class I (MMI), and for Class II (MMII) methanol masers

Figure 3 shows the distributions of the CS(2-1) widths of wings for bipolar outflows and for Class I and II methanol masers. A complex line shape was observed in 52$\%$ of the bipolar outflows, in 23$\%$ of the Class I methanol masers, and in 37$\%$ of the Class II methanol masers. We adopted as the wing of a CS line the HPBW of the pedestal. The wings of the CS lines have a negligible range:

  

Figure 3: Distributions of the CS(2-1) widths of wings for bipolar outflows (BO), for Class I (MMI), and for Class II (MMII) methanol masers

$\Delta V_{\rm wings}{\rm (CS)(BO)}=(6.15 \pm 0.38)~{\rm km~s}^{-1}$
$\Delta V_{\rm wings}{\rm (CS)(MMI)}=(8.37 \pm 0.97)~{\rm km~s}^{-1}$
$\Delta V_{\rm wings}{\rm (CS)(MMII)}=(8.71 \pm 1.28)~{\rm km~s}^{-1}$.

Thus, the results of our observations confirm the conclusion of Thronson & Lada (1984), that wide wings in CS are rare.

5.2 Column densities

An evaluation of the CS column density for an optically thin layer was done with the formula taken from Knee et al. (1990).

The results of the observations of the CS(2-1) line and of the isotopic C³⁴S(2-1) line allow us to calculate the value of the optical depth in CS (e.g. Zinchenko et al. 1994).

The resulting column density value should be defined more precisely in conformity with the equation:

$$N'=\frac {\tau} {1-{\rm e}^{-\tau}}N,$$ (1)

  

Figure 4: Distributions of the CS column density for bipolar outflows, for Class I, and for Class II methanol masers

 

Table 3: Column density of BO and MM

where $\tau$ is the optical depth and N is the CS column density for an optically thin layer. The results of the calculations are given in Table 3. First column - source name, second - optical depth for sources which were observed in both CS and C³⁴S, third - CS column density (optical depth was taken into consideration).

Figure 4 shows the distributions of the CS column density for bipolar outflows and for Class I and Class II methanol masers.

The average values $\overline{N}_{\rm{CS}}$ are the following:

$\overline{N}_{\rm CS}{\rm (BO)}=(2.0 \pm 0.6)\ 10^{14}~{\rm cm}^{-2}$
$\overline{N}_{\rm CS}{\rm (MMI)}=(9.8 \pm 0.9)\ 10^{14}~{\rm cm}^{-2}$,
$\overline{N}_{\rm CS}{\rm (MMII)}=(11.9 \pm 1.2)\ 10^{14}~{\rm cm}^{-2}$.

These estimates of the centres of bipolar outflows are in good agreement with others: for example, in one of the first surveys of molecular clouds, which was carried out by Liszt & Linke (1975). The typical value of the CS(2-1) concentration is 10¹⁴ cm^-2, but in methanol masers this value is an order of magnitude higher.

  

Figure 5: Distribution of the $T_{\rm A}^*$(CS)/$T_{\rm A}^*$(C34S) ratio for 51 sources observed in the C34S line

Errors of the average values are given as:

$${ \sigma=\sqrt{\frac{{\sum {(\bar x - x_i)}^2}}{n(n-1)}} }$$ (2)

where $\bar x$ is the average value, x_i is an individual value and n is the number of values.

Figure 5 shows the distribution of the $T_{\rm A}^*$(CS)/$T_{\rm A}^*$(C³⁴S) ratio for the 51 sources observed in the C³⁴S line. This distribution lies below the terrestrial value of 22.5 and for most of the sources the ratio is below 10. We conclude, therefore, that all our sources are optically thick.

  

Figure 6: Dependence between the IR and the CS luminosity for bipolar outflows (crosses), for Class I (circles), and for Class II (triangles) methanol masers

  

Figure 7: Dependence between the IR luminosity and the CS column density for bipolar outflows (crosses), for Class I (circles), and for Class II (triangles) methanol masers

  

Figure 8: Distributions of the antenna temperature in CS(2-1) line of our survey - x-axis and Bronfman et al. (1996) survey in CS(2-1) line - y-axis for bipolar outflows and for Class I and Class II methanol masers. The straight line is the best linear fit to the data

5.3 IR luminosity of the sources

The infrared data of the sources as measured by IRAS are presented in Table 4. The columns list the IRAS source name, the IRAS identification, the IRAS flux densities, the distance, partially taken from other papers, partially calculated with the help of the Brand $\&$ Blitz (1994) Galactic rotation curve, and IR luminosity L calculated from the Morgan $\&$ Ballyformula (1991):

$${ L({L}_{\odot})=23.0{\left(\frac{D}{500~{\rm pc}}\right)}^2 \int{\frac{S} {\lambda^2}{\rm d}\lambda}\,, }$$ (3)

where S is the IRAS flux density in Jy, D is the distance to the source in units of 500 pc, and $\lambda$ is the wavelength in $\mu$m. The integral is calculated as the sum of the 4 areas bounded by the IRAS wavelengths (12, 25, 60, and 100 $\mu$m) and by straight lines connecting the flux densities. No extrapolation is done to wavelengths below 12 and above 100 $\mu$m. References from where the distances were taken are presented in the last column of Table 4. The sizes of the CS regions are unknown. We have calculated the CS luminosity using the distances listed in Table 4 and the integrated intensities assuming that all sources are "point sources'' for the beam of the Onsala radio telescope. Figure 6 shows the dependence between the IR luminosity and the CS luminosity for bipolar outflows (crosses) and for Class I (circles) and Class II (triangles) methanol masers. One can see that the bipolar outflows are primarily located in the region of low intensity both in CS and in the IR. On the contrary, Class I and II methanol masers are stronger both in CS and in the IR.

  

Figure 9: Distributions of the antenna temperature in CS(2-1) line of our survey - x-axis and Anglada et al. (1996) in CS(1-0) line - y-axis for bipolar outflows and for Class I and Class II methanol masers. The straight line is the best linear fit to the data

 

Table 4: IRAS data

 

Table 4: continued

The 51 brightest sources in the CS line were observed in the C³⁴S line. Of these 51 sources, 37 were associated with IRAS sources. Figure 7 shows the dependence between the IR luminosity and the CS column density for bipolar outflows (crosses) and for Class I (circles) and Class II (triangles) methanol masers. The dependence shows that low luminosity IRAS objects are mainly associated with low column density and that high luminosity IRAS objects are associated with high column density.

From Figs. 6 and 7 we conclude that methanol masers are formed in denser regions than bipolar outflows. Besides, Figs. 6 and 7 indicate that distance estimates and IRAS identifications are relatively correct.