THE CHEMISTRY OF INTERSTELLAR MOLECULES CONTAINING THE HALOGEN ELEMENTS

The key chemical pathways leading to the formation and destruction of chlorine-bearing molecules have been elucidated in the papers of Jura (1974), Dalgarno et al. (1974), van Dishoeck & Black (1986; hereafter vDB86), Blake et al. (1986; hereafter BAH86), Schilke et al. (1995), Federman et al. (1995), and Amin (1996). In diffuse molecular clouds, the chemical network is initiated by reaction of Cl⁺ with H₂:

$$\begin{equation} \rm Cl^+ + H_2 \rightarrow HCl^+ + H, \end{equation} \tag{ 1 }$$

which is followed by dissociative recombination of HCl⁺ or a further H atom abstraction reaction to form H₂Cl⁺:

$$\begin{equation} \rm HCl^+ + H_2 \rightarrow H_2Cl^+ + H. \end{equation} \tag{ 2 }$$

The H₂Cl⁺ molecular ion undergoes dissociative recombination to form either HCl or Cl

$$\begin{equation} \rm H_2Cl^+ + e \rightarrow HCl + H \end{equation} \tag{ 3 }$$

$$\begin{equation} \rm H_2Cl^+ + e \rightarrow Cl + products. \end{equation} \tag{ 4 }$$

The branching ratio for dissociative recombination of H₂Cl⁺ has not yet been measured, but has been assumed in previous studies to be only 10% for production of HCl (reaction (3)). This assumption was largely motivated by the small HCl abundances observed in diffuse clouds (see Section 4 below.) HCl is destroyed by photodissociation, by photoionization and by reactions with He⁺, H⁺₃, and C⁺.

In regions where H₂ is present, reactions (1), (2), and (4) can rapidly convert Cl⁺ to Cl. The rate at which the reaction network is initiated (reaction (1)) is therefore limited by the availability of Cl⁺ ions. These are produced primarily by the photoionization of Cl, following the absorption of ultraviolet photons in the 912–958 Å wavelength range. Near cloud surfaces, the UV radiation field is dominated by starlight (i.e., by the interstellar radiation field (ISRF) or nearby OB associations), whereas in the deep interiors of dense clouds, the radiation largely comprises H₂ Lyman and Werner band emissions excited by the secondary electrons produced by cosmic rays. Here, proton transfer from H⁺₃ to Cl, producing HCl⁺, can also initiate the formation of Cl-bearing molecules.

Taking as our starting point the reaction list and compilation of rate coefficients in the UDFA (formerly UMIST) rate file (Woodall et al. 2007), we have reviewed the rate coefficients critically and implemented the following changes:

• 1.  
  For reaction of HCl with He⁺, H⁺₃, and C⁺, we have used the statistical adiabatic capture model (SACM; Troe 1985, 1987, 1996; see NWS05 for details of exactly how this was implemented) to estimate the temperature dependence of the capture rate. Over the temperature range 10–300 K, we found the capture rate to be proportional to T^−0.202 for rotationally cold HCl; accordingly we adopted a T^−0.202 dependence for the assumed reaction rate. Similar considerations lead to a T^−0.194 temperature dependence for the rate coefficient for the reaction of H₂O with H₂Cl⁺. We also adjusted the T = 300 K rate coefficients in the UDFA compilation, which were based upon measurements of the thermal rate coefficients, to account for the fact that HCl is primarily in J = 0 (i.e., rotationally cold) under the astrophysical conditions of typical interest; here again, we used the SACM model to estimate the necessary correction factors.
• 2.  
  As in NWS05, we adopted a rate coefficient of 2 × 10⁻⁷(T/300 K)^−1/2 cm³ s⁻¹ for the dissociative recombination of diatomic molecular ions (in the absence of experimentally determined values). For the dissociative recombination of H₂Cl⁺, we adopted a rate coefficient of 1.2 × 10⁻⁷(T/300 K)^−0.85 cm³ s⁻¹, based upon preliminary results from a recent laboratory measurement (W. D. Geppert & M. Hamberg 2009, private communication). Because the branching ratios for the production of HCl and Cl were not determined in this experiment, we followed previous authors in adopting—as our standard assumption—a branching ratio of 0.1 for the production of HCl. As discussed in Section 4.2 below, we also investigated how the model predictions depend upon the assumed value of this branching ratio.
• 3.  
  We adopted the rate coefficients of Pradhan & Dalgarno (1994) for charge transfer from H⁺ to Cl, and for the reverse reaction (from Cl⁺ to H). These reactions were not included in the UDFA compilation, but had been considered by BAH86, who assumed a large rate coefficient of 10⁻⁹ cm³s⁻¹ for the reaction of H⁺ with Cl and concluded that this process was among the subset of most significant reactions. The calculations of Pradhan & Dalgarno (1994), however, imply rate coefficients that are smaller than those guessed by BAH86 by factors of ∼20 and ∼250 at temperatures of 300 K and 100 K, respectively.
• 4.  
  We have also included the reaction of Cl with H₂ to form HCl and H, which is slightly endothermic (by ∼0.05 eV), along with its reverse reaction. This reaction, which is not included in the UDFA compilation, has been the subject of intensive investigation, both experimental (e.g., Kumaran et al. 1994; hereafter KLM94) and theoretical (e.g., Manthe et al. 2004). Here we adopted the rate coefficients recommended by KLM94 (their Equations (10), (11), and (6)), which were obtained by a fit to their own measurements together with those obtained in previous studies.
• 5.  
  In computing revised estimates of the HCl photodissociation and photoionization rates, we have used the photoabsorption cross-sections obtained by Brion et al. (2005) by means of dipole (e, e) spectroscopy using an electron energy loss spectrometer (EELS). This technique is believed to offer significant advantages over direct UV absorption measurements for the case of strong absorption bands in which line saturation is important (Chan et al. 1991). For example, in the case of excitation to the M¹Π state by photons near 110.3 nm, Brion et al. obtained an oscillator strength that was a factor of 4 larger than that obtained in the earlier UV absorption experiments of Nee et al. (1986). The continuous absorption cross-sections obtained by Brion et al. (2005) are in good agreement with previous UV absorption measurements (e.g., Cheng et al. 2002). To determine the photodissociation rate implied by the measured photoabsorption cross-sections, the photodissociation probability must also be known. For radiation longward of 115 nm, the fluorescence yield has been measured (Nee et al. 1986) and found to be small, so the photodissociation probability is very close to unity. For absorption in the 105.5–115 nm region, the fluorescence at wavelengths longer than 115 nm was observed to be weak, but the experiment of Nee et al. (1986) did not exclude the possibility of strong fluorescent emission in the 105.5–115 nm region. For the 97.3–105.5 nm spectral region, we are unaware of any experimental constraints on the fluorescent yield. In computing the photodissociation rate, we have assumed that the dissociation probability is unity⁵ for all radiation longward of the ionization threshold at ∼ 97.3 nm. This leads to a photodissociation rate of 1.7 × 10⁻⁹ s⁻¹ for an unshielded molecule exposed to the mean interstellar radiation field given by Draine (1978), a value that is ∼70% higher than that given by van Dishoeck et al. (1982; hereafter vDvHD). This difference is largely accounted for by the fact that the total oscillator strength shortward of 129 nm is now known to exceed significantly the simple estimate given by vDvHD. We obtain an HCl photoionization rate of 1.0 × 10⁻¹⁰ s⁻¹.In considering the effect of shielding upon the HCl photodissociation rate, we used a method similar to that adopted by NWS05. Here, we modeled the case of a semi-infinite slab that is illuminated isotropically, using the photodissociation region (PDR) model of Le Bourlot et al. (1993) and Le Petit et al. (2006) to determine how the UV radiation field varies with position. We assumed the photodissociation rate to diminish as E₂(kA_V), where A_V is the visual extinction in magnitudes behind the slab surface, E₂ is the exponential integral of order 2, and k is an adjustable parameter that we varied in order to obtain the best fit to the predicted photodissociation rate. The UV dust albedo assumed here was 0.32, the forward scattering function was 0.73 (Li & Draine 2001), and the best fit was obtained for k = 2.1.
• 6.  
  Our estimate of the Cl photoionization rate was based upon measurements of the ionization cross-section by Ruscic & Berkowitz (1983), which are in good agreement with theoretical calculations of Brown et al. (1980). Two autoionizing resonances are present at wavelengths longer than the Lyman limit, but make a negligible contribution to the overall photoionization rate. We derived a photoionization rate of 4.8 × 10⁻¹¹ s⁻¹ for an unshielded chlorine atom exposed to the mean interstellar radiation field given by Draine (1978), a value that lies a factor of ∼2 below that adopted by van Dishoeck (1988).Because the IP of atomic chlorine is only slightly less than that of H, there is only a narrow wavelength range, 912–958 Å, over which photoionization can occur. Radiation in this spectral region is subject not only to absorption by dust, but also to absorption by the H₂ Lyman and Werner bands and the H i Lyman lines. While the effect of H i absorption is small, that of H₂ absorption can be significant. We have considered dust and H₂ absorption independently, by running the Le Petit et al. (2006) PDR model both with and without H₂ absorption. We have found that the reduction in the Cl photoionization rate can be represented to good approximation by a factor

  $$\begin{equation} E_2(3.6\,A_V) \times {\exp (-N({\rm H}_2)/4.28 \times 10^{21}\,{\rm cm}^{-2}) \over 1 + \sqrt{N({\rm H}_2)/4.9 \times 10^{20}\,{\rm cm}^{-2}} }, \end{equation} \tag{ 5 }$$

  where N(H₂) is the column density of H₂ to the cloud surface.The photoionization of HCl occurs over a similarly narrow range of wavelengths. For that process, an identical treatment yields a reduction factor

  $$\begin{equation} E_2(3.45\,A_V) \times {\exp (-N({\rm H}_2)/3.5 \times 10^{21}\,{\rm cm}^{-2}) \over 1 + \sqrt{N({\rm H}_2)/3.2 \times 10^{20}\,{\rm cm}^{-2}} }. \end{equation} \tag{ 6 }$$
• 7.  
  Using the cross-sections cited in Equations (5) and (6) above, we have computed the rates of HCl photodissociation, HCl photoionization, and Cl photoionization resulting from H₂ Lyman and Werner band emissions excited by secondary electrons produced by cosmic rays. Here we used the same methodology adopted in NWS05.
• 8.  
  For the radiative recombination of Cl⁺, we adopt the value recommended by Mazzotta et al. (1998). Dielectronic recombination is negligible at the temperatures of present interest.

Our model does not include the photodissociation of molecular ions containing the halogen elements. With the exception of HCl⁺, for which photodissociation cross-sections have been presented by Pradhan et al. (1991) and by Andric et al. (2002), we are not aware of any estimates of the relevant cross-sections. The HCl⁺ photodissociation cross-sections imply an unshielded photodissociation rate of 5.6 × 10⁻¹¹χ_UV s⁻¹. In the region where HCl⁺ is most abundant, photodissociation makes a negligible contribution—relative to dissociative recombination—to the HCl⁺ destruction rate; we assume photodissociation to be similarly negligible for CF⁺ and H₂Cl⁺.

The full reaction list for chlorine-bearing species is given in Table 1. It contains 21 processes involving the following species: Cl, HCl, Cl⁺, HCl⁺, H₂Cl⁺, and CCl⁺.

Table 1. Reaction List for Cl-Bearing Species

Reaction	Rate or Rate Coefficient
Cl + H2 → HCl + H	2.52 × 10−11 exp (−2214 K/T) cm3 s−1(T ⩽ 354 K)
	2.86 × 10−12(T/300 K)1.72 exp (−1544 K/T) cm3 s−1 (T ⩾ 354 K)
HCl + H2 → Cl + H2	1.49 × 10−11 exp (−1763 K/T) cm3 s−1(T ⩽ 354 K)
	1.69 × 10−12(T/300 K)1.72 exp (−1093 K/T) cm3 s−1 (T ⩾ 354 K)
C+ + HCl → CCl+ + H	1.84 × 10−9(T/300 K)−0.202 cm3 s−1
H+3 + HCl → H2 + H2Cl+	6.35 × 10−9(T/300 K)−0.202 cm3 s−1
He+ + HCl → H + Cl+ + He	5.51 × 10−9(T/300 K)−0.202 cm3 s−1
Cl+ + H2 → HCl+ + H	1.0 × 10−9 cm3 s−1
HCl+ + H2 → H2Cl+ + H	1.3 × 10−9 cm3 s−1
CCl+ + e → C + Cl	2.0 × 10−7(T/300 K)−0.5 cm3 s−1
HCl+ + e → H + Cl	2.0 × 10−7(T/300 K)−0.5 cm3 s−1
H2Cl+ + e → HCl + H	1.2 × 10−8(T/300 K)−0.85 cm3 s−1
H2Cl+ + e → Cl + products	1.08 × 10−7(T/300 K)−0.85 cm3 s−1
H2Cl+ + CO → HCl + HCO+	7.8 × 10−10  cm3 s−1
H2Cl+ + H2O → HCl + H3O+	3.7 × 10−9(T/300 K)−0.194 cm3 s−1
Cl + H+3 → H2Cl+ + H	1.0 × 10−9 cm3 s−1
HCl + hν → H + Cl	$\,1.7 \times 10^{-9}\,\chi _{\rm UV} [\,{1 \over 2}E_2(2.1 A_V) + {1 \over 2}E_2(2.1 [A_{V,{\rm tot}}-A_V])]\,{\rm s}^{-1}\,$
	+  1370 ζp /(1 − ω)
HCl + hν → HCl+ + e	$\,1.0 \times 10^{-10}\,\chi _{\rm UV} [\,{1 \over 2}E_2(3.45 A_V) + {1 \over 2}E_2(3.45 [A_{V,{\rm tot}}-A_V])]\,{\rm s}^{-1}\,$
	× exp(−N(H2)/3.5 × 1021 cm−2)/(1 + [N(H2)/3.2 × 1020 cm−2]1/2)
	+  185 ζp /(1 − ω)
Cl + hν → Cl+ + e	$\,4.8 \times 10^{-11}\,\chi _{\rm UV} [\,{1 \over 2}E_2(3.6 A_V) + {1 \over 2}E_2(3.6 [A_{V,{\rm tot}}-A_V])]\,{\rm s}^{-1}\,$
	× exp(−N(H2)/4.28 × 1021 cm−2)/(1 + [N(H2)/4.9 × 1020 cm−2]1/2)
	+  61 ζp /(1 − ω)
Cl+ + e → Cl + hν	1.34 × 10−11(T/300 K)−0.738 cm3 s−1
Cl+ + H → Cl + H+	6.2 × 10−11(T/300 K)0.79 exp (−6920 K/T) cm3 s−1
Cl + H+ → Cl+ + H	9.3 × 10−11(T/300 K)0.73 exp (−232 K/T) cm3 s−1
HCl + H+ → HCl+ + H	3.3 × 10−9(T/300 K)1.00 cm3 s−1

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The chemical network for fluorine-bearing species has been discussed by NWS05. The chemistry is initiated by reaction of H₂ with F:

$$\begin{equation} \rm F + H_2 \rightarrow HF + H. \end{equation} \tag{ 7 }$$

Once the H₂ abundance becomes appreciable, HF becomes the dominant reservoir of fluorine; it is destroyed slowly by photodissociation, and by reactions with He⁺, H⁺₃, and C⁺. Reaction with C⁺ leads to the formation of CF⁺:

$$\begin{equation} \rm HF + C^+ \rightarrow CF^+ + H. \end{equation} \tag{ 8 }$$

The fluoromethylidynium ion, CF⁺, is destroyed rapidly by dissociative recombination, but can nevertheless account for as much as ∼1% of the gas-phase fluorine abundance. It has recently been detected in the interstellar medium (Neufeld et al. 2006).

For completeness, we have implemented five updates to the chemical network presented by NWS05. Of the following changes, the first three of which were noted in the UDFA reaction list (Woodall et al. 2007), only the first is expected to have any significant effect on the model predictions:

• 1.  
  For the rate coefficient for dissociative recombination of CF⁺, we now adopt the recent laboratory measurement of Novotny et al. (2005). The adopted rate coefficient lies factors of 4 and 1.5 below that assumed by NWS05 at temperatures of 300 and 10 K respectively.
• 2.  
  We have corrected an erroneous value adopted by NWS05 for the rate coefficient for reaction of F with H₂O. The correct value is 1.6 × 10⁻¹¹ cm⁻³ s⁻¹. This was stated correctly in the text of NWS05, but a value 10 times too large was erroneously given in the reaction list table (and erroneously implemented in our calculation).
• 3.  
  For the reaction of H₂ with F⁺, we include a channel that produces H⁺₂ in addition to that which produces HF⁺.
• 4.  
  For the cosmic ray induced photodissociation of HF, we include the effects of H Lyman alpha radiation. This results in a 50% increase in the adopted photodissociation rate.
• 5.  
  For the radiative recombination and dielectronic recombination of F⁺, we adopt the rate coefficients of Badnell (2006) and Badnell et al. (2003).

The full reaction list for fluorine-bearing species is given in Table 2. It contains 18 processes involving the following species: F, HF, F⁺, HF⁺, H₂F⁺, CF⁺, and SiF⁺.

Table 2. Reaction List for F-Bearing Species

Reaction	Rate or Rate Coefficient
F + H2 → HF + H	1.0 × 10−10 [ exp (−450 K/T) + 0.078 exp(−80 K/T)
	+0.0155 exp(−10 K/T)] cm3 s−1
$\bf F + H_2O \rightarrow HF + O$a	$\bf 1.6 \times 10^{-11} \, cm^3 \,s^{-1}$
C+ + HF → CF+ + H	7.2 × 10−9(T/300 K)−0.15 cm3 s−1
Si+ + HF → SiF+ + H	5.7 × 10−9(T/300 K)−0.15 cm3 s−1
H+3 + HF → H2 + H2F+	1.2 × 10−8(T/300 K)−0.15 cm3 s−1
He+ + HF → H + F+ + He	1.1 × 10−8(T/300 K)−0.15 cm3 s−1
$\bf F^+ + H_2 \rightarrow H_2^+ + F$	$\bf 6.24 \times \bf 10^{-10} \, cm^3 \,s^{-1}$
$\bf \rightarrow HF^+ + H$	$\bf 3.8 \times 10^{-10} \, cm^3 \,s^{-1}$
HF+ + H2 → H2F+ + H	1.3 × 10−9 cm3 s−1
$\bf CF^+ + e \rightarrow C + F$	$\bf 5.2 \times 10^{-8} \, (T/300 \bf \, K)^{-0.8} \, cm^3 \,s^{-1}$
SiF+ + e → Si + F	2.0 × 10−7(T/300 K)−0.5 cm3 s−1
HF+ + e → H + F	2.0 × 10−7(T/300 K)−0.5 cm3 s−1
${\rm \rm H}_2{\rm F}^+ + {\rm e} \rightarrow {\rm HF + H}$	3.5 × 10−7(T/300 K)−0.5 cm3 s−1
H2F+ + e → F + products	3.5 × 10−7(T/300 K)−0.5 cm3 s−1
F + CH → HF + C	1.6 × 10−10 cm3 s−1
F + OH → HF + O	1.6 × 10−10 cm3 s−1
${\rm \rm F + H}_3^+ \rightarrow {\rm H}_2{\rm F}^+ + {\rm H}$	4.8 × 10−10 cm3 s−1
$\bf HF + h\nu \rightarrow H + F$	$\,1.17 \times 10^{-10}\,\chi _{\rm UV} [\,{1 \over 2}E_2(2.21 A_V) + {1 \over 2}E_2(2.21 [A_{V,{\rm tot}}-A_V])]\,{\rm s}^{-1}\,$
	+ $\bf \, 124 \, \zeta _{p}\, /(1 - \omega)$

Note. ^aBoldface denotes those reactions for which the adopted rates are different from those assumed by NWS05.

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As in NWS05, we have used a modified version of the PDR models of Kaufman et al. (2006), Kaufman et al. (1999), Wolfire et al. (1990), and Tielens & Hollenbach (1985) to investigate the chemistry within diffuse and dense molecular clouds. The modifications to these models have been largely described in NWS05, with the exception of the following:

• 1.  
  For the radiative and dielectronic recombination of C⁺, we adopt the recently computed rate coefficients of Badnell (2006) and Badnell et al. (2003).
• 2.  
  In treating the depletion of fluorine and chlorine that results from freeze-out onto grain mantles within dense molecular clouds, we use Equation (5) of NWS05, but with the HF or HCl photodissociation rate augmented so as to include the effects of H₂ Lyman and Werner band emissions excited by the secondary electrons produced by cosmic rays. As in NWS05, we assume a gas-phase fluorine abundance of 1.8 × 10⁻⁸ relative to H nuclei in diffuse molecular clouds. For chlorine, we assume an analogous abundance of 1.8 × 10⁻⁷, the average value observed in three sightlines that intersect diffuse molecular clouds: ζ Oph (Federman et al. 1995), HD 192639 (Sonnentrucker et al. 2002), and HD 185418 (Sonnentrucker et al. 2006).

In our standard models, as in NWS05, we assume a primary cosmic-ray ionization rate of ζ_p = 1.8 × 10⁻¹⁷ s⁻¹ per H nucleus. Recent observations of H⁺₃ have led to the postulate of substantially larger rates in diffuse clouds (e.g., Indriolo et al. 2007). To investigate the effect of enhanced cosmic ray ionization rates upon the chemistry of interstellar halogens, we have also considered models for which the assumed ζ_p is increased by a factor 10.

Our standard models also compute the thermal balance and equilibrium gas temperature as a function of distance into the cloud. To investigate the possible effects of enhanced temperatures (such as might result from the passage of interstellar shocks), we have also considered a series of models in which the temperature is set to some depth-independent value (larger than that computed by our self-consistent treatment of the thermal balance).

For our standard models, we have followed previous authors in adopting a branching ratio of 0.1 for the production of HCl following dissociative recombination of H₂Cl⁺. To study the dependence upon this branching ratio, we have also considered diffuse cloud models in which values of 0, 0.3, and 1.0 were adopted.

In Figures 9–13, circles represent the key Cl-bearing species, with a color scale indicating their relative abundance. The color map extends from cyan to blue to purple to red (highest value), with gray circles denoting species that account for less than 10⁻⁸ of the gas-phase chlorine abundance. Arrows indicate the key reactions linking the various species: again, the colors of the arrows indicate the reaction rate per unit volume. The results apply to a one-sided model with n_H = 10⁴ cm⁻³ and χ_UV = 10⁴, and the different figures show the behavior at various depths into the cloud. The depths were chosen to illustrate several different regimes.

• 1.  
  A_V = 0. At the cloud surface, there is no shielding and the abundance of molecules is small. The Cl⁺/Cl ratio is ∼10⁵, being determined by the balance between photoionization and recombination. For the latter process, radiative recombination and charge transfer recombination with H—although endothermic by ∼ 0.6 eV—are of roughly equal importance.
• 2.  
  A_V = 0.8. Here, H₂ self-shielding has greatly increased the H₂ abundance. Reaction with H₂ is now the dominant destruction mechanism for Cl⁺, resulting in the formation of HCl⁺. However, the e/H₂ abundance ratio is still sufficient for dissociative recombination to dominate the destruction of HCl⁺, although the competing reaction with H₂ produces a small amount of H₂Cl⁺. The dissociative recombination of HCl⁺ leads to atomic Cl, which becomes the dominant gas-phase reservoir of chlorine. Beyond A_V ∼ 0.8, the abundances of the HCl⁺ and H₂Cl⁺ ions start to fall, along with that of Cl⁺.
• 3.  
  A_V = 2.0. The e/H₂ abundance ratio has now dropped sufficiently that HCl⁺ reacts primarily with H₂, rather than electrons, forming H₂Cl⁺. HCl is produced by dissociative recombination of H₂Cl⁺, although the dominant formation process for HCl is the slightly endothermic reaction of H₂ and Cl; this reaction is still possible at the ∼200 K temperature at this point within the PDR. At A_V = 2.0, HCl and Cl account respectively for ∼0.1% and ∼99.9% of elemental chlorine in the gas phase.
• 4.  
  A_V = 4.0. The gas temperature drops below the level at which HCl can be formed by reaction of H₂ with Cl, and the HCl abundance is lower than it was at A_V = 2.0. The Cl⁺/Cl ratio is now only 10⁻⁸, the photoionization rate of Cl having dropped dramatically. Thus the formation of HCl⁺ is dominated by reaction of H⁺₃ with Cl, not H₂ with Cl⁺. The H⁺₃ molecular ion is produced by the effects of cosmic rays; these ionize H₂, forming H⁺₂, which then transfers a proton to H₂ to form H⁺₃.
• 5.  
  A_V = 10.0. As at A_V = 4.0, HCl⁺ is produced primarily by reaction of H⁺₃ with Cl, and reaction of HCl⁺ with H₂ then forms H₂Cl⁺. At this depth, the electron fraction is so low that dissociative recombination of H₂Cl⁺ is no longer dominant. H₂Cl⁺ transfers a proton to a neutral species of higher proton affinity than HCl (e.g., CO or H₂O; this process is denoted by the arrow labeled "N"), yielding HCl. At this point, the external UV is almost completely attenuated, and the HCl destruction rate is very small. HCl now accounts for several ×10% of the gas-phase chlorine abundance, with atomic chlorine accounting for essentially all of the remainder. Our results in this regime are in good agreement with those obtained previously by Schilke et al (1995). H₂Cl⁺ and CCl⁺ are also present, but their abundances are just a few ×0.01% of gas-phase elemental chlorine. HCl reacts with H⁺₃ to form H₂Cl⁺, although this rapidly leads to reformation of HCl by proton transfer to other neutral species. Several other destruction processes are of comparable importance for HCl destruction: cosmic ray induced photodissociation, and reaction with the positive ions C⁺ and He⁺. In this regime, the rates of HCl formation and destruction all scale linearly with the cosmic-ray ionization rate, with the result that the HCl abundance is almost independent of the latter.

Although the diagrams shown in Figures 9–13 apply to just a single model, similar regimes exist for other values of χ_UV and n_H. Although the relevant regions move in or out (to larger or smaller A_V) as the assumed χ_UV/n_H ratio is increased or decreased, the same qualitative behavior is observed. In examining similar diagrams for the entire set of models, we have not identified any important reaction pathway that is not apparent in Figures 9–13.

To date, HF, CF⁺, and HCl are the only halogen-bearing molecules to have been detected in the interstellar medium. In regard to HF, our results are identical to those presented in NWS05: we predict HF to be the dominant gas-phase reservoir of fluorine within both diffuse and dense molecular clouds; we expect the Herschel Space Observatory to detect widespread absorption in the HF J = 1 − 0 transition. However, the abundances we predict for CF⁺ lie a factor ∼3 above the prediction of NWS05, a direct consequence of the smaller dissociation rate adopted for CF⁺ in the present study. As noted by Neufeld et al. (2006), the CF⁺ column densities inferred from observations of the Orion Bar were already a factor of ∼4 below the predictions of NWS05, and the discrepancy between theory and observation is now increased to more than an order of magnitude. This disagreement may indicate that we have overestimated the rate coefficient for reaction of C⁺ and HF. We are not aware of any laboratory studies of this reaction; the rate we adopt is simply the capture rate, and thus an upper limit on the true reaction rate. Laboratory measurements of this key reaction would be very desirable.

HCl has been observed in both diffuse and dense molecular clouds. In diffuse clouds, ultraviolet absorption studies have led to upper limits, and in one case, a tentative detection toward ζ Oph (Federman et al. 1995). The latter result, obtained using the Goddard High Resolution Spectrograph on Hubble Space Telescope (HST), yielded an HCl column density of 2.7 ± 1.0(1σ) × 10¹¹ cm⁻². Given an atomic chlorine column density of 3.0 ± 1.0(1σ) × 10¹⁴ cm⁻² for this sight-line (Federman et al. 1995), the corresponding N(HCl)/N(Cl) ratio is 9 × 10⁻⁴ (uncertain by a factor ∼2), a value in excellent agreement with predictions of the diffuse cloud models presented by vDB86. Very similar results are obtained from our updated treatment of Cl chemistry. In Figure 14, we show predictions from a series of models with χ_UV ranging from 10⁻¹ to 10². All models apply to a slab with parameters appropriate to ζ Oph, viz. density n_H = 10^2.5 cm⁻³ and total visual extinction of 0.8 mag. The horizontal axis shows the H₂ column density, for which the measured value is 4.2 × 10²⁰ cm⁻² along this sight line, while the vertical axis shows N(HCl)/N(Cl) (red curve), N(Cl⁺)/N(Cl) (orange), and N(HCl⁺)/N(Cl) (blue). Squares located along the curves show the results for χ_UV = 10⁻¹ to 10² from right to left. The H₂ column density along the ζ Oph sight line requires a χ_UV ∼ 10^0.5, in agreement with previous studies, and the predicted N(HCl)/N(Cl) is in good agreement with the observations. The almost exact agreement between the present model and that of vDB86 in regard to the predicted HCl abundance appears to result from the fortuitious cancellation of two changes in the photochemical network: the photodissociation rate for HCl and the photoionization rate for Cl are both increased by a factor of ∼2. As in the vDB86 models, the predicted Cl⁺ column density lies substantially below the observations. Federman et al. (1995) attributed this discrepancy to the presence of a significant Cl⁺ column density within H ii regions along the sight line. One important caveat must be noted. The results shown in Figure 14 were obtained by assuming a branching ratio of only 10% for the production of HCl following the dissociative recombination of H₂Cl⁺. This value was initially invoked primarily to explain the relative low HCl abundance derived from upper limits obtained with the Copernicus satellite. Models that we obtained for other branching ratios (0, 0.3, and 1.0) indicate that the HCl column density is linearly proportional to the branching ratio for values greater than 0.1 With a branching ratio of zero (i.e., with no production of HCl from dissociative recombination of H₂Cl⁺), a non-zero but negligible HCl column density (N(HCl)/N(Cl) ∼ 10⁻⁶) results from the endothermic reaction of H₂ with Cl.

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In dense clouds, HCl has been unequivocally detected in several sources by means of submillimeter observations of the J = 1 − 0 emission line. First detected using the Kuiper Airborne Observatory toward Orion (Blake et al. 1985) and then Sgr B2 (Zmuidzinas et al. 1995), the J = 1 −  0 transition has also been observed using the ground-based Caltech Submillimeter Observatory (CSO) under good atmospheric conditions. CSO observations have led to additional detections toward Orion A, Mon R2 (Salez et al. 1996) and several other sources (T. G. Phillips et al. 2009, in preparation), as well as mapping observations toward OMC-1 (Schilke et al. 1995). Typical column densities derived for these dense clouds lie in the few ×10¹³ to few ×10¹⁴ cm⁻² range, in reasonable agreement with the predictions of our model for regions at high density exposed to strong UV radiation (Figure 5). As noted in the observational studies cited above, depletion plays an important role in limiting the fractional abundance of HCl.

Our study identifies two additional Cl-bearing species that are potentially detectable: the molecular ions HCl⁺ and H₂Cl⁺. These ions are isoelectronic with OH and H₂S, respectively. They are most abundant near cloud surfaces, where the photoionization rate for HCl is highest, and show column densities that are an increasing function of χ_UV/n_H. Thus, PDRs subject to strong UV irradiation present attractive targets for searches for HCl⁺ and H₂Cl⁺ at millimeter and submillimeter wavelengths. For example, in a PDR with n_H = 10⁴ cm⁻³ and χ_UV = 10⁴, column densities of 5.7 and 2.6 × 10¹¹ cm⁻² are predicted for HCl⁺ and H₂Cl⁺. These values apply to sight lines perpendicular to the illuminated surface; in edge-on PDRs, they can be significantly enhanced by limb brightening. The rotational spectrum of HCl⁺ has been measured using laser magnetic spectroscopy (Lubic et al. 1989). The lowest lying rotational transition, the ²Π_3/2J = 5/2 → 3/2 multiplet near 207.6 μm, lies in a wavelength range accessible to the HIFI instrument on the Herschel Space Observatory. The rotational spectrum of H₂Cl⁺ has also been the subject of a laboratory study at high spectral resolution; here, the measurements of Araki et al. (2001) indicate that the lowest lying rotational line of ortho-H₂Cl⁺, the 1₁₀ − 1₀₁ transition, lie near 189.2 and 188.4 GHz respectively for the H³⁵₂Cl⁺ and H³⁷₂Cl⁺ isotopologues. (These transitions are split into six and four hyperfine components, covering ∼56 and 14 MHz, respectively.) This spectral region lies in the wing of the strong 183 GHz telluric water absorption line, but is nevertheless observable from ground-based observatories under favorable—but by no means unusual—atmospheric conditions. In one of the earliest studies of interstellar chlorine chemistry, the possibility of detecting HCl⁺ in diffuse molecular clouds was discussed by Jura (1974), who considered the A²Σ⁺ ← X²Π band that is accessible in the near-ultraviolet region. Given an oscillator strength of 4.15 × 10⁻⁴ for the strongest vibrational band (Pradhan et al. 1991), and given the abundances predicted in Figure 17, our results for ζ Oph would imply equivalent widths of only ∼4 × 10⁻⁶ Å, well below the limit of detectability.

Finally, we note that, unlike CF⁺, the CCl⁺ ion is typically predicted to have an extremely low abundance. Although CCl⁺ is produced rapidly by reaction of HCl and C⁺, these two species show very little overlap: the HCl abundance is small in the surface layers where C⁺ is abundant, unless the temperature is increased by shock heating, and the C⁺ abundance is small in the deep cloud interiors where HCl is relatively abundant. Enhanced CCl⁺ abundances are possible when shock heating is present along with UV irradiation.