Modeling of diffuse molecular gas applied to HD 102065 observations
Cyrine Nehme, Jacques Le Bourlot, Francois Boulanger, Guillaume Pineau des Forets, Cecile Gry
aa r X i v : . [ a s t r o - ph ] A p r Astronomy & Astrophysics manuscript no. 8374 c (cid:13)
ESO 2018October 24, 2018
Modeling of diffuse molecular gas applied to HD 102065observations
Cyrine Nehm´e , Jacques Le Bourlot , Fran¸cois Boulanger , Guillaume Pineau des Forˆets , and C´ecile Gry , LUTH, UMR 8102, CNRS, Universit´e Paris 7 and Observatoire de Paris, Place J. Janssen, 92195 Meudon, France Institut d’Astrophysique Spatiale, UMR8617, CNRS, Universit´e Paris Sud, Bat. 121, 91405 Orsay Cedex, France Laboratoire d’Astrophysique de Marseille, UMR 6110, CNRS, Universit´e de Provence, 38 rue Fr´ed´eric Joliot-Curie,13388 Marseille cedex 13, France European Space Astronomy Center, RSSD, P O Box 50727, 28080 Madrid, Spain LERMA, UMR 8112, CNRS, Observatoire de Paris, 61 Avenue de l’Observatoire, 75014 Paris, FranceReceived / Accepted 23-01-2008
ABSTRACT
Aims.
We model a diffuse molecular cloud present along the line of sight to the star HD 102065. We compare ourmodeling with observations to test our understanding of physical conditions and chemistry in diffuse molecular clouds.
Methods.
We analyze an extensive set of spectroscopic observations which characterize the diffuse molecular cloudobserved toward HD 102065. Absorption observations provide the extinction curve, H , C i , CO, CH, and CH + columndensities and excitation. These data are complemented by observations of C + , CO and dust emission. Physical conditionsare determined using the Meudon PDR model of UV illuminated gas. Results.
We find that all observational results, except column densities of CH, CH + and H in its excited ( J ≥
2) levels,are consistent with a cloud model implying a Galactic radiation field ( G ∼ . − and a temperature (60-80 K) set by the equilibrium between heating and cooling processes. To account for excited( J ≥
2) H levels column densities, an additional component of warm ( ∼
250 K) and dense (n H ≥ cm − ) gas within0.03 pc of the star would be required. This solution reproduces the observations only if the ortho-to-para H ratio atformation is ∼
1. In view of the extreme physical conditions and the unsupported requirement on the ortho-to-pararatio, we conclude that H excitation is most likely to be accounted for by the presence of warm molecular gas withinthe diffuse cloud heated by the local dissipation of turbulent kinetic energy. This warm H is required to account forthe CH + column density. It could also contribute to the CH abundance and explain the inhomogeneity of the COabundance indicated by the comparison of absorption and emission spectra. Key words.
Astrochemistry,ISM:clouds,ISM:molecules,ISM:structure,ISM:individual objects:Chamaeleon clouds,Stars:individual:HD102065
1. Introduction
Since the pioneering work of Black & Dalgarno (1977), ob-servations of diffuse molecular clouds continue to motivateand challenge efforts to model the thermal balance andchemistry of interstellar gas illuminated by UV photons.Models allow observers to determine physical conditionsfrom their data and observations contribute to models byquantifying physical processes of general relevance to stud-ies of matter in space such as H formation, photo-electricheating, and cosmic ray ionization.Many models of well characterized lines of sight havebeen presented (e.g. in the last years: Zsarg´o & Federman ,2003; Le Petit et al., 2004; Shaw et al., 2006). They aresuccessful in reproducing many observables apart fromsome molecular abundances, most conspicuously CH + ,which points to out-of-equilibrium chemistry. This molec-ular ion, and several of the molecular species com-monly observed in diffuse molecular clouds such asCH, OH and HCO + may be produced by MHD Send offprint requests to : Jacques Le Bourlot
Correspondence to : [email protected] shocks (Draine & Katz, 1986; Pineau des Forˆets et al.,1986; Flower & Pineau des Forˆets, 1998), and small scalevortices (Joulain et al., 1998; Falgarone et al., 2006) whereH is heated by the localized dissipation of the gas turbu-lent kinetic energy. Turbulent transport between the coldand warm neutral medium may also significantly impactthe chemistry of diffuse clouds (Lesaffre et al., 2007).Independently of gas chemistry, the presence of H at higher temperatures than that set by UV andcosmic-rays heating of diffuse molecular clouds, may beprobed through observations of the H level popula-tions (Cecchi-Pestellini et al., 2006). A correlation be-tween CH + and rotationally excited H was found byLambert & Danks (1986) using Copernicus observations.Falgarone et al. (2005) reported the detection of the S(0)to S(3) H lines in a line of sight towards the innerGalaxy away from star forming regions. They interprettheir observation as evidence for traces of warm molecu-lar gas in the diffuse interstellar medium. But the inter-pretation of the wealth of H observations provided bythe FUSE satellite is still a matter of debate. Gry et al.(2002) modeled FUSE H observations of three stars in Nehm´e et al.: Modeling of diffuse molecular gas
Chamaeleon using the Meudon Photon Dominated Regions(PDR) model (Le Bourlot et al., 1993). They show thatthe model cannot account for H column densities in ro-tational states with J >
2. A larger sample of H FUSEobservations (Tumlinson et al. , 2002; Gillmon et al., 2005;Wakker, 2006), including 2 of the 3 Chamaeleon linesof sight of Gry et al. (2002), have been analyzed on thebasis of model calculations presented by Browning et al.(2003). Their model, like other PDR models, takes into ac-count the formation of H on grains, its photo-dissociationby absorption of resonant UV photons, radiative transferand vibrational/rotational excitation resulting from colli-sions, H formation and UV pumping. Unlike the latestPDR models (Shaw et al., 2005; Le Petit et al., 2006), theBrowning et al. (2003) model does not derive the gas tem-perature from the thermal balance between heating andcooling processes. Browning et al. (2003) instead considergas temperature as a model parameter independent of thedensity, incident radiation field and cloud shielding (totalextinction). They conclude that H observations cannot beaccounted for with a single isothermal slab of gas. Theypropose solutions where the data are fitted with absorptionfrom two physically independent gas layers with distincttemperatures, UV illuminations and column densities. Acold ( ≤
100 K) component contributes most of the totalH column density while a warmer ( ∼
200 K) and thin-ner component with a higher UV field helps populate thehigh J states. For many of the model combinations consid-ered by Browning et al. (2003), the difference in UV fieldis too low to account for the corresponding difference intemperature. In particular, the combinations proposed forthe nearby diffuse interstellar medium require an additionalheating source in the warm component. For H observa-tions towards Galactic stars, some of the absorption mayarise from gas in the vicinity of the star (e.g. Boiss´e et al.,2005).In a companion paper (Nehm´e et al., 2008), we pre-sented a multi-wavelength study combining spectroscopicUV, optical, IR and radio observations of the interstel-lar matter, along the line of sight to the nearby (170 pc)moderately reddened (E(B-V) = 0.17) star HD 102065.Absorption observations provide the column densities of H in the J=0 to 5 states, C i in its three fine structure states,CO in the J=0 to 2 states, CH and CH + . They are comple-mented by observations of the C + , CO(2 −
1) and (1 − and CN optical absorption lines were transformed intoupper limits on column densities using oscillator strengthslisted by Gredel et al. (1991, 1993).The HD 102065 line of sight is well suited for de-tailed modeling of physical conditions, chemistry and H excitation, because of the large amount of available data(Table 1). The molecular fraction is not altered by the pres-ence of warm atomic gas along the line of sight. Comparisonof H I, H and dust extinction indicates that the bulk ( 90%)of the column density is accounted for by a diffuse molec-ular cloud identified on IRAS images. IRAS observationsplace a strong constraint on the presence of matter closeto the star. The abundance of CH + is high. This paper ex-tends the work of Gry et al. (2002), where only the FUSEH spectrum of HD 102065 was analyzed, to a wider set ofobservations, using an updated version of the Meudon PDRmodel (Le Petit et al., 2006). Kopp et al. (2000) used this sight line to discuss the impact of far-UV extinction on theCO abundance.The structure of the paper is as follow: Sect. 2 presentsthe PDR model used to characterize the diffuse molecu-lar cloud and Sect. 3 describes the main modeling results.First, a reference model is defined by fitting observationalconstraints together. Second, the model is compared witheach of the observations to assess the dependence of modelpredictions on the values of the physical parameters. InSect. 4, we present a detailed attempt to model H exci-tation with a warmer component located close to the star.Sect. 5 presents our conclusions.
2. Description of the PDR model
We use a comprehensive model of an interstellar cloud, thatdescribes the state of the gas and dust exposed to a ra-diation field as a function of optical depth . The modelis one-dimensional and stationary. It presents several im-provements over that previously used by Gry et al. (2002)and is described in detail in Le Petit et al. (2006). It com-putes simultaneously, in an iterative way : – the UV radiative transfer , taking into account thecontinuum absorption by dust and the line absorptionby the lowest levels of H . The UV radiation field canilluminate the cloud from both sides. – the thermal balance , taking into account all relevantheating and cooling processes. – the chemistry , typically coupling about 100 differentspecies through 800 chemical reactions. Model parameters (see Table 2) are kept fixed at values con-sistent with typical diffuse clouds and the measured char-acteristics of the HD 102065 line of sight. The model ig-nores the gas velocity structure and assumes that the threelow velocity components discussed by Nehm´e et al. (2008)make a single homogeneous cloud with a visual extinctionequal to the observed value to HD 102065. We look fora best fit model by varying only the UV radiation fieldstrength G (isotropic and incident on both sides of thecloud) measured in units of Draine’s radiation field, and thegas density n H . Density is constant throughout the cloud.Temperature is computed by solving for thermal balance.The standard Draine’s field ( G = 1, Draine, 1978) is equiv-alent to about 1.6 in units of Habing’s field (Habing, 1968).Element abundances are those measured for ζ Ophtaken from Savage & Sembach (1996). Fig. 1 shows thatHD 102065 measured abundances are close to these refer-ence values (Paper I). The grain distribution is kept fixed.It is a MRN type one with a power law size distribu-tion α = − . − and 1 . × − cm. Although that distribution does notreproduce the details of the smallest grains size distribu-tion required to account for the mid-infrared dust emission(Desert et al., 1990; Boulanger et al., 1994), it matches theVery Small Grains (VSG ) to total dust mass ratio of 0 . By VSG we mean any solid particle with a typical sizesmaller than 10 − cm, irrelevant of its precise nature.ehm´e et al.: Modeling of diffuse molecular gas 3 Table 1.
Observational constraints and best model results.Upper part are constraints used in Fig. 2, lower part com-pares unconstrained observations and results. Number inparentheses are powers of 10. X mod X obs σ obs N (CO) /N (H ) 1 . −
7) 1 . − ± . − .
15 ( − N (C i ) /N H . −
7) 6 . − ± . − N (C i ∗ J =1 ) /N (C i ) 0 .
17 0 . ± . N (C i ∗∗ J =2 ) /N (C i ) 0 .
03 0 . ± . f H = N (H ) N (H)+2 N (H ) . . ± . N (H o2 ) /N (H p2 ) 0 .
73 0 . ± . I (C + ) (erg / s cm sr) 2 . −
6) 2 . − ± .
85 ( − N (CH) /N (H ) 8 . −
9) 1 .
85 ( − ± . − N (CN) /N (H ) 1 . − < . − N (C ) /N (H ) 3 . − < . − N (CO J=0 ) /N (H ) 9 . −
8) 9 . − ± . − . − N (CO J=1 ) /N (H ) 5 . −
8) 6 . − ± . − . − N (CO J=2 ) /N (H ) 3 . − < . − Table 2.
Fixed model parameters. δ X are the gas phaseabundance of atom X relative to hydrogen. Parameter Value Comment A v .
67 mag Extinction ζ − s − Cosmic Rays ionization v turb . − Turbulent velocity R v . ω . − Dust albedo g . − Dust anisotropy factor G r .
57 10 − Dust to gas mass ratio ρ g .
59 g cm − Dust density α . a min − cm Dust minimum radius a max . − cm Dust maximum radius δ C .
32 10 − δ O .
19 10 − δ N .
50 10 − δ S .
86 10 − −4−3−2−1 0 1 O P Zn Si Cu Mn Mg Fe Cr Ni Co Ti [ X / H ] Element z oph CoolHD102065 Comp A+B Fig. 1.
Depletion [X/H] in the cool gas towards HD 102065compared with ζ Oph values. Data are taken from Paper I. formation equations In the present model, the H formation rate on grains isnot a free parameter, but is computed locally from the com-bined adsorption of H atoms from the gas on grains followedby recombination and desorption of H molecules:H + dust → H ad H ad + H ad → H where H ad is an hydrogen atom adsorbed on dust. If onlythose two processes are included and steady state applies,the production of H is independent of how H atoms even-tually manage to reach one another and may be computedby: d [H ] dt (cid:12)(cid:12)(cid:12)(cid:12) form = 12 k ad [H] = 12 s < σ n g > v H n(H) (1)where s is the sticking coefficient of H upon collision, v H itsmean velocity and < σn g > the mean grain cross sectionper unit volume.In the full model, other processes may compete withH formation to remove adsorbed hydrogen atoms (photodesorption, reactions on grains, etc...). In this paper, weneglect all of those processes, which allows the formationrate to be computed exactly. Results from Le Bourlot et al.(1995) show that the mean cross section can be written: < σn g > = 34 1 . H G r ρ g √ a min × a max n H (2)where G r is the dust-to-gas mass ratio, ρ g the densityof grain material, and integration is completed for theentire grain size distribution, using a MRN distribution(Mathis et al., 1977) with an index of 3 . a min to a max .Combining Eq (1) and (2) we can write: d [H ] dt (cid:12)(cid:12)(cid:12)(cid:12) form = R f p T gas s n H n (H) (3)where R f , the H formation rate in cm − s − , reads: R f = 1 . × − G r ρ g √ a min × a max (4)The resulting value of R f is 2 . × − cm − s − . Weuse a prescription from David Flower (see discussion inLe Petit et al., 2006) for the sticking coefficient s : s = q /T gas (K) (5)The ortho-to-para ratio on formation of H is set to avalue of three. One third (1.5 eV) of the formation energyis transferred into internal excitation, and is distributedover all H energy levels with a Boltzmann distribution(Le Petit et al., 2006). A second third of the formation en-ergy is converted into kinetic energy of H , and the lastthird, into grain heating. Nehm´e et al.: Modeling of diffuse molecular gas n H ( c m − ) Fig. 2. χ contours (Eq 6) using the top 7 quantities ofTable 1. The best fit is obtained for G = 0 . n H =80 cm − . Contours are labeled with the χ value.
3. Modeling the molecular cloud toward HD102065
To compare observations and model results, we haveselected s even quantities for which an observa-tional error bar could be computed: N (CO) /N (H ), N (C i ) /N H , N (C i ∗ J=1 ) /N (C i ), N (C i ∗∗ J=2 ) /N (C i ), f H = 2 N (H ) / ( N (H) + 2 N (H )), N (H o2 ) /N (H p2 ), and I (C + ), where N (X) is the column density of species X overthe whole cloud and H o2 and H p2 are ortho- and para-H respectively. From these quantities, we define a χ errorfunction by: χ = 17 X i =1 (cid:18) X obs i − X mod i σ obs (cid:19) (6)where X obs i is the quantity derived from observations, X mod i the same quantity from a model, and σ obs the observationaluncertainty (see Table 1) . We computed a grid of mod-els for gas densities ranging from 30 to 200 cm − and UVfields G from 0.25 to 1.0. Figure 2 shows the resulting χ iso-values. Contours are smooth, and limit a well definedminimum where χ <
1, i.e. where model results are, in themean , closer to observations than observational uncertain-ties.One can see that the best compromise is reached for arather low radiation field ( G = 0 .
4, which is close to thestandard Habing field) and a mean total proton densityof n H = 80 cm − . In the following we will refer to thosevalues as our reference model. The reference model resultsare compared to the observables in Table 1. Abundanceand temperature profiles are illustrated on Fig. 3, 4 and 5 .The H I to H transition occurs close to the cloud edge atan extinction of A v ∼ − . Most of the carbon is in theform of C + at all depths. The fraction of atomic carbon Note that X i need not be dimensionless because normalisa-tion by σ ensure that compatible quantities are summed The peculiar horizontal scale allows for logarithmic scalingtowards both sides of the cloud −2 −1 −5−4−3−2−10−1−2−3−4−5 3.35 10 −5 −3 −1 −3 −5 n ( X ) ( c m − ) Log (min(A v )/A v (c))HH Fig. 3.
H and H density profiles for the reference modelplotted versus the extinction from the nearest edge normal-ized to the central extinction. −11 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 −5−4−3−2−10−1−2−3−4−5 3.35 10 −5 −3 −1 −3 −5 n ( X ) ( c m − ) Log (min(A v )/A v (c))C + CCOCH
Fig. 4. C + , C, CO and CH density profiles for the referencemodel.C i is constant throughout the cloud. The density profilesof CO and CH molecules follow that of H . Temperaturevaries from 60 to 80 K, and is lowest at the cloud edge. Thetemperature bumps visible on Fig. 5 are due to heating byH formation.The gas heating rate is 1 . × − erg cm − s − at thecloud center and comes mainly from photo-electric effecton grains. In the outer layers where the temperature peaks,photo-electric heating reaches 3 . × − erg cm − s − andthere is a lower but significant heating due to H formation(2 . × − erg cm − s − ). Cooling is dominated by C + ,with H contributing up to 20% around 10 − A v . This leadsto an integrated C + emissivity of 2 × − erg cm − s − sr − in good agreement with the ISO observation.In the next sections, we discuss each of the observablesand their dependence on the two model parameters n H and G . ehm´e et al.: Modeling of diffuse molecular gas 5
50 55 60 65 70 75 80 −4−3−2−10−1−2−3−4 3.35 10 −5 −3 −1 −3 −5 T ( K ) Log (min(A v )/A v (c)) Fig. 5.
Temperature profile for the reference model. f n H (cm −3 )/ G G = 0.25G = 0.40G = 1.00 Fig. 6. H fraction f H as a function of n H /G for G =0 . , . .
0. The horizontal lines are the observed valuewith the error bars. O / P n H (cm −3 ) G = 0.25G = 0.40G = 1.00 Fig. 7.
Ortho-to-para ratio of H as a function of n H forthree values of G . T ( K ) n H (cm −3 ) G = 0.25G = 0.40G = 1.00 Fig. 8.
Mean gas temperature as a function of n H for threevalues of G . H formation rate and molecular fraction H fraction (f H ) is plotted versus density for three val-ues of G on Fig. 6. For the reference model ( G = 0 . n H = 80 cm − ) computed values for f H are around 0.9,significantly higher than the observed f H .Gry et al. (2002) have shown that f H , for a given valueof G , depends on the product n H × R , where H formationproceeds at a rate n H n (H) R . We note that their R incor-porates both the temperature dependence and the stickingcoefficient. Using our prescription for the sticking coeffi-cient s (section (2)), one finds that R is equal to √ R f and is independent of T gas .More generally, Fig. 6 shows that the molecular fractionfor a given total gas column density depends on n H × R/G .Gry et al. (2002) found that the observed f H is matched for n H × R = 2 . − s − , for a cloud illuminated on one sideby the Habing field (equivalent to G = 0 . n H √ R f = 5 . − s − ,a factor 2.5 higher. This difference explains why, in ourmodel, the molecular fraction is higher than the observedvalue. In the model, the formation of molecular hydrogen isthe only destruction path of adsorbed atomic hydrogen inthe present calculation. Other processes (such as photo des-orption) may limit the amount of H adsorbed on grains andlower further the H formation efficiency. We consider theagreement between model and observed H fraction sat-isfactory because the time scale of H formation, a few10 yr, is long compared to dynamical time scales in dif-fuse clouds. The observed value is thus not expected toaccurately match the model steady state value. Analysisof a large set of FUSE lines of sight will be required toestimate how observed molecular fractions scatter aboutmodel steady state values and constrain the H formationrate more precisely. H excitation The ortho-to-para H ratio, and the mean gas temperatureare shown in Fig. 7 and 8, and the H excitation diagramin Fig. 9. H column densities in the J = 0 and J = 1levels are reasonably well reproduced. The observed ortho Nehm´e et al.: Modeling of diffuse molecular gas
12 13 14 15 16 17 18 19 20 21 0 500 1000 1500 2000 2500 3000 l og ( N ( H J ) / g ) Energy (K) ObsModel
Fig. 9.
Observed H excitation diagram and referencemodel. Two excitation temperatures are plotted for J = 0and 1: T ex = 66 K, and for J = 3 to 5: T ex =248 K.to para ratio depends on the gas temperature. If it is at itsequilibrium value (this is a reasonable hypothesis for diffuseclouds where the time scale for ortho-to-para conversion isshorter than that of H formation), the N ( J = 1) /N ( J = 0)ratio can be considered a direct measure of the gas temper-ature. The excitation diagram in Fig. 9 implies an excita-tion temperature of 66 K (for J ≤ column densities derived fromthe model for J > J ≥
3, we derive an excitation temperature T ex = 248 K. This high J gas suggests the existence of awarmer gas component that will be discussed in Sect. 4.We used the model to check that an increase in the cosmic-rays ionization rate, a possibility considered by Shaw et al.(2006), is not a solution. Multiplying this rate by a fac-tor 20 to a value of 10 − s − increases the model columndensities in the J=3 and 4 levels by less than a factor of 2. The neutral atomic carbon abundance and fine structureexcitation, are presented in Fig. 10 and 11. Most of thecarbon is in C + and the fraction of carbon in the neutralform C i depends on both the gas density and the value of G . It increases with densities and decreases with increas-ing G . Our reference model is in good agreement with theobserved value.The neutral atomic carbon excitation in diffuseclouds is often considered as a measure of gas pressure(Jenkins & Tripp, 2001). In our model, this translates intoa dependence on the product n H × G with only small dif-ferences from one G to another. Our reference model, re-produces well the fraction of J = 1 fine structure level, butnot so well that of J = 2, which implies n H ≤
50 cm − for G = 0 .
4. It is often the case that C i excitation in diffuseclouds cannot be accounted for by gas at a single pressure(Jenkins & Tripp, 2001). However our observations show a C It o t/ NH n H (cm −3 ) G = 0.25G = 0.40G = 1.00 Fig. 10.
Neutral atomic carbon abundance as a function ofthe gas density n H for three values of the UV radiation fieldintensity factor G . C I * / C It o t CI**/CItot G = 0.25G = 0.4G = 1.0
Fig. 11.
Fraction of excited C i (J=1 and 2 fine structurelevels: C i ∗ and C i ∗∗ ) for various n H and G . Dashed linesare the observations with their 3- σ uncertainties. Alongeach line, the densities increase from left to right from 30to 200 cm − as in Fig. 10.lower C i ∗∗ / C i ∗ ratios than implied by the model, contraryto Jenkins & Tripp (2001) findings. Our reference model matches the observed abundance ofCO (Fig. 12). Table 1 shows that CO excitation is also wellpredicted by the model, although it was not used as a con-straint. The rise in the N (CO) /N (H ) ratio at low densityand low radiation field is a chemical effect. The formationof CO is illustrated in Fig. 13. The efficiency of CO for-mation depends on the ionization fraction. Photoionisationis proportional to the gas density n H , while recombinationproceeds at a rate that is proportional to the square of thatquantity. The degree of ionization therefore increases when ehm´e et al.: Modeling of diffuse molecular gas 7 C O / H n H (cm −3 ) G = 0.25G = 0.40G = 1.00 Fig. 12.
N(CO) / N(H ) variation with density. All othermodel parameters are as in Table 1. The horizontal linesshow the observed values with the error bars . Photon CO CO HCO
O O
OH H OH OH O++ + ++ Photon
Fig. 13.
A schematic illustration of CO formation routesin a low UV radiation field. Destruction is still dominatedby Photodissociation.the density decreases in a given radiation field. Enhancingthe ionization enhances O + formation via charge exchangewith H + and favors the formation of OH and H O. Bothmolecules interact with C + and lead either directly or indi-rectly to the formation of CO. The reaction involving OH isdominant. Photodestruction of CO is limited by the weak-ness of the radiation field.We are cautious about the model interpretation of theCO abundance. It is noticeable that the CO column den-sities in the J=1 and 2 levels, derived from UV spectra,are significantly smaller by factors 3 and 7, respectively,than the values derived from the emission radio spectra(Nehm´e et al., 2008). These differences indicate that theabundance of CO is inhomogeneous, which could be ac-counted for within the PDR model, by introducing clumpswith higher density than the mean value. However, the largeCH + abundance favors an alternative explanation, where asmall-scale increase in the CO abundance, traces the local-ized contribution of out-of-equilibrium chemistry to its for-mation. Liszt and Lucas (2000) have gathered results fromUV and radio absorption measurements of CO along diffuseinterstellar medium lines of sight. They relate the CO abun-dance to that of HCO + measurements, concluding that COformation through dissociative recombination of HCO + suf- − N ( CH ) / N ( H ) n H (cm −3 )/G G = 0.25G = 0.40G = 1.00 Fig. 14.
N(CH) / N(H ) variation with density and the ra-diation field. The horizontal lines show the observed valueswith the error bars.fice to account for the CO abundance in diffuse molecu-lar clouds. Falgarone et al. (2006) show that the observedabundance of HCO + ( ∼ × − ) cannot be accounted bystandard PDR chemistry and must be related, like CH + ,to warm out-of-equilibrium chemistry. A significant frac-tion of CO observed in diffuse molecular clouds may thusbe a product of out-of-equilibrium chemistry.This interpretation links CO abundance inhomo-geneities to the CH + chemistry but it is not specificallythe CH + rich gas that has an enhanced CO abundance.It is not ruled out by the observed velocity difference be-tween CH + and CO (Nehm´e et al., 2008). CO, unlike CH + ,is observed to be concentrated in the intermediate velocitycomponent C. This component may correspond to shieldedsections of the cloud where the CO photo-dissociation rateis reduced. In Nehm´e et al. (2008), we propose that the lineof sight to HD 102065 samples material ablated from theDcld 300.2-16.9 cloud by a cloud-supernova shock interac-tion. In this scenario, the matter flowing out of the cloudis expected to be very turbulent (Nakamura et al., 2006).In Fig. 14, we show that the CH abundance(N(CH) / N(H )) computed by the model depends linearlyon the ratio n H /G . The value for our reference model isa factor of two lower than observations. This mismatchbetween model and observations, might be an additionalmanifestation of the out-of-equilibrium chemistry, as al-ready proposed by e.g. Zsarg´o & Federman (2003) andRitchey et al. (2006). The “excess” of CH abundance maybe the product of CH + recombination with H . Finally, wenote that the model is consistent with the upper limits onCN and C abundances (Table 1).
4. Warm H The H excitation diagram (Fig. 9) shows that the observedcolumn densities at J > J column densities. This is commonlyobserved, towards many stars by Copernicus and FUSE.The model values, which take into account UV pumpingand H excitation upon formation are also roughly an orderof magnitude lower than the observations. Gry et al. (2002) Nehm´e et al.: Modeling of diffuse molecular gas N ( J = ) ( c m - ) n H (cm -3 ) 0.010.0150.020.030.050.1 Fig. 15. H ( J = 3) column densities for an A v = 10 − slab of gas close to the star (labels next to the curves is d inpc). The two dashed horizontal lines bracket the measuredcolumn density with its error bar.and others earlier (e.g. Draine & Katz, 1986; Joulain et al.,1998; Pineau des Forˆets et al., 1986) have proposed thatthis excited H traces warm gas in regions where kineticenergy is dissipated through shocks or vortices. Other au-thors have proposed that this warm H is the signature ofmolecular gas close to the star and thus exposed to a highUV field (e.g. Browning et al., 2003). The presence of CH + in quantities much larger than predicted by the PDR modelfavors the former explanation (Falgarone et al., 2005). Totest this preference, we have used the PDR model to quan-tify the latter possibility in the specific case of HD 102065.The ratio between the 100 µ m brightness in the IRASimages and the visible extinction towards HD 102065 in-dicates that most of the matter is fairly distant from thestar (Boulanger et al., 1994) and does not interact with it.The 60 and 100 µ m images only show a small brightnessenhancement at the position of HD 102065, point-like atthe IRAS resolution (angular size − ) of the stellar luminosity(Boulanger et al., 1994). If the absorbing matter occupiesa solid angle θ about the star, its UV/visible opacity is10 − × π/θ . Combining the constraint on the source di-ameter ( < ′ ), and the star distance (170 pc), we derive anupper limit for the distance, from the star to the absorbingmatter of 0 .
12 pc. HD102065 is a B9IV star with a luminos-ity ∼ L ⊙ and an effective temperature of 11300 K. Thestellar radiation field intensity is G ∗ = 0 . × ( d/ − inDraine units.For an extinction A v ∼ − the gas is molecular onlyfor large densities. To search for a more realistic solution, weassume that θ/ π ∼ .
1. To quantify with this assumption,the column density of warm H that could be associatedwith the IRAS far-IR emission, we compute a grid of modelswith constant A v = 10 − , varying the density n H from 10 to 3 × cm − , and the distance to the star from 0 . − pc (equivalent to G ∗ from 20 to 2 × ).Figure 15 shows the column densities of H ( J = 3), asa function of n H for various distances to the star. As dis-tance decreases, the radiation field increases, the H photo-dissociation rate rises, and higher densities are required to
26 28 30 32 34 36 38 40 42 0 1000 2000 3000 4000 5000 l og ( N ( J ) / g J ) E(J) (K)T exc = 245 K ([228:330])J = 2 ObservationsO/P form = 3O/P form = 1
Fig. 16. H excitation diagram for n H = 3 10 cm − , d =0 .
02 pc ( G ∼ ortho to para ratio at formation would be 1but no theoretical nor experimental study support a valuemuch different from 3.retain hydrogen in its molecular form. The stronger radia-tive pumping populates higher rotational levels, which ac-counts for the bell shape of the curves. The same trendoccurs at higher rotational levels, for which the curve max-ima are shifted towards higher densities.The observed excitation temperature of ∼
250 K is re-produced for the correct column densities, in a range ofmodels, as shown on Fig. 15. One typical example is illus-trated in Fig. 16. It can be clearly seen however that the J = 4 point lags under the J = 3 − through reactive collisions, with either H or H + .The only way to reproduce the J = 4 column density isto assume a formation ortho-to-para ratio that is differentfrom the statistical equilibrium value of 3. Fig. 16 showsthat an initial ratio of 1 provides robust results. We arehowever unaware of any theoretical or experimental resultthat would support such an initial ratio.We conclude that a pure steady-state PDR model isable to reproduce the excitation of H at J >
2, observedtowards HD 102065, with two ad hoc assumptions: the pres-ence of warm and dense gas close to the star at a pressure > K cm − , and an H ortho-to-para ratio, at formation,of 1. We checked the possibility that the warm H may bein a circumstellar disk. Upper limits on H column densitiesfrom the β Pictoris debris disk, are several orders of mag-nitude lower than the HD 102065 values (Lecavelier et al.,2001). The warm H column densities observed towardsHD 102065 are comparable to those detected from circum-stellar disks about the young AeBe Herbig stars HD 100546and HD 163296 (Lecavelier et al., 2003), but these disks aretraced by strong near to mid-infrared emission that is notobserved in HD 102065.Gillmon et al. (2005) and Wakker (2006) analyzed alarge set of FUSE Galactic H detections obtained towards ehm´e et al.: Modeling of diffuse molecular gas 9 Fig. 17.
Fraction of H in the J=3 level versus the total H column density. The data are taken from observations ofGalactic H towards extragalactic sources as analyzed byGillmon et al. (2005). The three data points at N(H ) > cm − correspond to the three Chamaeleon stars ofGry et al. (2002) including HD 102065 (filled square).extragalactic sources. Wakker (2006) showed that H exci-tation, for column density ratios between the 4 first J levels,follows a systematic trend with increasing total H columndensity. HD 102065, and the two remaining Chamaeleonstars studied by Gry et al. (2002), fall on the same trendextending to yet higher N(H ) values (Fig. 17). This agree-ment indicates that H excitation observed towards theChamaeleon stars, fit with observations towards extragalac-tic sources and is thus unlikely to be due to matter heatedby the stars. Qualitatively, the trend observed in Fig. 17 isin agreement with the fact that the gas temperature andthe H radiative pumping increase, as the H column den-sity decreases. But, based on the HD 102065 results, weanticipate that a warm out-of-equilibrium H componentis required to quantitatively reproduce the data. We con-clude that the presence of some H at temperatures higherthan the equilibrium temperature set by UV and cosmic-ray heating is a general characteristic of diffuse molecu-lar gas in the Solar Neighborhood. Modeling of the widesample of FUSE Galactic H measurements, is required tostatistically quantify the fraction of out-of-equilibrium H gas. This warm molecular gas traces the local dissipationof turbulent kinetic energy. It is the dissipation of turbu-lence that creates the non-equilibrium chemistry discussedin Sect. 3.5.
5. Conclusions
We have gathered a wide set of observations characteriz-ing the diffuse molecular cloud, observed towards the starHD 102065. These observations provide independent con-straints on physical conditions, which are analyzed with thelatest version of the Meudon PDR code.A single density ( n H = 80 cm − ) slab of gas, bathed in alow radiation field, accounts for most observations (molec-ular fraction, gas temperature inferred from the N(H , J =1) / N(H , J = 0), cooling in the C + line, C i abundance andexcitation). This model provides a physical and chemical reference upon which more elaborate interpretations canbe developed to account for observables not reproduced bythe model, namely the column densities of CH, CH + andH in its excited ( J ≥
2) levels.We consider the possibility that high J H is associatedwith matter close to the star. We place constraints on thispossibility using IRAS data on dust emission. We find a so-lution where dense (n H ≥ cm − ) gas with a high pres-sure (p / k > K cm − ) would be located within 0.03pc of the star. This solution requires the presence of highpressure gas close to the star and that the H ortho-to-pararatio at formation is 1. Such a departure from the statisticalexpectation is supported by no theoretical or experimentalstudy.The H excitation observed towards HD 102065 fits withthe general trend observed from FUSE Galactic H obser-vations towards extragalactic sources. We conclude that H excitation in the J > in the Solar Neighborhooddiffuse ISM. Our work supports earlier studies that pro-posed that H excitation in the J > , heated by the localized dissipation,in space and time, of turbulent kinetic energy within dif-fuse molecular clouds. The warm H is physically associatedwith the bulk of the molecular gas, traced by the J=0 and1 H absorptions, and is required to account for the CH + column density. In addition, the warm H2 could contributeto the CH abundance, and the inhomogeneity of the COabundance, as indicated by the comparison of absorptionand emission spectra.This paper outlines a framework for modeling the largenumber of Galactic H measurements derived from FUSEextragalactic observations, which cover 6 orders of magni-tudes in H column densities. In diffuse clouds, the timescale of H formation, a few 10 yr, is long compared todynamical time scales. Observed values of the gas fractionin H are thus not expected to match steady-state values.Modeling of the available data will quantify how observedmolecular fractions scatter about model values, and bet-ter constrain the H formation rate than the present study.Modeling of these observations will, in addition, statisti-cally quantify the presence of warm H , heated by localizeddissipation of kinetic energy. References
Black, J.H., & Dalgarno, A., 1977, ApJS, 34, 405Boiss´e, P., Le Petit, F., Rollinde, E., Roueff, E., Pineau des Forˆets,G., Andersson, B.-G., Gry, C. & Felenbok, P. 2005, A&A 429, 509Boulanger, F., Pr´evot, M.L. & Gry, C. 1994, A&A, 284, 256Browning, M.K., Tumlinson, J., & Shull, J.M. 2003, ApJ, 582, 810Cecchi-Pestellini, C., Casu, S. & Dalgarno, A. 2006, MNRAS 364,1309Draine, B.T. 1978, ApJS, 36, 595Draine, B.T., & Katz, N. 1986, ApJ, 310, 392Desert, F.-X., Boulanger, F., & Puget, J.-L. 1990, A&A, 237, 215, 236Falgarone, E., Verstraete, L., Pineau des Forˆets, G., & Hily-Blant, P.2005 A&A 433, 997Falgarone, E., Pineau des Forˆets, G., Hily-Blant, P. & Schilke, P. 2006A&A 452, 511Flower, D.R. & Pineau des Forˆets, G. 1998, MNRAS 297, 1182Gillmon, K., Shull, J.M., Tumlinson, J., & Danforth, C. 2006, ApJ636, 891Gredel, R., van Dishoeck, E. F. & Black, J. H. 1991, A&A,251, 625Gredel, R., van Dishoeck, E. F. & Black, J. H. 1993, A&A, 269, 477Gry, C., Boulanger, F., Falgarone, E., Pineau des Forˆets, G., &Lequeux, J. 1998, A&A, 331, 10700 Nehm´e et al.: Modeling of diffuse molecular gas