------------------------------------------------------------------------ \documentstyle[12pt,aasms4]{article} \def\hh{H$_{2}$} \def\cc{C$_{2}$} \def\km/s{km~s$^{-1}$} \def\um{${\mu}$m} \def\Vlsr{v$_{LSR}$} \def\wvnum{cm$^{-1}$} \defH$_{3}^{+}${H$_{3}^{+}$} \def\hhp{H$_{2}^{+}$} \def\kco{{\it k}$_{CO}$} \def\ke{{\it k}$_{e}$} \def\ne{n$_{e}$} \def\CO{$^{12}$CO} \def\co{$^{13}$CO} \begin{document} \title{Detection of H$_{3}^{+}$ in the Diffuse Interstellar Medium: The Galactic Center and Cygnus OB2 No. 12} \author{T. R. Geballe} \affil{Joint Astronomy Centre, Hilo, HI 96720} \authoremail{t.geballe@jach.hawaii.edu} \author{B. J. McCall} \affil{Department of Astronomy and Astrophysics, Department of Chemistry, and the Enrico Fermi Institute, University of Chicago, Chicago, IL 60637} \author{K. H. Hinkle} \affil{National Optical Astronomy Observatories\altaffilmark{1}, Tucson, AZ 85726} \author{T. Oka} \affil{Department of Astronomy and Astrophysics, Department of Chemistry, and the Enrico Fermi Institute, University of Chicago, Chicago, IL 60637} \altaffiltext{1}{Operated by the Association of Universities for Research in Astronomy, Inc.\ under cooperative agreement with the National Science Foundation} \begin{abstract} Absorption lines of H$_{3}^{+}$\ have been detected in the spectra of two infrared sources in the galactic center and also towards the heavily reddened star Cygnus OB2 No.\ 12, whose line of sight is believed to include only diffuse interstellar gas. The absorptions toward the galactic center sources (IRS3 and GCS3-2) probably are due to H$_{3}^{+}$\ both in diffuse gas and in molecular clouds. The ratios of H$_{3}^{+}$\ line equivalent width to extinction toward these three sources are much greater than those toward dense clouds where H$_{3}^{+}$\ has been detected previously. Analysis of the spectra coupled with a simple model for the abundance of H$_{3}^{+}$\ in the diffuse interstellar medium implies that the observed H$_{3}^{+}$\ is present at low densities along long pathlengths. These are the first detections of H$_{3}^{+}$\ in the diffuse interstellar medium. \end {abstract} \keywords{stars: individual (Cygnus OB2 No.\ 12) --- molecular processes --- ISM: clouds, molecules --- Galaxy: center --- Infrared: ISM: lines and bands} %SKIP \section{Introduction} The triatomic molecular ion H$_{3}^{+}$\ is widely regarded as a cornerstone of chemistry in the gaseous interstellar medium. Ion-molecule reactions involving it are the starting point of reaction chains which lead to the production of many of the molecules that have been detected in dense molecular clouds (Herbst \& Klemperer 1973; Watson 1973). H$_{3}^{+}$\ does not have a conventional pure rotational spectrum and astronomical searches for it had to await the measurement of its fundamental vibration-rotation band in the laboratory (Oka 1980) and the advent of sensitive high resolution infrared array spectrometers for astronomy. The first detections of H$_{3}^{+}$\ outside the solar system, via two absorption lines near 3.67~\um, were reported in two dense molecular cloud cores, along the lines of sight to the embedded young stellar objects, W33A and GL~2136 (Geballe \& Oka 1996). Since then, a small survey at this wavelength has resulted in the detection of H$_{3}^{+}$\ in several additional molecular clouds containing bright embedded young stellar objects (McCall, Geballe \& Oka 1999). In all of these cases the observed line strengths, which are very small, are consistent with the expected abundance of H$_{3}^{+}$\ as determined by its predicted rates of production (following ionization of \hh\ by cosmic rays) and destruction (by its reactions with other molecules, principally CO). In the course of carrying out the above survey, we observed the galactic center nuclear source IRS3 (Becklin et al.\ 1978) and detected the 3.67~\um\ H$_{3}^{+}$\ doublet in absorption. The absorption is unusually strong compared to those that have been measured in dense clouds, with a ratio of equivalent width to total extinction an order of magnitude larger than typical for dense clouds. We also detected absorption by H$_{3}^{+}$\ with similar strength in the galactic center ``quintuplet'' source GCS3-2 (Nagata et al.\ 1990), located a quarter of a degree from the nucleus, implying that the IRS3 result is not anomalous. The long lines of sight to the infrared sources in the galactic center include molecular clouds near the galactic center and in intervening spiral arms (Geballe, Baas \& Wade 1989) as well as considerable diffuse interstellar material, the last evidenced by the presence of a strong 3.4~\um\ absorption feature (Butchart et al.\ 1986; Okuda at al.\ 1990; Pendleton et al.\ 1994; Whittet et al.\ 1997). In order to better understand the origin of the large column density of H$_{3}^{+}$\ towards the galactic center, we obtained a spectrum near 3.67~\um\ of the heavily reddened star Cygnus OB2 No.\ 12, which is believed to be obscured almost entirely by diffuse, low density material (and toward which the 3.4~\um\ absorption feature also is present, Adamson, Whittet \& Duley 1990; Pendleton et al.\ 1994). The H$_{3}^{+}$\ doublet was detected in absorption there as well and its equivalent width, while not approaching that of the galactic center sources, is comparable to that seen toward sources embedded in dense molecular clouds, despite the much lower extinction. These observations clearly demonstrate that H$_{3}^{+}$\ exists in detectable quantities in the diffuse interstellar medium as well as in molecular clouds. Much of the H$_{3}^{+}$\ seen toward the galactic center and Cygnus OB2 No.\ 12 thus exists in an environment completely different from that of the dense clouds studied to date. Few, if any, polyatomic molecules have been reported in diffuse clouds. In the following sections we describe these new observations and several follow-up measurements in more detail and discuss the physical conditions and processes affecting the abundance of H$_{3}^{+}$\ in the diffuse interstellar medium. \section {Observations and Data Reduction} A log of the observations is provided in Table 1. The first detections of absorption by H$_{3}^{+}$\ in the galactic center sources IRS3 and GCS3-2 and in Cygnus OB2 No.\ 12 were of the R(1,0) and R(1,1)$^{+}$ {\it ortho-para} doublet at 3.67~\um\ (see Oka \& Jagod 1993 for an explanation of the spectroscopic notation). They were obtained on UT 1997 July 11 at the 3.8~m United Kingdom Infrared Telescope (UKIRT) on Mauna Kea with the facility spectrometer CGS4, and used its echelle, which provided a resolution of 15~\km/s. The observing techniques were standard and similar to those described in Geballe \& Oka (1996). The identification of the rather broad 3.67~\um\ absorption in the galactic center as due to H$_{3}^{+}$\ was supported by detection of a broad isolated line of H$_{3}^{+}$\ at 3.953~\um. A spectrum of the 3.715~\um\ R(1,1)$^{-}$ line of H$_{3}^{+}$\ was obtained toward Cygnus OB2 No.\ 12 on 1997 September 5 using the echelle spectrometer, Phoenix, at the 4.0~m Mayall Telescope on Kitt Peak. The resolution achieved by Phoenix was approximately 9~\km/s, somewhat higher than that by CGS4. To test for molecular material along the line of sight to Cygnus OB2 No.\ 12, CGS4 was used again on 1997 August 2 to obtain a spectrum of v=1-0 lines of the fundamental vibration rotation band of CO, near 4.65~\um\ at a resolution of 20~\km/s. Several narrow absorption lines from low-lying J levels were detected. Finally, spectra of the pure rotational J=2-1 emission lines of \CO\ and \co\ in the direction of the star were secured on 1997 August 5 and November 13 at the James Clerk Maxwell Telescope (JCMT) on Mauna Kea using the heterodyne receiver A2. A background sky position 30 arcminutes north of the star was used for the \co\ spectrum and a combination of sky positions was used for the \CO\ spectrum. Each of the spectra obtained with CGS4 was sampled every 1/3 resolution element; those obtained by Phoenix were sampled every 0.18 resolution element. Data reduction consisted of small wavelength shifts of the spectra to bring atmospheric features in the source and calibration star spectra into coincidence, ratioing of the source spectra by those of the comparison stars (adjusted for airmass using Beer's Law), and wavelength calibration (using telluric absorption lines). The comparison stars are expected to be featureless in the wavelength regions observed, except for the presence of H~I Pf~$\beta$ line at 4.654~\um. Wavelength calibration is accurate to $\pm 3$~\km/s\ for the CGS4 spectra and $\pm 2$~\km/s\ for the Phoenix spectra. Two of the three H$_{3}^{+}$\ lines observed near 3.7~\um\ are clear of strong telluric absorption lines. However, the shorter wavelength component of the 3.67~\um\ doublet is in near coincidence with a strong telluric absorption of methane centered at 3.6675~\um. Two telluric lines of HDO lie just longward in wavelength of the methane feature. For the galactic center sources, which have broad absorption profiles, the wavelengths of these telluric lines lie within the blended H$_{3}^{+}$\ profile. On the date that the doublet was measured toward Cygnus OB2 No.\ 12 the methane absorption coincided with the short wavelength edge of the R(1,1)$^{+}$ (shorter wavelength) line. Care was taken to observe each source and its calibration star close to the same airmass, and in fact the airmasses of the pairs of observations were equal to within four percent in the case of the galactic center and within two percent in the case of Cygnus OB2 No.\ 12 (for both the H$_{3}^{+}$\ and the CO spectra). Nevertheless, proper correction of the methane line is problematic. In both the galactic center and Cygnus 3.67~\um\ spectra it is likely that the ratioed spectra are distorted near the R(1,1)$^{+}$ line. Consequently the parameters derived from this line have relatively large uncertainties. At Kitt Peak measurement of the doublet was virtually impossible, due to the much stronger telluric absorption lines, and hence the single line at 3.715 \um\ was observed. \section{Results} The observed H$_{3}^{+}$\ lines originate from the lowest lying {\it ortho} and {\it para} states of the molecular ion. The R(1,1) absorptions are from the ground (J,K)~=~(1,1) {\it para} state and the R(1,0) absorptions are from the lowest {\it ortho} level, 33~K above the ground state. The lowest lying J=2 level (2,2) is 151~K above ground. Because of this and the low temperatures of dark clouds and the interiors of diffuse clouds (van Dishoeck 1990), J=1 levels are the only ones significantly populated in interstellar clouds (Oka \& Jagod, 1993). Although no radiative transitions are permitted between {\it ortho} and {\it para} states of H$_{3}^{+}$\ (Pan and Oka, 1986), collisions of H$_{3}^{+}$\ with \hh\ exchange protons and thereby maintain the relative populations of the two types of H$_{3}^{+}$\ in thermal equilibrium (Uy, Cordonnier \& Oka, 1997). \subsection{Galactic Center Sources} Figure 1 shows the spectrum of the galactic center nuclear source IRS3 and the quintuplet source GCS3-2 near the 3.67~\um\ H$_{3}^{+}$\ doublet. A broad absorption, extending over at least 0.003~\um\ (250~\km/s) is seen in each spectrum. The rest wavelengths of the components of the doublet are separated by only 0.00043~\um\ (35~\km/s). Thus, toward these objects a significant part of the line absorption extends over a wide range of velocities and the individual profiles of the lines in the doublet considerably overlap one another. A narrow doublet is observed toward IRS3 at \Vlsr~=~0~\km/s\ with the correct (4.3\AA) spacing, and also may be present toward GCS3-2, but is less obvious there. The measured equivalent widths of the observed lines toward both galactic center sources are given in Table~2. The equivalent width toward IRS3 has been separated into a broad component and a narrow component (the latter defined as absorption below 0.97, which corresponds to the \Vlsr~=~0 component). Also listed in Table~2 are the estimated column densities of H$_{3}^{+}$, obtained using the standard formula for an optically thin line, $W_{\lambda} = (8\pi^3\lambda/3hc)N|\mu|^2$, where {\it N} is the column density in the lower state of the transition and $\mu$ is the dipole moment of the transition (values have been provided by J.K.G. Watson and are listed by Geballe \& Oka 1996). In view of the detection of H$_{3}^{+}$\ toward Cygnus OB2 No.\ 12, the H$_{3}^{+}$\ absorptions toward the galactic center sources are expected to include both diffuse and dark cloud components, each of which should contribute to the overall line profile. Infrared absorption lines of the fundamental vibration-rotation band of carbon monoxide have been observed previously toward both IRS3 and GCS3-2 (Geballe, Baas \& Wade 1989; Okuda et al.\ 1990). The velocity profiles of these CO lines are complex and contain a number of discrete components, several of which are identified with specific dense clouds known from radio and millimeter spectral mapping. In the case of IRS3, the CO absorption lines, which are heavily saturated at low J levels, have strong components at \Vlsr~=~0~\km/s\ similar to H$_{3}^{+}$. Their centroids, however, are at \Vlsr~$\sim$~+30~\km/s\ and weak blueshifted absorption extending to -150~\km/s\ is present (Geballe, Baas \& Wade, 1989). For GCS3-2 strong absorption by CO is centered roughly at -70~\km/s. The observed H$_{3}^{+}$\ profiles and source-to-source differences are crudely similar to those of the CO observations. This suggests that some of the H$_{3}^{+}$\ observed toward the galactic center indeed is found in molecular clouds. \subsection{Cygnus OB2 No.\ 12} The spectral lines of H$_{3}^{+}$\ toward Cygnus OB2 No.\ 12 (reported initially by McCall et al.\ 1998) are shown in Fig.~2. Parameters derived from each line in Fig.~2 are listed in Table~3. In contrast to the galactic center, the components of the 3.67~\um\ doublet are well resolved from one another and no broad component is observed. The individual lines of the doublet were partially resolved by CGS4 and the R(1,1)$^{-}$ transition was more fully resolved by Phoenix. Each of the R(1,1) lines arises from the lowest lying {\it para} level and hence should yield the same column density. However, as pointed out above, possible non-cancellation of the telluric CH$_{4}$ line leads to large uncertainties in the column density and velocity width derived for the R(1,1)$^{+}$ line. Hence we rely on the measurement of the R(1,1)$^{-}$ line to determine the column density of {\it para}-H$_{3}^{+}$. We calculate a total H$_{3}^{+}$\ column density of 3.8~$\times$~10$^{14}$~cm$^{-2}$ towards Cygnus OB2 No.\ 12 and derive an intrinsic linewidth of $\sim$14~\km/s (FWHM). The infrared spectrum of CO towards Cygnus OB2 No.\ 12, which also was presented by McCall et al.\ (1998), is shown in Fig.~3 and the millimeter wave spectra of the J=2-1 lines of \CO\ and \co\ are shown in Fig.~4. Six narrow absorption lines of \CO\ can be seen in the infrared spectrum. The weaker ones of these are unresolved and therefore have widths much less than the resolution of 20~\km/s. The stronger lines appear to be partially resolved, although their profiles may be contaminated by incomplete removal of telluric CO lines. If they are composed of a few very narrow components, the stronger lines may be saturated. The CO absorption profiles are centered at \Vlsr~$\sim$~15~$\pm~4$~\km/s. The millimeter CO spectra, obtained at much higher spectral resolution but with an angular resolution of 21 arcseconds, much lower than the pencil beam of the infrared absorption spectra, show narrow emission lines at three velocities, -21, +7, and +12~\km/s. This suggests that the CO absorption lines are produced largely by the +7 and +12~\km/s\ clouds. Additional information on the molecular gas along the line of sight to Cygnus OB2 No.\ 12 is available from high resolution near infrared spectra of \cc\ obtained by Gredel \& M\"{u}nch (1994). Their spectra reveal four absorption components, at LSR velocities of +7, +12, +15, and +31~\km/s, with the last of these very weak compared to the first three. As in the case of the infrared CO lines, absorption at -21~\km/s\ was not detected and therefore the -21~\km/s\ cloud seen in emission in the millimeter wave spectra either does not fill the millimeter beam or lies beyond Cygnus OB2 No.\ 12. As pointed out earlier, the relative populations of {\it ortho} and {\it para} H$_{3}^{+}$\ are in LTE. The mean temperature of the H$_{3}^{+}$\ may be derived from the column densities of the lowest lying ortho and para levels, according to the formula \begin{equation} N_{ortho}/N_{para} = (g_{ortho}/g_{para})~e^{-32.87/T} \end{equation} \noindent Using the measured column densities derived from the R(1,0) and R(1,1)$^{-}$ lines (Table 3) we estimate the mean temperature of the H$_{3}^{+}$\ to be $\sim$~30~K. Gas temperatures of 35~K and 50~K were derived from the \cc\ spectra of Souza \& Lutz (1977) and Gredel \& M\"{u}nch (1994), respectively. Assuming LTE the relative strengths of the infrared CO lines (see Table 4) suggest a temperature of 5-10~K. However, the gas temperatures derived from \cc\ are more realistic than those from CO, because the long radiative relaxation time of \cc\ guarantees that \cc\ level populations are governed by collisions. Indeed the difference in these derived temperatures indicates that the rotational levels of CO are not in LTE, which is not surprising for diffuse clouds. From strengths of the the absorption lines of CO we estimate a total column density of CO of 3~$\times$~10$^{16}$~cm$^{-2}$ toward Cygnus OB2 No.\ 12. \section{Discussion} \subsection{Abundances of H$_{3}^{+}$\ in Molecular Clouds and Diffuse Clouds} In interstellar clouds most H$_{3}^{+}$\ is thought to be formed following cosmic ray ionization of \hh\ via the rapid reaction of the newly formed \hhp\ with \hh\ (Martin, McDaniel \& Meeks 1961). It is destroyed by recombination with free electrons or via reactions with any number of neutral atoms or molecules. In diffuse clouds the former destruction process should dominate; in dark molecular clouds, it is reactions with neutrals and molecules (in particular with CO) which are dominant. McCall et al.\ (1998) have given a general treatment for determining the density of H$_{3}^{+}$\ where both of the destructive processes are included. Here we separate the two cases of dark and diffuse clouds, which allows simple approximate expressions for the density of H$_{3}^{+}$\ to be derived for both. We then apply these to the observations in hand, those of Cygnus OB2 No.\ 12, where only the diffuse component is present, and those of galactic center, in which both environments exist along the line of sight. The analysis for molecular clouds has been given elsewhere (e.g., Geballe \& Oka 1990; 1996). To summarize, the concentration of H$_{3}^{+}$, derived from the approximate equation equating its rates of creation and destruction, is \begin{equation} n({\mathrm{H}}_{3}^{+}) = (\zeta/k_{\mathrm{CO}})~n({\mathrm{H}}_{2})/n({\mathrm{CO}}) \end{equation} \noindent where $\zeta$ is the cosmic ray ionization rate per \hh\ molecule and \kco\ is the reaction rate constant of H$_{3}^{+}$\ with CO. This simple equation arises because the proton hop from H$_{3}^{+}$\ to CO dominates the destruction of H$_{3}^{+}$. To evaluate the equation we use $\zeta$~=~3~$\times$~10$^{-17}$~s$^{-1}$, which is an average of recently used values (van Dishoeck \& Black 1986; Lee, Bettens \& Herbst 1996) and {\it k}$_{\rm{CO}}$~=~2~$\times$~10$^{-9}$~cm$^{3}$~s$^{-1}$ (Anicich and Huntress 1986), and the result from Lee, Bettens, \& Herbst that in dark clouds with gas phase C/H~=~7.3~$\times$~10$^{-5}$, {\it n}(CO)/{\it n}(\hh)~=~1.5~$\times$~10$^{-4}$ is constant over a wide range of conditions. (Note that Lacy et al.\ 1994 have measured {\it N}(CO)/{\it N}(\hh)~=~2.8~$\times$~10$^{-4}$ in one cloud, with a large uncertainty.) Then {\it n}(H$_{3}^{+}$)~$\sim$~1~$\times$~10$^{-4}$~cm$^{-3}$ is independent of cloud density and from the measured H$_{3}^{+}$\ column density one can estimate the distance through the dark cloud to the source. An interesting consequence of this result is that the column density of H$_{3}^{+}$\ is simply proportional to the column length of the cloud rather than the column density of all molecules in the cloud. For example, for two molecular clouds of equal masses but one with twice the linear dimensions of the other (i.e., with eight times lower density {\it n}(H$_2$)), {\it N}(H$_{3}^{+}$) in the larger cloud is twice as high even though the column density {\it N}(H$_{2}$) is four times less. In diffuse clouds H$_{3}^{+}$\ is formed in the same way as in dense clouds, but its destruction is dominated by recombination with electrons (van Dishoeck \& Black 1986). Thus, the steady state rate equation for H$_{3}^{+}$\ is \begin{equation} \zeta~n({\mathrm{H}}_{2}) = k_{e}~n(e)~n({\mathrm{H}}_{3}^{+}) \end{equation} \noindent Both atomic and molecular hydrogen are abundant in diffuse clouds and very little H is ionized; thus {\it n}(\hh) may be expressed as ({\it f}/2){\it n}($\Sigma$H) where {\it f} is the fraction of hydrogen in molecular form, {\it f}~=~2{\it n}(\hh)/[{\it n}(H)~+~2{\it n}(\hh)], and {\it n}($\Sigma$H)~=~{\it n}(H)~+~2{\it n}(\hh) is the density of H atoms in atomic and molecular form. Essentially all of the electrons in the diffuse interstellar medium are from carbon, which is nearly fully singly ionized and hence {\it n}({\it e}) may be expressed as {\it z}$_{\mathrm{C}}${\it n}($\Sigma$H), where {\it z}$_{\mathrm{C}}$ is the fractional abundance of {\it free} carbon. We thus obtain \begin{equation} n({\mathrm{H}}_{3}^{+}) = \zeta~f/(2~k_{e}~z_{C}) \end{equation} To estimate {\it n}(H$_{3}^{+}$) we use the same value for $\zeta$ as we used for dark clouds. If \hh-dissociating UV radiation is shielded from the regions where H$_{3}^{+}$\ is observed (which requires boundary column densities of $\sim$~10$^{20}$~cm$^{-2}$; Glassgold \& Langer 1974), {\it f} $\sim$~1/2 (see also van Dishoeck and Black 1986). Cardelli et al.\ 1996 and Sofia et al.\ 1997 have measured {\it z}$_{\mathrm{C}}$ to be 1.4~$\times$~10$^{-4}$ in diffuse clouds. The final parameter needed to estimate {\it n}(H$_{3}^{+}$) is the rate constant \ke\ for electron recombination of H$_{3}^{+}$. Experimental values of this constant have varied widely, but recent results seem to be converging to a value of \ke\ $\sim 10^{-7}$~cm$^3$~s$^{-1}$ at room temperature. Using Amano's (1988) value of 1.8~$\times$~10$^{-7}$ we obtain {\it n}(H$_{3}^{+}$)~$\sim$~3~$\times$~10$^{-7}$~cm$^{-3}$. Using the expression derived from storage ring experiments, \ke~=~4.6~$\times$~10$^{-6}$~T$^{-0.65}$~cm$^{3}$~s$^{-1}$ (Sundstr\"{o}m et al.\ 1994), and an assumed electron temperature of 30 K, we obtain {\it n}(H$_{3}^{+}$)~$\sim$~1~$\times$~10$^{-7}$~cm$^{-3}$. The uncertainty in \ke, along with that of $\zeta$, is the greatest uncertainty in the determination of {\it n}(H$_{3}^{+}$). Further experimental and theoretical results for \ke\ are eagerly awaited. Thus, under the above conditions, the volume density of H$_{3}^{+}$\ in diffuse clouds also is approximately independent of cloud density, but its value is roughly three orders of magnitude less than in dark clouds. Only if the path length through diffuse clouds is vastly greater than that through an individual dark cloud can the column density of H$_{3}^{+}$\ be comparable to its value through the dark cloud. \subsection{H$_{3}^{+}$\ towards Cygnus OB2 No.\ 12} From the visual extinction of 10.2 magnitudes to Cygnus OB2 No.\ 12 (Humphreys 1978), its distance of 1.7~kpc (Torres-Dodgen, Tapia \& Carroll 1991) and the standard gas-to-dust conversion factor (Bohlin, Savage \& Drake 1978), the column density of hydrogen atoms, {\it N}($\Sigma$H)~=~{\it N}(H)+2{\it N}(\hh), along the line of sight is roughly 2~$\times$~10$^{22}$~cm$^{-2}$. The analysis of the infrared CO absorption lines indicates that along the line of sight {\it N}(CO)/{\it N}($\Sigma$H)~$\sim$~1.5~$\times$~10$^{-6}$, which is much less than C/H. Thus at most a few percent of the carbon is in molecular form. This is consistent with the clouds in front of Cygnus OB2 No.\ 12 being diffuse. Using the measured value of {\it N}(H$_{3}^{+}$) and the values of {\it n}(H$_{3}^{+}$) calculated in section 4.1, the length of the absorbing column of H$_{3}^{+}$\ is roughly L~=~{\it N}(H$_{3}^{+}$)/{\it n}(H$_{3}^{+}$)~$\sim$~400--1200~pc. This path length seems unreasonably large (although it does not exceed the total distance to the star). The mean gas density over the path would be {\it N}($\Sigma$H)/L~$\sim$~10~cm$^{-3}$. Carbon monoxide at such low densities is virtually completely confined to the lowest rotational level (Zuckerman \& Palmer 1974) and could not produce the observed CO and \co\ J=2-1 line emission. The derived path length also is not in agreement with observations of rotational lines of CH (van Dishoeck, private communication) and the near infrared spectra of C$_2$ (Souza \& Lutz 1977; Gredel \& M\"{u}nch 1994). Those observations suggest that the bulk of the intervening molecular material exists in clouds with typical densities of a few hundred cm$^{-3}$. The total gas column density then implies that these clouds have an aggregate length of $\sim$~30~pc. If the H$_{3}^{+}$\ at densities of 1--3~$\times$~10$^{-7}$~cm$^{-3}$ were confined to such diffuse clouds it would have a column density more than an order of magnitude less than observed. Taken together these results suggest that most of the H$_{3}^{+}$\ is found where the other molecules do not exist. It is, of course, possible that the H$_{3}^{+}$\ does not trace the presence of other molecules, but there is no {\it a priori} reason to assume that it should not. On the other hand, if the observed H$_{3}^{+}$\ is confined solely to clouds containing CH and C$_{2}$ along a path length of $\sim$~30~pc, the density of H$_{3}^{+}$\ in them is $\sim$~4~$\times$~10$^{-6}$ cm$^{-3}$. This is more than an order of magnitude higher than the estimated density of H$_{3}^{+}$\ in diffuse clouds (see section 4.1). This density would imply either that the value of $\zeta$/\ke\ is at least one order of magnitude larger than used here (suggesting that one or both of these assumed constants needs to be revised) or that one or more processes in addition to the interaction of cosmic rays with \hh\ governs the production of H$_{3}^{+}$\ in diffuse clouds. Galactic rotation along the line of sight to Cygnus OB2 produces a range of radial velocities of approximately 3.3~\km/s, assuming a flat rotation curve with $v_c$ = 220~\km/s, R$_0$ = 8~kpc, and $\ell = 80.10^{\circ}$. The velocity dispersion of the interstellar medium ($\sigma \sim$ 6.6~\km/s implying FWHM~=~15.6~\km/s; Welty, Hobbs \& Kulkarni 1994) is considerably greater than this. The presence of H$_{3}^{+}$\ along a large fraction of the line of sight to Cygnus OB2 No.\ 12 thus is not ruled out by the observed linewidth and is consistent with typical velocity dispersions observed in the interstellar medium. If the path length over which H$_{3}^{+}$\ absorption occurs indeed is very long compared to those of other molecular absorption lines, the profiles of H$_{3}^{+}$\ lines should differ from those of the other molecules, probably in the sense of being more complex. Higher resolution spectroscopy of the H$_{3}^{+}$\ infrared absorption lines will test this possibility and will facilitate important comparisons with the C$_2$ near infrared and CO radio spectra, both of which show a few well defined velocity components. \subsection{H$_{3}^{+}$\ towards the galactic center} The total column density of H$_{3}^{+}$\ observed towards the galactic center source IRS3 is 25~$\times$~10$^{14}$~cm$^{-2}$, nearly an order of magnitude greater than those found in dense cloud cores (Geballe \& Oka 1996; McCall, Geballe \& Oka 1999) and along the line of sight to Cygnus OB2 No.\ 12. The visual extinction towards the nuclear sources in the galactic center is approximately 27 magnitudes (Wade et al.\ 1987). Various lines of evidence suggest that roughly one-third of the extinction occurs in molecular clouds and that two-thirds arises in diffuse gas (e.g., Whittet et al.\ 1997). However, there is no {\it a priori} reason that the division of H$_{3}^{+}$\ column density between the diffuse and molecular clouds should be the same as the division of visual extinctions. Neither can it be assumed that the column density of H$_{3}^{+}$\ in the diffuse gas toward the galactic center may be determined by scaling {\it N}(H$_{3}^{+}$) toward Cygnus OB2 No.\ 12 by the ratio of visual extinctions in diffuse gas, nor by the ratio of optical depths of the 3.4~\um\ absorption feature. It is likely that toward the galactic center substantial column densities of H$_{3}^{+}$\ are found in both dark and diffuse environments. For illustrative purposes we assume that the sharp H$_{3}^{+}$\ doublet is due to diffuse gas in the bulk of the galaxy. This assumption seems reasonable since gas on circular orbits at $\ell=0^{\circ}$ should appear near \Vlsr~$\sim$~0, which is where the doublet is seen. We assume that the remainder of the H$_{3}^{+}$\ line profile occurs in denser gas nearer the galactic center and presumably in non-circular orbits. For the diffuse gas we employ the H$_{3}^{+}$\ density estimates derived in section 4.1. For {\it N}(H$_{3}^{+}$)~$\sim$~7.5~$\times$~10$^{14}$~cm$^{-2}$ (Table 2) the H$_{3}^{+}$\ absorption towards IRS3 extends over $\sim$0.8--2.5 kpc. While this is a surprisingly extended path length, it is not completely unrealistic in view of the much larger distance to the galactic center than toward Cygnus OB2. However, as also pointed out for Cygnus OB2 No.\ 12, if \ke\ is lower or $\zeta$ higher than our assumptions in section 4.1, the derived path length would decrease proportionately. In molecular clouds, the number density of H$_{3}^{+}$\ is roughly three orders of magnitude greater, and for a column density of $\sim$~17.5~$\times$~10$^{14}$~cm$^{-2}$ we deduce a path length of $\sim$~6~pc. From the extinction produced by the molecular clouds (5-10 magnitudes; see Whittet et al.\ 1997); the standard gas-to-dust ratio (Bohlin, Savage \& Drake 1978), and the above path length, a mean gas density of $\sim$~1000~cm$^{-3}$ is derived. This is considerably less than the densities in the cloud cores in which H$_{3}^{+}$\ has been detected. The difference is not surprising, however, because the line of sight to the galactic center, which is known to pass through a number of massive clouds near the center as well as spiral arms, does not pass through or even very close to any cloud cores (e.g., Federman \& Evans 1981). Here we have discussed only the source IRS3. These conclusions should in general also apply to the quintuplet source GCS3-2, although in the case of this source it is difficult to separate the diffuse and dense cloud contributions to the H$_{3}^{+}$\ profile. \section{Conclusions} H$_{3}^{+}$\ has been detected in the diffuse interstellar medium toward two sources in the galactic center and toward the highly reddened star Cygnus OB2 No.\ 12. The column density of H$_{3}^{+}$\ observed towards the galactic center is nearly an order of magnitude greater than that toward the dense cloud cores where interstellar H$_{3}^{+}$\ has been found. Despite the relatively low extinction toward Cygnus OB2 No.\ 12 the column density of H$_{3}^{+}$\ in front of it is comparable to those found toward cloud cores. Using the best values currently available for the rates of cosmic ray ionization of \hh\ in diffuse clouds and dissociative recombination of H$_{3}^{+}$, the density of H$_{3}^{+}$\ in the diffuse interstellar medium is roughly three orders of magnitude less than in dark clouds, implying that toward both the galactic center and Cygnus OB2 No.\ 12 the observed H$_{3}^{+}$\ exists along very long path lengths. Measurements of H$_{3}^{+}$\ toward Cygnus OB2 No.\ 12 at higher spectral resolution coupled with more accurate values of the above two rates are required to understand the physical relation between the H$_{3}^{+}$\ and the other molecules observed along this line of sight. These detections open the way for organized study of the diffuse interstellar medium via infrared spectroscopy. Both CO and H$_{3}^{+}$\ are demonstrated here to have detectable infrared signatures for modest amounts of extinction by diffuse gas within the galaxy. It is likely that soon there will be detections of these features in the diffuse interstellar media of external galaxies. \acknowledgements We thank the staff of the Joint Astronomy Centre for the support of these measurements. We particularly thank G. Sandell and R. P. Tilanus for securing and reducing the JCMT spectra and E. F. van Dishoeck, L. M. Hobbs, N. J. Evans, and the referee, J. H. Lacy, for helpful discussions, comments, and information. The United Kingdom Infrared Telescope is operated by the Joint Astronomy Centre on behalf of the U.K. Particle Physics and Astronomy Research Council. The James Clerk Maxwell Telescope is operated by the Joint Astronomy Centre on behalf of the Particle Physics and Astronomy Research Council of the United Kingdom, the Netherlands Organisation for Scientific Research, and the National Research Council of Canada. B. J. McCall is supported by the Fannie and John Hertz Foundation. The University of Chicago portion of this work has been supported by NSF grant PHYS-9722691 and NASA grant NAG5-4234. \begin{deluxetable}{ccccccccc} \footnotesize \tablecaption{Log of Observations.} \tablenum{1} \tablehead{ \colhead{UT Date} & \colhead{Telescope} & \colhead{Instr.} & \colhead{Object} & \colhead{molecule} & \colhead{wavel.} & \colhead{Int. time} & \colhead{Std} & \colhead{res.} \\ \colhead{} & \colhead{} & \colhead{} & \colhead{} & \colhead{} & \colhead{or freq.} & \colhead{min.} & \colhead{} & \colhead{\km/s} } \startdata 970711 & UKIRT & CGS4 & GC IRS3 & H$_{3}^{+}$ & 3.668~\um & 29 & HR6486 & 15 \nl & & & GCS3-2 & H$_{3}^{+}$ & 3.668~\um & 7 & HR6486 & 15 \nl & & & GC IRS3 & H$_{3}^{+}$ & 3.953~\um & 16 & HR6486 & 16 \nl & & & Cyg OB2 12 & H$_{3}^{+}$ & 3.668~\um & 10 & HR7924 & 15 \nl 970802 & UKIRT & CGS4 & Cyg OB2 12 & CO & 4.65~\um & 3 & HR7924 & 20 \nl 970805 & JCMT & A2 & Cyg OB2 12 & \CO & 230~GHz & 4 & & 0.3 \nl 970905 & Mayall& Phoenix & Cyg OB2 12 & H$_{3}^{+}$ & 3.715~\um & 60 & HR7924 & 9 \nl 971113 & JCMT & A2 & Cyg OB2 12 & \co & 220~GHz & 30 & & 0.3 \nl \enddata \end{deluxetable} \clearpage \begin{deluxetable}{cccccc} \tablecaption{H$_{3}^{+}$\ line parameters toward galactic center.} \tablenum{2} \tablehead{ \colhead{Source} & \colhead{Line(s)} & \colhead{$\lambda$} & \colhead{W$_{\lambda}$} & \colhead{{\it N}$_{\rm{level}}$(H$_{3}^{+}$)} & \colhead{Level} \\ \colhead{} & \colhead{} & \colhead{\um} & \colhead{10$^{-6}$\um}\tablenotemark{a} & \colhead{10$^{14}$cm$^{-2}$}\tablenotemark{a} & \colhead{} } \startdata & {\bf narrow component}\tablenotemark{b} & & & & \nl GC IRS3 & R(1,1)$^{+}$ & 3.66808 & 12(4) & 5.1(1.7) & para \nl GC IRS3 & R(1,0) & 3.66852 & 9(4) & 2.4(1.1) & ortho \nl & {\bf broad component}\tablenotemark{c}& & & & \nl GC IRS3 & R(1,1)$^+$ + R(1,0) & 3.668 & 53(12) & 17.5(3.9) & total \nl GCS3-2 & R(1,1)$^{+}$ + R(1,0) & 3.668 & 83(8) & 27.7(2.4) & total \nl \enddata \tablenotetext{a}{Statistical uncertainties (3$\sigma$) are given in parentheses. Systematic errors are difficult to estimate and may be larger.} \tablenotetext{b}{The narrow component at \Vlsr$\approx$0, defined as the absorption below 0.97.} \tablenotetext{c}{Column densities for broad components are estimated assuming equal amounts of para- and ortho-H$_{3}^{+}$ and using an average value of $|\mu|^2$=0.0209 Debye$^2$.} \end{deluxetable} \clearpage \begin{deluxetable}{ccccccc} \tablecaption{H$_{3}^{+}$\ line parameters towards Cygnus OB2 No.\ 12.} \tablenum{3} \tablehead{ \colhead{Line} & \colhead{$\lambda$} & \colhead{W$_{\lambda}$} & \colhead{{\it N}$_{level}$} & \colhead{\Vlsr} & \colhead{FWHM$_{obs}$} & \colhead{FWHM$_{deconv}$} \\ \colhead{} & \colhead{\um} & \colhead{10$^{-6}$\um}\tablenotemark{a} & \colhead{10$^{14}$cm$^{2}$}\tablenotemark{a} & \colhead{\km/s}\tablenotemark{a} & \colhead{\km/s}\tablenotemark{a} & \colhead{\km/s} } \startdata R(1,1)$^{+}$ & 3.66808 & 3.9(9) & 1.6(4) & 8(5) & 17(5) & 8 \nl R(1,0)~ & 3.66852 & 5.4(9) & 1.4(2) & 11(5) & 22(5) & 16 \nl R(1,1)$^{-}$ & 3.71548 & 5.2(7) & 2.4(3) & 8(3) & 16(3) & 13 \nl \enddata \tablenotetext{a}{Statistical uncertainties (3$\sigma$) are given in parentheses.} \end{deluxetable} \clearpage \begin{deluxetable}{cccc} \tablecaption{CO infrared lines toward Cygnus OB2 No.\ 12.} \tablenum{4} \tablehead{ \colhead{Line} & \colhead{$\lambda_{obs}$} & \colhead{W$_{\lambda}$} & \colhead{\Vlsr} \\ \colhead{} & \colhead{\um} & \colhead{10$^{-6}$\um}\tablenotemark{a} & \colhead{\km/s}\tablenotemark{a} } \startdata R(3) & 4.63308 & 19(4) & 13(4) \nl R(2) & 4.64112 & 62(6) & 19(4) \nl R(1) & 4.64913 & 121(7) & 15(4) \nl R(0) & 4.65727 & 134(7) & 12(4) \nl P(1) & 4.67401 & 132(7) & 18(4) \nl P(2) & 4.68243 & 69(6) & 13(4) \nl \enddata \tablenotetext{a}{Statistical uncertainties (3$\sigma$) are given in parentheses. Systematic errors due to incomplete cancellation of telluric CO lines are difficult to estimate and may be larger.} \end{deluxetable} \clearpage \centerline{REFERENCES} \noindent Adamson, A. J., Whittet, D. C. B. \& Duley, W. W. 1990, \mnras, 243, 400 \noindent Anicich, V. G. \& Huntress, W. T., Jr. 1986, \apjs, 62, 553 \noindent Becklin, E. E., Matthews, K., Neugebauer, G. \& Willner, S. P. 1978, \apj, 219, 121 \noindent Bohlin, R. C., Savage, B. D. \& Drake, J. F. 1978, \apj, 224, 132 \noindent Butchart, I., McFadzean, A. D., Whittet, D. C. B., Geballe, T. R. \& Greenberg, J. M. 1986, \aap, 154, L5 \noindent Cardelli, J. A., Meyer, D. M., Jura, M. \& Savage B. D. 1996, \apj, 467, 334 \noindent Federman, S. R. \& Evans, N. J., II 1981, \apj, 248, 113 \noindent Geballe, T. R., Baas, F. \& Wade, R. 1989, \aap, 208, 255 \noindent Geballe, T. R. \& Oka, T. 1996, \nat, 384, 334 \noindent Glassgold, A. E. \& Langer, W. 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C. 1987, \apj, 320, 570 \noindent Watson, W. D. 1973, \apjl, 183, L17 \noindent Welty, D. E., Hobbs, L. M. \& Kulkarni, V. P. 1994, \apj, 436, 152 \noindent Whittet, D. C. B., Boogert, A. C. A., Gerakines, P. A., Schutte, W., Tielens, A. G. G. M., de Graauw, Th., Prusti, T., van Dishoeck, E. F., Wesselius, P. R. \& Wright, C. M. 1997, \apj, 490, 729 \noindent Zuckerman, B. \& Palmer, P. 1974, \araa, 12, 279 \begin{figure} \figurenum{1} \plotone{gccyg_fig1.eps} \caption{Spectrum of the galactic nuclear source IRS3 (upper trace) and the ``quintuplet'' source GCS3-2 (lower trace, shifted down by 0.05 units), near the R(1,1)$^{+}$ and R(1,0) doublet of H$_{3}^{+}$. The rest wavelengths of the lines are indicated by vertical bars. The noise levels are indicated by the point-to-point variations. \label{fig1}} \end{figure} \clearpage \begin{figure} \figurenum{2} \plotone{gccyg_fig2.eps} \caption{Spectrum of Cygnus OB2 No.\ 12 in two wavelength intervals near 3.7~\um. Lines of \hhhp\ are indicated. The high frequency noise near 3.6675~\um\ is a result of the correction for a strong telluric CH$_{4}$ line. \label{fig2}} \end{figure} \clearpage \begin{figure} \figurenum{3} \plotone{gccyg_fig3.eps} \caption{Spectrum of Cygnus OB2 No.\ 12 near 4.65~\um, showing absorption lines of \CO\ and emission lines of atomic hydrogen. \label{fig3}} \end{figure} \clearpage \begin{figure} \figurenum{4} \plotone{gccyg_fig4.eps} \caption{Spectra of pure rotational 2-1 lines of \CO\ and \co. The original data have been binned into 0.6~\km/s\ intervals and a 4~K offset has been given to the \CO\ spectrum. The vertical axis is detected antenna temperature corrected for the telescope efficiency. \label{fig4}} \end{figure} \end{document} ------------- End Forwarded Message ------------- ------------- End Forwarded Message -------------