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Interstellar H3+

Takeshi Oka

Department of Chemistry and Department of Astronomy and Astrophysics, The Enrico Fermi Institute, University of Chicago, 5801South Ellis Avenue, Chicago, Illinois 60637, United States

CONTENTS

1. Historical Sketch 87381.1. Discovery of H3

+ and H3+ versus H3:

Thomson, Stark, Bohr 87381.2. Chemistry of H3

+: Dempster, Hogness,Smyth, McDaniel 8739

1.3. Theory of H3+: Coulson, Hirschfelder, Eyring 8739

1.4. Spectroscopy of H3+ and H3: Herzberg 8740

2. Interstellar Chemistry of H3+ 8740

2.1. Basic Characteristics of Interstellar Chem-istry 8740

2.1.1. Interstellar Chemistry is a Hydrogen-Dominated Chemistry 8740

2.1.2. Interstellar Ion Chemistry is an HonestChemistry 8740

2.1.3. Interstellar Chemistry Is KinematicRather than Thermodynamic 8741

2.2. Production of H3+ 8741

2.2.1. H2 + H2+ → H3

+ + H, the Langevin Rate 87412.2.2. Cosmic Ray Ionization 87422.2.3. Charge Exchange Reaction between H2

+

and H 87422.3. Destruction and Number Density of H3

+ 87432.3.1. Dense Clouds 87432.3.2. Diffuse Clouds 87432.3.3. Dissociative Recombination of H3

+ 87442.4. H3

+: Initiator of Interstellar Chemistry 87442.4.1. H3: Universal Proton Donor, the Inter-

stellar Acid 87442.4.2. Deuterium Fractionation 87452.4.3. Effect of o-H2 8745

3. Spectroscopy of H3+ 8746

3.1. Infrared Vibration−Rotation Spectrum of H3+ 8746

3.1.1. ν2 Fundamental Band 87463.1.2. Overtone and Combination Bands and

Rigorous Theory 87483.2. Rotational Transitions 8748

3.2.1. Forbidden Rotational Transitions of H3+ 8748

3.2.2. H2D+ and HD2

+ (D3+) 8749

4. H3+ as an Astrophysical Probe 8749

4.1. What We Learn from H3+ Observation 8750

4.1.1. CO versus H3+ as Astrophysical Probes 8750

4.1.2. H3+ as Thermometer and Densitometer

(Cold Clouds) 87504.1.3. H3

+ as Thermometer and Densitometer(Warm Clouds) 8751

4.1.4. H3+ as Tracer for the Cosmic-Ray

Ionization Rate 87514.1.5. Saturation of the Effect of Ionization 8752

4.2. H3+ in the Galactic Disk 8752

4.2.1. H3+ in Dense Clouds 8752

4.2.2. H2D+ and HD2

+ in Dense Cloud Cores 87534.2.3. H3

+ in Diffuse Clouds 87544.3. H3

+ in the Galactic Center 87554.3.1. Revelation of a Vast Amount of Warm

and Diffuse Gas 87554.3.2. High Ionization Rate in the Central

Molecular Zone 87564.3.3. Morphology and the Expanding Molec-

ular Ring 8757Author Information 8758

Notes 8758Biography 8758

Acknowledgments 8758References 8758

1. HISTORICAL SKETCHThe history of H3

+ is a succession of inspiring discoveries,grueling hard work, big surprises, and many puzzles andmistakes with their unexpected resolutions. It is a showcase,involving great names, of how science develops slowly and intototally unexpected directions. Most of the work discussed inthis section is laboratory and theoretical, but it is the basis forastronomical studies discussed in later sections.

1.1. Discovery of H3+ and H3

+ versus H3: Thomson, Stark,Bohr

H3+ was discovered by J. J. Thomson in 1911.1 Thomson

(1856−1940) spent most of his laboratory time in the studiesof gaseous discharges. He first studied negatively chargedspecies (cathode rays) and discovered the electron in 1897 andlater studied positively charged species (canal rays) to providebetter understanding on his atomic model. With advances in

Special Issue: 2013 Astrochemistry

Received: May 14, 2013Published: November 6, 2013

Review

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© 2013 American Chemical Society 8738 dx.doi.org/10.1021/cr400266w | Chem. Rev. 2013, 113, 8738−8761

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vacuum technology, his experiments led to early prototypemass spectrometers and H3

+ was the first novel species to bediscovered using them. The tiny spot of H3

+ which appeared inhis plate2 is shown in Figure 1. The spot was not very

reproducible, and he called it “capricious”, “fugitive”, and“evanescent” in papers and monographs. He was furtherpuzzled by the fact that gas evaporated from solids gave morereproducible signals.3 As often happens, a discoverer is also askeptic of his own discovery. Because of his puzzlement,Thomson used “X3” instead of H3

+ or H3− which he had used in

his first two papers. When deuterium was discovered by HaroldUrey in 1932, Thomson published a paper in Nature saying“The evidence seems to me to leave little doubt that the gas Icalled H3 more than twenty years ago is the same as that whichis now called heavy hydrogen”.4 The problem of H3

+ versusHD+ took a few more years to settle, and it is in hisautobiography5 published 26 years after the discovery where hefinally made the clear statement “one of the first things by thephotographic method was the existence of H3

+”. However, hislater remark in the same book “though H3

+ is so evanescent, H3

itself is more durable” indicates he has not understood thechemistry of H3

+.The “stability” of H3 was accepted by many physicists.

Johannes Stark believed in its existence from his ownexperiment6 and proposed a triangular structure of H3.Although his picture (see Figure 486 of ref 6, reproduced inref 9) is close to the equilateral triangle, it was an intuitivepicture not based on theory, one in which the proton is noteven shown as a particle and just a historical curiosity.The first theoretical study on H3

+, H3, and H3− was published

in 1919 by Niels Bohr,7 who published the trilogy8a−c in 1913,part I of which is the famous paper on atomic hydrogen whichinitiated the old quantum mechanics and parts II and III are itsapplications to many electron atoms and molecules, respec-tively. Applying the method of part III to hydrogenic molecules,he predicted that H3 and H3

− had linear structure and werestable and that H3

+ was unstable, all of which were later shownto be false. Readers are referred to papers on the early history ofH3

+ and H3 by historian of science Helge Kragh9,10 and otherreviews.11−13

1.2. Chemistry of H3+: Dempster, Hogness, Smyth,

McDaniel

The true nature of H3+ was revealed by three young American

physicist/chemists who were free from the discoverer’s worrieswhich agonized Thomson for many years; they accepted H3

+

without apprehension. Using a higher pressure (10 mTorr) ofH2 and lower voltage (800 V) for discharge than those used byThomson, Arthur Dempster in Chicago was the first to show in1916 that the amount of H3

+ in the discharge can be higherthan that of H2

+.14,15 From this experiment, he concluded “H3cannot be regarded as a stable gas, since it is not present whenthere is no dissociation of the hydrogen molecules”. Thiscorrect conclusion published in Philosophical Magazine14 musthave been either missed or ignored by Thomson and Bohr.The predominance of H3

+ over H2+ in discharges was further

evidenced by experiments reported in many papers by HenrySmyth (e.g., ref 16), and it was in the 1925 paper by Hognessand Lunn17 of Berkeley where the celebrated ion-neutralreaction, H2

+ + H2 = H3+ + H, appears, which I rewrite for

convenience of this review as

+ → ++ +H H H H2 2 3 (1)

This highly exothermic (1.7 eV) proton-hop reaction with ahigh Langevin rate constant (∼ 2 × 10−9 cm3 s−1) is the mostfrequent reaction in hydrogen-dominated plasmas both inlaboratories and in space. Since H3

+ plays the central role ininterstellar chemistry, this is the most important reaction inastrochemistry. By the 1960s, the predominance of H3

+ overH2

+ in hydrogen plasmas was common knowledge among thespecialists on weakly ionized plasmas. In 1961 three plasmaphysicists from the Georgia Institute of Technology, Martin,McDaniel, and Meeks, wrote in the Astrophysical Journal “Itnow appears desirable to consider the possibilities for detectingH3

+ because this molecular ion may be present under somecircumstances to the virtual exclusion H2

+.”18 Perhaps this wasthe first time H3

+ was mentioned in astronomy. Nevertheless,H3

+ remained a little known exotic species, as there is not aword on it nor even on Thomson’s discovery of it in theauthoritative textbooks on weakly ionized plasmas by von Engel(1955)19 and McDaniel (1964).20

1.3. Theory of H3+: Coulson, Hirschfelder, Eyring

After the advent of quantum mechanics, the clarification ofchemical bond in 1927 by Heitler and London, andintroduction of the idea of molecular orbitals in 1928 byHund and Mulliken, the time was ripe to clarify the quantummechanics of H3

+, the simplest polyatomic molecule. CharlesCoulson in 1935, then a 24 year old graduate student inCambridge, was the first to apply the method of molecularorbitals to H3

+ following a suggestion by his thesis supervisorLennard-Jones. Coulson21 arrived at the equilateral trianglestructure with the equilibrium H−H distance of 0.85 Å (0.88Å), a vibrational frequency of ν1 = 3170 cm−1 (3178 cm−1), anda stabilization energy from H2 + H+, that is, the proton affinityof H2 of 2.0 eV (4.4 eV), where values in parentheses aremodern values.Coulson’s paper, which correctly predicted the equilateral

triangle structure and had other crucial quantities approx-imately right except for the H2 proton affinity, was neverthelessseverely criticized by the Wisconsin group of Hirschfelder andEyring,22 who used the method of Heitler and London andobtained a symmetric linear structure with an H−H distance of1.06 and 0.82 Å depending on the calculational methods and

Figure 1. Two m/e = 3 signals observed by Thomson. Small spot2

shown by the arrow in the left picture, which Thomson called“capricious”, etc., is due to H3

+. 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). Copyright1912 and 1913 Taylor & Francis.

Chemical Reviews Review

dx.doi.org/10.1021/cr400266w | Chem. Rev. 2013, 113, 8738−87618739

the H2 proton affinity of >2.0 eV. They were highly motivatedto clarify the quantum mechanics of H3 and H3

+ and publisheda series of 5 papers from 1936 to 1938. Henry Eyring wasquoted to have said that the problem of H3

+ was “the scandal ofmodern chemistry” since nothing was known about H3

+ otherthan it exists (e.g., see page 75 of ref 11). Toward the end of theseries of papers, Hirschfelder realized that a triangular structurewas more stable and gave molecular constants using the“approximate” equilateral triangle structure with an H−Hdistance of 1.79 Å (0.87 Å), ν1 = 1550 cm−1 (3178 cm−1), ν2 =1100 cm−1 (2522 cm−1)23 but still criticizing Coulson’s theory,while Eyring kept on believing the linear structure until muchlater as indicated by the withdrawal of his name from Parts IVand 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 “Buthe (Coulson) was unable to compute the integrals arising fromthe mutual repulsion of the electrons and make his resultsquantitative”23 must have hit Coulson hard since there isabsolutely no mention of H3

+ in his influential textbookValence24 published in 1952. Instead of quoting his own workon H3

+ which would have been the best demonstration of thepower of the molecular orbital method, Coulson included theincorrect conclusions of the linearity and stability of H3 by theWisconsin group as “accurate work”.With the arrival of the age of numerical calculations using

modern computers, the equilateral triangular structure of H3+

was beyond doubt.25,26 Many theoretical papers followed (see,e.g., ref 11) culminating in the epoch-making classic paper byCarney and Porter in 1976, who used the variational methodand predicted the vibrational frequencies with high accuracy.27

1.4. Spectroscopy of H3+ and H3: Herzberg

Thomson was the first to attempt spectroscopy of H3+/H3;

“Many attempts have been made to obtain spectroscopicevidence of X3 by putting mixtures of this gas and hydrogen in aquartz tube and photographing the spectrum obtained when adischarge was sent through the tube...” (page 122 of his 1913textbbook28). In the 1920s and 1930s numerous physicistsclaimed discovery of visible spectra of H3

+ or H3. Some of theseclaims were quoted by 22 year old Herzberg in his early paperon the spectrum of hydrogen29 (see also ref 11). All of thevisible lines turned out to be transitions between excitedelectronic states of H2 whose spectrum is so rich that a bookcompiling the H2 spectrum was published by Dieke. Theconfusion of spectral lines of excited H2 with those of H3

+ or H3continued even after genuine spectra of H3 and H3

+ werediscovered in 1979 and 1980, respectively.11

It was later determined theoretically that H3+ is unstable in

its electronic excited states except for a barely bound tripletstate,30 and therefore, no sharp electronic spectrum is expected,and the vibrational transition in the infrared is the onlyspectrum to be expected (see ref 11 for more details). Herzbergconsistently sought after the spectrum throughout his life. Hisfirst search in 1941 for infrared emission of H3

+ along with thatof HD+ is noted in his scientific autobiography.31 At the end ofhis presidential address to the Royal Society of Canada in 1967,titled “The spectra of Hydrogen and Their Role in theDevelopment of Our Understanding of the Structure of Matterand of the Universe”, in which he brilliantly summarized thefundamental role hydrogenic species such as H, H−, and H2have 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 dischargethrough hydrogen have not yet been successful, but will beresumed again shortly.”32 With the arrival of commercialinfrared Fourier transform spectrometers, Herzberg continuedto search for the H3

+ emission with H. Lew and J. J. Sloan. In1979 at the age of 74 he stumbled on broad emission spectra ofpredissociated H3 and D3 and opened up a rich field ofpolyatomic Rydberg spectroscopy.33,34 This led to high-resolution spectroscopy of H3, taking advantage of themetastable N = K = 0 level of the 2p 2A2′′ state by Helm35

and Ketterle et al.36 (Recently, Black37 suggested the presenceand possible detectability of H3 in astronomical environments.).However, observation of the infrared spectrum of H3

+ had towait till the advent of tunable laser infrared spectroscopy(section 3).

2. INTERSTELLAR CHEMISTRY OF H3+

H3+ is produced by the reaction H2 + H2

+ → H3+ + H (eq 1) in

which a proton in H2+ hops to molecular hydrogen. In

interstellar space, where cosmic rays capable of ionizing H2 arealways present, H3

+ is ubiquitous as long as H2 abounds. H3+

plays the central role in interstellar chemistry as proton donor(acid) through the proton-hop reaction discussed below.

2.1. Basic Characteristics of Interstellar Chemistry

2.1.1. Interstellar Chemistry is a Hydrogen-Domi-nated Chemistry. This is because 99.9% of atoms in theUniverse are either H (92.1%) or relatively inert He (7.8%) andheavier atoms like C, N, O, etc., which make chemistry so rich,together constitute only 0.1% . There are 6 stable purehydrogenic species H+, H, H−, H2

+, H2, and H3+. Although

hydrogenic cluster ions H3+(H2)n are stable and has been

mentioned in relation to astrochemistry38 they are not expectedto be abundant in interstellar space. Out of the six species, H+,the proton, is not spectroscopically observable. The broadabsorption of the near-infrared by H− causes the opacity of thesun39,40 and stars but does not show discrete spectral lines. H2

+

is not abundant because it is rapidly converted to H3+ by the

reaction in eq 1. This leaves H, H2, and H3+ discovered in

interstellar space in 1951,41,42 1970,43 and 1996,44 respectively,as the three pure hydrogenic species that are observable. H2 andH3

+ are particularly important in astrochemistry. They are bothproduced abundantly in space, but the steady state populationof H3

+ is very much less (10−7−10−8) than that of H2 becauseof its high chemical activity. Nevertheless, the dipole-inducedH3

+ infrared absorption is much stronger (109) than thequadrupole-induced infrared absorption of H2 and usuallymuch easier to observe in interstellar gas as discussed later insection 4. H2 does possess a strong and rich ultravioletspectrum, but that spectrum is not observable in manyinterstellar environments due to strong absorption andscattering of ultraviolet radiation by interstellar gas and dust.

2.1.2. Interstellar Ion Chemistry is an HonestChemistry. There are two reasons for this. First, because ofthe low temperature of the environment, Gibb’s free energy G= H − TS which governs chemistry is nearly equal to theenthalpy H. The entropy term TS, which makes the chemistryof stellar atmosphere so subtle as discussed by Tsuji,45 seldomneeds to be considered. The outcome of many chemicalreactions can be predicted simply from the enthalpies of theinvolved atoms and molecules. One can go a long way just byknowing the three basic chemical parameters; the protonaffinity, the ionization energy (potential), and the dissociation



energy. The values of these are listed in Table 1 for theprincipal atoms and molecules in interstellar chemistry. The

proton affinity is listed in the first column because it is the mostcrucial parameter for characterizing the interstellar chemistry ofH3

+. H3+ donates its extra proton to atoms or molecules with a

proton affinity greater than that of H2, that is, to any speciesbelow H2 in Table 1, via the universal proton-hop reaction

+ → ++ +H X H HX3 2 (2)

to produce chemically active HX+ from relatively inactiveneutral X and thus initiate interstellar chemistry. H3

+ is auniversal proton donor, that is, an interstellar acid. The onlyexceptions in Table 1, species that do not accept proton fromH3

+, are the three species above H2, that is, He, H, and N. O2has a proton affinity very close to that of H2, and therefore,production of HO2

+ is delicate.51 Other atoms and molecules inTable 1 and thousands more molecules47 all have protonaffinities higher than 4.39 eV and readily accept a proton fromH3

+. Of all species in Table 1, He is unique for its lowest protonaffinity and highest ionization energy. In general, species withlow proton affinity tend to have high ionization energy. Aremarkable exception of this rule is the pair H and H2; bothproton affinity and ionization energy of H2 are significantly (∼2eV) higher than those of H. Interstellar chemistry is deeplyaffected by this “accident”. It is sometimes said that chemistry isthe science of electrons. The simpler interstellar chemistry isthe science of protons.The second factor that makes interstellar ion chemistry so

simple is the universality of the Langevin rate constant. As morefully explained later in section 2.2.1, almost all exothermic ion-

neutral reactions have a very large rate constant, on the order of10−9 cm3 s−1, due to the long-range Langevin interaction withthe 1/r4 potential.52 Moreover, the rate constant is independentof temperature to a good approximation. The Langevin rateconstants for the proton-hop reaction of eq 2 are listed in thelast column of Table 1. By and large one can assume that anion-neutral reaction with decisive exothermicity will occur witha high Langevin rate. The only exception in this review is thecharge exchange reaction between He+ and H2 to be discussedat the end of section 2.4.1.

2.1.3. Interstellar Chemistry Is Kinematic Rather thanThermodynamic. This is because even in the densest andwarmest molecular clouds, molecules do not have enoughlifetime to become chemically thermalized. For example, CO inplenty of H2 does not have time to react to become thethermodynamically more stable CH4 and H2O.

53 Highlyunsaturated acetylenic compounds like HC5N, HC7N, andHC9N abound.54 This applies not only to the chemistry butalso to the rotational distribution of molecules. Because of thedifference between kinetic and radiative temperatures ofenvironment, molecular distributions never reach the thermal-ized Boltzmannian distribution corresponding to maximumentropy and nonthermal rotational distributions are more oftenthe rule than the exception. Interstellar space is full of maseremissions and other nonthermal phenomena. o-H2 do not fullyconvert to energetically lower p-H2 for the same reason.Interstellar chemistry is the exciting playing ground ofkinematics where individual characteristics of molecules appearin rare form rather than being washed out by the boringentropy maximum principle.

2.2. Production of H3+

The 1968 discovery of interstellar NH355 and H2O

56 byTownes’ group revealed the richness of interstellar chemistryand introduced the novel concept “molecular cloud”, regions ofinterstellar space with unexpected high densities, and affectedastrophysics in a most profound way. After these and otherdiscoveries in the centimeter region, radioastronomy quicklymoved to the millimeter region and the discovery of CO57 andHCO+58 followed. The serendipitous discovery of “X-ogen” byBuhl and Snyder, which was immediately conjectured to beHCO+ by Klemperer,59 was particularly important forinterstellar chemistry since it has led to the majesticastrochemical theory based on ion−molecule reactions byHerbst and Klemperer60 and Watson61,62 in which H3

+ playsthe central role. Watson61 was particularly explicit about thissaying in the abstract “Due to the widespread abundance of H2,ion-molecule reactions with H2 and H3

+ can be the chiefformation process for small interstellar molecules in a largefraction of the interstellar gas.”

2.2.1. H2 + H2+ → H3

+ + H, the Langevin Rate. Thechemistry of interstellar H3

+ is extremely simple. H3+ is

produced by cosmic ray ionization of H2 to H2+ followed by the

proton-hop reaction in eq 1. This reaction is very efficient witha high exothermicity of 1.74 eV, the difference between theproton affinity of H2 (4.39 eV) and H (2.65 eV), and a highLangevin cross section on the order of a few 100−1000 Å2 ininterstellar space depending on the temperature. When H2 andH2

+ approach at a distance of r, the positive charge on H2+ with

the Coulomb field of e/r2 polarizes H2 and induces a dipolemoment d = αe/r2, where α is the polarizability of H2. Thisleads to the attractive charge-induced dipole potential,63 VL =−de/2r2 = −αe2/2r4, the Langevin potential. The motion of a

Table 1. Proton Affinity (PA), Ionization Energy (IE), andDissociation Energy (D0

0, DE) of Atoms and Moleculeswhich Play Pivotal Roles in Interstellar Chemistry (in eV)a

species PAb IEc DEd kL

He 1.84 24.581H 2.65 13.595N 3.39 14.545O2 4.38 12.071 5.116H2 4.39 15.426 4.478O 5.04 13.615 0.80 ± 0.40N2 5.13 15.581 9.759 1.90 ± 0.40NO 5.51 9.264 6.497 1.25 ± 0.40CO2 5.68 13.769 5.453 2.00 ± 0.60CH4 5.72 12.99 4.406 2.40 ± 0.30CO 6.15 14.014 11.09 2.00 ± 0.20OH 6.2 12.90 4.392C 6.42 11.265HCCH 6.65 11.41 4.9 3.40 ± 0.80S 6.86 10.357C2 6.9 12.15 6.21H2O 7.22 12.62 5.114 5.40 ± 0.60HCN 7.43 13.91 5.65 7.80 ± 0.80CH 7.7 10.64 3.465NH3 8.85 10.15 4.38 4.50 ± 0.50

aThe last column gives experimental rate constants kL for the Langevinreaction H3

+ + X → H2 + HX+. Values of kL are approximate averagesof data in ref 46 in 10−9 cm3 s−1. bMostly from ref 47. Some arecalculated values from IE and DE of other species. cFrom refs 48(atoms), 49 (diatomic molecules), and 50 (polyatomic molecules).dFrom refs 49 (diatomic molecules) and 50 (polyatomic molecules).



neutral (H2) and ion (H2+) under this potential was discussed

by Langevin52 and in textbooks (e.g., Landau and Lifshitz64

section 18). The Langevin cross section σL in terms of Langevinradius ρL and the Langevin rate constant kL are given as

σ πρ π αμ

σ π αμ

= = = =ev

k v e2 and 2L L2

L L(3)

where μ is the reduced mass for H2 and H2+ which is nearly

identical to the mass of H and v is the relative velocity of H2and H2

+ long before the collision. Note that kL is independentof v and therefore of temperature. Thus, the Langevin reactionoccurs at the low temperature of the interstellar space. Thischaracteristic is special for the 1/r4 potential. Maxwell assumedthis potential in his paper on stress in rarified gases for sheersimplicity of mathematics.65 There are other forces such asquadrupole−quadrupole interaction between H2 and H2

+, butthey alternate between attraction and repulsion as themolecules rotate and tend to average out. Substituting theisotropic polarizability of H2,

66 α = 0.79 Å3, and ignoringanisotropic polarizability, we obtain from eq 3 kL= 2.08 × 10−9

cm3 s−1, which agrees well with observed values46 of (2.00−2.08) × 10−9 cm3 s−1, indicating that the above treatment byclassical mechanics works well. The Langevin cross section andradius for 10, 30, and 100 K are calculated to be σL= 590, 340,and 185 Å2 and ρL = 13.7, 10.4, and 7.7 Å, respectively. If H2and H2

+ approach with an impact parameter less than ρL, whichis typically 10 Å, they fall into each other as shown in Figure 2taken from Langevin’s paper.52 It is like quicksand. They cannotescape each other. Then the very strong chemical force takes

over and completes the very exothermic reaction of eq 1. Sincepolarizabilities of atoms and molecules X do not vary drastically(they are within a factor of 4 of that of H2 for all species inTable 1) and so are reduced mass for X and H3

+ and sinceheavier X tends to have larger polarizabitity, the Langevin ratecalculated above applies to all reactions for eq 2 within a factorof 2 as long as the reaction is decisively exothermic. This makesion chemistry very simple.

2.2.2. Cosmic Ray Ionization. The Langevin reaction isvery fast by the interstellar standard and occurs in 2 monthsand in 0.5 day for H2 number densities of 10

2 and 104 cm−3,respectively, which are typical number densities for diffuseclouds and dense clouds. The ionization rate of H2 by cosmicrays ζ ≈ 10−17−10−14 s−1 is many orders of magnitude lower.Therefore, the production rate of H3

+ is given by the rate-determining ionization rate of H2, that is

ζ

ζ

ζ

= Φ

= Φ

≈

+⎡⎣⎢

⎤⎦⎥

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

nt

n fkk

nf

fkk

nf

d (H )d

(H ) (H ),

(H )2

(H ),

(H )2

3

prod2 2

5

1

H2

25

1

H2

2

(4)

where nH = n(H) + 2n(H2) is the number density of allhydrogen and f(H2) = 2n(H2)/nH is the fraction of hydrogen inmolecular form. Φ is a correction factor to be discussed insection 2.2.3. For dense clouds f(H2) = 1 to a goodapproximation, while for diffuse clouds f(H2) may take valuesfrom 0.01 to 1. The last term in eq 4 is for an approximationwith k5 = k1/2 (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 observedintensities of high-energy cosmic rays to lower energy regions,they predicted ζH ≈ 10−15 s−1 as the cosmic ray ionization rateof H. (In this review we use ζH for the ionization rate of H andζ for that of H2. ζ = 2ζH holds for energy above 1 MeV.68).Spitzer and Tomasko69 gave ζH ≈ 6.8 × 10−18 s−1 based on theobserved cosmic rays extending to low energy, which howeveris much lower than the interstellar value due to deflection bythe solar magnetic field. Field et al. gave ζH ≈ 4 × 10−16 s−1.70

Whichever value is used, there is no question that the cosmicray ionization is the rate-determining process for H3

+

production. The simplicity of eq 4 and the chemistry discussedbelow make H3

+ the most direct and reliable probe to measureionization rate and hence the strength of low-energy cosmic rays ininterstellar space. The value of ζ on the order of 10−17 by Spitzerand Tomasko had been held as the caconical value for theionization rate for 30 years until it was shown to be muchhigher in diffuse clouds by the observation of H3

+ as discussedlater in section 4.1.4.H2 may also be ionized by extreme ultraviolet radiation and

X-rays from stars. Here, these effects are ignored as local. Forthe former, H2 is well protected by H and C, which have muchlower ionization energy than H2, and dust. For the latter, theE−7/2 dependence on energy of the photoelectric effect71 makesit negligible except in special environments.

2.2.3. Charge Exchange Reaction between H2+ and H.

Although production of H3+ is very simple for dense clouds

where hydrogen is dominantly in molecular form, acomplication arises for diffuse clouds where f(H2) may be

Figure 2. Fall to the center of the Langevin potential.52,64 Reprintedwith permission from ref 52. Copyright 1905 Elsevier.



significantly lower than 1. In this case, H2+ ions produced by

cosmic ray may encounter H rather than H2 and revert to H2through the charge exchange reaction

+ → ++ +H H H H2 2 (5)

which is exothermic by the difference of the ionization energiesof H2 and H, 1.83 eV. This reduces the effective production rateof eq 4 by a factor72

Φ = + −−⎛

⎝⎜⎞⎠⎟

⎛⎝⎜⎜

⎛⎝⎜

⎞⎠⎟⎞⎠⎟⎟f

kk

kk f

(H ), 12 1

(H )12

5

1

5

1 2

1

(6)

where k1 and k5 are rate constants for the reactions in eqs 1 and5, respectively. For special values of k5/k1 = 0, 1/2, and 1,Φ{f(H2)} = 1, f(H2), and f(H2)/{2 − f(H2)}, respectively.Although the value of k1 is well established as discussed insection 2.2.1, the value of k5 is not. The only reportedexperimental value73 is k5 = (6.4 ± 1.2) × 10−10 cm3 s−1, whichis much smaller than the Langevin rate constant, 2.34 × 10−9

cm3 s−1, calculated from eq 3. A theoretical paper gives crosssections which translate to 2.32 and 1.49 × 10−9 cm3 s−1

depending on theoretical methods.74 I here assume aconvenient number k5/k1 ≈ 1/2 which gives Φ{f(H2)} =f(H2) leading to the first expression in eq 4. When k5 is betterdetermined, one can calculate Φ{f(H2)} more accurately.2.3. Destruction and Number Density of H3

+

The destruction process of H3+ depends on the state of carbon

in the interstellar environment. Dense clouds with a numberdensity on the order of 104 cm−3 are gravitationally bound andon their way to star formation. The clouds have a dimension onthe order of 1 pc, and their interiors are well shielded from starradiation. Hydrogen is in the molecular form, f(H2) ≈ 1, andcarbon is mostly locked up as CO some of which are frozenonto dust grains depending on the cloud temperature. Diffuseclouds, with a typical number density on the order of 102 cm−3,on the other hand, have larger dimensions and are largelytransparent to stellar radiations. Hydrogen is in both H2 and H,f(H2) < 1, and carbon is in atomic form and ionized by stellarultraviolet radiation to C+. C is the first element to be ionizedamong species abundant in interstellar space because itsionization energy, 11.265 eV, is the lowest (see Table 1);hydrogen remains mostly neutral in diffuse clouds. There also isan interstellar environment intermediate between diffuse anddense clouds where carbon is mostly C but is less extensivethan the other two.75

2.3.1. Dense Clouds. In dense clouds where moleculesabound and the electron fraction is small, <10−7,76 H3

+ isdestroyed by the proton-hop reaction in eq 2. Being thedominant species, X = CO with an exothermicity of 1.76 eVand a Langevin rate constant of kCO = 2.00 × 10−9 cm3 s−1 playsthe main role but X = O with an exothermicity of 0.65 eV and arate constant of 0.80 × 10−9 cm3 s−1 also contributes.Considering there are other molecules like N2 with significantpopulation and Langevin rate constant, electron, etc., thedestruction rate in a dense cloud is estimated as

∼

∼

++

+

⎡⎣⎢

⎤⎦⎥

nt

k n n

k n n

d (H )d

1.4 (H ) (CO)

1.4 (H )

3

destr,denseCO 3

CO 3 C

where the factor of 1.4 is due to contributions of CO, O, N2,electron, etc., estimated from their abundances76 and rate

constants.46 For nC = 1 cm−3 the destruction rate isapproximately 3 × 10−9 s−1, corresponding to a H3

+ lifetimeof ∼10 years. Equating this destruction rate with the productionrate of eq 4 with f(H2) = 1, we have the steady state H3

+

number density in dense clouds of

ζ≈ ≈ ×+ − −nk

nn

(H )1

2.87 10 cm3 dense

CO

H

C

5 3

where the cosmic ray ionization rate of ζ ≈ 3 × 10−17 s−1 andthe depleted C/H ratio77,78,76 in a dense cloud of nC/nH = 7.3 ×10−5 is used in the numerical calculation. Note that although nHand nC are proportional to the number density of the cloud n,n(H3

+) is proportional to their ratio and hence independent ofn as long as ζ and the C/H ratio are constant along a sightline.This is because of the linearity of the H3

+ production rate to nHas in eq 4. This property makes H3

+ a special astrophysicalprobe complementary to CO. While an observed total columndensity of CO gives information on the mass of a cloud, the totalcolumn density for H3

+ gives information on the length of a cloud.This property makes N(H3

+) = Ln(H3+) a good approximation.

We therefore have

ζ = +L k Nnn

2.8 (H )CO 3C

H (7)

which can be used to obtain information on ζL from observedN(H3

+). In order to separate ζ and L, we need to know one ofthem from other observations or from an estimate for one ofthem.

2.3.2. Diffuse Clouds. In diffuse clouds where theultraviolet radiation from stars penetrates and singly ionizesvirtually all carbon atoms, the electron number density is veryhigh, n(e) ≥ 10−4nH, and dissociative recombination of H3

+

with electrons79

+ → + + ++ −H e H H H or H H3 2 (8)

is the dominant destruction process of H3+. Compared with the

Langevin reaction of eq 2 under the 1/r4 Langevin potential,recombination proceeds under the longer range 1/r Coulombpotential and has a rate constant on the order of 10−7 cm3 s−1,approximately 100 times larger than that of the Langevinreaction. Therefore, the destruction rate of H3

+ in diffuse cloudsis

= ≈+

+ +⎡⎣⎢

⎤⎦⎥

nt

k n n k n nd (H )

d(H ) (e) (H )3

destr,diffusee 3 e 3 C

where ke is the rate constant for dissociative recombination ofH3

+. In the last term an approximation n(e) ≈ nC is usedassuming that all electrons originated from the first ionizationof C. If nC ≈ 10−2 cm−3, the H3

+ lifetime is also on the order of10 years, similar to in dense clouds. Equating this destructionrate with the production rate in eq 4, we obtain the steady stateH3

+ number density in diffuse clouds

ζ

ζ

= Φ

≈

≈ ×

+

− −

⎛⎝⎜

⎞⎠⎟n

knn

ff

kk

knn

f

(H )(H )

2(H ),

(H )2

5 10 cm

3 diffusee

H

C

22

5

1

e

H

C

22

6 3



where the cosmic ray ionization rate in diffuse clouds is ζ ≈ 5 ×10−16 s−1 (using the value given by Indriolo and McCall,72 3.5× 10−16 s−1 with a correction on f(H2) = 0.67), the H3

+

dissociative recombination rate constants at 70 K is 1.5 × 10−7

cm3 s−1 (calculated from the experimental formula by McCall etal.80), and the depleted C/H ratio81 in diffuse clouds nC/nH =1.6 × 10−4 is used. Note that unlike the Langevin rate, thedissociative recombination rate has a temperature dependenceof ∼ T−0.5.Since the value of ζ is known to vary depending on the

proximity to supernova remnants,72 the H3+ number density

calculated above is an approximate average value. The value isabout one-tenth of the number density in dense clouds, butsince the dimensions of diffuse clouds are 10 larger, theobserved column densities in diffuse clouds are comparable tothose in dense clouds, a fact which was a surprise when firstobserved as discussed later in section 4.1.4.Just as in dense clouds, n(H3

+) is a constant and does notscale with the cloud density. Therefore

ζ = Φ

≈

+−

+ −

⎛⎝⎜⎜

⎛⎝⎜

⎞⎠⎟⎞⎠⎟⎟L k N

nn

f fkk

k Nnn

f

2 (H ) (H ) (H ),

2 (H ) (H )

e 3C

H2 2

5

1

1

e 3C

H2

2

(9)

which has been used to determine the values of ζL fromobserved N(H3

+).72 The remarkable independence of n(H3+)

on the cloud density is shown schematically in Figure 3.2.3.3. Dissociative Recombination of H3

+. The dis-sociative recombination rate constant of H3

+, ke, the onlylaboratory-measured value in the last term of eq 8, is the mostcrucial molecular parameter governing H3

+ chemistry in diffuse

clouds. The experimental value has fluctuated by as much as 104

over the years and poisoned a generation of chemical modelcalculations from 1980s to the beginning of 1990s.79 Thisconfusion has been settled by application of the storage ringmethod to H3

+ by Larsson and colleagues in 1993.83

Theoretical calculations also went through a recent tempestu-ous period. As late as in 2000, the theoretical value was stillmore than 2 orders of magnitude different from the currentexperimental values. This has been remedied since byKokoouline, Greene, and colleagues,84 who took into accountthe Jahn−Teller effect as playing the essential role in the H3

+

dissociative recombination and obtained theoretical resultswhich agree better with experiments. Subsequently, Jungen andPratt85 developed an analytical theory which supported thetheory by Greene’s group. In the laboratories, excellentagreement was reached between the measurements of Larsson’sgroup at the Manne Siegbahn Laboratory80 and Wolf’s group atthe Max-Planck Institute of Nuclear Physics both in energy-dependent resonant structure86 and in the absolute crosssection.87 Nevertheless, there still are some discrepanciesbetween theory and experiment in (a) the energy-dependentresonant structure of dissociative recombination88 and (b) thedependence on o- and p-H3

+.86 Those together with the recentrevelation that the rotational temperatures of H3

+ in the storagerings are much higher than previously assumed88 suggest thatthe rate constant determined by McCall et al.80 used in theabove calculation may need to be adjusted by a factor of a few.

2.4. H3+: Initiator of Interstellar Chemistry

2.4.1. H3: Universal Proton Donor, the InterstellarAcid. H3

+ plays the central role in interstellar chemistry bydonating its extra proton to atoms and molecules with protonaffinity more than that of H2 via the universal reaction in eq 2.Thus, from O, N2, NO, CO2, CH4, CO, OH, C, HCCH, S, C2,H2O, HCN, CH, and NH3 listed in Table 1, we have molecularions OH+, N2H

+, HNO+, HCO2+, CH5

+, HCO+, H2O+, CH+,

C2H3+, SH+, HC2

+, H3O+, HCNH+, CH2

+, and NH4+. All

reactions with significant exothermicity proceed with highLangevin rate constants kL as shown in Table 1. The molecularions thus produced are much more chemically active than theirparent neutrals and invigorate interstellar chemistry. Forexample, O and H2 do not react at the low temperature ofinterstellar space, but OH+ and H2 react vigorously, initiating achain of hydrogen abstraction reactions, XHn

+ + H2→ XHn+1+ +

H

→ →+ + +OH H O H O2 3

leading to protonated water H3O+ which produces H2O and

OH upon recombination with electrons. The two hydrogenabstraction reactions proceed with a Langevin rate constant of 1× 10−9 46 and 6.4 × 10−10 cm3 s−1,89 respectively. Molecularcations like H3

+, H3O+, NH4

+, CH5+, HCO+, HN2

+, andHCNH+ which are produced by adding a proton to ordinarymolecules H2, H2O, NH3, CH4, CO, N2, and HCN are oftencalled “protonated ions” as opposed to radical cations which areproduced by subtracting an electron, H2

+, H2O+, NH3

+, CH4+,

CO+, N2+, and HCN+.90 The carbon atom, which is not the

main form of carbon but still exists in a significant amount indiffuse clouds, is also invigorated by protonation to CH+, whichleads to a chain of hydrogen abstraction reactions

→ →+ + +CH CH CH2 3

Figure 3. Schematic diagram showing the relation between numberdensities n(X) of H2, CO, and H3

+ and the number density of thecloud, n(H). Note that n(H2) and n(CO) scale with n(H) whilen(H3

+) is independent of n(H) for typically dense and diffuse clouds.Reprinted with permission from ref 82. Copyright 2006 United StatesNational Academy of Sciences.



with Langevin rate constants 1.2 × 10−9 and 1 × 10−9 cm3 s−1,but the chain does not reach the final protonated ion CH5

+

since the hydrogen abstraction reaction from CH3+ to CH4

+ isendothermic by as much as 3.22 eV.Another universal ion producer in interstellar chemistry is

He+ with its highest ionization energy of 24.581 eV; it ionizesneutral species by charge transfer reaction

+ → ++ +He X He Xwhich are all exothermic. While H3

+ produces ions by adding aproton, He+ produces ions by subtracting an electron. Thisreaction is known to proceed with the Langevin rate for allspecies except for only one caseX = H2. Although allreactions

+ → + − + + −

+ −

+ + +

+

He H He H ( 9.16 eV), He H H ( 6.51 eV),

HeH H ( 8.36 eV)2 2

are highly exothermic, all of them have rate constants severalorders of magnitude smaller than the Langevin rate. The firstreaction, for example, has a rate constant one million timessmaller than the Langevin rate at a low temperature of 15−40K.91 This is also the case for Ne+ but not for Ar+ and Xe+.Mahan explained the nonreactivity of He + and H2 and thesubtle differences among rare gas atoms by considering thecorrelation between electronic states of the (rare gas−H2)

+

system.92 The nonreactivity has a huge effect on the chemistryof dense clouds since He+, produced by cosmic ray with a rateof ζHe ≈ 2 × 10−17 s−1,68 is not destroyed by H2 and insteadmainly leads to dissociative ionization of CO

+ → + ++ +He CO He C Oat a Langevin rate of 1.7 × 10−9 cm3 s−1.46 C+ thus producedinitiates a chain of carbon reactions producing organicmolecules that are observed abundantly in interstellar space.An example of flow charts for interstellar ion chemistry isshown in Figure 4.93

2.4.2. Deuterium Fractionation. A remarkable manifes-tation of the fundamental role H3

+ plays in interstellarchemistry is the observed ultrahigh deuterium fractionation inprestellar cores with high density (n ≥ 106 cm−3) and lowtemperature (T ≤ 10 K). Highly deuterated species like ND3and CD3OH, corresponding to a deuterium fractionation of 10orders of magnitude from the D/H ratio in interstellar space of∼1.5 × 10−5, are observable in such regions. The basicmechanism for the deuterium fractionation has been knownand understood for many years since the seminal paper byWatson.62

Roberts et al.94 has shown that the series of reactions

+ → ++ +H HD H D H (231.8 K)3 2 2

+ → ++ +H D HD HD H (187.2 K)2 2 2

+ → ++ +HD HD D H (233.8 K)2 3 2

can lead to an extreme deuterium fractionation of n(D3+)/

n(H3+) ≈ 20 corresponding to a fractionation of 1013 under the

condition T = 10 K and n(H2) = 1.5 × 106 cm−3. The numbersin parentheses in the above equations are accurate ab initiotheoretical values of the exothemicities95 due to the lowervibrational zero-point energy of the higher deuterated products.Such small exothermicities as ∼0.02 eV hardly matter inlaboratory plasmas but are huge driving forces with equilibriumconstants on the order of exp(200/10) ≈ 5 × 108 at that

temperature. Ultrahigh fractionation does not occur in warmerand less dense clouds because the fractionation process isdiluted through destruction of H3

+ and its deuterated species byCO, O, O2, and N2, which are more abundant than HD, via theproton-hop reaction in eq 2. It occurs only when those speciesare sufficiently depleted onto dust grains due to the lowtemperature of the environment so that the number density ofHD is comparable to or greater than their combined densities.Since deuterated H3

+ is the universal deuteron donor, theseclouds exhibit extremely rich deuterium chemistry.Because the dilution is critically dependent on the ratio of the

rate of the forward reaction kfn(HD) and those of dilutingreactions kCOn(CO) + kOn(O) + kO2 n(O2) + kN2n(N2), thevalue of kf is crucial in this discussion. In the above theory94 ahigh Langevin rate constant of 1.7 × 10−9 cm3 s−1 was used,while experiments at low temperature give a values 5 timessmaller96,97 (although later measurement by Hugo et al.98 givesa higher value; see section 4.1.2). This makes a huge differenceto the depletion on grains required for gases CO, O, O2, and N2in order to produce an observed high degree of fractionation.

2.4.3. Effect of o-H2. A complication in the abovemechanism of fractionation arises from the presence of o-H2in the J = 1 rotational level which is 170.48 K above the J = 0level of p-H2 as considered in a prescient paper by Pagani et

Figure 4. Flowchart of the ion chemistry of dense molecular clouds.Chemistry is initiated by cosmic ray ionization of H2 and He.Hydrocarbon molecules are in the central column, while O- and N-containing molecules are in the left and right columns, respectively.See Smith93 for more details. Some reactions in this diagram, such asproduction of CH3OH, have since been shown not to work. Reprintedwith permission from ref 93. Copyright 1987 Royal Society ofChemistry.



al.99 Since the ortho to para J = 1 → 0 transition is highlyforbidden both radiatively and collisionally, H2 tends topopulate the J = 1 level in far excess of the thermal equilibrium,another example of kinematically rather than thermodynami-cally governed chemistry. The excess energy of o-H2 togetherwith the energy of o-H2D

+ in the lowest ortho-rotational level,111, which is higher than the ground para level 000 by 86.37 K

100

will override the exothermicity of 238.1 K and make the firstfractionation reaction slightly endothermic, reverting H2D

+

back to H3+ and thus hampering deuteration. This is the case

for ordinary dense clouds where n(H2)J=1 > n(HD).The total nuclear spin angular momentum quantum number

I for Itotal = I1 + I2, which characterizes ortho (I = 1) and para (I= 0) H2, H2D

+s etc.s is not a rigorous quantum number,101,102

and in principle, the J = 1 H2 converts to J = 0 H2 by bothspontaneous emission103,104 and collision,102 but they are fartoo slow to be of practical interest. Conversion requires protonscrambling reaction either with H+ or with H3

+

‐ + → * → ‐ ++ + +o pH H (H ) H H2 3 2

‐ + → * → ‐ ++ + +o pH H (H ) H H2 3 5 2 3

where (H3+)* and (H5

+)* are reaction intermediates in whichproton scrambles to convert spin isomers. The first reaction istheoretically tractable105,106 but difficult to study experimen-tally, while the opposite is the case for the second reaction.Using infrared spectral lines of o-H3

+ with (J, K) = (1,0) and p-H3

+ with (1,1), Uy et al.,107 Cordonnier et al.,108 and Crabtreeet al.109,110 studied the second reaction which is composed ofproton-hop and proton-exchange reactions and determinedtheir ratio. Theoretical spin selection rules111 and statistical ratecalculations112 are used in their analyses.Since both H+ and H3

+ are not very abundant in interstellarspace, conversion of o-H2 to p-H2 takes a long time before theconcentration of o-H2 gets comparable to or smaller than thatof HD. Pagani et al.113,114 studied the effect of o-H2 ondeuterium fractionation systematically and estimated the timeof ortho to para conversion to be on the order of several millionyears. Completion of conversion is shown by the growth ofdeuterated ions, typically DCO+. They proposed that theappearance of DCO+ sets the upper limit on the age of starlessmolecular clouds.

3. SPECTROSCOPY OF H3+

Since H3+ in singlet electronic excites states are all

predissociated, no sharp electronic spectrum is expected inthe visible or ultraviolet region. The permanent electric dipolemoment of H3

+ does not exist due to its equilateral trianglestructure (D3h), and hence, no rotational spectrum is expected.The only fully allowed transition is the infrared-active ν2vibration rotation band with the band origin at 2521.6 cm−1,discussed below in section 3.1. The only exception is theforbidden rotational transition induced by spontaneous break-down of symmetry, to be discussed in section 3.2. Althoughthese transitions are yet to be observed in the laboratory, weknow their properties accurately from very accurate ab initiotheory. The partially deuterated species H2D

+ and HD2+ have

effective permanent dipole moments because the D3h symmetryis broken by deuterium substitution. Their rotational spectraare observable in the submillimeter region and discussed brieflyin section 3.2.2.

3.1. Infrared Vibration−Rotation Spectrum of H3+

3.1.1. ν2 Fundamental Band. H3+ has 3 normal modes of

vibration shown in Figure 5the totally symmetric ν1 mode

and two degenerate ν2 modes. The ν1 mode is infrared inactiveand therefore not observable. The doubly degenerate ν2vibration is infrared active with a large transition dipolemoment of 0.158 D.27 The X3-type molecule is unique amongnonlinear molecules in having only one pair of degeneratemodes, which generates unit vibrational angular momentum (ζ2= −1).115 The energy levels of H3

+ are specified by tworotational quantum numbers J and K for the ground vibrationalstate. While J is positive, K is either positive or negativedepending on whether H3

+ is rotating clockwise or counter-clockwise around the C3 symmetry axis. If this distinction isnecessary the signed quantum number k is used. There are twoadditional symmetry labels, the parity which is determined by(−1)K, and ortho (I = 3/2) and para (I = 1/2) states where I isthe quantum number for the total proton spin angularmomentum Itotal = I1 + I2 + I3. The three proton spins arelined up in o-H3

+, whereas one is antiparallel in p-H3+. Just as

ortho and para spin states for H2 are associated with rotationallevels with odd and even J, respectively, the ortho and para spinstates of H3

+ are associated with rotational levels having K = 3nand 3n ± 1, respectively, in order to satisfy the Pauli exclusionprinciple, that is, the total wave function must change sign uponexchange of two protons (fermions).116,102 The lowest (J, K) =(0. 0) level and other (J, 0) levels with even J are forbidden bythe Pauli principle; just as a spherical 1s orbital cannotaccommodate more than two electrons, the totally symmetricrotational levels cannot accommodate three protons. Thevibration−rotation transitions (left) and low rotational energylevels of H3

+ in the ground vibrational state with their rotationalquantum numbers and symmetry labels (right) are shown inFigure 6.For the ν2 excited state an extra quantum number is needed

for the vibrational angular momentum, = ±1, in addition to Jand 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 multipleof 3 or not. Therefore, a quantum number G ≡ |K − | is usedfor convenience. For the ground state in which = 0, G = K.The pair of levels (J, K +1, = +1) and (J, K − 1, = −1) withidentical J, G, and parity and hence with identical symmetry mixsignificantly. There is no quantum label to discriminate the twomixed levels; u and l are used to specify the upper and lowerlevels, respectively. A rotational level in the ν2 state is uniquely

Figure 5. Three normal modes of vibration of H3+. Totally symmetric

ν1 mode (3178.3 cm−1) is infrared inactive, while the two degenerateν2 modes (2521.3 cm−1) are active. Linear combinations of thedegenerate modes x ± iy = re±φ produces a quantized vibrationalangular momentum .



specified by J, G, and u or l, and the useful symmetry labels areparity, which is given by (−1)G−1 and ortho and para spin statesfor G = 3n and 3n ± 1, respectively. For G = 0 and G > J + 1the pair of levels does not exist and u and l labels are notnecessary.The selection rules for the ν2

1 ← 0 transition are

Δ = ± Δ =J G0 or 1 and 0

which automatically satisfy the parity rule + ↔ − and spin ruleΔI = 0, i.e., ortho ↔ ortho and para ↔ para. The labels u and ldo no specify symmetry and therefore do no appear in theselection rules. The ν2

1 ← 0 vibration−rotation transitions aredesignated R(1,1)l, Q(1,0), etc., which correspond to (ν2 J = 2G = 1 l) ← (0 J = 1 K =1) and (ν2 J = 1 G = 0) ← (0 J =1, K =0), respectively. Readers are referred to Herzberg Vol. II119 andLandau and Lifshitz Vol. 3120 for more general discussions onquantum numbers, symmetry, selection rules, etc., and toMcCall’s thesis121 for H3

+ in particular. A stick diagram of theν2 fundamental band of H3

+ observed in 1980122 is shown inFigure 7.Unlike in an ordinary vibration−rotation spectrum, Figure 7

shows no obvious regularity or symmetry. This is because theusual method of expressing energy levels in terms ofpolynomials of quantum numbers does not work due to thesmall mass of H3

+ and thus the relatively large Born−Oppenheimer constant; the traditional perturbation treatment(e.g., ref 123) does not converge well.

The most characteristic feature of this spectrum is the absenceof 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 astronomicalobservations are indicated in Figure 7. The details of the linesso far used in observations along with others that may be usefulin the future are given in Table 2. The P-branch lines arestrongly interfered by CO2 in the atmosphere and are notincluded in the table. The spectral strength |μ|2 is useful to

Figure 6. Vibration−rotation transitions of the ν2 fundamental band of H3+ (left) and the low-lying rotational levels of H3

+ in the ground vibrationalstate (right). The latter shows the ortho (I = 3/2 red) and para (I = 1/2 blue) spin modifications and the parity + and −. Thin arrows indicatespontaneous emissions due to forbidden rotational transitions discussed in section 3.2.1. Because of these rapid spontaneous emissions interstellarH3

+ 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 AmericanAstronomical Society. (Right) Reprinted with permission from ref 118. Copyright 2011 Royal Society of Chemistry.

Figure 7. Stick diagram of the observed ν2 vibration rotation band ofH3

+ with intensities calculated for the rotational temperature of 200 K.Lines used for astronomical observations are marked with asterisks andtheir assignments. Reprinted with permission from ref 122. Copyright1980 American Physical Society.



calculate the H3+ column density N(H3

+)lev in the lowerrotational level from the observed equivalent width Wλ =∫ [ΔI(λ)/I]dλ from

π λ μ

λ μ

= | |

= × | |λ

λ

+N hc W

W

(H ) (3 /8 )( / )/

2.4025 10 ( / )/3 level

3 2

18 2(10)

where |μ|2 is in Debye2 and N(H3+)level is in cm−2.

A major problem of ground-based astronomical infraredspectroscopy is the atmospheric interference. Subjectivedegrees of interference in arbitrary scale are included in thetable. They would be irrelevant if an airborne high-resolutionspectrometer is available in the future.3.1.2. Overtone and Combination Bands and Rig-

orous Theory. After the 1980 observation of the ν2fundamental band with the band origin at 4 μm, overtoneand combination bands were observed providing informationon the vibration−rotation states with increasingly higherenergies. Results to wavelengths as short as ∼1 μm arecompiled by Lindsay and McCall.124 Subsequently, spectros-copy reached the long wavelength edge of the visible region127

and is now deep in the visible.128 As spectroscopy reaches morehighly excited states spectral intensities are reduced. Spectrallines involving levels with the highest energies currentlyobserved, 16 700 cm−1, are weaker than the fundamentalband lines by more than 6 orders of magnitude. Such faint lineshave no direct application in astrochemistry. Nevertheless, thequantum mechanics of H3

+ developed to understand the highlyexcited states are very important to accurately characterize

other quantum effects of H3+ with applications to astrochem-

istry such as the forbidden transitions discussed in section 3.2.1.Since H3

+ is the simplest polyatomic molecule with only twoelectrons, a great many quantum chemical papers have beendevoted to obtaining its potential energy surface (PES) andreproduce the observed spectrum since the classic paper byCarney and Porter.27 After 1975 when the ab initio theory byKołos and Wolniewicz129 gave the dissociation energy androvibrational energies of H2, HD, and D2 to “spectroscopicaccuracy”, that is within a fraction of a cm−1 of experimentalvalues observed by Herzberg and colleagues,130 the rovibra-tional energy of H3

+ has been the benchmark for truly rigorousab initio theory. Variational treatment of its protons byTennyson and Sutcliffe131 played the leading role in thisdevelopment with increasingly accurate PES by Meyer,Botschwina, and Burton,132 Kutzelnigg and colleagues,133 andPavanello and Adamowicz et al.134 The most recent theoreticaldata agree with experiments within a fraction of cm−1 up to theenergy observed, 16 700 cm−1.128 A detailed review of thisamazing development is beyond the scope of this paper, andreaders are referred to the 3 special issues of the PhilosophicalTransactions on H3

+.135 For applications to astrochemistry thetour de force calculation of 3 million transitions by Neale,Miller, and Tennyson in 1996125 suffices.The only H3

+ spectrum other than the fundamental bandobserved in space has been the intense emission of the firstovertone 2ν2

2 → 0 band observed from Jupiter.136,137,12 Thetransition dipole moment of the band is 0.067 D,27 and thestrength of the transition |μ|2 is 5.4 times smaller than thefundamental band but the ν3 factor in the Einstein coefficientmore than compensates and the spontaneous emission of theovertone band is faster than the fundamental band. This bandin absorption may be useful for detecting interstellar H3

+ high Jand K levels because of the relatively lower atmosphericinterference in the K infrared window than in the L one. Theovertone band is included in Table 2 for this reason.The v2 = 2 state is 3-fold corresponding to = ±2 and 0. The

2v20 ← 0 transition is forbidden since both upper and lower

state are totally symmetric (A1′) and only the 2v22(E′) ← 0

transition is allowed. The selection rules are

Δ = ± Δ =J G0 or 1 and 3

The latter results from Δ = ±2 and Δk = ±1. Just as for theselection rules for the fundamental band, they automaticallysatisfy the parity rule +↔ − and spin rule ΔI = 0. The variationof G by three is expressed by t as in Table 2 (r, s, t for 1, 2, 3).

3.2. Rotational Transitions

Although H3+ does not have a permanent electric dipole

moment and hence has no rotational spectrum because of itsequilateral triangle equilibrium structure, breakdown of thesymmetry by vibration−rotation interaction or partial deutera-tion produces a dipole moment and rotational transitions. Bothof them play important roles in astronomical observations.

3.2.1. Forbidden Rotational Transitions of H3+. The

spontaneous symmetry breaking (SSB) is a general phenom-enon which occurs widely in various fields of physics. Theessence is that even under symmetric physical law, that is, asymmetric Hamiltonian, the symmetry of states may be broken.According to Nambu,138 “This is because the symmetry of aLagrangian, or an equation of motion, and symmetry of statesare two entirely different things. The latter may be a member ofa multiplet which as a whole represents the symmetry”. This

Table 2. Spectral Lines Useful for Observing Interstellar H3+

transitionsa ν (cm−1)b λ (μm) |μ|2 (D2)c interferenced

ν2 ← 0Q(1,0) 2529.724 3.95300 0.0254 3Q(1,1) 2545.420 3.92862 0.0128 1*R(1,1)l 2691.443 3.71548 0.0141 1*R(1,0) 2725.898 3.66852 0.0259 3*R(1,1)u 2726.220 3.66808 0.0158 3*R(2,2)l 2762.070 3.62047 0.0177 1R(2,1)l 2765.545 3.61592 0.0044 0R(2,2)u 2823.138 3.54216 0.0094 2R(2,1)u 2826.117 3.53842 0.0182 2*R(3,3)l 2829.925 3.53366 0.0191 5R(4,4)l 2894.488 3.45484 0.0197 1R(3,3)u 2918.026 3.42697 0.0071 3R(5,5)l 2956.073 3.38287 0.0199 4R(6,6)l 3014.364 3.31745 0.0200 10

2ν2 ← 0tR(6,6) 4777.226 2.09327 0.0044 2tR(5,5) 4820.598 2.07443 0.0041 4tR(4,4) 4861.790 2.05686 0.0038 3tR(3,3) 4900.393 2.04065 0.0034 2tR(2,2) 4936.000 2.02593 0.0030 2tR(1,1) 4968.272 2.01277 0.0024 8

aTransitions marked with asterisks are those most often used forspectroscopy of interstellar H3

+. bFrequencies are from thecompilation by Lindsay and McCall.124 cTransition strengths inDebye2 are calculated from the Einstein coefficients given by Neale,Miller, and Tennyson.125 dDegree of atmospheric interference in anarbitrary scale from 0 (nearly transparent) to 10 (almost completelyopaque) based on the Inf rared Atlas by Hinkle et al.126



phenomenon dominates the field of high-energy physics of aninfinite system in a most profound way. In molecular physics itappears as breaking of finite symmetry. There are countlessexamples of breaking 2-fold symmetry. A well-known means ofbreakdown of 3-fold symmetry is by the Jahn−Teller effect,139which results from the interaction between degeneratedelectronic and vibrational states. The SSB of rotational levelsof H3

+ occurs similarly through interaction between thevibrational and the rotational motion. Consider H3

+ rotatesrapidly around an axis in the plane of the molecule passing theapex proton 1 and bisecting the bases formed by protons 2 and3. The centrifugal force breaks the symmetry of the moleculefrom D3h to C2v, produces a small dipole moment on the orderof mDebye, and hence enables rotational transitions astheoretically formulated by Watson.140 In order to satisfy theparity changing (+ ↔ −) and spin conserving (ΔI = 0) rules,the selection rule has to be

Δ = ± Δ = ±J k0 or 1 and 3

These types of transitions are very weakly allowed. Theirspontaneous emission is negligible in the laboratory but ininterstellar space where a molecule remains in a rotational levelfor years such forbidden transitions is of primary importance indetermining the rotational distribution of molecules.The effect of this type of forbidden transition was first

studied for interstellar NH3, where the lifetimes of spontaneousemissions (2,2) → (1,1) (more accurately, they should bewritten (2,±2)→ (1,∓1)) and (3,3)→ (2,0) were calculated tobe 232 years and 43.3 years, respectively.141 These rates ofdecay are slower than collision rates in dense clouds by 1−2orders of magnitude, and thus, the forbidden transitions do notseriously affect thermalization of NH3 in dense clouds.However, the Einstein coefficient of this type of spontaneousemission is approximately proportional to B6, and the lighterH3

+ (B = 43.6 cm−1) decays more rapidly than NH3 (B = 9.94cm−1) by several orders of magnitude.142 The spontaneousemission lifetime of the (2,2) → (1,1) transition is 27.2days,125,143 corresponding to the critical densitythe density atwhich transitions by collisions are competitive to spontaneousemissionon the order of 200 cm−3 (estimated by dividing theEinstein coefficient by the Langevin rate constant of 2 × 10−9

cm3 s−1). This critical density is comparable to densities indiffuse clouds, and hence, the effect of the forbidden transitionis critical for calculation of the rotational distribution of H3

+ indiffuse clouds (see section 4.1.3). The frequencies and Einsteincoefficients of other forbidden rotational transitions are listed inref 143. Because of the ν3 factor, the spontaneous emissionrates 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 arepractically instantaneous compared to the collision scale indiffuse clouds. All H3

+ in high rotational levels cascade via thesespontaneous emissions to lower levels in diffuse clouds, andonly molecules in the lowest para-(1,1), the lowest ortho-(1,0),and metastable (3,3) have been observable so far. H3

+ in themetastable (3,3) level, which plays a crucial role in severalaspects of the H3

+ astronomy (section 4.3.1), cannot decaysince the possible ΔJ = −1 transition like (3,3) → (2,1) isforbidden by the ortho para rule and the ΔJ = −2 transitionrequires two-photon transitions. Both of them take longer thanthe 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 futurehotter clouds are found, higher metastable levels of H3

+ such as(4,4), (5,5), and (6,6) may be detectable. In the ionospheres ofthe outer planets H3

+ in many other levels have been observedbecause of the high temperature (as much as 1000 K) and highdensity (>1010 cm−3).12

3.2.2. H2D+ and HD2

+ (D3+). Although H3

+ does not have apermanent electric dipole moment, its partially deuteratedspecies has an effective dipole moment since their center ofmass is shifted from the center of charge. This type of dipolemoment and its associated rotational spectrum was initiallyconceived by Teller for HD+ (Herzberg, private communica-tion) and later applied to H2D

+ and HD2+.144 The magnitude of

the effective dipole moment is μa = 0.61 D for H2D+ and μb =

0.49 D for HD2+. Both dipole moments are aligned along the

C2 axis of the C2v symmetry, but that axis is associated with thesmallest moment of inertia in H2D

+ (hence the a axis) and withthe second smallest moment of inertia in HD2

+ (hence the baxis). With such large dipole moments spontaneous emissionsare rapid and most molecules are in the ground para-000 (IH =0) level or the lowest ortho-111 level (IH = 1) with energy 86.37K for H2D

+ and the ground ortho-000 level (ID = 2, 0) or lowestpara-101 level (ID = 1) with energy 50.24 K for HD2

+. The swapof ortho and para spin states for the ground 000 level is due tothe antisymmetric and symmetric requirement for the proton(fermion) and deuteron (boson). Therefore, the observablerotational transitions are mostly limited to a-type transitions ofH2D

+, the 101← 000 line at 1370.145836 GHz of p-H2D+, and

the 110 ↔ 111 line at 372.421384 GHz and 212 ← 111 line at2363.24282 GHz of o-H2D

+, and b-type transitions of HD2+,

the 111← 000 line at 1476.605460 GHz of o-HD2+ and the 110

↔ 101 line at 691.660483 GHz and the 212 ← 101 line ofp‑HD2

+ which is yet to be measured in the laboratory.Transitions between higher rotational levels may be observed inwarm and dense clouds in the future. Laboratory frequenciesfor such transitions have been measured by Amano and co-workers.145,100

D3+, like H3

+, does not have an electric dipole moment, andits detection in interstellar gas also can only be via its infraredrovibrational spectrum.146 Because of the larger mass thetransition strength of the D3

+ spectrum is smaller than that ofthe H3

+ spectrum by a factor of 2. The ortho (I = 3 and 0 and apart of I = 1) to para (I = 2 and a part of I = 1) ratio is 11 to 16.There are two problems, both very serious, for observing the

infrared spectrum of D3+. (1) The observation is limited to the

cold and dense region where the deuterium fractionationdiscussed in section 2.4.2 is extremely high. However, brightinfrared stars do not exist in such sightlines. (2) The bandorigin of the ν2 fundamental band of D3

+ is at 1834.7 cm−1 in aspectral region severely attenuated by atmospheric H2O.

4. H3+ AS AN ASTROPHYSICAL PROBE

Since H3+ is ubiquitous in an environment that contains H2

(section 2), the infrared absorption spectrum of H3+ serves as

the most general and universal astrophysical probe. It probesboth dense and diffuse regions. The only limitation, a seriousone, is that it is observable only toward bright infrared starswith smooth continuum. Nevertheless, observations of H3

+ canbe conducted toward a great many stars and provide several keyastrophysical data that cannot be obtained by otherastrophysical probes.



4.1. What We Learn from H3+ Observation

4.1.1. CO versus H3+ as Astrophysical Probes. In many

ways CO and H3+ are complementary. After H2, CO is the most

abundant molecule in dense clouds. The abundance of CO isthe result of its stability due to the high dissociation energy of11.1 eV, the highest in Table 1, and hence its longevity. Onceproduced, CO stays there for a long time, until it encountersions like H3

+, HN2+, and He+ (section 2.4.2), which are all not

that abundant. H3+ is produced much more rapidly than CO,

but its steady state concentration is low because of its highchemical activity. It is destroyed by practically all atoms andmolecules except He, H, and N (section 2.1.2) and very rapidlyby electrons (section 2.3.3). CO is mostly in dense clouds,whereas H3

+ exists both in dense and in diffuse clouds.Therefore, by observing infrared absorption lines of both COand H3

+ one can discriminate H3+ in dense clouds and H3

+ indiffuse clouds. This is particularly useful in the observationalstudies of the Galactic center (section 4.3) where the longsightlines cross foreground spiral arms. As discussed in section2.3.1, the number density of CO is proportional to the clouddensity and therefore its column density provides informationon the mass of clouds whereas the number density of H3

+ isconstant as long as it is in typical dense or diffuse clouds and itscolumn 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 powerfulastrophysical probes because of their ubiquity, strength due tothe high abundance of CO, relatively slow spontaneousemission, and ease of observation. Compared with them theinfrared absorption of H3

+ has a few serious drawbacks: thelimitation by the availability of stars, atmospheric interference,and difficulty of observations. Nevertheless, H3

+ can provideimportant astrophysical information which CO either cannotprovide or cannot as reliably. The value of H3

+ as anastrophysical probe is discussed in the following subsections,and its applications to various astronomical objects arediscussed later.4.1.2. H3

+ as Thermometer and Densitometer (ColdClouds). Any atomic or molecular probe with more than onelevel is potentially capable of providing information on thetemperature T of the environment. If more than 2 levels areobservable, information on the density n may also be obtained.From the observed relative intensities for a pair of levels oneobtains a relative column density and an excitation temperatureTex. Analysis of more than one Tex taking into account of bothradiative and collisional effects may provide T and n. There arefew molecules for which more than two levels are observablethat provide meaningful density constraints. The millimeterwave emissions of CS, HCN, HCO+, etc., which have largedipole moments (1.958, 2.985, and 3.30 D, respectively), havelifetimes of 6.6 days, 11.5 h, and 9.3 h against the J = 1 → 0spontaneous emission corresponding to critical densities147,148

on the order of from 104 to 3 × 105 cm−3. Since the rate ofspontaneous emission and the critical density are proportionalto J4/(2J + 1), the critical densities increase rapidly with J.Therefore, emissions of those molecules probe relatively highdensity regions. CO with its anomalously small dipole momentsof 0.10980 D can serve as a more general probe because ofslower spontaneous emission with a lifetime of 162, 16.1, and4.5 days for the J = 1 → 0, 2 → 1, and 3 → 2 emissions,respectively, and critical densities on the order of from 300 to 3× 104 cm−3 depending on the temperature. Thus, CO emissioncan serve as a probe to determine T and n for dense clouds with

relatively low to high density.149 NH3 is unique because itsinversion spectrum appears in the centimeter wave regionregardless of J and K and allows measurements of the columndensities of hot rotational levels.The high abundance of CO which makes extensive

observations of its emission possible introduces difficulty inits analysis. The difficulties are 2-fold. First, in general it isdifficult to determine the column density from the intensity ofthe emission spectrum because the effects of collision, whichare often not accurately known, need to be taken into account.Reliable column densities are more directly measured from theequivalent widths (integrated intensities) of the weak infraredabsorption spectrum, for which the effects of collisions areunimportant as long as the lines are not badly saturated.Second, the high optical depth of CO emission is difficult toassess. Radiative transfer in such medium, including theradiation trapping, is a complicated problem and hard to treatreliably. The method of large velocity gradient developed byGoldreich and Kwan150 and Scoville and Solomon151 is used,but the resultant column densities have high uncertainties. Texdetermined from such column densities is not very accurate.Infrared absorption lines of H3

+ are much weaker and harderto observe than the CO emission but once observed givereliable column densities by a straightforward analysis by eq 10.The accuracy of the column density is limited only by thesignal-to-noise ratio of the observed spectral lines which forrelatively strong lines is on the order of 10. For the low-temperature dense and diffuse clouds in the Galactic disk, onlythe lowest para-(1,1) level and the ortho-(1,0) level arepopulated. The ratio of their column densities gives anexcitation temperature from the formula

= −⎛⎝⎜

⎞⎠⎟

NN

KT

(1, 0)(1, 1)

2 exp32.86

ex

where 32.86 K is the energy separation between the (1,0) andthe (1,1) levels. Unlike in neutral molecules like H2 or NH3where the ortho−para conversion takes millions of years toequilibrate, the ortho−para conversion of H3

+ occurs rapidly bythe reaction

+ → * → ++ + +H H (H ) H H3 2 5 3 2 (11)

which was discussed earlier in section 2.4.3 as one of the twomain mechanisms to thermalize o- and p-H2. This reaction, thesimplest involving polyatomic molecules, has been studiedexperimentally107−110 and theoretically.111,112 In dense cloudswhere the lifetime of H3

+ is on the order of 10 years, thereaction occurs 1000 times during the life of H3

+ using the rateconstant of 3.5 × 10−10 cm3 s−1 obtained from measurement ofdeuterated species by Gerlich et al.96,97 o-H3

+ and p-H3+ are

well thermalized, and thus, T = Tk = Tex where Tk is the kinetictemperature. For diffuse clouds where the lifetime of H3

+ is also∼10 years, the reaction occurs on the order of 10 times;whether the ortho−para H3

+ thermalizes is less certain butprobable. Here again the small rate constant of the deuteratedversion of this reaction measured by Gerlich96,97 discussed insections 2.4.2 and 2.4.3 is crucial. If correct T = Tex is moreuncertain, 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 determinedfrom H3

+.



4.1.3. H3+ as Thermometer and Densitometer (Warm

Clouds). It has been found during the study of the gas near theGalactic center that the infrared spectrum of H3

+ is a verypowerful probe for measuring T and n of warm clouds. In thewarm gas near the Galactic center, the metastable (3,3) level,361 K above the lowest (1,1) level (Figure 7), is wellpopulated.153 Since H3

+ in this level is transferred to otherlevels only via collision-induced transitions, a detectablepopulation in that level is a sure sign of high kinetictemperature. Thus, H3

+ in the (3,3) metastable level acts as athermometer. On the other hand, H3

+ in the (2,2) unstablelevel acts as a densitometer. The lifetime of 27.2 days for the(2,2) → (1,1) spontaneous emission corresponds to a criticaldensity on the order of A/kL ≈ 200 cm−3 where the Langevinrate constant of kL = 2 × 10−9 cm3 s−1 is used for a roughestimate. This value may be an underestimate by a factor of afew because of the uncertainty of collision cross section, but inany case, it is on the order of the densities of diffuse clouds, andthus, the population in the (2,2) level is sensitive to theirnumber densities. In diffuse clouds in the Central MolecularZone (CMZ) at the Galactic center (section 4.3.1), where thetemperature is high enough that the (2,2) level would besignificantly populated in LTE, absorption lines starting fromthat level are generally not observable, indicating a smallpopulation in it and a huge population inversion between the(3,3) and the (2,2) levels.154 This is a sure sign that the numberdensity of the cloud is very much lower than the critical density.The combination shown in Figure 6 of the high-lyingmetastable (3,3) level and the lower (2,2) level with the lifeof 27 days forms an ideal probe to measure the temperatureand density of the warm and diffuse gas, a vast amount of whichhas been unexpectedly revealed in the CMZ155 (section 4.3.1).A model calculation of the rotational distribution143 of H3

+ asa function of T and n allows more quantitative discussions.Because of the rapid spontaneous emission via forbiddenrotational transitions, the rotational distribution in diffuseclouds is far from the thermal Boltzmannian distribution. Thedistribution is a result of a subtle balance of the spontaneousemission and collision-induced rotational transitions betweenH3

+ and H2 (eq 11), H, and He. The spontaneous decay is veryaccurately known (section 3.2.1), but little information isavailable for the collisional rates other than that they are on theorder of the Langevin rate and from estimates based on thestatistical treatment by Park and Light.112 Therefore, while T isdetermined with fair accuracy (with an uncertainty of ±50 K), ncan be off by a factor of a few. In order to be applicable to manyobservations the number of parameters in the model143 isminimized at the cost of introducing larger error. It is wellknown that the nuclear spin states follow selection rules111 inthe collision between H3

+ and H2 (eq 11), but those rules areignored since the extra parameter of ortho to para ratio of H2complicates analysis. The neglect is justified for para-rich H2 ofdiffuse clouds since the higher para to para collision-inducedtransitions tend to be overwhelmed by the fast spontaneousemission. The guiding principle in dealing with the collision isBoltzmann’s principle of detailed balancing,155 and some otherrules (e.g., Fermi’s golden rule) are sacrificed. Application tothe diffuse gas in the CMZ is discussed in section 4.3.1.4.1.4. H3

+ as Tracer for the Cosmic-Ray IonizationRate. Observations of H3

+ can provide information on theionization rate of interstellar H2 that neutral molecules like COdo not provide. The degree of ionization of the gas is animportant 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 isthe most effective and universal ionization process. The mostimportant role of H3

+ as an astrophysical probe is in providingin situ information on the flux of low-energy cosmic rays, thosewith energies from 1 to 100 MeV. Together with γ-rays whichact as an in situ probe of high-energy cosmic rays with energies≥ 1 GeV, H3

+ will greatly contribute to the understanding ofthe mystery of cosmic rays. This interplay betweenastrochemistry of H3

+ and high-energy particle astrophysics isan exciting recent development.37 Measurement of low-energycosmic rays is particularly useful since these cosmic rays aredeflected by the solar magnetic field and thus are not directlyobservable.H3

+ is by far the most reliable probe to measure low-energycosmic rays. As discussed in section 2.3, the simple chemistry ofits production and destruction allows us to express the productof the ionization rate ζ and the path length L in simple formsfor both dense (eq 7) and diffuse (eq 9) clouds. Prior to theadvent of H3

+ spectroscopy, production and destruction of H+

were used as a probe for cosmic rays. However, since H+ is notdirectly observable, its spectroscopic surrogates OH or HDwere used.156 The chemistry linking H+ to these molecules iscomplicated and has been estimated by numerical calculationrather than analytical formulas such as eqs 7 and 9. Moreseriously, destruction of H+ by radiative recombination is veryslow, and other destruction mechanisms such as grainneutralization have to be taken into account.157 The chemistryof H3

+ is clean, particularly in diffuse clouds since dissociativerecombination is more than 3 orders of magnitude faster thanradiative recombination and no other competing processescomplicate the calculation.The advent of H3

+ as an astrophysical probe has drasticallychanged the understanding of the spectrum of low-energycosmic rays. Since the lower limit of ζ ≈ 6.8 × 10−18 s−1 givenby Spitzer and Tomasko,69 values of ζ of a few to several times10−17 s−1 have been used for over 30 years bothobservationally156,158 and theoretically.159 Readers are referredto Dalgarno’s review160 for details. Starting from the surprisingdiscovery of strong H3

+ signals in diffuse clouds toward CygnusOB2 No. 12,161,162 systematic studies by McCall and others ofH3

+ in dense clouds163 and diffuse clouds164 have revealed thesurprising fact that the column densities of H3

+ in diffuse cloudsare comparable to those in dense clouds, in spite of thereddening E(B − V) and visual extinction AV being 10 timessmaller (Figure 8).121,82,165 Since the latter are proportional tothe column density of hydrogen NH, the H3

+/H ratio is 10times higher in diffuse clouds than in dense clouds. Inretrospect, these results together with the simple analysis givenin sections 2.3.1 and 2.3.2 were sufficient to conclude that theionization rate ζ in diffuse clouds is 10 times higher than indense clouds, that is, a few to several times 10−16 s−1, but thiswas first mentioned explicitly in 2003 by McCall et al.166 afterthe discovery of H3

+ toward ζ Persei. This conclusion has sincebeen firmly established by observations toward many moresightlines167,72 as discussed later in section 4.2.2. The lowerionization rate in dense clouds is most simply explained as dueto the presence of a previously unsuspected large population of1−10 MeV cosmic rays, which are attenuated near the surfacesof dense clouds but penetrate diffuse clouds.168

The column densities of H3+ toward the diffuse gas in the

Galactic center are over an order of magnitude higher thantoward other diffuse cloud sightlines in the Galactic disk162,153



as discussed later in section 4.3. This suggests that theionization rate in the Galactic center is considerably higher thanin diffuse clouds in the Galactic disk.Observations of H3

+ have thus revealed the followinghierarchy: ζ ≈ 3 × 10−17 s−1 for dense clouds, ζ ≈ 5 × 10−16

s−1 for diffuse clouds in the Galactic disk, and ζ ≥ 3 × 10−15 s−1

in diffuse gas in the Galactic center.154 The high ionization ratein diffuse clouds initially met with skepticism but now is beingaccepted. In fact, there now are arguments that these higherionization rates are not high enough to be in accord withestimates of in situ high-energy cosmic rays inferred from γ-raysand X-rays by Yusef-Zadeh et al.170 which indicate ζ ≈ 5 ×10−13 s−1 and by Becker et al.170 who estimate ζ ≈ 1 × 10−12

s−1, albeit for local environments. The connection between thedirectly observed high-energy cosmic rays and the low-energycosmic rays observed via H3

+ is an inspiring and difficultproblem171 whose clarification will no doubt increase theunderstanding of cosmic rays.4.1.5. Saturation of the Effect of Ionization. Treatment

of the H3+ chemistry described so far indicated that the number

density of H3+ is proportional to the ionization rate ζ. This is

because ζ entered only in the production of H3+, and its

negative effect of destroying H3+ by increasing electron density

was ignored. This is a good approximation for low values of ζup to 10−15 s−1 for which the electron density produced by ζ ismuch smaller than the electron density from phoionization ofC, which is assumed to be constant and equal to nC. As ζ getshigher than 10−15 s−1 as needed to explain the high observedH3

+ column densities toward the Galactic center, the negativeeffect needs to be taken into account.

The number density of electrons ne produced by ionization ζcan be estimated equating the production and destruction ratesof electrons

ζζ

+ = ≈ ≈+⎡⎣⎢

⎤⎦⎥n n k n n k n n

nk

(H )12

(H) (H ) as2e2 e e 3 e

2e

H

e

(12)

where ζ = 2ζH (section 2.2.2) is used and the positive chargesare assumed to end up all in H3

+. This latter assumption isclearly not valid for dense clouds where CO, O, O2, N2, H2O,etc., will deprive H3

+ of a proton but is a better approximationfor diffuse clouds where we need to examine the effect of high ζvalues. Nevertheless, atomic O is still there, and the electrondensity calculated from eq 12 should be taken as a lower limit.For a typical set of values, ζ = 10−15 s−1, nH = 100 cm−3, and ke= 10−7 cm3 s−1, eq 5 gives ne ≈ 7 × 10−4 cm−3, which is ∼5% ofnC. Since this is a lower limit, we see that the effect of ne isalready beginning to be significant at this ζ value.The electrons produced by ionization of H2 and H reduce

the number density of H3+ in diffuse clouds in two ways.172,173

First, it will increase the destruction rate of H3+; we need to

replace nC with nC + ne in the first equation of section 2.3.2.Because ne depends on ζ this introduces nonlinearity of n(H3

+)on ζ. Second, as the electron density increases the dissociativerecombination of H2

+, H2+ + e → H + H gets faster and

becomes competitive with the H3+-producing reaction H2

+ +H2 → H3

+ + H. This reduces the effective production rate ofH3

+ just like the charge exchange reaction discussed in section2.2.3. A model calculation by Liszt172 has shown that this effectis serious for diffuse clouds with small f(H2) where thenonlinearity on ζ sets in already at the level of ζ ≈ 10−16 s−1.Recent more detailed calculations by Ruaud, Le Petit, andRoueff174 using an extensive chemical network has shown thatproduction of H3

+ not only saturates but also decreases withincreasing ζ after certain values. As noted in section 4.4.1. byOka et al.154 and section 5.3 by Goto et al.117 we need to becautious about increasing the value of ζ much beyond 5 × 10−15

s−1. This sets a rough upper limit on ζ and hence a lower limiton the path length L.

4.2. H3+ in the Galactic Disk

4.2.1. H3+ in Dense Clouds. After 16 years of

searching,175,176 since laboratory detection,122 the infraredspectrum of interstellar H3

+ was detected in 1996 toward twobright infrared stars with high reddening, GL 2136 andW33A.44 Installment of a 256 × 256 array detector in the CGS4spectrometer was crucial for these detections, which were madeat the United Kingdom Infrared Telescope (UKIRT). Readersare referred to anecdotal stories of the discovery by Geballe177

and Oka.178 As shown in Figure 9, the signal-to-noise ratioswere not high, but the doublet shape and observed shift by theEarth’s motion made detection definitive.The observed total column densities of the two clouds (4.0 ±

0.9) × 1014 and (6.0 ± 2.2) × 1014 cm−2 were about the orderof magnitude expected from chemical model calculations andprovided the most direct evidence for the validity of the ion-neutral reaction scheme for production of interstellar moleculesinitiated by Herbst and Klemperer60 and by Watson61 that hadbeen assumed and already used for 23 years. The observedpopulation ratio between the ortho-(1,0) level and the groundpara-(1,1) level implied kinetic temperatures of ∼40 K for bothclouds.

Figure 8. Observed H3+ column densities N(H3

+) versus color excessE(B − V) for dense (upper) and diffuse clouds (lower).121,82 Note thatthe two categories of clouds have comparable N(H3

+), although theirE(B − V) are different by an order of magnitude. Reprinted withpermission from ref 82. Copyright 2006 United States NationalAcademy of Sciences.



Subsequently, H3+ has been observed in several dense

clouds.16,43,179,180 The observed column densities, values of ζLcalculated from eq 7, cloud lengths L calculated using anassumed value of ζ = 3 × 10−17 s−1, and temperatures are listedin Table 3.The observed column densities are on the order of 1014

cm−2, comparable to the column densities used in laboratoryspectroscopy.122 The H3

+ number density of ∼10−4 cm−3 indense clouds (section 2.3.1) is lower by 15 orders of magnitudethan in laboratory plasmas (∼1011 cm−3), but this isapproximately compensated by the large path lengths, on theorder of one parsec, compared to the typical laboratory pathlength of ∼10 m. The values of ζL, which range from 213 to 45cm s−1, are reliable, but the separation of ζ and L by assuming asingle value of ζ is not accurate since the value of ζ may differfor different clouds. Nevertheless, the values of L in the table,ranging from 0.5 to 2.3 pc, are the range of dimensionsexpected for dense clouds. The temperatures, ranging from 22to 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 104 cm−3;the embedded stars provide radiation for absorption spectros-copy of H3

+. There is, however, one significant exception. In theobservations of H3

+ in the Galactic center, to be discussed insection 4.3, the long sightlines cross three foreground spiralarms, the 3 kpc arm, the 4.5 kpc arm, and the local arm. The

near identical velocity profiles of H3+ and CO at −52, − 32, and

−5 km s−1 shown in Figure 10 indicate that much of the H3+

coexists with CO. The abundant CO demonstrates that theclouds are probably fully molecular, but the low estimatedvisual extinctions toward the Galactic center of AV < 40(mag)181,182 indicate that the number densities are considerablyless than 104 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 H3

+ number density discussedin section 2.3.1, H3

+ abounds in such clouds relative to itsabundance in the much denser clouds associated with the starslisted in Table 3. Quantitative studies of the gas in the spiralarms is yet to be done.

4.2.2. H2D+ and HD2

+ in Dense Cloud Cores. Theextremely high deuterium fractionation discussed in section2.4.2 makes detection of H2D

+ and HD2+ realistic in dense (n ≈

106 cm−3) and cold (T < 10 K) cloud cores. After a few falsedetections, the 110 → 111 emission at 372 GHz of o-H2D

+ wasbarely detected toward NGC 1333 IRAS 4A in 1999.183 After a

Figure 9. First detection of interstellar H3+ at the UKIRT toward two

young stars that are deeply embedded in their natal dense molecularclouds. Doublet at 3.66808 and 3.66852 μm are the R(1,1)u andR(1,0) transitions of o- and p-H3

+, respectively. Reprinted withpermission from ref 44. Copyright 1996 Macmillan Publications Ltd.

Table 3. Observed H3+ Column Densities in the (1,1) and (1,0) Levels, Total H3

+ Column Densities, ζL Calculated by Eq 7(section 2.3.1), Cloud Length L with the Assumed Value of ζ = 3 × 10−17 s−1, and Temperature in Dense Cloudsa

object N(1,1) (1014 cm−3) N(1,0) (1014 cm−3) Ntotal (1014 cm−3) ζL (cm s−1) L (parsec) T (K) ref

AFGL2136 1.9 1.9 3.8 155 1.7 47 163W33A 2.9 2.3 5.2 213 2.3 36 163Mon R2 IRS 3 0.8 0.6 1.4 57 0.6 31 163AFGL 961E 1.1 0.6 1.7 69 0.7 25 163AFGL 490 0.7 0.4 1.1 45 0.5 26 163AFGL 2591 1.2 1.0 2.2 90 1.0 38 163LkHα 101 1.4 0.9 2.3 94 1.0 23 179MWC 349 1.3 3.0 4.4 180 1.9 22 180

aThe H3+ 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 1080.180

Figure 10. R(1,1)l line of H3+ and the R(1) line of the v = 2 ← 0

(overtone) band of CO observed toward GCS 3-2. Three deep andsharp absorptions at −52, −32, and −5 km s−1 originate in foregroundspiral arms. High abundance of CO indicates molecular clouds, butlow reddening of the sightline indicates lower densities than the cloudslisted in Table 3. Reprinted with permission from ref 154. Copyright2005 American Astronomical Society.



more definitive detection in the prestellar core L1544 in2003,184 Caselli et al.185 detected the emission line in 7 starlesscores and 4 protostellar cores. The estimated high columndensities of o-H2D

+, (0.2 − 4.1) × 1013 cm−3 and (0.5 − 6.7) ×1013 cm−3 for assumed critical densities of 105 cm−3 and 106

cm−3, respectively, provide the most direct observationalevidence for deuterium fractionation of H3

+ discussed insection 2.4.2. Since the ortho−para conversion through theproton-scrambling reaction, o-H2D

+ + p-H2 → (H4D+)* → p-

H2D+ + p-H2, which is exothermic by 86.37 K, is forbidden by

the nuclear spin selection rules,97,111 the o-H2D+ in the 111

rotational level does not readily convert to p-H2D+. Reaction

with o-H2 is not spin forbidden, but the population of o-H2 islow at the reported low kinetic temperatures of 7−15 K.185 Inany case, detection of p-H2D

+ through the 101 ← 000 absorptionat 1370.145836 GHz is awaited using SOFIA or CCAT,although a sufficiently intense background radiation source at66 K may not be easy to find behind high-density, low-temperature cores.The far-infrared detection toward Sgr B2 of the 212 ← 111

absorption at 2363.24 GHz of o-H2D+, which yielded an

estimated column density of (2 − 5) × 1013 cm−2, byCernicharo et al.186 is noteworthy. Their estimated density isnot that high (a few times 104−105 cm−3), and their estimatedkinetic temperature is not that low (∼20 K). Detection must bedue in part to the high abundance of H3

+ in Sgr B.187 p-H2D+ in

the 000 level must be more abundant.p-D2H

+ was first detected through its 110 → 101 emission at691.66 GHz in the prestellar core 16293E by Vastel et al.188

and later more securely as extended emission in the prestellarcore L1688, in Ophiucus, by Parise et al.189 The observed highcolumn density of D2H

+ (comparable to or higher than that ofH2D

+) is partly due to lower separation of the ortho−paralevels of D2H

+ (50.24 K) than that of H2D+ (86.27 K) but

demonstrates the efficiency of H3+ deuterium fractionation and

also indicates a high degree of CO depletion. Such informationis important for understanding the early stages of starformation. Again, observation of much more abundant o-D2H

+ by its 111 ← 000 absorption at 1476.6 GHz is highlydesirable, although finding background radiation at 70.87 K iseven more difficult. A search for this transition in emission bythe Herschel HIFI instrument was negative as expected.190 Asearch for H2D

+ and HD2+ toward W 33A via infrared spectra

was unsuccessful (T. R. Geballe, private communication).4.2.3. H3

+ in Diffuse Clouds. While the H3+ column

densities on the order of 1014 cm−3 were expected from modelcalculations in dense clouds, observations of similar columndensities in diffuse clouds were surprising (Figure 8).161,162 Inthe simple model calculation given in sections 2.3.1 and 2.3.2for dense and diffuse clouds, respectively, carbon is all in CO inthe former but in C+ in the latter. Since the rate of dissociativerecombination of H3

+ is 100 times faster than the rate ofproton-hop reactions, the number density of H3

+ was expectedto be 100 times less in diffuse clouds than in dense clouds if thecosmic ray ionization rate is the same for both clouds.Therefore, even though the column lengths of diffuse cloudsare 10 times greater, the expected column densities are 10 timeslower, which would hardly be detectable. The unexpecteddetections of H3

+ in diffuse clouds with similar line strengths asin dense clouds has led to the conclusion discussed in section4.1.4 that the cosmic ray ionization rate in diffuse clouds mustbe an order of magnitude higher than in dense clouds. This hasbeen well established by the extensive work by McCall et al.164

and Indriolo et al.167,72

The observed H3+ column densities, N(1,1), N(1,0), Ntotal,

ζL, ζ, and Tex in diffuse clouds are listed in Table 4. The valuesof column densities and ζ are from Indriolo and McCall,72 andthe excitation temperatures Tex are calculated from N(1,1) and

Table 4. Observed H3+ Column Densities (in 1014 cm−2) in the (1,1) and (1,0) Levels, Total H3

+ Column Densities, ζL (in 104

cm s−1) Calculated by Eq 9 (section 2.3.2), Estimated Cosmic Ray Ionization Rate ζ (in 10−16 s−1), and Excitation Temperature(in K) in Diffuse Clouds

object N(1,1) N(1,0) N ζL ζ Tex ref

HD 20041 1.60 0.77 2.37 2.54 9.5 23 72HD 21389 0.50 0.37 0.87 0.93 7.1 33 72ζ Per 0.41 0.22 0.63 0.67 5.6 25 72X Per 0.48 0.25 0.73 0.78 5.9 24 72HD 29647 0.67 0.52 1.19 1.27 2.4 35 72HD 73882 0.61 0.29 0.90 0.96 9.7 23 193HD 110432 0.31 0.21 0.52 0.56 3.9 30 193HD 154368 0.65 0.29 0.94 1.01 4.2 22 72WR 104 1.25 1.05 2.30 2.46 2.4 38 164HD 168607 0.44 0.22 0.66 0.71 1.7 24 72HD 168625 0.66 0.40 1.06 1.13 3.0 28 72HD 169454 0.34 0.26 0.60 0.64 2.5 34 72W40 IRS 1A 1.51 1.13 2.64 2.82 3.3 33 72WR 118(5) 1.38 1.95 3.33 3.56 3.1 95 164WR 118(47) 1.47 1.64 3.11 3.33 3.1 56 164WR 121 1.12 2.20 2.35 3.0 164HD 183143(7) 0.72 0.54 1.26 1.35 10.6 23 164HD 183143(24) 0.90 0.59 1.49 1.59 7.8 33 164HD 229059 2.12 1.62 3.74 4.00 2.6 25 72Cyg OB2 5 1.21 1.21 2.42 2.59 8.1 24 164Cyg OB2 12 2.02 1.40 3.42 3.66 2.9 35 164HD 204827 1.29 0.61 1.90 2.03 9.3 23 72λ Cep 0.43 0.33 0.76 0.81 2.8 30 72



N(1,0) using the formula in section 4.1.2. The values of ζL havebeen calculated using the last form of eq 9 using the value ofthe dissociative recombination rate at T = 70 K. The ζL valuesof diffuse clouds are 2 orders of magnitude higher than those ofdense clouds due to factors of ∼10 higher values for both ζ andL. Separation of ζ and L is difficult but is more tractable than indense clouds because a variety of observed UV or visiblespectra are available. H2 column densities are known directlyfrom the H2 UV spectra191 or can be estimated from spectra ofother species such as CH and/or from the directly measuredE(B−V). The total hydrogen number densities nH have beenestimated from analysis of UV spectra of CO.192 The values ofζ in Table 4 are those published by Indriolo and McCall72

determined from estimated values of L. Indriolo and McCallneglected the correction given in eq 6; the values in Table 4should be multiplied by a factor of 1.5 to be consistent with theζL values of Table 4 (section 2.3.2).The excitation temperature of H3

+ of ∼30 K is considerablylower than the excitation temperature of H2 of ∼70 K in thesame clouds, which has been thought to give the actual kinetictemperature of the clouds. The difference has been ascribed152

to incomplete ortho−para thermalization of H3+ because of the

short lifetime of H3+ due to the rapid dissociative

recombination in diffuse clouds. The effect can also beexplained as due to fast spontaneous emission as discussed insection 3.2.1 (Figure 6 of ref 143).

4.3. H3+ in the Galactic Center

The 1997 discovery of large H3+ column densities, on the order

of 3 × 1015 cm−2, toward two stars, GC IRS 3 and GCS 3-2, byGeballe et al.162,194 opened up the H3

+ studies of the gas in theCentral Molecular Zone (CMZ),195 a region of radius ∼150 pc,at the Galactic center. The CMZ is a fascinating environmentcontaining a multitude of extraordinary phenomena and objectssuch as the central supermassive black hole Sgr A*, the threedense clusters of young and hot stars, high densities of stars andsupernova remnants, the huge radioarc and nonthermalradiofilaments, and intense and widespread X-ray emission.This center of astrophysical activities has been studied overmany years via its radiocontinuum emission, radioemission andabsorption lines of HI, OH, H2CO, CO, NH3, HCN, CS, etc.,far-infrared emission of atoms and dust, infrared spectrum ofCO, X-rays, and γ-rays.196,195,197,198 Observations of theinfrared spectrum of H3

+ provide new information unavailablefrom those observations.The CMZ is a huge region containing both dense and diffuse

clouds. The infrared spectrum of H3+ (refs 162, 153, 154, 117,

187, 118, 194, 199, and 200) has proven to be a powerfuldiagnostic of the diffuse gas in the CMZ due to the simple H3

+

chemistry. All observations toward infrared stars from 140 pc tothe West of Sgr A* to 120 pc East have shown that the H3

+

spectrum is largely formed in diffuse gas, indicating a near 100%surface-filling factor of the diffuse interstellar medium in theCMZ. For example, the H3

+ spectra toward the QuintupletCluster and other stars between Sgr A* and 30 pc to the East ofit (Figure 10 gives an example) indicate a diffuse gaseousenvironment in the CMZ but little evidence for denseclouds.117 The large column densities imply that the diffusegas must have a line of sight extent of tens of parsecs. To date,spectra indicating H3

+ in dense clouds in the CMZ have beenobserved only toward a few stars along sightlines to giantmolecular clouds associated with the radiosources Sgr A, B, C,and E. Spectra originating in these compact dense clouds200 are

affected by individual local conditions and difficult tocharacterize in general. Therefore, the following discussion ismostly limited to observations of H3

+ in diffuse gas in the CMZ.4.3.1. Revelation of a Vast Amount of Warm and

Diffuse Gas. The rotational energy level system of H3+

discussed in section 3.1.2 and shown in Figure 6, in whichthe 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 anddensity of the warm and diffuse gas in the CMZ. An example ofthe observed set of the R(1,1)l, R(3,3)l, and R(2,2)l absorptionsof H3

+ and the R(1) line of the first overtone transition v = 2←0 of CO toward the brightest infrared star GCS3-2 is shown inFigure 11. Comparison of the spectra of the two species allows

one to discriminate between H3+ absorption in the foreground

spiral arms and in the CMZ, as shown in Figure 10, but also canindicate dense clouds within the CMZ. Spectra show that mostof the CO in this sightline is in the spiral arms and relativelylittle exists in the CMZ apart from the CO which produces twominor absorptions at velocities of −97 and −82 km s−1.The top trace in Figure 11 is the R(1,1)l absorption by H3

+ inthe ground (1,1) level. After subtracting the absorption byforeground H3

+, which has a nearly identical velocity profile asCO, a broad trough extending from −160 to 20 km s−1

remains. This absorption, which is devoid of sharp velocity

Figure 11. Observed H3+ (top three) and CO absorptions toward

GCS 3-2. Three H3+ 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 theR(3,3)l and R(2,2)l absorption is multiplied by a factor of 2, and that ofthe CO absorption is divided by 2. Reprinted with permission from ref154. Copyright 2005 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 alarge distance along the line of sight. The second trace is theR(3,3)l absorption of H3

+ (magnified by a factor of 2), arisingfrom the metastable (3,3) level, 361 K above the (1,1) level.Unlike the R(1,1)l absorption, this absorption does not containsharp features, indicating that it is entirely due to H3

+ in theCMZ. Its overall structure is nearly identical to the trough ofthe R(1,1)l absorption. The strength of the R(3,3)l absorptionclearly indicates that the diffuse gas in the CMZ has a hightemperature. This absorption line has been sought in dense anddiffuse clouds in the Galactic disk but not surprisingly has notbeen found, as those diffuse clouds are cold. It is thus a uniquefingerprint of the gas in the Galactic center. The third trace isthe 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 discussedin section 3.2.1. Nondetection of this absorption as seen inFigure 11 demonstrates a nonthermal negative excitationtemperature between the (2,2) and the (3,3) levels and clearlyindicates that the density of the environments probed by H3

+ ismuch 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 SgrA117,200 and B.199 It is a fingerprint of dense and warm gas inthe CMZ.The model calculation143 discussed in section 4.1.3, together

with observed spectra, yields T ≈ 250 K and n ≤ 100 cm−3.154

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 itsubiquity and a high volume filling factor.117 Subsequentobservations187 toward several more stars from 140 pc Westto 85 pc East of Sgr A* have also shown similar gas, suggestingthat the warm and diffuse gas fills a large fraction of the CMZ.Previously, three categories of gas had been known in theCMZ:195 (1) dense molecular clouds observed by CO andother radioemissions, (2) hot (T ≈ 104−106 K) and highlyionized diffuse gas observed by recombination lines, FIR atomiclines, radiowave scattering, etc., and (3) ultrahot (T ≈ 108−109K) X-ray-emitting plasma gas. Observations of H3

+ haverevealed a new category of warm and diffuse gas with a highvolume filling factor and drastically changed the previousconcept of gas in the CMZ. Prior to the discovery and mappingof H3

+ in the CMZ, a conceptual picture201 indicated that theultrahot X-ray emitting gas (3) dominates the CMZ but verylikely the newly found warm and diffuse gas has the highestvolume filling factor in the CMZ.

4.3.2. High Ionization Rate in the Central MolecularZone. According to eq 9 the observed total H3

+ columndensity is an in situ indicator of the ionization rate in theenvironment. In applying this equation to the gas in the CMZ,three further considerations are needed: (1) The increase ofmetallicity from solar vicinity to the Galactic center increasesthe carbon to hydrogen ratio nC/nH by R = (nC/nH)GC/(nC/nH)SV. Since in diffuse clouds the carbon is singly ionized, thedestruction rate of H3

+ via dissociative recombination isincreased by the same factor. In a great many papers, increases

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

J17470898-2829561 (α) (left) and 2MASS J17432173-2951430 (ι) (right) which are in the region of Sgr E and Sgr B, respectively. Vertical scales ofthe 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.



of metallicity from R ≈ 3.6202 to R ≈ 6.7203 have been reported.If the idea of direct proportionality between the CO to H2conversion factor and the metallicity204 is assumed, the result ofSodoroski et al.205 gives R = 3−10. The minimum value R ≈ 3is used here to give a lower limit (ζL)min in the followingdiscussion.(2) The temperature-dependent rate constant of the H3

+

dissociative recombination80 is 7.7 × 10−8 cm3 s−1 at 250 K andreduces the value of ζL by a factor of a few, which tends tocancel the effect of R discussed above. (3) Unlike in denseclouds where f(H2) = 1 and diffuse clouds where f(H2) ≈ 0.67corresponding to n(H) ≈ n(H2) in the Galactic disk,72 thevalue of f(H2) is unknown in the Galactic center. Thus far,f(H2) = 1 has been used in the calculations, but the recentHerschel HIFI detections of H2O

+, OH+, CH+, etc., and theiranalyses206 indicated a very low value of f(H2) ≈ 0.1 or smaller.Some of these ions coexist with H3

+ as manifested by theirsimilar velocity profiles. Such a small value of f(H2) as 0.1 mayincrease the calculated values of ζL greatly. In terms of theuncertainties of the value, we use the minimum value of R = 3and the maximum value of f(H2) = 1 in the followingdiscussions. Therefore, the values of calculated (ζL)min used inthe following discussions are absolute lower limits; the truevales are very likely larger by at least a factor of 2 and possiblyby much more than that.The total column densities of N(H3

+) = (1.9−6.1) × 1015

cm−2 observed toward stars from Sgr A* to 30 pc to the East117

and higher values in the wider region of the CMZ are an orderof magnitude higher than those in dense and diffuse clouds inthe Galactic disk. This results in high values of (ζL)min = (1.7−4.5) × 105 cm s−1, which are higher than the ζL values fordense clouds (Table 3) and diffuse clouds (Table 4) by a factorof ∼2000 and ∼15, respectively. Separation of ζ and L is notpossible, but we can infer their magnitude from variousconsiderations. As an example, we discuss the averagemagnitude of (ζL)min = 3 × 105 cm s−1. Since the density forthe diffuse gas in the Galactic center n ≤ 100 cm−3 is lower thanthat of diffuse gas in the Galactic disk nH ≈ 200 cm−3 thefraction f(H2) must be lower. If we use the value of f(H2) =0.67, we have ζL = 7 × 105 cm s−1. It is clear that the value of ζ= 5 × 10−16 s−1 for diffuse clouds in the Galactic disk72 is too

small since the corresponding L = 450 pc does not fit in theCMZ. A set of ζ ≈ 3 × 10−15 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 inthe CMZ is an order of magnitude higher than in diffuse cloudsin the Galactic disk and the volume filling factor of the diffuseclouds is very high, perhaps on the order of 50%. The highionization rates met skepticism,207 but it is accepted in view ofthe high densities of supernova remnants in the CMZ.208

Analyses of γ-rays and X-rays give similar209 or evenhigher169,200 ζ values in the CMZ. For such high ζ values theeffect of saturation or decrease of the H3

+ density discussed insection 4.1.5 should be taken into account. This will have aneffect of increasing L.

4.3.3. Morphology and the Expanding MolecularRing. The extended and rich velocity profiles of the H3

+

absorption lines, as shown in Figure 11, vary in intricate waysdepending on the sightline. Figure 12 shows spectra of H3

+ andCO toward the star 2MASS J17432174-2951430 (nicknamedα) located 140 pc West of Sgr A* (right) and toward the star2MASS J17470898-2829561 (nicknamed ι, Iota) located 85 pcto the East (left).187 Star α is in the giant molecular cloud in thedirection of Sgr E, and star ι is in the direction of the giantmolecular cloud complex Sgr B. Both sightlines cross denseclouds as well as diffuse clouds. H3

+ in dense clouds is identifiedby accompanying deep CO absorptions at the same velocity,while H3

+ in diffuse clouds is identified for absorptions(indicated by arrows in Figure. 12) that are not accompaniedby CO absorptions at the same velocities. In the spectrumtoward α (right), the deep absorption at −60 km s−1 is frommolecular clouds in the 3 kpc spiral arm (the other two spiralarms do not contain molecular clouds in this sight line) and thedeep absorptions at −200 and −172 km s−1 are due to denseclouds local to Sgr E, the former of which was observed in13CO emission by Liszt.211 In the spectrum toward ι (left),which is located between Sgr B1 and B2 and shows a very richcloud structure toward Sgr B, a hotbed of any molecularspecies, the deep and sharp absorptions at −43 and −20 km s−1

are due to the 3 and 4.5 kpc spiral arms, respectively. COabsorption extends without interruption from −100 to +100km s−1 due to a great many dense clouds with varying radial

Figure 13. Circular (l, v) diagram obtained from observed H3+ 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 thedistribution of stars which have been found as suitable radiation sources for H3

+ 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 witharrow heads continue to low velocities.



velocities in the region. Spectra originating in compact denseclouds in the CMZ vary rapidly with sightline location, whilethose originating in diffuse gas change more slowly and providea larger scale morphological picture of the CMZ. Using thevelocity profiles of the infrared R(1,1)l and R(3,3)l absorptionsof H3

+ in diffuse clouds toward 13 stars plus a far-infrared 111 ←000 rotational absorption of H2O

+ toward Sgr B2 observed bythe Herschel HIFI instrument,212 one obtains the Galacticlongitude−velocity (l, v) diagram for diffuse gas shown inFigure 13. We use Sgr A* as the origin of the map and distancesfrom it instead of the Galactic longitude. The distance to theGalactic center is assumed to be 8 kpc for conversion fromGalactic longitude to pc. Bright stars tend to cluster, and it isdifficult to cover the wide region of the Galactic longitudecontinuously, but Figure 13 contains strong evidence for thepresence of an Expanding Molecular Ring (EMR) with a radiusof 140 pc and an expansion velocity of ∼140 km s−1.The EMR was initially reported by Kaifu et al.212 and

Scoville213 using radiolines of OH, NH3, H2CO, etc. Sofue214

identified the structure as an Expanding Molecular Shell using13CO emissions observed by Bally et al.215 The EMR of Figure13 obtained from diffuse clouds is smaller than those originallyreported (∼200 pc) and Sofue’s value (170 pc adjusted to amore recent distance to the GC). While those previous (l, v)diagrams are all ellipses, indicating rotational velocities of thering of 50−60 km s−1, Figure 13 indicates a circle, suggesting anonrotating, purely expanding ring. The longitude coverage isstill very patchy, but the strongest evidence for this is the near-zero velocities of the diffuse gas observed toward three stars α,α+, and β near Sgr E at the West end of Figure 13. AlthoughH3

+ has not been observed near the East end yet, it is knownthat the diffuse gas near Sgr D also has a near-zero velocity.210

A nonrotational expansion argues against a gravitational originfor the gas energy by the barred potential which predicts an (l−v) diagram of a parallelogram216 and is very unorthodox. Ifconstant velocity of expulsion is assumed, the radius of the ringand the velocity suggest a violent event one million years ago.The energy of expulsion is orders of magnitude lower than theenergy estimated by Kaifu et al. (1055−1056 erg), Scoville (4 ×1054 and 2 × 1055 erg), and Sofue (2 × 1054 erg) because of thelower density of the gas and lower thickness of the ring.Although the H3

+ observations indicate a purely expanding ring,perhaps it is not sufficiently extensive to exclude the possibilityof the parallelogram due to the barred potential.216

The study of the CMZ using the H3+ spectrum is in its

infancy. Many more suitable stars are needed to be found andobserved.

AUTHOR INFORMATION

Notes

With the richness of the subject covered in this review, thereferences are meant to be representative rather thanexhaustive.The author declares no competing financial interest.

Biography

Takeshi Oka received his Ph.D. degree from the University of Tokyoon the microwave spectroscopy of H2CO. After working as apostdoctoral fellow he became a research staff at the NationalResearch Council of Canada, where the Herzberg Institute ofAstrophysics was established in 1975. In 1981 he moved to theUniversity of Chicago, where he was jointly appointed to theDepartment of Chemistry and the Department of Astronomy andAstrophysics and later to the Enrico Fermi Institute.

ACKNOWLEDGMENTS

I am greatly indebted to T. R. Geballe who has read thismanuscript and revised extensively both its science andpresentation. I acknowledge useful suggestions on this paperby S. Saito and anonymous referees which considerablyimproved this paper.

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