CN AND HCN IN DENSE INTERSTELLAR CLOUDS

CN AND HCN IN DENSE INTERSTELLAR CLOUDS

Gai I. Boger and Amiel Sternberg

School of Physics and Astronomy and Wise Observatory, Beverly and Raymond Sackler Faculty of Exact Sciences,

Tel Aviv University, Tel Aviv 69978, Israel; [email protected]

Received 2005 March 3; accepted 2005 June 15

ABSTRACT

We present a theoretical investigation of CN and HCN molecule formation in dense interstellar clouds. Westudy the gas-phase CN and HCN production efficiencies from the outer photon-dominated regions (PDRs) intothe opaque cosmic-ray–dominated cores. We calculate the equilibrium densities of CN and HCN and of the asso-ciated species Cþ, C, and CO, as functions of the far-ultraviolet (FUV) optical depth. We consider isothermal gasat 50 K, with hydrogen particle densities from 102 to 106 cm�3. We study clouds that are exposed to FUV fieldswith intensities (at 1000 8) from 1 ; 10�18 to 1 ; 10�14 ergs s�1 cm�2 Hz�1 sr�1, or 20 to 2 ; 105 times the meaninterstellar FUV intensity. We assume cosmic-ray H2 ionization rates ranging from 5 ; 10�17 s�1 to an enhancedvalue of 5 ; 10�16 s�1. We also examine the sensitivity of the density profiles to the gas-phase sulfur abundance.

Subject headinggs: galaxies: ISM — ISM: evolution — molecular processes

Online material: color figures

1. INTRODUCTION

Millimeter-wave line emissions of CN and HCN moleculesare widely used probes of dense molecular gas and of photon-dominated regions (PDRs) in the Galactic interstellar medium(ISM). Observed sources include molecular interfaces in star-forming regions (Greaves & Church 1996; Simon et al. 1997;Young Owl et al. 2000; Savage et al. 2002; Schneider et al. 2003;Johnstone et al. 2003), reflection nebulae (Fuente et al. 1993,1995, 2003; Jansen et al. 1995), planetary nebulae (Bachilleret al. 1997a), and circumstellar envelopes and disks (Woottenet al. 1982; Truong-Bach et al. 1987; Bachiller et al. 1997b;Lindqvist et al. 2000; van Zadelhoff et al. 2003; Thi et al. 2004).Observations of CN and HCN have recently been used to studyPDRs in the starburst galaxy M82 and in other external systems(Fuente et al. 2005; Meier & Turner 2005).

In nearby objects, such as the Orion Bar and the reflectionnebulae NGC 2023 and NGC 7023, the molecular emissionshave been mapped across the PDRs. The CN/HCN intensityratios are largest near the stellar sources of the illuminating far-ultraviolet (FUV) radiation fields, and the intensity and densityratios decrease with increasing optical depth and distance fromthe stars. This behavior is broadly consistent with theoretical ex-pectations (Sternberg & Dalgarno 1995, hereafter SD95; Jansenet al. 1995) and is evidence of selective photodissociation ofHCN versus CN (van Zadelhoff et al. 2003; Thi et al. 2004).

Many discussions of gas-phase nitrogen chemistry in mo-lecular clouds have been presented in the literature (e.g., Herbst& Klemperer 1973; Prasad & Huntress 1980; Viala 1986;Pineau des Forets et al. 1990; Herbst et al. 1994; SD95; Leeet al. 1996; Turner et al. 1997). Comprehensive reviews of PDRobservations and theory and related subjects have been pre-sented by Hollenbach & Tielens (1997), Sternberg (2004), andvan Dishoeck (2004).

In this paper we focus on the gas-phase production of CN andHCN and present results for a wide range of conditions. Weanalyze how the CN and HCN formation and destruction se-quences vary with optical depth, first through the PDRs andthen into the opaque cosmic-ray–dominated cores. We discusshow the (equilibrium) density profiles depend on the cloudhydrogen gas densities and the incident FUV field intensities,

and we identify the qualitative changes in the density profilesthat may be expected in moving from low- to high-densitysystems. The production efficiencies of the carbon-bearing CNand HCN molecules depend on the availability of free Cþ ionsand C atoms in the gas, and we present and discuss the asso-ciated Cþ, C, and CO density profiles in the parameter space weconsider. In this paper we do not consider HNC or the isomericabundance ratio HCN/HNC (e.g., Watson 1974; Schilke et al.1992; Herbst et al. 2000), which, together with CN/HCN, maybe expected to vary with optical depth, density, and FUV fieldstrength.In x 2 we describe the basic ingredients of our models. In x 3

we discuss the gas-phase CN and HCN reaction sequences thatoperate in molecular clouds. In x 4 we present detailed resultsfor a ‘‘reference model’’ to illustrate the depth-dependent for-mation pathways and density profiles. In x 5 we present ourparameter study and discuss results for a range of gas densities,FUV field strengths, cosmic-ray ionization rates, and gas-phaseelemental abundances. We summarize in x 6.

2. MODEL INGREDIENTS

We performed our model computations using an updatedversion of the SD95 code. The models consist of static, plane-parallel, semi-infinite slabs, exposed on one side to isotropicFUV (6–13.6 eV) radiation fields. The steady-state abundancesof the atomic and molecular species are computed as functionsof the visual extinction AV from the cloud surface. The modelsaccount for scattering and absorption of the FUV photons bydust grains and the resulting depth-dependent attenuation of theatomic and molecular photodissociation and photoionizationrates. The effects of H2 and CO absorption-line shielding arealso included. Themolecular chemistry is driven by the combinedaction of FUV photoionization and photodissociation togetherwith cosmic-ray impact ionization. The resulting sequences of(two-body) gas-phase ion-molecule and neutral-neutral reactionsare mediated by dissociative recombination and photodestruction.We assume that the spectral shapes of the incident FUV

fields are identical to the Draine (1978) representation of theinterstellar field in the solar neighborhood (see also Parravanoet al. 2003). The field intensity is parameterized by a scaling

A

302

The Astrophysical Journal, 632:302–315, 2005 October 10

# 2005. The American Astronomical Society. All rights reserved. Printed in U.S.A.

factor �, where for � ¼ 1 the FUV intensity at 1000 8 is 5:4 ;10�20 ergs s�1 cm�2 Hz�1 sr�1. We construct models for � rang-ing from 20 to 2 ; 105, appropriate for PDRs in the vicinity ofyoung OB stars and clusters (Sternberg et al. 2003).

In our computations we include the same set of 70 atomicand molecular carbon-, nitrogen-, oxygen-, sulfur-, and silicon-bearing species1 considered by SD95. Complex hydrocarbonsand polycyclic aromatic hydrocarbons (PAHs) are excluded.We solve the depth-dependent equations of chemical equilibriumXjl

kijl(T )njnl þXj

��ij þ �ij� �

nj

¼ niXjl

kjilnl þXj

��ji þ �ji� �" #

; ð1Þ

as functions ofAV. In these equations, ni are the densities (cm�3)

of species i and kijl(T ) are the (temperature-dependent) rate co-efficients (cm3 s�1) for chemical reactions between species j andl that lead to the production of i. The parameters ��ij and �ij arethe FUV photon and cosmic-ray destruction rates (s�1) of spe-cies jwith products i. We solve equation (1) via Newton-Raphsoniteration and use Bulirsch-Stoer integration to compute the col-umn densities.

In our computations we include all reactions listed in theUMIST99 database (Le Teuff et al. 2000) for which the reac-tants and products are species in our set. We adopt the recom-mended UMIST99 rate coefficients kijl, with several alterationsand updates.2

The depth-dependent FUV photodissociation and photoion-ization rates are crucial quantities. They depend on the intensityand spectral shape of the incident radiation field, on the pho-todissociation and photoionization cross-sections, and on thedust grain scattering and absorption properties. Dust attenua-tion is the primary mechanism for the reduction of the photo-rates. Line shielding is also important for the special cases of H2

and CO photodissociation.3 For the depth-dependent photo-dissociation and photoionization rates, we adopt the biexpo-nential representations

�i ¼ Ci exp ��iAV � �iA2V

� �ð2Þ

and coefficientsCi,�i, and�i, calculated bySD95 for the radiativetransfer of aDraine field penetrating a cloud of large (AV tot ¼ 100)total optical depth (Roberge et al. 1991).We assume a dust-to-gasratio such that AV ¼ 4:75 ; 10�22(NH þ 2NH2

) (SD95; see alsoDraine 2003), where NH and NH2

are the atomic and molecular

hydrogen column densities (cm�2). In Figure 1 we plot the CNand HCN photodissociation rates as functions of AV , for � ¼ 1and a total cloud thickness AV tot ¼ 100.

The much more rapid attenuation of the CN photodissocia-tion rate compared to HCN is an important feature of the modelsand reflects the fact that the energetic photons (>12.4 eV) re-quired to dissociate CN (van Dishoeck 1987; Thi et al. 2004)are more readily absorbed by the dust grains.

The cosmic-ray destruction rates �ij in equation (1) includeimpact ionizations of H, H2, and He by the primary cosmic raysand secondary electrons and induced FUV photodissociationand photoionization of the heavier molecules (Gredel et al.1989). In most of our models we adopt a ‘‘dense-cloud’’ H2

cosmic-ray ionization rate, � ¼ 5 ; 10�17 s�1 (e.g., Williamset al. 1998), but we also examine the effect of increasing � by upto a factor 10 (McCall et al. 2003; Brittain et al. 2004). Thecosmic rays are ‘‘freely penetrating,’’ and � is independent ofcloud depth. Cosmic-ray ionization is the only source of Hþ,Hþ

2 , and Heþ in our models. X-ray ionization (Maloney et al.1996; Spaans & Meijerink 2005) is excluded.

The cosmic-ray–induced photoionization and photodissoci-ation rates are given by

�i ¼�pi

1� !; ð3Þ

where ! is the grain albedo and pi are the photoabsorption‘‘efficiency factors’’ (Gredel et al. 1989). We adopt the effi-ciency factors pi listed in the UMIST99 compilation, and we set! ¼ 0:5 (SD95).

Molecule formation requires the presence of H2. We assumethat hydrogen molecules are formed on grain surfaces with arate coefficient

R ¼ 3 ; 10�18T1=2yF cm3 s�1; ð4Þ

where T is the gas temperature and yF is a ‘‘formation effi-ciency’’ that depends primarily on the grain temperature(Manico et al. 2001; Biham et al. 2001; Biham&Lipshtat 2002;

1 We assume that the abundances of all other elements are negligible in thegas phase, including heavy elements such asMg and Fe, which, when abundant,may become important positive-charge carriers in dense molecular clouds(Oppenheimer & Dalgarno 1974; de Boisanger et al. 1996).

2 Our input list of rate coefficients is available at ftp://wise3.tau.ac.il /pub/amiel/pdr. In our compilation we use recent determinations of the rate coeffi-cients and branching ratios for dissociative recombinations (Vejby-Christensenet al. 1997; Larson et al. 1998; Vikor et al. 1999; Jensen et al. 2000; McCall et al.2003; Geppert et al. 2004). For some neutral-neutral reactions we use rate-coefficients listed in UMIST95 or as given by Herbst et al. (2000) and Smith et al.(2004).

We do not assume the small (�50 K) activation barriers postulated byPineau des Forets et al. (1990) for the neutral-neutral reactions (see x 3)involved in the nitrogen chemistry.

3 We set the Doppler parameter equal to 2 km s�1 for all absorption lines. Asin SD95, we include H2 transitions in the Lyman and Werner bands, neglectingthe rotational structure. We use the Federman et al. (1979) self-shielding formulaefor H2 and the van Dishoeck & Black (1989) shielding function for CO.

Fig. 1.—Photodissociation rates of CN and HCN as functions of visualextinction for a unit Draine field. [See the electronic edition of the Journal fora color version of this figure.]

CN AND HCN IN DENSE INTERSTELLAR CLOUDS 303

Cazaux & Tielens 2002; Vidali et al. 2004). We set yF ¼ 1,appropriate for low-temperature (�10–20 K) dust grains. Wedo not consider accretion or ejection of other molecular speciesonto or from the grains.

PDRs consist of several distinct zones or layers with sizesand locations that depend on gas density and FUV fieldstrength. As discussed by SD95, these include the outer H i

zone, followed by the C ii, S ii, and Si ii zones, terminated by afully cosmic-ray–dominated dark core. In the H i zone, rapidphotodissociation keeps the hydrogen in atomic form. In the C ii

zone, the hydrogen ‘‘self-shields’’ and becomes molecular, butphotoionization maintains the carbon as Cþ. In the S ii, zonethe carbon is fully incorporated into CO, but photoionizationand charge-transfer maintain the sulfur as Sþ. In the Si ii layerthe silicon is maintained as Siþ, but the sulfur is either atomic oris incorporated into molecules. The relative efficiencies of thevarious molecular formation sequences and the resulting mo-lecular densities vary with cloud depth and from zone to zone.For example, in the model considered by SD95, for which thehydrogen particle density n ¼ 106 cm�3 and � ¼ 2 ; 105, theCN/HCN density ratio is large (�10) in the H i, C ii, and S ii

layers but then decreases and becomes small (�10�4) in thedark core. A large CN/HCN ratio was therefore identified as animportant feature of (dense) PDRs. SD95 identified additionalmolecular diagnostic ratios of FUV irradiated gas, includingOH/H2O, CO

þ/HCOþ, and SOþ/SO (see also Sternberg et al.1996).

The sizes and locations of the various zones also dependon the total gas-phase elemental abundances. In our calcu-lations we set the gas-phase elemental abundances equal tothe interstellar values observed in the diffuse cloud toward �Oph. Thus, we set C/H ¼ 1:32 ; 10�4 (Cardelli et al. 1993),N/H ¼ 7:50 ; 10�5 (Meyer et al. 1997), O/H ¼ 2:84 ; 10�4

(Meyer et al. 1998), Si/H ¼ 1:78 ; 10�6 (Cardelli et al. 1994),and S/H ¼ 8:30 ; 10�6 (Lepp et al. 1988). We adopt a heliumabundance He/H ¼ 0:1. In most of our models we keep the gas-phase abundances fixed at these values and independent of

cloud depth. In one model we examine the effect of reducingthe S (and Si) abundances by a factor of 100.In this paper, we study the behavior in cool isothermal clouds.

Our results are insensitive to the temperature for T P 200 K, andwe adopt a representative gas temperature of T ¼ 50 K. Weconsider isobaric clouds, so that the total hydrogen particledensities n � nH þ nH2

are constant through the clouds. Thedensities of all other species increase by a factor of 2 at the H toH2 transition layer. We present results for n ranging from 102 to106 cm�3.

Fig. 2.—CN and HCN formation pathway 1 via carbon hydride intermediates.

Fig. 3.—CN formation pathway 2 via oxygen hydride intermediates.

BOGER & STERNBERG304 Vol. 632

Explicit thermal balance computations (Sternberg &Dalgarno1989; Burton et al. 1990) show that in dense (nk104 cm�3)PDRs the temperatures in the outer H i zones may exceed 103 K.Molecular synthesis may then proceed via a ‘‘hot gas’’ chemis-try in a thin outer layer (e.g., via the efficient production of thereactive intermediate OH). However, the contributions to thetotal CN and HCN column densities from the hot layers areexpected to be small (SD95). Here we exclude considerations ofhot gas and focus on the chemistry in the more extended coolerregions.

3. CN AND HCN FORMATION AND DESTRUCTION

There are three major pathways to the gas-phase formation ofCN and HCN, as illustrated in Figures 2–4. In pathway 1,production occurs via the formation of carbon hydrides andintermediate CH and CH2 radicals. In pathway 2 an additionalroute to CN (but not HCN) occurs via oxygen hydrides and theintermediates OH and NO. In pathway 3 the molecules areproduced via nitrogen hydrides and parent H2CN

þ ions. Wedescribe each of these pathways in turn.

3.1. Pathway 1

In pathway 1, which is important at all cloud depths, CN andHCN are formed via the neutral-neutral reactions4

CHþ N ! CNþ H ðR1Þ

and

CH2 þ N ! HCN þ H: ðR2Þ

The required CH and CH2 intermediates are produced in threeways. First is via radiative association,

Cþ þ H2 ! CHþ2 þ �; ðR3Þ

followed by rapid abstraction,

CHþ2 þ H2 ! CHþ

3 þ H; ðR4Þ

and dissociative recombination,

CHþ3 þ e ! CH2 þ H; ðR5Þ

CHþ3 þ e ! CHþ H2: ðR6Þ

Second is cosmic-ray–driven proton transfer,

H2 þ cr ! Hþ2 þ e; ðR7Þ

Hþ2 þ H2 ! Hþ

3 þ H; ðR8Þ

Cþ Hþ3 ! CHþ þ H2; ðR9Þ

followed by

CHþ þ H2 ! CHþ2 þ H ðR10Þ

and then (R4), (R5), and (R6).

Fig. 4.—CN and HCN formation pathway 3 via nitrogen hydride intermediates.

4 Reactions (R1) and (R2) play central roles in the formation of CN andHCN.In our computations we assume a rate coefficient of 2:0 ; 10�10 cm3 s�1 at 50 Kfor (R1), as implied by pulsed laser experiments in room-temperature dischargeflows, and a theoretical extrapolation to low temperature (Brownsword et al.1996). This is an order-of-magnitude larger than the rate coefficient reported byMessing et al. (1981) and widely used in many previous PDR models includingSD95. For reaction (R2) we use the theoretical value of 5:9 ; 10�11 cm3 s�1

recently calculated by Herbst et al. (2000).

CN AND HCN IN DENSE INTERSTELLAR CLOUDS 305No. 1, 2005

A third possibility is direct formation5 via slow radiativeassociation,

Cþ H2 ! CH2 þ �; ðR11Þ

which may become competitive in dense clouds where thefractional ionizations and the relative Hþ

3 densities, nHþ3/n,

become small.In the outer PDR, the CH and CH2 radicals are removed by

FUV photodissociation and photoionization. In shielded re-gions they are removed by

CHþ O ! CO þ H; ðR12Þ

CH2 þ O ! COþ H2 ðR13Þ

in rapid reactions with the available oxygen atoms.

3.2. Pathway 2

Pathway 2 is an additional route to CN (but not HCN) andbecomes important mainly in shielded regions. In this pathwayCN is formed via the intermediates OH and NO in the reactionpair

OHþ N ! NO þ H; ðR14Þ

NOþ C ! CN þ O: ðR15Þ

The main source of OH is cosmic-ray–driven proton transfer,

Oþ Hþ3 ! OHþ þ H2; ðR16Þ

followed by abstractions

OHþ þ H2 ! H2Oþ þ H; ðR17Þ

H2Oþ þ H2 ! H3O

þ þ H ðR18Þ

and dissociative recombination

H3Oþ þ e ! OHþ Hþ H; ðR19Þ

H3Oþ þ e ! OHþ H2: ðR20Þ

Major removal mechanisms for OH and NO are photodisso-ciation and reactions with atomic oxygen and nitrogen,

OHþ O ! O2 þ H; ðR21Þ

NOþ N ! N2 þ O; ðR22Þ

in the shielded regions.

3.3. Pathway 3

Finally, in pathway 3 both CN and HCN are produced viadissociative recombination,

H2CNþ þ e ! HCNþ H; ðR23Þ

H2CNþ þ e ! CNþ H2; ðR24Þ

where the parent H2CNþ ions are formed via

NH þ Cþ ! CNþ þ H; ðR25Þ

NH2 þ Cþ ! HCNþ þ H ðR26Þ

followed by

CNþ þ H2 ! HCNþ þ H; ðR27Þ

HCNþ þ H2 ! H2CNþ þ H: ðR28Þ

This pathway is mainly important in shielded regions but mayalso operate in the outer H i zone.In shielded regions, where the N2 density becomes large, NH

and NH2 are produced by the cosmic-ray–driven sequence

Heþ þ N2 ! Nþ þ Nþ He; ðR29Þ

Nþ þ H2 ! NHþ þ H; ðR30Þ

NHþ þ H2 ! NHþ2 þ H; ðR31Þ

NHþ2 þ H2 ! NHþ

3 þ H; ðR32Þ

followed by

NHþ3 þ e ! NH þ H2; ðR33Þ

NHþ3 þ e ! NH2 þ H: ðR34Þ

In the H i zone, NH may be formed via

Nþ H�2 ! NHþ H; ðR35Þ

where H�2 refers to the sum over all FUV-pumped hydrogen

molecules in vibrational states with energies large enough toovercome the endothermicity of the reaction.

3.4. Destruction

The CN and HCN density profiles also depend on the varyingefficiencies of the destruction mechanisms. In the outer PDR,photodissociation,

CNþ � ! Cþ N; ðR36Þ

HCNþ � ! CNþ H; ðR37Þ

dominates. In shielded layers the CN radical is removed by

CNþ N ! N2 þ C; ðR38Þ

CNþ O ! CO þ N: ðR39Þ

Reaction (R38) dominates at intermediate cloud depths, wherea high abundance of nitrogen atoms is maintained by photodis-sociation. At large depths (R39) becomes the dominant removalprocess. The saturated HCN molecule is removed primarily bycosmic-ray–induced photodissociation,

HCNþ crp ! CN þ H: ðR40Þ5 Reaction (R11) was not included in the SD95 study. Here we adopt

k11 ¼ 1:0 ; 10�17 cm3 s�1 for the rate coefficient (Smith et al. 2004).


Photodissociation of HCN operates as an important source ofCN, both in the PDR and in the dark core. Additional removalprocesses for HCN in the dark core are

HCNþ Hþ ! HCNþ þ H; ðR41Þ

HCNþ HCOþ ! H2CNþ þ CO: ðR42Þ

Reaction (R41) is important in low-density clouds (nP103 cm�3), where a large proton density is maintained bycosmic-ray ionization. Reaction (R42) becomes important indense clouds (nk103 cm�3).

3.5. Free Carbon: C+ and C

The efficiencies of the CN and HCN formation sequencesdepend on the availability of ‘‘free carbon’’ particles, either asCþ ions or C atoms. As we discuss in x 4, the CN and HCNprofiles are closely related to the Cþ and C density distributions.

In the outer parts of the PDR, Cþ is produced by FUVphotoionization,

Cþ � ! Cþ þ e: ðR43Þ

In shielded regions the main source is cosmic-ray–drivenhelium-impact dissociative ionization of CO,

Heþ cr ! Heþ þ e; ðR44Þ

Heþ þ CO ! Cþ þ Oþ He: ðR45Þ

In the outer PDR, where the electron density is high, the Cþ

ions are removed by radiative recombination,

Cþ þ e ! Cþ �: ðR46Þ

In shielded regions, radiative association ([R3]) and chargetransfer neutralization,

Cþ þ S ! Sþ þ C; ðR47Þ

become important. Charge transfer with atomic sulfur plays aparticularly important role in the partially shielded layers. Inthe dark core

Cþ þ O2 ! CO þ Oþ; ðR48Þ

Cþ þ O2 ! COþ þ O ðR49Þ

dominate.Carbon atoms are produced by radiative recombination and

charge transfer ([R46] and [R47]), FUV photodissociation,

CO þ � ! Cþ O; ðR50Þ

and cosmic-ray–induced photodissociation,

COþ crp ! Cþ O: ðR51Þ

The C atoms are removed by photoionization in the outer PDR,by proton transfer and radiative association ([R9] and [R11]),and cosmic-ray–induced photoionization,

Cþ crp ! Cþ þ e; ðR52Þ

at intermediate depths and by

Cþ O2 ! CO þ O; ðR53Þ

Cþ SO ! Sþ CO; ðR54Þ

Cþ SO ! CSþ O ðR55Þ

in the shielded cores.

4. REFERENCE MODEL

The results of ourmodel calculations are displayed in Figures 5,6, and 7, which show cuts through the �, n, � parameter space wehave considered. For each set of cloud parameters we display theCþ, C, CO, CN, and HCN densities (cm�3) and column densities(cm�2), as well as the CN/HCN density and column density ra-tios, as functions of AV . The column densities are integrated fromthe cloud surface in the normal direction. We also display theelectron density profiles.

We first discuss our results for a specific reference model,with n ¼ 104 cm�3, � ¼ 2 ; 103, and � ¼ 5 ; 10�17 s�1. We usethis model to analyze the depth-dependent formation sequencesand resulting density profiles. We also use it as a point ofcomparison, as the cloud parameters are varied. Our referencemodel is displayed in Figures 5c, 5d, 5e, and again in Figures 6and 7.

In our reference model and in our parameter study we adoptT ¼ 50 K. For our assumed set of reaction rate coefficients theresults we describe below are quite insensitive to the assumedgas temperature, provided the gas is cold, with T P 200 K. Forexample, relative to our results for 50 K, the CN and HCNdensities change by less than a factor of 2 at all AV , if T isdecreased to 20 K or increased to 200 K.

4.1. C+, C, and CO Density Profiles

The Cþ, C, and CO density profiles in our reference modelshow the familiar structure seen in numerous PDR calculations(Tielens & Hollenbach 1985; van Dishoeck & Black 1989; LeBourlot et al. 1993a; Flower et al. 1994; SD95; Jansen et al.1995; Bakes & Tielens 1998). The carbon is ionized in the outerlayers and undergoes a conversion to CO as the ionizing FUVradiation is attenuated. An important feature is the double-peaked atomic carbon density profile.

The first C peak is associated with the sharp transition of theavailable gas-phase carbon from fully ionized to molecularform near the inner edge of the C ii zone. In our reference modelthis occurs at AV ¼ 2.

Due to the rapid production of CO at this location, the Cdensity at the peak reaches only �20% of the total gas-phasecarbon abundance. The transition is, effectively, directly fromCþ to CO. After the conversion to CO only trace quantities of Cand Cþ remain.

An important property of the Cþ/C/CO transition region isthat photodissociation of CO continues to dominate the pro-duction of the free carbon well beyond the point at which the


conversion to CO is complete. For example, in our referencemodel, photodissociation dominates up to AV ¼ 2:5, well insidethe S ii zone. Up to this point, Cþ continues to be produced byphotoionization, and the Cþ/C density ratio is set by the balancebetween recombination and photoionization. Thus, in the C ii

zone, where the production rate of atomic carbon via recombi-nation is constant (since ne � nCþ ), the C density increases as the

photoionization rate is attenuated. However, once the conver-sion to CO is complete the atomic carbon density drops as theCO photodissociation rate decreases. This behavior gives rise tothe first C peak.We note that for PAH abundances k10�7 mutual neutrali-

zation, Cþ þ PAH� ! Cþ PAH, can compete with radiativerecombination (Lepp et al. 1988) leading to a slight shift in the

Fig. 5.—Model results for n equal to 103, 104, 105, and 106 cm�3 (top to bottom) for constant ionization parameter �/n ¼ 0:2 cm3. The cosmic-ray ionization rate� ¼ 5 ; 10�17 s�1 in all four models. Displayed profiles are for Cþ, C, CO, CN, HCN, and electrons, as functions of AV . The left-hand panels display the volumedensities. The middle panels show the integrated column densities. The right-hand panels show the volume (dashed lines) and column (solid lines) CN/HCN densityratios. The second row, with n ¼ 104 cm�3, � ¼ 2 ; 103 is our reference model. [See the electronic edition of the Journal for a color version of this figure.]


positions of the Cþ/C/CO transition layers (Bakes & Tielens1998). We do not include the effects of PAHs in our analysis.Similarly, the process of ‘‘grain-assisted’’ ion-electron recom-bination may become important when ne�r/n�g < 1, where �r

(equal to 1:4 ; 10�11 cm�3 s�1 at 50 K, for Cþ ions) and �gP10�14 cm3 s�1 are the radiative and grain-assisted recombina-tion rate coefficients. The efficiency of grain-assisted recom-bination depends on the grain population size distribution andon the grain charge (Weingartner & Draine 2001). In the com-

putations we present here we exclude this process. Including itcan increase the C densities at the first C peak. We have verifiedthat the CN and HCN density profiles we discuss below are notaffected significantly.

At larger depths, e.g., for AV > 2:5 in our model, the rateof CO photodissociation becomes vanishingly small and theprimary source of free carbon becomes cosmic-ray–drivenhelium-impact ionization of CO ([R44] and [R45]). The re-sulting Cþ ions are neutralized by radiative recombination

Fig. 6.—Model results for n ¼ 104 cm�3, and � equal to 2 ; 102, 2 ; 103, 2 ; 104, and 2 ; 105 cm�3, and � ¼ 5 ; 10�17 s�1. The second row is our referencemodel. [See the electronic edition of the Journal for a color version of this figure.]


([R46]), and by rapid charge transfer of the Cþ ions with Satoms [(R47]). The rapid neutralization keeps the free carbon inatomic form, so that nC/nCþ 31. Because the rate of heliumimpact ionization is independent of cloud depth, the C densityincreases with AV so long as photoionization dominates theremoval of the carbon atoms, and as the photoionization rate isattenuated. The second C peak occurs at the point where radi-ative association with H2 [(R11]), cosmic-ray–induced pho-

toionization ([R52]), and proton transfer reactions with Hþ3

([R9]) begin to dominate the removal of the carbon atoms. Inour reference model this occurs at AV ¼ 3:7.The C density at this location may be estimated analytically,

nC � �XHe

2p52�=nþ k9nHþ3=nþ k11

; ð5Þ

Fig. 7.—Results for n ¼ 104 cm�3 and � ¼ 2 ; 103. In the upper row the gas phase abundances of S and Si are reduced by a factor of 100. The second row is ourreference model, with standard abundances and � ¼ 5 ; 10�17 s�1. In the third and fourth rows, � is increased to 1:5 ; 10�16 and 5 ; 10�16 s�1. [See the electronicedition of the Journal for a color version of this figure.]


where k9 ¼ 2:0 ; 109 and k11 ¼ 1:0 ; 10�17 cm3 s�1 are the ratecoefficients for (R9) and (R11), the parameter p52 ¼ 1:0 ; 103

is the efficiency factor for (R52), and XHe ¼ 0:1 is the Heabundance. The first two terms in the denominator becomessmall for nk 104 cm�3, and nC is then independent of n. In thislimit, nC � 0:25 cm�3 for � ¼ 5 ; 10�17 s�1, in good agreementwith the numerical value of 0.40 cm�3 at the second C peak.Beyond this point the C density decreases, particularly as the O2

and SO densities rise and as the removal reactions (R53), (R54),and (R55) become more effective. A sharp drop in the C densityoccurs at AV � 7, and the C density finally stabilizes to a valueof 3:6 ; 10�4 cm�3 in the cosmic-ray–dominated dark core. Theatomic carbon density in the core depends on n and �, as dis-cussed further in x 5.

The second C peak marks the point at which removal of the Catoms by FUV photoionization becomes inefficient comparedto chemical reactions and cosmic-ray–induced photoionization.The minimum between the two atomic carbon peaks occursnear to the point at which helium impact dissociative ionizationof CO replaces photodissociation of CO as the primary sourceof free carbon particles.

4.2. CN and HCN Profiles

In our reference model a pronounced peak is present in theCN density profile at AV ¼ 2, at the inner edge of the C ii zone,and close to the location of the first C peak. A small HCN peakis also present at this location. Throughout the C ii zone, the CNand HCN molecules are produced primarily via pathway 1,where the formation of the CH and CH2 intermediates is initi-ated by radiative association of Cþ with H2 ([R3]). The CNdensity peak occurs where the Cþ density is still close to itsmaximum possible value but where the photodissociation ratesare diminished. The CN density then decreases with clouddepth as the Cþ density drops across the Cþ/C/CO transitionlayer.

Because the carbon is fully ionized in the C ii zone, moleculeformation is ‘‘recombination limited’’ in this part of the cloud.The CN density at the inner edge of the C ii zone may thereforebe expected to scale linearly with the gas density n for a fixedvalue of the ‘‘ionization parameter’’ �/n. This may be seenanalytically by writing

nCH � k3nCþnH2

��0CH

fCH � k3

��0CH

fCHXCn2 ð6Þ

and

nCN � k1nCHnN

��0CN

� k1k3

�0CH�

0CN

fCHXCXN

n

�

� �2

n: ð7Þ

In these expressions, k1 ¼ 2:0;10�10 and k3 ¼ 5:7;10�16 cm3 s�1

are the rate coefficients for reactions (R1) and (R3), and��0CH ¼

1:7 ; 10�8 and ��0CN ¼ 5:0;10�10 s�1 are the attenuated photo-

dissociation rates at the inner edge of the C ii zone. The fractionof recombining of CHþ

3 ions that fragment to CH is fCH ¼ 0:43,and XC ¼ 1:32 ; 10�4 and XN ¼ 7:50 ; 10�5 are the gas phaseabundances of carbon and nitrogen. For n ¼ 104 cm�3 and � ¼103 this gives nCN ¼ 5:7 ; 10�5 cm�3, in good agreement withour numerically computed value of 9:0 ; 10�5 cm�3 at the peak.The photoattenuation factors (see eq. [2]) depend on the visualextinctions at the termination points of the C ii zones and there-fore scale with �/n. Equation (7) shows that for fixed �/n the CNdensity at the peak is proportional to the product of the carbonand nitrogen abundances and to the cloud density n and is inde-

pendent of �. These simple scalings are verified by our numer-ical results in x 5.

The CN density decreases as the supply of free carbon pro-duced by CO photodissociation diminishes. However, when theprimary source of free carbon switches to helium impact ioni-zation, the CN density stops decreasing and a pronounced‘‘plateau’’ appears in the density profile. In our reference modelthe CN density plateau extends from AV ¼ 3 to 6.

The CN density profile flattens for a combination of reasons.First, while the CH and CH2 formation efficiencies decrease asthe Cþ disappears, this is offset by a more rapid decline in theCH and CH2 photodestruction rates. Second, the rise in theatomic carbon density up to the second C peak leads to an in-creased efficiency of the proton-transfer sequence initiated by(R9) in pathway 1. Third, CN formation via pathway 2 also be-gins to play a significant role as theOH andNOdensities increase.

Furthermore, while HCN (formed via [R2]) is removed byphotodissociation, at these cloud depths CN is removed byneutral-neutral reactions with N atoms ([R38]). Photodestruc-tion of CN is ineffective in the plateau because of the severeattenuation of the CN photodissociation rate (see Fig. 1). Im-portantly, photodissociation of HCN becomes a major sourceof CN in the plateau. The HCN density therefore rises as theFUV field is attenuated, but because the atomic nitrogen densityremains large throughout, the resulting CN density remains in-sensitive to AV .

At these cloud depths molecule formation is ‘‘ionizationlimited,’’ since only a trace amount of free-carbon is releasedfrom the CO molecules by helium impact ionization. BecauseCN is removed in reactions with a neutral species (N atoms), theCN density is proportional to the cosmic-ray ionization rate andindependent of the gas density. For a simple analytic estimatewe assume that CN formation is initiated by proton transfer inreactions of C with Hþ

3 ([R9]), or by radiative association of Cwith H2 ([R11]), in pathway 1. We also assume and that everyHCN formation event leads to CN via photodissociation. Weassume further that the CH and CH2 intermediates are removedby reactions with atomic oxygen [(R12) and (R13)], and thatthese reactions proceed with equal approximate rate coefficientskO ¼ 2 ; 10�10 cm3 s�1. Setting kN ¼ 1 ; 10�10 cm3 s�1 forboth (R1) and (R2), it follows6 that

nCN � 0:5�1

k38

kN

kO

XHe

XO

; ð8Þ

where k38 ¼ 3 ; 10�10 cm3 s�1 is the rate coefficient for removalreactions of CN with N. Evaluating for XHe ¼ 0:1, XO ¼2:84 ; 10�4, and � ¼ 5 ; 10�17 s�1 yields nCN ¼ 9 ; 10�6 cm�3,in good agreement with the numerically computed nCN � 2 ;10�5 cm�3 in the CN plateau (see Fig. 5). Thus, nCN is propor-tional to � and independent of n, and given the above assump-tions,7 is independent of both the gas-phase nitrogen and carbonabundances.

The CN density plateau is maintained up to the point at whichphotodissociation by the incident FUV photons is the dominantHCN removal mechanism, or up to AV ¼ 6 in our referencemodel. TheHCNdensity reaches a peak value of 8:6;10�4 cm�3

at this point. At larger depths cosmic-ray–induced photodisso-ciation becomes the dominant HCN destruction mechanism,

6 The factor of 0.5 in this expression enters because the cosmic-ray ioni-zation rate of He is half that of H2.

7 These assumptions break down if, for example, XC > XO so that C atomsbecome abundant rather than being mainly locked in CO, or if XC becomes sosmall such that formation via pathway 1 becomes negligible.


proceeding at a rate independent of AV . CN is removed by reac-tions with oxygen atoms ([R39]). The CN and HCN formationefficiencies both decline as less C and Cþ are available, and theCN and HCN densities decrease to their dark core values of 1:2 ;10�6 and 2:6 ; 10�5 cm�3, respectively.

Figure 5e shows that the CN column density rises sharply toNCN ¼ 6 ; 1012 cm�2 at the CN peak at AV ¼ 2 and that much ofthe CN column is built up at this location. The HCN columnremains small, at AV ¼ 2, but continues to increase with clouddepth. NHCN approaches 7 ; 1014 cm�2 at AV ¼ 6, where theHCN volume density is at its maximum. The ratio NCN/NHCN �10 at AV ¼ 2, and decreases to �0.1 at AV ¼ 6 (see Fig. 5f ).

5. PARAMETER STUDY

5.1. Density

Figure 5 displays our results for n ¼ 103, 105, and 106 cm�3,in addition to our 104 cm�3 reference model, and illustrates theeffects of varying the cloud density. In this sequence we keepthe ionization parameter �/n constant at 0.2 cm�3, so that theCþ/C/CO transition layers occur at the same location (AV ¼ 2)in all four models.

For fixed �/n, the depth at which helium impact ionization ofCO replaces photodissociation of CO as the source of freecarbon, increases with the cloud density n. However, the depthat which removal of atomic carbon by photoionization becomesineffective compared to proton transfer or radiative association([R9] or [R11]), is independent of n. Therefore, the relativeheight of the second C peak (at AV ¼ 4:2) decreases with n, andthe peak disappears at sufficiently high densities (k105 cm�3).For densities above 104 cm�3, nC � 0:4 cm�3 at this location,consistent with equation (5). At lower densities all of theavailable carbon is atomic at the location of the second C peak,and nC is then limited by the carbon abundance XC (see Fig. 5a).

At low n, the free carbon density remains relatively high atlarge AV and in the dark core. At high n the free carbon densitybecomes small. As we discuss below, this behavior reflects thetransition from the ‘‘high-ionization phase’’ to ‘‘low-ionizationphase’’ in the cosmic-ray–dominated core (Le Bourlot et al.1993b, 1995; Lee et al. 1998). The asymptotic values of the Cdensities in the dark core influence the shapes of the atomiccarbon density profiles at intermediate depths in the PDRs.

Figure 5 shows that the CN density at AV ¼ 2 increaseslinearly with n, from �10�5 to 10�2 cm�3, in accordance withequation (6). The ‘‘CN peak’’ becomes more pronounced as n in-creases. In the n ¼ 106 cm�3 model, the density of FUV-pumpedH2 becomes large, and CN is also formed via pathway 3 initiatedby (R35). For n � 104 cm�3 the ‘‘CN plateau’’ from AV ¼ 3 to�6 is apparent. At these depths nCN � 2 ; 10�5 cm�3 indepen-dent of n, consistent with equation (8). At low n, the CN density re-mains large to high AV due to the elevated free carbon densities.

For fixed �/n, FUV photodissociation of HCN is effective togreater depths as n increases. The location of the HCN densitypeak therefore moves from a visual extinction of 5.6 to 7.2 asthe gas density is increased from 104 to 106 cm�3. The columndensity ratio NCN/NHCN remains large to greater depths as n isincreased, but the density ratio nCN/nHCN falls off sharply withAV (see Fig. 5).

5.2. FUV Intensity, Sulfur Abundance, and Cosmic-RayIonization Rate

In Figure 6, we set n equal to 104 cm�3, and we vary � from2 ; 102 to 2 ; 106. This illustrates the effects of varying theincident FUV field intensity. The location of the Cþ/C/CO

transition layer moves from AV ¼ 1:3 to 3.5 for this density andrange of FUV intensities. The position of the second C peak isalso shifted to larger AV , as is the location of the sharp drop inthe C density, which moves from AV ¼ 6 to 9. The approach tothe dark-core conditions occurs at greater AV as � is increased.Correspondingly, the locations of the CN peak and the inner

HCN peak also move inward as � is increased. Because theCN photodissociation rate declines most rapidly with AV (seeFig. 1), nCN/nHCN and NCN/NHCN at the CN peak increase with�, from �10 to 40 in our models.In Figure 7, we show the effects of a reduced gas-phase S

(and Si) abundance and an increased cosmic-ray ionization rate,for our n ¼ 104 cm�3 and � ¼ 103 model. In Figures 7a, 7b,and 7c, the S (and Si) abundances are reduced by a factor of 100.Charge transfer ([R47]) between Cþ and S is then less ef-

fective as a neutralizing mechanism, and the second C peak atlarge AV is reduced. The formation efficiency of HCN in path-way 1, via radiative association of C with H2 ([R11]) followedby the reaction of CH2 with N ([R2]), is therefore also dimin-ished, leading to a reduction of the inner HCN density peak(compare Figs. 7a and 7d ). The resulting CN/HCN ratios aretherefore enhanced in the CN plateau region, and in the darkcore.The bottom two rows of Figure 7 show the effects of in-

creasing the cosmic-ray ionization rate, by factors of 3 and 10,to 1:5 ; 10�16 and 5 ; 10�16 s�1. Increasing � mainly affects theatomic carbon density profile. The first C peak is unaltered be-cause it is controlled by purely photoprocesses. However, thesecond C peak is enhanced by the increased rate of heliumimpact destruction of CO ([R44]). The behavior is consistentwith equation (5). Initially, the C density increases linearly with�. However, for sufficiently large � the atomic carbon is re-moved by cosmic-ray–induced photoionization ([R52]) andproton transfer reactions with Hþ

3 ([R9]), rather than by radia-tive association with H2 ([R11]). In this limit the C density isindependent of � and all of the available gas phase carbon be-comes atomic, as occurs for our � ¼ 5 ; 10�16 s�1 model.The free carbon densities remain large throughout the cloud

for high �. As we now discuss, the shift from a low to high freecarbon density with increasing � is related to a ‘‘phase change’’that occurs in the dark core.

5.3. Dark Core

In Figure 8 we display the densities, ni, and density fractions,ni/n, for C

þ, C, CO, CN, HCN, and free electrons, for fullyopaque dark core conditions. Externally incident FUV photonsare excluded, and the chemistry is driven entirely by cosmic-rayionization. For these conditions, it follows from equation (1) thatthe density fractions ni/n depend on a single parameter, the ratioof the cloud density to the ionization rate. In Figure 8 we plot thesolutions as functions of n/��17, where ��17 is the cosmic-rayionization rate normalized to 1:0 ; 10�17 s�1. The phenomenonof ‘‘bistability’’ (Le Bourlot et al. 1993b, 1995; Lee et al. 1998)is apparent in Figure 8, where for densities between 370 and675 cm�3 two stable solutions exist. A high-ionization phase(HIP) occurs at low n, and a low-ionization phase (LIP) occurs athigh n. The two phases may coexist where the gas is bistable. Wewill present our own discussion of bistability elsewhere (G. Boger& A. Sternberg 2005, in preparation).Because bistability occurs for a narrow range of densities, the

transition from the HIP to LIP may be said to occur near a‘‘critical density’’ ncrit /��17 � 500 cm�3 (for our assumed gas-phase abundances). In our computations, ne /nk10�5 in the HIPand ne/nP10�6 in the LIP, and the fractional ionization drops


by a factor�10 at the transition density. The Cþ and C densitiesare large in the HIP, with nC/nCO � 1, and small in the LIP, withnC/nCO < 10�3, consistent with the findings of Flower et al.(1994). Correspondingly, nCN/n and nHCN/n are large for n < ncritand small for n > ncrit. Furthermore, nCN/nHCN is large in thelow-density HIP and becomes small in the high-density LIP. Inthe HIP, nCN/nHCN decreases from �20 to 0.07 for n/��17 rang-ing from 10 to 675 cm�3. In the LIP, nCN/nHCN decreases from0.4 to 3 ; 10�3 cm�3 for n/��17 ranging from 370 to 105 cm�3.

Returning now to Figure 7, we note that the increase in thefree carbon density at large AV that occurs as � is increased isdue to the rise in ncrit, and a corresponding transition from LIPto HIP conditions, for the specific gas density of 104 cm�3. Thephase transition is affected by the presence of some FUV ra-diation. For example, for � ¼ 1:5 ; 10�16 s�1 it occurs atAV � 7 rather than in the fully opaque core (see Fig. 7g). As theionization rate is increased further, the gas is converted to theHIP throughout (see Fig. 7j).

6. DISCUSSION AND SUMMARY

CN and HCN molecules have been observed in diverse Ga-lactic and extragalactic sources, and the CN/HCN intensity anddensity ratios have been used as diagnostic probes of FUV ir-radiated molecular gas. One recent and interesting example isthe well-known starburst galaxy M82 (d ¼ 3:9 Mpc, L ¼ 3:7 ;1010 L�; e.g., Forster-Schreiber et al. 2003). Fuente et al. (2005)have reported measurements of CN 1–0 (113.490 GHz), CN 2–1 (226.874 GHz), and HCN 1–0 (88.631 GHz) line emissionsacross the inner 650 pc star-forming molecular disk in M82.They find that NCN/NHCN � 5 and argue that the large ratio isindicative of a giant and dense PDR bathed in the intense field ofthe starburst. They derive n � 104–105 cm�3 and � � 104.Fuente et al. (2005) conclude that AV P5 in the M82 clouds,since for optically thicker clouds the CN/HCN column densityratio would be smaller than observed. Our results provide sup-port for these conclusions. In this picture �10 to 20 individualclouds along the line of sight are required, since for character-istic elemental abundances the computed CN and HCN columnsfor AV P 5 (see Figs. 5 and 6) are about an order of magni-tude smaller than observed [NCN ¼ 2 � 0:5ð Þ ; 1014 cm�2 andNHCN ¼ 4 � 0:5ð Þ ; 1013 cm�2].

Alternatively, the large CN/HCN ratio might be a signatureof a very large cosmic-ray ionization rate, up to�5 ; 10�15 s�1,as invoked by Suchkov et al. (1993) for M82 and other starburstgalaxies. For such high ionization rates the CN/HCN ratio couldremain k1 even in dense and opaque cores if these are main-tained in the high-ionization phase. Our results indicate that for� ¼ 5 ; 10�15 s�1 the HIP is maintained up to n � 4 ; 105 cm�3

(see Fig. 8). This possibility is perhaps more compatible withthe large C/CO ratio k0.5 inferred from observations of the492 and 809 GHz C i fine-structure lines in M82 (Schilke et al.1993; Stutzki et al. 1997; see also Gerin & Phillips 2000). Asdiscussed above, a large C/CO ratio is a signature of the HIP.

In this paper we have presented a theoretical study of CN andHCN molecule formation in dense interstellar clouds exposedto intense FUV radiation fields. We have analyzed the behaviorof the CN/HCN density ratio for a wide range of conditions,with the aim of showing how this molecular ratio may be usedas a diagnostic probe of molecule formation in FUV irradiatedgas. For this purpose, we have constructed detailed models inwhich we solve the equations of chemical equilibrium as func-tions of optical depth for uniform density clouds at constant gastemperature (50 K). Our results are insensitive to the gas temper-ature for cold clouds with T P 200 K. We consider clouds with

Fig. 8.—Densities of CN, HCN, Cþ, C, CO, and electrons, in the cosmic-ray–dominated cores, showing the high- and low-ionization phases. (a) and(b): Densities ni /��17 and density fractions ni /n, as functions of n/��17, where��17 is the cosmic-ray ionization rate normalized to 1:0 ; 10�17 s�1, and n isthe hydrogen (H2) gas density. (c): Density ratio nCN/nHCN in the HIP and LIP.[See the electronic edition of the Journal for a color version of this figure.]


hydrogen particle densities ranging from n ¼ 102 to 106 cm�3,and FUV radiation intensities ranging from � ¼ 20 to 2 ; 105,appropriate for star-forming clouds near young OB stars and clus-ters. We present results for cosmic-ray ionization rates rangingfrom 5 ; 10�17 to 5 ; 10�16 s�1, and we also examine the effectsof large (factor 100) sulfur depletions on the computed densityprofiles. We present calculations of the density profiles for CNand HCN, and for the associated species Cþ, C, and CO. We an-alyze the behavior from the outer FUV photon-dominated re-gions into the fully opaque cosmic-ray–dominated cores.

In this paper, we adopt a fixed characteristic shape for theFUV radiation spectrum, and we do not examine the possiblesignatures of ‘‘soft’’ versus ‘‘hard’’ FUV fields (van Zadelhoffet al. 2003). Time-dependent effects due to episodic shadowing(Storzer et al. 1997), fluctuating radiation fields (Parravanoet al. 2003), grain processing (Charnley et al. 2001), turbulentmixing and diffusion (Papadopoulos et al. 2004), and otherdynamical processes are not considered here.

Our models show how observations of the CN/HCN abun-dances ratio in molecular clouds may used as probes of FUVand cosmic-ray–driven gas-phase chemistry for a wide range ofconditions. We find that in dense gas, CN molecules are char-acteristically and preferentially produced near the inner edgesof the C ii zones in the PDRs. This is where Cþ begins torecombine and where atomic carbon is incorporated into CO.Molecule formation is ‘‘recombination limited’’ at these depths,and for fixed �/n, the CN density is proportional to the clouddensity and to the gas-phase carbon and nitrogen abundances.For nk104 cm�3, and for clouds with linear sizes correspond-ing to visual extinctions AV P 10, the entire integrated CN col-umn density is built up at the Cþ/C/CO transition layer. Forcharacteristic interstellar carbon and nitrogen gas-phase abun-dances, the predicted CN columns are �3 ; 1013 cm�2. HCN israpidly photodissociated in the outer parts of the PDRs, includ-ing the Cþ/C/CO transition layers. Because HCN is more vul-nerable to photodissociation, the CN/HCN density ratio is largeat low AV and decreases with increasing optical depth. We find

that the CN/HCN density ratio typically decreases fromk10 inthe Cþ/C/CO transition layers toP0.1 in the opaque cores.At intermediate and large depths, the bulk of the gas-phase

carbon is locked in CO molecules, and the CN and HCN den-sities depend on the rate at which carbon is released from CO bycosmic-ray–driven helium impact ionization. Molecule forma-tion is then ‘‘ionization limited’’ and occurs with an efficiencyproportional to the cosmic-ray ionization rate. In dense clouds,an enhanced abundance of atomic carbon is maintained at inter-mediate depths, where charge transfer of Cþ with S is effective,and where photodestruction reduces the efficiency with whichthe carbon atoms are removed in reactions with molecules. Atthese intermediate depths the CN density is insensitive to AV .However, the HCN densities increase with AV as the destructiveFUV photons are absorbed.The Cþ, C, CO, CN, and HCN densities in the opaque cores

depend on whether the cores are in the ‘‘low-ionization’’ or‘‘high-ionization’’ phases that are possible for such gas. Wepresent computations for gas in both phases. The transition fromthe HIP to LIP occurs at a critical value n/��17 ¼ 103 cm�3,consistent with previous findings. The CN/HCN density ratiocan become largek1 in the LIP, but it remains small in the HIP.For dense gas in Galactic molecular clouds and for charac-

teristic cosmic-ray ionization rates, a large CN/HCN densityratio may be interpreted reliably as an indicator of moleculeformation in PDRs. In clouds exposed to enhanced fluxes ofcosmic rays, as perhaps occurs in starburst galaxies, a highCN/HCN ratio may alternatively be an indicator of opaqueclouds in the high-ionization phase. Measurements of the C/COratio can be used to distinguish between these two possibilities.

We thank A. Dalgarno, A. Fuente, O. Gnat, and C. F. McKeefor discussions, and the referee for helpful comments andsuggestions. This research is supported by the Israel ScienceFoundation, grant 221/03.

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