CO+ as a probe of the origin of CO in diffuse interstellar clouds
aa r X i v : . [ a s t r o - ph . GA ] M a r Astronomy & Astrophysicsmanuscript no. coplus-revised-final © ESO 2021March 2, 2021 CO + as a probe of the origin of CO in diffuse interstellar clouds M. Gerin and H. Liszt LERMA, Observatoire de Paris, PSL Research University, CNRS, Ecole Normale Supérieure, Sorbonne Université, F-75005 Paris,France. e-mail: [email protected] National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA.Received 2020
ABSTRACT
Context.
The chemistry of the di ff use interstellar medium is driven by the combined influences of cosmic rays, ultraviolet (UV)radiation and turbulence. Previously detected at the outer edges of photo-dissociation regions (PDRs) and formed from the reactionof C + and OH, CO + is the main chemical precursor of HCO + and CO in a thermal, cosmic-ray and UV-driven chemistry. Aims.
To test whether the thermal cosmic-ray and UV-driven chemistry is producing CO in di ff use interstellar molecular gas throughthe intermediate formation of CO + . Methods.
We searched for CO + absorption with the Atacama Large Millimeter Array (ALMA) towards two quasars with knownGalactic foreground absorption from di ff use interstellar gas, J1717-3342 and J1744-3116, targeting the two strongest hyperfine com-ponents of the J = Results.
We could not detect CO + but obtained sensitive upper limits toward both targets. The derived upper limits on the CO + columndensities represent about 4 % of the HCO + column densities. The corresponding upper limit on the CO + abundance relative to H is < . × − . Conclusions.
The non-detection of CO + confirms that HCO + is mainly produced in the reaction between oxygen and carbon hydridesCH + or CH + induced by supra-thermal processes while CO + and HOC + result from reactions of C + with OH and H O. The densitiesrequired to form CO molecules at low extinction are consistent with this scheme.
Key words.
ISM : cloud – ISM-molecules – Radio lines : ISM
1. Introduction
The di ff use interstellar medium (ISM) hosts a rich chem-istry where many species reach molecular abundances simi-lar to those in denser and darker regions despite the lowerdensities (a few tens to a few hundred particules per cm − )and the relatively unattenuated far ultraviolet (FUV) illumina-tion by the interstellar radiation field (Snow & McCall 2006;Gerin et al. 2016; Liszt et al. 2014a,b, 2018; Gerin et al. 2019).Di ff use and translucent interstellar clouds (Snow & McCall2006) have long been used as testbeds of interstellar chem-istry (Glassgold & Langer 1975, 1976; Black & Dalgarno 1977;Van Dishoeck & Black 1986; van Dishoeck & Black 1988).These e ff orts were successful in explaining the measured col-umn densities for H and small trace molecules such as CH, OHand CN using chemical reactions at temperatures 30 - 80K corre-sponding to kinetic temperatures measured in H (Savage et al.1977) although in some cases assuming regions of density > ∼ − along the line of sight. However the observed col-umn densities of CO and the common presence of high columndensities of CH + presented challenges to such models of ther-mal, cosmic-ray and UV-driven ion-chemistry in di ff use molec-ular gas.The observed CO column densities are empirically explainedby the serendipitous detection of unexpectedly high column den-sities of HCO + seen in absorption at 89.2 GHz (Lucas & Liszt1996). A nearly constant abundance of HCO + relative to H ,X(HCO + ) = N(HCO + ) / N(H ) = × − ± . are observed directly in op- tical / UV absorption (She ff er et al. 2008; Weselak et al. 2009,2010). With such significant column densities, the observedHCO + ions will recombine with ambient thermal electrons atdensities n(H) > ∼
100 cm − to produce the observed CO columndensities (Liszt & Lucas 2000; Visser et al. 2009).The 1970’s-1980’s era chemistry is qualitatively correct inpredicting a fixed abundance ratio N(HCO + ) / N(OH) via a dom-inant chemical chain that proceeds from C + + OH → CO + + H (Glassgold & Langer 1975, 1976; Dagdigian 2019) to CO + + H → HCO + + H and HCO + + e − → CO + H. However,the observed N(HCO + ) / N(OH) ≈ /
30 is roughly thirty timeshigher than the predicted value through this simple chemicalscheme. Some HCO + can also be produced in this chemistry bythe reaction of C + and H O whose abundance is 28% that ofOH (Gerin et al. 2016; Wiesemeyer et al. 2016). Both reactions , CO + + H and C + + H O produce equal amounts of HCO + andthe slightly less tightly-bonded isomer HOC + that is observedwith N(HOC + ) / N(HCO + ) = . ± .
003 (Gerin et al. 2019).This disparity in the abundances of HCO + and HOC + is muchtoo large to be explained by the isomerization reaction H + HOC + → H + HCO + as discussed below.To reproduce the observed HCO + abundance at the low meandensities of di ff use clouds, the most successful models includetransient production mechanisms that involve dynamical pro-cesses in magnetized gas such as low-velocity shocks or turbu-lent vortices, in which ions and neutral species are partially de-coupled (Godard et al. 2014; Lesa ff re et al. 2020). The resultingslow velocity drift can therefore be used as an additional energysource to drive endothermic chemical reactions that could notoperate otherwise (She ff er et al. 2008; Visser et al. 2009), espe- Article number, page 1 of 8 & Aproofs: manuscript no. coplus-revised-final cially the reaction C + + H → CH + + H that is endothermic by0.36 eV or about 4300 K. These models therefore include a spe-cific chemical pathway to CO, which starts from CH + , and isfollowed by a series of rapid hydrogen abstraction reactions pro-ducing CH + and CH + . These two ions react with atomic oxygento produce the required HCO + , and not HOC + . In this scheme,HCO + is once again the precursor of CO but the predicted COand HCO + abundances fit the observations well and the relativerarity of HOC + arises very naturally.Therefore the relative abundances of the three molecularions CO + , HCO + and HOC + provide key information on themechanisms at the origin of CO in di ff use gas. Despite the piv-otal role played by CO + in some versions of the chemistry, itsabundance relative to H is much less well constrained thanthose of HCO + and HOC + . CO + was first identified in the in-terstellar medium towards the bright photo dissociation region(PDR) M17SW and the young, high-excitation planetary neb-ula NGC 7027 (Latter et al. 1993). CO + is now routinely ob-served in dense PDRs such as the Orion Bar (Goicoechea et al.2017) or MonR2 (Treviño-Morales et al. 2016). In such regionsCO + is located at the very edge close to the HI / H transition,and its abundance relative to HCO + ranges from one to sev-eral tens of percent (Fuente et al. 2003). In dense PDRs the in-tense FUV radiation can pump H into vibrationally excited lev-els that can reach a significant population (Agúndez et al. 2010)The internal energy of this vibrationally excited H can triggerthe endothermic reaction of C + + H forming CH + as shownby the widespread distribution of CH + emission in such regions(Goicoechea et al. 2019). Paradoxically, the presence of CO + indense PDRs is a sign that non-thermal chemical processes areworking, while non-thermal processes are invoked in models ofdi ff use molecular gas to remove the need to produce CO + on thepath to CO.There are no reported detections of CO + in the di ff use andtranslucent interstellar medium: in this paper we present obser-vations with the Atacama Large Millimeter Array (ALMA) thatconstrain the abundance of CO + there for the first time. The ob-servation strategy is presented in section 2 and the results arediscussed in section 3 together with the implications for the COchemistry that are emphasized in sections 4 and 5. The conclu-sions are summarized in section 6.
2. Spectroscopy and observations
Absorption spectroscopy represents the best method to probethe molecular content of di ff use clouds because the molecu-lar excitation is weak at the low densities (few tens to fewhundred cm − ) and pressure (p / k ≈ × − K-cm − )of these regions (Jenkins & Tripp 2011a; Gerin et al. 2015;Goldsmith et al. 2018) and the level populations are concen-trated in the lowest rotational levels. As a Σ molecular ion,the energy levels of CO + are described by three quantum num-bers; N the rigid body angular momentum quantum number, S = / J = N + S = N ± /
2, the total angular momentumquantum number (Sastry et al. 1981).The CO + ground state rotational transitions at 117.7 GHzand 118.1 GHz are close to a strong atmospheric line frommolecular oxygen at 118.75 GHz, rendering their observationfrom the ground very di ffi cult. Hence observations of CO + havegenerally targeted excited transitions where the sky transmis-sion is much better. We chose to search for the N = → Table 1.
Spectroscopic parameters of observed lines
Transition a Frequency A N (CO + ) / R τ dv b N , J MHz s − cm − km − s2,3 / / . × − . × / / . × − . × / / . × − . × Transition a Frequency A N ( CO) / R τ dv c J MHz s − cm − km − s2 - 1 220398.684 6 . × − . × Transition a Frequency A N (C O) / R τ dv c J MHz s − cm − km − s2 - 1 219560.354 6 . × − . × Notes. ( a ) The spectroscopic data are extracted from the CDMSdatabase (Müller et al. 2001, 2005; Endres et al. 2016). ( b ) Foran excitation temperature of 2.73 K. ( c ) For an excitationtemperature of 5 K.transitions because the frequencies of this first excited transi-tion near 236 GHz are easily accessible from ground-based radioobservatories and the level population remains significant evenin di ff use interstellar gas. This N = → ffi cient and the conversion factor be-tween the integrated line opacity and the molecule column den-sity N (CO + ) / R τ dv assuming that the energy level populationis determined by the cosmic microwave background at 2.73 K.Apart from CO + , the setting of the ALMA correlator in-cluded spectral windows targeting the CO(2 − O(2 − CO(3 , − , ) transitions that were accessible with thesame receiver tuning while including a dedicated spectral win-dow for continuum phase calibration. Properties of the CO linesare given in Table 1 where the column density / optical depth con-version is calculated for an excitation temperature of 5 K that istypical for this more easily-excited species in di ff use moleculargas (Goldsmith et al. 2018). The targeted sources are J1717-3342 and J1744-3116, two brightquasars situated at small galactic latitude behind the Galac-tic bulge that were known to have high intervening columndensities of Galactic neutral gas detected in molecular absorp-tion (Gerin & Liszt 2017; Liszt & Gerin 2018; Riquelme et al.2018). Their positions, continuum flux densities S ν , channel-channel baseline rms line / continuum noise and line profile in-tegrals and velocity intervals used here as integration intervalsfor the targeted CO + transitions are given in Table 2. Compara-ble quantities for the CO(2-1) and C O(2-1) lines are given inTable 4.
The observations were performed with ALMA band 6 receiverstuned near 236 GHz during ALMA Cycle 7 under the projectcode 2019.1.00120.S. The CO + lines were observed with a chan-nel spacing of 244 kHz, corresponding to a velocity resolution of0.31 kms − . The channel spectral resolution is twice the channelspacing. As in our earlier observations toward these sources, the Article number, page 2 of 8. Gerin and H. Liszt : CO + as a probe of the origin of CO in di ff use interstellar clouds Fig. 1.
Absorption spectra observed towards J1717-3342 (left) and J1744-3116 (right). The spectra have been normalized by the continuum fluxdensity. The CO + spectra have been shifted vertically and multiplied by 10. HCO + is shown in black, CO + in red and CO(2-1) in blue forcomparison. The HCO + data are taken from Liszt & Gerin (2018) and Gerin & Liszt (2017). -40 -20 0 20 401.00.50.0-0.5 li n e / c on t i nuu m - , T [ K e l v i n ] HCO+J1717 13CO 12CO HI/80-40 -20 0 20 4010 VLSR (KM S-1) li n e / c on t i nuu m - , T [ K e l v i n ] HI/100HCO+J1744 12CO/313CO C18O x 3
Fig. 2.
Comparison of the HCO + (1-0) (black) and CO (2-1) (green)absorption with the CO (blue) and scaled HI (grey) emission. J1717-3342 is shown in the top and J1744-3116 in the bottom. C O(2-1) isalso shown in orange for J1744-3116. bandpass calibrator was fixed to J1924-2914. Absorption spectrawere extracted from the standard pipeline-processed data prod-ucts at the peak of the continuum map in each spectral window.The ALMA spectra of CO, CO + and HCO + are displayed inFig. 1. The H CO (3 , − , ) line was detected in both direc-tions and will be discussed elsewhere. Also shown in Figures 1 and 2 are 89.2 GHz ALMA HCO + J = − channel spac-ing and 0.41 km s − spectral resolution from our earlier work(Gerin & Liszt 2017; Liszt & Gerin 2018). Profile integrals arequoted in Table 3, assuming excitation in equilibrium with theCMB and using N(HCO + ) = . × cm − R τ dv as before.Also shown in Fig. 2 are the nearest λ = ′ . λ ◦ ). The CO emission profile forJ1744-3116 at l,b = ◦ ,-1 ◦ is very nearly along the samesightline; for J1717-3342, the CO profile at 352.75 ◦ ,2.5 ◦ is cen-tered 6 ′ .
3. Results and discussion
Absorption spectra of HCO + , CO and CO + toward bothsources are shown in Fig. 1, and Fig. 2 presents a comparison ofthe absorption spectra of CO and HCO + with emission spectraof HI and CO(1-0) described in section 2.4. Column densitiesof HCO + , CO, C O and H (N(H ) = N(HCO + ) / × − ) aregiven in Tables 3 and 4. To compute N( CO) and N(C O) weassume an excitation temperature of 5 K (Table 1) that is con-sistent with the observed brightness of the CO emission that isseen toward or near these sources, 1 − . ff use nature of the gas along these lines ofsight has previously been discussed by Gerin & Liszt (2017),Liszt & Gerin (2018) and Riquelme et al. (2018). High gas col-umn densities accumulate over long paths through the Galacticdisk at low galactic latitude even without encountering denseclouds. This is indicated in our new data by the large ratioof CO and C O integrated optical depths or column densi-ties, N( CO) / N(C O) = ± O / O ∼
520 and C / C ∼
65 (Wilson & Rood 1994;Milam et al. 2005; Keene et al. 1998; Giannetti et al. 2014), afully molecular gas would have N( CO) / N(C O) = O and,
Article number, page 3 of 8 & Aproofs: manuscript no. coplus-revised-final
Table 2.
Summary of CO + observations Source l b
LSR Velocity a Line Flux density S ν σ l / c R τ dv bo o km s − Jy km s − J1717-3342 352.7333 2.3911 -14..10 CO + J = / / < + J = / / < + J = / / < + J = / / < a Velocity interval used to integrate the line profile. b Upper limits are 3 σ .more likely, fractionation of CO through endothermic carbonisotope exchange when the majority of the free gas phase carbonis in C + (Liszt 2017). Our value for N( CO) toward J1744-3116in Table 4 agrees with that given by Riquelme et al. (2018) basedon J = CO) = . × cm − .In our earlier work we also derived carbon isotope ratiosH CO + / H CO + = ± ± ff erentfrom what is observed inside the Galactic bulge. Thus althoughthe sight-lines employed here cross the Galactic bulge, the lowvelocity gas that is analyzed in CO and CO + resides relativenearby in the disk and will be discussed under the assumptionthat local conditions are applicable.Overall the CO(1-0) emission is spread over the same veloc-ity range as the HCO + absorption. Towards J1744-3116, there isa fair correspondence of the main CO emission peaks with theHCO + absorption features but the HCO + absorption profiles aremore complex. The positive velocity component towards J1744-3116 is detected in CO(2-1) and C O(2-1) absorption and isassociated with a self-absorption feature in the H I spectrumthat was discussed in Liszt & Gerin (2018). The presence of thethree CO isotopologues indicates that this velocity componenthas probably the largest extinction and mean density and couldbe associated with translucent rather than di ff use gas. There isno self-absorption in the HI profile coincident with the negativevelocity component, but the main CO(2-1) absorption is asso-ciated with a faint C O(2-1) feature.The CO(1-0) emission di ff ers more from the HCO + absorp-tion towards J1717-3342 where the direction of the emissionspectrum is 6.6 ′ away. Of the 8 main HCO + absorption features,only one is detected in CO(2-1) and none in C O(2-1) show-ing that the gas is more di ff use along this line of sight. The COemission is weaker than towards J1744-3116, barely reaching1 K. As discussed by Liszt et al. (2010), in di ff use gas the CO(1-0) emission is highly variable as it traces the regions where COreaches column densities above N(CO) = cm − that are highenough to produce detectable emission. This transition occursover a small range of H column densities and depends on thelocal physical conditions but CO emission at the level of 1 K-km s − integrated intensity is not observed in regions where themolecular fraction of H-nuclei in H is much below 0.6.The comparison of the emission and absorption profilestherefore demonstrates that the two observed lines of sight en-counter matter with variable physical conditions, ranging fromdi ff use to translucent gas. The upper limits for the CO + inte-grated opacities shown in Table 2 provide constraints on theCO + column densities and abundances for the whole range ofphysical conditions. For the di ff use molecular gas sampled inabsorption the molecule excitation is dominated by the cosmicmicrowave background because of the low gas densities. There-fore, the CO + column densities have been derived assuming an excitation temperature of 2.73 K. They are reported in Table 3together with the HCO + column densities in the same veloc-ity intervals. The achieved upper limit on CO + column densi-ties leads to a very low value for the N(CO + ) / N(HCO + ) ratio,of about 0.04. The corresponding upper limit on the CO + abun-dance relative to H is X(CO + ) < . × − , using the stan-dard value for the HCO + abundance relative to H in the di ff usemolecular gas, 3 × − (Lucas & Liszt 1996; Gerin et al. 2019).These values are a factor a few times higher than those estab-lished for HOC + , N(HOC + ) / N(HCO + ) = .
015 and X(HOC + ) = . × − (Gerin et al. 2019). + as a source ofHCO + Despite the excellent sensitivity with achieved fractional rmsflux density levels ∆ S ν / S ν of 0.22% and 0.83% for J1717-3342and J1744-3116 respectively, CO + was not detected towardsthese sources. The derived 3 σ upper limits N(CO + ) / N(HCO + ) < ∼ .
04 and N(CO + ) / N(H ) < . − . × − are similar for bothsources in Table 2 because J1717-3342 with smaller interveningcolumn density is much brighter in the continuum. The achievedupper limit on the relative abundance is somewhat above the val-ues seen in dense PDRs where emission lines from CO + are de-tected and X(CO + ) reaches a few times 10 − . They are belowthe relative abundances seen in the exceptional case of the youngplanetary nebula NGC 7027 where N(CO + ) / N(H ) = × − (Fuente et al. 2003).It is straightforward to show that the relative abundanceof CO + is too small to provide a major source of the ob-served HCO + in di ff use molecular gas, even independent of theHCO + abundance. In chemical terms, the reaction CO + + H → HCO + + H forming HCO + can be compared with the rate atwhich HCO + recombines with electrons with rates as given inTable 5.Equating formation and recombination of HCO + , neglect-ing photodissociation that is four orders of magnitude sloweraccording to the Kinetic Database for Astrochemistry (KIDA)(Wakelam et al. 2015) k n (CO + ) n (H ) = α ( T ) n (HCO + ) n ( e )and rearranging, we have n (CO + ) / n (HCO + ) = ( α ( T ) / k ) n ( e ) / n (H )or equivalently n (CO + ) / n (HCO + ) = (2 / f H ) ( α ( T ) / k ) x ( e )where f H is the fraction of H-nuclei in H , x ( e ) is the elec-tron fraction, n (H ) is the density of H molecules, and n (H)is the total density of H-nuclei. Taking x ( e ) = × − cor-responding to the observed free gas-phase carbon abundance Article number, page 4 of 8. Gerin and H. Liszt : CO + as a probe of the origin of CO in di ff use interstellar clouds Table 3.
HCO + and CO + column densities Source N(HCO + ) N(CO + ) N(CO + ) / N(HCO + ) N(CO + ) / N(H ) a cm − cm − J1717-3342 7 . ± . < . < < . × − J1744-3416 23 . ± . < . < < . × − a N(H ) = N(HCO + ) / × − . n (C + ) / n (H) = . × − (Sofia et al. 2004) with a small addedcontribution from cosmic ray ionization of atomic hydrogen inlargely molecular gas, the required amount of CO + needed torestore the HCO + lost to recombination is n (CO + ) / n (HCO + ) = (0 . / f H ) × (40 / T ) . This is some 25 times higher than our upper limit if f H = =
40 K. We noted above that CO emission even at thelow levels shown in Fig. 2 does not arise in regions of very smallmolecular fraction and temperatures high enough to trigger theformation of CH + , such regions are only characteristic of regionsof strong turbulent energy dissipation.Alternatively, equating the HCO + formation and recombina-tion rates once again but setting n (HCO + ) / n (H ) = × − and x ( e ) = × − = × − (2 n (H ) / f H ), one derives for the re-quired relative abundance of CO + X (CO + ) = (1 . × − / f H ) × (40 / T ) . . This is comparable to the CO + relative abundance seen inNGC 7027 ( ∼ × − , Fuente et al. (2003)) and is at least 15times above the upper limit achieved here, 1 . × − , if T =
40K (Table 2). In this simplified analysis, reducing X(CO + ) belowour upper limit would require temperatures of about 2000 K thatare more nearly characteristic of the turbulence-driven chem-istry, which can only be present in small and intermittent regionsof space and time, where other thermal and non-chemical pro-cesses are operating. CO + is responsible for producing at most afew percent of the HCO + that recombines with ambient thermalelectrons to form CO in di ff use molecular gas.
4. The thermal chemistry of CO + , HOC + and HCO + Our upper limits show that CO + cannot be responsible forforming the observed CO in di ff use molecular gas becauseCO + does not exist in su ffi cient quantity to replenish HCO + as it recombines with ambient electrons. However, beyondthat, our limits combined with the observed relative abundanceN(HOC + ) / N(HCO + ) = . ± . × − (Gerin et al. 2019) canbe used to gain further insights into the thermal chemistry thatis working in di ff use molecular gas. Most of the reactions thatform HCO + also form HOC + , yet their observed abundancesdi ff er by a factor 70. To explore this, we extended the thermalCO + and HOC + chemistry discussed by Gerin et al. (2019) toinclude some hypotheticals corresponding to uncertainties in re-action rates in the KIDA reaction rate database (Wakelam et al.2015) and molecular abundances (Gerin et al. 2016). As dis-cussed in Gerin et al. (2019), some of the rates of the reac-tions controlling the formation of CO + and HCO + were not wellknown, especially the reaction C + + OH → CO + + H / CO + H + and the isomerization reaction destroying HOC + and formingHCO + , HOC + + H → HCO + + H , whose rate is reported as4 × − cm s − at 25 K and 300 K (Smith et al. 2002), about1 / + can be formed by the reaction of C + with OH, andalso by the reaction of O with CH + . CO + is destroyed by recom-bination with electrons and in chemical reactions with atomicand molecular hydrogen, and photo-dissociated with a free spacerate 1 × − s − that is always at least 300 times slower than theother destruction rates in the calculations discussed here. TheOH relative abundance to H , X(OH) = . ± . × − variesonly narrowly and is well-determined in local di ff use clouds(Weselak et al. 2009, 2010) such as those probed in this work.The excellent correspondence of the OH and H O absorptionline profiles and of the H O and HCO + profiles along longsight-lines across the Galactic plane (Wiesemeyer et al. 2016;Gerin et al. 2019) further indicates that this value of the OHabundance holds for the Galactic disk as well. The rate of thereaction of OH and C + was recently calculated by Dagdigian(2019), providing accurate information on the rate coe ffi cientand branching ratio over a temperature range 10 – 1000 K.We approximate the rate constant for C + + OH forming CO + as k = . × − (300 / T) . cm s − (see Table 5 ). By contrast theabundance of CH + is locally variable and CH + may not co-existwith the other species if it is predominantly formed in the non-thermal chemistry (Godard et al. 2014; Valdivia et al. 2017). Wetake X(CH + ) as a free parameter with X(CH + ) = − by defaultin the following discussion.HOC + can be formed in the reaction of H with CO + andin the reaction of C + with H O whose fixed relative abundanceX(H O) = . × − we take from Gerin et al. (2016). We ig-nore HOC + formation by the reaction of O with CH + becausethe formation of CH + is an aspect of the non-thermal chem-istry. HOC + recombines with electrons and is susceptible to pho-todissociation, but most importantly is isomerized to HCO + inreaction with H . The rate constant for the isomerization reac-tion of H and HOC + has alternatives in the KIDA databaseas discussed previously. Here we consider the two extreme val-ues for the rate constant, 10 − cm s − given for 10-280 K and4 . × − cm s − given at 305 K.The CO + and HOC + chemistry is simple when other molecu-lar abundances are held fixed but it involves the thermal and ion-ization balance for the temperature-sensitive recombination ratesand the atomic / molecular hydrogen balance for various reactionswith CO + and HOC + . To treat this we performed calculationslike those done earlier to account for the observations of HF andCF + (Liszt et al. 2015). In brief we calculated the self-consistentglobal atomic / molecular, ionization and thermal equilibrium ingas spheres of constant total hydrogen number and column den-sity, subject to the usual interstellar radiation fields. The hydro-gen column density was varied and molecular abundances wereintegrated along the central line of sight to form the results thatare displayed here. Plotting the results against N(H ) removessome model sensitivities, for instance to the impact parameterabout the cloud center used for the line of sight integration.The results are shown in Fig. 3. At left is a baseline modelusing default values (Table 5). The model produces CO + rela-tive abundances about 2.5 times smaller than our observed upper Article number, page 5 of 8 & Aproofs: manuscript no. coplus-revised-final N () / N ( HC O + ) mean observed HOC+upper limit CO+ CO+HOC+ s l o w H O C + - > H C O + i n t e r c o n v e r s i o n slow HOC+->HCO+interconversion i g n o r i n g H + C O + - > H O C + + H i gno r i ng H + C O + - > H O C + + H CO+HOC+CO+HOC+ i g n o r i n g C + + H O - > H O C + + H i gno r i ng C ++ H O - > H O C ++ H X(CH+)=X(OH)X(CH+)=X(OH)
CO+HOC+
Fig. 3.
Models of the thermal chemistry for the relative abundances N(CO + ) / N(HCO + ) and N(HOC + ) / N(HCO + ) with default rates at left anddeviations in the middle and right panels. In all panels results for HOC + are shown in green and for CO + in orange. In all cases N(HCO + ) is takento be the observed value N(HCO + ) = × − N(H ). Left panel: Baseline models with the observed upper limit for N(CO + ) / N(HCO + ) from thiswork and the mean N(HOC + ) / N(HCO + ) ratio from Gerin et al. (2019) illustrated schematically as horizontal dashed lines. Middle panel: The solidlines represent the case that the rate constant of H + HOC + → HOC + + H interconversion is taken as 10 − cm s − . The dashed-dotted linesrepresent model results when the rate constant for the reaction H + CO + → HOC + + H is set to 0. Right panel: The solid lines show models inwhich the reaction of C + and H O does not form HOC + and the dashed-dotted lines show model results when CH + is as abundant as OH, X(CH + ) = − . limits, and about twice as much HOC + as observed. Declinesin the abundances of CO + and HOC + for very high N(H ) arisefrom the recombination of the free gas-phase carbon from C + toneutral carbon and CO.In the middle panel the solid lines show results when H -catalyzed HOC + → HCO + isomerization has the rate constant10 − cm s − , a factor 2.5 above the default value. The greencurve for HOC + shows that the predicted abundance of HOC + grows even further above what is observed when the HOC + → HCO + interconversion is slow. The orange curves show whathappens when the rate constant for HOC + formation via H + CO + → HOC + + H is set to 0. The predicted amount of CO + grows well above our upper limits and the abundance of HOC + falls far below the observed mean. We conclude that HOC + isforming mostly via C + + OH followed by CO + + H but muchor most of the HOC + so produced is lost to isomerization intoHCO + .In the right side panel of Fig. 3 the solid curves show modelresults when the reaction of C + and H O does not form HOC + :all of the observed HOC + can indeed be made by the reactionof C + and OH, and agreement with the observed HOC + / HCO + ratio is somewhat better when the contribution from H O is ne-glected. However, H O is observed to be present with X(H O) = . × − (Gerin et al. 2016) and would be expected to formsome amount of HOC + . The default model may be predicting anoverabundance of CO + or perhaps some aspect of the reaction ofC + and H O is not fully understood: a slower rate or a branchingratio that favors HCO + would lead to a lower contribution of thisreaction to the HOC + formation.CH + may not co-exist with the other species if it is predomi-nantly formed in the non-thermal chemistry (Godard et al. 2014;Valdivia et al. 2017) and X(CH + ) is negligible (10 − ) in the de-fault model. The final deviation from the default model is rep-resented by the dash-dot lines in the righthand panel showingresults when X(CH + ) = X(OH) = − is large. The reactionof O + CH + becomes an important source of CO + in the ther-mal chemistry when X(CH + ) > ∼ × − and our upper limitson CO + by themselves imply X(CH + ) / X(OH) < ∼
3. At such highCH + abundances the discrepancy in HOC + grows even larger. Fig. 4.
Number density n (H) / G vs reddening E(B-V) (Green et al.2019) derived by equating CO formation and photo-destruction forsight-lines with HCO + and CO column densities measured in absorp-tion (Liszt & Lucas 1998; Liszt et al. 2019), as discussed in Section 5.
5. Conditions for the growth of CO
Balancing the formation of CO through dissociative recombi-nation of HCO + and destruction of CO by photodissociationcan constrain the physical conditions where CO might form indi ff use molecular gas. With a free-space photodissociation rate k d = . × − s − for the Draine radiation field (defined as G =
1) and an attenuation scaling as e − γ A V this balance locallyimplies n (CO) n (HCO + ) = α ( T ) x ( e ) n (H) G k d e − γ A V For a uniform slab, integrating the attenuation term from 0up to half the slab extinction, N (CO) N (HCO + ) = α ( T ) x ( e ) n (H) G k d . γ A V − e − . γ A V n (H) / G can therefore be expressed as Article number, page 6 of 8. Gerin and H. Liszt : CO + as a probe of the origin of CO in di ff use interstellar clouds Table 4.
CO isotopologues J = Source line Flux σ l / c R τ dv N a Jy km s − cm − J1717-3342 CO 0.818 0.0024 0.260(0.004) 6.3(0.4)C O 0.822 0.0123 < < . CO 0.244 0.0073 2.975(0.023) 72.0(0.6)C O 0.244 0.0084 0.102(0.018) 2.5(0.4) a Upper limit is 3 σ . Table 5.
Rates and rate coe ffi cients Reaction Symbol Rate Coe ffi cient Referencecm − s − C + + OH → CO + + H k . × − (300 / T) . Dagdigian (2019)CO + + H → HCO + + H k . × − KIDAC + + H O → HCO + + H k . × − KIDAC + + H O → HOC + + H k . × − KIDA, Martinez et al. (2008)HOC + + H → HCO + + H k × − Smith et al. (2002)HOC + + H → HCO + + H k × − KIDAHCO + + e − → CO + H α ( T ) 1 . × − / T . Hamberg et al. (2014)Reaction Symbol Rate References − CO + h ν → C + O k d . × − exp( − . A V ) KIDA, Heays et al. (2017)CO + + h ν → C + + O 1 . × − KIDA n (H) / G = N (CO) N (HCO + ) k d (1 − e − . γ A V ) α ( T ) x ( e )0 . γ A V where we approximate A V = . γ = .
88 and use the reaction rates and rate coe ffi -cients given in Table 5. Fig. 4 presents the variation of n (H) / G as a function of the reddening E(B-V) for the existing sampleof QSO sight lines with HCO + and CO column densities deter-mined in absorption (Liszt & Lucas 1998; Liszt et al. 2019). Weuse conditions as described in Section 2, a uniform temperatureof 40K and a uniform electron fraction x ( e ) = × − .The mean value for the sample is < n (H) / G > ∼
300 cm − .For a standard interstellar radiation field of G =
1, the calcu-lated densities n(H) ∼ −
300 cm − are modest for E(B-V) > ∼ . . The higher densities n (H) ∼ − − calculated at E(B-V) < ∼ ∼ + emission inthese directions (Liszt 2020). Thermal pressures p / k ∼
40 K × − are an order of magnitude higher than typical valuesin the di ff use molecular gas (Jenkins & Tripp 2011b) and wouldmore likely represent the conditions under which a turbulence-driven chemistry forms HCO + . A lower value of the radiationfield toward these sight-lines would bring the derived densitiescloser to the mean values. The data shown in this plot includethe sight lines with CO and HCO + detections, which may biasthe derived n (H / G to somewhat high values as a higher densityimplies a faster CO production rate.The inverse variation of n (H) / G with E(B-V) in Fig. 4, mir-roring the functional dependence on Av, reflects the fact thatthe observed values of N(CO) / N(HCO + ) are not correlated withE(B-V) and show a moderate scatter of at most a factor of 1.A majority of the selected sight-lines have N(CO) / N(HCO + ) between 1000 and 2000. We also plotted n (H) / G againstthe molecular fraction f H = ) / N(H) taking N(H ) = N(HCO + ) / × − and N(H) = a × E(B-V). Requiring f H ≤ a > ∼ × H − nuclei cm − mag − but thereis no trend for n (H) / G H calculated in this way.
6. Summary and conclusions
We sought to test the origin of CO in di ff use molecular gaswithin the generally accepted framework that CO is predomi-nantly formed through the dissociative electron recombinationof HCO + . HCO + is widely observed in di ff use molecular gas,with a relative abundance N(HCO + ) / N(H ) = × − .In a quiescent, thermal, cosmic-ray and UV-driven chem-istry, HCO + is predominantly formed in the reactions C + + OH → CO + + H and CO + + H → HCO + + H. Using Cycle 7 ALMABand 6 observations at 236 GHz (Table 1) we searched for CO + absorption toward two bright compact extragalactic mm-wavecontinuum sources seen at low latitude in the inner Galaxy andknown to be occulted by high column densities of HCO + -bearingdi ff use molecular gas (see Section 2 and Table 2). We failed todetect CO + at levels su ffi cient to demonstrate in Section 3 thatthe reaction CO + + H → HCO + + H cannot replenish morethan a few percent of the observed HCO + that recombines. Thenon-detection of CO + confirms that HCO + is mainly produced inthe reaction between oxygen and carbon hydrides CH + or CH + induced by supra-thermal processes while CO + and HOC + re-sult from reactions between C + and OH and H O in the thermalchemistry that occurs in quiescent di ff use molecular gas. The ob-served CO + and HOC + abundances relative to H set an upperlimit on the rate coe ffi cient of these reactions.In Section 4 we explored the coupled thermal chemistries ofCO + and HOC + given our observational upper limits on CO + andexisting observations of HOC + showing N(HOC + ) / N(HCO + ) = . ± . + by a factor two, but Article number, page 7 of 8 & Aproofs: manuscript no. coplus-revised-final by as much as a factor six if the isomerization reaction HOC + + H → HCO + + H does proceed rapidly. The option of a lowrate for this reaction in the KIDA database should probably beignored. The predicted HOC + abundance is in better agreementwith observation if the reaction of C + and H O preferentiallyforms HCO + , rather than HOC + . We placed a weak limit on therelative abundance of CH + in quiescent gas, N(CH + ) / N(OH) < ∼ + ) / X(H ) < ∼ × − such that the reaction O + CH + does not become an important source of CO + , substantially over-producing it.In Section 5 we derived characteristic number densities n (H)at which CO would form in di ff use molecular gas with observedabundances. For E(B-V) > ∼ n (H) ∼ −
300 cm − but for CO-bright regions of low ex-tinction E(B-V) ∼ . − . n (H) ∼ − × cm − and such heavily over-pressuredgas is more properly considered in the context of a turbulent dis-sipation chemistry. The presence of CO in sight-lines of low red-dening could also indicate a lower radiation field intensity. Acknowledgements.
The authors thanks the referee Helmut Wiesemeyer for histhoughtful comments and suggestions. This paper makes use of the follow-ing ALMA data: ADS / JAO.ALMA / NRAO and NAOJ. The National Radio Astronomy Ob-servatory is a facility of the National Science Foundation operated under coop-erative agreement by Associated Universities, Inc. This work was supported bythe Programme National ”Physique et Chimie du Milieu Interstellaire” (PCMI)of CNRS / INSU with INC / INP co-funded by CEA and CNES.
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