Herschel Survey of Galactic OH+, H2O+, and H3O+: Probing the Molecular Hydrogen Fraction and Cosmic-Ray Ionization Rate
Nick Indriolo, D. A. Neufeld, M. Gerin, P. Schilke, A. O. Benz, B. Winkel, K. M. Menten, E. T. Chambers, John H. Black, S. Bruderer, E. Falgarone, B. Godard, J. R. Goicoechea, H. Gupta, D. C. Lis, V. Ossenkopf, C. M. Persson, P. Sonnentrucker, F. F. S. van der Tak, E. F. van Dishoeck, Mark G. Wolfire, F. Wyrowski
aa r X i v : . [ a s t r o - ph . GA ] D ec Herschel
Survey of Galactic OH + , H O + , and H O + : Probing theMolecular Hydrogen Fraction and Cosmic-Ray Ionization Rate. Nick Indriolo , , D. A. Neufeld , M. Gerin , P. Schilke , A. O. Benz , B. Winkel ,K. M. Menten , E. T. Chambers , John H. Black , S. Bruderer , E. Falgarone ,B. Godard , J. R. Goicoechea , H. Gupta , D. C. Lis , , V. Ossenkopf , C. M. Persson ,P. Sonnentrucker , F. F. S. van der Tak , , E. F. van Dishoeck , , Mark G. Wolfire ,F. Wyrowski , ABSTRACT
In diffuse interstellar clouds the chemistry that leads to the formation of theoxygen bearing ions OH + , H O + , and H O + begins with the ionization of atomichydrogen by cosmic rays, and continues through subsequent hydrogen abstractionreactions involving H . Given these reaction pathways, the observed abundances Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA Current address: Department of Astronomy, University of Michigan, Ann Arbor, MI 48109, USA LERMA, CNRS UMR 8112, Observatoire de Paris & Ecole Normale Sup´erieure, Paris, France I. Physikalisches Institut der Universit¨at zu K¨oln, Z¨ulpicher Str. 77, 50937 K¨oln, Germany Institute of Astronomy, ETH Z¨urich, Switzerland MPI f¨ur Radioastronomie, Bonn, Germany Department of Earth and Space Sciences, Chalmers University of Technology, Onsala Space Observatory,SE-43992 Onsala, Sweden Max Planck Institut f¨ur Extraterrestrische Physik, Garching, Germany Instituto de Ciencias de Materiales de Madrid (CSIC), E-28049 Cantoblanco, Madrid, Spain California Institute of Technology, Pasadena, CA 91125, USA Sorbonne Universit´es, Universit´e Pierre et Marie Curie, Paris 6, CNRS, Observatoire de Paris, UMR8112, LERMA, Paris, France Space Telescope Science Institute, Baltimore, MD 21218 SRON Netherlands Institute for Space Research, Landleven 12, 9747 AD Groningen, The Netherlands Kapteyn Astronomical Institute, University of Groningen, The Netherlands Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands Department of Astronomy, University of Maryland, College Park, MD 20742 ζ H ) and molecular hydrogen fraction ( f H ). We presentobservations targeting transitions of OH + , H O + , and H O + made with the Her-schel Space Observatory along 20 Galactic sight lines toward bright submillimetercontinuum sources. Both OH + and H O + are detected in absorption in multiplevelocity components along every sight line, but H O + is only detected along 7sight lines. From the molecular abundances we compute f H in multiple distinctcomponents along each line of sight, and find a Gaussian distribution with meanand standard deviation 0 . ± . + and H O + primarily reside in gas with low H fractions. We also infer ζ H through-out our sample, and find a log-normal distribution with mean log( ζ H ) = − . ζ H = 1 . × − s − ), and standard deviation 0.29 for gas within the Galacticdisk, but outside of the Galactic center. This is in good agreement with themean and distribution of cosmic-ray ionization rates previously inferred from H +3 observations. Ionization rates in the Galactic center tend to be 10–100 timeslarger than found in the Galactic disk, also in accord with prior studies.
1. INTRODUCTION
Astrochemistry is a flourishing field, with over 180 molecules (300 when accountingfor isotopologues) detected in interstellar and circumstellar environments (Lovas & Snyder2014). Several of the more recent detections, including those of OH + (Wyrowski et al. 2010a)and H O + (Ossenkopf et al. 2010), were made possible as new technology has pushed bothground and space-based observatories into the THz frequency range. Of particular impor-tance was the Herschel Space Observatory (Pilbratt et al. 2010), which offered a view of theTHz regime unimpeded by atmospheric absorption. As the inventory of interstellar moleculesand complexity of chemical reaction networks grow, it remains imperative that we are ableto select the most important reactions governing the abundance of a particular species, andunderstand how observations of closely related species can be utilized to infer properties ofthe interstellar medium (ISM).A basic understanding of how the chemistry involving different species proceeds in theISM can be garnered from knowledge of a few key atomic and molecular properties, one ofwhich is the first ionization potential (FIP). Neutral-neutral reactions proceed slowly at the Herschel is an ESA space observatory with science instruments provided by European-led PrincipalInvestigator consortia and with important participation from NASA + and H +3 —both of which are primarily formedvia cosmic-ray ionization of H and H , respectively—and so the chemistry surrounding thesespecies can be considered cosmic-ray driven. Oxygen falls into this latter category (FIP =13 .
62 eV), so the abundances of various oxygen-bearing molecules are closely linked to thecosmic-ray ionization rate.Another controlling parameter is the bond-dissociation energy, D . If D > .
48 eV(dissociation energy of H ) for a species XH + , then the reaction X + + H → XH + + H isexothermic. This is especially important for interstellar chemistry at low temperatures,where there is little kinetic energy to aid in reactions. Dissociation energies of OH + , H O + ,and H O + are all greater than 4.48 eV, and O + , OH + , and H O + all react exothermically withH . As H is the most abundant molecule in the universe, the abundances of these molecularions—specifically with respect to each other—are highly dependent on the amount of H available for reactions.The properties of O and oxygen-bearing ions described above explain the particularutility of OH + , H O + , and H O + in constraining conditions in the ISM. The formation ofeach larger molecule requires one more hydrogen abstraction reaction with H , a processthat competes primarily with dissociative recombination with electrons in destroying theseions. This makes the ratios n (H O + ) /n (H O + ) and n (OH + ) /n (H O + ) sensitive to the ratio n ( e ) /n (H ). If the fractional abundance of electrons with respect to total hydrogen ( x e ≡ n ( e ) /n H , where n H ≡ n (H) + 2 n (H )) is known, then these ratios can also be used to inferthe molecular hydrogen fraction, f H ≡ n (H ) /n H . Initial results from observations ofOH + and H O + along the sight lines toward W49N and W31C showed f H . .
1, implyingthat both species reside in gas that is primarily atomic (Gerin et al. 2010b; Neufeld et al.2010). This conclusion is supported by the distribution of OH + and H O + absorption invelocity space, which more closely matches that of atomic H than that of H O and HF(both tracers of molecular gas). Similar results are found from observations of electronictransitions of OH + in the ultraviolet, as it is better correlated with CH + than with speciestracing denser molecular gas such as CH, CN, and OH (Kre lowski et al. 2010; Porras et al.2014). In many sight lines, absorption of OH + and H O + arises at or near the systemicvelocity of the background source as well, and is thought to trace the irradiated outflows 4 –near massive protostars. Even for these objects though, the OH + /H O + and H O/H O + ratios are interpreted as indicating relatively low-density, mostly atomic gas (Benz et al.2010; Bruderer et al. 2010; Wyrowski et al. 2010b). Only rarely have OH + and H O + columndensities required high molecular fractions (e.g., Orion KL; Gupta et al. 2010).As the formation of OH + in diffuse gas begins with the ionization of H by cosmic rays,its abundance is useful in constraining the cosmic-ray ionization rate of atomic hydrogen, ζ H . While other molecules are also used for this purpose, OH + is unique in its ability toprobe ζ H in gas with 0 . . f H . .
1. Estimates of the cosmic-ray ionization rate in diffuseclouds based on molecular abundances have been made for roughly 40 years now, with theearliest utilizing observations of OH and HD in diffuse clouds (O’Donnell & Watson 1974;Black & Dalgarno 1977; Black et al. 1978; Hartquist et al. 1978). Those studies typicallyfound ionization rates on the order of a few times 10 − s − , as did later studies usingthe same molecules (Federman et al. 1996), although van Dishoeck & Black (1986) requiredionization rates of a few times 10 − s − to reproduce observed column densities with a moredetailed model. Findings were generally in good agreement with estimates of ζ H based on thelocal interstellar proton spectrum measured by Voyager (Webber 1998). As a result, it wasthought that the cosmic-ray ionization rate was relatively uniform throughout the Galaxy,and a canonical value of ζ H = 3 × − s − was frequently adopted.The detection of H +3 in the ISM (Geballe & Oka 1996) introduced a new, less compli-cated tracer of the ionization rate, and subsequent surveys of H +3 pointed to an ionizationrate in diffuse clouds nearly ten times larger than that found previously: ζ H ≈ × − s − (McCall et al. 2003; Indriolo et al. 2007; Indriolo & McCall 2012). In addition, the distri-bution of ionization rates inferred from H +3 was found to vary by over 1 order of magnitude,suggesting that the low-energy cosmic-ray flux is not uniform throughout the Galaxy. Itnow seems likely that most early estimates of ζ H were too low because they assumed thatnearly every instance of hydrogen being ionized by a cosmic ray led to the formation ofOH or HD. However, destruction of H + by polycyclic aromatic hydrocarbons (PAHs) andsmall grains is highly competitive with the charge transfer reactions driving the oxygen anddeuterium chemistries (Wolfire et al. 2003), making the chemical pathways from H + to OHand HD “leaky.” This mechanism was recognized by Liszt (2003) as a way to reconcile thedifferences in ionization rates inferred from OH and HD with those inferred from H +3 . Neu-tralization of H + on grains is also important in the chemistry leading to OH + and H O + ,and its effects are now accounted for when using these species to infer the ionization rate(Neufeld et al. 2010; Hollenbach et al. 2012; Indriolo et al. 2012).While infrared and radio observations of interstellar molecules—carefully interpreted inthe context of astrochemical models—can be used to determine the density of low-energy 5 –cosmic rays ( E .
10 MeV), gamma-ray observations provide a complementary probe ofhigh-energy cosmic rays ( E &
300 MeV). The latter interact with atomic nuclei in theinterstellar gas, producing neutral pions ( π ) that rapidly decay into pairs of gamma-rayphotons (Beringer et al. 2012). Observations of these gamma-rays can be used to estimatethe density of high-energy cosmic rays as a function of location within the Galaxy. Ourunderstanding of the gamma-ray sky has greatly improved following the launch of the FermiGamma-ray Space Telescope , with recent observations of the outer Galaxy suggesting thatthe cosmic-ray density is relatively uniform outside the solar circle, and declines less rapidlywith Galactocentric radius ( R gal ) than predicted by propagation models (Ackermann et al.2011). An interesting question is whether the density of low-energy particles shows thesame behavior, or whether the significantly smaller amount of material through which suchparticles can travel before losing all of their energy leads to a different result.Observations of H +3 have primarily been limited to the local ISM (within about 2 kpc ofthe Sun; McCall et al. 2002; Indriolo & McCall 2012) due to the necessity for high spectralresolution and high continuum level signal-to-noise ratio (S/N). The most notable exceptionshave been ongoing surveys of the Galactic center region which reveal a large amount ofwarm, diffuse gas that experiences a large flux of cosmic rays, with ionization rates above10 − s − (Oka et al. 2005; Goto et al. 2008, 2011; Geballe & Oka 2010). Even the dense gasin the Galactic center experiences a cosmic-ray ionization rate 10–100 times larger than thedense gas elsewhere in the Galactic disk, as determined from observations of H O + , H CO + ,and H +3 (van der Tak & van Dishoeck 2000; van der Tak et al. 2006; Goto et al. 2013, 2014),suggesting an increased particle flux in the Galactic center at all energies. Still, all of theseobservations have only probed ionization rates in the Galactic center and the local ISM.To expand this coverage to wider portions of the Galaxy and answer the question posedabove, other tracers of the cosmic-ray ionization rate are needed, and Herschel provided theopportunity to use observations of OH + and H O + for this purpose. Oxygen chemistry in diffuse clouds is thought to be relatively simple (e.g., Hollenbach et al.2012), with the network of ion-neutral reactions initiated by the ionization of atomic hydro-gen by cosmic rays, H + CR → H + + e − + CR ′ . (1)Ionization of H is followed by endothermic charge transfer to oxygen to form O + ,H + + O + ∆ E ←→ O + + H , (2) 6 –where ∆ E = 226 K represents the endothermicity of the forward reaction (for O in the lowestenergy fine-structure level, P , of the ground state), and the double-sided arrow shows thatthe exothermic back-reaction proceeds uninhibited. The rate of the forward reaction foroxygen in each of the P J ( J = 0 , ,
2) fine-structure levels is highly dependent on the gaskinetic temperature (about 100 K on average in diffuse clouds), and the total forward rateon the relative population in the fine-structure levels of atomic oxygen (Stancil et al. 1999). Also, the O in reaction (2) competes with electrons and neutral and charged small grainsand PAHs in destroying H + (Wolfire et al. 2003),H + + PAH → H + PAH + , H + + PAH − → H + PAH , H + + e − → H + hν, all of which decrease the efficiency at which ionization of H leads to the formation of OH + (Liszt 2003). Once O + is formed it can undergo the back-reaction with H, or it can reactwith H to form OH + , O + + H → OH + + H , (3)which is either destroyed by further hydrogen abstraction to form H O + ,OH + + H → H O + + H , (4)or by dissociative recombination with electrons,OH + + e − → products . (5)The same is true for H O + , H O + + H → H O + + H , (6)H O + + e − → products , (7)but H O + is primarily destroyed by dissociative recombination with electrons,H O + + e − → products , (8)as further hydrogen abstraction reactions with H do not proceed. It is apparent fromreactions (3) through (8) that the abundances of these species are controlled by competitionbetween hydrogen abstraction from H and dissociative recombination with electrons. Rate coefficients for reaction (2) at low temperature are based solely on quantum mechanical calculationsand remain uncertain. It is possible that the most frequently adopted coefficients (Stancil et al. 1999) aretoo large (Spirko et al. 2003), in which case the oxygen chemistry proceeds more slowly. This may contributeto the low efficiency in forming OH + from H + discussed below. +3 → OH + + H , (9)where H +3 is formed following cosmic-ray ionization of H and subsequent reaction of H +2 with another H . To compete with reactions (1)–(3), this pathway requires a substantialfraction of hydrogen to be in molecular form. In gas with small f H , cosmic-ray ionizationwill produce significantly more H + than H +2 . Additionally, H +2 is likely to undergo chargeexchange with the abundant H (i.e., H +2 + H → H + H + ), prior to finding another H ,limiting the formation of H +3 . Combined, these two effects inhibit the pathway to OH + through reaction (9) in gas that is mostly atomic. As we will show that most of the gasunder consideration in this study is diffuse with low molecular hydrogen fraction, we omitthis formation route from our analysis, and focus instead on the pathway following reactions(1)–(3).The utility of OH + and H O + abundances in constraining the molecular hydrogenfraction and cosmic-ray ionization rate has been demonstrated in multiple studies (e.g.,Gerin et al. 2010b; Neufeld et al. 2010; Indriolo et al. 2012), and makes observations of thesespecies important for studying properties of the diffuse Galactic ISM. As part of the PRIS-MAS (PRobing InterStellar Molecules with Absoprtion line Studies) Key Program, andmotivated by the astrochemical and astrophysical considerations discussed above, we carriedout a survey of OH + and H O + line absorption toward nine bright submillimeter contin-uum sources using the Heterodyne Instrument for the Far-Infrared (HIFI; de Graauw et al.2010) on Herschel . The target sources all lie in the Galactic plane, and are all known to ex-hibit absorption by molecules in foreground molecular clouds not associated with the sourcesthemselves. Results from three of the targeted sight lines—W31C, W49N, and W51e—havebeen reported previously, but those studies only utilized a portion of the data that are nowavailable. In this paper we have compiled the full set of observations of OH + and H O + fromPRISMAS, as well as observations from other Herschel programs toward 11 more sight lineswith the intent of exploring f H and ζ H throughout the Galaxy. The sample of observations isdescribed in Section 2; the analysis of these data and findings in Section 3; and a discussionof the findings in Section 4.
2. OBSERVATIONS
All observations presented herein were made using the HIFI instrument on board
Her-schel . Multiple transitions of the oxygen-bearing ions OH + , H O + , and H O + were targetedin several different observing programs. A list of the targeted transitions is given in Table 8 –1. Sight lines along which observations were made are listed in Table 2, and Figure 1 showstheir distribution in the Galactic disk. Observations were performed using the dual beamswitch mode, with the telescope beam centered at the coordinates given in Table 2, andthe reference positions located at offsets of 3 ′ on either side of each source. Multiple localoscillator (LO) frequencies separated by small offsets were used to confirm the assignment ofany observed spectral feature to either the upper or lower sideband of the double sidebandHIFI receivers. All data were acquired using the Wide Band Spectrometer, which provides aspectral resolution of 1.1 MHz and a bandwidth of ∼
3. ANALYSIS AND RESULTS3.1. Spectra
Table 3 lists the double sideband (DSB) continuum antenna temperature, T A (DSB),measured for each of the target sources at the relevant observing frequencies, together withthe root mean square (RMS) noise in the co-added spectra. Because HIFI employs dou-ble sideband receivers, the complete absorption of radiation in any observed spectral linereduces the antenna temperature to roughly one-half its continuum value. The fractionaltransmission at any frequency is given by F ( ν ) F (cont) = (cid:20) T A ( ν ) − T A (DSB)(1 + Γ) (cid:21) (cid:20) T A (DSB)(1 + Γ − ) (cid:21) − , (10)where Γ is defined as the continuum antenna temperature coming from the sideband con-taining the frequency of interest divided by the continuum antenna temperature comingfrom the opposite sideband. In the special case with Γ = 1, i.e., both sidebands contributeequally to T A (DSB), equation (10) simplifies to F ( ν ) /F (cont) = 2 T A ( ν ) /T A (DSB) −
1. Forall transitions of H O + and H O + , and for the 909 GHz and 1033 GHz transitions of OH + Γ = 1 is adopted in converting spectra from antenna temperature to fractional transmis-sion (justified by measurements of sideband ratios reported in Higgins et al. 2014). In caseswhere absorption by the 971 GHz transition of OH + is saturated, the relative intensities ofthe different hyperfine components of the transition are assumed constant, and the measured 9 –optical depth of the weakest component is used to predict the optical depth of the strongestcomponent. This enables the determination of Γ, and is an important step as small changesin saturated absorption correspond to large differences in optical depth and thus inferredcolumn density.The resulting spectra for all observed transitions and sources are presented in Figures2 through 21. OH + and the ortho spin modification of H O + are detected in absorptiontoward all of the targeted sight lines, while H O + and the para form of H O + are each seenin absorption toward only 7 sight lines. Fits to the absorption features (fitting proceduredescribed below) are shown as red curves (blue curves for the sight lines toward Sgr B2),and for transitions with hyperfine splitting the green curves show only absorption due to thestrongest hyperfine component. Stick diagrams above spectra mark the hyperfine structurewhen applicable. The basic fitting procedure used in our analysis has been described previously byNeufeld et al. (2010), but due to some differences we briefly review it here. Absorptionfeatures are assumed to result from the combination of multiple components with Gaussianopacity profiles. Each component is defined by a centroid velocity, velocity full-width athalf-maximum, and maximum optical depth which act as variables in the fitting process.For transitions with hyperfine structure each component consists of multiple Gaussians inopacity. The strongest hyperfine feature is defined as above, and the other hyperfine featuresare forced to have the same velocity width, with fixed relative intensities and fixed velocityseparations—with respect to the strongest feature—defined by transition frequencies, statis-tical weights, and spontaneous emission coefficients. Some number of velocity components(between 2 and 20 depending on the complexity of the absorption profile) is initially cho-sen, and the sum of those components is used to fit the absorption profile. The number ofcomponents is then revised as needed to produce a reasonable fit to the spectra. These fitsare shown as the red curves in Figures 2–3 and 6–21. To determine the actual distributionof molecules in velocity space when considering a transition with hyperfine splitting, we ex-amine the portion of the fit caused only by the strongest hyperfine feature, as shown by thegreen curves in Figures 2–21). Imagine convolving the hyperfine structure stick diagrams in Figures 2–21 with a Gaussian line profileto picture absorption from a single velocity component.
10 –
From the above fitting procedure we determine the optical depth and differential columndensity ( dN/dv ) as functions of LSR velocity along a line of sight. The column density inany velocity range can then be determined by integrating dN/dv over that range. Usingthe OH + and o -H O + absorption profiles (green curves) we select velocity intervals thatcorrespond to what appear to be separate absorption components, and integrate dN/dv overthose intervals. Column densities determined from this analysis for all species are reportedin Tables 4 and 5. In all cloud components we assume nearly all molecules are in theground rotational state for the purpose of determining the total column density of OH + and H O + from our observations. Gas densities in diffuse clouds are sufficiently low thatcollisional excitation is unimportant, and spontaneous radiative decay rates for the studiedtransitions are large (see Table 1), so the excitation temperature is very likely controlledby the cosmic microwave background radiation (i.e., T ex ∼ . + and H O + molecules are in the ground rotational state is thus justified inthe diffuse ISM, although in components where the molecules reside in gas that is part ofthe envelope surrounding the H ii regions used as background sources this may no longerbe the case. For H O + , most of our observations do not probe the lowest lying state, noris the above assumption valid, so we only report state-specific column densities. In caseswhere multiple transitions of a given species are observed, the column densities determinedfrom individual transitions are weighted by 1 /σ (i.e., inverse of the square of the standarddeviation presented as uncertainty in Table 4) when determining the average column densityfor that species (e.g., OH + toward G029.96 − + toward W31C and W49N), onlythe unsaturated transition is used to determine the column density. When p -H O + is notdetected, an ortho -to- para ratio (OPR) of 3 is assumed in determining N (H O + ) from N ( o -H O + ). Only for the Sgr B2 sight lines is a different analysis used, where absorption featurescaused by all transitions of a given species (e.g., 909 GHz, 971 GHz, and 1033 GHz forOH + ; 1115 GHz and 1139 GHz for o -H O + ) are fit simultaneously to determine dN/dv (Schilke et al. 2013). These velocity intervals are identified in Tables 4 and 5.
11 –
A steady-state analysis of the H O + abundance governed by reactions (4), (6), and (7)gives the equation n (OH + ) n (H ) k = n (H O + )[ n (H ) k + n ( e ) k ] , (11)where k i is the rate coefficient for reaction i within this paper. Through substitutions andrearrangement as shown in Indriolo et al. (2012) this is solved for the molecular hydrogenfraction, f H = 2 x e k /k N (OH + ) /N (H O + ) − k /k . (12)This assumes constant densities (for the conversion from number density to column density)and constant temperature ( k is temperature dependent) over the region probed. In deter-mining f H we take x e = 1 . × − (assuming x e = x (C + ); Cardelli et al. 1996; Sofia et al.2004) and T = 100 K (typical value of the H i spin temperature) in computing the variousreaction rate coefficients. Resulting values are presented in Table 5. A similar analysis of steady-state chemistry for OH + gives ǫζ H n (H) = n (OH + )[ n (H ) k + n ( e ) k ] . (13)This equation accounts for the dominant reaction partners by which OH + is destroyed (i.e.,H and electrons), but not every instance of hydrogen ionization results in the formationof OH + due to the backward version of reaction (2) and the neutralization of protons ondust grains and PAHs (Wolfire et al. 2003; Liszt 2003; Hollenbach et al. 2012). To accom-modate this fact, we follow Neufeld et al. (2010) in introducing the efficiency factor, ǫ , onthe left-hand side of equation (13). Given the same assumptions as above, substitution andrearrangement leads to ǫζ H = N (OH + ) N (H) n H (cid:20) f H k + x e k (cid:21) , (14)and the substitution of equation (12) for f H to ǫζ H = N (OH + ) N (H) n H x e (cid:20) k N (OH + ) /N (H O + ) − k /k + k (cid:21) . (15) Rate coefficients are taken from the UMIST database for astrochemistry (McElroy et al. 2013).
12 –In addition to the column densities of OH + and H O + , this analysis also requires the columndensity of atomic hydrogen, N (H), and values are reported in Table 5. In several of our targetsight lines N (H) is determined from 21 cm absorption observations analyzed by Winkel et al.2015 (in prep), and in the remainder we have used H i spectra reported in various works (seeTable 5 description for references). The number density of hydrogen nuclei is also neededin calculating the ionization rate, and we adopt n H = 35 cm − following the reasoning inIndriolo et al. (2012). This value arises from assuming that the diffuse atomic outer layersof a cloud with T = 100 K are in pressure balance with the diffuse molecular interior with T = 70 K and n H = 100 cm − , and it is in very good agreement with the mean thermalpressure (log( P/k ) = 3 .
58) inferred from fine-structure excitation of C i in diffuse clouds(Jenkins & Tripp 2011). Still, the determination of interstellar densities is highly uncertain,and we discuss the effects this may have on our analysis below.Observed column densities of OH + , H O + , and H are then used in concert with ratecoefficients and adopted values of T , x e , and n H to calculate ǫζ H in each cloud component.To convert ǫζ H to the cosmic-ray ionization rate the efficiency factor must be known, and weadopt ǫ = 0 .
07 as found during our previous study of the W51e sight line where H +3 observa-tions were used to independently determine the ionization rate and calibrate ǫ (Indriolo et al.2012). The value of ǫ = 0 . ± .
04 presented in Indriolo et al. (2012) is the only observa-tional determination of the efficiency factor, although it has also been computed as partof chemical models studying OH + , H O + , and H O + presented by Hollenbach et al. (2012).Those authors find 0 . . ǫ . .
2, with the value changing for different densities, ionizationrates, depth into a cloud, etc. While our single observational determination of ǫ falls withinthe range based on chemical modeling, there is clearly still large uncertainty, and we discussbelow the effects that variations in ǫ have on our analysis. Assuming ǫ = 0 .
07 we calculatethe cosmic-ray ionization rate of atomic hydrogen, and values of ζ H are presented in Table5. T , x e , n H , and ǫ During our analysis we have made various assumptions regarding certain variables,namely that x e = 1 . × − , n H = 35 cm − , T = 100 K, and ǫ = 0 .
07 in all cloudcomponents. Here we discuss the uncertainties associated with these parameters.Temperature (specifically gas kinetic temperature) can affect the rates at which cer-tain chemical reactions occur. The hydrogen abstraction reactions relevant to our analysis(3, 4, and 6) are temperature independent, while dissociative recombination with electrons(reactions 5 and 7) is only weakly dependent on temperature ( k ∝ T − . ). Inferred tempera- 13 –tures for diffuse molecular clouds do not vary widely ( T ≈ T shouldnot significantly affect our results.The electron fraction is frequently approximated by the C + fractional abundance indiffuse clouds where singly ionized carbon is responsible for the majority of free electrons.This has been found to be about 1 . × − with moderate variance across observed sightlines that probe gas within about 1 kpc of the Sun (Cardelli et al. 1996; Sofia et al. 2004).Metallicities tend to increase at smaller Galactocentric radii (Rolleston et al. 2000), and atypical assumed gradient in carbon abundance results in a factor of 2–3 increase in x (C) at R gal = 3 kpc (e.g., Wolfire et al. 2003; Pineda et al. 2013; Langer et al. 2014). It is not clearhow exactly x e changes with Galactocentric radius, but it is reasonable to assume variationsof about a factor of 3 with respect to the adopted value across our sample due to variationsin the carbon abundance.While the contribution to the electron abundance from ionized species other than C + (e.g., Si + , S + ) is generally negligible in diffuse gas, as ζ H increases the H + abundance canbecome comparable to or exceed that of C + . A prescription for calculating the steady-statevalue of x e as a function of ζ H in purely atomic gas is given by Draine (2011), and includes theeffects of grain-assisted recombination (Weingartner & Draine 2001). The resulting electronfraction is dependent on input parameters such as temperature, density, and interstellarradiation field, and for our assumed density x e is relatively constant for ζ H . − s − , andincreases roughly as √ ζ H for larger ionization rates. In this regime, the approximation inequations (14) and (15) that x e is independent of ζ H begins to break down, and N (OH + ) nolonger increases linearly with ζ H (similar to findings for H +3 ; Liszt 2007; Goto et al. 2008).In components where we find high ionization rates, x e may in fact be significantly largerthan we have assumed (up to a factor of about 20 for ζ H ∼ − s − ), which would inturn give even larger ionization rates and larger molecular hydrogen fractions than we havereported. Still, given the relationship between x e and ζ H , the values we report remain validlower limits.Interstellar gas densities are difficult to constrain and typically have large uncertain-ties. Estimates of n H are often made using the relative populations in excited states ofatoms and molecules. A recent analysis of CO observations gives densities in the range n H ≈ − (Goldsmith 2013), while C observations result in n H ≈ − (Sonnentrucker et al. 2007) for diffuse molecular clouds. Excitation of the fine-structure lev-els of O i has been used to find n H ≈ − in diffuse gas (Sonnentrucker et al. 2002,2003), while excitation of C i has been used to determine thermal pressures that are consis-tent with n H ≈ − (Jenkins & Tripp 2001, 2011). Observations of C + in many of 14 –the same sight lines studied herein are used to infer n H ≈ − (Gerin et al. 2014).Clearly, there is large variance among inferred densities for diffuse clouds, although much ofthis may be due to the specific region probed (i.e., molecular interior versus atomic exterior).If we take the extreme values given above as limits, our adopted value of n H ≈
35 cm − canvary up or down by roughly a factor of 10 between different components. However, given thedensity estimates from Gerin et al. (2014) and pressures inferred by Jenkins & Tripp (2011),it seems likely that this uncertainty is more commonly only a factor of 3 or so in the diffuseforeground gas along our targeted sight lines. The efficiency factor ǫ (fraction of instances where cosmic-ray ionization of H leads toformation of OH + ) has only a single constraint via observations ( ǫ = 0 . ± . . ≤ ǫ ≤ . T , n H , relative abundances), and will varybetween different clouds. Our best estimate on the uncertainty in ǫ comes from the chemicalmodels of Hollenbach et al. (2012), so we consider limits of about a factor of 2 below and afactor of 3 above the adopted value of ǫ = 0 . In order to explore any correlation that f H or ζ H may have with Galactocentric radiuswe use a kinematic analysis to estimate R gal for the various velocity intervals of absorbinggas along each line of sight. We adopt the functional form of the rotation curve presentedby Persic et al. (1996), and use the input parameters recommended by Reid et al. (2014),including a distance to the Galactic center of 8.34 kpc and a rotation speed of 240 km s − .This allows us to determine the expected line-of-sight velocity as a function of R gal giventhe Galactic longitude of each sight line. Within each velocity interval along a sight line wechoose a single velocity—usually corresponding to maximum absorption—which is used indetermining R gal for that component. From R gal we determine the near and far kinematicdistances to each absorption component. In several cases, departures from the expectedvelocity due to peculiar motions cause this analysis to produce unphysical results. When theresulting Galactocentric radius is smaller than the radius of the tangent point along a line ofsight, we set R gal equal to the tangent point radius. When the kinematic distance is largerthan the assumed distance of the background source (see Table 2 and Section 4.1) we setthe distance equal to that of the background source and correct R gal accordingly. When the Note that we do not simply adopt densities determined from C + as this species also traces gas with large f H where densities are likely higher than the regions containing most of the OH + and H O + .
15 –kinematic distance is smaller than 0.1 kpc we set it equal to 0.1 kpc (and adjust R gal ) so thatthe gas is outside of the local bubble. For most sight lines the kinematic distance ambiguityis solved because the background source is on the near side of the tangent point. In caseswhere the ambiguity remains (e.g., W49N) both distances are reported. Some of our targetsight lines have distance estimates to foreground clouds available in the literature, which wetake to be more robust than our own kinematic analysis. For these sight lines (M − − − −
4. DISCUSSION
As described above, spectra for each sight line were divided into velocity intervalsroughly corresponding to absorption features for the purpose of analyzing our data. A total of105 separate components containing OH + absorption are defined in our sample, of which 100also show o -H O + absorption. In contrast, H O + absorption is only seen in 16 components(12 of which are in the Galactic center), and p -H O + absorption in 11 components (4 of whichare in the Galactic center). In many cases though, potential for detection of the p -H O +
607 GHz line is impeded by emission from the J = 7–6 transition of H CO + (607.1747 GHz)and the J K a ,K c = 12 , –11 , transition of CH OH (607.2158 GHz). Similarly, the 631 GHztransition of p -H O + is often obscured by emission from the J K a ,K c = 9 , –8 , transition ofH CO (631.7028 GHz). The rest frequency of the H O + − redshift) that of the 2 , –1 , transition of H O, making a confirmed de-tection difficult. Only in two sight lines (W31C and W49N) do we present the 1655 GHzspectra, as in all others where the transition was covered we are confident the absorptionsignals are due to H
O (identification aided by absorption profiles of the 1 , –0 , transitionof H O presented in van der Tak et al. 2013b). A more detailed description of our findingsin each line of sight follows. 16 – − − − − Two well known molecular clouds in the Galactic center region are M − − − − − and Sgr A +50 km s − clouds due to their respective radial velocities. Both are within 10 pc of the Galactic cen-ter (Ferri`ere 2012), which is 8.34 ± ii regions—source SgrA–G from Ho et al. (1985) in the case of M − − − − − − − − + absorption across the entire velocity range from −
210 km s − to 30 km s − (Figure 2). Absorption at v LSR . −
60 km s − is thought to be due entirely to gasin the central molecular zone (CMZ) within the Galactic center region (Sonnentrucker et al.2013), while at v LSR & −
60 km s − there is some combination of foreground spiral arms thatabsorb at distinct velocities and gas in the CMZ. We attribute absorption at −
50 km s − ≤ v LSR ≤ −
40 km s − to the 3 kpc spiral arm (Dame & Thaddeus 2008), and at −
40 km s − ≤ v LSR ≤ −
15 km s − to the 4.5 kpc spiral arm (Menon & Ciotti 1970), although both intervalsare likely contaminated by gas in the Galactic center as well. Absorption from −
15 km s − to 30 km s − is due to some combination of local gas and the CMZ, including the cloud inwhich the continuum source is embedded (i.e., the +20 km s − cloud). The o -H O + spectrumfollows a similar pattern, but with weaker absorption in many components. H O + absorptionis only seen in a narrow component at 12 km s − , coming from the molecular cloud itself. Similarly, M − − + and o -H O + absorption from −
210 km s − to70 km s − (Figure 3). We assume roughly the same breakdown between CMZ and fore-ground gas, with the 3 kpc spiral arm at −
61 km s − ≤ v LSR ≤ −
47 km s − , the 4.5 kpcspiral arm at −
47 km s − ≤ v LSR ≤ −
13 km s − , and the CMZ at v LSR ≤ −
61 km s − and v LSR ≥ −
13 km s − . The background molecular cloud (Sgr A +50 km s − ) is responsiblefor absorption between 20 km s − and 70 km s − . Again, the background source is the onlycomponent that shows substantial H O + absorption, although there may also be a weakfeature at −
140 km s − . Both the 607 GHz and 631 GHz transitions of p -H O + were alsotargeted toward M − − The spectrum is truncated below v LSR ≤ −
90 km s − due to interference from the 971 GHz transitionof OH + in the other sideband.
17 – −
140 km s − that coincide with the strongest o -H O + absorption to be detections. Valuesof N ( p − H O + ) derived from both transitions are in agreement.It must be noted that for both sight lines blending of absorption from foreground spi-ral arms and from the CMZ complicates our analysis. We have attributed absorption inselect velocity intervals entirely to foreground clouds following previous studies of molec-ular absorption toward the Galactic center (e.g., Monje et al. 2011; Sonnentrucker et al.2013; Schilke et al. 2010, 2014), but other studies have shown that the entire velocity rangeunder consideration also contains absorption from gas in the CMZ (e.g., Oka et al. 2005;Geballe & Oka 2010; Goto et al. 2011, 2014). Results inferred from absorption in these ve-locity ranges—i.e., those assigned to the 3 kpc and 4.5 kpc spiral arms—should be viewedwith caution. The same is true for select velocity intervals in the Sgr B2 sight lines discussedbelow. Sgr B2 is a giant molecular cloud within the Galactic center region that contains multi-ple cores—including Sgr B2(M) and Sgr B2(N)—where prolific star formation is occurring.Different studies place Sgr B2 in front of (Reid et al. 2009) or behind (Molinari et al. 2011)Sgr A*, but always within ∼
150 pc, and we adopt d = 8 .
34 kpc, as the precise location isnot vital to our study. At this distance the projected separation between Sgr B2 and Sgr A*is about 100 pc, and the projected separation between the Sgr B2(M) and Sgr B2(N) coresis 1.8 pc.Spectra of OH + , H O + , and H O + toward Sgr B2(M) and Sgr B2(N) are largely similar(Figures 4 and 5) with strong absorption extending from about −
120 km s − to 40 km s − .Absorption across this entire velocity range is likely caused by gas within the Galactic centerand foreground spiral arms that contribute at specific velocities. The lack of sharp, well-defined features makes it difficult to attribute absorption to any particular spiral arm, but weassume that absorption in the −
60 km s − . v LSR . −
30 km s − interval arises in the 3 kpcarm, and in the −
30 km s − . v LSR . − − interval in the 4.5 kpc arm, with the caveatthat there is likely considerable contamination from gas within the Galactic center as well.Systemic velocities of the background sources differ slightly, about 63 km s − for Sgr B2(M)and 66 km s − for Sgr B2(N), and both sources show absorption, but Sgr B2(N) has anadditional absorption component near 80 km s − seen only in H O + . The Sgr B2 sight linesare unique in our survey in that H O + absorption is detected in all velocity components.While we only list column densities in the 1 +0 state, a much more thorough analysis utilizingtransitions out of 11 levels of H O + in these sight lines (beyond the scope of this paper) has 18 –been carried out by Lis et al. (2014). Our reported values for N (1 +0 ) are in good agreementwith theirs.Although several spectra of both ortho and para H O + toward Sgr B2(M) have beenpresented and analyzed in previous studies (Ossenkopf et al. 2010; Schilke et al. 2010, 2013),we reproduce the 1115 GHz and 1139 GHz absorption lines here to facilitate comparison withOH + . Both the 971 GHz and 1033 GHz lines of OH + are saturated, and knowledge of thevelocity structure is almost entirely dependent on the 909 GHz transition. Still, the OH + and o -H O + profiles are nearly identical in velocity structure for both Sgr B2(M) and Sgr B2(N).These sight lines are also unique in that p -H O + is detected in all velocity components asshown by Schilke et al. (2013), and where available we use column densities determined fromthat study in computing the OPR shown in Table 4, as well as total N (H O + ). The ultracompact H ii region W28A (also known as G005.89 − ′ south of the W28 supernova remnant, although it is unclear if the two sources arephysically related or a chance projection. Molecular line observations give a systemic velocityof 9 km s − for W28A (Harvey & Forveille 1988; Nicholas et al. 2011). OH + shows threedistinct absorption components at about 7 km s − , 13 km s − , and 23 km s − (Figure 6).The first two of these are detected in o -H O + , but the component at 23 km s − is clearlyabsent. In the two components where both ions are detected, we find molecular hydrogenfractions of about 0.085, above average in our sample. Neither p -H O + nor H O + is detectedin absorption toward W28A, but it is possible that the weak emission at 9 km s − in theH O + spectrum is arising in the background source itself. Also commonly referred to as G010.62 − ii region within the W31complex, and has a systemic velocity of about − − (Godard et al. 2010; Gerin et al.2010a). The H ii region has a large peculiar motion with respect to the Galaxy’s rota-tion curve, and is 4.95 kpc away from the Sun as determined by H O maser observations(Sanna et al. 2014). A detailed picture of the velocity components along the line of sight isgiven by Corbel & Eikenberry (2004), and we use their distance estimates rather than simplekinematic rotation curve estimates in our analysis. 19 –OH + shows absorption from about −
10 km s − to 50 km s − , and although the 971 GHztransition is saturated in multiple components the velocity profile of the 909 GHz transitionis rather well matched by that of o -H O + (Figure 7). The strongest OH + and o -H O + ab-sorption is in a narrow component centered at about 40 km s − , which also shows absorptionfrom H O + in both the 1655 GHz and 984 GHz lines (full analysis in Lis et al. 2014) and p -H O + in the 607 GHz line. A feature in the p -H O +
631 GHz spectrum may also berelated to this narrow component, but given the noise level we treat it as a non-detection.A broad, weak feature in the H O +
984 GHz spectrum from about 13 km s − to 30 km s − is also thought to be caused by H O + . Absorption near − − in the 1655 GHz H O + spectrum, however, is likely caused entirely by the 2 , –1 , transition of H O mentionedabove.All species studied here (OH + , o -H O + , p -H O + , and H O + ) were previously reportedin absorption by Gerin et al. (2010b). A direct comparison of derived column densities iscomplicated by the different velocity intervals chosen. An analysis of the OPR of H O + toward W31C was performed by Gerin et al. (2013), and our results (see Table 4) are inrough agreement with their findings despite the use of different velocity intervals. Lis et al.(2014) also performed a multi-level analysis of H O + (using 6 transitions) in this sight line,and our reported column densities agree within uncertainties. Trigonometric parallax observations of water masers in the W33 star forming complexput the region—including the massive young stellar object W33A—at a distance of 2.4 kpc(Immer et al. 2013). W33A (also identified as the H ii region G012.90 − − as measured from various emission lines (e.g. van der Tak et al.2000; Wienen et al. 2012; San Jos´e-Garc´ıa et al. 2013). OH + shows four separate absorptionfeatures from − − to 16 km s − , 20 km s − to 25 km s − , 25 km s − to 36 km s − and36 km s − to 45 km s − (Figure 8), all of which are also detected in o -H O + absorption. Inall of these components we find 0 . ≤ f H ≤ .
09, above the average value for foregroundgas. Neither p -H O + nor H O + are detected along this sight line. − The ultracompact H ii region G029.96 − − , very near the tangent velocity, and absorption occurs nearly continuouslyfrom there down to 0 km s − in several distinct velocity components, as can be seen in ourOH + and o -H O + spectra (Figure 9). Neither H O + nor p -H O + are conclusively detected,although there is a weak (2 σ ) feature in the 607 GHz spectrum at 71 km s − (where thestrongest OH + and o -H O + absorption occurs) that may be due to p -H O + . Interestingly,three of the components along this sight line (those centered at 53 km s − , 83 km s − , and92 km s − ) have the three lowest values of the cosmic-ray ionization rate inferred by ouranalysis. G034.3+00.15 shows molecular emission at about 59 km s − (HCO + from Godard et al.2010), and the compact H ii region is about 3.8 kpc away from the Sun as determined by akinematic analysis (Fish et al. 2003). Absorption between about 44 km s − and 70 km s − is likely associated with the background source and molecular cloud itself, while absorptionat lower velocities is due to foreground material. The OH + and o -H O + spectra (Figure 10)show relatively similar absorption profiles, and H O + is not detected. The p -H O +
607 GHzspectrum shows weak absorption at 8–16 km s − and 40–55 km s − , both ranges that matchthe strongest OH + features. No absorption is detected from the p -H O +
631 GHz transition.
W49N contains several ultracompact H ii regions, and at 11.11 kpc away (determinedfrom H O maser observations of Zhang et al. 2013) this is the most distant source we haveobserved. Molecular emission peaks near 0–8 km s − for HCO + (Godard et al. 2010) and CH(Gerin et al. 2010a), marking the systemic velocity for W49N, and these emission featurestend to be broad with FWHM ∼
10 km s − . Absorption extends up to about 80 km s − goingfrom the background source to the tangent point (Figure 11), and then sweeps back downto 0 km s − going from the tangent point to the Sun (Fish et al. 2003). This means that arotation curve analysis of the gas velocities will result in both a near and far estimate, makingdistance determinations highly uncertain. Because unassociated clouds will be absorbing atthe same velocities the determination of abundance ratios, f H , and ζ H will also be highlyuncertain, and results from this sight line should be viewed with caution.OH + and o -H O + were previously analyzed toward W49N by Neufeld et al. (2010),although only the 971 GHz OH + data were available at that time. Column densities based 21 –on both the 909 GHz and 971 GHz transitions are similar to those reported by Neufeld et al.(2010). The 607 GHz transition of p -H O + is also seen in absorption from about 35 km s − to 70 km s − , and has previously been analyzed by Gerin et al. (2013) for the purpose ofstudying the OPR of H O + . Although their analysis split the H O + absorption into 5 km s − bins, the resulting OPR agree well with those we present in Table 4. There is a hint ofabsorption from the 631 GHz line of p -H O + near 35 km s − , but interference from a strongemission line due to H CO complicates the analysis of this feature. The 984 GHz H O + transition may show weak emission at the source velocity, but is not seen in absorption. The1655 GHz H O + transition potentially shows absorption (2 σ level) at 34 km s − (matchesstrongest OH + and H O + in velocity), but near the systemic velocity there is likely strongblending with H O absorption as was the case for W31C.
The W51 region consists of a massive molecular cloud and several active star formingcomplexes, and has an inferred distance of 5.41 kpc from H O maser observations (Sato et al.2010). The compact H ii regions W51 e1 and W51 e2 (Mehringer 1994) were used as back-ground continuum sources for our observations, and show molecular emission features cen-tered at 55 km s − (Ho & Young 1996; Sollins et al. 2004). Narrow absorption at 70 km s − is caused by a cold dense clump (Mookerjea et al. 2014), while a more broadly distributedforeground cloud absorbs at 62–70 km s − , and gas between about 44 km s − and 62 km s − is associated with the giant molecular cloud itself (Kang et al. 2010). Gas absorbing at lowervelocities (e.g., 7 km s − and 24 km s − ) is well in the foreground, and likely more diffuse(Carpenter & Sanders 1998; Sonnentrucker et al. 2010).Observations of o -H O + from the WISH (Water In Star-Forming regions with Herschel )program were previously presented by Wyrowski et al. (2010b), and observations of o -H O + and OH + from the PRISMAS program by Indriolo et al. (2012). Our column densities arein good agreement with those reported in the above studies, but should supersede previousvalues as the o -H O + spectra we present utilize a combination of WISH, PRISMAS, andOT1 dneufeld 1 data, and have significant improvement in S/N (Figure 12). Analyses ofOH + from both the 909 GHz and 971 GHz transitions are in good agreement, and differencesin derived column densities can be attributed to interference from a weak emission line dueto the 5 +5 , –6 +4 , and 5 − , –6 − , transitions of CH OH at 909.0744 GHz that can be seen in the909 GHz spectrum as a poor fit near 85 km s − . This causes an underestimate of N (OH + )in the 42 km s − ≤ v LSR ≤
55 km s − interval, and overestimate in the − − ≤ v LSR ≤
16 km s − interval. As a result, only the 971 GHz line is used in determining N (OH + ) over 22 –these intervals.The diffuse cloud near 6 km s − shows absorption from the 607 GHz transition of p -H O + (absorption near 50 km s − is also likely, but interference from a strong emission lineof CH OH complicates the analysis there). Additionally, the components at 55–75 km s − are two of only four outside the Galactic center in our survey where H O + absorption isdetected via the 984 GHz transition. The features are very weak, but match exceptionallywell in velocity space with absorption peaks in the o -H O + spectrum and both OH + spectra.This H O + absorption denotes gas that has a high molecular fraction and is likely in a densecloud interior rather than the diffuse outer layers (following the model of Hollenbach et al.2012), a hypothesis supported by the fact that this velocity component shows the strongestabsorption in HF and H O along the W51e sight line (Sonnentrucker et al. 2010).
AFGL 2591 is a cluster of high mass protostars with a bipolar outflow likely drivenby the source associated with 1.3 cm and 3.6 cm continuum emission identified as VLA 3(Trinidad et al. 2003). The molecular gas associated with the protostars has a velocityof − . − (van der Tak et al. 1999), and H O maser observations give a distance of3.33 kpc (Rygl et al. 2012). OH + and H O + show two components in absorption towardAFGL 2591, at 3 km s − and −
17 km s − , neither of which matches the systemic velocity (Fig-ure 13). The gas at 3 km s − may be associated with a foreground cloud previously reportedat 0 km s − in tracers of molecular gas (Emprechtinger et al. 2012; van der Wiel et al. 2013),but this requires a velocity offset between the molecular cloud and the atomic outer layerswhere the oxygen ions presumably reside. The blueshifted component at −
17 km s − maybe associated with a molecular outflow (Mitchell et al. 1989; van der Tak et al. 1999, 2013b;van der Wiel et al. 2013), a hypothesis that could explain the larger value of f H = 0 .
09 foundin this component. Both OH + and H O + have previously been studied toward AFGL 2591(Bruderer et al. 2010; Benz et al. 2013) along with several other light hydrides. The columndensities that we derive for the two velocity components are in relatively good agreementwith those found by Bruderer et al. (2010), as well as the line of sight column densitiesreported by Benz et al. (2013). H O + absorption is not detected, likely due to the low con-tinuum level signal-to-noise ratio, although emission from the 4 +3 − − transition has beenobserved at the systemic velocity (Benz et al. 2013). A more detailed study of light hydridesin AFGL 2591 is currently underway (Benz et al. 2015, in preparation). 23 – DR21C and DR21(OH) are compact H ii regions that are parts of the DR21 molecularridge, a region of massive star formation about 1.5 kpc away from the Sun (determinedfrom H O maser observations by Rygl et al. 2012). Systemic velocities for both sources areabout − − (van der Tak et al. 2010; Zapata et al. 2012). The sources are separatedby 3.1 ′ on sky, corresponding to a projected separation of 1.3 pc at the adopted distance.The OH + and o -H O + absorption profiles for DR21C and DR21(OH) are largely similar(Figures 14 and 15). In the OH + spectra there is a shallow absorption wing from about25 km s − to 15 km s − , followed by a rapid increase to maximum absorption near 9 km s − .The absorption then gradually decreases until it disappears around −
15 km s − . The mostnotable difference between the spectra is that toward DR21C there is a local minimum inabsorption at − − , while for DR21(OH) the absorption decreases monotonically below0 km s − . Spectra of o -H O + show the same general structure. Differences in the absorptionprofiles between the two sources only occur near the systemic velocities, suggesting that mostof the absorption arises in a common foreground cloud. Indeed, the strongest absorption at9 km s − matches a foreground cloud observed in CO and HCO + associated with the nearbysource W75N (Schneider et al. 2010). Neither the 607 GHz nor the 631 GHz transition of p -H O + is detected toward DR21(OH), but the 607 GHz line shows absorption toward DR21C,although there is likely interference from emission lines of CH OH and H CO + . H O + is not detected in either sight line. Previous observations of o -H O + toward DR21C werereported by Ossenkopf et al. (2010), and our resulting column densities are in relatively goodagreement. Our inferred column densities for OH + and H O + are also in good agreementwith those found as part of a more detailed analysis of the DR21C sight line (Chambers etal. 2015, in preparation) The hyper-compact H ii region NGC 7538 IRS1 is 2.65 kpc distant as determined viatrigonometric parallax of CH OH masers (Moscadelli et al. 2009) and has a systemic velocityof −
59 km s − observed in several molecules (Zhu et al. 2013). OH + and o -H O + show verysimilar absorption profiles with components at −
50 km s − , −
33 km s − , −
28 km s − , − − , and 0 km s − , the exception being that the −
28 km s − component is missing in o -H O + (Figure 16). Absorption from −
60 km s − to −
40 km s − is likely associated withmaterial at the background source, while the other components arise in foreground gas. Adetailed analysis of light hydrides in NGC 7538 IRS1 is forthcoming in Benz et al. 2015 (inpreparation). 24 – Both W3(OH) and W3 IRS5 are located in the W3 molecular cloud complex, a site ofactive star formation within the Galaxy. W3(OH) is an ultracompact H ii region thought toharbor a massive young star, while W3 IRS5 is a protocluster of a few high mass stars. Multi-epoch VLBA observations of water masers toward both sources have been used to determinedistances of 2 . ± .
07 kpc (Hachisuka et al. 2006) and 1 . ± .
14 kpc (Imai et al. 2000) forW3(OH) and W3 IRS5, respectively. Molecular line observations show systemic velocitiesof −
46 km s − for W3(OH) (Wilson et al. 1991) and −
39 km s − for W3 IRS5 (Wang et al.2013). The two sources are 16.6 ′ apart in the sky, corresponding to a projected separationof about 9.7 pc at the distance of the background sources.The absorption profiles of OH + and o -H O + toward W3(OH) and W3 IRS5 are largelysimilar, with absorption from about 7 km s − to −
27 km s − (Figures 17 and 18). Thesefeatures are due to foreground clouds that have previously been observed in H i absorptionat about 0 km s − and −
20 km s − , and which are estimated to be at distances of 0.7 kpcand 1.5 kpc, respectively (Normandeau 1999). Toward W3(OH) the absorption between −
41 km s − and −
50 km s − is likely associated with material surrounding the backgroundsource itself, and similar for the −
37 km s − to −
47 km s − absorption toward W3 IRS5.Neither line of sight shows a conclusive detection of the p -H O + line at 607 GHz, nor is H O + detected toward W3(OH). Emission features in the 909 GHz spectrum toward W3(OH) andin the 971 GHz spectrum toward W3 IRS5 are due to CH OH.Analyses of light hydrides in the W3 IRS5 sight line have been previously reportedby Benz et al. (2010, 2013). Column densities that we find for OH + and o -H O + in theforeground gas are consistent with those reported by Benz et al. (2010), within uncertainties.For the gas associated with the background source, however, our column densities are abouthalf of the values reported in Benz et al. 2015 (in preparation). The difference arises becausewe assume the entire populations of both species are in the ground state, while Benz et al.2015 (in preparation) adopt a higher excitation temperature to account for heating by UVradiation, assuming the gas is located in the cavity wall of a protostellar outflow. G327.3 − − − (San Jos´e-Garc´ıa et al. 2013; Leurini et al.2013), and a distance of 3.3 kpc was determined via a kinematic analysis of H i absorption 25 –data (Urquhart et al. 2012). OH + and o -H O + show similar absorption profiles for the mostpart (Figure 19). Absorption from −
31 km s − to −
55 km s − likely arises within thecloud containing the background source, while features at v LSR ≥ −
26 km s − are causedby foreground material. It is unclear why the expected absorption due to the weakesthyperfine component of the OH +
971 GHz transition fails to match the observed spectrumnear −
75 km s − . The sources NGC 6334 I (a hot molecular core) and NGC 6334 I(N) (a mid-IR quiethigh mass protostellar object) are both within the NGC 6334 complex of molecular cloudsand H ii regions, located at a distance of 1.35 kpc (Wu et al. 2014). Systemic velocitiesfor the two sources are − − and − − , respectively, and they are separatedby 1.9 ′ on sky, corresponding to projected separation of 0.74 pc at the adopted distance.Absorption profiles of OH + and o -H O + are nearly identical between the two sight lines withpeaks at 3 km s − and − − , although NGC 6334 I also shows a weaker componentnear −
10 km s − (Figures 20 and 21). None of these components are well-matched to thoseseen in H O (van der Tak et al. 2013b) and HF (Emprechtinger et al. 2012) that have beenattributed to protostellar envelopes, outflows, and foreground clouds, further highlightingthe different regions traced by such molecules. Given the similarities between the two sightlines though, we can conclude that the absorption features at 3 km s − and − − likelyarise in a common foreground cloud. A detailed analysis of light hydrides in the backgroundsources will be presented by Benz et al. 2015 (in preparation). Column densities of OH + and H O + toward NGC 6334 I have previously been reported by Zernickel et al. (2012). Ourfindings for OH + where they adopt an excitation temperature of 2.7 K are in good agreement,but for H O + their adopted value of T ex = 24 K leads to a much larger column density. O + ortho-to-para ratio (OPR) Out of our entire survey, 11 velocity intervals show conclusive detections of the p -H O + line at 607 GHz, and only 6 of those are above a 3 σ level. Four of the detectionsare along Galactic center sight lines, including one toward M − − O + , which is given in Table 4 column 9. In all cases,within uncertainties the OPR is consistent with a value of 3, the ratio expected in the hightemperature limit based solely on nuclear spin statistical weights. While it is possible that 26 –reactive collisions, temperature, forbidden spontaneous emission (Tanaka et al. 2013), andstate-specific formation and destruction can skew the OPR away from 3, observations thusfar have not conclusively demonstrated any such deviations in the diffuse ISM (Gerin et al.2013; Schilke et al. 2013). O + Detections H O + is only detected in absorption in 16 components, 12 of which are in sight linestoward the Galactic center. Models of the chemistry surrounding oxygen-bearing ions findthat H O + will only form in observable abundances in gas that is well shielded from theinterstellar radiation field (visual extinction, A V & +3 → OH + + H rather thanreaction (3), so abundances are linked to the ionization rate of H instead of H. The smallnumber of H O + detections in our sample suggests that most of the components we considerhave low A V , and are comprised of diffuse gas. This supports the use of diffuse cloudchemistry in our analysis, the link between OH + and the ionization rate of atomic hydrogen,and the assumption that molecules are almost entirely in their respective ground states. + to H O + ratio The abundance ratio N (OH + ) /N (H O + ) is inversely related to f H , as clearly seen inequation (12). Conceptually this is easy to understand as more H will drive the OH + +H reaction more rapidly, converting more OH + into H O + . Values of N (OH + ) /N (H O + )and f H are given in columns 5 and 9 of Table 5, respectively, and the distribution of f H ispresented as a histogram in Figure 22. The observed OH + and H O + abundances favor gaswith low molecular hydrogen fractions, as all but three of the components in the Galacticdisk have f H < .
1, and only in the Galactic center does f H exceed 0.15. Excluding datain the Galactic center sight lines, the distribution of molecular hydrogen fractions in oursample has mean 0.053 and standard deviation 0.026.We have also considered whether or not f H differs in velocity intervals that are poten-tially associated with material surrounding our target background sources (contain absorp-tion within 5 km s − of systemic velocity). The distribution of f H in these components isshown by the red bars in Figure 22, and it is clear that they tend to have larger molecularhydrogen fractions. If these components potentially associated with background sources arealso excluded from our analysis, the mean and standard deviation of f H in our sample change 27 –to 0.042 ± + and H O + observations for the same purpose (Gerin et al. 2010b; Neufeld et al. 2010;Indriolo et al. 2012; van der Tak et al. 2013a), as well as with models of oxygen chemistry(Hollenbach et al. 2012), confirming the trend that the two species predominantly reside inmostly atomic gas.A plot of the molecular hydrogen fraction versus Galactocentric radius is shown in thebottom panel of Figure 23. Red diamonds denote velocity intervals more likely associatedwith background sources and black squares those thought to be foreground clouds, and thereis distinct separation between the bulk of the two samples as would be expected given thediscussion above. There does not appear to be any relation between f H and R gal , eitherfor the entire sample or for the sub-samples separately. If metallicity increases toward theGalactic center though (Wolfire et al. 2003, and references therein), x e should as well, andlarger values of f H would be required to produce the observed N (OH + ) /N (H O + ) ratios.Whether or not f H changes with R gal then hinges on the underlying assumption that x e iseither constant or variable with Galactocentric radius. The final column of Table 5 gives the cosmic-ray ionization rates inferred from ouranalysis, and the distribution of ζ H is presented in the bottom panel of Figure 24. Upperlimits on ζ H are the result of optically thick 21 cm H i absorption that only allows us to placelower limits on N (H). Lower limits on ζ H arise when we are only able to place a lower limiton N (OH + ). A range of ionization rates is reported when H O + is not detected, with theupper bound determined by the upper limit on N (H O + ), and the lower bound determinedin the limit where N (H O + ) →
0. Uncertainties in ζ H only account for the uncertaintiesin observed column densities, and do not include the effects discussed in Section 3.6. Asbefore, in Figure 24 the grey bars represent the total sample of velocity intervals where theionization rate has been determined, and the red bars denote the sub-sample of clouds thatmay be associated with background sources. All components with ζ H > − s − arise insight lines toward the Galactic center, and due to the unique nature of this region we excludeall data from the M − − − − + and H O + appears to be log-normal. We find the mean value of log( ζ H ) to be -15.75 ( ζ H = 1 . × − s − ) with standarddeviation 0.29. The distribution in components potentially associated with backgroundsources does not differ appreciably, although it lacks some of the highest ionization rates seen 28 –in the foreground clouds. Shown in the top panel of Figure 24 is the distribution of ionizationrates in diffuse molecular clouds found by Indriolo & McCall (2012) using observations ofH +3 . Ionization rates of molecular hydrogen ( ζ ) reported therein have been scaled by 1.5/2.3to convert to the ionization rate of atomic hydrogen (Glassgold & Langer 1973, 1974). Thissample has a mean value of -15.55 ( ζ H = 2 . × − s − ) and standard deviation 0.24.Despite slight differences, mean ionization rates calculated using the different moleculesare in agreement. To check whether or not the two distributions of ionization rates differ,we performed a two-sample K-S test, and we cannot reject the hypothesis that the twosamples are drawn from the same underlying distribution. The greatest difference in thetwo distributions occurs for ζ H . . × − s − , and no ionization rates inferred from H +3 are below 10 − s − . Likely this is because H +3 absorption lines are fairly weak (only a fewpercent deep at most), and at low ionization rates the molecule will not be produced indetectable abundances. This means OH + and H O + are important tracers of ζ H in a regimewhere H +3 is unobservable.Cosmic-ray ionization rate versus Galactocentric radius is shown in the top panel ofFigure 23. Outside a radius of 5 kpc there does not seem to be any relation between ζ H and R gal . This appears to agree with the conclusion of a uniform cosmic-ray density drawnfrom gamma-ray observations tracing the flux of E &
300 MeV protons (Ackermann et al.2011). Within the Galactic center itself there is a large range of ionization rates, includingsix components with ζ H > − s − . These are the highest values found in our study,and they all come from gas toward M − − − − −
159 km s − ≤ v LSR ≤ −
85 km s − and toward Sgr B2(M) and Sgr B2(N) with −
130 km s − ≤ v LSR ≤−
60 km s − . OH + shows continuous, substantial absorption over these velocities (see Figures2–5), while H i only has minimal absorption in the same range (Figure 7 in Lang et al. 2010;Dwarakanath et al. 2004, Figure 5 position 7). As mentioned above, at such high ionizationrates equation (15) is no longer a valid approximation because electrons freed during theionization of H and H make x e strongly dependent on ζ H . Because our adopted value of x e is likely an underestimate, the high ionization rates reported in the Galactic center shouldstill be valid lower limits. Smaller ionization rates in the Galactic center are found in thevelocity intervals corresponding to all four of the background sources—regions known to belargely molecular. Indeed, the strong H O + absorption in these components requires largeH abundances and denser gas. The diffuse cloud chemistry used to infer f H and ζ H isalmost assuredly not valid in these regions, and the higher ionization rates found in othercomponents will be more indicative of the particle flux in the Galactic center. Previousstudies of the Galactic center region also find cosmic-ray ionization rates on the order of10 − –10 − s − . Observations of H +3 show the molecule to be widespread in the CMZ, andinferred ionization rates are several times 10 − s − on average (Oka et al. 2005; Goto et al. 29 –2008). Analysis of the 6.4 keV Fe K α line, gamma rays, and radio synchrotron emission inthe Galactic center also points to a large population of energetic particles, and estimates ofthe resulting ionization rate range from a few times 10 − s − up to 5 × − s − dependingon the location in question (Yusef-Zadeh et al. 2007, 2013).Sight lines toward the Galactic center also show OH + and H O + absorption from the3 kpc and 4.5 kpc spiral arms. Ionization rates in these components tend to be higherthan most of those found at larger R gal , and lower than those found in the Galactic center,indicative of a gradient in ζ H . Such a gradient was predicted by Wolfire et al. (2003), andis expected given the high concentration of energetic sources in the inner Galaxy leadsto more particle acceleration than elsewhere in the disk. However, we must re-emphasizethat absorption attributed to these spiral arms is very likely blended with absorption fromgas within the CMZ, so it is possible that the intermediate ionization rates are simply acombination of high ionization rates in the Galactic center and average ionization rates inthe spiral arms. Additional observations at R gal ≤ ζ H and N H ≡ N (H) + 2 N (H ), the total column density of a given cloud. The cross section forionization of H and H by cosmic rays increases with decreasing energy, meaning the flux oflow-energy particles ( E ≤
100 MeV) is most important in controlling ζ H , and such particleswill quickly be removed from the cosmic-ray spectrum due to these energy losses (e.g.,Padovani et al. 2009). Cosmic-ray ranges (expressed as the product of density and distance,i.e., column density, through which a particle can propagate before losing all of its energy toionization interactions) have been calculated as a function of particle energy and are availablevia a NIST web query. Ranges for 1 MeV, 10 MeV, and 100 MeV protons propagatingthrough a gas of purely atomic hydrogen are Rn (H) = 5 . × cm − , 3 . × cm − ,and 2 . × cm − , respectively. Given these ranges and an average diffuse cloud with N H = 10 cm − , the higher-energy particles will pass through the entirety of the cloud,while the lower energy particles—those most important for ionization—will be stopped partof the way through the cloud. The expected result then, is that ζ H will decrease withincreasing N H as the particles most efficient at ionization are removed from the spectrum.In Figure 25 we plot ζ H versus N H for the sample studied herein, and for ionization ratesdetermined from H +3 observations (Indriolo & McCall 2012). We see no change in ζ H over therange N H = 0 . × cm − , consistent with our previous findings. Only for clouds with N H & cm − do reported ionization rates decrease significantly (e.g., see Padovani et al.
30 –2009, and references therein), hinting at the loss of low-energy cosmic rays. The lack of acorrelation between ζ H and N H in diffuse clouds may be due to multiple effects. Even if thecolumn density along a line of sight is large enough to stop low-energy particles, it is possiblethat the amount of material a particle would have traverse to reach that point moving in theplane of the sky is much lower. It is also possible that what appears as a single absorptionfeature in velocity space is actually composed of several discrete clouds along the line ofsight, each with column densities much smaller than the total. Finally, due to the smallmolecular hydrogen fractions we have concluded that OH + and H O + reside predominantlyin the outer layers of clouds. This means that our inferred ionization rates are based onmaterial expected to experience a mostly unattenuated flux of low-energy cosmic rays.
5. SUMMARY
We have surveyed 20 sight lines in the Galactic disk with the
Herschel Space Observatory ,all of which show absorption from OH + and o -H O + . Sight lines have been sub-dividedby velocity intervals into a total sample of 105 components where we determine columndensities for the observed species. H O + is detected in only 4 components outside of theGalactic center, suggesting the majority of the gas being probed is diffuse and at A V . f H ≤ . + and H O + reside in primarily atomic gas, likelyin the outer layers of clouds. We find a distinct difference in the distribution of f H inforeground components versus the distribution in components potentially associated withmaterial surrounding background sources (i.e., envelopes, outflows), with the latter showinglarger molecular hydrogen fractions. The distribution of f H in foreground components isdescribed by a Gaussian function with mean and standard deviation 0 . ± . x e . If the electron fraction varies with R gal (perhaps in unison with the known metallicity gradient), then f H would increase toward theGalactic center.Our study has more than doubled the sample of Galactic diffuse molecular clouds wherethe cosmic-ray ionization rate has been determined. Ionization rates inferred from OH + and H O + outside the Galactic center show a log-normal distribution with mean -15.75( ζ H = 1 . × − s − ) and standard deviation 0.29. This distribution is consistent withthat found using H +3 observations along diffuse molecular cloud sight lines, and the meanionization rates found using the different molecular tracers agree within uncertainties. Given 31 –these results and the size of our sample, we confirm the findings that average cosmic-rayionization rates in the Galactic disk are on the order of 10 − s − .Cosmic-ray ionization rates in the Galactic center are 1–2 orders of magnitude largerthan those found in the Galactic disk, again consistent with previous findings. It is possiblethat there is a gradient in ζ H , with the ionization rate decreasing from the Galactic centerout to R gal ≈ R gal > ζ H shows no correlation with Galactocentric radius.This is in agreement with the gamma-ray signature from E ≥
300 MeV protons interactingwith ambient gas, and it is interesting that particles at these different energies show similarbehavior despite significantly different ranges.Support for this work was provided by NASA through an award issued by JPL/Caltech.N.I. and D.A.N. are funded by NASA Research Support Agreement No. 1393741 pro-vided through JPL. J.R.G. thanks the Spanish MINECO for funding support under grantsCSD2009-00038 and AYA2012- 32032. The authors thank Vincent Fish for providing digitalcopies of H i spectra from his 2003 paper, and the anonymous referee for insightful commentsand suggestions. HIFI has been designed and built by a consortium of institutes and univer-sity departments from across Europe, Canada and the United States under the leadershipof SRON Netherlands Institute for Space Research, Groningen, The Netherlands and withmajor contributions from Germany, France and the US. Consortium members are: Canada:CSA, U.Waterloo; France: CESR, LAB, LERMA, IRAM; Germany: KOSMA, MPIfR, MPS;Ireland, NUI Maynooth; Italy: ASI, IFSI-INAF, Osservatorio Astrofisico di Arcetri-INAF;Netherlands: SRON, TUD; Poland: CAMK, CBK; Spain: Observatorio Astronmico Na-cional (IGN), Centro de Astrobiologa (CSIC-INTA). Sweden: Chalmers University of Tech-nology - MC2, RSS & GARD; Onsala Space Observatory; Swedish National Space Board,Stockholm University - Stockholm Observatory; Switzerland: ETH Zurich, FHNW; USA:Caltech, JPL, NHSC. REFERENCES
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This preprint was prepared with the AAS L A TEX macros v5.2.
38 – Y ( k p c ) SgrAG327 W3 NGC 7538AFGL 2591DR21W31CW28AW33AG29G34 W49NW51eSgrB2NGC 6334 Locus of Tangent Points Solar Circle
Fig. 1.— Distribution of observed sight lines as viewed from the North Galactic Pole. Manysource names have been shortened for clarity. The Galactic center is located at (0,0), andthe Sun is assumed to be 8.34 kpc away (Reid et al. 2014). The blue solid curve shows thesolar circle, and the red dashed curve the locus of tangent velocities. Only the W49N line ofsight significantly samples both near and far kinematic distances, leading to severe blendingof absorption features arising in physically separated clouds. 39 – L i n e - t o - C o n t i n uu m R a t i o -250 -200 -150 -100 -50 0 50 100 LSR velocity (km s -1 ) +
971 GHzo-H O + O +
984 GHz
M-0.13-0.08 (Sgr A +20 km s -1 ) Fig. 2.— Single sideband normalized spectra toward M − − − cloud)showing transitions of OH + , H O + , and H O + . Stick diagrams above spectra show thehyperfine structure where applicable. Red curves are fits to the absorption features, andgreen curves show only the strongest hyperfine component of the fits. The vertical dashed linemarks the systemic velocity of the background source. Vertical axes give line-to-continuumratio, with labels alternating between the left and right sides for clarity. 40 – L i n e - t o - C o n t i n uu m R a t i o -250 -200 -150 -100 -50 0 50 100 LSR velocity (km s -1 ) +
971 GHzo-H O + M-0.02-0.07 (Sgr A +50 km s -1 ) p-H O +
631 GHzp-H O +
607 GHzH O +
984 GHz
Fig. 3.— Same as Figure 2 but for M − − − cloud). 41 – L i n e - t o - C o n t i n uu m R a t i o -200 -150 -100 -50 0 50 100 150 200 LSR velocity (km s -1 ) Sgr B2(M) H O +
984 GHzOH +
909 GHzOH +
971 GHzOH + O + O + Fig. 4.— Same as Figure 2 but for Sgr B2(M). In this case, however, fits shown by bluecurves were made by using absorption from all relevant transitions (e.g., 909 GHz, 971 GHz,and 1033 GHz transitions of OH + ) simultaneously. 42 – L i n e - t o - C o n t i n uu m R a t i o -200 -150 -100 -50 0 50 100 150 200 LSR velocity (km s -1 ) Sgr B2(N) H O +
984 GHzOH +
909 GHzOH +
971 GHzOH + O + O + Fig. 5.— Same as Figure 4 but for Sgr B2(N). 43 – L i n e - t o - C o n t i n uu m R a t i o LSR velocity (km s -1 ) W28A p-H O +
607 GHzo-H O + O +
984 GHzOH +
971 GHz
Fig. 6.— Same as Figure 2 but for W28A. 44 – L i n e - t o - C o n t i n uu m R a t i o LSR velocity (km s -1 ) +
971 GHzo-H O + W31C p-H O +
631 GHzp-H O +
607 GHzH O + O +
984 GHzOH +
909 GHz
Fig. 7.— Same as Figure 2 but for W31C. 45 – L i n e - t o - C o n t i n uu m R a t i o LSR velocity (km s -1 ) +
971 GHzo-H O + W33A p-H O +
631 GHzp-H O +
607 GHzH O +
984 GHz
Fig. 8.— Same as Figure 2 but for W33A. 46 – L i n e - t o - C o n t i n uu m R a t i o LSR velocity (km s -1 ) G029.96-00.02 p-H O +
607 GHzo-H O + O +
984 GHzOH +
971 GHzOH +
909 GHz
Fig. 9.— Same as Figure 2 but for G029.96 − L i n e - t o - C o n t i n uu m R a t i o LSR velocity (km s -1 ) +
971 GHzo-H O + G034.3+00.15 p-H O +
631 GHzp-H O +
607 GHzH O +
984 GHzOH +
909 GHz
Fig. 10.— Same as Figure 2 but for G034.3+00.15. 48 – L i n e - t o - C o n t i n uu m R a t i o LSR velocity (km s -1 ) +
971 GHzo-H O + W49N p-H O +
631 GHzp-H O +
607 GHzH O + O +
984 GHzOH +
909 GHz
Fig. 11.— Same as Figure 2 but for W49N. 49 – L i n e - t o - C o n t i n uu m R a t i o LSR velocity (km s -1 ) O +
631 GHz
W51e p-H O +
607 GHzo-H O + O +
984 GHzOH +
971 GHzOH +
909 GHz
Fig. 12.— Same as Figure 2 but for W51e. 50 – L i n e - t o - C o n t i n uu m R a t i o LSR velocity (km s -1 ) + O + O +
984 GHz
AFGL 2591
Fig. 13.— Same as Figure 2 but for AFGL 2591. 51 – L i n e - t o - C o n t i n uu m R a t i o LSR velocity (km s -1 ) DR21C p-H O +
607 GHzo-H O + O +
984 GHzOH +
971 GHzOH +
909 GHz
Fig. 14.— Same as Figure 2 but for DR21C. 52 – L i n e - t o - C o n t i n uu m R a t i o LSR velocity (km s -1 ) +
971 GHzo-H O + DR21(OH) p-H O +
631 GHzp-H O +
607 GHzH O +
984 GHz
Fig. 15.— Same as Figure 2 but for DR21(OH). 53 – L i n e - t o - C o n t i n uu m R a t i o -100 -80 -60 -40 -20 0 20 40 60 LSR velocity (km s -1 ) +
971 GHzOH + O + NGC 7538 IRS 1
Fig. 16.— Same as Figure 2 but for NGC 7538 IRS 1. 54 – L i n e - t o - C o n t i n uu m R a t i o -100 -80 -60 -40 -20 0 20 40 60 LSR velocity (km s -1 ) W3 IRS5 p-H O +
607 GHzo-H O + + +
971 GHz
Fig. 17.— Same as Figure 2 but for W3 IRS5. 55 – L i n e - t o - C o n t i n uu m R a t i o -100 -80 -60 -40 -20 0 20 40 60 LSR velocity (km s -1 ) W3(OH) p-H O +
607 GHzo-H O + O +
984 GHzOH +
971 GHzOH +
909 GHz
Fig. 18.— Same as Figure 2 but for W3(OH). 56 – L i n e - t o - C o n t i n uu m R a t i o -100 -80 -60 -40 -20 0 20 LSR velocity (km s -1 ) o-H O + +
971 GHz
G327.30-00.60
Fig. 19.— Same as Figure 2 but for G327.30 − L i n e - t o - C o n t i n uu m R a t i o LSR velocity (km s -1 ) o-H O + + NGC 6334 I
Fig. 20.— Same as Figure 2 but for NGC 6334 I. 58 – L i n e - t o - C o n t i n uu m R a t i o LSR velocity (km s -1 ) o-H O + + NGC 6334 I(N)
Fig. 21.— Same as Figure 2 but for NGC 6334 I(N). 59 – N Molecular Hydrogen Fraction
Fig. 22.— Distribution of f H as determined from our analysis of OH + and H O + abundances.The filled gray bars show all velocity intervals where f H is computed, and the red barsmark the distribution for velocity intervals within 5 km s − of the systemic velocity of thebackground source (i.e., that may be associated with material surrounding the continuumsource). 60 – M o l e c u l a r H y d r o g e n F r a c t i o n -17 -16 -15 -14 C o s m i c - R a y I o n i za t i o n R a t e , z H ( s - ) Fig. 23.— Top: Cosmic-ray ionization rate versus Galactocentric radius. Bottom: Molecularhydrogen fraction versus Galactocentric radius. Red diamonds denote velocity intervalswithin 5 km s − of the systemic velocity of the background source. Black squares denoteforeground clouds. Upper limits and lower limits are marked by arrows, and use the samecolor scheme denoting foreground versus background. Note there are 4 components, all inthe Galactic center, with f H > .
25, but we have scaled the axis to more clearly show theentire data set. 61 – N N -17.0 -16.0 -15.0 -14.0 log (z H ) z H from H z H from OH + and H O + Fig. 24.— Histogram of ζ H as determined from abundances of OH + and H O + (bottompanel) and from H +3 in diffuse clouds (top panel; Indriolo & McCall 2012, and unpublisheddata). In the bottom panel filled gray bars show all velocity intervals where ζ H is computed,and the red bars mark the distribution for velocity intervals within 5 km s − of the systemicvelocity of the background source (i.e., that may be associated with material surrounding thecontinuum source). In the top panel, only diffuse cloud sight lines where H +3 is detected havebeen used in creating the histogram of ionization rates. Over half of all sight lines observedsearching for H +3 resulted in non-detections; upper limits on the ionization rate range froma few times 10 − s − up to 10 − s − . 62 – -17 -16 -15 -14 C o s m i c - R a y I o n i za t i o n R a t e , z H ( s - ) N H (cm -2 ) Fig. 25.— Cosmic-ray ionization rate versus total hydrogen column density, N H . We haveestimated N H using values of N (H) and f H reported in Table 5. Black diamonds are fromthe present study, and grey squares from H +3 observation of Indriolo & McCall (2012). Allionization rates above 10 − s − are from sight lines toward the Galactic center. 63 –Table 1. Targeted Transitions Molecule Transition Rest Frequency E l /k g u g l A (MHz) (K) (10 − s − ) N ′ – N ′′ J ′ – J ′′ F ′ – F ′′ OH + + a + a + + + + + + a N ′ K ′ a K ′ c – N ′′ K ′′ a K ′′ c J ′ – J ′′ F ′ – F ′′ p -H O + –1 p -H O + –1 o -H O + –0 o -H O + –0 o -H O + –0 a o -H O + –0 o -H O + –0 o -H O + –0 o -H O + –0 o -H O + –0 o -H O + –0 a J ± K – J ∓ K H O + − − +1 O + − − +0 + data are fromBekooy et al. (1985). H O + data are from M¨urtz et al. (1998), but the frequencies for the transitions at1115 GHz have been shifted by +5 MHz. This shift provides the best match between o -H O + and OH + ab-sorption profiles in velocity space, and agrees with the findings of Neufeld et al. (2010). The H O + transitionfrequencies are from Yu et al. (2009). Energy level diagrams depicting the specific states studied herein areavailable for OH + (L´opez-Sepulcre et al. 2013), H O + (Schilke et al. 2010; Ossenkopf et al. 2010), and H O + (Verhoeve et al. 1988, 1989). a Indicates the strongest of the hyperfine transitions for a specific ∆ J which was used to set the velocityscale during our analysis.
64 –Table 2. Target List
Target Right Ascension Declination Gal. Long. Gal. Lat. Distance Ref.(hh:mm:ss.s) (dd:mm:ss.s) (deg) (deg) (kpc)M − − ∗ +20 km s − cloud] 17:45:37.4 − − − − ∗ +50 km s − cloud] 17:45:50.5 − − − − − − − − − − − − − − − − − − − − − − − ′′ , 22 ′′ , and 34 ′′ FWHM at 1100 GHz,950 GHz, and 600 GHz, respectively). Distance references are given below; unless otherwise noted, distance determinations arefrom trigonometric parallax.References: 1-Reid et al. (2014); 2-Ferri`ere (2012); 3-Reid et al. (2009); 4-Molinari et al. (2011); 5-Motogi et al. (2011); 6-Sanna et al. (2014); 7-Immer et al. (2013); 8-Zhang et al. (2014); 9-Fish et al. (2003, kinematic analysis); 10-Zhang et al. (2013);11-Sato et al. (2010); 12-Rygl et al. (2012); 13-Moscadelli et al. (2009); 14-Imai et al. (2000); 15-Hachisuka et al. (2006); 16-Urquhart et al. (2012, kinematic analysis); 17-Wu et al. (2014)
65 –Table 3. Double Side Band Continuum Level Antenna Temperature and RMS Noise
Source 909 GHz 971 GHz 1033 GHz 1115 GHz 607 GHz 631 GHz 984 GHz T A (DSB) T A (DSB) T A (DSB) T A (DSB) T A (DSB) T A (DSB) T A (DSB)(K) (K) (K) (K) (K) (K) (K)M − − ± ± ± − − ± ± ± ± ± a ± ± ± ± ± a ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± − ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± − ± ± ± ± ± ± a These two sight lines were observed in Spectral Scan Mode which produces a single sideband spectrum as the output dataproduct. To approximate the DSB antenna temperatures we have simply doubled the single sideband antenna temperatures.
Table 4. Derived column densities
Source v LSR range N (OH + ) N (OH + ) N (OH + ) N ( o -H O + ) N ( p -H O + ) N ( p -H O + ) H O + OPR H O + N (1 +0 )909 GHz 971 GHz 1033 GHz 1115 GHz 607 GHz 631 GHz 984 GHz(km s − ) (10 cm − ) (10 cm − ) (10 cm − ) (10 cm − ) (10 cm − ) (10 cm − ) (10 cm − )M − − > ± − − > ± − − > ± − − > ± < − − ± ± < − − > ± < − − a ... 20.77 ± ± ± − − a ... 1.96 ± ± < − − ± ± < < − − > ± ± ± ± − − > ± < < − − ± ± < < < − − > ± < < < − − ± ± < < < − − ± ± < < < − − ± ± < < < − − ± ± < < < − − a ... 14.21 ± ± < < ± ± ± ± ± ± ± ± a ... ... ... ... ... ... ... 7.02 ± ± ± ± ± a ... ... ... ... ... ... ... 12.57 ± a ... 2.19 ± ± < < a ... 1.27 ± ± < ± < < a < ± < < a ± ± ± < Table 4—Continued
Source v LSR range N (OH + ) N (OH + ) N (OH + ) N ( o -H O + ) N ( p -H O + ) N ( p -H O + ) H O + OPR H O + N (1 +0 )909 GHz 971 GHz 1033 GHz 1115 GHz 607 GHz 631 GHz 984 GHz(km s − ) (10 cm − ) (10 cm − ) (10 cm − ) (10 cm − ) (10 cm − ) (10 cm − ) (10 cm − )W31C [12, 24] 7.91 ± ± ± ± ± > ± < < ± > ± ± ± ± ± ± ± ± ± < ± < ± ± < < < ± ± < < < a ... 1.99 ± ± < < a ... 1.44 ± ± < − ± ± ± < < − ± ± ± < < − ± ± ± < < − ± ± < < < − ± ± ± < < − ± ± ± < < − ± ± ± < < − ± ± ± < < − ± ± ± < < − ± ± ± < < − ± ± ± < < − a ± ± ± < < − a ± ± ± < ± ± ± < < < ± ± ± < < < ± ± ± < < < ± ± ± < < < ± ± ± ± ± < a ± ± ± < ± ± < < < a ± ± ± < < a ± ± ± < ± > ± < ± > ± < ± ± ± ± < ± < Table 4—Continued
Source v LSR range N (OH + ) N (OH + ) N (OH + ) N ( o -H O + ) N ( p -H O + ) N ( p -H O + ) H O + OPR H O + N (1 +0 )909 GHz 971 GHz 1033 GHz 1115 GHz 607 GHz 631 GHz 984 GHz(km s − ) (10 cm − ) (10 cm − ) (10 cm − ) (10 cm − ) (10 cm − ) (10 cm − ) (10 cm − )W49N [51, 66] 11.59 ± > ± ± < ± < ± > ± < < ± ± ± ± < ± < ± ± ± < < < ± ± ± < < < ± ± ± < < < ± ± ± < < < a ± ± ± < a ± ± ± ± ± ± ± ± a ... ... 1.55 ± ± < a ... ... 8.65 ± ± < a ± ± ± < < a ± ± ± < < ± ± ± ± ± < a ... 1.58 ± ± < < < a ... 4.50 ± ± < ± ± < a ... 0.94 ± ± ± ± ± ± ± ± < ± ± ± ± ± ± a ... 0.63 ± ± ± ± ± ± ± ± ± < a ± ± ± < ± ± ± < ± ± ± < < − a ... 2.71 ± ± − a ... 1.16 ± ± − ± ± − ± ± Table 4—Continued
Source v LSR range N (OH + ) N (OH + ) N (OH + ) N ( o -H O + ) N ( p -H O + ) N ( p -H O + ) H O + OPR H O + N (1 +0 )909 GHz 971 GHz 1033 GHz 1115 GHz 607 GHz 631 GHz 984 GHz(km s − ) (10 cm − ) (10 cm − ) (10 cm − ) (10 cm − ) (10 cm − ) (10 cm − ) (10 cm − )G327.3 − ± ± a ... ... 0.47 ± ± a ... ... 1.83 ± ± ± ± a ... ... 1.68 ± ± ± ± + , H O + , and H O + are presented here. Because thetotal OH + and H O + column densities for Sgr B2(M) and Sgr B2(N) are determined by simultaneously fitting all available transitions, we do not report individualcolumn densities in those sight lines. Also shown are ortho -to- para ratios for H O + in cases where p -H O + is detected. For Sgr B2(M) ortho -to- para ratios aredetermined using the data from Schilke et al. (2013). Upper limits are given when absorption lines are not detected, and lower limits are given when the absorptionfeatures are saturated; both are reported at the 1 σ level. a Denotes velocity range within 5 km s − of the background source systemic velocity. Table 5. Total column densities and inferred results
Source v LSR range N (OH + ) N (H O + ) N (OH + ) /N (H O + ) N (H) R gal d f H ζ H (km s − ) (10 cm − ) (10 cm − ) (10 cm − ) (kpc) (kpc) (10 − s − )M − − > ± ≥ < < > − − > ± ≥ ± < > − − > ± ≥ ± < > − − > ± ≥ > < − − ± ± ± ± ± ± − − > ± ≥ ± < > − − a ± ± ± > ± < − − a ± ± ± > ± < − − ± ± ± ± − − > ± ≥ ± < > − − > ± ≥ ± < > − − ± ± ± ± ± ± − − > ± ≥ ± < > − − ± ± ± ± ± ± − − ± ± ± ± ± ± − − ± ± ± ± ± ± − − ± ± ± > ± < − − a ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± a ± ± ± > ± < ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± a ± ± ± > ± < a ± ± ± > ± < a ± ± ± ± ± ± ± < ≥ ± < . ≤ ζ H ≤ . a ± < ≥ > < < a ± ± ± > ± < ± ± ± ± ± ± Table 5—Continued
Source v LSR range N (OH + ) N (H O + ) N (OH + ) /N (H O + ) N (H) R gal d f H ζ H (km s − ) (10 cm − ) (10 cm − ) (10 cm − ) (kpc) (kpc) (10 − s − )W31C [24, 36] 9.97 ± ± ± > ± < ± ± ± > ± < ± ± ± ± ± ± ± ± ± > ± < ± ± ± > ± < a ± ± ± > ± < a ± ± ± > ± < − ± ± ± ± ± ± − ± ± ± ± ± ± − ± ± ± ± ± ± − ± < ≥ ± < . ≤ ζ H ≤ . − ± ± ± ± ± ± − ± ± ± ± ± ± − ± ± ± ± ± ± − ± ± ± ± ± ± − ± ± ± ± ± ± − ± ± ± ± ± ± − ± ± ± ± ± ± − a ± ± ± ± ± ± − a ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± > ± < ± ± ± ± ± ± ± ± ± ± ± ± a ± ± ± > ± < ± < ≥ ± < . ≤ ζ H ≤ . a ± ± ± ± ± ± a ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Table 5—Continued
Source v LSR range N (OH + ) N (H O + ) N (OH + ) /N (H O + ) N (H) R gal d f H ζ H (km s − ) (10 cm − ) (10 cm − ) (10 cm − ) (kpc) (kpc) (10 − s − )W51e [-4, 11] 3.25 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± a ± ± ± ± ± ± a ± ± ± ± ± ± ± ± ± > ± < a ± ± ± ± ± ± a ± ± ± ± ± ± a ± ± ± ± ± ± a ± ± ± > ± < ± ± ± > ± < a ± ± ± ± ± ± a ± ± ± > ± < ± ± ± > ± < a ± ± ± ± ± ± ± ± ± < ≥ < ± ± ± ± ± ± ± ± ± ± ± ± a ± ± ± > ± < ± ± ± ± ± ± ± ± ± ± ± ± a ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± − a ± ± ± > ± < − a ± ± ± ± ± ± − ± ± ± ± ± ± − ± ± ± ± ± ± − ± ± ± ± ± ± a ± ± ± > ± < a ± ± ± > ± < Table 5—Continued
Source v LSR range N (OH + ) N (H O + ) N (OH + ) /N (H O + ) N (H) R gal d f H ζ H (km s − ) (10 cm − ) (10 cm − ) (10 cm − ) (kpc) (kpc) (10 − s − )NGC 6334 I [1, 14] 1.84 ± ± ± ± ± ± a ± ± ± > ± < ± ± ± ± ± ± N (H) are as follows: Winkel et al. 2015 (in prep.)–Sgr B2(M), Sgr B2(N), W31C, W33A, G034.3+00.15, W49N, W51e, DR21C, DR21(OH);extracted from the Canadian Galactic Plane Survey (CGPS; Taylor et al. 2003) data (Winkel, private communication)–AFGL 2591, W3 IRS5, W3(OH); extractedfrom H i spectra in Fish et al. (2003)–W28A, G029.96 − i data cube in Lang et al. (2010)–M − − i optical depth in position 7 of Dwarakanath et al. (2004)–M − − i spectrum toward G111.61+0.37 in Lebr´on et al. (2001)–NGC 7538 IRS1; extracted from H i spectum in Urquhart et al. (2012)–G327.30 − ǫ = 0 .
07 (Indriolo et al. 2012). a Denotes velocity range within 5 km s − of the background source systemic velocity. Table A1. Observation IDs
Source Transition Obs IDsM − − +
971 GHz a − − O + − − O +
607 GHz 1342206354, 1342206355, 1342206356M − − O +
631 GHz 1342206351, 1342206352, 1342206353M − − +
971 GHz a − − O +
984 GHz 1342253697M − − O + − − O + +
909 GHz 1342206455Sgr B2(M) OH +
971 GHz a ,b O + c +
909 GHz 1342204829Sgr B2(N) OH +
971 GHz a ,b O + c O +
607 GHz 1342216832, 1342216833, 1342216834W28A OH +
971 GHz a O + O + O +
607 GHz 1342191575, 1342191576, 1342191577, 1342230391, 1342230392, 1342230393W31C H O +
631 GHz 1342191572, 1342191573, 1342191574W31C OH +
909 GHz 1342229777, 1342229778, 1342229779W31C OH +
971 GHz a O + O + O +
607 GHz 1342208052, 1342208053, 1342208054W33A H O +
631 GHz 1342208058, 1342208059, 1342208060W33A OH +
971 GHz a O + O + − O +
607 GHz 1342268573, 1342268574, 1342268575G029.96 − +
909 GHz 1342268594, 1342268595, 1342268596G029.96 − +
971 GHz a − O + O +
607 GHz 1342219278, 1342219279, 1342219280, 1342230372, 1342230373, 1342230374G034.3+00.15 H O +
631 GHz 1342219284, 1342219285, 1342219286
Table A1—Continued
Source Transition Obs IDsG034.3+00.15 OH +
909 GHz 1342242871, 1342242872, 1342242873G034.3+00.15 OH +
971 GHz a O + O + O +
607 GHz 1342194520, 1342194521, 1342194522, 1342230378, 1342230379, 1342230380W49N H O +
631 GHz 1342194514, 1342194515, 1342194516W49N OH +
909 GHz 1342244378, 1342244379, 1342244380W49N OH +
971 GHz a O + O + O +
607 GHz 1342219272, 1342219273, 1342219274, 1342268576, 1342268577, 1342268578W51e H O +
631 GHz 1342219269, 1342219270, 1342219271W51e OH +
909 GHz 1342268597, 1342268598, 1342268599W51e OH +
971 GHz a O + O + + O +
984 GHz 1342195019AFGL 2591 H O + O +
607 GHz 1342232699DR21C OH +
909 GHz 1342231441DR21C OH +
971 GHz a O + O +
607 GHz 1342199161, 1342199162, 1342199163DR21(OH) H O +
631 GHz 1342199155, 1342199156, 1342199157DR21(OH) OH +
971 GHz a O + O + +
971 GHz 1342227536NGC 7538 IRS1 OH + O + O +
607 GHz 1342201530, 1342201531W3 IRS5 OH +
971 GHz 1342227535W3 IRS5 OH + O + Table A1—Continued
Source Transition Obs IDsW3(OH) H O +
607 GHz 1342268579, 1342268580, 1342268581W3(OH) OH +
909 GHz 1342268497, 1342268498, 1342268499W3(OH) OH +
971 GHz a O + − +
971 GHz 1342227539G327.3 − O + Herschel ; PI–Ewine van Dishoeck) and HEXOS (
Herschel observations of EXtra-Ordinary Sources; PI–Ted Bergin) andthe open time programs OT1 dneufeld 1 (PI–David Neufeld), OT1 vossenko 4 (PI–Volker Ossenkopf), and OT1 cpersson 1 (PI–Carina Persson). a The H O + − –1 +0 transition at 984 GHz is also covered in this observation. b The OH + J ′ – J ′′ = 1–1 transition at 1033 GHz is also covered in this observation. c The o -H O + J ′ – J ′′ = 1 //