OH Survey along Sightlines of Galactic Observations of Terahertz C+
Ningyu Tang, Di Li, Carl Heiles, Nannan Yue, J. R. Dawson, Paul F. Goldsmith, Marko Kr?o, N. M. McClure-Griffiths, Shen Wang, Pei Zuo, Jorge L. Pineda, Jun-Jie Wang
aa r X i v : . [ a s t r o - ph . GA ] M a r Preprint typeset using L A TEX style emulateapj v. 12/16/11
OH SURVEY ALONG SIGHTLINES OF GALACTIC OBSERVATIONS OF TERAHERTZ C+
Ningyu Tang , Di Li , Carl Heiles , Nannan Yue , J. R. Dawson
5, 6 , Paul F. Goldsmith , Marko Krˇco , N. M.McClure-Griffiths , Shen Wang , Pei Zuo , Jorge L. Pineda and Jun-Jie Wang ABSTRACTWe have obtained OH spectra of four transitions in the Π / ground state, at 1612, 1665, 1667,and 1720 MHz, toward 51 sightlines that were observed in the Herschel project Galactic Observationsof Terahertz C+. The observations cover the longitude range of (32 ◦ , 64 ◦ ) and (189 ◦ , 207 ◦ ) in thenorthern Galactic plane. All of the diffuse OH emissions conform to the so-called ‘Sum Rule’ of thefour brightness temperatures, indicating optically thin emission condition for OH from diffuse cloudsin the Galactic plane. The column densities of the H i ‘halos’ N (H i ) surrounding molecular cloudsincrease monotonically with OH column density, N (OH), until saturating when N (H i ) = 1 . × cm − and N (OH) ≥ . × cm − , indicating the presence of molecular gas that cannot be traced byH i . Such a linear correlation, albeit weak, is suggestive of H i halos’ contribution to the UV shieldingrequired for molecular formation. About 18% of OH clouds have no associated CO emission (CO-dark)at a sensitivity of 0.07 K but are associated with C + emission. A weak correlation exists between C + intensity and OH column density for CO-dark molecular clouds. These results imply that OH seemsto be a better tracer of molecular gas than CO in diffuse molecular regions. Subject headings:
ISM: clouds — ISM: evolution — ISM: molecules. INTRODUCTION
The hydroxyl radical (OH) is a relatively abundant,simple hydride, and thus a potentially important probeof interstellar medium (ISM) structure. It was first de-tected in absorption against continuum sources (Wein-reb et al. 1963) and then in emission toward interstellardust clouds (Heiles 1968). A large number of studieshave revealed the widespread existence of OH through-out dense, dusty clouds (Turner & Heiles 1971; Turner1973; Crutcher 1977), high-latitude translucent clouds(Grossmann et al. 1990; Barriault et al. 2010; Cottenet al. 2012), and diffuse regions outside the CO-brightmolecular clouds (Wannier et al. 1993; Allen et al. 2012).Four 18 cm ground-state transitions of OH at 1612,1665, 1667, and 1720 MHz can be readily observed in Lband. Local thermodynamic equilibrium (LTE) was ini-tially considered to be valid for these four transitions(e.g., Heiles 1969). Under optically thin assumption,LTE implies the ratios T A (1612) : T A (1665) : T A (1667) : T A (1720) = 1 : 5 : 9 : 1. Subsequent observations re-vealed anomalies in satellite (1612, 1720 MHz) and main(1665, 1667 MHz) lines (e.g., Turner 1973; Guibert etal. 1978; Crutcher 1979). On-source absorption and off- National Astronomical Observatories, CAS, Beijing 100012,China; Email: [email protected], [email protected] University of Chinese Academy of Sciences, Beijing 100049,China Key Laboratory of Radio Astronomy, Chinese Academy ofScience Department of Astronomy, University of California, Berke-ley, 601 Campbell Hall 3411, Berkeley, CA 94720-3411 Department of Physics and Astronomy and MQ ResearchCentre in Astronomy, Astrophysics and Astrophotonics, Mac-quarie University, NSW 2109, Australia Australia Telescope National Facility, CSIRO Astronomyand Space Science, PO Box 76, Epping, NSW 1710, Australia Jet Propulsion Laboratory, California Institute of Technol-ogy, 4800 Oak Grove Drive, Pasadena, CA 91109, USA Research School for Astronomy & Astrophysics, AustralianNational University, Canberra, ACT 2611, Australia source emission observations toward continuum sourceshave been used to obtain the optical depth and excitationtemperature of each transition independently. The afore-mentioned surveys have found non-LTE gas with a typi-cal excitation temperature difference of | ∆ T ex | ∼ − , does not trace molecular gas well in re-gions with intermediate extinctions 0 . − . i -H transition regions, throughout this work.OH and C + are key initiators of the chemistry that leadsto CO in diffuse and translucent regions through the re-actions (van Dishoeck & Black 1988)C + + OH → CO + + H,CO + + H → HCO + + H,HCO + + e → CO + H.OH has been detected toward the outer shells, alsoreferred to as ‘halos’, of molecular clouds with low COabundances (e.g., Wannier et al. 1993; Allen et al. 2012),and clouds toward continuum sources (Li et al. 2015).In order to improve the understanding of the distri-bution of OH and of the ISM traced by OH, large andsensitive surveys of OH in diffuse gas are necessary. Thefirst “blind” survey of diffuse OH taken by Penzias (1964)was unsuccessful. Turner (1979) carried out OH surveynear Galactic plane with a sensitivity of 0.18 K. Thesurveys with high sensitivity (a few mK RMS) by Allenet al. (2012, 2015) covered regions ( l, b )=(108.0 ◦ , 5.0 ◦ )and (105.0 ◦ , 1.0 ◦ ) with the 25 m radio telescope of theOnsala Space Observatory and Green Bank telescope,respectively. The Southern Parkes Large-Area Survey inHydroxyl (SPLASH) covered ( l, b )=(334 ◦ -344 ◦ , -2 ◦ -2 ◦ )in a pilot region, and will cover l ranges of (332 ◦ , 10 ◦ ), | b | ≤ ◦ including some additional coverage of higher al-titude around the Galactic centre (Dawson, in prep). In Tang et al.these regions, observations of C + are not available.In this work, we adopted a more limited and focusedapproach by following up on Galactic Observations ofTerahertz C+ (GOTC+) survey (Langer et al. 2010;Pineda et al. 2013) with OH observations. With a dataset of the three important tracers of molecular gas, C + ,OH, and CO, we here examine their correlation and theirrelative efficiency in tracing molecular gas.This paper is organized as follows: In sections 2 and 3,we describe the observations and data reduction of OHand associated spectral data. In section 4 we show pro-cedures for gaussian decomposition and analysis of OH,H i , and CO column density. The results are presented insection 5. In section 6 we provide a discussion of OH col-umn density and atomic/molecular transition. In section7 we provide the conclusions from our study. OBSERVATIONS AND DATA
OH Observations
There are 92 sightlines of the GOTC+ project thatare covered by the Arecibo telescope. We chose observedsightlines based on the following three criteria: (1) if thesightline can be observed for at least half an hour, (2) ifthere exist “CO-dark” candidates toward the sightline,and (3) if there exist abundant H i self-absorption fea-tures, C + , and CO emission toward the sightline. Crite-ria (1) and (2) have higher priority. All sightlines satis-fying criteria (1) and (2) have been observed.In this survey, OH spectra toward 51 sightlines wereobtained. The positions of these sightlines covering 43points in the Galactic longitude range of (32 ◦ , 64 ◦ )(range A) and 8 points in the Galactic longitude rangeof (189 ◦ , 207 ◦ ) (range B) are shown in Figure 1.The OH observations were carried out with the Arecibotelescope in two periods, September 15th to November7th, 2014 and February 26th to March 3rd, 2015. The ob-servations were made with the Interim Correlator back-end with bandwidth of 3.125 MHz, providing a velocityresolution of 0.28 km s − at 1.66 GHz. The integra-tion time for each sightline was half an hour. To reducethe effect of radio frequency interference (RFI) and theinstability of the receiver and to avoid difficulty in choos-ing a clean “OFF” position, we developed an observationscript that changes the central reference velocity by 200km s − every 15 min. This is equivalent to frequencyswitching, which is not supported in Arecibo. CO Observations
Corresponding CO(1-0) and CO(1-0) observationswere made with the Delingha 13.7m telescope betweenMay 4th and 10th, 2016. The 13.7m telescope, locatedin northwestern China, has an angular resolution of 1arcmin (FWHP, Full Width at Half Power) at 115 GHz.The system temperature varied from 250 K to 360 Kwith a typical value of 300 K during the observations.The observations were taken using position switching.The total observation time per target was 30 min or 45min depending on the system temperature. The backendhas a 1 GHz bandwidth and 61 kHz spectral resolution,corresponding to a velocity resolution of 0.16 km/s at115.271 GHz.
Archival C + and H i Data C + data were obtained from the GOT C+ project(Pineda et al. 2013; Langer et al. 2014). The data havealready been smoothed into a channel width of 0.8 kms − with an average rms noise of 0.1 K.The H i data representing brightness temperature weretaken from the Galactic Arecibo L-band Feed Array H i (GALFA-H i ; Peek et al. 2011) with a noise level of 0.33K in a 0.18 km s − channel. DATA REDUCTION AND PROCESSING
Description of Data Reduction and Processing
The OH data were reduced with our IDL procedures.Scans with obvious RFI were firstly removed by checkingthe correlation map of the data. RFI was further checkedby comparing averaged spectra in two separate 15 minobservations. This is especially important for the 1612MHz spectra, which are significantly affected by RFI.After deriving the bandpass spectrum, we ignored theedges of the spectrum where gain of the bandpass variesand only fitted middle part of the spectrum. Spectralchannels with obvious OH lines were marked to avoidbeing included in the bandpass fit. Most of the band-pass spectra are flat and can be fitted with a first-orderpolynomial. The other spectra were fitted with higher-order polynomials. Weak OH emission/absorption lineswith wide velocity widths (full width at half maximum > − ) may be missed during this step. The finalnoise level is 35 mK in a 0.28 km s − channel.A main beam efficiency of 0.52 was used to transformCO antenna temperatures to main-beam brightness tem-peratures. The GILDAS software was used for baselinefitting and spectral smooth of CO data. The CO spectrawere smoothed to 0.32 km/s to reach a velocity reso-lution comparable to that of OH data. The final noiselevel of main-beam brightness temperature is ∼
70 mKfor CO(1-0) in 0.32 km s − and ∼
40 mK for CO(1-0)in 0.33 km s − channel width.The H i data were smoothed to a velocity resolution of0.36 km s − that is comparable to the velocity resolutionof OH and CO data. The rms noise level after smoothingis 0.23 K. Detection Statistics
With a rms of ∼
35 mK, the detection statistics ofthe 4 OH lines are displayed in Figure 1. OH emis-sion/absorption is detected in 44 of 51 sightlines. OHmain lines appear in 9 of 44 sightlines alone while OHsatellite lines appear in 2 of 44 sightlines alone.The detection rate of OH main and satellite lines variesdepending on their locations in the Galaxy. No OH satel-lite lines were detected in the outer Galaxy. Figure 1indicates that the detection rate of OH lines (includingboth the main and satellite lines) in the outer galaxyis 62.5%, much smaller than that of 93.0% in the innergalaxy. This is consistent with the fact that the amountof CO-bright molecular gas in the outer galactic plane issmaller than that in the inner galactic plane (e.g., Dameet al. 2001). Absorption features are commonly presentin OH main lines in the inner Galaxy even though thereis no H II region in the beam. But absorption features H Survey along Sightlines of Galactic Observations of Terahertz C+ 3
Fig. 1.—
Detection information toward observed 51 sightlines indifferent survey region. The top and bottom panel show sightlinesin the Galactic longitude range of (185 ◦ , 210 ◦ ) and (30 ◦ , 65 ◦ ),respectively. Circle, plus, and cross signs represent detection ofOH main lines, detection of OH satellite lines, and no detection,respectively. are absent in OH main lines in the outer Galaxy, indicat-ing a lower level of continuum background in the outergalaxy. ANALYSIS
Gaussian Decomposition
We developed an IDL script to decompose OH, C + andCO spectra. This script uses the classical nonlinear leastsquares technique, which utilizes analytically-calculatedderivatives, to iteratively solve for the least squares co-efficients. For each spectrum, the number of Gaussiancomponents was fixed. Initial guesses of each Gaussiancomponent were required. The decomposition resultswere then checked by eye.We fit the OH profiles first. In general, central ve-locities of the four OH lines should be the same for acloud. A switch from emission to absorption as a func-tion of velocity in OH satellite lines exists in some clouds.In these clouds, the central velocities of the main linesare the same as the cross points of the satellite lines.An example is shown in Figure 2 and discussed in Sec-tion 6.1. This always occurs in the clouds near H IIregions and can be explained by infrared pumping of the Π / J = 5 / + andCO data.Finally, 151 cloud components with OH emission orabsorption lines were identified. An example is shown inFigure 3. OH Column Density
The brightness temperature ratio between the 4 OHlines (T :T :T :T ) is 1:5:9:1 under assump-tions of LTE and optically thin emission (e.g., Robinson& McGee 1967). An anomalous ratio of OH lines thatdeviates from the 1:5:9:1 ratio cannot be explained byoptical depth effects. An OH anomaly implies non-LTEconditions leading to differential excitation of 4 OH lines.Satellite line anomaly is seen more often than main lineanomaly. The main line transitions occur between levels Fig. 2.—
An example of OH spectra that show clear flip ofsatellite lines. The dotted line represents the fitted gaussian cen-tral velocity of 1667 MHz, 13.2 km s − . This corresponds to thevelocity where the 1612 and 1720 MHz flips occur. with the same total angular momentum quantum number(F). For satellite lines, transitions occur between energylevels with different F, which are easily affected by non-thermal excitation (Crutcher 1977). Inversion of satellitelines is commonly seen without inversion of main lines(see Figures 2 and 3 for examples), making it difficult tocalculate the OH column density with satellite lines. Wethus calculated OH column densities only for clouds withmain line emission.The radiative transfer of the main lines in LTE can bewritten as T = F b ( T ex − T bg )(1 − e − τ / . ) , (1) T = F b ( T ex − T bg )(1 − e − τ ) , (2)where T and T are the brightness temperaturesof 1665 and 1667 MHz lines, respectively, F b is the beamfilling factor, T ex is the excitation temperature, and T bg isthe background continuum temperature at 1.6-1.7 GHz.In high latitude regions, T bg ∼ . ∼ . ∼ . ∼ . p c (0 < p c <
1) was utilized to derivecontinuum contribution behind OH cloud. With the as-sumption that the continuum contribution is uniformlydistributed along the sightline across the Milky Way, p c is represented as ( d sightline − d cloud ) /d sightline , in which d cloud is distance to OH cloud and d sightline is the sight-line length across the Milky Way. During the calcula-tions, we applied the Milky Way rotation curve in Brand Tang et al. Fig. 3.— H i , C + , CO, and OH spectra toward G036.4+0.0. Red solid lines are the gaussian fits to individual velocity component. & Blitz (1993) and a maximum galactocentric radius of16 kpc. The values of p c vary from 0.48 to 0.98 with amedian of 0.90. Finally, a correction of 3.1 K was addedback to derive T bg at 1.6-1.7 GHz. The uncertainties arediscussed in the end of this section.The OH column density N (OH) can be calculated withthe following two general equations (Turner & Heiles1971; Liszt & Lucas 1996) N (OH) = 4 . × cm − T ex T ex − T bg f τ f ex Z T mb (1665) dυ, (3) N (OH) = 2 . × cm − T ex T ex − T bg f τ f ex Z T mb (1667) dυ, (4)where T mb (1665) and T mb (1667) are the main beambrightness temperatures of the 1665 MHz and 1667MHz lines, respectively. f τ = R τ dυ/ R (1 − e − τ ) dυ is the correction factor for the optical depth τ of theOH transitions. The correction factor for T ex , f ex =( hν/kT ex ) / (1 − e − hν/kT ex ), approaches 1 when T ex ≫ .
08 K.In LTE, the ratio between brightness temperature ofmain lines ( R / = T /T ) varies between 1.8for optically thin conditions and 1.0 for infinite opticaldepth (Heiles 1969). When R / was in the rangeof [1.0, 1.8], the combination of equation 1 and equation2 can solve for T ex and τ simultaneously. Then T ex and τ can be inserted into equation 3 or 4 to solve forN(OH). Previous OH observations have revealed ubiqui-tous anomalies between excitation temperatures of themain lines. Non-LTE excitation can lead to ratios mim-icking LTE range (Crutcher 1979). Beside this, LTE cal- culations are limited by satisfaction of sum rule, whichimplies small optical depth as described in Section 5.1.The values of R / in 29 OH clouds are in theLTE range. As shown in Figure 4, the values of τ in 4 clouds are smaller than 0.5 with the LTE assump-tion. With consideration of satisfying sum rule implyingoptically thin as described in Section 5.1, we adoptedLTE calculation results for these 4 clouds. The methodfor non-LTE OH clouds in case 3 described below wasadopted to calculate OH column densities of the remain-ing 25 clouds. As shown in Figure 4, LTE assumptiongenerally leads to higher optical depth, τ LTE1667 > . N (OH) LTE > . × cm − than non-LTE assumption.We now consider the non-LTE cases. As shown inEquation 3 and 4, OH column density and its uncer-tainty are very sensitive to T ex through the function, g ( T ex ) = | T ex / ( T ex − T bg ) | . It would be ten times lowerfor g ( T ex ) = 1 than that of g ( T ex ) = 10. But there ex-ists a constraint on g ( T ex ) in order that OH be detectedwith our sensitivity as shown in Figure 5. It requires alarger deviation of T ex /T bg from 1 for small N (OH) tobe detected. Moreover, we are able to apply reasonableassumptions to different non-LTE cases. The followingcases are clearly non-LTE when we consider the mainlines (masers are ignored here).1) The existence of 1665 MHz line alone.2) The existence of 1667 MHz line alone.3) Both 1665 and 1667 MHz lines are present, but R / is out of the LTE range.H Survey along Sightlines of Galactic Observations of Terahertz C+ 5 Fig. 4.—
Comparison between LTE and non-LTE calculationsfor 29 clouds having LTE line ratios. N (OH) LTE and τ LTE1667 repre-sent total OH column density and optical depth of 1667 line usingthe LTE assumption, respectively. N(OH) represents total OH col-umn density using non-LTE assumption. The vertical dashed linerepresents N(OH)
LTE /N(OH) ratio of 1. The horizontal dashedline represents τ LTE1667 = 0 . In case 1, the existence of the 1665 MHz line alonewith the absence of the 1667 MHz line implies theequality between excitation and background temper-ature of 1667 line, T ex (1667) = T bg (1667). Previ-ous emission/absorption observations toward continuumsources revealed | T ex (1667) − T ex (1665) | ∼ . − T ex (1665) − T ex (1667) = ± | T ex (1665) / ( T ex (1665) − T bg (1665)) | = 6.0or 8.0 when T ex (1667) = 7 . T bg (1665) = T bg (1667) due to minor difference betweenthem.A similar strategy for calculations in case 2 wasadopted. We cannot exclude the possibility of a de-tection limit that leads to absence of 1665 MHz detec-tion in case 2, since 1665 MHz line is generally weakerthan 1667 MHz line. But the expected 1665 intensities( T A (1665) = 5 T A (1667) /
9) are greater than 3 σ rms in63% of case 2 clouds and are greater than 2 σ rms inall clouds of case 2. Thus the assumption of case 2 isreasonable. Uncertainties in case 1 and 2 are given with | T ex (1667) − T ex (1665) | in the range of [0.5, 2.0] K.The value of | T ex / ( T ex − T bg ) | for case 1 and case 2ranges from 4.3 to 11.5 with a median 7.04. We appliedthis median value for all calculations in case 3. The un-certainty in case 3 is given with | T ex / ( T ex − T bg ) | rangesof [4.3,11.5].The optically thin assumption was applied to cloudsunder non-LTE conditions. This assumption is reason-able because there is no deviation from the ‘sum rule’as presented in Section 5.1. During the calculation of N (OH) of case 1, equation 3 was employed. Equation 4was employed for cases 2 and 3.OH column densities of 117 clouds with main line emis-sion were calculated. N (OH) ranges from 1 . × cm − to 1 . × cm − with a median of 1 . × cm − . Fig. 5.—
Brightness temperature of the 1665 MHz line as a func-tion of the OH column density, N(OH), and the temperature factor T ex /( T ex - T bg ). Positive excitation temperature T ex was consid-ered, leading to temperature factor range of (- ∞ ,0) and (1, ∞ ).The two red vertical lines represent values of 0 and 1 for the tem-perature factor. A typical background continuum temperature of 8K and FWHM of 1.5 km s − in this survey were adopted, and op-tically thin condition was assumed. The grey shaded region coversthe parameter space within the 3 σ detection limit of 0.21 K. OHlines within that region cannot be detected in our survey. Whenwe zoom to the temperature factor in the range of [-0.06, 0.01] for N (OH) = 1 . × cm − , T mb approaches a constant value whenthe temperature factor approaches 0 as shown in the small plot. Compared to OH column densities in clouds previouslyobserved, this median value is about one order of mag-nitude larger than that determined explicitly throughon/off observations toward 3C 133 and is more than 3times the value in the W44 molecular cloud (Myers 1975;Crutcher 1979).Two main uncertainties exist in the above assumptionsof p c . The first originates from the distance ambiguityfor directions toward the inner Galaxy. For OH cloudsassociated with H i self absorption, near distance is pre-ferred (Jackson et al. 2002; Roman-Duval et al. 2009) aswe have adopted. For other OH clouds, the distance am-biguity leads to a maximum difference of p c between nearand far distance of 0.57. Only 17 OH clouds are affected.The deviation factor of N (OH) caused by the distanceambiguity ranges from 0.049 to 2.0 with a median of 1.6.The second uncertainty is the difference between three-dimensional distribution of radio continuum emissionover the entire Galaxy and the uniform distribution weassumed. Beuermann et al. (1985) reproduced a three-dimensional model of the galactic radio emission from408 MHz continuum map (Haslam et al. 1982), andfound exponentially decreasing distribution of emissiv-ities along galactic radius (4 kpc < R <
16 kpc) in thegalactic plane. We adopted the detailed radial distribu-tion in Fig. 6a of Beuermann et al. (1985). The differ-ences of p c varies from -0.01 to 0.24 with a median valueof 0.028. The deviation factor of N (OH) caused by three-dimensional model of radio emission ranges from 6 × − to 0.1 with a median value of 0.02. Thus the uncertaintyfrom three-dimensional model is much smaller than thatfrom intrinsic excitation temperature. H i Column Density H i permeates in the Milky Way. The H i spectrumincludes all H i contributions along a sightline and to- Tang et al.ward the Galactic plane is broad in velocity. It is diffi-cult to distinguish a single H i cloud without the help ofspecial spectral features, e.g., H i narrow self absorption(HINSA) against a warmer H i background (e.g., Gibsonet al. 2000; Li & Goldsmith 2003).The excitation temperature (T x ) and optical depth ( τ )of the HINSA cloud is essential for deriving the H i col-umn density for a cloud with a HINSA feature. Krˇcoet al. (2008) introduced a method of fitting the secondderivative of the H i spectrum to derive the backgroundspectrum and fitted τ HINSA of HINSA cloud. We com-bine the radiation transfer equations in Li & Goldsmith(2003) and the analysis method in Krˇco et al. (2008) forcalculation of N(H i ).We assume a simple three-body radiative transfer con-figuration with background warm H i gas, cold H i cloud,and foreground warm H i gas. The background H i spec-trum without absorption of cold H i cloud, T H i , is relatedto the observed spectrum in which continuum has beenremoved, T R through the following equation (see detailsof equation 8 in Li & Goldsmith (2003)), T H i = T R + ( T c − T k )(1 − τ f )(1 − e − τ )1 − p (1 − e − τ ) (5)where T c represents the background continuum temper-ature contributed by the cosmic background and theGalactic continuum emission, T k is the excitation tem-perature of the atomic hydrogen in the cold cloud, whichis equal to the kinetic temperature, τ is the optical depthof the cold cloud. τ f and τ b are the optical depths ofwarm H i gas in front and behind the HINSA cloud. Thetotal optical depth of warm H i gas along the line of sight, τ h = τ f + τ b . p is defined as the fraction of backgroundwarm H i , p = τ b /τ h . The value of p is calculated through p = Z behind Σ( r ) dr/ Z entire − LOS Σ( r ) dr, (6)where R behind Σ( r ) dr and R entire − LOS Σ( r ) dr are the inte-grated H i surface densities behind the HINSA cloud andalong the all line of sight. The surface density distri-bution in Nakanishi & Sofue (2003) and the Milky Wayrotation curve in Brand & Blitz (1993) were used for thiscalculation.We try to recover the background spectrum with Equa-tion 5 to fit the second derivative as that in Krˇco etal. (2008). Information on the kinetic temperature isneeded. HINSA features are pervasive in the Taurusmolecular cloud. Analysis of pixels with both CO and CO emission in this region reveals a kinetic tempera-ture in the range of [3,21] K, but concentrated in range of[6, 12] K. In most cases, we choose a fixed kinetic temper-ature of 12 K for CO that is widely used in molecularclouds (Goldsmith et al. 2008) and an initial HINSA op-tical depth of 0.1. The fitting result with a comparablethermal temperature of H i gas to 12 K was chosen, oth-erwise we modify the initial parameter, e.g., relax thekinetic temperature in the range of [6,15] K as a free pa-rameter. An example is shown in Figure 6. The HINSAcolumn density is given by the fitted τ and FWHM ofHINSA cloud, ∆ V by N (HINSA) = 1 . × τ ∆ V T k cm − , (7) Fig. 6.—
T op panel : HINSA spectrum at ∼ − alongG032.6+0.5. The observed H i spectrum ( T R ) and derived H i background spectrum ( T H i ) are represented by the black and redsolid lines, respectively. The dotted line shows the residual spec-trum. During the fitting, the kinetic temperature of CO was fixedat 12 K. The original and fitted optical depths are 0.1 and 0.31. Middle panel : Second derivatives of H i and H i background spec-tra. Bottom panel : Corresponding CO spectrum of HINSA. Thegreen vertical line marks the fitted central velocity of the HINSAcloud from CO. where T k is the kinetic temperature of the HINSA cloud.The HINSA column density depends on the value of thekinetic temperature, thus uncertainties are given fromkinetic temperature in the range of [6,15] K.HINSA traces the cold component of neutral hydrogenin a molecular cloud which may have a warm H i halo (An-dersson et al. 1991). We were able to determine H i col-umn density of the H i halo of molecular clouds with andwithout HINSA features through the H i spectra. Dueto the omnipresence of H i in the Galactic plane, we didnot apply gaussian decomposition to H i profiles withoutHINSA feature. We derived the column density of H i gas through the integrated H i intensity. The integratedH i intensity of recovered background spectrum was usedfor clouds with HINSA features. With the assumption oflow optical depth, the H i column density N (H i ) is givenby N (H i ) = 1 . × Z T b dυ cm − , (8)where the H i intensity is obtained through integratingthe velocity channels determined by OH lines. The effectof adopting different velocity widths of H i is discussed inSection 5.2.1. N (H i ) derived using this method is lim-ited by the optically thin assumption, the intensity con-tribution from clouds in neighboring velocities, and H i absorption features corresponding to OH emission lines(e.g., Li & Goldsmith 2003).The HINSA column density, N (HINSA) derived in 52clouds ranges from 8 . × cm − to 4 . × cm − with a median value of 8 . × cm − , which is 1/36of the median N (H i ) of the H i halos of these clouds.The median N (HINSA) is consistent with that derivedin HINSA survey outside the Taurus Molecular CloudComplex, log ( N HINSA )=18.8 ± CO Column Density
H Survey along Sightlines of Galactic Observations of Terahertz C+ 7Six masks are defined for different detection cases.They are shown in Table 1. When CO, CO were de-tected simultaneously (mask 3 and 6 in Table 1), theclouds should be dense molecular gas. In this case, COis assumed to be optically thick with τ ≫ T , theexcitation temperature of CO, is given by T = 5 . { ln[1 + 5 . T + 0 .
819 ] } − , (9)where T is the brightness temperature of CO.The total column density of CO, N COtot , is given by(Qian et al. 2012) N COtot = 3 . × Z T K dυ km s − f u f τ f b f beam cm − , (10)where T is the brightness temperature of CO. f τ = R τ dυ/ R (1 − e − τ ) dυ is the correction factor of τ ,the optical depth of CO(1 − τ is given by τ = − ln(1 − T T ) , (11)in which τ ≫ T = T are adopted. Theseare reasonable when the excitation is dominated by colli-sions. The Galactic distribution of C / C ratio derivedfrom synthesized observations of CO,CN, and H CO inMilam et al. (2005) was adopted to convert N ( CO) to N ( CO), C / C = 6 . GC +18 .
71, where D GC is dis-tance to the Galactic center. We adopted the Milky Wayrotation curve of Brand & Blitz (1993) to derive D GC .Velocity dispersions and non-circular motions (Clemens1985) are expected to affect the calculations of D GC withan uncertainty of < ∼
1% in C / C.For clouds with detection of only CO (masks 2 and5 in Table 1), it is difficult to determine N (CO) withoutobservations of higher lines, e.g., CO(2-1). With the as-sumption that CO is optically thin, we derive a lowerlimit. Adoption of a 3 σ detection of the CO will givean upper limit to the column density. Combining thesetwo facts, we adopted the average value of upper limitand lower limit for N ( CO). Under the optically thinassumption, the total column density of CO can beexpressed as N COtot = 3 . × Z T b K dυ km s − f u f τ f b f beam cm − , (12)where T b is the brightness temperature, f u = Q ( T ex ) /g u exp( − hν/kT ex ) is the level correction factor, f τ = R τ dυ/ R (1 − e − τ ) dυ is the correction factor ofopacity and f τ = 1 was adopted under optically thin con-dition, f b = 1 / [1 − ( e hν/kT ex − / ( e hν/kT bg − f beam is the beam fillingfactor of the cloud (assumed to be 1.0).A common excitation temperature of T ex = 12 K inmolecular regions (e.g., Taurus molecular cloud; Gold-smith et al. 2008) was adopted during the calculation. Q ( T ex ) ≈ T ex / .
76 K is the partition function. g u rep-resents the degeneracy of the upper transition level and equals 3 for CO(1-0) transition. τ is the opacity of the CO(1-0) transition. τ ≪ N ( CO) by a factor of ∼ τ = 5. T bg is the background brightness temperature,adopted to be 2.73 K.A 3 σ upper limit on CO of 0.12 K was adopted inequations 10 and 11 for calculation of the upper limit to N ( CO).The column density of CO ranges from 2 . × cm − to 1 . × cm − with a median value of 6 . × cm − . The median value of N ( CO) for clouds withboth CO and CO emission is 9 . × cm − , whichis ∼
11 times that in clouds with CO emission alone. RESULTS
Sum Rule of Brightness Temperature
Robinson & McGee (1967) presented a brightness tem-perature ‘sum rule’, which relates the intensities of thefour OH ground-state transitions under the assumptionsof small optical depths, a flat background continuumspectrum, and T ex ≫ .
08 K. The ‘sum rule’ is, T b (1612) + T b (1720) = T b (1665) / T b (1667) / . (13)Diffuse OH emission and absorption in the pilot regionof SPLASH survey followed this relation, (where “dif-fuse” OH is defined as signal from the extended molec-ular ISM, in which maser action is either absent or veryweak). Similar to Dawson et al. (2014), we found no devi-ation from the ‘sum rule’ by more than 3 σ for all diffuseOH emission and absorption. An example is shown inFigure 7.According to Appendix A, the ‘sum rule’ is valid foroptically thin condition despite the existence of strongdifferences between the excitation temperatures of fourOH lines. The deviation from the ‘sum rule’ is domi-nated by the opacity of OH lines. No deviation from the‘sum rule’ confirms the validity of the optically thin as-sumption that has been used for calculation in Section4.2.Maser amplification, which indicates strong non-LTEbehavior and large optical depth, leads to deviation fromthe ‘sum rule’ as shown in Figure 7. Based on this fact,the ‘sum rule’ can be used as a filter for finding masercandidates. Comparison between Different Lines H i is the tracer of atomic gas while CO is a tracerof molecular gas. C + emission traces both atomic andmolecular gas. All OH clouds have associated H i emis-sion. Spectra of these lines toward G036.4+0.0 are shownin Figure 3. The statistics of clouds with C + and COemission corresponding to OH are listed in Table 1. C + and CO are present in 45% and 80% of all the OH clouds,respectively. We present a detailed comparison betweencolumn density of H i , CO line and intensity of C + linewith N (OH) in the following sections. Comparison between OH and H i data There exist uncertainties in both the OH and H i data.Thus we adopt the IDL procedure f itexy.pro for fitting,which considers uncertainties in both x and y directions(corresponding to logN(OH) and logN(H i ), respectively) Tang et al. Fig. 7.—
Top panel: residual spectrum representing T b (1612) + T b (1720) − T b (1665) / − T b (1667) /
9. The 1 σ and 3 σ levels ofthe spectrum are indicated by in dashed and dash-dotted lines,respectively. Significant deviations are present for the peaks around64 km s − and 90 km s − , which represent an evolved stellar maserassociated with the infrared source IRAS 18510+0203. Bottompanel: OH spectra for G035.1+0.5 are displayed as solid lines withdifferent colors. TABLE 1Summary of detections of all 151 OH clouds.
Mask OH C + 12 CO CO Number a HINSA b √ x x x 17 12 √ x √ x 17 53 √ x √ √
50 244 √ √ x x 10 15 √ √ √ x 9 26 √ √ √ √
48 16 a The number of clouds in each mask. b The number of HINSA detection in each mask. during linear least-squares fitting. The value of the fittedslope is larger than that when x error is not consideredduring fitting (see Table 2 for comparison).As shown in Table 2, the linear fit forclouds with HINSA in Figure 8 is expressed as,log N (H i )=0 . +0 . − . log N (OH)+15 . +3 . − . . The valueof the slope is 0.20 with an uncertainty of 0.20, indi-cating a weak correlation. The linear fit for H i halois log N (H i )=1 . +0 . − . log N (OH) + 4 . +0 . − . . Thevalue of the slope is 1.0 with an uncertainty of 0.028,indicating a strong correlation. These results show thatthe correlation between OH and warm H i is better thanthat between OH and HINSA. This seems to conflictwith the fact that cold H i rather than warm H i is mixedwith molecular gas (e.g., Goldsmith & Li 2005). Theexplanation may be in part the following.1) Goldsmith & Li (2005) studied local dark clouds notin directions toward the Galactic plane. There wasthus little velocity ambiguity for these observations.In the present study of sightlines along the Galacticplane, the OH velocity width was used for calculat-ing N (H i ) for H i halo gas. This may produce a biastoward apparent correlation.We note that the velocity width for the H i halo is al-ways larger than that of molecular tracers, e.g., CO.But no strong correlation between them is found (An- dersson et al. 1991). Lee et al. (2012) comparedcorrelation between derived N (H i ) with different H i widths and 2MASS extinction, finding the best cor-relation between H i emission and extinction at 20km s − around the CO velocities. The width is muchlarger than linewidth found for CO, OH, and H i self-absorption, making such a correlation suspicious. Thelogic here almost runs in a circle if one tries to studythe behavior of H i associated H by only looking at thevelocity range best associated with H . The analysistoward clouds in the Galactic plane is more compli-cated. Firstly, the extinction along a sightline repre-sents sum of all clouds in this sightline. Secondly, thebrightness temperature in velocity range of a molec-ular cloud would be diluted by extended emission ofother clouds in this sightline. Thus, we adopted theOH velocity range to calculate H i column density ofto examine the possible H i halo around our targets.2) Two correlations with contrary behavior exist be-tween HINSA and OH. Firstly, HINSA content hasa positive correlation with increasing molecular cloudsize, which can be represented by N(OH). Secondly, H i is depleted to form H , leading decreasing N(HINSA)as the proportion of OH increases. If these two factorsare comparable, the absence of correlation betweenHINSA column density and OH column density is ex-pected.A feature in Figure 8 is that N (H i ) trends to saturateat 1 . × cm − when N (OH)) & . × cm − . Asimilar feature is seen in Spider and Ursa Major cirrusclouds, where the asymptotic value of N (H i ) is 5 × cm − when N (OH) > . × cm − (Barriault etal. 2010). The asymptotic values of N (H i ) between thisstudy and Barriault et al. (2010) are consistent but thecritical value of N (OH) in this paper is larger by twoorders of magnitude. This asymptotic behavior impliesthat the mass of H i halo will be same for different cloudswhen the molecular core is large enough. This behavioralso implies that a portion of molecular gas may be notwell traced by H i in the halo. Comparison between OH and CO data
The OH column densities are compared with CO col-umn densities in Figure 9. There is no obvious correla-tion between N ( CO) and N (OH). A possible reasonfor this is that OH may reveal larger fraction of molec-ular gas than CO, e.g., the “CO-dark” gas component,the fraction of which can reach 0.3 even in CO emissionclouds (Wolfire et al. 2010).The ratio between CO and OH column density, N (CO)/ N (OH) varies from 3.7 to 1 . × with a me-dian value of 59 for clouds with both CO and COemission. It varies from 0.81 to 52 with a median valueof 7.1 for clouds with only CO emission. These resultsconfirm that OH will be depleted to form CO, resulting inlarger N (CO)/ N (OH) ratios in more massive molecularclouds. Comparison between OH and C + Emission
The C + µ m fine-structure transition is sensitiveto column density, volume density, and kinetic temper-ature of H i and H , making it difficult to determine C + H Survey along Sightlines of Galactic Observations of Terahertz C+ 9
TABLE 2Fitting information in Figure 8 (ID 1 and 2) and Figure 10 (ID 3).
ID Parameters Category Fitted slope a Fitted intercept a Fitted slope (SLLS) b i ) vs N(OH) H i halo 1.05 ± ± ± i ) vs N(OH) HINSA 0.20 ± ± ± + ) vs N(OH) CO-dark 0.63 ± ± ± a Fitted slope and intercept considering uncertainties in both X and Y coordinates. b Fitted slope with standard linear least-square (SLLS) method when X error is not considered.
Fig. 8.— H i column density, N (H i ) in HINSA and H i halo versusOH column density, N (OH). Integrated emission spectra were usedto derive N (H i ) in H i halo. The two red solid lines show linear fitfor two category of samples. column density based on present data. We adopted C + intensity rather than C + column density as a parameterfor comparison. C + emission can be produced by bothphoton-dominated regions (PDRs) and the ionized gasin H ii regions. The average ratio of C + emission fromH ii and PDRs in IC 342 is 70:30 (R¨ollig et al. 2016).This fact is included in estimating the uncertainty of C + intensity. We compared the relation between I(C + ) andN(OH) in CO-dark clouds (mask 4) and molecular clouds(mask 5 and 6).The clouds were divided into two categories, CO-brightand CO-dark. As seen in Figure 10, no correlation wasfound between I (C + ) and N (OH) for CO-bright cate-gory. But this comparison is limited by the large un-certainty in the C + data and the fact that C + tracesboth atomic and molecular components. For the CO-dark category, the fitted slope is 0 . ± .
46 (Table 2)with fitted Chi-squre χ = 1 .
84, indicating a linear cor-relation. Based on the fact that C + is a good tracer ofH in not well-shielded gas (e.g., Pineda et al. 2013), thecorrelation is consistent with the suggestion that OH isa better trace of H than CO in diffuse clouds, thoughthe sample size is small. DISCUSSION
OH Column Density
Crutcher (1979) found that OH column density is
Fig. 9.—
Comparison of N ( CO) with N (OH) on a log-logscale for 100 clouds. The green filled circles represent 24 OH cloudswith CO emission alone. The blue filled squares represent 76 OHclouds with both CO and CO emission. Solid, dotted, dashed,and dash dotted lines represent N (CO)/ N (OH) values of 1, 15,225, and 3375, respectively. The error bars of N ( CO) for cloudswith CO detections represent upper and lower limits. For cloudswith detections of both CO and CO, statistical uncertaintiesof the CO spectrum are given. The uncertainty of N (OH) is thesame as that described in Figure 8. proportional to the extinction following N (OH) /A V ≈ × cm − mag − in A V within the range of 0.4–7 mag, which implies OH/H ≈ × − . The mini-mum value of N (OH) found in this study is 1 . × cm − , which corresponds to an extinction of 2.3 mag.If the N (OH) /A V relation extends to higher extinction,the maximum and median N (OH) values would corre-spond to 138 mag and 24 mag. The value of 24 magis comparable to the largest extinction in Taurus cloud(Pineda et al. 2010) while the value of 138 mag requiresmore dense gas. One possible reason is that the valueof N (OH) /A V is larger than 8 × cm − mag − when A V > N (OH).Some satellite lines of OH show ‘flip’ feature invertingfrom emission to absorption at a velocity. An example isshown in Figure 2. This feature can be interpreted withoverlap of infrared transition of OH and implies a tran-sition column density of N OH / ∆V ≈ cm − km − s,where ∆V is the full width at half-maximum of OH line(e.g., Crutcher 1977; Brooks & Whiteoak 2001). These‘flip’ features were found in three clouds of this survey.The values of N(OH) for ‘flip’ feaure in these clouds canbe derived. To compare the results that derived with0 Tang et al. Fig. 10.—
Comparison of C + intensity with OH column densities on a log-log scale for 54 clouds. Statistical uncertainty of C + spectrumis shown in error bar of C + intensity. The uncertainty in N (OH) is the same as that described in Figure 8. Left : Forty-seven CO-brightclouds with CO emission are indicated by green filled circles.
Right : Seven CO-dark clouds without CO emission are indicated by bluecircles. The red solid line represents a linear fit to these clouds.
TABLE 3OH column density for three clouds with ‘flip’ of satellitelines.
Sightline V lsr ∆V N(OH) non − LTE a N(OH) flip b km s − km s − cm − cm − G033.8-0.5 11.0 1.3 0 . +0 . − . . +4 . − . . +0 . − . a N(OH) calculated with non-LTE method in Section 4.2. b N(OH) calculated with N OH ≈ ∗ ∆V cm − . non-LTE assumption in Section 4.2, we listed calculated N (OH) with two different methods in Table 3. The re-sults are consistent within a factor of 2.5, confirming thevalidity of our calculation of N (OH) in Section 4.2. CO-dark Molecular Gas and Atomic/MolecularTransition
A large fraction of molecular gas is expected to exist inthe transition region between the fully molecular CO re-gion and the purely atomic H i region. The molecular gasin this region, which is called the “CO-dark moleculargas” (DMG), cannot be traced by CO, but is associatedwith ions or molecules that are precursors of CO forma-tion. C + and OH are two of them. One example of aDMG cloud is shown around a velocity of 41.9 km s − in Figure 3. There exist OH and C + emission withoutcorresponding CO detections with a sensitivity of 0.07K. Twenty seven DMG clouds, which comprise 18% ofall OH clouds, are identified as shown in Table 1. Thisfraction is smaller than that of ∼ . ∼ . + is the main reservoir of carbon in diffuse gas. Itconverts to CO quickly through C + -OH chemical reac-tions once OH is formed (e.g., van Dishoeck & Black1988). Thus C + and OH are expected to have a tightcorrelation. As shown in Figure 10, a I (C + )- N (OH) cor-relation may exist for DMG clouds but not for all clouds.The atomic to molecular transition occurs in the DMGregion. Though HINSA other than warm H i gas is asso-ciated with molecular formation, the H i halo outside theDMG region provides shielding from UV radiation. Theasymptotic value of N (H i ), 1 . × cm − in Figure 8,corresponding visual extinction A V of 0.5 mag, approach-ing extinction A V = 0 . − , which hasa large self-shielding coefficient and can be the dominantform of hydrogen even when A V > .
02 mag (Wolfire etal. 2010). Thus a large fraction of DMG will exist beforeabundant CO formation. CONCLUSIONS
We have obtained OH spectra of four 18 cm lines to-ward 51 GOT C+ sightlines with the Arecibo telescope.Using Gaussian decomposition, we identified 151 OHcomponents. A combined analysis of OH, CO,H i , andHINSA reveals the following results.1) OH emission is detected in both main and satellitelines in the inner Galactic plane but is only detectedin the main lines in the outer galaxy. A large frac-tion of detected main lines show absorption featuresin the inner galaxy but no OH absorption feature wasfound in the outer galaxy. This is in agreement withH Survey along Sightlines of Galactic Observations of Terahertz C+ 11more molecular gas and a higher level of continuumbackground emission being present in the inner galaxythan in the outer galaxy.2) There is no deviation from the ‘sum rule’ by morethan 3 σ for all of the detected diffuse OH emission,suggesting small opacities of OH lines for clouds inthe Galactic plane.3) The H i column density N (H i ) in the H i cloud halos has an obvious correlation withthe OH column density N (OH) followinglog N (H i )=1 . +0 . − . log N (OH) + 4 . +0 . − . . N (H i )reaches an asymptotic value of 1 . × cm − when N (OH) > . × cm − .4) No correlation was found between the cold H i columndensity N (HINSA) from H i narrow self-absorptionfeature and N (OH).5) N (OH)/ N (CO) ratios are ten times lower in translu-cent clouds with only CO detection than in denseclouds with both CO and CO detections. Thisconfirms that OH is depleted to form CO. No corre-lation between N (OH) and N (CO) was found.6) A weak correlation was found between C + intensity I (C + ) and N (OH) for CO-dark molecular clouds.This is consistent with OH being better tracer of H in diffuse molecular clouds as C + traces H well in not well-shielded gas. No correlation was found for I (C + )and N (OH) for CO-bright molecular clouds. ACKNOWLEDGMENTS
We thank anonymous referee for significantly improv-ing this paper by pointing out uncertainties that hadbeen missed. This work is supported by InternationalPartnership Program of Chinese Academy of SciencesNo.114A11KYSB20160008, the Strategic Priority Re-search Program “The Emergence of Cosmological Struc-tures” of the Chinese Academy of Sciences, Grant No.XDB09000000, National Natural Science Foundation ofChina No. 11373038, and National Key Basic ResearchProgram of China ( 973 Program ) 2015CB857100, theChina Ministry of Science. This work was carried outin part at the Jet Propulsion Laboratory, which is oper-ated for NASA by the California Institute of Technology.M. K. acknowledges the support of Special Funding forAdvanced Users, budgeted and administrated by Cen-ter for Astronomical Mega-Science, Chinese Academy ofSciences (CAMS). N. M. M.-G. acknowledges the sup-port of the Australian Research Council through grantFT150100024. The Arecibo Observatory is operated bySRI International under a cooperative agreement withthe National Science Foundation (AST-1100968), andin alliance with Ana G. M´endez-Universidad Metropoli-tana, and the Universities Space Research Association.CO data were observed with the Delingha 13.7m tele-scope of the Qinghai Station of Purple Mountain Obser-vatory. We appreciate all the staff members of the Del-ingha observatory and Zhichen Pan for their help duringthe observations.
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DERIVATION OF SUM RULE
The column densities of upper and lower levels of each transition, N i and N j , are related by N i N j = g i g j e − hν/kT ij (A1)where T exij is the excitation temperature of OH transition line, N i and N j are partition weight the OH transition, and g i and g j are the statistical weights of i and j levels, respectively. For OH lines, g = 2 F + 1, where F is the totalangular momentum quantum number. The transition of 1612 MHz gives N N = g ( F = 1) g ( F = 2) e − hν /kT . (A2) N and N are upper and lower level of 1612 MHz line as shown in Figure 11.Similarly, N N , N N , and N N are derived from 1665, 1667, and 1720 MHz transitions, respectively. Considering the factthat N N × N N = N N × N N , we have ν T + ν T = ν T + ν T . (A3)The optical depth τ ν at frequency ν is given by τ ν = c π A ij ν N i ( e hν ij /kT ij − φ ( ν ) . (A4)With hν ij /kT ij ≪ ν ij T ij = 8 πc kh ν A ij N i Z τ ν dν. (A5)When most OH molecules are in the ground state of Π / ( J = 3 / N OH , is sum ofmolecules in four energy levels, N OH = N + N + N + N =16 / N =16 / N . R τ ν dν = τ peak ν ∆ V / .
93, where τ peak ν ispeak optical depth and ∆ V is full width at half maximum of transition line. Combining equations A3, equation A5,and values of four OH transition coefficients, we derive τ + τ = τ / τ / , (A6)where τ , τ , τ ,and τ are peak optical depth of four OH transitions. The only requirement for Equation A6is hν ij /kT ij ≪
1. Thus Equation A6 is valid even for non-LTE conditions.The brightness of emission line, T b , is calculated through T b = ( T ex − T bg )(1 − e − τ ), where T bg is backgroundcontinuum temperature, τ is optical depth of transition line. When T ex − T bg is the same for the four OH lines, whichis valid under LTE conditions, we derive the ‘sum rule’ for brightness temperature under optically thin conditions T b (1612) + T b (1720) = T b (1665) / T b (1667) / . (A7)To estimate the contribution of non-LTE and optical depth leading to deviation from Equation A7, we plot deviationfraction and maximum optical depth of OH as function of T ex (1665) and N (OH) in Figure 12. The deviation from thesum rule (DSR) is significant when N (OH) ≥ . × cm − . In this parameter space with significant deviation, theoptical depth of OH lines τ max (OH) is greater than 0.5. We conclude that the condition of large optical depth resultsin significant DSR.H Survey along Sightlines of Galactic Observations of Terahertz C+ 13 N N N N Fig. 11.—
Energy levels responsible for the OH lines. This figure is reproduced from Dawson et al. (2014).
Fig. 12.—
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