HERSCHEL/HIFI DISCOVERY OF HCL⁺ IN THE INTERSTELLAR MEDIUM

An open-shell molecule with a ²Π_3/2 electronic ground state, HCl⁺ exhibits a complex rotational spectrum, which results from the presence of electronic orbital and spin angular momenta, as well as hyperfine coupling of the Cl nucleus. Because of the large ratio of the spin–orbit constant to the rotational constant (A/B ∼ −66), coupling between electronic and rotational angular momenta is best described by Hund's case (a). As Figure 2 shows, the largest of these effects is spin–orbit coupling, which gives rise to two parallel fine-structure ladders of rotational transitions, Ω = 1/2 and Ω = 3/2—the latter lower in energy because of the large, negative spin–orbit constant, A (−926 K). The next smaller effect is Λ-doubling, which splits each rotational level, J, into two symmetrical levels (denoted by the parity symbols, e and f). The smallest effect, the hyperfine interaction of Cl nucleus (I = 3/2 for both isotopes), splits each Λ-doubled level into four levels; the blow-up of the ²Π_3/2J = 5/2–3/2 transition in Figure 2 shows this pattern which consists of 18 hyperfine-split components allowed by the selection rules: ΔJ = ±1; ΔF = 0, ±1; e↔e; and f↔f.

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The spectroscopic constants of HCl⁺, including Λ-doubling and the hyperfine coupling of chlorine, have recently been refined by a combined analysis of optical data from the literature (Sheasley 1972) and newly measured pure rotational transitions, and are reported in the accompanying Letter (Gupta et al. 2012). These constants are so accurate that they allow the frequencies of the ²Π_3/2J = 5/2–3/2 transition to be calculated to an accuracy approaching 0.3 MHz (Table 1) or 0.06 kms⁻¹ at 1444 GHz.

The sight lines toward the high-mass star-forming regions and strong continuum sources W31C and W49N have been the subject of several studies, which describe and compare the velocity distribution of the intervening gas traced by various molecules (e.g., Godard et al. 2010; Persson et al. 2010, and references therein). The mean of the line width distribution, found through Gaussian decomposition of the absorption profiles, is between 1.5 and 4.5 km s⁻¹, depending on the species (Godard et al. 2012). The gas associated directly with W31C is detected in the velocity range V_LSR ≃ −15 to 5 km s⁻¹, while the foreground gas is detected at V_LSR ≃ 5 to 55 km s⁻¹. In the case of W49N, the velocity ranges pertaining to background and foreground gas are V_LSR ≃ −10 to 23 km s⁻¹ and V_LSR ≃ 23 to 75 km s⁻¹, respectively.

In modeling the HCl⁺ absorption, it is desirable to have molecular absorption lines that are detected with good signal to noise and are optically thin over the entire velocity range. While CH and ¹³CH⁺ fulfill both criteria (Gerin et al. 2010b; Falgarone et al. 2010a), they trace with different weighting the various environments aligned along the lines of sight, so they present significant discrepancies in the relative depth of the absorption peaks, especially in correspondence with the velocity ranges pertaining to the star-forming regions and their surroundings.

Because HCl and H₂Cl⁺ (R. Monje et al. 2012, in preparation; Neufeld et al. 2012b) are chemically related to HCl⁺, their absorption might be expected to show similarities to that of HCl⁺. Although H³⁵Cl is observed in the foreground of W31C, a reliable opacity profile could not be extracted for the entire velocity range because of the low signal to noise of the absorption and the occurrence of emission at the velocities associated with the background source. The analysis of H³⁵Cl in W49N is even more complicated because of the presence of strong self-absorption, and a possible outflow signature, as well as the absence of absorption in the foreground clouds. In contrast, higher signal to noise has been achieved in the H₂Cl⁺ spectra toward both W31C and W49N, and deconvolved opacity profiles have been produced.¹⁰ The column density estimates for these species are 7.2 × 10¹³ cm⁻² for H³⁵Cl in W31C (in the 14–42 km s⁻¹ velocity range), 8.4 × 10¹³ cm⁻² for H³⁵₂Cl⁺ in W31C, and 6 × 10¹³ cm⁻² for H³⁵₂Cl⁺ in W49N.

Chemical models predict HCl⁺ to be present in clouds of low extinction (A_V < 1; Neufeld & Wolfire 2009), suggesting that HCl⁺ may reside in the same gas as OH⁺ (whose absorption profiles are saturated) and H₂O⁺.

In the case of HCl⁺, the fine and hyperfine structure of the ²Π_3/2J = 5/2–3/2 transition is entangled with the absorption pattern of the sources, producing the intricate profiles observed. Although this makes comparison with models necessary, a satisfactory match of the models with the complex patterns observed makes the identification extremely reliable.

The observed absorption profiles are modeled by convolving each velocity channel of the opacity profiles τ(v) of a known molecular tracer (hereafter template) of the gas, with the pattern of transitions reported in Table 1. The contributions to the opacity of all the channels are then summed, and a scaling factor—the sole free parameter—is applied to match the observed opacity by minimizing the quantity ∫|residuals|dv/∫τdv. The minimization excludes frequency ranges in which the difference between the horizontal and vertical polarization or between the two pipelines for data reduction is larger than five times the rms noise.

Given the complex line structure and the possible occurrence of instrumental artifacts, the described approach has been preferred over the more common methods of multi-Gaussian decomposition, because it uses far fewer free parameters, and thus avoids the risk of building ad hoc models. It is based on the conservative but simplistic assumption that the same HCl⁺/template opacity ratio holds for all the line-of-sight clouds. Despite this, Figure 3 shows that the observed absorption is reproduced well, suggesting a posteriori that the assumption is reasonable, at least for some of the templates.

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Figure 4 also serves to prove the validity of our approach to modeling and identifying the broad and complex absorption observed. The model profiles built using different templates have been rigidly shifted—thus conserving the internal line structure—relative to the predicted frequency, within ±300 MHz. Figure 4 shows the dependences of ∫|residuals|dv/∫τdv on the frequency shift. The well-defined minima close to zero shift indicate that the observationally constrained rest frequencies, having an accuracy of about 30 MHz, because of the intrinsic discrepancies among the template opacity profiles, the noise in the data, and the model assumptions, are in perfect agreement with the predicted values. Moreover, given the sub-MHz accuracy of the calculated frequencies, the quality of the match to the data of the different models provides valuable information about the chemistry of the traced environments.

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The assignment of the observed absorption features to the ²Π_3/2J = 5/2–3/2 transition of H³⁵Cl⁺ is strongly supported by a number of reasons.

• 1.  
  The astronomically inferred rest frequencies, for both H³⁵Cl⁺ and H³⁷Cl⁺, are in excellent agreement with predictions based on recent laboratory measurements (Gupta et al. 2012).
• 2.  
  The best match is found, for both H³⁵Cl⁺ and H³⁷Cl⁺ in W31C, when the closely related molecule H³⁵₂Cl⁺ is used as a template.
• 3.  
  The identification of the absorption features near 1444.2 GHz with H³⁷Cl⁺, at the predicted frequency and with the expected isotopic abundance (see Section 3.5), further supports the assignment of the carrier to HCl⁺.
• 4.  
  Models employing just one free parameter are able to reproduce well the absorption in both sources.
• 5.  
  Observation of the same pattern with both sidebands rules out the possibility that it is due to instrumental artifacts alone.

The column densities were derived using the following formula, valid for ground-state transitions:

$$\begin{equation} N = Q(T_{{\rm ex}}) \frac{8 \pi \nu _{0}^3}{c^3} \frac{1}{g_u A_{{\rm ul}}} [1 - e^{-h\nu _0/kT_{{\rm ex}}}]^{-1} \int {\tau dv}, \end{equation} \tag{ 1 }$$

where ν₀, g_u, and A_ul are the rest frequency, the upper level degeneracy, and the spontaneous emission rate of the observed transition; Q(T_ex) is the partition function; c is the speed of light; and ∫τdv is performed over the whole absorption pattern, thus including the contribution of all the fine- and hyperfine-structure components. Assuming a single excitation temperature T_ex = 5 K for all levels and taking into account the relative intensity in Table 1 of the F = 4–3(f–f) component, Equation (1) becomes $N(\rm {H^{35}Cl^{+}}) = 6.52 \times 10^{12} \int {\tau \it dv}\ cm^{-2}$, and we find N(H³⁵Cl⁺) = 8.2 ± 2.5 × 10¹³ cm⁻² for W31C, and N(H³⁵Cl⁺) = 8.7 ± 2.6 × 10¹³ cm⁻² for W49N. The 1σ uncertainty of 30% in the column density is dominated by the error in the baseline fitting,¹¹ while other sources of uncertainty—continuum level fluctuations among the different tunings, residual standing waves, uncertainty in the dipole moment, deviations from unity of the sideband ratio, and velocity range of the integration—contribute under 10%.

Similarly, for H³⁷Cl⁺ in W31C we obtain¹² $N(\rm {H^{37}Cl^{+}}) = 6.52 \times 10^{12} \int {\tau \it dv} = 4 \pm 3 \times 10^{13}\ cm^{-2}$, implying an isotopic ratio of 2.1 ± 1.5, comparable to the solar abundance value 3.1.

For W31C, a comparison with H³⁵₂Cl⁺ (Neufeld et al. 2012b) and H³⁵Cl (R. Monje et al. 2012, in preparation) column densities gives a column density ratio of unity for both species (HCl⁺ : H₂Cl⁺ : HCl ∼ 1).

In chemical models of diffuse clouds, HCl⁺—like OH⁺ (Neufeld et al. 2010a)—is predicted to be most abundant in clouds of small extinction where the molecular hydrogen fraction is ∼1% (Neufeld & Wolfire 2009). Along the sight lines to W31C and W49N, Godard et al. (2010) estimated the H i column densities within such clouds, for the velocity ranges not associated with the background sources, as 1.2 × 10²² cm⁻² and 1.4 × 10²² cm⁻², respectively. Thus, the HCl⁺ column densities derived here for the same velocity ranges imply abundances of 9 × 10⁻⁹ relative to atomic hydrogen for the W31C sight line, and 6 × 10⁻⁹ for the W49N sight line,¹³ corresponding, respectively, to 5% and 3% of the gas-phase chlorine abundance. These values are several times larger than the maximum fractions (∼1%) predicted by theoretical models (e.g., Neufeld & Wolfire 2009), in which HCl⁺ is produced primarily by the reaction of Cl⁺ with H₂. A similar discrepancy is observed for the case of H₂Cl⁺ (Lis et al. 2010; Neufeld et al. 2012b), whose abundance is also underestimated by theoretical models. Thus, the larger-than-expected abundance we derived here does not in itself argue against our identification of HCl⁺; rather, it may suggest some deficiency in existing models for the production of chlorine-bearing molecules in the diffuse ISM.