HERSCHEL OBSERVATIONS OF INTERSTELLAR CHLORONIUM^*

The Sgr A (+50 km s⁻¹ cloud) and W31C spectra show H₂Cl⁺ absorption over a wide range of velocities, a behavior that is typical of other molecules observed in absorption toward these sources. The observed molecular absorption is believed to arise largely in foreground diffuse clouds, unassociated with the background sources of continuum radiation.

In Figures 2 and 3, we present the observed flux for the two sources showing H³⁵₂Cl⁺ and H³⁷₂Cl⁺ in absorption, now normalized with respect to the continuum flux in a single sideband. Here, we assume a sideband gain ratio of unity (Roelfsema et al. 2012), and thus we plot the quantity 2T_A/T_A(cont) − 1. Using the procedure described by Neufeld et al. (2010b), we have deconvolved the hyperfine structure to obtain the spectra shown in red; these are the spectra that would have resulted if the hyperfine splitting were zero. For comparison, the spectra (see figure captions for the sources of these spectra) of four other molecules detected with HIFI are shown: CH (the 536.761 GHz transition in green), HF (the 1232.476 GHz transition in brown), para-H₂O (the 1113.343 GHz transition in magenta), and OH⁺ (the 971.804 GHz transition in blue). In addition, the H i 21 cm spectrum is shown in dark green. Vertical offsets have been introduced for clarity.

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The spectra shown in Figures 2 and 3 indicate that all the absorbing species show broadly similar distributions in velocity space, but with HF, H₂O, and CH—all believed to be good tracers of molecular hydrogen—showing the strongest mutual resemblance. Toward the Sgr A (+50 km s⁻¹ cloud), chloronium is apparently distinctive among the molecules in exhibiting a lack of absorption at LSR velocities smaller than ∼ − 70 km s⁻¹ (and specifically a lack of absorption at ∼ − 130 km s⁻¹, which normally arises within the Expanding Molecular Ring in the inner region of the Galaxy.) In this regard, the distribution of H₂Cl⁺ in velocity space is more similar to that of atomic hydrogen than that of any of the other molecules shown in Figure 3. Although, given the sensitivity of the observations, this behavior is only tentatively established, it argues in favor of theoretical predictions (see Section 5.1 below) that the chloronium abundance is largest within clouds that are primarily atomic.

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In Table 2, the column densities of para-H³⁵₂Cl⁺ and para-H³⁷₂Cl⁺ are given for various velocity ranges, computed with the approximation that all para-chloronium molecules are in the ground 0₀₀ state. As for other hydrides observed toward these sources, that approximation is justified by the large spontaneous radiative rate for the observed transition,¹⁸ the low density of the foreground clouds responsible for the absorption, and the weak continuum radiation field at the frequency of the observed transition and at the location of the absorbing material. Table 2 also presents the total H₂Cl⁺ column density (both isotopologues) for an assumed ortho-to-para ratio (OPR) of 3. For each velocity range, the H i column density is also given, determined from 21 cm absorption spectra (Fish et al. 2003 for W31C; Lang et al. 2010 for Sgr A +50 km s⁻¹ cloud) for an assumed H i spin temperature of 100 K. Since the observed H₂Cl⁺ is expected to arise primarily in clouds of small H₂ fraction (see Section 5.1 below), we also give the N(H₂Cl⁺)/N(H i) abundance ratios in Table 2. The mean value obtained for the 0–50 km s⁻¹ LSR velocity range in W31C, $N({\rm H_2Cl^+})/N({{\rm H\,\mathsc{i}}}) = 1.15 \times 10^{-8}$, corresponds to ∼12% of the gas-phase chlorine abundance within diffuse atomic clouds (1.0 × 10⁻⁷; Moomey et al. 2012); that obtained for the −70 to −30 km s⁻¹ LSR velocity range in Sgr A (+50 km s⁻¹ cloud), $N({\rm H_2Cl^+})/N({{\rm H\,\mathsc{i}}}) = 4.4 \times 10^{-9}$, corresponds to ∼4% of the gas-phase chlorine abundance. For most velocity intervals, in both sources, the H³⁵₂Cl⁺/H³⁷₂Cl⁺ abundance ratio is similar to the ³⁵Cl⁺/³⁷Cl⁺ isotopic ratio of 3 observed in the solar system (Lodders 2003).

The absorption-line observations discussed above provide robust estimates of the H₂Cl⁺ column densities, because almost all para-chloronium molecules are in the ground 0₀₀ state (see Section 4.1 above), but the interpretation of the emission-line observations is less straightforward. At the densities of the H₂Cl⁺ emission region in the Orion Bar—n(H₂) ∼ 3 × 10⁴ cm⁻³ and n(e) ∼ 5 cm⁻³ (discussed further below)—the molecule will be subthermally excited, with most para-H₂Cl⁺ molecules in the ground 0₀₀ state, and thus the emission line intensity will depend crucially upon the rate coefficients for collisional excitation of H₂Cl⁺. Because all excitations, to any excited rotational state, will be followed by a radiative cascade resulting in the emission of a 1₁₁ − 0₀₀ line photon, the relevant parameter is the total rate of collisional excitation out of the ground rotational state. As far as we are aware, no detailed calculations of the latter have been performed. For excitation by H₂, we therefore adopt the results obtained (Faure et al. 2007) for the isovalent para-H₂O molecule, which yield a total rate coefficient for excitation from 0₀₀ that is well approximated by q_tot(H₂) = 2 × 10⁻¹⁰T^0.5₂exp [ − E(1₁₁)/kT] cm³ s⁻¹, where E(1₁₁) is the energy of the lowest excited state (1₁₁), T is the kinetic temperature, and T₂ = T/100 K. For the case of collisional excitation by electrons, we used the Coulomb–Born approximation to relate the spontaneous radiative rate for the 1₁₁–0₀₀ transition to the rate of electron impact excitation. With the aid of Equations (15), (12), and (11) in Neufeld & Dalgarno (1989), we thereby obtained an estimate for the rate coefficient for excitation from 0₀₀ that can be fit by q_tot(e) = 2.6 × 10⁻⁶T^−0.37₂exp [ − E(1₁₁)/kT] cm³ s⁻¹, where E(1₁₁) = 23 K for the case of H₂Cl⁺. We have also considered—and then rejected—the possibility that excited states of H₂Cl⁺ might be populated significantly when the molecule is formed. Even if every H₂Cl⁺ is formed in an excited state, this so-called "formation pumping" can be shown to be negligible by means of an argument that equates the rate of formation of H₂Cl⁺ to the rate of its destruction through DR and proton transfer to neutral species.¹⁹

The molecular hydrogen density in the Orion Bar has been estimated previously by means of PDR modeling (e.g., Jansen et al. 1995). The consensus estimate, which we adopt here, implies a total density of hydrogen nuclei of n_H ∼ 6 × 10⁴ cm⁻³, although previous studies have suggested the presence of denser clumps with a small filling factor (e.g., Lis & Schilke 2003); in this paper, we neglect the latter because their contribution to the overall emission is expected to be small. Theoretical studies for the chemistry of chlorine-bearing molecules (e.g., Neufeld & Wolfire 2009, hereafter NW09) suggest that H₂Cl⁺ is most abundant near the cloud surface where carbon is fully ionized, hydrogen is largely atomic, and the gas temperature is ∼500 K. In this region, the atomic hydrogen density is essentially the hydrogen nucleon density, $n({{\rm H\,\mathsc{i}}}) \sim n_{\rm H}$, and we estimate the collisional excitation rate (per H₂Cl⁺ molecule) as R_surface = q_tot(H₂)n_H + q_tot(e)n_e = 3.8 × 10⁻⁵ s⁻¹. Here, we assumed that the rate of collisional excitation by H is equal to that for H₂, and we adopted an electron abundance equal to the gas-phase abundance of carbon (∼1.6 × 10⁻⁴ relative to H nuclei; Sofia et al. 2004). We also considered the conditions existing far from the cloud surface, in the cloud interior, where the fractional ionization is low, hydrogen is primarily molecular, and the gas temperature is ∼30 K; if the H₂Cl⁺ originates primarily in such a region, the collisional excitation is R_interior = q_tot(H₂)n_H/2 = 1.5 × 10⁻⁶ s⁻¹. Unfortunately, these estimates are quite uncertain, given the absence of reliable rate coefficients for H₂Cl⁺. In particular, several shortcomings in the Coulomb–Born approximation have been discussed by Faure & Tennyson (2001), and there may be significant differences in the rates of excitation of H₂Cl⁺ and H₂O in collisions with H₂.

In the limit of subthermal excitation, the integrated brightness temperature of the 1₁₁ − 0₀₀ line is related to the column density of para-H₂Cl⁺ by the expression

$$\begin{equation} 8 \pi k \int T_b dv = h c \lambda ^2 R N({\rm p\mbox{-}H_2Cl^+}), \end{equation} \tag{ 1 }$$

where N(p-H₂Cl⁺) is the beam-averaged column density of para-H₂Cl⁺. In deriving Equation (1), we adopted the standard definition of Rayleigh–Jeans brightness temperature, T_b = I_νλ²/2k, where I_ν is the specific intensity; and we assumed that the line emission is optically thin and isotropic, with the frequency-integrated specific intensity given by hνRN(p-H₂Cl⁺)/4π.

Given an integrated antenna temperature of 411 mK km s⁻¹ for the 1₁₁–0₀₀ transition of H³⁵₂Cl⁺, and a main beam efficiency of 0.76 (Roelfsema et al. 2012), this expression yields an estimate of 7 × 10¹² cm⁻² for the beam-averaged column density of para-H³⁵₂Cl⁺, if assumed to originate in a region close to the cloud surface (where R = R_surface). Alternatively, if the para-H³⁵₂Cl⁺ originates in the cloud interior (where R = R_interior), the estimated column density is even higher: 1.6 × 10¹⁴ cm⁻². For an assumed OPR of 3 for chloronium, corresponding to the equilibrium value expected at diffuse cloud temperatures, and for a H³⁵₂Cl⁺/H³⁷₂Cl⁺ ratio of 3, these values correspond to total H₂Cl⁺ column densities of 2.9 × 10¹³ cm⁻² and 7.0 × 10¹⁴ cm⁻², respectively, for a cloud surface and cloud interior source of the observed H³⁵₂Cl⁺ emission. These estimates both apply to the beam-averaged column density and represent two extreme cases that are expected to bracket the actual value.

In the Orion South molecular condensation, the gas density is believed to be higher than in the Orion Bar PDR (and UV radiation field to be smaller.) Mundy et al. (1988) estimated the virial mass of Orion S to be 80 M_☉ from interferometric CS J = 2–1 observations, and—assuming a thickness along the line of sight based on the observed angular size—obtained an estimate of 3 × 10⁶ cm⁻³ for the H₂ density, n(H₂) = n_H/2. A better density estimate comes from fits to the J = 4–3, J = 10–9, J = 12–11, and J = 16–15 transitions of HC₃N, observed by Bergin et al. (1996), who mapped the entire Orion ridge in these transitions with an angular resolution of about 50''. Assuming a gas temperature of 30 K, Bergin et al. obtained a density estimate n(H₂) > 1.2 × 10⁶ cm⁻³ at the position of Orion S, with n(H₂) ∼ 10⁶ cm⁻³ at adjacent positions. For a higher assumed gas temperature ∼100 K, the density limit for Orion S would be lower by about a factor of three. Finally, Rodríguez-Franco et al. (2001) combined observations of the N = 1–0, N = 2–1, and N = 3–2 lines of CN to estimate a density n(H₂) = 2 × 10⁵ cm⁻³ for the region near Orion S, for an assumed gas temperature of 80 K. In our analysis of the H₂Cl⁺ emission detected from Orion S, we have adopted a density estimate n(H₂) = 3 × 10⁵ cm⁻³, based on these previous values presented in the literature.

The gas temperature in Orion South has been estimated from observations of two symmetric top molecules: NH₃ (Batrla et al. 1983) and CH₃CN (Ziurys et al. 1990). Although Batrla et al. mapped the (1,1) and (2,2) inversion lines of NH₃ with a resolution of 43'', only for a few select positions were observations of the higher inversion lines made and temperatures quoted. One such position was within 11'' of Orion South (their position S6). These observations and those of Ziurys et al. are consistent with a gas temperature of about 100 K for Orion S, a value that we adopt in deriving the H₂Cl⁺ column density.²⁰

With no clear evidence in Orion South for a PDR of the same prominence as that in the Orion Bar, we expect collisions with H₂ to dominate the excitation of chloronium. Given an integrated antenna temperature of 395 mK km s⁻¹, and the density and temperature estimates discussed above, we derive a para-H³⁵₂Cl⁺ column density of 3 × 10¹² cm⁻², corresponding to a total chloronium column density of 1.6 × 10¹³ cm⁻² for an assumed OPR of 3 and H³⁵₂Cl⁺/H³⁷₂Cl⁺ ratio of 3. We estimate the beam-averaged H₂ column density as 4 × 10²³ cm⁻², based upon the 1.3 mm dust continuum map obtained by Mezger et al. (1990), which implies an N(H₂Cl⁺)/N(H₂) abundance ratio of 4 × 10⁻¹¹. This value corresponds to a fraction ∼2 × 10⁻⁴ of the gas-phase Cl abundance determined for diffuse atomic clouds. By means of a similar analysis, we found that the upper limit on the H₂Cl⁺ line flux obtained toward Orion H₂ Peak 1 yields a limit of 5 × 10⁻¹⁰ on the N(H₂Cl⁺)/N(H₂) abundance ratio at that position, a value that is a factor ∼10 higher than the abundance inferred for the Orion South condensation.

To help interpret the H₂Cl⁺ observations of diffuse clouds along the sight lines to Sgr A (+50 km s⁻¹ cloud) and W31C, we have used the Meudon PDR code (Le Petit et al. 2006) to obtain predictions for the H₂Cl⁺ abundance. The approach is rather similar to that adopted by NW09, but includes an improved treatment of the depth dependence of the photochemistry and of the self-shielding of molecular hydrogen from photodissociation. In particular, the photodissociation and photoionization rates for such species as H, H₂, Cl, HCl, HCl⁺, and CO have been computed by integrating the corresponding cross-sections over the radiation field intensity in an "exact" UV transfer approach where possible self-shielding, line overlap, and continuum gas phase and dust absorption are taken into account. The contribution of the dust extinction is computed from the shape of the extinction curve whose analytic expression is given and discussed in Fitzpatrick & Massa (1999). The mean Galactic curve extinction has been used here as our standard assumption. The radiation field is assumed to impinge isotropically on both sides of a slab of fixed visual extinction A_{V, tot}. The reaction network is the same as that adopted by NW09.

In Figure 4, we present the predicted fractions of gas-phase chlorine present in the HCl⁺ and H₂Cl⁺ ions, $\bar{f}({\rm HCl}^+)$ and $\bar{f}({\rm H_2Cl}^+)$, averaged along a sight line through a diffuse molecular cloud of total visual extinction A_{V, tot}, together with the average H₂ fraction, $\bar{f}({\rm H_2}) = 2N({\rm H}_2)/ [2N({\rm H}_2)+ N({{\rm H\,\mathsc{i}}})]$. Although the diffuse-cloud abundances of HCl⁺ and H₂Cl⁺ show very little dependence upon the cosmic-ray ionization rate, we note that the results presented in Figure 4 were computed for an assumed primary cosmic-ray ionization rate of 1.8 × 10⁻¹⁶ s⁻¹ per H nucleus, a value corresponding to the "enhanced ionization rate" considered by NW09 and in agreement with recent estimates obtained from the analysis of H⁺₃ (Indriolo et al. 2007) and OH⁺ abundances (Neufeld et al. 2010b) in diffuse clouds. The different panels in Figure 4 show the results for different ratios of the gas density, n_H, to the radiation field, χ_UV, the latter normalized with respect to the mean radiation field given by Draine (1978). Regardless of n_H/χ_UV, the maximum value of ${\bar{f}}({\rm H_2Cl}^+)$ is typically obtained in clouds with ${\bar{f}}({\rm H}_2) \sim 0.3$. In Figure 5, we show (magenta diamonds) the ratio of the H₂Cl⁺ column density to that of atomic hydrogen, $N({\rm H_2Cl^+})/N({{\rm H\,\mathsc{i}}})$, together with the corresponding ratio for HCl⁺ (blue triangles). The maximum $N({\rm H_2Cl^+})/N({{\rm H\,\mathsc{i}}})$ ratio predicted for any parameters, 1 × 10⁻⁹, is a factor of 4 and 12 below the average values measured toward Sgr A (+50 km s⁻¹ cloud) and W31C, respectively. A very similar discrepancy has been reported in the case of HCl⁺, the tentative detection of which has been presented recently by De Luca et al. (2011). Indeed, if we assume a N(H₂Cl⁺)/N(HCl⁺) ratio of 1, the value implied for W31C given the De Luca et al. detection, the maximum predicted $N({\rm H_2Cl^+})/N({{\rm H\,\mathsc{i}}})$ ratio is 5 × 10⁻¹⁰, a factor of ∼20 below the measured value.

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We have investigated several explanations for the discrepancies described above, none of which appears to be entirely satisfactory. First, we have examined the effect of reducing the rate coefficient assumed for DR of HCl⁺ to 2 × 10⁻⁸ cm³ s⁻¹(T/300 K)^−1/2; this value is 10 times smaller than that adopted by NW09 as the typical DR of diatomic molecular ions, but equal to the experimental value obtained by Djurić et al. (2001) for HF⁺. The result of this change is quite modest, however; for the cloud model that yields the maximum H₂Cl⁺ abundance, with A_{V, tot} = 0.3 and n_H/χ_UV = 32, the predicted HCl⁺ and H₂Cl⁺ abundances increase by factors of 2.7 and 1.3, respectively. Second, we investigated the effect of increasing the rate coefficient assumed for charge transfer between Cl and H⁺. That reaction was assumed by Blake et al. (1986) to have a rate coefficient of 10⁻⁹ cm³ s⁻¹ and was identified as an important route to the formation of Cl⁺, but subsequently found to have a considerably smaller rate coefficient (by factors of ∼20 and ∼250 at 300 K and 100 K, respectively) in calculations performed by Pradhan & Dalgarno (1994). For the cloud model with A_{V, tot} = 0.3 and n_H/χ_UV = 32, the predicted HCl⁺ and H₂Cl⁺ abundances only increase by 7% and 6%, respectively, if a rate coefficient of 10⁻⁹ cm³ s⁻¹ is assumed in place of that computed by Pradhan & Dalgarno (1994). Third, we have examined the effect of adopting an interstellar radiation field with a spectral shape corresponding to a 30,000 K blackbody in place of that assumed by Draine (1978; but with the absolute intensity constrained to be equal at 1000 Å.) At photon energies above the ionization potential of atomic chlorine (12.97 eV), the former drops less rapidly than the latter, leading to an enhanced photoionization rate for Cl. However, even for this harder (and arguably extreme) radiation field, the resultant HCl⁺ and H₂Cl⁺ abundances are only increased by factors of 1.4 and 1.3, respectively. Fourth, we have investigated the dependence of the model predictions upon the wavelength dependence of the dust opacity, assumed in our standard model to follow the average Galactic extinction law of Fitzpatrick & Massa (1999). We have considered a case in which the dust opacity is assumed to rise less rapidly as the wavelength decreases, following the extinction curve of HD 294264 (Fitzpatrick & Massa 2005). Here, the peak H₂Cl⁺ abundances are achieved at somewhat larger A_{V, tot}, but the effect on the peak abundances are small: the peak predicted HCl⁺ and H₂Cl⁺ abundances are only increased by 3% and 12%, respectively.

We note two additional systematic uncertainties that might help account for the discrepancy between theory and observation. First, the chloronium column densities derived from the absorption-line observations are inversely proportional to the square of the assumed dipole moment, for which we adopted a value of 1.89 D, the result of unpublished calculations by Müller. This value is already fairly large, and thus an unusually large dipole moment (larger than ∼4–5 D) would be needed to bring the theory and observation into acceptable agreement. Second, the chloronium column densities predicted by theory are roughly inversely proportional to the assumed DR rate for H₂Cl⁺. The value we adopted was that obtained in recent laboratory measurements (W. D. Geppert & M. Hamberg 2009, private communication) performed with the use of an ion storage ring, but there is always the possibility that some degree of H₂Cl⁺ rotational excitation in the laboratory environment may lead to results that differ from those applicable in the interstellar environment (where most molecules are in the ground rotational state); in this regard, we note that Petrignani et al. (2011) have recently argued that studies of DR in ion storage rings may typically involve ions with higher rotational temperatures than had previously been appreciated.

Finally, we note that the theoretical models employed to date obtain steady-state abundances for the chlorine-bearing molecules under investigation. Because the timescale for H₂ formation is relatively long—of order 10 (100 cm⁻³/n_H) Myr—time-dependent effects may be important as molecular clouds either form or disperse. In the case of molecular cloud formation, the H₂ abundance lags relative to its equilibrium value, which is unfavorable for the formation of chloronium; but the case of cloud dispersal may be more favorable for the production of enhanced H₂Cl⁺ abundances and is worthy of future investigation.

The chloronium column density predicted by NW09 (their Figure 5) for conditions appropriate to the Orion Bar PDR—n_H ∼ 6 × 10⁴ cm⁻² and χ_UV ∼ 3 × 10⁴ (Herrmann et al. 1997)—is N(H₂Cl⁺) ∼ 3 × 10¹¹ cm⁻², a factor ∼100 smaller than the observed value (see Section 4.2 for the case of a surface source of H₂Cl⁺). These two column densities are not directly comparable, however, because the theoretical prediction is of the perpendicular column density of chloronium, whereas the Orion Bar PDR is viewed nearly edge-on. Nevertheless, the geometric enhancement in the measured column density is expected to be a factor ∼4 (e.g., Neufeld et al. 2006), and thus the theory still appears to underpredict the observed column density by more than an order of magnitude. Clearly, the uncertainties here are considerably larger than those involved in the comparison of theory and observation in diffuse clouds, but nevertheless it appears that the discrepancy is similar in size (and direction).

Whereas the chemistry leading to chloronium in diffuse clouds is driven by photoionization of Cl, the chemical network in dense clouds is initiated by cosmic-ray ionization. In Figure 6, we show theoretical predictions for the H₂Cl⁺ abundance in the shielded interior of a dense cloud, shown here relative to that of gas-phase chlorine. These predictions are based upon an assumed cosmic-ray ionization rate of 1.8 × 10⁻¹⁷ s⁻¹ (primary ionization rate per H nucleus); this is the "standard value" adopted by NW09, believed to be most appropriate for dense molecular clouds. Once again, the observed H₂Cl⁺ abundance of ∼1.5 × 10⁻⁴ relative to the diffuse cloud gas-phase chlorine abundance (Section 4.3) is more than an order of magnitude greater than the model prediction. The discrepancy becomes even greater if the chlorine depletion in the Orion South condensation is larger than that in the diffuse ISM, as suggested by observations of HCl by Schilke et al. (1995).

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