4. Derived gas parameters
4.1. Analysis procedures
By means of statistical-equilibrium calculations and using the three observed lines of SiO and SO, it is possible to estimate their total column densities (N) as well as the kinetic temperatures () and the hydrogen densities (). We have used the Large Velocity Gradient (LVG) code we already considered in previous works about both the molecular species (Codella & Muders 1997, Codella et al. 1999). The collision rates given by Turner et al. (1992), for SiO, and by Green (1994), for SO, have been utilized. These calculations have been performed with the values of the intensities of the spectra at different wavelenghts expressed in the mean-beam brightness temperature scale, without correction due to the beam filling factor. It is worth noting that, as already discussed by Codella et al. (1999), if the source sizes were definitely smaller than the three beamwidths, i.e. a sort of point-like sources, the LVG code would lead to an overestimate of the excitation conditions. In this case, the kinetic temperatures and the hydrogen densities can be reduced by factors of 1.2 and 2, respectively, while the total column densities can decrease up to a factor of 9.
For the CH3OH data, in order to estimate the rotational temperatures and column densities, the standard rotation diagram method (e.g. Cummins et al. 1986) has been used. Moreover, the gas densities have been estimated from the methanol data using, as proposed by Bachiller et al. (1998, see their Fig. 9), the parameters R3(0) and R5(0) based on ratios between line intensities (e.g. R3(0) = (30 - 20E)/(3-1 - 2-1E)).
For the other molecular species, the total column densities have been calculated using the spectroscopic constants given in the literature (e.g. Lovas 1978, Blake et al. 1987, Swade 1989, Mangum & Wootten 1993, Mangum et al. 1993, Omont et al. 1993, Williams et al. 1998) and considering the temperature estimates derived from the CO data and from the LVG results.
The LVG results based on the SiO spectra taken along the outflow axis lead to kinetic temperatures of about 100 K and 5 105-1 106 cm-3, indicating the association of silicon monoxide with high temperature and density material. The total SiO column densities are around 1013 cm-2, while an estimate for a position offset from the outflow (0,+50", that reported in Fig. 2) and based on the J = 2-1 observation yields 4 1012 cm-2.
On the other hand, the SO LVG results show that along the outflow the temperature is 100 K and the hydrogen densities are between 1 and 5 105 cm-3, suggesting that SO is tracing gas at lower density with respect to SiO. Regarding the position offset from the outflow, if we assume that the low velocity SO component is associated with ambient quiescent gas, as suggested by the small linewidths and by the similar central velocities, we find temperatures of about 20 K and 4 105 cm-3. The total SO column densities are between 5 1013 and 3 1014 cm-2.
The least-square fits to all detected lines in the CH3OH rotation diagram give rotational temperatures () of about 20 K for the outflow region, while the total methanol column densities are between 3 1015 and 1 1016 cm-2. Using the tentative detection at the (0,+50") position, a 15 K and a 3 1014 cm-2 have been derived. Thus, the rotation temperature presents only a small increase moving from the (0,+50") position to the outflow. However, as already discussed e.g. in Bachiller et al. (1998), in the range of physical conditions typical of the outflows, the CH3OH molecule is very subthermally excited. The estimate of the hydrogen densities along the outflow performed using the R5(0) parameter and assuming a kinetic temperature of 100 K yields values close to 5 105-106 cm-3, as well as the density obtained through R3(0) (and a temperature of 20 K) for the (0,+50") position is about 106 cm-3.
Taking into account the temperature estimation got from the CO, SiO, SO and CH3OH data, the total column densities for the other molecular species have been calculates considering a kinetic temperature of 20 K for CO, CS and H13CO+, while a warmer gas has been assumed (50 K) for OCS, SO2, H2S and H2CO, i.e. for those species usually connected with shock-chemistry and clearly associated with the outflow as shown in Sect. 3. Fig. 10 reports the values of the total column densities along the main outflow axis: is about 5-8 1016 cm-2, 5-8 1013 cm-2, is between 5 1011 and 2 1012 cm-2, 1014 cm-2, 2 1014 cm-2, is situated between 5 1013 and 2 1014 cm-2, while is around 3 1014 cm-2. For the (0,+50") position, we obtained 1016 cm-2 and 1013 cm-2. A rough estimation of the uncertainty due to the assumption of the kinetic temperature can be done calculating the column densities with different temperatures: moving from 20 to 50 K, the obtained values can be changed by factors between 2 and 6, depending on the molecule. The obtained values of the total column densities, their change as well as the change of the abundance ratios along the outflow axis will be discussed in the next section.
© European Southern Observatory (ESO) 1999
Online publication: October 4, 1999