Determination of the Ortho to Para Ratio of H2Cl+ ... - ACS Publications

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Determination of the Ortho to Para Ratio of H2Cl+ and H2O+ from Submillimeter Observations Maryvonne Gerin,*,† Massimo de Luca,† Dariusz C. Lis,‡ Carsten Kramer,§ Santiago Navarro,§ David Neufeld,∥ Nick Indriolo,∥ Benjamin Godard,⊥ Franck Le Petit,⊥ Ruisheng Peng,‡ Thomas G. Phillips,‡ and Evelyne Roueff⊥ †

LERMA, Observatoire de Paris, ENS, and UMR8112 du CNRS, 24 rue Lhomond, Paris 75231 cedex 05, France MC301-17, Cahill Center for Astronomy and Astrophysics, CalTech, Pasadena, California 91125, United States § IRAM, Instituto de RadioAstronomìa Milimétrica, Avenida Divina Pastora, 7, Núcleo CentralE 18012 Granada, Spain ∥ Department of Physics and Astronomy, Johns Hopkins University, 3400 North Charles Street, Baltimore, Maryland 21218, United States ⊥ LUTH, Observatoire de Paris and UMR8102 du CNRS, Place J. Janssen, 92190 Meudon, France ‡

ABSTRACT: The opening of the submillimeter sky with the Herschel Space Observatory has led to the detection of new interstellar molecular ions, H2O+, H2Cl+, and HCl+, which are important intermediates in the synthesis of water vapor and hydrogen chloride. In this paper, we report new observations of H2O+ and H2Cl+ performed with both Herschel and groundbased telescopes, to determine the abundances of their ortho and para forms separately and derive the ortho-to-para ratio. At the achieved signal-to-noise ratio, the observations are consistent with an ortho-to-para ratios of 3 for both H2O+ and H2Cl+, in all velocity components detected along the lines-of-sight to the massive star-forming regions W31C and W49N. We discuss the mechanisms that contribute to establishing the observed ortho-to-para ratio and point to the need for a better understanding of chemical reactions, which are important for establishing the H2O+ and H2Cl+ ortho-to-para ratios.

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INTRODUCTION The diffuse interstellar medium occupies a significant fraction of the Galaxy volume and therefore represents an important constituent. With an average pressure of ∼3000 K cm−3 determined by Jenkins and Tripp,1 the densities and temperatures of the neutral gas are moderate and the medium is transparent to the stellar visible and ultraviolet radiation. Many molecules are nevertheless present in this hostile environment, and their formation pathways remain to be fully understood. One key species is the H3+ molecular ion, extensively studied in the laboratory by Oka and detected in the diffuse and dense interstellar gas by infrared absorption spectroscopy of its fundamental vibration band by Geballe, Oka, and co-workers.2,3 The Herschel Space Observatorya,4 has significantly contributed to the molecular inventory of the diffuse interstellar gas, by giving access to the fundamental rotational transitions of most interstellar hydrides (e.g., Gerin et al.5 and references therein). As the comparison of the detected molecular column densities or abundances with predictions of chemical models is not always straightforward, given the complexity of the structure of the diffuse interstellar medium and the large number of physical and chemical processes that need to be taken into account,6 it is interesting to use other properties of interstellar species to probe their formation pathways. For species with two identical hydrogen atoms, such as water vapor, the nuclear spin statistics lead to two separate spin symmetry © 2013 American Chemical Society

states: the ortho state with a total nuclear spin angular momentum I = 1, and the para state with I = 0. The statistical weights of these two states are 2I + 1; hence, we have values of 3 for the ortho state and 1 for the para state. The ratio between the densities or column densities in the ortho and para states is the ortho-to-para ratio, or OPR. For water the OPR is 3 at high temperature. Given the low gas densities, these nuclear spin symmetry states of molecules or ions which are not coupled radiatively, are only loosely coupled by reactive collisions. Therefore, the spin symmetry states can be long-lived and provide information on the formation process of the parent molecules, provided the mechanisms determining the spin symmetry states are well understood. It is believed that exothermic gas-phase processes can lead to populating the spin symmetry states according to the high temperature limit, whereas formation processes involving cold dust surfaces will lead to level populations thermalized at the temperature of the dust surfaces. This line of reasoning has been used in studies of molecules with two hydrogen atoms that have an ortho and a Special Issue: Oka Festschrift: Celebrating 45 Years of Astrochemistry Received: January 15, 2013 Revised: July 19, 2013 Published: July 19, 2013 10018

dx.doi.org/10.1021/jp4004533 | J. Phys. Chem. A 2013, 117, 10018−10026

The Journal of Physical Chemistry A

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Table 1. List of Observed Lines transition

frequency (MHz)

gu

Eu (K)

11,1−00,0, J = 3/2 − 1/2, F = 3/2 − 1/2 11,1−00,0, J = 3/2 − 1/2, F = 1/2 − 1/2 11,1−00,0, J = 3/2 − 1/2, F = 5/2 − 3/2 11,1−00,0, J = 3/2 − 1/2, F = 3/2 − 3/2 11,1−00,0, J = 3/2 − 1/2, F = 1/2 − 3/2 11,0−10,1, J = 3/2 − 3/2, F = 3/2 − 2/2 11,0−10,1, F = 1/2 − 1/2 11,0−10,1, F = 1/2 − 3/2 11,0−10,1, F = 5/2 − 5/2 11,0−10,1, F = 3/2 − 1/2 11,0−10,1, F = 5/2 − 3/2 11,0−10,1, F = 3/2 − 5/2 11,0−10,1, F = 3/2 − 3/2 11,1−00,0, F = 3/2 − 3/2 11,1−00,0, F = 5/2 − 3/2 11,1−00,0, F = 1/2 − 3/2

1115150.75 1115186.18 1115204.15 1115262.90 1115298.33 607227.339 189200.369 189224.383 189225.063 189231.910 189238.598 189242.471 189255.994 485413.427 485417.670 485420.796

4 2 6 4 2 4 6 6 18 12 18 12 12 4 6 2

53.5 53.5 53.5 53.5 53.5 29.1 9.1 9.1 9.1 9.1 9.1 9.1 9.1 23.3 23.3 23.3

species +

o-H2O

p-H2O+ o-H2Cl+

p-H2Cl+

para state like formaldehyde (H2CO) since the 1980s7,8 and more recently applied to water vapor (H2O).9,10 The OPR ratios of H2O are discussed by Lis et al.11 and by Schilke et al.12 for H2O+. The detection of two new molecular ions with Herschel, H2O+ and H2Cl+, gives the opportunity to further probe the chemical networks by comparing both their absolute column densities and the ratio between the column densities in the ortho and para symmetry states.

OBSERVATIONS The target lines and associated spectroscopic parameters are listed in Table 1, which makes use of the line lists provided by the CDMS database.13 These line lists are based on previous spectroscopy work by Mürtz et al.14 and by Strahan et al.15 for H2O+ and by Araki16 for H2Cl+. Note that although the H2Cl+ transitions have been accurately measured in the laboratory, the H2O+ line lists are based on laser magnetic resonance studies with an accuracy on the order of 1 MHz. The dipole moments have been computed by Weis17 for H2O+ and by Müller18 for H2Cl+. In the following we write H2Cl+ for H235Cl+. The observations are summarized in Table 2. As the target lines were expected to show up as absorption features against Table 2. Summary of Observations

Herschel/ HIFI

IRAM30m CSO

sourcea,b

date/ObsID

frequency (GHz)

Tcc (K)

rmsd (%)

W31C

1342218940/41/42

485

0.38

4.0

W49N W31C W49N

485 607 607 607 1115 1115 189

0.65 0.73 1.10

3.6 1.2 1.3

W31C W49N W31C

1342229865/66 1342191575/76/77 1342194520/22/22 1342230378/79/80 1342191694/95/96 1342195064/65/66 26-Feb-2012

3.1 4.6 0.5

2.4 2.6 6.4

W49N W49N

25-Feb-2012 19-May-2012

189 189

1.0 0.4

6.3 1.8

1.72 2.75 3.10 1.38 3.44 6.19 2.35 1.16 9.86 5.87 4.23 6.34 1.88 1.58 1.58 1.58

× × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−3 10−3 10−5 10−4 10−5 10−5 10−5 10−5 10−5 10−3 10−3 10−3

the strong continuum emission of the background sources, all observations have been performed in the double beam switching mode, where the signal from the source is compared with that at two nearby positions, located symmetrically on each side of the source. This mode ensures an accurate removal of all possible instrumental drifts and a good measurement of the continuum flux of the background source. The coordinates of the background sources, W31C and W49N, are also given in Table 2. These massive star-forming regions are located in the Galactic plane, along sight-lines known for the presence of diffuse interstellar gas. They have been extensively observed by Herschel, with previously reported detections of OH+, H2O+, HCl+, and H2Cl+ among other species.19−21 For the Herschel/HIFI observations, we provide the ObsId identification number that allows accessing information pertaining to these data in the Herschel archive developed by ESA (http://herschel.esac.esa.int/Science_Archive.shtml). The observations were performed with a heterodyne instrument that allows sensitive spectroscopic measurements at an excellent spectral resolution. For the HIFI instrument,22,23 we used the wide band spectrometer, with a spectral resolution of 1.1 MHz, corresponding to a velocity resolution of ∼0.6−0.3 km s−1 depending on the line frequency. The IRAM and CSO observations were obtained with high spectral resolution fast Fourier transform spectrometers (FFTS), with a spectral resolution of ∼200 kHz, corresponding to a velocity resolution of ∼0.31 km s−1 at 189 GHz. To improve the S/N ratio, the data are presented with a velocity resolution of ∼0.6 km s−1. The spectra are displayed using velocities expressed in the Local Standard of Rest (LSR) reference frame, suitable for sources in the Milky Way galaxy.b The Herschel data have been first processed with the Herschel Interactive Processing Environment (HIPE) software (http:// herschel.esac.esa.int/HIPE_download.shtml), and subsequently exported to FITS files. The final data processing has been performed with the CLASS software provided by IRAM (http://www.iram.fr/IRAMFR/GILDAS). The IRAM-30m and CSO data have also been processed with CLASS. For all lines, the data processing involves the removal of instrumental fringes, if any, the combination of the different integrations, and the determination of the continuum intensities for each detector. The data have subsequently been divided by the

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instrument

A (s−1)

W31C, RA=18h10m28.7s, Dec = −19°55′50.0″ (J2000). bW49N, RA=19h10m13.2s, Dec = 09°06′12.0″ (J2000). cTc is the intensity of the continuum emission in Kelvin. drms is the root-mean-square deviation of the intensity in a spectral resolution element, expressed in percentages of the continuum intensity. a

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Figure 1. CSO spectrum toward W49N. The lower axis shows the LSR velocity relative to the frequency of the strongest o-H2Cl+ hyperfine component (11,0−10,1, F = 5/2 − 5/2 at 189225.0625 MHz). The upper axis shows the rest frequency. The positions of the o-H2Cl+ and o-H237Cl+ lines are indicated. The vertical axis is the antenna temperature in Kelvin.

Figure 2. Herschel/HIFI normalized spectra of the ground state lines of o-H2O+ (lower) and p- H2O+ (upper) detected in absorption. For o-H2O+, the horizontal axis shows the LSR velocity relative to the rest frequency of the 11,1−00,0, J = 3/2 − 1/2, F = 5/2 − 3/2 hyperfine component. For pH2O+, the axis shows the LSR velocity relative to the transition frequency. The left plot presents the data toward W31C and the right plot those toward W49N. The p-H2O+ spectra are partially blended with the H13CO+ (J = 7−6 at 607174.646 MHz) and CH3OH (12+2,10−11+1,10 at 607215.814 MHz) transitions. They have been shifted vertically for clarity. The hyperfine structure of the o-H2O+ ground state line is indicated.

Figure 3. Normalized spectra of the ground state lines of p-H2Cl+ (lower) and o-H2Cl+ (upper) detected in absorption. The left plot presents the data toward W31C and the right plot toward W49N. The p-H2Cl+ data have been obtained with Herschel/HIFI and the o-H2Cl+ data with IRAM30m. The hyperfine structure is indicated for both transitions. The o-H2Cl+ spectra have been vertically shifted for clarity.

IRAM-30m and CSO data have been obtained from the ground in a spectral region where the transmission is strongly affected by water vapor in the Earth’s atmosphere. Despite the excellent atmospheric conditions, the calibration accuracy is estimated to be about 30%. However, the relative calibration between the line and continuum is not affected by the uncertainty in the sky

continuum intensities to obtain normalized spectra. This last step was performed differently according to the instrument. Indeed, the Herschel data have been obtained outside the Earth atmosphere and therefore benefit from a calibration accuracy better than 10%. The accuracy of the determination of the continuum and line intensities is excellent. Conversely, the 10020



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Figure 4. Illustration of the result of the deconvolution of the hyperfine structure for the o-H2O+ spectra toward W31C (left) and W49N (right). The black histograms show the original o-H2O+ spectra, and the gray line is the sum of the five hyperfine components obtained after the deconvolution. Each hyperfine component is displayed separately in a different color. The velocity scale is the LSR velocity relative to the frequency of the strongest hyperfine component, shown in blue. The spectra have been shifted vertically for clarity. The ground state transition of HF at 1.232 THz28,29 is shown with a dotted line to illustrate the velocity structure along these lines of sight. For W31C, the emission and absorption at velocities between −10 and +10 km s−1 are associated with the background source, whereas the W49N background source is detected between 0 and 20 km s−1.

of the population of these molecules will be in their ground states, enabling an easy and accurate derivation of the column densities from the deconvolved line opacities. As the telescope collects all the emission along the line of sight, the main information extracted from the spectra is the total number of molecules per unit area integrated along the line of sight also called the column density: Nmol = ∫ nmol(s) ds. Using the spectroscopic parameters listed in Table 1, we have derived the following relationships between the column densities and velocity integrated opacities of the main hyperfine component. The opacity at line center τ0 of a line of frequency νul is related to the molecular column density Nmol, the transition Einstein coefficient Aul and the level degeneracies gu and gl as

transmission and only depends on the ratio of the receiver gains in the signal and image sidebands. The IRAM-30m observations have been obtained with the EMIR/E1 receiver tuned at the upper edge of its tuning range. To check the gain ratios, we chose a frequency setup such that the H2Cl+ and H237Cl+ 11,0−10,1 lines were accessible in the upper sideband, whereas the HCN and HCO+ (J = 2 → 1) lines were accessible in the lower sideband. By comparing the strengths of those lines with previous, well calibrated, observations with the same telescope,24 we derived the gain of the image sideband to be ∼0.1 and ∼0.15 for W31C and W49N, respectively. To illustrate the richness of the line emission spectra, the CSO spectrum toward W49N is shown in Figure 1. The normalized spectra are shown in Figures 2 and 3 for H2O+ and H2Cl+, respectively.

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τ0 =

RESULTS Deconvolution of the Hyperfine Structure. Except for the ground state line of p-H2O+, all probed transitions are composed of several hyperfine components. With the complex velocity profile of the absorption feature, due to the presence of multiple clouds along the line of sight, spread over tens of km s−1, these hyperfine components are blended with one another. We used tools developed for the analysis of Herschel data to deconvolve the hyperfine structure from the normalized spectra and recover the intrinsic absorption profile, described in previous analysis of Herschel absorption data.19,21,25−27 Figure 4 presents the results obtained for the o- H2O+ line toward W31C and W49N. Column Densities and OPR. The physical conditions of the diffuse gas along the line of sight to W31C and W49N are similar, with densities lower than 104 cm−3 and moderate kinetic temperatures: 20−100 K.10,24 Therefore, it is expected that the excitation temperature of the hydride lines will be close to 2.73 K, the temperature of the Cosmic Microwave Background. At terahertz frequencies, the far-infrared background provided by the continuum radiation of dust grains must be taken into account, which can increase the excitation temperature to ∼5 K as discussed by Black.30 In all cases, most

⎞ ⎛ g Nmolϕ(v)⎜⎜xl u − x u⎟⎟ 8πν ⎠ ⎝ gl

A ul c 3 3

(1)

where xu and xl stand for the fractional populations of the upper and lower levels and ϕ(v) is the line profile normalized to unity, ∫ ϕ(v) dv = 1. Assuming local thermal equilibrium at a temperature T, the fractional populations can be expressed as xu/xl = (gu/ gl)e−hνul/kBT, and we get τ0 =

A ul c 3 8πν

3

Nmolϕ(v)xl

gu gl

(1 − e−hνul / kBT ) (2)

We can simplify further by relating the fractional population in the lower level xl to the partition function Q(T) as xl = (gl/ Q(T))e−El/kBT. This leads to the final expression for the total molecular column density as a function of the integrated line opacity: Nmol =

8πν 3 Q (T )e E l / kBT A ul c 3g u 1 − e−hνul / kBT

∫ τ dv

(3)

This general expression can be simplified for ground state transitions in which El = 0 and at low temperature where kBT 10021



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Figure 5. OPR for H2O+. The OPR have been computed in velocity intervals of 5 km s−1. For each source, the symbols indicate two different velocity intervals, free of contamination by emission lines, and tracing gas at different Galacto-centric distances.

Figure 6. OPR for H2Cl+. The OPR have been computed in velocity intervals of 5 km s−1.

≪ hνul, as expected for the physical conditions under study in this paper. Note that in that case T does not represent the kinetic temperature but the excitation temperature. Nmol =

8πν 3 Q (T ) A ul g uc 3

∫ τ dv

This formula is not sensitive to the assumed excitation temperature, as long as kBT remains significantly lower than the energy difference between the ground state and the first excited level. For H2Cl+, we get in a similar way

(4)

N (o‐H 2Cl+) = 1.38 × 1013

Assuming T = 5 K, an appropriate value for ground state transition in the diffuse medium as explained above, and substituting the appropriate spectroscopic information, we derive for o-H2O+ N (o‐H 2O+) = 4.18 × 1012

∫ τo dv cm−2

∫ τp dv cm−2

(5)

N (p‐H 2Cl+) = 0.47 × 1013

∫ τo dv N (o ‐ H 2 O ) + = 0.798 N (p ‐ H 2 O ) ∫ τp dv

∫ τp dv cm−1

(9)

where we use the opacity of the 11,1−00,0, F = 5/2 − 3/2 hyperfine component at 485.417 GHz. This leads to the expression for the OPR of H2Cl+:

(6)

using the 11,0−10,1, J = 3/2 − 3/2, F = 3/2 − 2/2 line at 607.227 GHz. Therefore, we can compute the OPR for H2O+ as

OPR(H 2Cl+) =

∫ τo dv N (o‐H 2Cl+) + = 2.94 N (p‐H 2Cl ) ∫ τp dv

(10)

+

+

OPR(H 2O+) =

(8)

where we use the opacity of the 11,0−10,1, F = 5/2 − 5/2 hyperfine component at 189.225 GHz and assume the excitation temperature to be equal to the Cosmic Background Temperature, 2.73 K, an appropriate hypothesis for these lower frequency transitions.24 The analogous formula for p-H2Cl+ is

where we use the opacity of the 11,1−00,0, J = 3/2 − 1/2, F = 5/ 2 − 3/2 hyperfine component at 1115.204 GHz. The column density for p-H2O+ is N (p‐H 2O+) = 5.24 × 1012

∫ τo dv cm−2

H2Cl has a similar level structure to H2O, with the para form being the most stable, but with a smaller energy difference between the ortho and para species (14.06 cm−1 or 19.7 K). At

(7) 10022



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to approach the thermalization of the OPR as well, in the absence of efficient destruction of H3+. The difference in spin temperatures between H2 and H3+ can be understood as resulting from the competition between dissociative recombination with electrons and thermalization via reactive reactions with H2. The situation is expected to be similar for both H2O+ and H2Cl+, the difference being that H2O+ can also react with H2 to form H3O+. The large abundance of OH+ relative to H2O+ on the two studied sight-lines W31C and W49N indicates, as explained by Neufeld et al.,19 that both ions reside in gas with a low fraction of hydrogen in molecular form, less than ∼10%. In this nearly atomic gas, the kinetic temperature can be deduced from the neutral hydrogen emission and is Tkin ∼ 100 K. H2Cl+ is expected to be present in gas with a larger fraction of molecular hydrogen, in conditions more similar to those favorable for H3+ production.21,36 H2Cl+ is formed in the exothermic reaction between HCl+ and H2, and destroyed by dissociative recombination with electrons. Although the reaction network leading to H2Cl+ is very simple, the observed H2Cl+ abundances are surprisingly high compared to the model predictions, suggesting that the chlorine chemistry is not fully understood. Following Grussie et al.,35 we can derive the average number of reactive collisions with H or H2, Nrc, before the dissociative recombination of a molecular ion as

high temperatures, the OPR is equal to 3, the ratio of the degeneracies due to spin statistics, whereas the equilibrium value at 10 K is 1.35. The situation is reversed for H2O+, with the ortho species being the most stable. The difference in energy between the ground states of the ortho and para species is 20.86 cm−1 or 30 K. At high temperatures, the OPR is also equal to 3. The OPR is expected to increase at low temperatures, with an equilibrium value of ∼20 at 10 K and ∼4 at 20 K. Figures 5 and 6 present the measured OPR in H2O+ and H2Cl+, respectively. We have smoothed the data to a lower spectral resolution of 5 km s−1 to improve the S/N ratio, and restricted the measurements to spectral regions free of line contamination. This explains the reduced number of usable points for H2O+ as compared with H2Cl+, because the p-H2O+ spectra are contaminated by two emission lines. The average value are OPR(H2O+) = 2.7 ± 0.4 for W31C and OPR(H2O+) = 3.4 ± 0.6 for W49N. For H2Cl+, we get OPR(H2Cl+) = 4.1 ± 0.4 and 4.3 ± 1.6 for W31C and W49N, respectively.

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DISCUSSION AND CONCLUSIONS For H2O+, the average value of the OPR for both sight-lines are consistent with the high temperature limit of OPR(H2O+) = 3. Local deviations may be present in some velocity intervals but are of limited statistical significance at the present S/N level. Through a thorough analysis of the water vapor line profiles, Flagey et al.10 deduced the OPR ratios along six sight-lines through the Galactic Plane including W31C and W39N. Except for two velocity features along the W49N sight-line, they also obtained an OPR of 3 for the water vapor in the diffuse interstellar gas. The same conclusion applies to H2Cl+. The OPR values are consistent with the high temperature value of 3, despite the significant scatter due to the limited signal-to-noise ratio. Both the faintness of the H2Cl+ spectral lines and the larger number of hyperfine components lead to higher uncertainties on the molecular column density in specific velocity intervals. As the ground-based data provide the main source of uncertainty on the OPR, it should be possible to improve these measurements with deeper integrations, and by adding more sight-lines. In particular, a comparison between the properties of the diffuse interstellar medium in the Galactic Plane and those in the Galactic Center, as probed by the sight-lines toward the massive molecular clouds in the central molecular zone (CMZ) (SgrB2, G-0.02-0.07, G-0.13-0.08) should be interesting as non-LTE values of the OPR of water have been reported there.9 As discussed by Sonnentrucker et al.,31 the abundance of water vapor is larger in the CMZ than in the diffuse interstellar gas elsewhere in the Galaxy. In their analysis of H3+ infrared absorption lines toward sightlines sampling the diffuse ISM, Crabtree et al.32 found evidence of nonequilibrium ortho to para ratio for H3+ in all the sampled sight-lines. More precisely, the kinetic temperature of the diffuse molecular gas sampled along these sight-lines is Tkin ∼ 70 K whereas the diffuse atomic gas is slightly warmer with Tkin ∼ 100 K. The excitation temperature deduced from the ratio of the H3+ OPR is ∼30 K, significantly lower than the gas kinetic temperature. Subsequent theoretical and laboratory work on the H3+ ortho to para ratio in contact with H2 have been performed at various temperatures from 350 to 45 K.33−35 The conclusion of these studies is that H2 thermalization occurs through collisions with protons and with H3+. For H3+, the reactive collisions with H2 are expected to be efficient enough

Nrc =

k rcn kDR n(e−)

(11)

where krc is the rate for reactive collisions, n is the density of the collision partner, and kDR is the rate for dissociative recombination. In the atomic gas, the electrons are mostly produced by the ionization of carbon, leading to n/n(e−) = 7 × 103 using the average gas-phase abundance of carbon of C/H = 1.4 × 10−4.37 This ratio is a factor of 2 lower in diffuse molecular gas, when H2 becomes the dominant form of hydrogen, and increases again when ionized carbon get neutralized and the electron abundance decreases. Using typical values for kDR ∼ 10−7 cm3 s−1 and krc ∼ 10−9 cm3 s−1, we get Nrc = 70

k rc 10−7 n/n(e−) 10−9 kDR 7 × 103

(12) +

The rate of dissociative recombination for H2O is kDR = 4.3 × 10−7(T/300 K)−0.5 cm3 s−1 38 and reaches 7.5 × 10−7 cm3 s−1 at 100 K, the temperature of the diffuse gas where it is detected. The rate of reactive collisions with either H or H2 leading to spin flip is not known, but the rate of the abstraction reaction with H2 leading to H3O+ has been measured and is kH3O+ = 6.4 × 10−10 cm3 s−1.39 Using the same rate as an order of magnitude for the rate of the spin conversion in the reaction with atomic hydrogen, we can compute the average number of H2O+ reactive collisions with H before dissociation: Nrc(H2O+) ∼ 6. This estimate shows that the thermalization may not be complete for H2O+. This analysis does not include the role of reactions with molecular hydrogen, which could be efficient as well and help to equilibrate the spin temperature with the kinetic temperature, the analysis also neglects other destruction pathways of H2O+, the route to H3O+ and photodissociation, which both shorten the lifetime of H2O+ in the diffuse medium. The order of magnitude obtained with the simple formula should therefore be correct. From this simple analysis, we 10023



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conclude that the destruction of H2O+ is likely to be too fast for a complete spin thermalization at the kinetic temperature of the gas to occur. For H2Cl+ molecular hydrogen is expected to play the main role as this ion reaches its highest abundance in gas with a fraction of hydrogen in molecular form larger than 50%.36 H2Cl+ does not react with H2; hence the rate for spin flip may be larger than that for H2O+ and approach the Langevin rate. However, because H2Cl+ exists in molecular gas with a lower temperature than H2O+ (∼50 K) as discussed by, e.g., Indriolo et al.,40 the rate of dissociative recombination is increased to 1.2 × 10−7(T/300)−0.85 = 5.5 × 10−7 cm3 s−1 similar to that of H2O+. The rate of dissociative recombination of H2Cl+ as used in the chemical modeling by Neufeld and Wolfire36 is somewhat uncertain as it has not been measured yet. In addition, the n/n(e−) factor is reduced by a factor two for molecular gas. The average number of reactive collisions is therefore comparable to that of H2O+, Nrc(H2Cl+) ∼ 10, and the conclusion is similar. On average, the fraction of gas in molecular form is slightly lower toward W49N than toward W31C. With more statistics, it may be interesting to search for a relationship between the OPR ratio and the fraction of gas in molecular form as the fraction of molecular gas is expected to have a direct impact on the rate of spin thermalization. As discussed by Schilke et al.,41 it is difficult to theoretically compute the H2O+ ortho to para ratio accurately, because the dependency of the formation and destruction rates on the H2 OPR ratio is not known. Herbst and Roueff42 have shown that the H2O+ OPR can be expressed as a function of the H2 OPR, in the limit that the equilibration of the spin symmetry states is slow as OPR(H 2O+) =

investigated as this reaction contributes to the H 2 O + destruction. Another effect worthy of theoretical investigations is the possible dependence of the rate of dissociative recombination on the spin symmetry state. Such an effect has been theoretically predicted for H3+ 44 and measured in a flowing afterglow experiment.45 As dissociative recombination is among the main destruction channels for both ions, a difference in the rate of dissociative recombination is likely to have an impact on the ortho to para ratio.

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Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work could not have been prepared without the pioneering and inspiring work by Oka, both for his fundamental spectroscopy work and for his more recent involvement in astronomy, with the beautiful detection of the H3+ ion. We thank the anonymous referee for his/her comments that help to significantly improve this paper. This material is based upon work at the Caltech Submillimeter Observatory, which is operated by the California Institute of Technology under cooperative agreement with the National Science Foundation (AST-0838261). HIFI has been designed and built by a consortium of institutes and university departments from across Europe, Canada, and the United States (NASA) under the leadership of SRON, Netherlands Institute for Space Research, Groningen, The Netherlands, and with major contributions from Germany, France, and the U.S. Consortium members: (Canada) CSA, U. Waterloo; (France) CESR, LAB, LERMA, IRAM; (Germany) KOSMA, MPIfR, MPS; (Ireland) NUI Maynooth; (Italy) ASI, IFSI-INAF, Osservatorio Astrofisico di Arcetri-INAF; (Netherlands) SRON, TUD; (Poland) CAMK, CBK; (Spain) Observatorio Astronomico Nacional (IGN), Centro de Astrobiologia; (Sweden) Chalmers University of Technology - MC2, RSS & GARD, Onsala Space Observatory, Swedish National Space Board, Stockholm University - Stockholm Observatory; (Switzerland) ETH Zurich, FHNW; (USA) CalTech, JPL, NHSC. M.G., E.R., and B.G. acknowledge the support from the Centre National de Recherche Spatiale (CNES) and the SCHISM project (ANR-09-BLAN-0231).

fpo + foo OPR(H 2) fpp + fop OPR(H 2)

AUTHOR INFORMATION

(13)

where f po and f pp represent the respective fractions of o-H2O+ and p-H2O+ formed in the reaction of OH+ with p-H2, and foo and fop represent the respective fractions of o-H2O+ and p-H2O+ formed in the reaction of OH+ with o-H2. A similar formula can be deduced for H2Cl+. Herbst and Roueff42 note that the f factors can be computed using the angular momentum approach of Oka,43 but that the result is ambiguous as it depends on the hydrogen abstraction reaction mechanism, namely whether it involves a long-lived complex where all protons are equivalent, or whether it can be better described as a proton hop. At the typical temperature of diffuse clouds, equal amounts of H2 exist in ortho and para forms leading to OPR(H2) ∼ 1. With this value Herbst and Roueff42 predict OPR(H2O+) ∼ 2 for the reaction mechanism involving a longlived complex, and OPR(H2O+) = 3 for the hydrogen hoping mechanism. Hence a difference in the rates of reactions leading to H2O+ and H2Cl+ according to the H2 spin symmetry state may have an effect on the production of the two spin symmetry states of H2O+ and H2Cl+. The astronomical data tend to favor a formation mechanism in which OPR(H2O+) ∼ OPR(H2Cl+) ∼ 3, although the S/N ratio should be improved, especially for H2Cl+. A thorough investigation of the production reactions of these important molecular ions, including the dependency on the H2 spin symmetry state is clearly needed. The dependency of the rate of the hydrogen abstraction reaction leading to H3O+ on the H2O+ and H2 spin symmetry states should also be

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ADDITIONAL NOTES Herschel is an ESA space observatory with science instruments provides by European-led Principal Investigator consortia and with important participation from NASA. b The Local Standard of Rest (LSR) reference frame is defined by the International Astronomy Union (IAU) as the reference frame moving at the mean motion at the distance of the sun from the center of the Galaxy a

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Determination of the Ortho to Para Ratio of H2Cl+ ... - ACS Publications

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