4. CH3CN, CH3CCH and CH3OH
We have measured transitions of several symmetric top molecules as well as methanol lines in the line of sight toward RAFGL7009S. The resulting set of observations has to be separated in two parts. Indeed, during interferometric observations of the CH3CN 1211 transitions, we find evidence for a shift of 3" between the position used in the ISO observations and the first observations done at the IRAM 30m telescope. The true position of the (compact HII) source, which coincide with the continuum emission, is then:
This change has little effect on the discussion of absorption measurements (such as the ones in the solid or gas phase transitions made with ISO) as the flux scales proportionally, and the line to continuum ratio remains constant. However, for millimetre data, it is important to note this difference when comparing lines observed before and after this pointing "correction". The observations observed before the new pointing position are: for CH3CN the 65 and 1211 transitions; for CH3CCH the 65 transition; for CH3OH the 21, 32 and 54 (measured before and after the new position was known) transitions.
4.1. Analysis: The modified rotational diagram
Rather than the classical rotational diagram method (e.g. Cummins et al. 1986), in which one assumes the lines to be optically thin we prefer to use a simple minimisation to estimate the basic molecular parameters such as the rotational temperature, column density and source size.
The temperature as observed with a telescope with a Gaussian beam and pointing toward a Gaussian shaped emitting source is given by:
where is given by:
where is the normalised line shape of the transition (assumed here to be Gaussian), the rotational excitation temperature, the Einstein coefficient of the transition, the frequency of the transition, N the total number of molecules, the number in the upper state, its degeneracy and the upper state energy.
In the radio range one often replaces by . When , in the classical rotation diagram there exist a linear relationship between the logarithm of the integrated temperature of the line (generally named W) and , with an axis intercept defined by (see for example Cummins et al. 1986). Fitting a slope to this curve gives access to both and . However, this method presents two major disadvantages:
These two reasons lead us to analyse the data by generating models with known parameters and performing a maximum likelihood minimisation to determine the best parameters. In particular, this takes into account any line saturation. It is an intermediate method between the purely optically thin assumption and LVG calculations which also involve some approximations. We thus maximize the function:
where is the rms noise, T the rotational temperature and the source extension (full width at half maximum), assuming a Gaussian distribution pattern. The maximum of the function gives the best values for the parameters T, N and and the contours at 1% of the maximum allow to derive the extent of the 3 confidence range in these parameters. We proceed in two steps to estimate the correct value of . We first calculate the likelihood function with the sigma estimated from the noise of the spectrum. Then, we estimate the standard deviation from the difference between our best model and the observed spectrum. In this way we also partly take into account the uncertainties due to model imperfections.
If the maximum likelihood function is well-behaved, each probability contour has the shape of a distorted ellipsoid ("boomerang like") in a three parameter space minimisation. Except for the case for the optically thin lines, this is the case in our calculations. In the optically thin case it is not possible to differentiate between column density effects and beam dilution effects as these two quantities are strongly correlated. The line intensity is a function of the product of the opacity and dilution factor of the source in the beam.
Unless otherwise stated, in this paper, when no source size is explicitly given, we assumed , performing the minimisation in a two parameter space (T,N). If the source size can be estimated by other means, the column density has to be corrected by this factor.
The Plateau de Bure interferometer maps of CH3CN, are shown in Fig. 5a and 5b. In the 1211 transitions, the source has an extent of about 1 arc-second. In the optically thin limit, the column densities for CH3CN given in the caption of Fig. 6 have then to be enhanced by a (sometimes very large) factor , corresponding to the beam dilution.
An extension in the E-W direction is clearly visible in both maps at 3mm (6-5) and 1mm (12-11). This structure is more pronounced in the CH3CN(65). We associate this component with the molecular outflow known to be present in this source at larger scales (Shepherd & Churchwell 1996). The absence of a symmetrical counterpart might imply there exist a difference in the densities in which the jet expands for the other component.
The observed spectra of methyl acetylene and model fit are displayed in Fig. 7. We believe methyl acetylene CH3CCH to be also found in a compact region of roughly the same extent as for methyl cyanide with therefore the same correction to be applied to the column density estimates, as is generally the case in ultra compact HII regions (Hatchell et al. 1998).
To estimate the physical parameters (T,N) for this molecule, we used the optically thin limit estimate as we do not see clear evidence for saturation in the maximum likelihood minimisation. If the lines are thermalised, due to the lower temperature, the molecule emission must be more extended than for the methyl cyanide case. From the derived column densities presented in Fig. 7, and assuming the kinetic temperature is the same for both transitions, we estimate the source size around 6-10" .
In order to derive the best column densities, it is crucial to estimate the source size as accurately as possible. Using the interferometric maps, we showed, in Sect. 4 above, that the millimetre compact emitting region is located 3" away from the ISO position which was used in the first millimetre observations as the map centre. This means that we have to correct the observed antenna temperature by a factor that takes into account the shape of the 30m telescope beam at a given wavelength and the new accurate position in order to make suitable comparisons between the data.
However, this additional complication allows us to derive the source size from the observation of the same molecular transitions at the centre position used before and after the interferometric observations. This is the case for the 54 methanol transitions around 241 GHz.
Indeed, the observed antenna temperature of a Gaussian shaped emitting region as seen with a Gaussian beam, pointing at an offset position given by and from the source centre, is proportional to:
with , and .
The ratio of the observed integrated temperature of a given line at the source centre and at an offset from the centre is simply given by the ratio of and the above equation. Conversely, the source size can be estimated given observed intensity values. Of course, this analysis can not be done when in which case the ratio equals one whatever the offset.
We benefitted from this in the case of the 241 GHz (54) methanol lines. We calculated the expected line ratio knowing the offset from the true position was 3" in the first run of observations. The observed (241 GHz) methanol transitions before and after centre correction are shown in the Fig. 9. The source size can then be derived from the comparison of the two spectra, assuming the relative calibration is reliable. Including a 30% relative calibration uncertainty we are able to say the methanol emitting region size is about 8" wide.
The three molecules (CH3CN, CH3CCH and CH3OH) are associated with the presence of a hot core. However, the CH3CN transitions are emitted from a compact region surrounding the central star and is probably directly created in a hot core chemistry (following or not grain evaporation). The methyl acetylene molecule, followed by the methanol molecule seem to pertain to an intermediate region between the hot core region and a more quiescent region.
This last molecule (CH3OH) must be a direct product of the grain evaporation as its abundance in the solid phase (Dartois et al. 1999) in this object is more than two orders of magnitude higher than in the gas phase.
The lower excitation temperature of the methanol molecule as compared to the high temperature of both methyl cyanide and propyne molecules supports the view that methanol lies in an intermediate region between the "pure" hot core and the halo surrounding it.
Indeed, given the high densities, we do expect the methanol to be globally thermalised.
Other authors have surveyed the molecular line emission of these molecules toward HII regions (Hatchell et al. 1998). In their sample, the source size is larger in methanol than in methyl cyanide, leading to the same conclusion. Thus methanol seems to be a very powerful molecule to follow grain evaporation or equivalently to trace the interface volume between a hot core and the cooler surrounding region.
© European Southern Observatory (ESO) 2000
Online publication: October 10, 2000