Volume 521, October 2010
Herschel/HIFI: first science highlights
Article Number L11
Number of page(s) 7
Section Letters
Published online 01 October 2010

Online Material

Appendix A: The spectroscopy of H$_{\sf 2}$O+

The rotational spectrum of oxidaniumyl was measured by laser magnetic resonance (LMR) (Mürtz et al. 1998; Strahan et al. 1986); further infrared and electronic spectral measurements have been summarized in Zheng et al. (2008). Observations of the NKaKc = 111-000, J = 1.5-0.5 fine structure component near 1115 GHz with Herschel/HIFI (Ossenkopf et al. 2010) as well as subsequent observations raised the issue which of the two sets of spectroscopic parameters from LMR measurements provide more reliable frequency predictions. Latest observations as well as reinterpretations of older ones favor the parameters from Mürtz et al. (1998) even though there seem to be small discrepancies of order of $\pm$5 MHz or 1.35 km s-1 between various observations for the specific transition mentioned above. Observations carried out toward Sgr B2(M) or Orion KL for the HEXOS program are probably less suited to derive rest frequencies than certain other observations. Therefore, a preliminary catalog entry has been constructed for the CDMS catalog (Müller et al. 2005,2001); the final entry is intended to be a common CDMS and JPL (Pickett et al. 1998) catalog entry.

All infrared data and all ground state combination differences (GSCDs) derived from electronic spectra as summarized in Zheng et al. (2008) were used in the fit as long as they were deemed reliable. These data are uncertain to between 0.005 and 0.030 cm-1 or between 150 and 900 MHz. Mürtz et al. (1998) provided for their measured data extrapolated zero-field frequencies as well as residuals between observed and calculated frequencies along with uncertainties. From these data weighted averages of the hypothetical experimental zero-field frequencies and of their uncertainties were derived; these uncertainties were of order of 2 MHz with a considerable scatter. Strahan et al. (1986) do not give sufficient data for this purpose. However, Mürtz et al. (1998) published calculated frequencies for the 111-000 transition. Because of the importance of this transition for the astronomical observation as well as for the fit, these calculated frequencies were also used in the fit with presumable uncertainties corresponding to 2 MHz. The quantum numbers, calculated frequencies, and uncertainties for the two observed rotational transitions are given in Table A.1. Even though the LMR data fit well within their uncertainties, the calculated frequencies should be viewed with some caution because it is not clear how reliable the zero-field extrapolation is. Moreover, the large centrifugal distortion effects affecting the spectra of this ion require additional caution with respect to any extrapolation. It is worthwhile mentioning that the 111-000 transition frequencies in that table are essentially identical to the ones given in Mürtz et al. (1998). The situation is different for the 110 - 101 transition. The J = 1.5-1.5 fine structure splitting derived from term values given in Table V of Mürtz et al. (1998) differs from the value in Table A.1 by less than 4 MHz whereas the remaining fine structure intervals differ by up to 80 MHz. On the other hand, calculations directly from the Mürtz et al. (1998) parameters differ from values in Table A.1 by less than 10 MHz.

Table A.1:   Quantum numbers of rotational transitions of H2O+ described in the present work, calculated frequencies (MHz) with uncertainties in parenthesesa; lower state energies $E_{\rm lo}$ (K) and Einstein A-values (10-3 s-1)

\end{figure} Figure A.1:

Detail of the energy level diagram of H2O+. Hyperfine splitting has been omitted for the ortho-levels. Rotational level assignments NKaKc are given below the levels, fine structure level assignments J to the side. Magenta arrows mark transitions observed in the course of the present investigation. All other transitions shown can be observed with HIFI. The thickness of the arrows indicates the relative strengths of the transitions and the numbers the approximate frequencies. Frequencies of the weaker components are given in parentheses. The only transitions connecting to levels with N = 1 which are not shown are 221-110 and 220-111 near 2.85 and 3.0 THz which are not observable with HIFI but with PACS.

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As can be seen in Fig. A.1, the ground state para level 101 of H2O+ is $\sim$30.13 and 30.01 K above the 000 level for the J = 0.5 and 1.5 fine structure components respectively. Both para and ortho ground state levels are split into 2 because of the fine and hyper fine structure splitting, respectively. The quantum numbers are 0.5 and 1.5 in both cases, giving g = 2 and 4, respectively, and hence $Q \approx 6$ at low temperatures if ortho and para states are treated independently. This 1 : 1 ratio for Q at low temperatures approaches 3:1 at room temperarture; it is about 1.5:1 and 2:1 at $\sim$40 and 75 K, respectively. Table A.2 gives selected partition function values for para- and ortho-H2O+, assuming they are completely non-interacting species.

The mixing of ortho and para states can be mediated by terms such the off-diagonal electron spin-hydrogen nuclear spin coupling term Tab or the off0diagonal hydrogen nuclear spin coupling term Cab + Cba. The radical NH2 and PH2 are isoelectronic and isovalent to H2O+. Model calculations have shown the largest perturbations to occur between the 101 and 111 levels, but they are with less than 5 (Gendriesch et al. 2001) and less than 3 kHz (Margulès et al. 2002), respectively, rather small, maybe even negligible. Model calculations suggest that perturbations of the two rotational transitions described in the present study are less than 3 kHz. Slightly larger perturbations may occur at higher quantum numbers.

Table A.2:   Partition functions for para- and ortho-H2O+, assuming LTE.

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