Astron. Astrophys. 318, 608-620 (1997)

4. Physical conditions

In this section we determine the structure of the temperature and the column density of H₂ in OMC-1. In particular, we address the question of whether intensity variations in the S(1) 1-0 emission are due to temperature or density fluctuations. We also examine in more detail the H₂ emission conditions in the North-jet and address the question of how thick the emitting layer is.

4.1. Molecular temperature

Our observations provide two different means to measure the temperature of molecular hydrogen. We firstly have spectra in the range 1.99 to 2.20 µm through a long slit covering the eastern and southern part of OMC-1. We secondly also have the Fabry-Pérot images in a number of H₂ transitions which cover the other parts of OMC-1.

4.1.1. K band spectrum of Peak 2

For our spectroscopic observations the slit was positioned onto the bright region of Peak 2 and passed south of Peak 3 (cf. Fig. 6, top left). Besides S(1) 1-0 (2.121 µm), the spectrum shows the H₂ transitions S(4) 2-1 (2.003 µm), S(2) 1-0 (2.033 µm), S(3) 2-1 (2.072 µm) and S(2) 2-1 (2.154 µm). We have sufficient signal in these lines and can use various ratios to determine both, rotational and vibrational temperatures. A vibrational temperature is provided by S(2) 1-0 and S(2) 2-1 and a rotational temperature via S(2) 1-0 and S(1) 1-0. In the latter case, the energies of the upper levels are relatively close which leads to larger errors in the temperature measurement. The best combination in terms of line strength and energy difference can be obtained with the S(3) 2-1/S(1) 1-0 ratio which we denote (Fig. 7). The observational errors are dominated by the uncertainties involved with the continuum subtraction particularly in the outskirts of the nebulosity where the fluxes are low.

Fig. 7. Molecular temperatures through Peak 2 region. Rotational/vibrational temperature , pure vibrational and rotational (dashed) temperatures along the slit. Only a few representative error bars are plotted. East is to the left. The spatial intensity distribution along the slit of S(1) 1-0 is shown in the top panel. For the slit position and orientation see Fig. 6.

The ro-vibrational temperature we measure is remarkably constant at about 2000 K over most of the nebulosity except at the edges where it increases slightly by a few hundred K. The vibrational temperature is systematically higher, between 2500 K and 4000 K and shows a steeper increase at the edges. The broad depression in and between and - , occurs in the most luminous region of the Peak 2 area. The rotational temperature is systematically lower than but consistent with outside of the Peak 2 area.

The maxima in to the west of Peak 2 tend to coincide with low emission regions which occur between different jet-like features. These variations are however barely significant and might be mimicked by variable extinction. We have not applied any reddening corrections to the intensity ratios because the extinction is likely to be rather patchy. An increase of the line ratio S(2) 1-0/ S(2) 2-1 by 30% in the inter-jet regions would remove the structure in . This would correspond to a local increase of the dust absorption by 0.25 mag. Such reddening variations have been measured by Scoville et al. (1982) who also concluded that in some parts of OMC-1, the H₂ emission is anti-correlated with the extinction. It is therefore likely that most of the structure in can be attributed to variable extinction.

The difference between and in the Peak 2 area can not be due to extinction because the wavelength separation of the respective transitions are similar. on the other hand is very little affected by extinction because the transitions are only separated by 0.05 µm in wavelength and we therefore believe that this ratio provides the best temperature estimator. A possible explanation for the difference between and at high S(1) fluxes is that regions of strong S(1) 1-0 emission correspond to locations where the gas densities are such as to effect rotational thermalisation, whereas the excited vibrational levels remain slightly overpopulated as a result of shock heating. At the lowest gas densities, overpopulation of both higher rotational and excited vibrational levels is more pronounced, since gas densities are insufficient to thermalise either.

Fig. 8 summarizes the behaviour of and as a function of the intensity of the S(1) 1-0 line. The low temperatures occur where the S(1) line is strong whereas, at locations where it is weak, the temperature seems markedly increased. In regions with moderate to strong S(1) 1-0 emission the temperature is rather constant with 1600 K and 2300 K. At low emission levels, both and converge to a hotter temperature around 4000 K. As outlined above, this upturn is at least partly due to variable extinction whereas the difference between and at high S(1) 1-0 intensity levels is attributable to incomplete thermalisation.

Fig. 8. Rotational (squares) and vibrational (crosses) temperature versus the relative intensity of the H2 S(1) 1-0 line.

4.1.2. Fabry-Pérot images

We can use our Fabry-Pérot images to obtain further spatial information about the H₂ temperature distribution. Best suited are the transitions for which emission was detected over as large parts of the object as possible. This leaves the S(3) 2-1, S(1) 1-0 and S(0) 1-0 transitions. Because of still appreciable extinction even in the K band, we selected the S(3)/S(1) ratio because the respective transitions have similar wavelengths. The resulting temperature corresponds to of the previous section. We note that the use of the S(3)/S(0) ratio would lead to a qualitatively similar temperature structure, although the error bars would be larger.

In this section we mainly focus on the morphological structure of the molecular temperature rather than numerical values. In Fig. 9 we display the H₂ temperature distribution of OMC-1 as obtained from the S(3)/S(1) ratio together with its wavelet transform at three different scales. The wavelet scales are the same as those described in Sect. 3.1 (Fig. 5).

Fig. 9. Morphological structure of the H2 temperature and column density in OMC-1. Upper row: map (left) and its structure at various scales from wavelet analysis. Lower row: Same for column density. Note that the dominant structure in the temperature occurs at scale 4 while for the column density it occurs at scales 2 and 3.

The most striking feature in Fig. 9 is, that the H₂ temperature is rather uniform across the face of the object. The scale 4 wavelet transform shows that there is a large scale radial gradient in the sense that the outer rim is slightly hotter than the central part. The lowest temperatures of around 1700 K occur in the innermost regions around Peak 1. The temperature also increases westwards to up to about 2400 K and south-eastwards to 2800 K, which is, within the expected error bars, consistent with the spectroscopic results of the previous section. The wavelet scales 2 and 3 do only show very little or no structure at all. The bright spots in both scales are due to amplified image artifacts or represent areas where the temperature is not defined because of too low flux levels of S(3) 2-1.

In conclusion, we find that in OMC-1 the temperature structure shows only variation at the scale of a few arcseconds and that in particular, the linear jet-like features are not due to local temperature enhancements.

4.2. H₂ column density

The column density of molecular hydrogen N (H₂) can be obtained from:

where is the partition function of H₂ and , and are the observed intensity, transition probability and frequency of the transition in question. stands for the energy and the statistical weight of the upper level. The partition function Z was taken from Irwin (1987).

The resulting column density distribution across OMC-1 was deduced with the continuum subtracted image of S(1) 1-0 and the temperature distribution from the previous section. We have not applied any extinction correction because we are interested in the morphological structure of the column density rather than numerical values. At large scales the column density retains its blobby character whereas at scales 2 and 3 the linear jet-like features are apparent again although they are less conspicuous than in the direct images (Fig. 9). Clearly, there is a striking difference in the morphological structure of the H₂ column density and molecular temperature at all scales.

4.3. Physical conditions in the North-jet

In Fig. 10 we show cuts from the above intensity, temperature, and column density images along the North-jet (marked in Fig. 5). The horizontal axis is given in arcseconds and starts at the bright knot north-east of the BN object. The "blob" structure mentioned above shows up clearly as a series of fairly evenly spaced peaks in the intensity. This pattern is followed closely by the density. But the temperature - with the exception of a small peak some from the origin (which may be an artifact) - increases slowly and fairly evenly towards the northern edge of OMC-1. Assuming that the thickness of the emitting region is similar to the jet width, a typical column would by cm and with an observed column density of a few times 10¹⁸ molecules per cm², the average density of molecular hydrogen becomes only about 500 cm^-3. This assumes that the jet is homogeneously filled with hydrogen molecules. If, on the other hand, the level population is thermalised, a H₂ density of at least 10⁶  cm^-3 is required. In this case only a thin layer of molecular hydrogen can account for the observed emission. In that situation the H₂ emitting surface is only a thin sheet with a thickness of less than 10¹²  cm which corresponds to 0.05 % of the jet cross section. It is thus conceivable that the molecular hydrogen is entrained from the surrounding molecular cloud into the jet and is rapidly destroyed as it is sucked inwards.

Fig. 10. Physical conditions in the jet heading north (marked in Fig. 6). Top panel: Intensity profile of the H2 S(1) 1-0 line integrated across the width of the jet in units of 10-14 ergs cm-2 s-1. Center: Molecular temperature from the S(3) 2-1/S(1) 1-0 line ratio. Bottom: Column density of H2 in units of 1018 molecules per cm2.

This argument, that the H₂ emission is generated in an extremely thin layer, rests on the assumption that the Boltzmann level population of molecular hydrogen is maintained by H₂ - H₂ collisions, the efficiency of which then requires n (H₂) 10⁶ cm^-3. New calculations of Mandy & Martin (1993) indicate however that neutral hydrogen may be a more efficient collision partner. For the (1,3) level the critical density lies around 6 10³ cm^-3 at a temperature of 2000 K and if the density of neutral hydrogen is n (H) 0.1 n (H₂), the molecular hydrogen can already be thermalised at densities n (H₂) 5 10⁴ cm^-3. However, even in such a situation, the H₂ emitting material in the North-jet could still not originate from the full width of the jet. It would come from a thicker layer as above but it still would have a width of only about 1 % of the total jet cross section.

© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998
helpdesk.link@springer.de