B. J. McCall, ^* T. R. Geballe, K. H. Hinkle, T. Oka

The molecular ion H₃⁺ is considered the cornerstone of interstellar chemistry because it initiates the reactions responsible for the production of many larger molecules. Recently discovered in dense molecular clouds, H₃⁺ has now been observed in the diffuse interstellar medium toward Cygnus OB2 No. 12. Analysis of H₃⁺ chemistry suggests that the high H₃⁺ column density (3.8 × 10¹⁴ per square centimeter) is due not to a high H₃⁺ concentration but to a long absorption path. This and other work demonstrate the ubiquity of H₃⁺ and its potential as a probe of the physical and chemical conditions in the interstellar medium.

B. J. McCall and T. Oka, Department of Astronomy and Astrophysics, Department of Chemistry, and the Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, USA.
T. R. Geballe, Joint Astronomy Centre, University Park, Hilo, HI 96720, USA.
K. H. Hinkle, National Optical Astronomy Observatories, Tucson, AZ 85726, USA.
^*   To whom correspondence should be addressed.

The recent discovery of interstellar H₃⁺ in dense molecular clouds toward the young stellar objects GL2136 and W33A (2), which are deeply embedded within the clouds, has provided direct observational evidence supporting the ion-neutral reaction scheme for the chemical evolution of molecular clouds. Subsequent observations have revealed the presence of abundant H₃⁺ in many other dense clouds (3). Because of the simplicity of the H₃⁺ chemistry, these observations provide direct estimates of the most fundamental properties of the clouds: number density, column length, and temperature.

In the course of carrying out this survey, we observed strong and broad H₃⁺ absorption lines in the direction of the galactic center source GC IRS 3 (4). This finding suggested that H₃⁺ is abundant not only in gravitationally bound dense clouds with high density (n ~10³ to 10⁵ cm³) but also in unbound diffuse clouds with low density (~10 to 10³ cm³). To test this possibility, Cygnus OB2 No. 12 was observed, as this source is believed to be obscured largely by diffuse low-density clouds containing little molecular material (5). We report here the detection of a large amount of H₃⁺ in the diffuse clouds in the direction of Cygnus OB2 No. 12.

Cygnus OB2 No. 12 (or VI Cygni 12) is the 12th member of the Cygnus OB2 association of young stars and was discovered in 1954 (6). This association is estimated to be 1.7 kpc (7) from Earth or about one-fifth of the distance to the center of the galaxy. The star Cygnus OB2 No. 12 suffers the largest extinction of any of the members of the association, A_v ~ 10, indicating that it has the largest column of absorbing material along its line of sight (8). On the basis of its extinction, distance, spectral type (B5), and luminosity class (Ie), the star Cygnus OB2 No. 12 is one of the most luminous stars in the galaxy (absolute visual magnitude ~10), more than a million times brighter than our sun (9).

Although Cygnus OB2 No. 12 suffers higher extinction than other members of its association, it is generally accepted that all the extinction occurs in a spatially patchy distribution of the interstellar dust (5). The absence of the 3.08-µm water ice absorption feature, associated with dense molecular clouds, and the presence of a 3.4-µm hydrocarbon feature (5), associated with diffuse interstellar gas, indicate that no dense molecular clouds occur along the line of sight. The identification of the gas with a circumstellar shell is rejected on the basis of a lack of excess infrared emission and the unusually strong stellar wind (~1400 km s¹) of Cygnus OB2 No. 12 (10).

We detected two closely spaced lines of H₃⁺ near 3.67 µm toward Cygnus OB2 No. 12 on 11 July 1997, using the CGS4 spectrometer at the United Kingdom Infrared Telescope (UKIRT) (11). A third line near 3.71 µm was detected on 17 September 1997 with the use of the Phoenix infrared spectrometer on the 4.0-m Mayall telescope of the Kitt Peak National Observatory (KPNO) (12). To further constrain the chemistry of the line of sight toward Cygnus OB2 No. 12, we also obtained spectra of CO (13).

The reduced H₃⁺ spectra are shown in Fig. 1. The left portion of the figure, taken with CGS4, shows absorption of the R(1,1)⁺ line of para-(p-)H₃⁺ and the R(1,0) line of ortho-(o-)H₃⁺. The right portion, obtained with Phoenix, shows absorption of the R(1,1) line of p-H₃⁺. The reduced CO absorption spectrum from CGS4 is relatively weak (Fig. 2). In dense molecular cloud sources, the fundamental CO lines are often saturated, so the relatively weak absorption toward Cygnus OB2 No. 12 suggests that the relative abundance of CO is much lower than in dense molecular clouds.

The amount of H₃⁺ toward Cygnus OB2 No. 12 can be expressed as the column density N(H₃⁺), which can be defined as the integral of the H₃⁺ number density (in molecules per cubic centimeter) along the line of sight N  [H₃⁺]d. The equivalent width (or area) of an absorption line, W  (1  ^I)d, taken from the spectrum can be related to the column density of the level N_level (for an optically thin line) by the standard equation W = (8³/3hc) N_level|µ|². In these formulas, |µ|² is the square of the transition dipole moment (a measure of the inherent strength of the transition) (14),  and I are the wavelength and intensity of the radiation, respectively, h is Planck's constant, and c is the speed of light.

Because the two p-H₃⁺ lines R(1,1)⁺ and R(1,1) arise from the same energy level, the column densities N derived from the two should agree. The large discrepancy (Table 1) is most likely due to the effect of a strong (~45% deep) terrestrial line of CH₄ at 3.6675 µm, which was nearly coincident with the R(1,1)⁺ line at the time of measurement. For the remainder of this discussion, we adopt a value for the H₃⁺ column density of N(H₃⁺) = N_ortho + N_para = 3.8 × 10¹⁴ cm². From the CO spectrum (Fig. 2) we estimate a value of N(CO) = 2 × 10¹⁶ cm² (15).

Table 1. Observed H3+ lines and column densities derived from each line. Statistical uncertainties (3) are given in parentheses, but systematic errors are difficult to estimate and may be larger. Also listed are the Doppler velocities with respect to the local standard of rest vLSR and the observed linewidths v (full width at half maximum). The uncertainty in the equivalent width (and column density) of the R(1,1)+ line is large as a result of the effects of a nearly overlapping telluric CH4 line. Rest wavelengths are from (27). Transition Rest wave- length (µm) |µ|2 (D2) W (µm) Nlevel (cm2)  v (km s1) vLSR (km s1) R(1,1)+ 3.668084 0.0158 3.9(9) × 106 1.6(4) × 1014 17(5) 8(5) R(1,0) 3.668516 0.0259 5.4(9) × 106 1.4(2) × 1014 22(5) 11(5) R(1,1) 3.715478 0.0140 5.2(7) × 106 2.4(3) × 1014 16(3) 8(3)

To interpret the observed column densities of H₃⁺ and CO, we developed a model of the H₃⁺ chemistry of the interstellar medium (16). Using this model, we can extract [H₃⁺], L (the effective path length of the absorption), and [H] (the total number density of H atoms).

The molecular ion H₃⁺ is formed by a two-step process: cosmic-ray ionization of H₂ to form H₂⁺ and reaction of H₂⁺ with H₂ to form H₃⁺. Because the second step is faster than the first by many orders of magnitude, the formation rate of H₃⁺ can be expressed as [H₂], where  is the cosmic-ray ionization rate. There are two primary destruction paths for H₃⁺: recombination with an electron and ion-neutral reaction with a neutral atom or molecule. The rate due to the former reaction is k_e[e][H₃⁺], where k_e is the rate constant for electron recombination and [e] is the number density of electrons. The dominant ion-neutral destruction path for H₃⁺ is assumed to be reaction with CO, with a rate of k_CO[CO][H₃⁺], where k_CO is the rate constant. If we assume a steady state, the rates of H₃⁺ formation and destruction are equal, so that

(1)

Because not all of the number densities in this equation can be obtained by observations, some assumptions must be made to reduce the number of unknowns in this equation. First, we assume that all electrons in diffuse clouds come from ionization of atomic C to form C⁺ (17), so that [e] = [C⁺]. Second, we assume that all C is in the form of either C⁺ or CO, so that [C] = [C⁺]+[CO], where [C] denotes the total concentration of gaseous C atoms in any form (18). Third, we assume that nearly all H is in the form of H or H₂, so that [H] = [H] + 2 [H₂].

To understand the meaning of Eq. 1, we introduce a parameter that represents the fraction of H in molecular form, f  2[H₂]/[H], or [H₂] = (f/2)[H]. We also introduce a parameter that represents the fraction of C in molecular form   [CO]/[C], so that [CO] = [C] and [C⁺] = (1)[C]. Substituting these relations into Eq. 1 and solving for [H₃⁺] yields

(2)

Note that the number density of H₃⁺ does not depend on the absolute number density of the gas.

With the observed value of N(H₃⁺), one can determine the effective path length L of the absorption using the approximate relation N(H₃⁺) = [H₃⁺]L, which implies

(3)

To obtain an expression for the number density [H], the definition of  can be rewritten as  = ([CO]/[H])([H]/[C]). Substituting the approximate relation [CO]/[H]  N(CO)/N(H) into this and solving for N(H) gives

(4)

Equations 3 and 4 can be combined to derive an expression for the number density of the cloud

(5)

To determine [H₃⁺], L, and [H], we used  ~ 3 × 10¹⁷ s¹ (19), f ~ 0.5 (20), [H]/[C] ~ 10⁴ (21), k_e ~ 1.8 × 10⁷ cm³ s¹ (22), and k_CO ~ 2.0 × 10⁹ cm³ s¹ (23). For N(H₃⁺) and N(CO) we used our adopted observational values. The parameter  is difficult to estimate, and we leave it as a free parameter.

The resulting values of [H₃⁺] and L for Cygnus OB2 No. 12 as a function of  (Fig. 3) show that, as  increases (more C is in molecular form) from 0 to 1, [H₃⁺] increases from 4 × 10⁷ to 4 × 10⁵ cm³ and L decreases from ~300 to ~3 pc. The limit  = 0 corresponds to the case where H₃⁺ destruction is dominated by electron recombination (very diffuse clouds), and the limit  = 1 corresponds to the case where H₃⁺ destruction is dominated by reaction with CO (very dense clouds).

The key parameter in these estimates () has not been determined, but, on the basis of observations and theoretical models of diffuse clouds (17), we infer that it is less than 0.1. From Fig. 3 we estimate [H₃⁺] ~4 × 10⁷ cm³ and L ~300 pc. Unlike [H₃⁺] and L, [H] changes a lot for  < 0.1 (Fig. 4). From the visual extinction we can estimate N(H), assuming the standard gas-to-dust ratio (24). If all of the extinction arises from the region where H₃⁺ is observed (25), we estimate N(H) ~ 2 × 10²² cm². The calculated L ~ 300 pc then implies [H] ~ 20 cm³.

Because H₃⁺ undergoes constant chemical reactions with H₂ at a Langevin rate (26) and because there are no radiative transitions between o-H₃⁺ and p-H₃⁺, H₃⁺ is in thermal equilibrium with H₂ in the cloud. By measuring the column densities of o- and p-H₃⁺, one can estimate the kinetic temperature of the cloud. In thermal equilibrium, the ratio of the two states is given by the Boltzmann expression

(6)

where the g values are the statistical weights of the o- and p-H₃⁺ states, E is the energy difference between them, k is the Boltzmann constant, and T is temperature. Using the data in Table 1, we obtain an estimate of the cloud temperature of 27 K. This temperature is higher than the excitation temperature derived from the CO spectrum (Fig. 2), which is 10 K. This difference in temperatures may be reasonable because spontaneous emission will lower the excitation temperature of CO in diffuse clouds, where the collisional pumping to higher rotational states is slow as a result of the low number density.

These observations indicate that N(H₃⁺) in the diffuse clouds toward Cygnus OB2 No. 12 (3.8 × 10¹⁴ cm²) is comparable to that of the dense clouds toward the young stellar objects GL2136 (4.0 × 10¹⁴ cm²) and W33A (6.0 × 10¹⁴ cm²) (2). This is not because of a higher number density [H₃⁺] but because of a large effective path length L toward Cygnus OB2 No. 12, which may cross many diffuse clouds. Although large column densities of H₃⁺ have been predicted in diffuse clouds (17), these calculations were based on a value of the H₃⁺ electron recombination rate that has since been shown to be more than three orders of magnitude too low (22). This detection and analysis extend the diagnostic powers of H₃⁺ to a new class of objects that are chemically quite different from dense molecular clouds and may allow us to gain further insight into the physical and chemical conditions of diffuse interstellar clouds.

REFERENCES AND NOTES

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2. T. R. Geballe and T. Oka, Nature 384, 334 (1996)
3. B. J. McCall, T. R. Geballe, K. H. Hinkle, T. Oka, in preparation.
4. T. R. Geballe, B. J. McCall, K. H. Hinkle, T. Oka, in preparation.
5. A. J. Adamson, D. C. B. Whittet, W. W. Duley, Mon. Not. R. Astron. Soc. 243, 400 (1990); D. C. B. Whittet, et al., Astrophys. J. 490, 729 (1997).
6. W. W. Morgan, H. L. Johnson, N. G. Roman, Publ. Astron. Soc. Pac. 66, 85 (1954).
7. A. V. Torres-Dodgen, M. Tapia, M. Carroll, Mon. Not. R. Astron. Soc. 249, 1 (1991). One parsec (1 pc) is ~3.1 × 10¹⁸ cm.
8. S. Sharpless, Publ. Astron. Soc. Pac. 69, 239 (1957). The quantity A_v is the number of magnitudes by which a star would be brighter if there were no interstellar absorption. Magnitude is defined as 2.5 log (brightness), so 2.5 magnitudes corresponds to one power of ten in brightness.
9. P. Massey and A. B. Thompson, Astron. J. 101, 1408 (1991).
10. P. Persi and M. Ferrari-Toniolo, Astron. Astrophys. 111, L7 (1982); J. H. Bieging, D. C. Abbott, E. B. Churchwell, Astrophys. J. 340, 518 (1989).
11. The UKIRT is operated by the Joint Astronomy Centre on behalf of the U.K. Particle Physics and Astronomy Research Council. CGS4 is a grating spectrometer for the region from 1 to 5 µm, currently incorporating a 256 by 256 InSb array. For details on the CGS4 spectrometer, see C. M. Mountain, D. J. Robertson, T. J. Lee, R. Wade, Proc. Soc. Photo.-Opt. Instrum. Eng. 1235, 25 (1990).
12. The KPNO, a division of the National Optical Astronomy Observatories, is operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. For details on the Phoenix spectrometer, see K. H. Hinkle et al., Proc. Soc. Photo.-Opt. Instrum. Eng., in press.
13. We observed the fundamental band of ¹²CO near 4.66 µm in absorption on 1 August 1997 using CGS4 at UKIRT and also on 16 September 1997 using Phoenix on the 2.1-m telescope at KPNO. Millimeter-wave spectra of ¹²CO (J = 21) and ¹³CO (J = 21) were also obtained at the James Clerk Maxwell Telescope (JCMT) on 5 August 1997 and 13 November 1997, respectively. The JCMT is operated by the Joint Astronomy Centre on behalf of the U.K. Particle Physics and Astronomy Research Council, the Netherlands Organisation for Scientific Research, and the National Research Council of Canada. We obtained the CO measurements at the JCMT using the heterodyne receiver A2.
14. The values of |µ|² were provided to us by J. K. G. Watson.
15. This adopted value assumes that the CO lines are unsaturated and that the populations of the J > 2 levels are negligible. The measured equivalent widths are R(2) = 7.0 × 10⁵ µm, R(1) = 1.3 × 10⁴ µm, R(0) = 1.4 × 10⁴ µm, P(1) = 1.3 × 10⁴ µm, and P(2) = 7.2 × 10⁵ µm. These values are uncertain by perhaps a factor of 2 because the atmospheric CO lines were nearly overlapping the interstellar CO lines at the time of measurement, causing the atmospheric correction to be quite imprecise. The line widths are ~20 to 30 km s¹. The Doppler velocity with respect to the local standard of rest v_LSR (~15 km s¹) of the CO lines is in rough agreement with the H₃⁺ data, although the systematic uncertainty due to atmospheric interference is difficult to estimate.
16. Many models of H₃⁺ chemistry in the interstellar medium have been discussed in the literature. See, for example, S. Lepp, A. Dalgarno, A. Sternberg, Astrophys. J. 321, 383 (1987), and J. H. Black, E. F. van Dishoeck, S. P. Willner, R. C. Woods, ibid. 358, 459 (1990).
17. E. F. van Dishoeck and J. H. Black, Astrophys. J. Suppl. Ser. 62, 109 (1986).
18. In diffuse clouds, models (17) indicate that atomic C is another abundant form of carbon. However, [C] can be included in [CO] in these expressions, as it has a similar Langevin rate constant for reaction with H₃⁺, so it behaves just like CO with respect to H₃⁺ chemistry.
19. The adopted value of  varies in the literature. We have adopted an average of the value  = 1 × 10¹⁷ s¹ used in model calculations of dense clouds [ H.-H. Lee, R. P. A. Bettens, E. Herbst, Astron. Astrophys. Suppl. Ser. 119, 111 (1996)] and the value  = 5 × 10¹⁷ s¹ used for diffuse clouds (17). We expect that further H₃⁺ observations will lead to a better estimate of this important parameter.
20. A. E. Glassgold and W. D. Langer, Astrophys. J. 193, 73 (1974).
21. J. A. Cardelli, D. M. Meyer, M. Jura, B. D. Savage, ibid. 467, 334 (1996).
22. T. Amano, ibid. 329, L121 (1988).
23. V. G. Anicich and W. T. Huntress Jr., Astrophys. J. Suppl. Ser. 62, 553 (1986).
24. The standard gas-to-dust ratio can be expressed as N(H)/E(B-V) ~ 5.8 × 10²¹ [ R. C. Bohlin, B. D. Savage, J. F. Drake, Astrophys. J. 224, 132 (1978)], and R  A_v/E(B-V) = 3.09 [ G. H. Rieke and M. J. Lebofsky, Astrophys. J. 288, 618 (1985)]. The optical depth of the silicate feature at 9.7 µm [ G. H. Rieke, Astrophys. J. 193, L81 (1974)] may also constrain the column density of H.
25. This assumption is supported by the currently available spectral data on Cygnus OB2 No. 12. The C₂ observations of R. Gredel and G. Münch [Astron. Astrophys. 285, 640 (1994)] show that at least 90% of the C₂ along this line of sight has v_LSR between ~6 and 15 km s¹, whereas there is only a small component at v_LSR ~ 30 km s¹. In addition, the K I spectroscopy of F. H. Chaffee Jr. and R. E. White [Astrophys. J. Suppl. Ser. 50, 169 (1982)] shows evidence of K I absorption only near the observed velocity of H₃⁺.
26. D. Uy, M. Cordonnier, T. Oka, Phys. Rev. Lett. 78, 3844 (1997).
27. T. Oka, Philos. Trans. R. Soc. London Ser. A 303, 543 (1981).
28. We thank G. Sandell and R. P. Tilanus for obtaining the JCMT CO spectra; E. Herbst, L. M. Hobbs, T. P. Snow, P. Thaddeus, and E. F. van Dishoeck for helpful conversations and correspondences; and J. H. Black for assistance in interpreting the C₂ data and for many other helpful comments. B.J.M. is supported by the Fannie and John Hertz Foundation. The University of Chicago portion of this work was supported by NSF grant PHYS-9722691 and NASA grant NAG5-4234.

Volume 279, Number 5358 Issue of 20 March 1998, pp. 1910 - 1913
©1998 by The American Association for the Advancement of Science.