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The galactic cosmic ray rate SPECIAL FEATURE

A. Dalgarno†

Harvard–Smithsonian Center for , 60 Garden Street, Cambridge, MA 02138

Edited by William Klemperer, Harvard University, Cambridge, MA, and approved June 7, 2006 (received for review March 15, 2006)

The chemistry that occurs in the in response to Dense Clouds cosmic ray ionization is summarized, and a review of the ionization Typical values for the ionization rate in dense gas lie in the range rates that have been derived from measurements of molecular from1to5ϫ 10Ϫ17 sϪ1 (7–14), depending on the details of the abundances is presented. The successful detection of large abun- ؉ measurements, the physical model, and the chemistry. There dances of H3 in diffuse clouds and the recognition that dissociative may be real variations in the ionizing flux. In some cases, values ؉ Ϫ Ϫ recombination of H3 is fast has led to an upward revision of the of ␨ as high as 10 15 s 1 have been derived and the enhanced rate derived ionization rates. In dense clouds the molecular abundances tentatively attributed to x-rays from a central source (15). A are sensitive to the depletion of monoxide, atomic , range of values with an average of (2.8 Ϯ 1.6) ϫ 10Ϫ17 sϪ1 was , , and metals and the presence of large derived by van der Tak and van Dishoeck (16) from measure- and grains. Measurements of the relative abundances of deuter- ments of HCOϩ in several dense molecular clouds in the ated species provide information about the removal mecha- ϩ direction of massive young stars, but from measurements of H3 nisms, but uncertainties remain. The models, both of dense and (17) rates in excess of 10Ϫ16 sϪ1 were obtained. A later analysis diffuse clouds, that are used to interpret the observations may be of the cloud in the direction of the massive star-forming region seriously inadequate. Nevertheless, it appears that the ionization AFGL 2591 yielded a rate of 5.6 ϫ 10Ϫ17 sϪ1, good to a factor rates differ in dense and diffuse clouds and in the intercloud of three (18). There was a discrepancy between the rates derived medium. ϩ ϩ from HCO and H3 that could easily be removed by a modifi- cation of the assumed distribution of material in front of the interstellar chemistry source.

Because of the relative simplicity of the chemistry, the most he fractional ionization is a fundamental parameter, distin- direct determination of ␨ would seem to be from studies of the ϩ Tguishing the different physical regimes that occur in the abundance of H3 (17, 19, 20). In a cloud of H2 molecules, cosmic ϩ interstellar medium. Because of the presence of and rays ionize H2 and produce H that immediately react with 2 ϩ positive ions the gas dynamics is modified by the coupling to the H2 in a fast ion- process to yield H ions (4, 5, 21). The ϩ 3 magnetic field which controls the transfer of angular momentum H3 ions are removed by transfer reactions with the and the dissipation of turbulence. The fractional ionization neutral constituents X, where X is any of interstellar CO, O, N2, determines the strength of the coupling and is a crucial aspect of H2O, and HD and D. If k(X) is the rate coefficient for the the evolution of the interstellar gas and the formation of stars reaction and planets. Energetic cosmic rays penetrate planetary atmo- ϩ ϩ 3 ϩ ϩ spheres and create low-altitude ionospheric regions and drive a H3 X HX H2, [1] low-altitude chemistry. ϩ Local regions of ionization are created in the interstellar then in equilibrium the number density of H3 is given by (22) medium by hot stars and prestellar objects radiating at UV and x-ray wavelengths and are found also in warm regions of the gas ͑ ϩ͒ ϭ ␨ ͑ ͒ ͸ ͑ ͒ ͑ ͒ n H3 n H2 Ͳ k X n X . [2] subjected to energetic shock waves generated by stellar outflows X and supernovae. Cosmic rays are a global source of ionization distributed through the . Measurements have been made The rate coefficient for the reaction with CO of the cosmic ray flux at high energies, but at energies below 100 ϩ ϩ 3 ϩ ϩ MeV the cosmic rays are excluded from the by the H3 CO HCO H2 [3] and the total ionization rate cannot be directly Ϫ Ϫ ϩ determined. is 1.7 ϫ 10 9 cm3⅐s 1 (23). The HCO ion then undergoes Spitzer and Tomasko (1) used the available data to obtain a dissociative recombination ϫ Ϫ18 Ϫ1 ␨ probable lower limit of 6.7 10 s for the ionization rate ϩ ϩ 3 ϩ of and from a general consideration of energies HCO e H CO. [4] released in supernovae estimated a probable upper limit of 1.2 ϫ ϩ ϩ HCO is also removed by H O, producing H O . The reactions 10Ϫ15 sϪ1. More recently, Webber (2) used data from the 2 3 with atomic oxygen, Voyager and Pioneer spacecraft acquired at distances from the out to 60 AU to determine a probable minimum rate of ϩ ϩ 3 ϩ ϩ H3 O OH H2 [5] (3–4) ϫ 10Ϫ17 sϪ1 for H atoms. Webber drew attention to the Ϫ16 Ϫ1 3 ϩ ϩ possibility of enhanced rates exceeding 10 s near massive H2O H, [6] stars with strong stellar winds. Ϫ Ϫ Cosmic rays heat the interstellar gas and drive an interstellar have a total rate coefficient of 8.0 ϫ 10 10 cm3⅐s 1 (24). The chemistry. Following the attribution by Klemperer (3) of an process initiates an ion-molecule sequence that terminates in interstellar emission line at 89,188 MHz to the molecular ion HCOϩ, the influence of cosmic rays on the chemistry of dense clouds was discussed by Herbst and Klemperer (4) and Watson Conflict of interest statement: No conflicts declared. (5) and on the chemistry of diffuse clouds by Black and Dalgarno This paper was submitted directly (Track II) to the PNAS office. (6). It is applications of chemical models to interpret measure- Abbreviation: PAH, polycyclic aromatic hydrocarbon. ments of interstellar molecular abundances that has yielded the †E-mail: [email protected]. values of ␨ in use today. © 2006 by The National Academy of Sciences of the USA

www.pnas.org͞cgi͞doi͞10.1073͞pnas.0602117103 PNAS ͉ August 15, 2006 ͉ vol. 103 ͉ no. 33 ͉ 12269–12273 Downloaded by guest on October 2, 2021 ϩ ϩ Ϫ H3O (4), which in turn leads to OH (22). The observation of PAH ϩ PAH 3 PAH products, [16] ϩ H3O would be a valuable diagnostic of oxygen depletion (25). ϩ The reaction with N2 is similar to that for CO. It produces N2H , formed by attachment processes which can be lost by dissociative recombination, e ϩ PAH 3 PAHϪ [17] ϩ ϩ 3 ϩ N2H e H N2 ϩ (34, 35). The equilibrium abundance of H3 may be written 3 N ϩ NH, [7] ͑ ϩ͒ ϭ ␨ ͑ ͒ ͸ ͑ ͒ ͑ ͒ ϩ ͸ ͑ ͒ ͑ ͒ and by reaction with CO, n H3 n H2 Ͳͭ n X k X n M k M X M ϩ ϩ 3 ϩ ϩ N2H CO HCO N2. [8] ϩ ϩ ␣ ͑ ͒ ϩ ͑ ͒ ϩ ͑ Ϫ͒ Eq. 2 shows that the abundance of H is a constant, increasing n e k0n PAH k1n PAH ͮ , [18] 3 with the ionizing flux and with the amount of depletion of the heavy neutral gas components. For ␨ ϭ 5 ϫ 10Ϫ17 sϪ1 and no ϩ ϭ ϫ Ϫ5 Ϫ3 where k0 is the rate coefficient of depletion, n(H3 ) 5 10 cm . With increasing depletion dissociative recombination ϩ ϩ 3 ϩ ϩ ϩ H3 PAH H2 (H PAH) [19] ϩ ϩ 3 ϩ H3 e H H2 [9] and k1 is the rate coefficient of 3 ϩ ϩ H H H [10] ϩ ϩ Ϫ 3 ϩ ϩ H3 PAH H2 H PAH. [20] becomes significant. The rate of 9 and 10 was once thought to be negligible. It is now known to be rapid (26), and most of the early Model chemistries of dense clouds appear not to include reac- estimates of ␨ in diffuse clouds are too small. If ␣ is the rate tions involving PAHs, presumably on the assumption that any ϩ PAH molecules that are present are absorbed onto grains and do coefficient of 9 and 10 combined, the abundance of H3 is given by not remain in the gas phase. Their influence could be substantial (36). Recombination onto grain surfaces may be still more significant (27, 32). We add n(g)k(g) to the denominator of Eq. ͑ ϩ͒ ϭ ␨ ͑ ͒ ͸ ͑ ͒ ͑ ͒ ϩ ␣ ͑ ͒ n H3 n H2 Ͳͭ n X k X n e ͮ , [11] 18. Inclusion of any metals or PAHs or grains will increase the X inferred ionization rate. The possible effects of depletion, metals, large molecules, and where n(e) is the number density. ϩ grains can be assessed by a consideration of the deuteration of Positive ions X may also be removed by charge transfer with molecular ions by fractionation processes. Observations show metal atoms M, that the ratio of the abundances of molecular ions such as DCOϩ ϩ ϩ ϩ to HCO and neutral molecules such as H CO and HDCO is X ϩ M 3 X ϩ M . [12] 2 often much enhanced above the cosmic [D͞H] ratio. Doubly and A simple model of the effects of charge transfer was given by triply deuterated isotopologs have also been detected (37). The Oppenheimer and Dalgarno (27), and more complex studies of fractionation is driven by the exothermic reaction (38) its influence on the ionization balance of protoplanetary discs ϩ ϩ 3 ϩ ϩ have been carried out by Fromang et al. (28) and by Ilgner and H3 HD H2D H2. [21] Nelson (29, 30). The ionization source is cosmic rays and x-rays H Dϩ is removed by the reverse reaction from the parent star (31). If k(M) is the rate coefficient of 12, 2 ϩ ϩ 3 ϩ ϩ H2D H2 H3 HD [22] ͑ ϩ͒ ϭ ␨ ͑ ͒ ͸ ͑ ͒ ͑ ͒ n H3 n H2 Ͳͭ n X k X ϩ and by the same set of reactions that destroyed H3 .Weget X n͑H Dϩ͒ 2 ϭ ͑ ͒ ͑ ͒ ϩ ͸ ͑ ͒ ͑ ͒ ϩ ͸ ͑ ͒ ͑ ͒ ϩ ␣ ͑ ͒ ͑ ϩ͒ kfn HD Ͳͭ kbn H2 k X n X n M k M n e ͮ . [13] n H3 X M ϩ ␣n͑ ͒ ϩ ͸ n͑ ͒k͑ ͒ ϩ k n͑ ͒ The metal ions are unreactive and recombine slowly by radiative e M M 0 PAH recombination and dielectronic recombination, M

ϩ M ϩ e 3 M ϩ ␯. [14] ϩ ͑ Ϫ͒ ϩ ͑ ͒ ͑ ͒ k1 PAH n g k g ͮ , [23] The molecular ions and the metal ions may also be removed by neutralization on grain surfaces (27, 32). where k is the rate coefficient of reaction 21, k is the rate The ionization balance and the ion distribution may be greatly f b coefficient of reaction 22, and the other rate coefficients refer to modified by the presence of large molecules such as the poly- the deuterated analogues of the reactions in the denominator of cyclic aromatic hydrocarbons (PAHs). PAHs are expected to be 18. The forward and backward rate coefficients are related by present in dense interstellar clouds (33). PAHs have ionization k ϭ k exp(ϪT͞T*). A value of T* ϭ 220 K is usually adopted potentials of typically 6.5 eV, and charge transfer b f together with a forward rate coefficient of 1.7 ϫ 10Ϫ9 cm3⅐sϪ1 Mϩ ϩ PAH 3 M ϩ PAHϩ [15] (37) although they have been brought into question by measure- ments of Gerlich and Schlemmer (39). The consequences to will occur for most of the interstellar ions. The PAHϩ ions will interstellar chemistry have been explored by Gerlich, Herbst, be removed by recombination with electrons and by mutual and Roueff (40). They appear to indicate a small increase in the neutralization with anions PAHϪ, ionization rate. The rate coefficients in 23 may be taken equal

12270 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0602117103 Dalgarno Downloaded by guest on October 2, 2021 ␣ ϩ to those in 17 except for , which is about half that of H3 (41). depletion (47). PAHs are not usually considered explicitly, but Then it is clear from expressions 18 and 23 that the abundance their influence is incorporated in the recombination in collisions ϩ ϩ ϩ SPECIAL FEATURE of H3 and the ratio of H2D to H3 increase together with the of ions with grains. (The observations place an upper limit of Ϫ7 depletion of CO and O and N2 (22) and provide a powerful probe Ϸ10 for the fraction of PAHs.) Grain recombination has been ϩ of star-forming regions. The deuterated ion H2D has been explicitly included in models of dense cloud cores (47), proto- detected in a low-mass protostar (42), a prestellar core (43), and planetary discs (48), and completely depleted prestellar cores circumstellar discs (44). Ceccarelli et al. (44) interpreted the (49). In reproducing the measured abundances, all models take molecular data with a sophisticated chemistry to conclude that Ϫ Ϫ implicit account of grain recombination. In the absence of ␨ ϭ 5 ϫ 10 17 s 1 for the disk source TW Hya and a magnitude dissociation events the chemistry depends not on ␨ itself but on lower for DM Tau. The values of ␨ are uncertain because they ␨͞ ϩ the ratio n(H2) so that some of the variation in the derived depend on assumptions about depletion and the ratio n(H2D )͞ ␨ ϩ values of may be due to differences in the adopted densities. n(H3 ) is not known. ϩ ϩ Some of the variations are probably real. No definitive value for Because reactions of H3 and H2D with CO are the ϩ ϩ dense clouds emerges from the numerous studies, but it appears principal sources of HCO and DCO , of which there have ϫ Ϫ17 Ϫ1 ϩ ϩ that the canonical traditional value of 1 10 s is too small been many measurements (7, 45), the ratio of H2D to H3 can and 5 ϫ 10Ϫ17 sϪ1, even 1 ϫ 10Ϫ16 sϪ1, may be a more realistic be obtained from the ratio of DCOϩ to HCOϩ. Other ions are ϩ ϩ mean value. also useful, particularly N2D and N2H (10). Expression 23 is modified by processes involving atomic . Because Diffuse Molecular Clouds of fractionation and the resulting high abundances of deuter- Values of ␨ have been obtained from analyses of the chemical ated ions there is a large supply of deuterium atoms through composition of diffuse clouds for which reactions driven by dissociative recombination, play a major role and atomic hydrogen and molecular DCOϩ ϩ e 3 D ϩ CO. [24] hydrogen are both present in significant amounts. Diffuse clouds have visual extinctions Av up to one magnitude or so, and the The atomic D͞H ratio is considerably enhanced over the cosmic molecules that have been detected are mostly diatomic species ϩ ϩ ratio and reactions of D atoms, (50). Cosmic rays ionize H and H2 and produce H and H2 at ␨ Ϫ1 ␨ Ϫ1 ϩ ϩ rates, respectively, of (H) s and (H2)s . The ratio of D ϩ H 3 H ϩ H D [25] ASTRONOMY 3 2 ␨(H2)͞␨(H) depends on the mixture of H and H2 in the gas (51), ϩ ϩ but the conventional assumption that ␨(H ) ϭ 2␨(H) is an D ϩ HCO 3 H ϩ DCO , [26] 2 adequate approximation for most purposes. ␨ The molecules OH and HD are direct probes of the ionization may contribute to the fractionation when is large (46). ϩ To a close approximation, n(DCOϩ)͞n(HCOϩ) ϭ (1/ rates (6). H atoms are ionized and the H ions undergo charge ϩ ͞ ϩ transfer 3)n(H2D ) n(H3 ). The measured ratio provides an upper limit to any one of the individual terms in the denominator of Eq. 23. ϩ ϩ 3 ϩ ϩ Thus defining the parameter f by the relationship H O H O . [30] n͑H Dϩ͒ n͑HD͒ The rate coefficient is sensitive to temperature (52, 53). If there 2 ϭ Ϫ1 ͑ ϩ͒ ͑ ͒ f [27] is little H2 in the gas, Eq. 30 is followed by its reverse (54). If H2 n H3 n H2 ϩ is present, O reacts with H2 in a sequence that leads to OH and we may write Eq. 23 in the form H2O (4). The sequence can be entered also from the reactions 5 and 6. OH is destroyed by ϭ ͑Ϫ ͞ ͒ ϩ ␣ ͑ ͒ ϩ ͑ ͒ ͑ ͒ ϩ 3 ϩ f exp T* T ͫ x e ͸ k X x X O OH O2 H. [31] X It is also destroyed by photodissociation by the interstellar ϩ ͸ ͑ ͒ ͑ ͒ ϩ ͑ ͒ ͑ ͒ field and the cosmic ray-induced radiation (55, 56). k M x M k0 PAH x PAH M Equating the production and loss rates of OH, we may obtain the ionization rate. Hartquist, Black, and Dalgarno (57) reported rates of 1.5 ϫ 10Ϫ17 sϪ1, 2.2 ϫ 10Ϫ17 sϪ1, and 2.5 ϫ 10Ϫ16 sϪ1 for ϩ ͑ Ϫ͒ ͑ Ϫ͒ ϩ ͑ ͒ ͑ ͒ k1 PAH x PAH k g x g ͬͲ kf, [28] clouds in the direction of ␨ Oph, ␨ Per, and ␱ Per, respectively. They suggested that the enhanced rate for ␱ Per was a reflection of the energetic event that gave rise to the observed motion of where x(Y) is the fractional abundance n(Y)͞n(H ). Then 2 the ␱ Per cloud. Black and Dalgarno (58) had earlier obtained ͑ ͒ Ͻ ͞␣͑ ͒ ͑ ͒ Ͻ ͞ ͑ ͒ ϫ Ϫ17 Ϫ1 ␨ x e kf f e and x Y kf f k Y [29] 1.6 10 s for Oph and Black, Hartquist, and Dalgarno (59) the same value for ␨ Per. These values were consistent with for any of the neutral atoms and molecules, metals, PAHs, values inferred from measurements of HD. HD is made by PAHϪs, or grains. Depending on the physical environment, reactions initiated by the ionization of H and H. Thus ϩ 2 different terms of f may control the loss of H . When one term 3 ϩ ϩ 3 ϩ ϩ dominates, f provides an actual measure of the corresponding D H2 H HD [32] fractional abundance. Of special importance is the fractional ϩ ionization x(e). Estimates for low-mass cloud cores lie between (5, 60), with D supplied by Ϫ8 Ϫ6 Ϫ7.5 Ϫ6.5 10 and 10 (47), between 10 and 10 (7), and between ϩ ϩ H ϩ D 3 H ϩ D , [33] 1.5 ϫ 10Ϫ8 and 7.5 ϫ 10Ϫ8 (11). With modest depletion the rates ϩ of removal of H3 by neutral atoms and molecules, by metals, and is a source of HD as is the dense cloud sequence possibly by PAHϪ may be comparable to dissociative recombi- ϩ ϩ 3 ϩ ϩ nation. To reproduce the measured fractionation, depletion, H3 D H2D H [34] often severe, must be invoked in the chemical models. Obser- ϩ ϩ 3 ϩ vations of other molecular species are used to estimate the H2D e HD H. [35]

Dalgarno PNAS ͉ August 15, 2006 ͉ vol. 103 ͉ no. 33 ͉ 12271 Downloaded by guest on October 2, 2021 Ϫ5 ؊2 Analysis of the HD abundances yielded a value of 2 ϫ 10 for Table 1. Range of R ؋ n(H2)cm) the cosmic ratio [D͞H].) The most comprehensive studies of Proton energy, MeV R ϫ n(H2) diffuse clouds were those of van Dishoeck and Black (61) using 1 2.5 ϫ 1020 data on the column densities of CO, OH, C2, CN, OH, HD, and 2 8.8 ϫ 1020 rotationally excited H2. They were seeking a value of ␨ common to the clouds in front of ␨ Oph, ␱ Per, ␹ Oph, and ␨ Per, and they 10 1.6 ϫ 1022 selected ␨ ϭ 5 ϫ 10Ϫ17 sϪ1. These early values were obtained at 20 5.9 ϫ 1022 ϩ 50 3.2 ϫ 1023 a time when it was believed dissociative recombination of H3 was ϫ 24 slow. However, van Dishoeck and Black did consider the pos- 100 1.2 10 sibility that it was fast, as we now believe, and they revised the values of ␨ upwards to 4 ϫ 10Ϫ16 sϪ1 for ␨ Oph, 1–2 ϫ 10Ϫ16 sϪ1 for ␨ Per, and 8 ϫ 10Ϫ16 sϪ1 for ␱ Per. Federman, Weber, and Chemistry of the Intercloud Medium ␨ ϭ ϫ Ϫ17 Lambert (62) derived for the ionization rate of H2, 4 10 The density of the intercloud medium is low, and the chemistry Ϫ Ϫ Ϫ s 1 for ␱ Per and 3 ϫ 10 17 s 1 for ␨ Per. The different rates stem is limited to the recombination of cations with electrons, from the assumptions made about the intensity of the UV PAHs, and grains if any are present. The electrons are photons that dissociate OH and the value of ␣. primarily due to photoionization of atoms like carbon, silicon, From a consideration of HD abundances resulting from Hϩ and iron that have ionization potentials of Ͻ13.6 eV and a and the loss of Hϩ in collisions with grains, Liszt (63) proposed secondary contribution from cosmic ray ionization of hydro- Ϫ16 Ϫ1 ϩ ϩ 4 ϫ 10 s as a lower limit to the ionization rate of H2 in gen and . The H ions and the He ions reveal their diffuse clouds, but he may have underestimated the source from presence by radio recombination lines. Hughes, Thompson, ϩ Ϫ Ϫ reaction 35. In a major discovery, McCall et al. (26) detected H and Colvin (70) gave an estimate of 2 ϫ 10 15 s 1, Shaver (71) 3 Ϫ Ϫ in the ␨ Per cloud. The chemistry is simple. The Hϩ ions are reported an upper limit of 2 ϫ 10 16 s 1, and Payne, Salpeter, Ϫ Ϫ removed by dissociative recombination, which in a diffuse gas is and Terzian (72) recommended an upper limit of 1.ϫ10 15 s 1 much faster than the other loss processes that complicate the for the ionization rate of H atoms from comparisons of chemistry of dense clouds. Then in equilibrium, free–free absorption and 21-cm data, but Liszt (63) has argued that taking into account recombination of Hϩ in collisions with ͑ ϩ͒ ϭ ␨ ͑ ͒͞␣ ͑ ͒ Ϫ n H3 n H2 n e . [36] PAHs and PAH s and grains will allow an increase in these upper limits. These limits were important because they cast In a diffuse cloud, n(e) ϳ n(Cϩ). The absorption measurements doubt on the validity of the two-phase model of the interstellar ϩ ϩ yield the column densities N(H3 ) and N(C ), which are medium (73) and perhaps should be reexamined. ϩ ϩ integrals of n(H3 ) and n(C ) along the line of sight. McCall et al. (26) assumed that the density distribution was uniform so that Variability of the Ionization Rate ϩ ͞ ϩ ϭ ϩ ͞ ϩ ␨ the n(H3 ) n(C ) N(H3 ) N(C ). With the assumption that The different estimates of raise the question of its possible Ϫ3 n(H2) ϭ 250 cm throughout the cloud, they obtained ␨ ϭ 1.2 ϫ variation. The cosmic rays lose energy in ionizing and exciting 10Ϫ15 sϪ1. Le Petit, Roueff, and Herbst (64) constructed a more the gas through which they travel. The corresponding path length elaborate two-phase model consisting of an extended diffuse R traversed by the cosmic rays is inversely proportional to the gas ϭ ϩ ϭ Ϫ3 density. Table 1 lists the range in the form of the column depth region with a density nH n(H) 2n(H2) 100 cm and a Ϫ 4 Ϫ3 of penetration Rn(H )cm 2 for incident energies from 1 to 100 dense edge with nH ϭ 2 ϫ 10 cm , and they explored the 2 possible contribution of shocks to the formation of molecules. MeV of protons moving along a straight line path (74). The ␨ ␨ They reproduced the measured abundances of a wide range of column densities NH of gas in front of the stars Oph, Per, and ␱ Per are, respectively, 1.4 ϫ 1021, 1.6 ϫ 1021, and 1.6 ϫ 1021 atoms, ions, and molecules to within a factor of three with an Ϫ2 ϫ Ϫ16 Ϫ1 ϩ cm . If the origin of the cosmic rays is external to the clouds, ionization rate of 2.5 10 s . The column density N(H3 ) was 2.9 ϫ 1013 cmϪ2 compared with the measured value of 8.0 ϫ some loss of the low-energy flux of protons may occur. In the ϩ ␱ 1013 cmϪ2. Increases in ␨ to bring N(H ) into agreement are case of Per there appears to be an enhancement of the cosmic 3 rays. Hartquist and Morfill (75) attributed it to stochastic constrained by the column density of OH. ϩ acceleration in an associated remnant. The possible H has been detected in the direction of the star OB2 3 influence of magnetic fields was noted by Greenberg (76) and No. 12 (20, 65) in what is thought to be diffuse gas. McCall et al. further discussed by Nakano and Tademaru (77) and Cesarsky (65) adopted a uniform density model with n(H) ϭ 10 cmϪ3, and ϩ and Volk (78). Hartquist, Doyle, and Dalgarno (79) considered they noted that the path length needed to reproduce N(H3 ) was the intercloud cosmic ray ionization rate, taking into account the extreme. The difficulties encountered in their model would be screening mechanism of Skilling and Strong (80). They calcu- ϫ Ϫ16 Ϫ1 alleviated by a larger ionization rate of 3 10 s or more lated intercloud rates 20–100 times the diffuse cloud rates. (20). Gredel, Black, and Yan (66) developed a comprehensive Padoan and Scalo (81) have developed a comprehensive de- model with greater densities in which the ionization is due to scription of the confinement of cosmic rays by from x-rays. They obtained agreement with a range of molecular Ϫ Ϫ self-generated Alfven waves, and they predicted that large observations with ␨ ϭ (0.6–3.0) ϫ 10 16 s 1. variations would occur in the cosmic ray intensities in the An alternative model was suggested by Cecchi-Pestellini and interstellar medium. They cited the case of ␨ Per as an example. Dalgarno (67, 68). In their model, clumps of material with a In conclusion, considerable uncertainties attend the values of the Ϫ mean density of 100 cm 3 and a visual extinction of 1.6 mag are cosmic ray ionization rates in the interstellar medium, but there are embedded in a tenuous interclump medium. The clumps contain indications that the range could be narrow, lying between 10Ϫ16 and ϩ Ϫ15 Ϫ1 dense cores. The ionizing flux that reproduces the measured H3 10 s from dense cores in molecular clouds to the intercloud abundance is 6 ϫ 10Ϫ17 sϪ1. Some support for the model is medium. The interesting question may be not why are they so provided by the detection of HCOϩ (69). different but why are they so similar.

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