In this section, we briefly discuss our results; more detailed analysis and comparison of our results with data of other investigators will be given in subsequent papers.
Tables 4, 5, and 6 show that the source densities are of the order of and kinetic temperatures of the order of 20 K, with only one exception - W3(OH). The source sizes are of the order of . Similar sizes have been obtained in interferometric observations of some star-forming regions in the lines of CS and of other high-density gas tracers (Plambeck and Menten, 1990; Pratap and Menten, 1993). The uncertainties of E-methanol abundance determinations are very large. One can notice, however, that the values providing the best fit to the observational data are enclosed in the range for all sources except Cep A. Such abundances are typical for dark clouds (Friberg et al., 1988; Kalenskii and Sobolev, 1994) and are much smaller than the methanol abundance in Ori-KL and some other "hot cores"(Menten et al., 1986, 1988a) or in regions with young bipolar outflows (Bachiller et al., 1995). The methanol abundance in Cep A providing the best fit to observational data, proved to be ; however, the lower limit of the abundance is below .
Slysh et al. (1994) detected the methanol line toward a number of molecular clouds and determined the methanol abundance for the majority of them. Their results were revised by Kalenskii and Sobolev (1994). Our methanol abundance agrees within a factor of two with the values obtained by Kalenskii and Sobolev for common sources - NGC 2264, ON1, and DR 21(OH).
The best-fit kinetic temperatures from Table 4 are typically about 1.5 times smaller than kinetic temperatures derived from ammonia observations of the same sources (Batrla et al., 1983; Churchwell et al., 1990; Güsten & Ungerechts, 1985; Mauersberger et al., 1986; Wouterloot et al., 1988). It is possible that we simply missed good parameter samples with temperatures, close to the ammonia ones. This could be the case, because we made cross-sections around "initial guesses" instead of varying temperature, density, and methanol abundance over the whole region of their possible values. To check this possibility, we made cross-sections in the planes for 34.26+0.15, DR 21(OH), and Cep A, taking kinetic temperatures equal to the ammonia ones. In all cases we obtained worse fits ( for ammonia temperatures proved to be 10 - 50% larger than for methanol temperatures) and therefore our temperature estimates agree better with the 96 and 157 GHz data. We believe that this discrepancy may be due to variations of gas temperature along the lines of sight. Note that most of the upper levels of the 96 and 157 GHz lines are below 20 K, and therefore our analysis relates to very cold gas.
No correlations between source sizes and linewidths or between densities and linewidths were found. This is not surprising because large scatter is typical for these dependencies and large data sets are necessary to establish them.
Thus, our results show that massive young stars are often associated with clumps of gas with temperatures 20-50 K, densities of the order of , methanol abundance of the order of , and sizes of about 0.3 pc.
© European Southern Observatory (ESO) 1997
Online publication: June 30, 1998