Interstellar H 3. Takeshi Oka CONTENTS 1. HISTORICAL SKETCH

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1 pubs.acs.org/cr Interstellar H 3 Takeshi Oka Department of Chemistry and Department of Astronomy and Astrophysics, The Enrico Fermi Institute, University of Chicago, 5801 South Ellis Avenue, Chicago, Illinois 60637, United States CONTENTS 1. Historical Sketch Discovery of H 3 and H 3 versus H 3 : Thomson, Stark, Bohr Chemistry of H 3 : Dempster, Hogness, Smyth, McDaniel Theory of H 3 : Coulson, Hirschfelder, Eyring Spectroscopy of H 3 and H 3 : Herzberg Interstellar Chemistry of H Basic Characteristics of Interstellar Chemistry Interstellar Chemistry is a Hydrogen- Dominated Chemistry Interstellar Ion Chemistry is an Honest Chemistry Interstellar Chemistry Is Kinematic Rather than Thermodynamic Production of H H 2 H 2 H 3 H, the Langevin Rate Cosmic Ray Ionization Charge Exchange Reaction between H 2 and H Destruction and Number Density of H Dense Clouds Diffuse Clouds Dissociative Recombination of H H 3 : Initiator of Interstellar Chemistry H 3 : Universal Proton Donor, the Interstellar Acid Deuterium Fractionation Effect of o-h Spectroscopy of H Infrared Vibration Rotation Spectrum of H ν 2 Fundamental Band Overtone and Combination Bands and Rigorous Theory Rotational Transitions Forbidden Rotational Transitions of H H 2 D and HD 2 (D 3 ) H 3 as an Astrophysical Probe What We Learn from H 3 Observation CO versus H 3 as Astrophysical Probes H 3 as Thermometer and Densitometer (Cold Clouds) H 3 as Thermometer and Densitometer (Warm Clouds) H 3 as Tracer for the Cosmic-Ray Ionization Rate Saturation of the Effect of Ionization H 3 in the Galactic Disk H 3 in Dense Clouds H 2 D and HD 2 in Dense Cloud Cores H 3 in Diffuse Clouds H 3 in the Galactic Center Revelation of a Vast Amount of Warm and Diffuse Gas High Ionization Rate in the Central Molecular Zone Morphology and the Expanding Molecular Ring 8757 Author Information 8758 Notes 8758 Biography 8758 Acknowledgments 8758 References HISTORICAL SKETCH The history of H 3 is a succession of inspiring discoveries, grueling hard work, big surprises, and many puzzles and mistakes with their unexpected resolutions. It is a showcase, involving great names, of how science develops slowly and into totally unexpected directions. Most of the work discussed in this section is laboratory and theoretical, but it is the basis for astronomical studies discussed in later sections Discovery of H 3 and H 3 versus H 3 : Thomson, Stark, Bohr H 3 was discovered by J. J. Thomson in Thomson ( ) spent most of his laboratory time in the studies of gaseous discharges. He first studied negatively charged species (cathode rays) and discovered the electron in 1897 and later studied positively charged species (canal rays) to provide better understanding on his atomic model. With advances in Special Issue: 2013 Astrochemistry Received: May 14, 2013 Published: November 6, American Chemical Society 8738

2 Chemical s vacuum technology, his experiments led to early prototype mass spectrometers and H 3 was the first novel species to be discovered using them. The tiny spot of H 3 which appeared in his plate 2 is shown in Figure 1. The spot was not very Figure 1. Two m/e = 3 signals observed by Thomson. Small spot 2 shown by the arrow in the left picture, which Thomson called capricious, etc., is due to H 3. Streak in the right picture marked by 3, which was more reproducible, 3 was later shown to be due to HD. Reprinted with permission from refs 2(left) and 3 (right). Copyright 1912 and 1913 Taylor & Francis. reproducible, and he called it capricious, fugitive, and evanescent in papers and monographs. He was further puzzled by the fact that gas evaporated from solids gave more reproducible signals. 3 As often happens, a discoverer is also a skeptic of his own discovery. Because of his puzzlement, Thomson used X 3 instead of H 3 or H 3 which he had used in his first two papers. When deuterium was discovered by Harold Urey in 1932, Thomson published a paper in Nature saying The evidence seems to me to leave little doubt that the gas I called H 3 more than twenty years ago is the same as that which is now called heavy hydrogen. 4 The problem of H 3 versus HD took a few more years to settle, and it is in his autobiography 5 published 26 years after the discovery where he finally made the clear statement one of the first things by the photographic method was the existence of H 3. However, his later remark in the same book though H 3 is so evanescent, H 3 itself is more durable indicates he has not understood the chemistry of H 3. The stability of H 3 was accepted by many physicists. Johannes Stark believed in its existence from his own experiment 6 and proposed a triangular structure of H 3. Although his picture (see Figure 486 of ref 6, reproduced in ref 9) is close to the equilateral triangle, it was an intuitive picture not based on theory, one in which the proton is not even shown as a particle and just a historical curiosity. The first theoretical study on H 3,H 3, and H 3 was published in 1919 by Niels Bohr, 7 who published the trilogy 8a c in 1913, part I of which is the famous paper on atomic hydrogen which initiated the old quantum mechanics and parts II and III are its applications to many electron atoms and molecules, respectively. Applying the method of part III to hydrogenic molecules, he predicted that H 3 and H 3 had linear structure and were stable and that H 3 was unstable, all of which were later shown to be false. Readers are referred to papers on the early history of H 3 and H 3 by historian of science Helge Kragh 9,10 and other reviews Chemistry of H 3 : Dempster, Hogness, Smyth, McDaniel The true nature of H 3 was revealed by three young American physicist/chemists who were free from the discoverer s worries which agonized Thomson for many years; they accepted H 3 without apprehension. Using a higher pressure (10 mtorr) of H 2 and lower voltage (800 V) for discharge than those used by Thomson, Arthur Dempster in Chicago was the first to show in 1916 that the amount of H 3 in the discharge can be higher than that of H 2. 14,15 From this experiment, he concluded H 3 cannot be regarded as a stable gas, since it is not present when there is no dissociation of the hydrogen molecules. This correct conclusion published in Philosophical Magazine 14 must have been either missed or ignored by Thomson and Bohr. The predominance of H 3 over H 2 in discharges was further evidenced by experiments reported in many papers by Henry Smyth (e.g., ref 16), and it was in the 1925 paper by Hogness and Lunn 17 of Berkeley where the celebrated ion-neutral reaction, H 2 H 2 =H 3 H, appears, which I rewrite for convenience of this review as (1) H H H H This highly exothermic (1.7 ev) proton-hop reaction with a high Langevin rate constant ( cm 3 s 1 ) is the most frequent reaction in hydrogen-dominated plasmas both in laboratories and in space. Since H 3 plays the central role in interstellar chemistry, this is the most important reaction in astrochemistry. By the 1960s, the predominance of H 3 over H 2 in hydrogen plasmas was common knowledge among the specialists on weakly ionized plasmas. In 1961 three plasma physicists from the Georgia Institute of Technology, Martin, McDaniel, and Meeks, wrote in the Astrophysical Journal It now appears desirable to consider the possibilities for detecting H 3 because this molecular ion may be present under some circumstances to the virtual exclusion H Perhaps this was the first time H 3 was mentioned in astronomy. Nevertheless, H 3 remained a little known exotic species, as there is not a word on it nor even on Thomson s discovery of it in the authoritative textbooks on weakly ionized plasmas by von Engel (1955) 19 and McDaniel (1964) Theory of H 3 : Coulson, Hirschfelder, Eyring After the advent of quantum mechanics, the clarification of chemical bond in 1927 by Heitler and London, and introduction of the idea of molecular orbitals in 1928 by Hund and Mulliken, the time was ripe to clarify the quantum mechanics of H 3, the simplest polyatomic molecule. Charles Coulson in 1935, then a 24 year old graduate student in Cambridge, was the first to apply the method of molecular orbitals to H 3 following a suggestion by his thesis supervisor Lennard-Jones. Coulson 21 arrived at the equilateral triangle structure with the equilibrium H H distance of 0.85 Å (0.88 Å), a vibrational frequency of ν 1 = 3170 cm 1 (3178 cm 1 ), and a stabilization energy from H 2 H, that is, the proton affinity of H 2 of 2.0 ev (4.4 ev), where values in parentheses are modern values. Coulson s paper, which correctly predicted the equilateral triangle structure and had other crucial quantities approximately right except for the H 2 proton affinity, was nevertheless severely criticized by the Wisconsin group of Hirschfelder and Eyring, 22 who used the method of Heitler and London and obtained a symmetric linear structure with an H H distance of 1.06 and 0.82 Å depending on the calculational methods and 8739

3 Chemical s the H 2 proton affinity of >2.0 ev. They were highly motivated to clarify the quantum mechanics of H 3 and H 3 and published a series of 5 papers from 1936 to Henry Eyring was quoted to have said that the problem of H 3 was the scandal of modern chemistry since nothing was known about H 3 other than it exists (e.g., see page 75 of ref 11). Toward the end of the series of papers, Hirschfelder realized that a triangular structure was more stable and gave molecular constants using the approximate equilateral triangle structure with an H H distance of 1.79 Å (0.87 Å), ν 1 = 1550 cm 1 (3178 cm 1 ), ν 2 = 1100 cm 1 (2522 cm 1 ) 23 but still criticizing Coulson s theory, while Eyring kept on believing the linear structure until much later as indicated by the withdrawal of his name from Parts IV and V in which Herschfelder advocated the triangular structure. With the hindsight, the result of Coulson s theory was right in many ways. However, the valid criticism by Hirschfelder But he (Coulson) was unable to compute the integrals arising from the mutual repulsion of the electrons and make his results quantitative 23 must have hit Coulson hard since there is absolutely no mention of H 3 in his influential textbook Valence 24 published in Instead of quoting his own work on H 3 which would have been the best demonstration of the power of the molecular orbital method, Coulson included the incorrect conclusions of the linearity and stability of H 3 by the Wisconsin group as accurate work. With the arrival of the age of numerical calculations using modern computers, the equilateral triangular structure of H 3 was beyond doubt. 25,26 Many theoretical papers followed (see, e.g., ref 11) culminating in the epoch-making classic paper by Carney and Porter in 1976, who used the variational method and predicted the vibrational frequencies with high accuracy Spectroscopy of H 3 and H 3 : Herzberg Thomson was the first to attempt spectroscopy of H 3 /H 3 ; Many attempts have been made to obtain spectroscopic evidence of X 3 by putting mixtures of this gas and hydrogen in a quartz tube and photographing the spectrum obtained when a discharge was sent through the tube... (page 122 of his 1913 textbbook 28 ). In the 1920s and 1930s numerous physicists claimed discovery of visible spectra of H 3 or H 3. Some of these claims were quoted by 22 year old Herzberg in his early paper on the spectrum of hydrogen 29 (see also ref 11). All of the visible lines turned out to be transitions between excited electronic states of H 2 whose spectrum is so rich that a book compiling the H 2 spectrum was published by Dieke. The confusion of spectral lines of excited H 2 with those of H 3 or H 3 continued even after genuine spectra of H 3 and H 3 were discovered in 1979 and 1980, respectively. 11 It was later determined theoretically that H 3 is unstable in its electronic excited states except for a barely bound triplet state, 30 and therefore, no sharp electronic spectrum is expected, and the vibrational transition in the infrared is the only spectrum to be expected (see ref 11 for more details). Herzberg consistently sought after the spectrum throughout his life. His first search in 1941 for infrared emission of H 3 along with that of HD is noted in his scientific autobiography. 31 At the end of his presidential address to the Royal Society of Canada in 1967, titled The spectra of Hydrogen and Their Role in the Development of Our Understanding of the Structure of Matter and of the Universe, in which he brilliantly summarized the fundamental role hydrogenic species such as H, H, and H 2 have played in the development of sciences, Herzberg noted Attempts by Dr. J. W. C. Johns and myself to find this fundamental in emission in the infrared spectrum of a discharge through hydrogen have not yet been successful, but will be resumed again shortly. 32 With the arrival of commercial infrared Fourier transform spectrometers, Herzberg continued to search for the H 3 emission with H. Lew and J. J. Sloan. In 1979 at the age of 74 he stumbled on broad emission spectra of predissociated H 3 and D 3 and opened up a rich field of polyatomic Rydberg spectroscopy. 33,34 This led to highresolution spectroscopy of H 3, taking advantage of the metastable N=K=0level of the 2p 2 A 2 state by Helm 35 and Ketterle et al. 36 (Recently, Black 37 suggested the presence and possible detectability of H 3 in astronomical environments.). However, observation of the infrared spectrum of H 3 had to wait till the advent of tunable laser infrared spectroscopy (section 3). 2. INTERSTELLAR CHEMISTRY OF H 3 H 3 is produced by the reaction H 2 H 2 H 3 H (eq 1) in which a proton in H 2 hops to molecular hydrogen. In interstellar space, where cosmic rays capable of ionizing H 2 are always present, H 3 is ubiquitous as long as H 2 abounds. H 3 plays the central role in interstellar chemistry as proton donor (acid) through the proton-hop reaction discussed below Basic Characteristics of Interstellar Chemistry Interstellar Chemistry is a Hydrogen-Dominated Chemistry. This is because 99.9% of atoms in the Universe are either H (92.1%) or relatively inert He (7.8%) and heavier atoms like C, N, O, etc., which make chemistry so rich, together constitute only 0.1%. There are 6 stable pure hydrogenic species H,H,H,H 2,H 2, and H 3. Although hydrogenic cluster ions H 3 (H 2 ) n are stable and has been mentioned in relation to astrochemistry 38 they are not expected to be abundant in interstellar space. Out of the six species, H, the proton, is not spectroscopically observable. The broad absorption of the near-infrared by H causes the opacity of the sun 39,40 and stars but does not show discrete spectral lines. H 2 is not abundant because it is rapidly converted to H 3 by the reaction in eq 1. This leaves H, H 2, and H 3 discovered in interstellar space in 1951, 41, , 43 and 1996, 44 respectively, as the three pure hydrogenic species that are observable. H 2 and H 3 are particularly important in astrochemistry. They are both produced abundantly in space, but the steady state population of H 3 is very much less ( ) than that of H 2 because of its high chemical activity. Nevertheless, the dipole-induced H 3 infrared absorption is much stronger (10 9 ) than the quadrupole-induced infrared absorption of H 2 and usually much easier to observe in interstellar gas as discussed later in section 4. H 2 does possess a strong and rich ultraviolet spectrum, but that spectrum is not observable in many interstellar environments due to strong absorption and scattering of ultraviolet radiation by interstellar gas and dust Interstellar Ion Chemistry is an Honest Chemistry. There are two reasons for this. First, because of the low temperature of the environment, Gibb s free energy G =H TS which governs chemistry is nearly equal to the enthalpy H. The entropy term TS, which makes the chemistry of stellar atmosphere so subtle as discussed by Tsuji, 45 seldom needs to be considered. The outcome of many chemical reactions can be predicted simply from the enthalpies of the involved atoms and molecules. One can go a long way just by knowing the three basic chemical parameters; the proton affinity, the ionization energy (potential), and the dissociation 8740

4 Chemical s energy. The values of these are listed in Table 1 for the principal atoms and molecules in interstellar chemistry. The Table 1. Proton Affinity (PA), Ionization Energy (IE), and Dissociation Energy (D 0 0, DE) of Atoms and Molecules which Play Pivotal Roles in Interstellar Chemistry (in ev) a species PA b IE c DE d k L He H N O H O ± 0.40 N ± 0.40 NO ± 0.40 CO ± 0.60 CH ± 0.30 CO ± 0.20 OH C HCCH ± 0.80 S C H 2 O ± 0.60 HCN ± 0.80 CH NH ± 0.50 a The last column gives experimental rate constants k L for the Langevin reaction H 3 X H 2 HX. Values of k L are approximate averages of data in ref 46 in 10 9 cm 3 s 1. Mostly from ref 47. Some are calculated values from IE and DE of other species. From refs 48 (atoms), 49 (diatomic molecules), and 50 (polyatomic molecules). d From refs 49 (diatomic molecules) and 50 (polyatomic molecules). proton affinity is listed in the first column because it is the most crucial parameter for characterizing the interstellar chemistry of H 3.H 3 donates its extra proton to atoms or molecules with a proton affinity greater than that of H 2, that is, to any species below H 2 in Table 1, via the universal proton-hop reaction H3 X H2 HX (2) to produce chemically active HX from relatively inactive neutral X and thus initiate interstellar chemistry. H 3 is a universal proton donor, that is, an interstellar acid. The only exceptions in Table 1, species that do not accept proton from H 3, are the three species above H 2, that is, He, H, and N. O 2 has a proton affinity very close to that of H 2, and therefore, production of HO 2 is delicate. 51 Other atoms and molecules in Table 1 and thousands more molecules 47 all have proton affinities higher than 4.39 ev and readily accept a proton from H 3. Of all species in Table 1, He is unique for its lowest proton affinity and highest ionization energy. In general, species with low proton affinity tend to have high ionization energy. A remarkable exception of this rule is the pair H and H 2 ; both proton affinity and ionization energy of H 2 are significantly ( 2 ev) higher than those of H. Interstellar chemistry is deeply affected by this accident. It is sometimes said that chemistry is the science of electrons. The simpler interstellar chemistry is the science of protons. The second factor that makes interstellar ion chemistry so simple is the universality of the Langevin rate constant. As more fully explained later in section 2.2.1, almost all exothermic ionneutral reactions have a very large rate constant, on the order of 10 9 cm 3 s 1, due to the long-range Langevin interaction with the 1/r 4 potential. 52 Moreover, the rate constant is independent of temperature to a good approximation. The Langevin rate constants for the proton-hop reaction of eq 2 are listed in the last column of Table 1. By and large one can assume that an ion-neutral reaction with decisive exothermicity will occur with a high Langevin rate. The only exception in this review is the charge exchange reaction between He and H 2 to be discussed at the end of section Interstellar Chemistry Is Kinematic Rather than Thermodynamic. This is because even in the densest and warmest molecular clouds, molecules do not have enough lifetime to become chemically thermalized. For example, CO in plenty of H 2 does not have time to react to become the thermodynamically more stable CH 4 and H 2 O. 53 Highly unsaturated acetylenic compounds like HC 5 N, HC 7 N, and HC 9 N abound. 54 This applies not only to the chemistry but also to the rotational distribution of molecules. Because of the difference between kinetic and radiative temperatures of environment, molecular distributions never reach the thermalized Boltzmannian distribution corresponding to maximum entropy and nonthermal rotational distributions are more often the rule than the exception. Interstellar space is full of maser emissions and other nonthermal phenomena. o-h 2 do not fully convert to energetically lower p-h 2 for the same reason. Interstellar chemistry is the exciting playing ground of kinematics where individual characteristics of molecules appear in rare form rather than being washed out by the boring entropy maximum principle Production of H 3 The 1968 discovery of interstellar NH 3 55 and H 2 O 56 by Townes group revealed the richness of interstellar chemistry and introduced the novel concept molecular cloud, regions of interstellar space with unexpected high densities, and affected astrophysics in a most profound way. After these and other discoveries in the centimeter region, radioastronomy quickly moved to the millimeter region and the discovery of CO 57 and HCO 58 followed. The serendipitous discovery of X-ogen by Buhl and Snyder, which was immediately conjectured to be HCO by Klemperer, 59 was particularly important for interstellar chemistry since it has led to the majestic astrochemical theory based on ion molecule reactions by Herbst and Klemperer 60 and Watson 61,62 in which H 3 plays the central role. Watson 61 was particularly explicit about this saying in the abstract Due to the widespread abundance of H 2, ion-molecule reactions with H 2 and H 3 can be the chief formation process for small interstellar molecules in a large fraction of the interstellar gas H 2 H 2 H 3 H, the Langevin Rate. The chemistry of interstellar H 3 is extremely simple. H 3 is produced by cosmic ray ionization of H 2 to H 2 followed by the proton-hop reaction in eq 1. This reaction is very efficient with a high exothermicity of 1.74 ev, the difference between the proton affinity of H 2 (4.39 ev) and H (2.65 ev), and a high Langevin cross section on the order of a few Å 2 in interstellar space depending on the temperature. When H 2 and H 2 approach at a distance of r, the positive charge on H 2 with the Coulomb field of e/r 2 polarizes H 2 and induces a dipole moment d = αe/r 2, where α is the polarizability of H 2. This leads to the attractive charge-induced dipole potential, 63 V L = de/2r 2 = αe 2 /2r 4, the Langevin potential. The motion of a 8741

5 Chemical s neutral (H 2 ) and ion (H 2 ) under this potential was discussed by Langevin 52 and in textbooks (e.g., Landau and Lifshitz 64 section 18). The Langevin cross section σ L in terms of Langevin radius ρ L and the Langevin rate constant k L are given as 2 e α σl = πρ = 2π and k = vσ = 2πe L L L v μ where μ is the reduced mass for H 2 and H 2 which is nearly identical to the mass of H and v is the relative velocity of H 2 and H 2 long before the collision. Note that k L is independent of v and therefore of temperature. Thus, the Langevin reaction occurs at the low temperature of the interstellar space. This characteristic is special for the 1/r 4 potential. Maxwell assumed this potential in his paper on stress in rarified gases for sheer simplicity of mathematics. 65 There are other forces such as quadrupole quadrupole interaction between H 2 and H 2, but they alternate between attraction and repulsion as the molecules rotate and tend to average out. Substituting the isotropic polarizability of H 2, 66 α = 0.79 Å 3, and ignoring anisotropic polarizability, we obtain from eq 3 k L = cm 3 s 1, which agrees well with observed values 46 of ( ) 10 9 cm 3 s 1, indicating that the above treatment by classical mechanics works well. The Langevin cross section and radius for 10, 30, and 100 K are calculated to be σ L = 590, 340, and 185 Å 2 and ρ L = 13.7, 10.4, and 7.7 Å, respectively. If H 2 and H 2 approach with an impact parameter less than ρ L, which is typically 10 Å, they fall into each other as shown in Figure 2 taken from Langevin s paper. 52 It is like quicksand. They cannot escape each other. Then the very strong chemical force takes Figure 2. Fall to the center of the Langevin potential. 52,64 Reprinted with permission from ref 52. Copyright 1905 Elsevier. α μ (3) over and completes the very exothermic reaction of eq 1. Since polarizabilities of atoms and molecules X do not vary drastically (they are within a factor of 4 of that of H 2 for all species in Table 1) and so are reduced mass for X and H 3 and since heavier X tends to have larger polarizabitity, the Langevin rate calculated above applies to all reactions for eq 2 within a factor of 2 as long as the reaction is decisively exothermic. This makes ion chemistry very simple Cosmic Ray Ionization. The Langevin reaction is very fast by the interstellar standard and occurs in 2 months and in 0.5 day for H 2 number densities of 10 2 and 10 4 cm 3, respectively, which are typical number densities for diffuse clouds and dense clouds. The ionization rate of H 2 by cosmic rays ζ s 1 is many orders of magnitude lower. Therefore, the production rate of H 3 is given by the ratedetermining ionization rate of H 2, that is d n(h 3 ) dt prod k 5 = ζn(h 2) Φ f(h 2), k1 = ζn f (H 2) k5 H Φ f (H 2), 2 k1 ζn f 2 (H 2) H 2 where n H = n(h) 2n(H 2 ) is the number density of all hydrogen and f(h 2 )=2n(H 2 )/n H is the fraction of hydrogen in molecular form. Φ is a correction factor to be discussed in section For dense clouds f(h 2 ) = 1 to a good approximation, while for diffuse clouds f(h 2 ) may take values from 0.01 to 1. The last term in eq 4 is for an approximation with k 5 = k 1 /2 (see section 2.2.3). Hayakawa et al. 67 in 1961 were the first to consider the effect of cosmic rays on interstellar gas. Extrapolating the observed intensities of high-energy cosmic rays to lower energy regions, they predicted ζ H s 1 as the cosmic ray ionization rate of H. (In this review we use ζ H for the ionization rate of H and ζ for that of H 2. ζ =2ζ H holds for energy above 1 MeV. 68 ). Spitzer and Tomasko 69 gave ζ H s 1 based on the observed cosmic rays extending to low energy, which however is much lower than the interstellar value due to deflection by the solar magnetic field. Field et al. gave ζ H s Whichever value is used, there is no question that the cosmic ray ionization is the rate-determining process for H 3 production. The simplicity of eq 4 and the chemistry discussed below make H 3 the most direct and reliable probe to measure ionization rate and hence the strength of low-energy cosmic rays in interstellar space. The value of ζ on the order of by Spitzer and Tomasko had been held as the caconical value for the ionization rate for 30 years until it was shown to be much higher in diffuse clouds by the observation of H 3 as discussed later in section H 2 may also be ionized by extreme ultraviolet radiation and X-rays from stars. Here, these effects are ignored as local. For the former, H 2 is well protected by H and C, which have much lower ionization energy than H 2, and dust. For the latter, the E 7/2 dependence on energy of the photoelectric effect 71 makes it negligible except in special environments Charge Exchange Reaction between H 2 and H. Although production of H 3 is very simple for dense clouds where hydrogen is dominantly in molecular form, a complication arises for diffuse clouds where f(h 2 ) may be (4) 8742

6 Chemical s significantly lower than 1. In this case, H 2 ions produced by cosmic ray may encounter H rather than H 2 and revert to H 2 through the charge exchange reaction H2 H H2 H (5) which is exothermic by the difference of the ionization energies of H 2 and H, 1.83 ev. This reduces the effective production rate of eq 4 by a factor 72 k 5 2k5 1 Φ f (H 2), = 1 1 k k f(h ) where k 1 and k 5 are rate constants for the reactions in eqs 1 and 5, respectively. For special values of k 5 /k 1 = 0, 1/2, and 1, Φ{f(H 2 )} = 1, f(h 2 ), and f(h 2 )/{2 f(h 2 )}, respectively. Although the value of k 1 is well established as discussed in section 2.2.1, the value of k 5 is not. The only reported experimental value 73 is k 5 = (6.4 ± 1.2) cm 3 s 1, which is much smaller than the Langevin rate constant, cm 3 s 1, calculated from eq 3. A theoretical paper gives cross sections which translate to 2.32 and cm 3 s 1 depending on theoretical methods. 74 I here assume a convenient number k 5 /k 1 1/2 which gives Φ{f(H 2 )} = f(h 2 ) leading to the first expression in eq 4. When k 5 is better determined, one can calculate Φ{f(H 2 )} more accurately Destruction and Number Density of H 3 The destruction process of H 3 depends on the state of carbon in the interstellar environment. Dense clouds with a number density on the order of 10 4 cm 3 are gravitationally bound and on their way to star formation. The clouds have a dimension on the order of 1 pc, and their interiors are well shielded from star radiation. Hydrogen is in the molecular form, f(h 2 ) 1, and carbon is mostly locked up as CO some of which are frozen onto dust grains depending on the cloud temperature. Diffuse clouds, with a typical number density on the order of 10 2 cm 3, on the other hand, have larger dimensions and are largely transparent to stellar radiations. Hydrogen is in both H 2 and H, f(h 2 ) < 1, and carbon is in atomic form and ionized by stellar ultraviolet radiation to C. C is the first element to be ionized among species abundant in interstellar space because its ionization energy, ev, is the lowest (see Table 1); hydrogen remains mostly neutral in diffuse clouds. There also is an interstellar environment intermediate between diffuse and dense clouds where carbon is mostly C but is less extensive than the other two Dense Clouds. In dense clouds where molecules abound and the electron fraction is small, <10 7, 76 H 3 is destroyed by the proton-hop reaction in eq 2. Being the dominant species, X = CO with an exothermicity of 1.76 ev and a Langevin rate constant of k CO = cm 3 s 1 plays the main role but X = O with an exothermicity of 0.65 ev and a rate constant of cm 3 s 1 also contributes. Considering there are other molecules like N 2 with significant population and Langevin rate constant, electron, etc., the destruction rate in a dense cloud is estimated as d n(h 3 ) dt destr,dense CO 3 C 1.4 k n(h ) n CO k n(h ) n(co) where the factor of 1.4 is due to contributions of CO, O, N 2, electron, etc., estimated from their abundances 76 and rate 1 (6) constants. 46 For n C = 1 cm 3 the destruction rate is approximately s 1, corresponding to a H 3 lifetime of 10 years. Equating this destruction rate with the production rate of eq 4 with f(h 2 ) = 1, we have the steady state H 3 number density in dense clouds of 1 ζ nh 7 10 cm 2.8 k n dense CO C n(h ) where the cosmic ray ionization rate of ζ s 1 and the depleted C/H ratio 77,78,76 in a dense cloud of n C /n H = is used in the numerical calculation. Note that although n H and n C are proportional to the number density of the cloud n, n(h 3 ) is proportional to their ratio and hence independent of n as long as ζ and the C/H ratio are constant along a sightline. This is because of the linearity of the H 3 production rate to n H as in eq 4. This property makes H 3 a special astrophysical probe complementary to CO. While an observed total column density of CO gives information on the mass of a cloud, the total column density for H 3 gives information on the length of a cloud. This property makes N(H 3 )=Ln(H 3 ) a good approximation. We therefore have nc ζ L = 2.8 kcon(h 3 ) nh (7) which can be used to obtain information on ζl from observed N(H 3 ). In order to separate ζ and L, we need to know one of them from other observations or from an estimate for one of them Diffuse Clouds. In diffuse clouds where the ultraviolet radiation from stars penetrates and singly ionizes virtually all carbon atoms, the electron number density is very high, n(e) 10 4 n H, and dissociative recombination of H 3 with electrons 79 H3 e H H H or H2 H (8) is the dominant destruction process of H 3. Compared with the Langevin reaction of eq 2 under the 1/r 4 Langevin potential, recombination proceeds under the longer range 1/r Coulomb potential and has a rate constant on the order of 10 7 cm 3 s 1, approximately 100 times larger than that of the Langevin reaction. Therefore, the destruction rate of H 3 in diffuse clouds is d n(h 3 ) dt destr,diffuse e 3 e 3 C = kn(h ) n(e) kn(h ) n where k e is the rate constant for dissociative recombination of H 3. In the last term an approximation n(e) n C is used assuming that all electrons originated from the first ionization of C. If n C 10 2 cm 3, the H 3 lifetime is also on the order of 10 years, similar to in dense clouds. Equating this destruction rate with the production rate in eq 4, we obtain the steady state H 3 number density in diffuse clouds 3 diffuse n(h ) ζ n H f (H 2) k = Φ f (H 2), ke nc 2 k 2 ζ nh f (H 2) ke nc cm

7 Chemical s where the cosmic ray ionization rate in diffuse clouds is ζ s 1 (using the value given by Indriolo and McCall, s 1 with a correction on f(h 2 ) = 0.67), the H 3 dissociative recombination rate constants at 70 K is cm 3 s 1 (calculated from the experimental formula by McCall et al. 80 ), and the depleted C/H ratio 81 in diffuse clouds n C /n H = is used. Note that unlike the Langevin rate, the dissociative recombination rate has a temperature dependence of T 0.5. Since the value of ζ is known to vary depending on the proximity to supernova remnants, 72 the H 3 number density calculated above is an approximate average value. The value is about one-tenth of the number density in dense clouds, but since the dimensions of diffuse clouds are 10 larger, the observed column densities in diffuse clouds are comparable to those in dense clouds, a fact which was a surprise when first observed as discussed later in section Just as in dense clouds, n(h 3 ) is a constant and does not scale with the cloud density. Therefore n C k ζ L = 2 ken(h 3 ) f(h 2) Φ f(h 2), nh k nc 2 kn(h ) n f 2 e 3 (H 2) H 5 1 which has been used to determine the values of ζl from observed N(H 3 ). 72 The remarkable independence of n(h 3 ) on the cloud density is shown schematically in Figure Dissociative Recombination of H 3. The dissociative recombination rate constant of H 3, k e, the only laboratory-measured value in the last term of eq 8, is the most crucial molecular parameter governing H 3 chemistry in diffuse 1 (9) clouds. The experimental value has fluctuated by as much as 10 4 over the years and poisoned a generation of chemical model calculations from 1980s to the beginning of 1990s. 79 This confusion has been settled by application of the storage ring method to H 3 by Larsson and colleagues in Theoretical calculations also went through a recent tempestuous period. As late as in 2000, the theoretical value was still more than 2 orders of magnitude different from the current experimental values. This has been remedied since by Kokoouline, Greene, and colleagues, 84 who took into account the Jahn Teller effect as playing the essential role in the H 3 dissociative recombination and obtained theoretical results which agree better with experiments. Subsequently, Jungen and Pratt 85 developed an analytical theory which supported the theory by Greene s group. In the laboratories, excellent agreement was reached between the measurements of Larsson s group at the Manne Siegbahn Laboratory 80 and Wolf s group at the Max-Planck Institute of Nuclear Physics both in energydependent resonant structure 86 and in the absolute cross section. 87 Nevertheless, there still are some discrepancies between theory and experiment in (a) the energy-dependent resonant structure of dissociative recombination 88 and (b) the dependence on o- and p-h Those together with the recent revelation that the rotational temperatures of H 3 in the storage rings are much higher than previously assumed 88 suggest that the rate constant determined by McCall et al. 80 used in the above calculation may need to be adjusted by a factor of a few H 3 : Initiator of Interstellar Chemistry H 3 : Universal Proton Donor, the Interstellar Acid. H 3 plays the central role in interstellar chemistry by donating its extra proton to atoms and molecules with proton affinity more than that of H 2 via the universal reaction in eq 2. Thus, from O, N 2, NO, CO 2,CH 4, CO, OH, C, HCCH, S, C 2, H 2 O, HCN, CH, and NH 3 listed in Table 1, we have molecular ions OH,N 2 H, HNO, HCO 2,CH 5, HCO,H 2 O,CH, C 2 H 3, SH, HC 2, H 3 O, HCNH, CH 2, and NH 4. All reactions with significant exothermicity proceed with high Langevin rate constants k L as shown in Table 1. The molecular ions thus produced are much more chemically active than their parent neutrals and invigorate interstellar chemistry. For example, O and H 2 do not react at the low temperature of interstellar space, but OH and H 2 react vigorously, initiating a chain of hydrogen abstraction reactions, XH n H 2 XH n1 H 2 3 OH H O H O Figure 3. Schematic diagram showing the relation between number densities n(x) of H 2, CO, and H 3 and the number density of the cloud, n(h). Note that n(h 2 ) and n(co) scale with n(h) while n(h 3 ) is independent of n(h) for typically dense and diffuse clouds. Reprinted with permission from ref 82. Copyright 2006 United States National Academy of Sciences. leading to protonated water H 3 O which produces H 2 O and OH upon recombination with electrons. The two hydrogen abstraction reactions proceed with a Langevin rate constant of and cm 3 s 1, 89 respectively. Molecular cations like H 3, H 3 O, NH 4, CH 5, HCO, HN 2, and HCNH which are produced by adding a proton to ordinary molecules H 2,H 2 O, NH 3,CH 4, CO, N 2, and HCN are often called protonated ions as opposed to radical cations which are produced by subtracting an electron, H 2,H 2 O,NH 3,CH 4, CO,N 2, and HCN. 90 The carbon atom, which is not the main form of carbon but still exists in a significant amount in diffuse clouds, is also invigorated by protonation to CH, which leads to a chain of hydrogen abstraction reactions 2 3 CH CH CH 8744

8 Chemical s with Langevin rate constants and cm 3 s 1, but the chain does not reach the final protonated ion CH 5 since the hydrogen abstraction reaction from CH 3 to CH 4 is endothermic by as much as 3.22 ev. Another universal ion producer in interstellar chemistry is He with its highest ionization energy of ev; it ionizes neutral species by charge transfer reaction He X He X which are all exothermic. While H 3 produces ions by adding a proton, He produces ions by subtracting an electron. This reaction is known to proceed with the Langevin rate for all species except for only one case X = H 2. Although all reactions He H2 He H 2 ( 9.16 ev), He H H ( 6.51 ev), HeH H ( 8.36 ev) are highly exothermic, all of them have rate constants several orders of magnitude smaller than the Langevin rate. The first reaction, for example, has a rate constant one million times smaller than the Langevin rate at a low temperature of K. 91 This is also the case for Ne but not for Ar and Xe. Mahan explained the nonreactivity of He and H 2 and the subtle differences among rare gas atoms by considering the correlation between electronic states of the (rare gas H 2 ) system. 92 The nonreactivity has a huge effect on the chemistry of dense clouds since He, produced by cosmic ray with a rate of ζ He s 1, 68 is not destroyed by H 2 and instead mainly leads to dissociative ionization of CO He CO He C O at a Langevin rate of cm 3 s C thus produced initiates a chain of carbon reactions producing organic molecules that are observed abundantly in interstellar space. An example of flow charts for interstellar ion chemistry is shown in Figure Deuterium Fractionation. A remarkable manifestation of the fundamental role H 3 plays in interstellar chemistry is the observed ultrahigh deuterium fractionation in prestellar cores with high density (n 10 6 cm 3 ) and low temperature (T 10 K). Highly deuterated species like ND 3 and CD 3 OH, corresponding to a deuterium fractionation of 10 orders of magnitude from the D/H ratio in interstellar space of , are observable in such regions. The basic mechanism for the deuterium fractionation has been known and understood for many years since the seminal paper by Watson. 62 Roberts et al. 94 has shown that the series of reactions H HD H D H (231.8 K) H D HD HD H (187.2 K) HD HD D H (233.8 K) can lead to an extreme deuterium fractionation of n(d 3 )/ n(h 3 ) 20 corresponding to a fractionation of under the condition T=10 K and n(h 2 ) = cm 3. The numbers in parentheses in the above equations are accurate ab initio theoretical values of the exothemicities 95 due to the lower vibrational zero-point energy of the higher deuterated products. Such small exothermicities as 0.02 ev hardly matter in laboratory plasmas but are huge driving forces with equilibrium constants on the order of exp(200/10) at that Figure 4. Flowchart of the ion chemistry of dense molecular clouds. Chemistry is initiated by cosmic ray ionization of H 2 and He. Hydrocarbon molecules are in the central column, while O- and N- containing molecules are in the left and right columns, respectively. See Smith 93 for more details. Some reactions in this diagram, such as production of CH 3 OH, have since been shown not to work. Reprinted with permission from ref 93. Copyright 1987 Royal Society of Chemistry. temperature. Ultrahigh fractionation does not occur in warmer and less dense clouds because the fractionation process is diluted through destruction of H 3 and its deuterated species by CO, O, O 2, and N 2, which are more abundant than HD, via the proton-hop reaction in eq 2. It occurs only when those species are sufficiently depleted onto dust grains due to the low temperature of the environment so that the number density of HD is comparable to or greater than their combined densities. Since deuterated H 3 is the universal deuteron donor, these clouds exhibit extremely rich deuterium chemistry. Because the dilution is critically dependent on the ratio of the rate of the forward reaction k f n(hd) and those of diluting reactions k CO n(co) k O n(o) k O2 n(o 2 )k N2 n(n 2 ), the value of k f is crucial in this discussion. In the above theory 94 a high Langevin rate constant of cm 3 s 1 was used, while experiments at low temperature give a values 5 times smaller 96,97 (although later measurement by Hugo et al. 98 gives a higher value; see section 4.1.2). This makes a huge difference to the depletion on grains required for gases CO, O, O 2, and N 2 in order to produce an observed high degree of fractionation Effect of o-h 2. A complication in the above mechanism of fractionation arises from the presence of o-h 2 in the J = 1 rotational level which is K above the J =0 level of p-h 2 as considered in a prescient paper by Pagani et 8745

9 Chemical s al. 99 Since the ortho to para J =1 0transition is highly forbidden both radiatively and collisionally, H 2 tends to populate the J=1level in far excess of the thermal equilibrium, another example of kinematically rather than thermodynamically governed chemistry. The excess energy of o-h 2 together with the energy of o-h 2 D in the lowest ortho-rotational level, 1 11, which is higher than the ground para level 0 00 by K 100 will override the exothermicity of K and make the first fractionation reaction slightly endothermic, reverting H 2 D back to H 3 and thus hampering deuteration. This is the case for ordinary dense clouds where n(h 2 ) J=1 > n(hd). The total nuclear spin angular momentum quantum number I for I total = I 1 I 2, which characterizes ortho (I = 1) and para (I =0)H 2,H 2 D s etc.s is not a rigorous quantum number, 101,102 and in principle, the J =1H 2 converts to J =0H 2 by both spontaneous emission 103,104 and collision, 102 but they are far too slow to be of practical interest. Conversion requires proton scrambling reaction either with H or with H o H H (H )* p H H o H H (H )* p H H where (H 3 )* and (H 5 )* are reaction intermediates in which proton scrambles to convert spin isomers. The first reaction is theoretically tractable 105,106 but difficult to study experimentally, while the opposite is the case for the second reaction. Using infrared spectral lines of o-h 3 with (J, K) = (1,0) and p- H 3 with (1,1), Uy et al., 107 Cordonnier et al., 108 and Crabtree et al. 109,110 studied the second reaction which is composed of proton-hop and proton-exchange reactions and determined their ratio. Theoretical spin selection rules 111 and statistical rate calculations 112 are used in their analyses. Since both H and H 3 are not very abundant in interstellar space, conversion of o-h 2 to p-h 2 takes a long time before the concentration of o-h 2 gets comparable to or smaller than that of HD. Pagani et al. 113,114 studied the effect of o-h 2 on deuterium fractionation systematically and estimated the time of ortho to para conversion to be on the order of several million years. Completion of conversion is shown by the growth of deuterated ions, typically DCO. They proposed that the appearance of DCO sets the upper limit on the age of starless molecular clouds. 3. SPECTROSCOPY OF H 3 Since H 3 in singlet electronic excites states are all predissociated, no sharp electronic spectrum is expected in the visible or ultraviolet region. The permanent electric dipole moment of H 3 does not exist due to its equilateral triangle structure (D 3h ), and hence, no rotational spectrum is expected. The only fully allowed transition is the infrared-active ν 2 vibration rotation band with the band origin at cm 1, discussed below in section 3.1. The only exception is the forbidden rotational transition induced by spontaneous breakdown of symmetry, to be discussed in section 3.2. Although these transitions are yet to be observed in the laboratory, we know their properties accurately from very accurate ab initio theory. The partially deuterated species H 2 D and HD 2 have effective permanent dipole moments because the D 3h symmetry is broken by deuterium substitution. Their rotational spectra are observable in the submillimeter region and discussed briefly in section Infrared Vibration Rotation Spectrum of H ν 2 Fundamental Band. H 3 has 3 normal modes of vibration shown in Figure 5 the totally symmetric ν 1 mode Figure 5. Three normal modes of vibration of H 3. Totally symmetric ν 1 mode ( cm 1 ) is infrared inactive, while the two degenerate ν 2 modes ( cm 1 ) are active. Linear combinations of the degenerate modes x ± iy = re ±φ produces a quantized vibrational angular momentum. and two degenerate ν 2 modes. The ν 1 mode is infrared inactive and therefore not observable. The doubly degenerate ν 2 vibration is infrared active with a large transition dipole moment of D. 27 The X 3 -type molecule is unique among nonlinear molecules in having only one pair of degenerate modes, which generates unit vibrational angular momentum (ζ 2 = 1). 115 The energy levels of H 3 are specified by two rotational quantum numbers J and K for the ground vibrational state. While J is positive, K is either positive or negative depending on whether H 3 is rotating clockwise or counterclockwise around the C 3 symmetry axis. If this distinction is necessary the signed quantum number k is used. There are two additional symmetry labels, the parity which is determined by ( 1) K, and ortho (I = 3/2) and para (I =1/2) states where I is the quantum number for the total proton spin angular momentum I total = I 1 I 2 I 3. The three proton spins are lined up in o-h 3, whereas one is antiparallel in p-h 3. Just as ortho and para spin states for H 2 are associated with rotational levels with odd and even J, respectively, the ortho and para spin states of H 3 are associated with rotational levels having K =3n and 3n ± 1, respectively, in order to satisfy the Pauli exclusion principle, that is, the total wave function must change sign upon exchange of two protons (fermions). 116,102 The lowest (J, K) = (0. 0) level and other (J, 0) levels with even J are forbidden by the Pauli principle; just as a spherical 1s orbital cannot accommodate more than two electrons, the totally symmetric rotational levels cannot accommodate three protons. The vibration rotation transitions (left) and low rotational energy levels of H 3 in the ground vibrational state with their rotational quantum numbers and symmetry labels (right) are shown in Figure 6. For the ν 2 excited state an extra quantum number is needed for the vibrational angular momentum, = ±1, in addition to J and K. While the parity is given by ( 1) K as in the ground state, the ortho and para label is given by whether K is a multiple of 3 or not. Therefore, a quantum number G K is used for convenience. For the ground state in which =0,G = K. The pair of levels (J, K 1, = 1) and (J, K 1, = 1) with identical J, G, and parity and hence with identical symmetry mix significantly. There is no quantum label to discriminate the two mixed levels; u and l are used to specify the upper and lower levels, respectively. A rotational level in the ν 2 state is uniquely 8746

10 Chemical s Figure 6. Vibration rotation transitions of the ν 2 fundamental band of H 3 (left) and the low-lying rotational levels of H 3 in the ground vibrational state (right). The latter shows the ortho (I = 3/2 red) and para (I = 1/2 blue) spin modifications and the parity and. Thin arrows indicate spontaneous emissions due to forbidden rotational transitions discussed in section Because of these rapid spontaneous emissions interstellar H 3 are populated mostly in the 4 levels (1,1), (1,0), (2,2), and (3,3). (Left) Reprinted with permission from ref 117. Copyright 2008 American Astronomical Society. (Right) Reprinted with permission from ref 118. Copyright 2011 Royal Society of Chemistry. specified by J, G, and u or l, and the useful symmetry labels are parity, which is given by ( 1) G 1 and ortho and para spin states for G =3n and 3n ± 1, respectively. For G = 0 and G>J1 the pair of levels does not exist and u and l labels are not necessary. The selection rules for the ν transition are Δ J = 0or± 1andΔ G = 0 which automatically satisfy the parity rule and spin rule ΔI = 0, i.e., ortho ortho and para para. The labels u and l do no specify symmetry and therefore do no appear in the selection rules. The ν vibration rotation transitions are designated R(1,1) l, Q(1,0), etc., which correspond to (ν 2 J =2 G=1l) (0 J =1K=1) and (ν 2 J =1G=0) (0 J=1, K = 0), respectively. Readers are referred to Herzberg Vol. II 119 and Landau and Lifshitz Vol for more general discussions on quantum numbers, symmetry, selection rules, etc., and to McCall s thesis 121 for H 3 in particular. A stick diagram of the ν 2 fundamental band of H 3 observed in is shown in Figure 7. Unlike in an ordinary vibration rotation spectrum, Figure 7 shows no obvious regularity or symmetry. This is because the usual method of expressing energy levels in terms of polynomials of quantum numbers does not work due to the small mass of H 3 and thus the relatively large Born Oppenheimer constant; the traditional perturbation treatment (e.g., ref 123) does not converge well. Figure 7. Stick diagram of the observed ν 2 vibration rotation band of H 3 with intensities calculated for the rotational temperature of 200 K. Lines used for astronomical observations are marked with asterisks and their assignments. Reprinted with permission from ref 122. Copyright 1980 American Physical Society. The most characteristic feature of this spectrum is the absence of lines over a wide frequency range, from 2570 to 2690 cm 1, due to the missing (0,0) level required by the Pauli principle. Spectral lines with relatively low J and K useful for astronomical observations are indicated in Figure 7. The details of the lines so far used in observations along with others that may be useful in the future are given in Table 2. The P-branch lines are strongly interfered by CO 2 in the atmosphere and are not included in the table. The spectral strength μ 2 is useful to 8747

11 Chemical s Table 2. Spectral Lines Useful for Observing Interstellar H 3 transitions a ν (cm 1 ) b λ (μm) μ 2 (D 2 ) c interference d ν 2 0 Q(1,0) Q(1,1) *R(1,1) l *R(1,0) *R(1,1) u *R(2,2) l R(2,1) l R(2,2) u R(2,1) u *R(3,3) l R(4,4) l R(3,3) u R(5,5) l R(6,6) l ν 2 0 t R(6,6) t R(5,5) t R(4,4) t R(3,3) t R(2,2) t R(1,1) a Transitions marked with asterisks are those most often used for spectroscopy of interstellar H 3. b Frequencies are from the compilation by Lindsay and McCall. 124 c Transition strengths in Debye 2 are calculated from the Einstein coefficients given by Neale, Miller, and Tennyson. 125 d Degree of atmospheric interference in an arbitrary scale from 0 (nearly transparent) to 10 (almost completely opaque) based on the Infrared Atlas by Hinkle et al. 126 calculate the H 3 column density N(H 3 ) lev in the lower rotational level from the observed equivalent width W λ = [ΔI(λ)/I]dλ from 3 2 N(H 3 ) level = (3 hc/8 π )( Wλ / λ)/ μ 18 2 = ( Wλ / λ)/ μ (10) where μ 2 is in Debye 2 and N(H 3 ) level is in cm 2. A major problem of ground-based astronomical infrared spectroscopy is the atmospheric interference. Subjective degrees of interference in arbitrary scale are included in the table. They would be irrelevant if an airborne high-resolution spectrometer is available in the future Overtone and Combination Bands and Rigorous Theory. After the 1980 observation of the ν 2 fundamental band with the band origin at 4 μm, overtone and combination bands were observed providing information on the vibration rotation states with increasingly higher energies. Results to wavelengths as short as 1 μm are compiled by Lindsay and McCall. 124 Subsequently, spectroscopy reached the long wavelength edge of the visible region 127 and is now deep in the visible. 128 As spectroscopy reaches more highly excited states spectral intensities are reduced. Spectral lines involving levels with the highest energies currently observed, cm 1, are weaker than the fundamental band lines by more than 6 orders of magnitude. Such faint lines have no direct application in astrochemistry. Nevertheless, the quantum mechanics of H 3 developed to understand the highly excited states are very important to accurately characterize other quantum effects of H 3 with applications to astrochemistry such as the forbidden transitions discussed in section Since H 3 is the simplest polyatomic molecule with only two electrons, a great many quantum chemical papers have been devoted to obtaining its potential energy surface (PES) and reproduce the observed spectrum since the classic paper by Carney and Porter. 27 After 1975 when the ab initio theory by Kołos and Wolniewicz 129 gave the dissociation energy and rovibrational energies of H 2, HD, and D 2 to spectroscopic accuracy, that is within a fraction of a cm 1 of experimental values observed by Herzberg and colleagues, 130 the rovibrational energy of H 3 has been the benchmark for truly rigorous ab initio theory. Variational treatment of its protons by Tennyson and Sutcliffe 131 played the leading role in this development with increasingly accurate PES by Meyer, Botschwina, and Burton, 132 Kutzelnigg and colleagues, 133 and Pavanello and Adamowicz et al. 134 The most recent theoretical data agree with experiments within a fraction of cm 1 up to the energy observed, cm A detailed review of this amazing development is beyond the scope of this paper, and readers are referred to the 3 special issues of the Philosophical Transactions on H For applications to astrochemistry the tour de force calculation of 3 million transitions by Neale, Miller, and Tennyson in suffices. The only H 3 spectrum other than the fundamental band observed in space has been the intense emission of the first overtone 2ν band observed from Jupiter. 136,137,12 The transition dipole moment of the band is D, 27 and the strength of the transition μ 2 is 5.4 times smaller than the fundamental band but the ν 3 factor in the Einstein coefficient more than compensates and the spontaneous emission of the overtone band is faster than the fundamental band. This band in absorption may be useful for detecting interstellar H 3 high J and K levels because of the relatively lower atmospheric interference in the K infrared window than in the L one. The overtone band is included in Table 2 for this reason. The v 2 = 2 state is 3-fold corresponding to = ±2 and 0. The 2v transition is forbidden since both upper and lower state are totally symmetric (A 1 ) and only the 2v 2 2 (E ) 0 transition is allowed. The selection rules are Δ J = 0or± 1andΔ G = 3 The latter results from Δ = ±2 and Δk =±1. Just as for the selection rules for the fundamental band, they automatically satisfy the parity rule and spin rule ΔI = 0. The variation of G by three is expressed by t as in Table 2 (r, s, t for 1, 2, 3) Rotational Transitions Although H 3 does not have a permanent electric dipole moment and hence has no rotational spectrum because of its equilateral triangle equilibrium structure, breakdown of the symmetry by vibration rotation interaction or partial deuteration produces a dipole moment and rotational transitions. Both of them play important roles in astronomical observations Forbidden Rotational Transitions of H 3. The spontaneous symmetry breaking (SSB) is a general phenomenon which occurs widely in various fields of physics. The essence is that even under symmetric physical law, that is, a symmetric Hamiltonian, the symmetry of states may be broken. According to Nambu, 138 This is because the symmetry of a Lagrangian, or an equation of motion, and symmetry of states are two entirely different things. The latter may be a member of a multiplet which as a whole represents the symmetry. This 8748

12 Chemical s phenomenon dominates the field of high-energy physics of an infinite system in a most profound way. In molecular physics it appears as breaking of finite symmetry. There are countless examples of breaking 2-fold symmetry. A well-known means of breakdown of 3-fold symmetry is by the Jahn Teller effect, 139 which results from the interaction between degenerated electronic and vibrational states. The SSB of rotational levels of H 3 occurs similarly through interaction between the vibrational and the rotational motion. Consider H 3 rotates rapidly around an axis in the plane of the molecule passing the apex proton 1 and bisecting the bases formed by protons 2 and 3. The centrifugal force breaks the symmetry of the molecule from D 3h to C 2v, produces a small dipole moment on the order of mdebye, and hence enables rotational transitions as theoretically formulated by Watson. 140 In order to satisfy the parity changing ( ) and spin conserving (ΔI = 0) rules, the selection rule has to be Δ J = 0or± 1andΔ k = ± 3 These types of transitions are very weakly allowed. Their spontaneous emission is negligible in the laboratory but in interstellar space where a molecule remains in a rotational level for years such forbidden transitions is of primary importance in determining the rotational distribution of molecules. The effect of this type of forbidden transition was first studied for interstellar NH 3, where the lifetimes of spontaneous emissions (2,2) (1,1) (more accurately, they should be written (2,±2) (1, 1)) and (3,3) (2,0) were calculated to be 232 years and 43.3 years, respectively. 141 These rates of decay are slower than collision rates in dense clouds by 1 2 orders of magnitude, and thus, the forbidden transitions do not seriously affect thermalization of NH 3 in dense clouds. However, the Einstein coefficient of this type of spontaneous emission is approximately proportional to B 6, and the lighter H 3 (B = 43.6 cm 1 ) decays more rapidly than NH 3 (B = 9.94 cm 1 ) by several orders of magnitude. 142 The spontaneous emission lifetime of the (2,2) (1,1) transition is 27.2 days, 125,143 corresponding to the critical density the density at which transitions by collisions are competitive to spontaneous emission on the order of 200 cm 3 (estimated by dividing the Einstein coefficient by the Langevin rate constant of cm 3 s 1 ). This critical density is comparable to densities in diffuse clouds, and hence, the effect of the forbidden transition is critical for calculation of the rotational distribution of H 3 in diffuse clouds (see section 4.1.3). The frequencies and Einstein coefficients of other forbidden rotational transitions are listed in ref 143. Because of the ν 3 factor, the spontaneous emission rates increase rapidly for higher rotational levels. For example, the lifetimes of transitions (3,0) (3,3), (3,1) (2,2), and (3,2) (2,1) are 3.8, 7.9, and 16 h, respectively, which are practically instantaneous compared to the collision scale in diffuse clouds. All H 3 in high rotational levels cascade via these spontaneous emissions to lower levels in diffuse clouds, and only molecules in the lowest para-(1,1), the lowest ortho-(1,0), and metastable (3,3) have been observable so far. H 3 in the metastable (3,3) level, which plays a crucial role in several aspects of the H 3 astronomy (section 4.3.1), cannot decay since the possible ΔJ = 1 transition like (3,3) (2,1) is forbidden by the ortho para rule and the ΔJ = 2 transition requires two-photon transitions. Both of them take longer than the age of the Universe. In some clouds that are warm and denser than diffuse clouds, absorption from the (2,2) level has been observed, and the (2,1) level is possibly also observable in them. If in the future hotter clouds are found, higher metastable levels of H 3 such as (4,4), (5,5), and (6,6) may be detectable. In the ionospheres of the outer planets H 3 in many other levels have been observed because of the high temperature (as much as 1000 K) and high density (>10 10 cm 3 ) H 2 D and HD 2 (D 3 ). Although H 3 does not have a permanent electric dipole moment, its partially deuterated species has an effective dipole moment since their center of mass is shifted from the center of charge. This type of dipole moment and its associated rotational spectrum was initially conceived by Teller for HD (Herzberg, private communication) and later applied to H 2 D and HD The magnitude of the effective dipole moment is μ a = 0.61 D for H 2 D and μ b = 0.49 D for HD 2. Both dipole moments are aligned along the C 2 axis of the C 2v symmetry, but that axis is associated with the smallest moment of inertia in H 2 D (hence the a axis) and with the second smallest moment of inertia in HD 2 (hence the b axis). With such large dipole moments spontaneous emissions are rapid and most molecules are in the ground para-0 00 (I H = 0) level or the lowest ortho-1 11 level (I H = 1) with energy K for H 2 D and the ground ortho-0 00 level (I D = 2, 0) or lowest para-1 01 level (I D = 1) with energy K for HD 2. The swap of ortho and para spin states for the ground 0 00 level is due to the antisymmetric and symmetric requirement for the proton (fermion) and deuteron (boson). Therefore, the observable rotational transitions are mostly limited to a-type transitions of H 2 D, the line at GHz of p-h 2 D, and the line at GHz and line at GHz of o-h 2 D, and b-type transitions of HD 2, the line at GHz of o-hd 2 and the line at GHz and the line of p HD 2 which is yet to be measured in the laboratory. Transitions between higher rotational levels may be observed in warm and dense clouds in the future. Laboratory frequencies for such transitions have been measured by Amano and coworkers. 145,100 D 3, like H 3, does not have an electric dipole moment, and its detection in interstellar gas also can only be via its infrared rovibrational spectrum. 146 Because of the larger mass the transition strength of the D 3 spectrum is smaller than that of the H 3 spectrum by a factor of 2. The ortho (I = 3 and 0 and a part of I=1) to para (I=2and a part of I=1) ratio is 11 to 16. There are two problems, both very serious, for observing the infrared spectrum of D 3. (1) The observation is limited to the cold and dense region where the deuterium fractionation discussed in section is extremely high. However, bright infrared stars do not exist in such sightlines. (2) The band origin of the ν 2 fundamental band of D 3 is at cm 1 in a spectral region severely attenuated by atmospheric H 2 O. 4. H 3 AS AN ASTROPHYSICAL PROBE Since H 3 is ubiquitous in an environment that contains H 2 (section 2), the infrared absorption spectrum of H 3 serves as the most general and universal astrophysical probe. It probes both dense and diffuse regions. The only limitation, a serious one, is that it is observable only toward bright infrared stars with smooth continuum. Nevertheless, observations of H 3 can be conducted toward a great many stars and provide several key astrophysical data that cannot be obtained by other astrophysical probes. 8749

13 Chemical s 4.1. What We Learn from H 3 Observation CO versus H 3 as Astrophysical Probes. In many ways CO and H 3 are complementary. After H 2, CO is the most abundant molecule in dense clouds. The abundance of CO is the result of its stability due to the high dissociation energy of 11.1 ev, the highest in Table 1, and hence its longevity. Once produced, CO stays there for a long time, until it encounters ions like H 3,HN 2, and He (section 2.4.2), which are all not that abundant. H 3 is produced much more rapidly than CO, but its steady state concentration is low because of its high chemical activity. It is destroyed by practically all atoms and molecules except He, H, and N (section 2.1.2) and very rapidly by electrons (section 2.3.3). CO is mostly in dense clouds, whereas H 3 exists both in dense and in diffuse clouds. Therefore, by observing infrared absorption lines of both CO and H 3 one can discriminate H 3 in dense clouds and H 3 in diffuse clouds. This is particularly useful in the observational studies of the Galactic center (section 4.3) where the long sightlines cross foreground spiral arms. As discussed in section 2.3.1, the number density of CO is proportional to the cloud density and therefore its column density provides information on the mass of clouds whereas the number density of H 3 is constant as long as it is in typical dense or diffuse clouds and its column density provides information on the length of the cloud. The millimeter wave emissions of CO for the J =1 0, 2 1, 3 2, and higher transitions have been the most powerful astrophysical probes because of their ubiquity, strength due to the high abundance of CO, relatively slow spontaneous emission, and ease of observation. Compared with them the infrared absorption of H 3 has a few serious drawbacks: the limitation by the availability of stars, atmospheric interference, and difficulty of observations. Nevertheless, H 3 can provide important astrophysical information which CO either cannot provide or cannot as reliably. The value of H 3 as an astrophysical probe is discussed in the following subsections, and its applications to various astronomical objects are discussed later H 3 as Thermometer and Densitometer (Cold Clouds). Any atomic or molecular probe with more than one level is potentially capable of providing information on the temperature T of the environment. If more than 2 levels are observable, information on the density n may also be obtained. From the observed relative intensities for a pair of levels one obtains a relative column density and an excitation temperature T ex. Analysis of more than one T ex taking into account of both radiative and collisional effects may provide T and n. There are few molecules for which more than two levels are observable that provide meaningful density constraints. The millimeter wave emissions of CS, HCN, HCO, etc., which have large dipole moments (1.958, 2.985, and 3.30 D, respectively), have lifetimes of 6.6 days, 11.5 h, and 9.3 h against the J=1 0 spontaneous emission corresponding to critical densities 147,148 on the order of from 10 4 to cm 3. Since the rate of spontaneous emission and the critical density are proportional to J 4 /(2J 1), the critical densities increase rapidly with J. Therefore, emissions of those molecules probe relatively high density regions. CO with its anomalously small dipole moments of D can serve as a more general probe because of slower spontaneous emission with a lifetime of 162, 16.1, and 4.5 days for the J=1 0, 2 1, and 3 2 emissions, respectively, and critical densities on the order of from 300 to cm 3 depending on the temperature. Thus, CO emission can serve as a probe to determine T and n for dense clouds with relatively low to high density. 149 NH 3 is unique because its inversion spectrum appears in the centimeter wave region regardless of J and K and allows measurements of the column densities of hot rotational levels. The high abundance of CO which makes extensive observations of its emission possible introduces difficulty in its analysis. The difficulties are 2-fold. First, in general it is difficult to determine the column density from the intensity of the emission spectrum because the effects of collision, which are often not accurately known, need to be taken into account. Reliable column densities are more directly measured from the equivalent widths (integrated intensities) of the weak infrared absorption spectrum, for which the effects of collisions are unimportant as long as the lines are not badly saturated. Second, the high optical depth of CO emission is difficult to assess. Radiative transfer in such medium, including the radiation trapping, is a complicated problem and hard to treat reliably. The method of large velocity gradient developed by Goldreich and Kwan 150 and Scoville and Solomon 151 is used, but the resultant column densities have high uncertainties. T ex determined from such column densities is not very accurate. Infrared absorption lines of H 3 are much weaker and harder to observe than the CO emission but once observed give reliable column densities by a straightforward analysis by eq 10. The accuracy of the column density is limited only by the signal-to-noise ratio of the observed spectral lines which for relatively strong lines is on the order of 10. For the lowtemperature dense and diffuse clouds in the Galactic disk, only the lowest para-(1,1) level and the ortho-(1,0) level are populated. The ratio of their column densities gives an excitation temperature from the formula N(1, 0) 32.86K = 2exp N(1, 1) T ex where K is the energy separation between the (1,0) and the (1,1) levels. Unlike in neutral molecules like H 2 or NH 3 where the ortho para conversion takes millions of years to equilibrate, the ortho para conversion of H 3 occurs rapidly by the reaction (11) H H (H )* H H which was discussed earlier in section as one of the two main mechanisms to thermalize o- and p-h 2. This reaction, the simplest involving polyatomic molecules, has been studied experimentally and theoretically. 111,112 In dense clouds where the lifetime of H 3 is on the order of 10 years, the reaction occurs 1000 times during the life of H 3 using the rate constant of cm 3 s 1 obtained from measurement of deuterated species by Gerlich et al. 96,97 o-h 3 and p-h 3 are well thermalized, and thus, T = T k = T ex where T k is the kinetic temperature. For diffuse clouds where the lifetime of H 3 is also 10 years, the reaction occurs on the order of 10 times; whether the ortho para H 3 thermalizes is less certain but probable. Here again the small rate constant of the deuterated version of this reaction measured by Gerlich 96,97 discussed in sections and is crucial. If correct T = T ex is more uncertain, whereas the more recent larger value by Hugo et al. 98 makes thermalization more certain. 152 In typical cold clouds only the above two levels are observed, and hence, the densities of such clouds cannot be determined from H

14 Chemical s H 3 as Thermometer and Densitometer (Warm Clouds). It has been found during the study of the gas near the Galactic center that the infrared spectrum of H 3 is a very powerful probe for measuring T and n of warm clouds. In the warm gas near the Galactic center, the metastable (3,3) level, 361 K above the lowest (1,1) level (Figure 7), is well populated. 153 Since H 3 in this level is transferred to other levels only via collision-induced transitions, a detectable population in that level is a sure sign of high kinetic temperature. Thus, H 3 in the (3,3) metastable level acts as a thermometer. On the other hand, H 3 in the (2,2) unstable level acts as a densitometer. The lifetime of 27.2 days for the (2,2) (1,1) spontaneous emission corresponds to a critical density on the order of A/k L 200 cm 3 where the Langevin rate constant of k L = cm 3 s 1 is used for a rough estimate. This value may be an underestimate by a factor of a few because of the uncertainty of collision cross section, but in any case, it is on the order of the densities of diffuse clouds, and thus, the population in the (2,2) level is sensitive to their number densities. In diffuse clouds in the Central Molecular Zone (CMZ) at the Galactic center (section 4.3.1), where the temperature is high enough that the (2,2) level would be significantly populated in LTE, absorption lines starting from that level are generally not observable, indicating a small population in it and a huge population inversion between the (3,3) and the (2,2) levels. 154 This is a sure sign that the number density of the cloud is very much lower than the critical density. The combination shown in Figure 6 of the high-lying metastable (3,3) level and the lower (2,2) level with the life of 27 days forms an ideal probe to measure the temperature and density of the warm and diffuse gas, a vast amount of which has been unexpectedly revealed in the CMZ 155 (section 4.3.1). A model calculation of the rotational distribution 143 of H 3 as a function of T and n allows more quantitative discussions. Because of the rapid spontaneous emission via forbidden rotational transitions, the rotational distribution in diffuse clouds is far from the thermal Boltzmannian distribution. The distribution is a result of a subtle balance of the spontaneous emission and collision-induced rotational transitions between H 3 and H 2 (eq 11), H, and He. The spontaneous decay is very accurately known (section 3.2.1), but little information is available for the collisional rates other than that they are on the order of the Langevin rate and from estimates based on the statistical treatment by Park and Light. 112 Therefore, while T is determined with fair accuracy (with an uncertainty of ±50 K), n can be off by a factor of a few. In order to be applicable to many observations the number of parameters in the model 143 is minimized at the cost of introducing larger error. It is well known that the nuclear spin states follow selection rules 111 in the collision between H 3 and H 2 (eq 11), but those rules are ignored since the extra parameter of ortho to para ratio of H 2 complicates analysis. The neglect is justified for para-rich H 2 of diffuse clouds since the higher para to para collision-induced transitions tend to be overwhelmed by the fast spontaneous emission. The guiding principle in dealing with the collision is Boltzmann s principle of detailed balancing, 155 and some other rules (e.g., Fermi s golden rule) are sacrificed. Application to the diffuse gas in the CMZ is discussed in section H 3 as Tracer for the Cosmic-Ray Ionization Rate. Observations of H 3 can provide information on the ionization rate of interstellar H 2 that neutral molecules like CO do not provide. The degree of ionization of the gas is an important astrophysical quantity which affects star formation, heating of the gas, magnetohydrodynamics of interstellar space, etc. As discussed in section 2.2.2, the cosmic ray ionization is the most effective and universal ionization process. The most important role of H 3 as an astrophysical probe is in providing in situ information on the flux of low-energy cosmic rays, those with energies from 1 to 100 MeV. Together with γ-rays which act as an in situ probe of high-energy cosmic rays with energies 1 GeV, H 3 will greatly contribute to the understanding of the mystery of cosmic rays. This interplay between astrochemistry of H 3 and high-energy particle astrophysics is an exciting recent development. 37 Measurement of low-energy cosmic rays is particularly useful since these cosmic rays are deflected by the solar magnetic field and thus are not directly observable. H 3 is by far the most reliable probe to measure low-energy cosmic rays. As discussed in section 2.3, the simple chemistry of its production and destruction allows us to express the product of the ionization rate ζ and the path length L in simple forms for both dense (eq 7) and diffuse (eq 9) clouds. Prior to the advent of H 3 spectroscopy, production and destruction of H were used as a probe for cosmic rays. However, since H is not directly observable, its spectroscopic surrogates OH or HD were used. 156 The chemistry linking H to these molecules is complicated and has been estimated by numerical calculation rather than analytical formulas such as eqs 7 and 9. More seriously, destruction of H by radiative recombination is very slow, and other destruction mechanisms such as grain neutralization have to be taken into account. 157 The chemistry of H 3 is clean, particularly in diffuse clouds since dissociative recombination is more than 3 orders of magnitude faster than radiative recombination and no other competing processes complicate the calculation. The advent of H 3 as an astrophysical probe has drastically changed the understanding of the spectrum of low-energy cosmic rays. Since the lower limit of ζ s 1 given by Spitzer and Tomasko, 69 values of ζ of a few to several times s 1 have been used for over 30 years both observationally 156,158 and theoretically. 159 Readers are referred to Dalgarno s review 160 for details. Starting from the surprising discovery of strong H 3 signals in diffuse clouds toward Cygnus OB2 No. 12, 161,162 systematic studies by McCall and others of H 3 in dense clouds 163 and diffuse clouds 164 have revealed the surprising fact that the column densities of H 3 in diffuse clouds are comparable to those in dense clouds, in spite of the reddening E(B V) and visual extinction A V being 10 times smaller (Figure 8). 121,82,165 Since the latter are proportional to the column density of hydrogen N H, the H 3 /H ratio is 10 times higher in diffuse clouds than in dense clouds. In retrospect, these results together with the simple analysis given in sections and were sufficient to conclude that the ionization rate ζ in diffuse clouds is 10 times higher than in dense clouds, that is, a few to several times s 1, but this was first mentioned explicitly in 2003 by McCall et al. 166 after the discovery of H 3 toward ζ Persei. This conclusion has since been firmly established by observations toward many more sightlines 167,72 as discussed later in section The lower ionization rate in dense clouds is most simply explained as due to the presence of a previously unsuspected large population of 1 10 MeV cosmic rays, which are attenuated near the surfaces of dense clouds but penetrate diffuse clouds. 168 The column densities of H 3 toward the diffuse gas in the Galactic center are over an order of magnitude higher than toward other diffuse cloud sightlines in the Galactic disk 162,

15 Chemical s The number density of electrons n e produced by ionization ζ can be estimated equating the production and destruction rates of electrons Figure 8. Observed H 3 column densities N(H 3 ) versus color excess E(B V) for dense (upper) and diffuse clouds (lower). 121,82 Note that the two categories of clouds have comparable N(H 3 ), although their E(B V) are different by an order of magnitude. Reprinted with permission from ref 82. Copyright 2006 United States National Academy of Sciences. as discussed later in section 4.3. This suggests that the ionization rate in the Galactic center is considerably higher than in diffuse clouds in the Galactic disk. Observations of H 3 have thus revealed the following hierarchy: ζ s 1 for dense clouds, ζ s 1 for diffuse clouds in the Galactic disk, and ζ s 1 in diffuse gas in the Galactic center. 154 The high ionization rate in diffuse clouds initially met with skepticism but now is being accepted. In fact, there now are arguments that these higher ionization rates are not high enough to be in accord with estimates of in situ high-energy cosmic rays inferred from γ-rays and X-rays by Yusef-Zadeh et al. 170 which indicate ζ s 1 and by Becker et al. 170 who estimate ζ s 1, albeit for local environments. The connection between the directly observed high-energy cosmic rays and the low-energy cosmic rays observed via H 3 is an inspiring and difficult problem 171 whose clarification will no doubt increase the understanding of cosmic rays Saturation of the Effect of Ionization. Treatment of the H 3 chemistry described so far indicated that the number density of H 3 is proportional to the ionization rate ζ. This is because ζ entered only in the production of H 3, and its negative effect of destroying H 3 by increasing electron density was ignored. This is a good approximation for low values of ζ up to s 1 for which the electron density produced by ζ is much smaller than the electron density from phoionization of C, which is assumed to be constant and equal to n C.Asζgets higher than s 1 as needed to explain the high observed H 3 column densities toward the Galactic center, the negative effect needs to be taken into account. 1 ζn ζ n(h ) n = k n n k n n 2 (H) (H ) 2 as H 2 e e 3 e e e 2ke (12) where ζ = 2ζ H (section 2.2.2) is used and the positive charges are assumed to end up all in H 3. This latter assumption is clearly not valid for dense clouds where CO, O, O 2,N 2,H 2 O, etc., will deprive H 3 of a proton but is a better approximation for diffuse clouds where we need to examine the effect of high ζ values. Nevertheless, atomic O is still there, and the electron density calculated from eq 12 should be taken as a lower limit. For a typical set of values, ζ =10 15 s 1, n H = 100 cm 3, and k e =10 7 cm 3 s 1, eq 5 gives n e cm 3, which is 5% of n C. Since this is a lower limit, we see that the effect of n e is already beginning to be significant at this ζ value. The electrons produced by ionization of H 2 and H reduce the number density of H 3 in diffuse clouds in two ways. 172,173 First, it will increase the destruction rate of H 3 ; we need to replace n C with n C n e in the first equation of section Because n e depends on ζ this introduces nonlinearity of n(h 3 ) on ζ. Second, as the electron density increases the dissociative recombination of H 2,H 2 e H H gets faster and becomes competitive with the H 3 -producing reaction H 2 H 2 H 3 H. This reduces the effective production rate of H 3 just like the charge exchange reaction discussed in section A model calculation by Liszt 172 has shown that this effect is serious for diffuse clouds with small f(h 2 ) where the nonlinearity on ζ sets in already at the level of ζ s 1. Recent more detailed calculations by Ruaud, Le Petit, and Roueff 174 using an extensive chemical network has shown that production of H 3 not only saturates but also decreases with increasing ζ after certain values. As noted in section by Oka et al. 154 and section 5.3 by Goto et al. 117 we need to be cautious about increasing the value of ζ much beyond s 1. This sets a rough upper limit on ζ and hence a lower limit on the path length L H 3 in the Galactic Disk H 3 in Dense Clouds. After 16 years of searching, 175,176 since laboratory detection, 122 the infrared spectrum of interstellar H 3 was detected in 1996 toward two bright infrared stars with high reddening, GL 2136 and W33A. 44 Installment of a array detector in the CGS4 spectrometer was crucial for these detections, which were made at the United Kingdom Infrared Telescope (UKIRT). Readers are referred to anecdotal stories of the discovery by Geballe 177 and Oka. 178 As shown in Figure 9, the signal-to-noise ratios were not high, but the doublet shape and observed shift by the Earth s motion made detection definitive. The observed total column densities of the two clouds (4.0 ± 0.9) and (6.0 ± 2.2) cm 2 were about the order of magnitude expected from chemical model calculations and provided the most direct evidence for the validity of the ionneutral reaction scheme for production of interstellar molecules initiated by Herbst and Klemperer 60 and by Watson 61 that had been assumed and already used for 23 years. The observed population ratio between the ortho-(1,0) level and the ground para-(1,1) level implied kinetic temperatures of 40 K for both clouds. 8752

16 Chemical s near identical velocity profiles of H 3 and CO at 52, 32, and 5 kms 1 shown in Figure 10 indicate that much of the H 3 Figure 9. First detection of interstellar H 3 at the UKIRT toward two young stars that are deeply embedded in their natal dense molecular clouds. Doublet at and μm are the R(1,1) u and R(1,0) transitions of o- and p-h 3, respectively. Reprinted with permission from ref 44. Copyright 1996 Macmillan Publications Ltd. Subsequently, H 3 has been observed in several dense clouds. 16,43,179,180 The observed column densities, values of ζl calculated from eq 7, cloud lengths L calculated using an assumed value of ζ = s 1, and temperatures are listed in Table 3. The observed column densities are on the order of cm 2, comparable to the column densities used in laboratory spectroscopy. 122 The H 3 number density of 10 4 cm 3 in dense clouds (section 2.3.1) is lower by 15 orders of magnitude than in laboratory plasmas ( cm 3 ), but this is approximately compensated by the large path lengths, on the order of one parsec, compared to the typical laboratory path length of 10 m. The values of ζl, which range from 213 to 45 cm s 1, are reliable, but the separation of ζ and L by assuming a single value of ζ is not accurate since the value of ζ may differ for different clouds. Nevertheless, the values of L in the table, ranging from 0.5 to 2.3 pc, are the range of dimensions expected for dense clouds. The temperatures, ranging from 22 to 47 K also are reasonable. All of the stars listed in Table 3 reside within their natal dense clouds, which have densities on the order of 10 4 cm 3 ; the embedded stars provide radiation for absorption spectroscopy of H 3. There is, however, one significant exception. In the observations of H 3 in the Galactic center, to be discussed in section 4.3, the long sightlines cross three foreground spiral arms, the 3 kpc arm, the 4.5 kpc arm, and the local arm. The Figure 10. R(1,1) l line of H 3 and the R(1) line of the v =2 0 (overtone) band of CO observed toward GCS 3-2. Three deep and sharp absorptions at 52, 32, and 5 kms 1 originate in foreground spiral arms. High abundance of CO indicates molecular clouds, but low reddening of the sightline indicates lower densities than the clouds listed in Table 3. Reprinted with permission from ref 154. Copyright 2005 American Astronomical Society. coexists with CO. The abundant CO demonstrates that the clouds are probably fully molecular, but the low estimated visual extinctions toward the Galactic center of A V < 40 (mag) 181,182 indicate that the number densities are considerably less than 10 4 cm 3. We believe that the clouds in the spiral arms have densities near the lower limit of the permissible range for dense clouds. Because of the constancy of the H 3 number density discussed in section 2.3.1, H 3 abounds in such clouds relative to its abundance in the much denser clouds associated with the stars listed in Table 3. Quantitative studies of the gas in the spiral arms is yet to be done H 2 D and HD 2 in Dense Cloud Cores. The extremely high deuterium fractionation discussed in section makes detection of H 2 D and HD 2 realistic in dense (n 10 6 cm 3 ) and cold (T < 10 K) cloud cores. After a few false detections, the emission at 372 GHz of o-h 2 D was barely detected toward NGC 1333 IRAS 4A in After a Table 3. Observed H 3 Column Densities in the (1,1) and (1,0) Levels, Total H 3 Column Densities, ζl Calculated by Eq 7 (section 2.3.1), Cloud Length L with the Assumed Value of ζ = s 1, and Temperature in Dense Clouds a object N(1,1) (10 14 cm 3 ) N(1,0) (10 14 cm 3 ) N total (10 14 cm 3 ) ζl (cm s 1 ) L (parsec) T (K) ref AFGL W33A Mon R2 IRS AFGL 961E AFGL AFGL LkHα MWC a The H 3 absorption was not detectable toward Orion BN, NGC 2024 IRS 2, Mon R2 IRS 2, AFGL 989, Elias 29, M17 IRS 1, W3 IRS 5, S140 IRS 1, 163 and MWC

17 Chemical s Table 4. Observed H 3 Column Densities (in cm 2 ) in the (1,1) and (1,0) Levels, Total H 3 Column Densities, ζl (in 10 4 cm s 1 ) Calculated by Eq 9 (section 2.3.2), Estimated Cosmic Ray Ionization Rate ζ (in s 1 ), and Excitation Temperature (in K) in Diffuse Clouds object N(1,1) N(1,0) N ζl ζ T ex ref HD HD ζ Per X Per HD HD HD HD WR HD HD HD W40 IRS 1A WR 118(5) WR 118(47) WR HD (7) HD (24) HD Cyg OB Cyg OB HD λ Cep more definitive detection in the prestellar core L1544 in 2003, 184 Caselli et al. 185 detected the emission line in 7 starless cores and 4 protostellar cores. The estimated high column densities of o-h 2 D, ( ) cm 3 and ( ) cm 3 for assumed critical densities of 10 5 cm 3 and 10 6 cm 3, respectively, provide the most direct observational evidence for deuterium fractionation of H 3 discussed in section Since the ortho para conversion through the proton-scrambling reaction, o-h 2 D p-h 2 (H 4 D )* p- H 2 D p-h 2, which is exothermic by K, is forbidden by the nuclear spin selection rules, 97,111 the o-h 2 D in the 1 11 rotational level does not readily convert to p-h 2 D. Reaction with o-h 2 is not spin forbidden, but the population of o-h 2 is low at the reported low kinetic temperatures of 7 15 K. 185 In any case, detection of p-h 2 D through the absorption at GHz is awaited using SOFIA or CCAT, although a sufficiently intense background radiation source at 66 K may not be easy to find behind high-density, lowtemperature cores. The far-infrared detection toward Sgr B2 of the absorption at GHz of o-h 2 D, which yielded an estimated column density of (2 5) cm 2, by Cernicharo et al. 186 is noteworthy. Their estimated density is not that high (a few times cm 3 ), and their estimated kinetic temperature is not that low ( 20 K). Detection must be due in part to the high abundance of H 3 in Sgr B. 187 p-h 2 D in the 0 00 level must be more abundant. p-d 2 H was first detected through its emission at GHz in the prestellar core 16293E by Vastel et al. 188 and later more securely as extended emission in the prestellar core L1688, in Ophiucus, by Parise et al. 189 The observed high column density of D 2 H (comparable to or higher than that of H 2 D ) is partly due to lower separation of the ortho para levels of D 2 H (50.24 K) than that of H 2 D (86.27 K) but demonstrates the efficiency of H 3 deuterium fractionation and also indicates a high degree of CO depletion. Such information is important for understanding the early stages of star formation. Again, observation of much more abundant o- D 2 H by its absorption at GHz is highly desirable, although finding background radiation at K is even more difficult. A search for this transition in emission by the Herschel HIFI instrument was negative as expected. 190 A search for H 2 D and HD 2 toward W 33A via infrared spectra was unsuccessful (T. R. Geballe, private communication) H 3 in Diffuse Clouds. While the H 3 column densities on the order of cm 3 were expected from model calculations in dense clouds, observations of similar column densities in diffuse clouds were surprising (Figure 8). 161,162 In the simple model calculation given in sections and for dense and diffuse clouds, respectively, carbon is all in CO in the former but in C in the latter. Since the rate of dissociative recombination of H 3 is 100 times faster than the rate of proton-hop reactions, the number density of H 3 was expected to be 100 times less in diffuse clouds than in dense clouds if the cosmic ray ionization rate is the same for both clouds. Therefore, even though the column lengths of diffuse clouds are 10 times greater, the expected column densities are 10 times lower, which would hardly be detectable. The unexpected detections of H 3 in diffuse clouds with similar line strengths as in dense clouds has led to the conclusion discussed in section that the cosmic ray ionization rate in diffuse clouds must be an order of magnitude higher than in dense clouds. This has been well established by the extensive work by McCall et al. 164 and Indriolo et al. 167,72 The observed H 3 column densities, N(1,1), N(1,0), N total, ζl, ζ, and T ex in diffuse clouds are listed in Table 4. The values of column densities and ζ are from Indriolo and McCall, 72 and the excitation temperatures T ex are calculated from N(1,1) and 8754

18 Chemical s N(1,0) using the formula in section The values of ζl have been calculated using the last form of eq 9 using the value of the dissociative recombination rate at T = 70 K. The ζl values of diffuse clouds are 2 orders of magnitude higher than those of dense clouds due to factors of 10 higher values for both ζ and L. Separation of ζ and L is difficult but is more tractable than in dense clouds because a variety of observed UV or visible spectra are available. H 2 column densities are known directly from the H 2 UV spectra 191 or can be estimated from spectra of other species such as CH and/or from the directly measured E(B V). The total hydrogen number densities n H have been estimated from analysis of UV spectra of CO. 192 The values of ζ in Table 4 are those published by Indriolo and McCall 72 determined from estimated values of L. Indriolo and McCall neglected the correction given in eq 6; the values in Table 4 should be multiplied by a factor of 1.5 to be consistent with the ζl values of Table 4 (section 2.3.2). The excitation temperature of H 3 of 30 K is considerably lower than the excitation temperature of H 2 of 70 K in the same clouds, which has been thought to give the actual kinetic temperature of the clouds. The difference has been ascribed 152 to incomplete ortho para thermalization of H 3 because of the short lifetime of H 3 due to the rapid dissociative recombination in diffuse clouds. The effect can also be explained as due to fast spontaneous emission as discussed in section (Figure 6 of ref 143) H 3 in the Galactic Center The 1997 discovery of large H 3 column densities, on the order of cm 2, toward two stars, GC IRS 3 and GCS 3-2, by Geballe et al. 162,194 opened up the H 3 studies of the gas in the Central Molecular Zone (CMZ), 195 a region of radius 150 pc, at the Galactic center. The CMZ is a fascinating environment containing a multitude of extraordinary phenomena and objects such as the central supermassive black hole Sgr A*, the three dense clusters of young and hot stars, high densities of stars and supernova remnants, the huge radioarc and nonthermal radiofilaments, and intense and widespread X-ray emission. This center of astrophysical activities has been studied over many years via its radiocontinuum emission, radioemission and absorption lines of HI, OH, H 2 CO, CO, NH 3, HCN, CS, etc., far-infrared emission of atoms and dust, infrared spectrum of CO, X-rays, and γ-rays. 196,195,197,198 Observations of the infrared spectrum of H 3 provide new information unavailable from those observations. The CMZ is a huge region containing both dense and diffuse clouds. The infrared spectrum of H 3 (refs 162, 153, 154, 117, 187, 118, 194, 199, and 200) has proven to be a powerful diagnostic of the diffuse gas in the CMZ due to the simple H 3 chemistry. All observations toward infrared stars from 140 pc to the West of Sgr A* to 120 pc East have shown that the H 3 spectrum is largely formed in diffuse gas, indicating a near 100% surface-filling factor of the diffuse interstellar medium in the CMZ. For example, the H 3 spectra toward the Quintuplet Cluster and other stars between Sgr A* and 30 pc to the East of it (Figure 10 gives an example) indicate a diffuse gaseous environment in the CMZ but little evidence for dense clouds. 117 The large column densities imply that the diffuse gas must have a line of sight extent of tens of parsecs. To date, spectra indicating H 3 in dense clouds in the CMZ have been observed only toward a few stars along sightlines to giant molecular clouds associated with the radiosources Sgr A, B, C, and E. Spectra originating in these compact dense clouds 200 are affected by individual local conditions and difficult to characterize in general. Therefore, the following discussion is mostly limited to observations of H 3 in diffuse gas in the CMZ Revelation of a Vast Amount of Warm and Diffuse Gas. The rotational energy level system of H 3 discussed in section and shown in Figure 6, in which the population of the metastable (3,3) level and of the (2,2) unstable level act as a thermometer and a densitometer, respectively, is custom-made for measuring temperature and density of the warm and diffuse gas in the CMZ. An example of the observed set of the R(1,1) l, R(3,3) l, and R(2,2) l absorptions of H 3 and the R(1) line of the first overtone transition v =2 0 of CO toward the brightest infrared star GCS3-2 is shown in Figure 11. Comparison of the spectra of the two species allows Figure 11. Observed H 3 (top three) and CO absorptions toward GCS 3-2. Three H 3 absorptions are (from the top) the R(1,1) l, R(3,3) l, and R(2,2) l transitions, and the CO absorption is the R(1) transition of the v =2 0 overtone band. Vertical scaling of the R(3,3) l and R(2,2) l absorption is multiplied by a factor of 2, and that of the CO absorption is divided by 2. Reprinted with permission from ref 154. Copyright 2005 American Astronomical Society. one to discriminate between H 3 absorption in the foreground spiral arms and in the CMZ, as shown in Figure 10, but also can indicate dense clouds within the CMZ. Spectra show that most of the CO in this sightline is in the spiral arms and relatively little exists in the CMZ apart from the CO which produces two minor absorptions at velocities of 97 and 82 km s 1. The top trace in Figure 11 is the R(1,1) l absorption by H 3 in the ground (1,1) level. After subtracting the absorption by foreground H 3, which has a nearly identical velocity profile as CO, a broad trough extending from 160 to 20 km s 1 remains. This absorption, which is devoid of sharp velocity 8755

19 Chemical s Figure 12. Spectra of the R(1,1)l absorption of H3 and the four lowest lying transitions of the v = 2 1 overtone band of CO toward 2MASS J (α) (left) and 2MASS J (ι) (right) which are in the region of Sgr E and Sgr B, respectively. Vertical scales of the H3 absorptions are magnified by 4 and 3, respectively, for the purpose of comparison. Arrows indicates absorptions of H3 in diffuse clouds used for the morphological studies. Reprinted with permission from ref 187. Copyright 2010 American Astronomical Society. features, is due to H3 in the diffuse interstellar medium in the CMZ. Its high-velocity dispersion indicates that the gas covers a large distance along the line of sight. The second trace is the R(3,3)l absorption of H3 (magnified by a factor of 2), arising from the metastable (3,3) level, 361 K above the (1,1) level. Unlike the R(1,1)l absorption, this absorption does not contain sharp features, indicating that it is entirely due to H3 in the CMZ. Its overall structure is nearly identical to the trough of the R(1,1)l absorption. The strength of the R(3,3)l absorption clearly indicates that the diffuse gas in the CMZ has a high temperature. This absorption line has been sought in dense and diffuse clouds in the Galactic disk but not surprisingly has not been found, as those diffuse clouds are cold. It is thus a unique fingerprint of the gas in the Galactic center. The third trace is the R(2,2)l absorption of H3, from the unstable (2,2) level, which decays to the ground (1,1) level in 27 days as discussed in section Nondetection of this absorption as seen in Figure 11 demonstrates a nonthermal negative excitation temperature between the (2,2) and the (3,3) levels and clearly indicates that the density of the environments probed by H3 is much less than the critical density of 200 cm 3. The R(2,2)l absorption has so far been observed only in the vicinities of Sgr A117,200 and B.199 It is a fingerprint of dense and warm gas in the CMZ. The model calculation143 discussed in section 4.1.3, together with observed spectra, yields T 250 K and n 100 cm Warm and diffuse gas with similar temperatures and densities (i.e., similar H3 spectra) has also been detected toward 7 other stars, from Sgr A* to 30 pc to the East of it, suggesting its ubiquity and a high volume filling factor.117 Subsequent observations187 toward several more stars from 140 pc West to 85 pc East of Sgr A* have also shown similar gas, suggesting that the warm and diffuse gas fills a large fraction of the CMZ. Previously, three categories of gas had been known in the CMZ:195 (1) dense molecular clouds observed by CO and other radioemissions, (2) hot (T K) and highly ionized diffuse gas observed by recombination lines, FIR atomic lines, radiowave scattering, etc., and (3) ultrahot (T K) X-ray-emitting plasma gas. Observations of H3 have revealed a new category of warm and diffuse gas with a high volume filling factor and drastically changed the previous concept of gas in the CMZ. Prior to the discovery and mapping of H3 in the CMZ, a conceptual picture201 indicated that the ultrahot X-ray emitting gas (3) dominates the CMZ but very likely the newly found warm and diffuse gas has the highest volume filling factor in the CMZ High Ionization Rate in the Central Molecular Zone. According to eq 9 the observed total H3 column density is an in situ indicator of the ionization rate in the environment. In applying this equation to the gas in the CMZ, three further considerations are needed: (1) The increase of metallicity from solar vicinity to the Galactic center increases the carbon to hydrogen ratio nc/nh by R = (nc/nh)gc/(nc/ nh)sv. Since in diffuse clouds the carbon is singly ionized, the destruction rate of H3 via dissociative recombination is increased by the same factor. In a great many papers, increases 8756

20 Chemical s Figure 13. Circular (l, v) diagram obtained from observed H 3 lines in diffuse clouds indicating a nonrotating expanding molecular ring. Longitude (abscissa) is expressed in parsec with Sgr A* at the origin from West (right) to East (left). Velocity (ordinate) is in km s 1. Upper part shows the distribution of stars which have been found as suitable radiation sources for H 3 spectroscopy. Only a fraction of them have been observed so far. Observed half widths at half-maximum of the velocities are plotted by the vertical bars. They represent the front of the expanding gas. Bars with arrow heads continue to low velocities. of metallicity from R to R have been reported. If the idea of direct proportionality between the CO to H 2 conversion factor and the metallicity 204 is assumed, the result of Sodoroski et al. 205 gives R=3 10. The minimum value R 3 is used here to give a lower limit (ζl) min in the following discussion. (2) The temperature-dependent rate constant of the H 3 dissociative recombination 80 is cm 3 s 1 at 250 K and reduces the value of ζl by a factor of a few, which tends to cancel the effect of R discussed above. (3) Unlike in dense clouds where f(h 2 ) = 1 and diffuse clouds where f(h 2 ) 0.67 corresponding to n(h) n(h 2 ) in the Galactic disk, 72 the value of f(h 2 ) is unknown in the Galactic center. Thus far, f(h 2 ) = 1 has been used in the calculations, but the recent Herschel HIFI detections of H 2 O,OH,CH, etc., and their analyses 206 indicated a very low value of f(h 2 ) 0.1 or smaller. Some of these ions coexist with H 3 as manifested by their similar velocity profiles. Such a small value of f(h 2 ) as 0.1 may increase the calculated values of ζl greatly. In terms of the uncertainties of the value, we use the minimum value of R =3 and the maximum value of f(h 2 ) = 1 in the following discussions. Therefore, the values of calculated (ζl) min used in the following discussions are absolute lower limits; the true vales are very likely larger by at least a factor of 2 and possibly by much more than that. The total column densities of N(H 3 ) = ( ) cm 2 observed toward stars from Sgr A* to 30 pc to the East 117 and higher values in the wider region of the CMZ are an order of magnitude higher than those in dense and diffuse clouds in the Galactic disk. This results in high values of (ζl) min = ( ) 10 5 cm s 1, which are higher than the ζl values for dense clouds (Table 3) and diffuse clouds (Table 4) by a factor of 2000 and 15, respectively. Separation of ζ and L is not possible, but we can infer their magnitude from various considerations. As an example, we discuss the average magnitude of (ζl) min = cm s 1. Since the density for the diffuse gas in the Galactic center n 100 cm 3 is lower than that of diffuse gas in the Galactic disk n H 200 cm 3 the fraction f(h 2 ) must be lower. If we use the value of f(h 2 )= 0.67, we have ζl = cm s 1. It is clear that the value of ζ = s 1 for diffuse clouds in the Galactic disk 72 is too small since the corresponding L = 450 pc does not fit in the CMZ. A set of ζ s 1 and L 75 pc is plausible. Actual values of ζ and L are likely higher than these values. From these considerations we believe that the ionization rate in the CMZ is an order of magnitude higher than in diffuse clouds in the Galactic disk and the volume filling factor of the diffuse clouds is very high, perhaps on the order of 50%. The high ionization rates met skepticism, 207 but it is accepted in view of the high densities of supernova remnants in the CMZ. 208 Analyses of γ-rays and X-rays give similar 209 or even higher 169,200 ζ values in the CMZ. For such high ζ values the effect of saturation or decrease of the H 3 density discussed in section should be taken into account. This will have an effect of increasing L Morphology and the Expanding Molecular Ring. The extended and rich velocity profiles of the H 3 absorption lines, as shown in Figure 11, vary in intricate ways depending on the sightline. Figure 12 shows spectra of H 3 and CO toward the star 2MASS J (nicknamed α) located 140 pc West of Sgr A* (right) and toward the star 2MASS J (nicknamed ι, Iota) located 85 pc to the East (left). 187 Star α is in the giant molecular cloud in the direction of Sgr E, and star ι is in the direction of the giant molecular cloud complex Sgr B. Both sightlines cross dense clouds as well as diffuse clouds. H 3 in dense clouds is identified by accompanying deep CO absorptions at the same velocity, while H 3 in diffuse clouds is identified for absorptions (indicated by arrows in Figure. 12) that are not accompanied by CO absorptions at the same velocities. In the spectrum toward α (right), the deep absorption at 60 km s 1 is from molecular clouds in the 3 kpc spiral arm (the other two spiral arms do not contain molecular clouds in this sight line) and the deep absorptions at 200 and 172 km s 1 are due to dense clouds local to Sgr E, the former of which was observed in 13 CO emission by Liszt. 211 In the spectrum toward ι (left), which is located between Sgr B1 and B2 and shows a very rich cloud structure toward Sgr B, a hotbed of any molecular species, the deep and sharp absorptions at 43 and 20 km s 1 are due to the 3 and 4.5 kpc spiral arms, respectively. CO absorption extends without interruption from 100 to 100 km s 1 due to a great many dense clouds with varying radial 8757

21 Chemical s velocities in the region. Spectra originating in compact dense clouds in the CMZ vary rapidly with sightline location, while those originating in diffuse gas change more slowly and provide a larger scale morphological picture of the CMZ. Using the velocity profiles of the infrared R(1,1) l and R(3,3) l absorptions of H 3 in diffuse clouds toward 13 stars plus a far-infrared rotational absorption of H 2 O toward Sgr B2 observed by the Herschel HIFI instrument, 212 one obtains the Galactic longitude velocity (l, v) diagram for diffuse gas shown in Figure 13. We use Sgr A* as the origin of the map and distances from it instead of the Galactic longitude. The distance to the Galactic center is assumed to be 8 kpc for conversion from Galactic longitude to pc. Bright stars tend to cluster, and it is difficult to cover the wide region of the Galactic longitude continuously, but Figure 13 contains strong evidence for the presence of an Expanding Molecular Ring (EMR) with a radius of 140 pc and an expansion velocity of 140 km s 1. The EMR was initially reported by Kaifu et al. 212 and Scoville 213 using radiolines of OH, NH 3,H 2 CO, etc. Sofue 214 identified the structure as an Expanding Molecular Shell using 13 CO emissions observed by Bally et al. 215 The EMR of Figure 13 obtained from diffuse clouds is smaller than those originally reported ( 200 pc) and Sofue s value (170 pc adjusted to a more recent distance to the GC). While those previous (l, v) diagrams are all ellipses, indicating rotational velocities of the ring of km s 1, Figure 13 indicates a circle, suggesting a nonrotating, purely expanding ring. The longitude coverage is still very patchy, but the strongest evidence for this is the nearzero velocities of the diffuse gas observed toward three stars α, α, and β near Sgr E at the West end of Figure 13. Although H 3 has not been observed near the East end yet, it is known that the diffuse gas near Sgr D also has a near-zero velocity. 210 A nonrotational expansion argues against a gravitational origin for the gas energy by the barred potential which predicts an (l v) diagram of a parallelogram 216 and is very unorthodox. If constant velocity of expulsion is assumed, the radius of the ring and the velocity suggest a violent event one million years ago. The energy of expulsion is orders of magnitude lower than the energy estimated by Kaifu et al. ( erg), Scoville ( and erg), and Sofue ( erg) because of the lower density of the gas and lower thickness of the ring. Although the H 3 observations indicate a purely expanding ring, perhaps it is not sufficiently extensive to exclude the possibility of the parallelogram due to the barred potential. 216 The study of the CMZ using the H 3 spectrum is in its infancy. Many more suitable stars are needed to be found and observed. AUTHOR INFORMATION Notes With the richness of the subject covered in this review, the references are meant to be representative rather than exhaustive. The author declares no competing financial interest. Biography Takeshi Oka received his Ph.D. degree from the University of Tokyo on the microwave spectroscopy of H 2 CO. After working as a postdoctoral fellow he became a research staff at the National Research Council of Canada, where the Herzberg Institute of Astrophysics was established in In 1981 he moved to the University of Chicago, where he was jointly appointed to the Department of Chemistry and the Department of Astronomy and Astrophysics and later to the Enrico Fermi Institute. ACKNOWLEDGMENTS I am greatly indebted to T. R. Geballe who has read this manuscript and revised extensively both its science and presentation. I acknowledge useful suggestions on this paper by S. Saito and anonymous referees which considerably improved this paper. REFERENCES (1) Thomson, J. J. Philos. Mag. 1911, 21, 225. (2) Thomson, J. J. Philos. Mag. 1912, 24, 209. (3) Thomson, J. J. Proc. R. Soc. 1913, A89, 1. (4) Thomson, J. J. Nature 1934, 133, 280. (5) Thomson, J. J. Recollections and Reflections; MacMillan: New York, (6) Stark, J. Z. Elektrochem. 1913, 18, 862. (7) Bohr, N. Medd. K. Vetenskapsakad. 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