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Appendix A: SiC spectroscopy

Table A.1:   Observed SiC₂ transitions J^u .

Silacyclopropynylidene, SiC₂, is a triangular molecule with a dipole moment of 2.393 (6) D (Suenram et al. 1989) along the a-axis. R-branch transitions with are the strongest ones. The molecule is fairly asymmetric, ; therefore, Q-branch transitions with and transitions with also have considerable intensities. Measurements of such transitions, even at low frequencies, may improve predictions of R-branch transitions at higher frequencies. SiC₂ has a low-lying asymmetric bending mode , this may lead to non-negligible changes in the dipole moment with K_a. Only transitions with even K_a are allowed because of the spin statistics associated with the two equivalent C nuclei. The rotational spectrum of the main isotopic species of SiC₂ has been studied to some extent. Thaddeus et al. (1984) reported the first detection of this species towards IRC +10216 based on laboratory measurements of several rotational lines. Cernicharo et al. (1986) reported the detection of ²⁹SiC₂ and ³⁰SiC₂ based on astronomical observations. Suenram et al. (1989) recorded the J = 1 - 0 transitions of the three silicon isotopologs of SiC₂. The detection of Si¹³CC in space was reported by Cernicharo et al. (1991) based on astronomical and laboratory observations. In the same paper they reported tens of SiC₂, ²⁹SiC₂, ³⁰SiC₂, and Si¹³CC lines detected in IRC +10216 with frequency accuracies ranging between 0.2 and 1.0 MHz. At about the same time, Gottlieb et al. (1989) reported 34 transitions recorded between 90 and 370 GHz. Even though the number of parameters (15) was large, the data were only reproduced to within four times the quoted uncertainties. He et al. (2008) found that the data could be reproduced almost within the reported uncertainties if, instead of Watson's A-, the S-reduction was used with two more parameters plus an additional one that was estimated. To obtain a balanced fit, the uncertainties from Gottlieb et al. (1989) were multiplied by 1.5. The resulting fit was the basis of the CDMS catalog entry (Müller et al. 2001,2005).

The issue of the uncertainties reported for the laboratory lines of Gottlieb et al. and their choice of parameters to fit thedata has already been discussed in the He et al. (2008) paper. There it is pointed out that, despite a large number of spectroscopic parameters used in the fit, the experimental data was only reproduced within four times the reported uncertainties. He et al. were able to reproduce the data much better by switching from the A reduction (which was providing negative energies for J>25 using the Gottlieb et al. parameters) to the S reduction and by increasing the number of parameters somewhat. However, they were only able to reproduce the laboratory data within 1.5 times the experimental uncertainties. This finding suggests that the experimental error estimates may have been too optimistic, at least as long as no model is available to reproduce the experimental data better than the model of He et al. Moreover, the increase in experimental uncertainties by 50% may well be too little because a rather large set of spectroscopic parameters was needed to fit a rather small set of experimental lines of this admittedly non rigid molecule. As discussed below, we found in the present investigation that the modified uncertainties by He et al. are appropiate for our present, more larger data set. The strong transitions are predicted quite well up to about 500 GHz, but the quality of the prediction deteriorates rapidly at higher frequencies, as it turned out, in particular for lower values of K_a. Therefore, the SiC₂ transition frequencies from the present HIFI observations were subjected to a combined fit with the laboratory data. Table A.2 compares the present parameters with those from He et al. (2008). All parameters were improved, especially the ones that depend particularly on J. Even though the parameter L_J was newly introduced, the uncertainty of H_J also decreased. In most cases, the parameter values differ only slightly from the previous ones, validating the previous model. Some changes outside the uncertainties are likely caused by including L_J in the fit. He et al. (2008) have already found that only slight modifications of the parameter values are required to fit isotopic data from their, and previous astronomical (Cernicharo et al. 1991) and laboratory data (Suenram et al. 1989). The SiC₂ lines detected in the HIFI 1b survey, their uncertainties, and residuals are listed in Table A.1.

Table A.2:   Spectroscopic parameters^a (MHz) for SiC₂ obtained in the present investigation compared to a previous study.