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Astron. Astrophys. 348, 584-593 (1999)

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4. Analysis

Table 2 gives intensities and column densities for each line at the head of the jet from slit 2. To calculate the intensities, the emission lines were fitted with single Gaussians, with uncertainties from a least squares fit. The line column densities can be calculated from (Gredel 1994):


where [FORMULA] is the specific intensity of the line, [FORMULA] is the Einstein A coefficient of the transition, [FORMULA] is the wavelength of the transition, and [FORMULA] is the population of the upper level.


Table 2. [FORMULA] intensities and column densities for the bow shock. Numbers in brackets are the associated uncertainties

A reliable estimate of the excitation temperature for molecules undergoing rotational and vibrational transitions can be obtained from the rotation diagram. This method can be applied if the lines are optically thin and the level populations are characterised by a single rotation temperature.

The total [FORMULA] column density can then be calculated (Gredel 1994), using coefficients taken from Irwin (1987) for the partition function of [FORMULA]:


where [FORMULA] is the population of the upper level, [FORMULA] is the statistical weight for the transition, [FORMULA] is the total [FORMULA] column density, Z is the [FORMULA] partition function, [FORMULA] is the energy of the upper level and [FORMULA] is the rotation temperature.

The rotation diagram for the jet head is shown in Fig. 4. The error bars are from the uncertainties in the line integrated intensities. A straight line fit to the rotation diagram at the head of the jet, gives a rotational temperature of 2200 K from the gradient, and a total [FORMULA] column density of 1.10 [FORMULA] cm-2, from the y intercept and the hydrogen partition function. This fit is shown in Fig. 4. The single rotation temperature fit, shown in Fig. 4, does not produce a good fit to the v=2-1 or v=3-2 lines. From the diagram, it is possible to see that the v=2-1 lines may be fit with a shallower slope, which is indicative of a higher temperature. Rotation diagrams for individual sets of lines with the same v at the head of the jet were plotted, to test whether a single rotation temperature is appropriate in this case. The results are summarised in Table 3. The v=1-0 lines dominate the rotation diagram, as they are more numerous, and have less uncertainty associated with them due to their relative strength. The Q lines, which could be affected by the atmospheric variation at the edge of the window, do not significantly affect the calculated temperature. The v=2-1 lines indicate a higher rotation temperature of between 2300 K and 2900 K. The v=3-2 lines are very weak, and the uncertainties are such that the fit to these lines only is unconstrained and no reliable rotation temperature can be calculated. However a temperature of 3800 K can be calculated from the combined 2-1 and 3-2 lines. The higher temperatures derived from the higher energy lines are indicative of either a higher temperature component or perhaps non-LTE processes, possibly due to the differential streaming in ambipolar diffusion (O'Brien & Drury 1996), becoming significant for the population levels in the higher energy lines. UV fluorescence would also take the population levels out of LTE, but would produce stronger emission from lines with higher v, which is not observed.

[FIGURE] Fig. 4. Rotation diagram for the head of the jet. The gradient gives a temperature of 2200 K. The y intercept gives a hydrogen column density of 1017 cm-2.


Table 3. Temperatures at the head of the jet for differing sets of v

Similar calculations have been carried out for several positions along the length of the jet. Due to the drop in intensity along the length of the jet, it is the 1-0 lines which dominate these calculations, although all detected lines are included. Table 4 gives the total [FORMULA] column densities and temperatures found from slit 2, along the length of the jet. The intensity from each line was summed across a number of rows, corresponding to the size of the peaks and troughs. Nearer to the source, the line intensities become weaker and the temperatures and column densities become correspondingly more uncertain. These results are shown graphically in Fig. 5, which also shows the confidence limits on the derived parameters. This figure shows that there is probably a difference in temperature between the peaks and the troughs. The jet head, while having a similar temperature to the peaks, has a much higher column density.

[FIGURE] Fig. 5. Confidence regions on temperature and column density from rotation diagram fits at various positions along the slit. Confidence levels are [FORMULA] (heavy) and [FORMULA] (light).


Table 4. Temperature and total [FORMULA] column densities along the jet from slit 2. Refer to Fig. 3 for the position.

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© European Southern Observatory (ESO) 1999

Online publication: July 26, 1999