Dust-Gas Scaling Relations and OH Abundance in the Galactic ISM
Hiep Nguyen, J. R. Dawson, M.-A. Miville-Deschênes, Ningyu Tang, Di Li, Carl Heiles, Claire E. Murray, Snežana Stanimirović, Steven J. Gibson, N. M. McClure-Griffiths, Thomas Troland, L. Bronfman, R. Finger
DDraft version May 31, 2018
Preprint typeset using L A TEX style emulateapj v. 12/16/11
DUST-GAS SCALING RELATIONS AND OH ABUNDANCE IN THE GALACTIC ISM
Hiep Nguyen , J. R. Dawson , M.-A. Miville-Deschˆenes , Ningyu Tang , Di Li , Carl Heiles , Claire E.Murray , Sneˇzana Stanimirovi´c , Steven J. Gibson , N. M. McClure-Griffiths , Thomas Troland , L.Bronfman , R. Finger Draft version May 31, 2018
ABSTRACTObservations of interstellar dust are often used as a proxy for total gas column density N H . Bycomparing Planck thermal dust data (Release 1.2) and new dust reddening maps from Pan-STARRS1 and 2MASS (Green et al. 2018), with accurate (opacity-corrected) H i column densities and newly-published OH data from the Arecibo Millennium survey and 21-SPONGE, we confirm linear corre-lations between dust optical depth τ , reddening E ( B − V )and the total proton column density N H in the range (1–30) × cm − , along sightlines with no molecular gas detections in emission. Wederive an N H / E ( B − V ) ratio of (9.4 ± × cm − mag − for purely atomic sightlines at | b | > ◦ ,which is 60% higher than the canonical value of Bohlin et al. (1978). We report a ∼
40% increase inopacity σ = τ / N H , when moving from the low column density ( N H < × cm − ) to moderatecolumn density ( N H > × cm − ) regime, and suggest that this rise is due to the evolution of dustgrains in the atomic ISM. Failure to account for H i opacity can cause an additional apparent rise in σ , of the order of a further ∼ N H fromour derived linear relations, and hence derive the OH/H abundance ratio of X OH ∼ × − for allmolecular sightlines. Our results show no evidence of systematic trends in OH abundance with N H in the range N H ∼ (0.1 − × cm − . This suggests that OH may be used as a reliable proxy forH in this range, which includes sightlines with both CO-dark and CO-bright gas. Subject headings:
ISM: clouds — ISM: molecules — ISM: dust, reddening, extinction. INTRODUCTION
Observations of neutral hydrogen in the interstellarmedium (ISM) have historically been dominated by tworadio spectral lines: the 21 cm line of atomic hydrogen(H i ) and the microwave emission from carbon monox-ide (CO), particularly the CO(J=1–0) line. The for- Department of Physics and Astronomy and MQ Re-search Centre in Astronomy, Astrophysics and Astrophoton-ics, Macquarie University, NSW 2109, Australia. Email: [email protected] Australia Telescope National Facility, CSIRO Astronomyand Space Science, PO Box 76, Epping, NSW 1710, Australia Institut d’Astrophysique Spatiale, CNRS, Univ. Paris-Sud,Universit´e Paris-Saclay, Bˆat. 121, 91405, Orsay Cedex, France Laboratoire AIM, Paris-Saclay, CEA/IRFU/DAp - CNRS -Universit´e Paris Diderot, 91191, Gif-sur-Yvette Cedex, France National Astronomical Observatories, CAS, Beijing 100012,China Key Laboratory of Radio Astronomy, Chinese Academy ofScience University of Chinese Academy of Sciences, Beijing 100049,China Department of Astronomy, University of California, Berke-ley, 601 Campbell Hall 3411, Berkeley, CA 94720-3411 Space Telescope Science Institute, 3700 San Martin Drive,Baltimore, MD 21218, USA Department of Astronomy, University of Wisconsin-Madison, 475 North Charter Street, Madison, WI 53706, USA Department of Physics and Astronomy, Western KentuckyUniversity, Bowling Green, KY 42101, USA Research School of Astronomy and Astrophysics, AustralianNational University, Canberra, ACT 2611, Australia Department of Physics and Astronomy, University of Ken-tucky, Lexington, Kentucky 40506 Departamento de Astronom´ıa, Universidad de Chile, Casilla36, Santiago de Chile, Chile Astronomy Department, Universidad de Chile, Camino ElObservatorio 1515, 1058 Santiago, Chile mer provides direct measurements of the warm neutralmedium (WNM), and the cold neutral medium (CNM)which is the precursor to molecular clouds. The latteris widely used as a proxy for molecular hydrogen (H ),often via the use of an empirical ‘X-factor’, (e.g. Bolattoet al. 2013). The processes by which CNM and molec-ular clouds form from warm atomic gas sows the seedsof structure into clouds, laying the foundations for starformation. Being able to observationally track the ISMthrough this transition is of key importance.However, there is strong evidence for gas not seen ineither H i or CO. This undetected material is often called“dark gas”, following Grenier et al. (2005). These au-thors found an excess of diffuse gamma-ray emission fromthe Local ISM, with respect to the expected flux due tocosmic ray interactions with the gas mass estimated fromH i and CO. Similar conclusions have been reached usingmany different tracers, including γ -rays (e.g. Abdo et al.2010, Ackermann et al. 2012, Ackermann et al. 2011),infra-red emission from dust (e.g. Blitz et al. 1990; Reachet al. 1994; Douglas & Taylor 2007; Planck Collaborationet al. 2011, 2014a), dust extinction (e.g. Paradis et al.2012; Lee et al. 2015), C ii emission (Pineda et al. 2013;Langer et al. 2014; Tang et al. 2016) and OH 18 cm emis-sion and absorption (e.g. Wannier et al. 1993; Liszt &Lucas 1996; Barriault et al. 2010; Allen et al. 2012, 2015;Engelke & Allen 2018).While a minority of studies have suggested that cold,optically thick H i could account for almost all the miss-ing gas mass (Fukui et al. 2015), CO-dark H is generallyexpected to be a major constituent, particularly in theenvelopes of molecular clouds (e.g. Lee et al. 2015). Indiffuse molecular regions, H is effectively self-shielded, a r X i v : . [ a s t r o - ph . GA ] M a y Hiep Nguyen et al. (2018)but CO is typically photodissociated (Tielens & Hollen-bach 1985a,b; van Dishoeck & Black 1988; Wolfire et al.2010; Glover & Mac Low 2011; Lee et al. 2015; Glover& Smith 2016), meaning that CO lines are a poor tracerof H in such environments. Indeed Herschel observa-tions of C ii suggest that between 20–75% of the H inthe Galactic Plane may be CO-dark (Pineda et al. 2013).For the atomic medium, the mass of warm H i can becomputed directly from measured line intensities underthe optically thin assumption. However, cold H i withspin temperature T s (cid:46) i absorption and emission profilesobserved towards (and immediately adjacent to) bright,compact continuum background sources. Such studiesfind that the optically thin assumption underestimatesthe true H i column by no more than a few 10% alongmost Milky Way sightlines (e.g. Dickey et al. 1983, 2000,2003; Heiles & Troland 2003a,b; Liszt 2014a; Lee et al.2015), although the fraction missed in some localised re-gions may be much higher (Bihr et al. 2015).Since dust and gas are generally well mixed, absorp-tion due to dust grains has been widely used as a proxyfor total gas column density. Early work (e.g. Savage &Jenkins 1972, Bohlin et al. 1978) observed Lyman- α andH absorption in stellar spectra to calibrate the relation-ship between total Hydrogen column density N H , andthe color excess E ( B − V ). Similar work was carried outby comparing X-ray absorption with optical extinction, A V (Reina & Tarenghi 1973, Gorenstein 1975). Bohlinet al’s value of N H / E ( B − V )=5.8 × cm − mag − hasbecome a widely accepted standard.Dust emission is also a powerful tool, and requiresno background source population. The dust emissionspectrum in the bulk of the ISM peaks in the FIR-to-millimeter range, and arises mostly from large grainsin thermal equilibrium with the ambient local radiationfield (Draine 2003, Draine & Li 2007). It has long beenrecognized that FIR dust emission could potentially be abetter tracer of N H than H i and CO (de Vries et al.1987,Heiles et al.1988, Blitz et al.1990, Reach et al. 1994).An excess of dust intensity and/or optical depth above alinear correlation with N H (as measured by H i and CO)is typically found in the range A V =0.3 − can exist.Alternative explanations cannot be definitively ruled out,however. These include (1) the evolution of dust grainsacross the gas phases; (2) underestimation of the totalgas column due to significant cold H i opacity; (3) in-sufficient sensitivity for CO detection. It has also beenimpossible to rule out remaining systematic effects in the Planck data or bias in the estimate of τ introduced bythe choice of the modified black-body model.In this study, we examine the correlations betweenaccurately-derived H i column densities and dust-basedproxies for N H . We make use of opacity-corrected H i column densities derived from two surveys: the AreciboMillennium Survey (MS, Heiles & Troland 2003b, here-after HT03), and 21-SPONGE (Murray et al. 2015), bothof which used on-/off-source measurements towards ex-tragalactic radio continuum sources to derive accurate physical properties for the atomic ISM. We also make useof archival OH data from the Millennium Survey, recentlypublished for the first time in a companion paper, Li et al.(2018). OH is an effective tracer of diffuse molecular re-gions (Wannier et al. 1993; Liszt & Lucas 1996; Barriaultet al. 2010; Allen et al. 2012, 2015; Xu et al. 2016; Li et al.2018), and has recently been surveyed at high sensitivityin parts of the Galactic Plane (Dawson et al. 2014; Bihret al. 2015). There exists both theoretical and obser-vational evidence for the close coexistence of interstellarOH and H . Observationally, they appear to reside inthe same environments, as evidenced by tight relationsbetween their column densities (Weselak & Kre(cid:32)lowski2014). Theoretically, the synthesis of OH is driven bythe ions O + and H +3 but requires H as the precursor;once H becomes available, OH can be formed efficientlythrough the charge-exchange chemical reactions initiatedby cosmic ray ionization (van Dishoeck & Black 1986).Here we combine H i , OH and dust datasets to obtain newmeasurements of the abundance ratio, X OH = N OH / N H – a key quantity for the interpretation of OH datasets.The structure of this article is as follows. In Section2, the observations, the data processing techniques andcorrections on H i are briefly summarized. In Section 3,the results from OH observations are discussed. Section4 discusses the relationship between τ , E ( B − V ) and N H in the atomic ISM. We finally estimate the OH/H abundance ratio in Section 5, before concluding in Sec-tion 6. DATASETS
In this study, we use the all-sky optical depth( τ ) map of the dust model data measured byPlanck/IRAS (Planck Collaboration et al. 2014a – here-after PLC2014a), the reddening E ( B − V ) all-sky mapfrom Green et al. (2018), H i data from both the 21-SPONGE Survey (Murray et al. 2015) and the Millen-nium Survey (Heiles & Troland 2003a, HT03), OH datafrom the Millennium Survey (Li et al. 2018), CO datafrom the Delingha 14m Telescope, the Caltech Submil-limeter Observatory (CSO) and the IRAM 30m telescope(Li et al. 2018). H i and OH H i data from the Millennium Arecibo 21-CentimeterAbsorption-Line Survey (hereafter MS) was taken to-wards 79 strong radio sources (typically S (cid:38) √ i columndensity, N HI (scaled as described below), and use the off-source (expected) MS emission profiles to compute theust-Gas Scaling Relations 3H i column density under the optically thin assumption, N ∗ HI , where required. We compute OH column densitiesourselves, as described in Section 3. All OH emission andabsorption spectra are scaled to a main-beam tempera-ture scale using a beam efficiency of η b =0.5 (Heiles et al.2001), appropriate if the OH is not extended comparedto the Arecibo beam size of 3 (cid:48) .In order to increase the source sample, we also use H i data from the Very Large Array (VLA) 21-SPONGE Sur-vey, which observed 30 continuum sources, including 16in-common with the Millennium Survey sample (Mur-ray et al. 2015). 21-SPONGE used on-source absorp-tion data from the VLA, combining them with off-sourceemission profiles observed with Arecibo. Murray et al.(2015) report an excellent agreement between the opticaldepths measured by the two surveys, demonstrating thatthe single dish Arecibo absorption profiles are not signifi-cantly contaminated with resolved 21 cm emission. Notethat in this work we have used an updated scaling ofthe 21-SPONGE emission profiles, which applies a beamefficiency factor of 0.94 to the Arecibo spectra. The to-tal number of unique sightlines presented in this workis therefore 93. The locations of all observed sources inGalactic coordinates are presented in Figure 1. Wheresources were observed in both the MS and 21-SPONGE,we use the MS data. H i Intensity Scale Corrections
We check our N ∗ HI against the Leiden-Argentine-Bonnsurvey (LAB, Hartmann & Burton 1997; Kalberla et al.2005) and the HI4PI survey (HI4PI Collaboration et al.2016). Both are widely regarded as a gold standardin the absolute calibration of Galactic H i . We findthat the optically thin column densities derived from 21-SPONGE are consistent with LAB and HI4PI. However,the MS values are systematically lower than both LABand HI4PI by a factor of ∼ N HI may in fact be obtained from the tabulated valuesof HT03, with no need to perform a full reanalysis ofthe data. For warm components, the tabulated values of N HI are simply scaled by 1.14 – appropriate since thesewere originally computed directly from the the integratedoff-source (expected) profiles under the optically thin as-sumption. For cold components, we recall that the ra-diative transfer equations for the on-source and off-source(expected) spectra in the MS dataset are given by: T ONB ( v ) = ( T bg + T c ) e − τ v + T s (1 − e − τ v ) + T rx (1) T OFFB ( v ) = T bg e − τ v + T s (1 − e − τ v ) + T rx , (2)where T OFFB ( v ) and T ONB ( v ) are the main beam tempera-tures of the off-source spectrum and on-source spectrum,respectively. T s is the spin temperature, τ v is the opticaldepth, T rx is the receiver temperature ( ∼
25 K), and T c isthe main-beam temperature of the continuum source, ob-tained from the line-free portions of the on-source spec- trum. T bg is the continuum background brightness tem-perature including the 2.7 K isotropic radiation fromCMB and the Galactic synchrotron background at thesource position. Equations (1) and (2) may be solved for τ v and T s : e − τ v = T ONB ( v ) − T OFFB ( v ) T c , (3) T s = T OFFB ( v ) − T bg e − τ v − T rx − e − τ v . (4)From Equation (3), it is clear that optical depth is un-changed by any rescaling, which will affect both thenumerator and denominator of the expression identi-cally. Only T s must be recomputed. This is doneon a component-by-component basis from the tabu-lated Gaussian fit parameters for peak optical depth, τ ,peak brightness temperature (scaled by 1.14), and thelinewidth ∆ v . The corrected N HI is obtained from N HI [10 cm − ] = 1 . · τ · T s [ K ] · ∆ v [km s − ] , (5)where the factor 1.94 includes the usual constant 1.8224and the 1.065 arising from the integration over the Gaus-sian line profile. N HI vs N ∗ HI We show in Figure 2 the correlation between N HI and N ∗ HI towards all 93 positions. While opti-cally thin H i column density is comparable with thetrue column density in diffuse/low-density regions with N HI (cid:46) × cm − , opacity effects start to become ap-parent above ∼ × cm − .If a linear fit is performed to the data, the ra-tio f = N HI / N ∗ HI may be described as a function oflog( N ∗ HI /10 ) with a slope of (0.19 ± ± N ∗ HI data with T s ∼
144 K also yields a good agree-ment with our datapoints, as illustrated in Figure 2 (seealso Liszt 2014b). This approach also better fits the low N HI plateau, N HI < × cm − , below which N ∗ HI ≈ N HI .While a single component with a constant spin temper-ature is a poor physical description of interstellar H i , itcan provide a reasonable (if crude) correction for opacity. CO As described in Li et al. (2018), a CO follow-up surveywas conducted towards 44 of the sightlines considered inthis work. The J=1–0 transitions of CO, CO, andC O were observed with the Delingha 13.7m telescopein China. CO(J=2–1) data for 45 sources and J=3–2data for 8 sources with strong CO emission were takenwith the 10.4m CSO on Mauna Kea, with further supple-mentary data obtained by the IRAM 30m telescope. Inthis work we use CO data solely to identify and excludefrom some parts of the analysis positions with detectedCO-bright molecular gas – comprising 19 of the 44 ob-served positions. These positions are identified in Figure1. Hiep Nguyen et al. (2018) −9 −6 −3 Fig. 1.—
Locations of all 93 sightlines considered in this study, overlaid on the map of dust optical depth τ . Squares show H i absorption detections (93/93); red circles show OH absorption detections (19/72) and black circles non-detections (51/72); red trianglesshow CO detections (19/44) and black triangles non-detections (25/44). For purely atomic sightlines (those with no molecular detectionat the threshold discussed in Section 4), the squares are colored red. Note that the absence of a symbol indicates that the sightline wasnot observed in that particular tracer. The labeled sightline towards 3C132 (far left) shows the single position detected in H i and OH butnot detected in CO emissions. The “X” marker labels the center of the Milky Way. Note that the symbols for a small number of sightlinesentirely overlap due to their proximity on the sky. N HI [10 cm − ] N H I / N ∗ H I N HI (ON / OFF method from MS & 21 − SPONGE)Same as black, but for the 34 atomic sightlinesN HI (T s ∼ Fig. 2.—
The ratio f = N HI / N ∗ HI as a function of opacity-corrected N HI along 93 sightlines from the MS and 21-SPONGEsurveys. Circles show accurate N HI obtained via on- and off-source observations (HT03; scaled as described in the text),with the 34 atomic sightlines (selection criteria described in Sec-tion 4) filled grey and all other points filled black. Red tri-angles show N HI obtained from N ∗ HI assuming a single isother-mal component of T s ∼
144 K. The vertical dashed line is plot-ted at N HI =5 × cm − , the horizontal dashed line marks where N HI = N ∗ HI . Dust
To trace the total gas column density N H we usepublicly-available all-sky maps of the 353 GHz dust opti-cal depth ( τ ) from the Planck satellite. The τ mapwas obtained by a modified black-body (MBB) fit to thefirst 15 months of 353, 545, and 857 GHz data, togetherwith IRAS 100 micron data (for details see PLC2014a). The angular resolution of this dataset is 5 arcmin. Inthis work we use the R1.20 data release in Healpix for-mat (G´orski et al. 2005). For dust reddening, we em-ploy the newly-released all-sky 3D dust map of Greenet al. (2018) at an angular resolution of 3 (cid:48) .4-13 (cid:48) .7, whichwas derived from 2MASS and the latest Pan-STARRS1 data photometry. In contrast to emission-based dustmaps that depend on the modeling of the temperature,optical depth, and the shape of the emission spectrum,in maps based on stellar photometry reddening valuesare more directly measured and not contaminated fromzodiacal light or large-scale structure. Here we convertthe Green et al. (2018) Bayestar17 dust map to E ( B − V )by applying a scaling factor of 0.884, as described in thedocumentation accompanying the data release . OH DATA ANALYSIS
The Millennium Survey OH data consists of on-sourceand off-source ‘expected’ spectra for each of the OH lines.In our companion paper Li et al. (2018), we use themethod of HT03 to derive OH optical depths, excitationtemperatures and column densities. Namely, we obtainsolutions for the excitation temperature, T ex , and τ viaGaussian fitting (to both the on-source and off-sourcespectra) that explicitly includes the appropriate treat-ment of the radiative transfer. In the present work weuse a simpler channel-by-channel method for the deriva-tion of T ex . http : //healpix.sourceforge.net http://argonaut.skymaps.info/usage ust-Gas Scaling Relations 5The radiative transfer equations for the on-source andoff-source (expected) spectra are identical to those for H i ,given above in Equations (1) and (2). All terms and theirmeanings are identical, with the exception that the spintemperature, T s is replaced by T ex . T bg is the contin-uum background brightness temperature including the2.7 K isotropic radiation from CMB and the Galacticsynchrotron background at the source position. For con-sistency with HT03 and Li et al. (2018), we estimate thesynchrotron contribution at 1665.402 MHz and 1667.359MHz from the 408 MHz continuum map of Haslam et al.(1982), by adopting a temperature spectral index of 2.8,such that T bg = 2 . T bg , ( ν OH / − . , (6)resulting in typical values of around 3.5 K. The back-ground continuum contribution from Galactic HII re-gions may be safely ignored, since the continuum sourceswe observed are either at high Galactic latitudes orGalactic Anti-Center longitudes. Thus, in line-free por-tions of the off-source spectra: T OF F B ( v ) = T bg + T rx . (7)In the absence of information about the true gas distri-bution, we assume that OH clouds cover fully both thecontinuum source and the main beam of the telescope.We may therefore solve equations (1) and (2) to derive T ex and τ v for each of the OH lines, as shown in Equa-tions (3) and (4) for the case of H i .We fit each OH opacity spectrum (cf. Equation 3) witha set of Gaussian profiles to obtain the peak optical depth( τ ,n ), central velocity ( v ,n ) and FWHM (∆ v n ) of eachcomponent, n . Equation (4) is then used to calculate ex-citation temperature spectra. Examples of e − τ v , T OFFB ,and T ex spectra are shown in Figure 3, together withtheir associated Gaussian fits. It can be seen that the T ex spectra are approximately flat within the FWHM ofeach Gaussian component. We therefore compute an ex-citation temperature for each component from the mean T ex in the range v ,n ± ∆ v/ τ and T ex values obtained fromour method with those of Li et al. (2018), demonstrat-ing that the two methods generally return consistent re-sults. Minor differences arise only for the most com-plex sightlines through the Galactic Plane (G197.0+1.1,T0629+10) where the spectra are not simple to ana-lyze; however, even these points are mostly consistentto within the errors.We compute total OH column densities, N OH , inde-pendently from both the 1667 and 1665 MHz lines via: N OH , [10 cm − ] = 2 . · τ · T ex , [ K ] · ∆ v [km s − ] , (8) N OH , [10 cm − ] = 4 . · τ · T ex , [ K ] · ∆ v [km s − ] , (9)where the constants include Einstein A-coefficients of A = 7 . × − s − and A = 7 . × − s − for the OH main lines (Destombes et al. 1977). Allvalues of τ , T ex and N OH are tabulated in Table 1. Fig. 3.—
Example of OH 1667 MHz e − τ v (top), expected T OFFB (middle), and T ex (bottom) spectra for the source P0428+20. TheFWHM of the Gaussian fits to the absorption profile are used todefine the range over which T ex is computed for each component,shown as white regions in the bottom panel. − − τ Li(2018) − − τ T ex Li(2018) [K] T e x [ K ] Fig. 4.—
Comparison between derived values of the peak opticaldepth τ (left panel), and T ex (right panel) for both OH main lines,1667 MHz (black) and 1665 MHz (gray), as obtained from ourcompanion paper by Li et al. (2018) and the present work. Thedashed lines mark where the two values are equal. DUST-BASED PROXIES FOR TOTAL NEUTRAL GASCOLUMN DENSITY
In this section we will investigate the correlations be-tween dust properties and the total gas column den-sity N H . Specifically, we consider dust optical depth at353 GHz, τ , and reddening, E ( B − V ), with datasetssourced as described in Section 2.3. When these quanti-ties are used as proxies for N H , a single linear relationshipbetween the measured quantity and N H is typically as-sumed. In this work, our H i dataset provides accurate(opacity-corrected) atomic column densities, while com-plementary OH and CO data allow us to identify andexclude sightlines with molecular gas (dark or not). We Hiep Nguyen et al. (2018)
22 23 24282930 τ [ − ]
197 198 199−16−15−14
189 190 191−28−27−26
38 39 40171819
22 23 24282930 E ( B − V )[ m a g ]
197 198 199−16−15−14 189 190 191−28−27−26 38 39 40171819
Fig. 5.—
Example maps of the immediate vicinity of 4 “purely atomic” sightlines towards background radio sources. Dust maps (3 × τ , Nside = 2048) and Green et al. 2018 ( E ( B − V ), Nside= 1024). The “X” markers show the locations of the radio sources. The contours represent the integrated intensity W CO(1 − from theall-sky extension to the maps of Dame et al. (2001) (T. Dame, private communication). The base level is at 0.25 K kms − , the typicalsensitivity of CfA CO survey, and the other contour levels are evenly spaced from the base to the maximum in each map area. Equivalentmaps for the remaining 30 purely atomic sightlines are given in Appendix A and 19 OH-bright sightlines in Appendix B. are therefore able to measure τ / N H and E ( B − V )/ N H along a sample of purely atomic sightlines for which N H is very well constrained.In the following, we consider 34/93 sightlines to be“purely atomic”. These are defined as either (a) sight-lines where CO and OH were observed and not de-tected in emission (16/93); or (b) sightlines where COwas not observed but OH was observed but not de-tected (18/93 sightlines). In both cases we require thatOH be undetected in the 1667 MHz line to a detectionlimit of N OH < × cm − (see Li et al. 2018), whichexcludes some positions with weaker continuum back-ground sources. We may confidently assume that thesesightlines contain very little or no H , and note that allbut one of them lie outside the Galactic plane ( | b | > ◦ ).Figure 5 shows example maps of the immediate vicinityof 4 of these sightlines in τ and E ( B − V ). Identicalmaps for the remaining 30 atomic sightlines, as well asall 19 sightlines with OH detections (see also Section 5),are shown in the appendices.In all following subsections, N H is therefore taken to beequal to N HI , the opacity-corrected H i column density, asderived along sightlines with no molecular gas detectedin emission. N H from dust optical depth τ We adopt the all-sky map of dust optical depth τ computed by PLC2014a. This was derived from a MBBempirical fit to IRAS and Planck maps at 3000, 857, 545and 353 GHz, described by the expression: I ν = τ B ν ( T dust ) (cid:16) ν (cid:17) β dust . (10)Here, τ , dust temperature, T dust , and spectral index, β dust , are the three free parameters, and B ν ( T dust ) is thePlanck function for dust at temperature T dust which is, inthis model, considered to be uniform along each sightline(see PLC2014a for more details). The relation between dust optical depth and total gas column density can thenbe written as: τ = I B ( T dust ) = κ rµm H N H = σ N H , (11)where σ is the dust opacity, κ is the dust emissivitycross-section per unit mass (cm g − ), r is the dust-to-gasmass ratio, µ is the mean molecular weight and m H isthe mass of a hydrogen atom.Figure 6 shows the correlation between N H and τ .A tight linear trend can be seen with a Pearson co-efficient of 0.95. The value of σ from the orthog-onal distance regression (Boggs & Rogers 1990) linearfit is (7.9 ± × − cm H − (the intercept is set to0), where the quoted uncertainties are the 95% confi-dence limits estimated from pair bootstrap resampling.This is consistent to within the uncertainties with thatobtained by PLC2014a based on all-sky H i data fromLAB, (6.6 ± × − cm H − . Note that here we havequoted the PLC2014a measurement made towards low N HI positions, because the lack of any H i opacity cor-rection in that work makes this value the most reliable.However, our fit is consistent with all of σ values pre-sented in that work (which was based on the PlanckR1.20 data release), to within the quoted uncertainties.Small systematic deviations from the linear fit, evidentat the high and low column density ends of the plot, arediscussed further in § N H along the 34 atomic sightlines, we estimateupper limits on N H from the 3 σ OH detection limits us-ing an abundance ratio of X OH =10 − (see Section 5).These values are tabulated in Table 1, and the resultingupper limits on N H are shown as gray triangles in Figure6. As expected, the σ obtained from the fit to theseupper limits is lower, at (6.4 ± × − cm H − . How-ever, while some molecular gas may indeed be present atlow levels, these limits should be considered as extremeust-Gas Scaling Relations 7upper bounds on the true molecular column density. Thisis particularly true for the most diffuse sightlines withthe lowest column density ( N HI < × cm − ), wherethe observational upper limits may appear to raise N H by up to ∼ N H [10 cm − ] τ [ − ] Linear fitPLC2014aFukui et al. (2015)Upper limit with N H from OH detection limits Fig. 6.— τ vs N H along the 34 purely atomic sightlines de-scribed in the text. Grey triangles indicate the upper limits for N H along these 34 atomic sightlines with N H estimated from the 3 σ OH detection limits using an abundance ratio N OH / N H =10 − .The thick solid line shows the linear fit to the data in this work,the dotted-line shows the conversion factor derived by PLC2014a,and the dashed line shows the conversion factor derived by Fukuiet al. (2015). (Note that all these works use the same τ map). τ error bars are from the uncertainty map of PLC2014a; theshaded region represents the 95% confidence intervals for the lin-ear fit, estimated from pair bootstrap resampling. We next compare our results with the dust opacity σ derived by Fukui et al. (2015) (plotted on Figure 6 as adashed line). These authors derived a smaller value thanin the present work (by a factor of ∼ i . They then applied this factor tothe Planck τ map (excluding | b | < ◦ and CO-brightsightlines) to estimate N HI , assuming that the contri-bution from CO-dark H was negligible. This resultedin N HI values ∼ i exists than isusually assumed. However, we find that while the σ ofFukui et al. (2015) may be a good fit to some sightlinesin the very low N HI regime ( (cid:46) × cm − ), it overes-timates N HI at larger column densities by ∼ σ is not expectedto remain constant as dust evolves. This (combinedwith some contribution from CO-dark H ) may recon-cile the apparent discrepancy between their findings andabsorption/emission-based measurements of the opacity-corrected H i column. N H [10 − cm − ] E ( B − V ) [ − m a g ] Linear fitUpper limit with N H from OH detection limits Fig. 7.—
Correlation between N H and dust reddening E ( B − V )from Green et al. (2018) along 34 atomic sightlines. Grey trian-gles indicate the upper limits for N H along these 34 atomic sight-lines, with N H estimated from the 3 σ OH detection limits usingan abundance ratio N OH / N H =10 − . The errorbar on E ( B − V )along each sightline is the standard deviation of the 20 MarkovChain realisations of E ( B − V ) at infinite distance; the shaded re-gion represents the 95% confidence intervals for the linear fit, esti-mated from pair bootstrap resampling. N H from dust reddening E ( B − V )Reddening caused by the absorption and scattering oflight by dust grains is defined as: E ( B − V ) = A V R V = 1 . κ V R V rµm H N H (12)where A V is the dust extinction, R V is an empirical co-efficient correlated with the average grain size and allother symbols are defined as before. In the Milky Way, R V is typically assumed to be 3.1 (Schultz & Wiemer1975), but it may vary between 2.5 and 6.0 along differ-ent sightlines (Goodman et al. 1995; Draine 2003).The ratio (cid:104) N H / E ( B − V ) (cid:105) =5.8 × cm − mag − (Bohlin et al. 1978) is a widely-accepted standard, usedin many fields of astrophysics to connect reddening mea-surements to gas column density. This value was derivedfrom Lyman- α and H line absorption measurementstoward 100 stars (see also Savage et al. 1977), and hasbeen replicated over the years via similar methodology(e.g. Shull & van Steenberg 1985; Diplas & Savage 1994;Rachford et al. 2009). However, a number of recentworks using H i E ( B − V ) from Greenet al. (2018) to estimate the ratio N H / E ( B − V ) for oursample of purely atomic sightlines, at | b | > ◦ . The resultsare shown in Figure 7. It can be seen that E ( B − V ) and N H are strongly linearly correlated, with a Pearson co-efficient of 0.93. The ratio obtained from the linear fitis N H / E ( B − V )=(9.4 ± × cm − mag − (the inter-cept is also set to be 0), where the quoted uncertaintiesare the 95% confidence limits estimated from pair boot-strap resampling. This value is a factor of 1.6 higherthan Bohlin et al. (1978).The value obtained here is consistentwith the estimate of Lenz et al. (2017): N H / E ( B − V )=8.8 × cm − mag − (no uncertainty isgiven in that work). These authors compared opticallythin H i column density from HI4PI Collaboration et al.(2016) with various estimates of E ( B − V ) from Schlegel Hiep Nguyen et al. (2018)et al. (1998), Peek & Graves (2010), Schlafly et al.(2014), PLC2014a, and Meisner & Finkbeiner (2015).We note that the estimate of Lenz et al. (2017) isonly valid for N H < × cm − , where it seems safeto assume that the 21 cm emission is optically thin.Our value is also close to Liszt (2014a), who find N HI / E ( B − V )=8.3 × cm − mag − (also given with-out uncertainty) for | b |≥ ◦ and 0.015 (cid:46) E ( B − V ) (cid:46) i data from LAB and E ( B − V ) fromSchlegel et al. (1998). The methodology used by thesetwo studies differs in a number of details. For instance,Liszt (2014a) did not apply a gain correction to theSchlegel et al. (1998) map (whereas Lenz et al. (2017)scaled it down by 12%), and did not smooth it to theLAB angular resolution (30 (cid:48) ). However, Liszt (2014a)did apply an empirical correction factor to account forH i opacity (albeit one whose effects on high-latitudesightlines was small). These details may account forthe difference between the values obtained by these twootherwise similar studies.We also note that, like the present work, these studiesdid not take into account the potential contribution ofdust associated with the diffuse warm ionized gas (WIM).This would tend to produce a flattening of the E ( B − V )vs N HI relation at low N HI and therefore increase thevalue of N HI / E ( B − V ) artificially. Because we are ableto accurately probe a large column density range (upto 3 × cm − ), we would naively expect our estimateof N H / E ( B − V ) to be less affected by WIM bias thaneither Liszt (2014a) or Lenz et al. (2017) (which wouldtend to have a greater effect on lower column datapoints).While more work is needed to quantify the contributionof the WIM on dust emission/absorption measurementsat low E ( B − V ), we consider it unlikely to account forthe difference between our work and historically lowermeasurements of the N H / E ( B − V ) ratio.Despite minor differences between these three studies,it is clear that they point at a N HI / E ( B − V ) value of( ∼ × cm − mag − . This is 40–60% higher thanthe traditional value of Bohlin et al. (1978), which hasbeen used by most models of interstellar dust as a ref-erence point to set the dust-to-gas ratio (e.g. Draine& Fraisse 2009; Jones et al. 2013). We note that if N H is replaced with upper limits (as discussed in § N H / E ( B − V ) climbs yet higher, leaving this key conclu-sion unaffected. Disentangling the effects of grain evolution anddark gas on σ A number of studies have used the correlation between τ and N H , particularly with regards to the search fordark gas (e.g. Planck Collaboration et al. 2011; Fukuiet al. 2014, 2015; Reach et al. 2015). It is clear that τ and N H are in general linearly correlated only if σ is a constant. However, it is recognized that σ issensitive to grain evolution, and significant variations inthe ratio N H / τ have been observed, particularly whentransitioning to the high-density, molecular regime (e.g.Planck Collaboration et al. 2014a, 2015; Okamoto et al.2017; Remy et al. 2017). The origin of observed varia-tions in σ may relate to a change in dust propertiesvia κ , and/or a variation in the dust-to-gas ratio r ,but may also include a contribution due to the presence N H [10 cm − ] σ = τ / N H [ − c m H − ] This workX CO =1 × (PLC2014a)X CO =2 × (PLC2014a)X CO =3 × (PLC2014a) Fig. 8.—
Dust opacity σ versus total column density N H along the 34 purely atomic sightlines presented in this work (redpoints), overlaid on σ derived for the whole sky at 30 (cid:48) reso-lution from PLC2014a. Here, blue points assume an X-factor of X CO =1.0 × , black assume X CO =2.0 × , and violet assume X CO =3.0 × . The grey envelope is the standard deviation ofthese all-sky measurements for X CO =2.0 × . The red and blackdashed lines show respectively the constant σ derived from thelinear fit in Section 4.1 and that obtained from PLC2014a for thelow column-density regime. of dark gas, if this is unaccounted for in the estimated N H .PLC2014a presented the variation in σ with N H at30 (cid:48) resolution over the entire sky. In that work, N H wasderived from ( N ∗ HI + X CO W CO ), thus dark gas (both op-tically thick H i and CO-dark H ) was unaccounted for.We reproduce their data in Figure 8. It can be seenthat σ is roughly flat and at a minimum in a nar-row, low-column density range N H =(1 − × cm − ,then increases linearly until N H =15 × cm − , by whichpoint it is almost a factor of 2 higher. It then re-mains approximately constant for the canonical value of X CO =2.0 × cm − K − km − s. A key issue for dark gasstudies is disentangling how much of the initial rise in σ is due to changing grain properties, and how muchis due to the contribution of unseen material, whetherit be opaque H i or diffuse H . (Note also the upturn in σ seen at the lowest N H , which may be due to thepresence of unaccounted-for protons in the warm ionizedmedium.)The column density range probed by our purelyatomic sightlines, N H =(1 ∼ × cm − well samplesthe range where σ undergoes its first linear increase.Dark gas is also fully accounted for in our data, sinceH i is opacity-corrected, and no molecular gas is detectedin emission along these sightlines. To quantify the ef-fect of ignoring H i opacity on σ we compare σ de-duced from the true, opacity-corrected N HI with that de-duced under the optically thin assumption. The resultsare shown in Figure 9. In low column density regions( N H < × cm − ), each σ pair from N HI and N ∗ HI are comparable. However, at higher column densities( N H > × cm − ) σ from true N HI is systematicallylower than that measured from N ∗ HI . On average, σ obtained from optically thin H i column density increasesby ∼ σ from true N HI increases by ∼ i opacity is not explicitly correctedfor, it can account for around one third (1/3) of the in-ust-Gas Scaling Relations 9 N H [10 cm − ] σ = τ / N H [ − c m H − ] N H = N ∗ HI N H = N HI Fig. 9.—
Dust opacity σ versus total column density N H along the 34 purely atomic sightlines presented in this workusing true N HI (red) and N ∗ HI (black) as the total gas col-umn density N H . The vertical line is at 5 × cm − . Thelarge datapoints are the average values for the low-density( N H < × cm − ) and high-density ( N H > × cm − ) regions(error bars on these points are the standard error on the mean).Note that two datapoints, one black ( σ =27.2 × − cm H − )and one red ( σ =16.1 × − cm H − ), at N H =18.2 × cm − are not shown, but are included in the averages. crease of σ observed during the transition from diffuseto dense atomic regimes. The remaining of two thirds(2/3) must arise due to changes in dust properties.From Equation 11, we see that σ is a function ofthe dust-to-gas mass ratio, r , and the dust emissivitycross-section, κ , which depends on the compositionand structure of dust grains. Given the uncertainties onthe efficiency of the physical processes involved in theevolution of interstellar dust grains, it is difficult at thispoint to conclude if the variations of σ observed hereare due to an increase of the dust mass (i.e., r ) or to achange in the dust emission properties (i.e., κ ). Us-ing the dust model of Jones et al. (2013), Ysard et al.(2015) suggest that most of the variations in the dustemission observed by Planck in the diffuse ISM couldbe explained by relatively small variations in the dustproperties. That interpretation would favor a scenarioin which the increase of σ from diffuse to denser gas iscaused by the growth of thin mantles via the accretion ofatoms and molecules from the gas phase. Even thoughthis process would increase the mass of grains (and there-fore increase r ) the change of the structure of the grainsurface would lead to a larger increase in κ . Alter-natively, it is possible that this systematic variation of τ / N H could be due to residual large-scale systematiceffects in the Planck data, or to the fact that the modi-fied black-body model introduces a bias in the estimateof τ . Neither of these explanations can be ruled out.Figure 8 shows σ as a function of N H superim-posed on the results from PLC2014a. It can be seenthat we observe a similar rise in σ in the column den-sity range ( ∼ − × cm − , but less extreme. In par-ticular, most of our data points in the higher columndensity range ( N H > × cm − ) are found below thePLC2014a trend, which is derived from the mean valuesof σ over the whole sky in N H bins. This is true evenif we use N ∗ HI rather than N HI to derive σ , indicat-ing that optically thick H i alone cannot shift our data-points high enough for a perfect match. This is consistentwith the fact that we are examining purely atomic sight- N H [10 cm − ] E ( B − V ) / N H [ − m a g c m H − ] N H = N ∗ HI N H = N HI Fig. 10.—
The ratio E ( B − V )/ N H as a function of N H alongthe 34 purely atomic sightlines presented in this work, using true N HI (red) and N ∗ HI (black) as the total gas column density N H .The dashed line is at 5 × cm − . The large datapoints are theaverage values for the low-density ( N H < × cm − ) and high-density ( N H > × cm − ) regions (error bars on these points arethe standard error on the mean). lines, and likely happens because we are sampling com-paratively low number densities ( n H (cid:46) − ;a mixture of WNM and CNM), whereas the sample inPLC2014a includes molecular gas in the N H bins, pre-sumably with a higher κ . However, in diffuse regionswith N H < × cm − , the mean value of σ from oursample is comparable with that from PLC2014a. E ( B − V ) as the more Reliable Proxy for N H ? We have seen that along 34 atomic sightlines E ( B − V )shows a tight linear correlation with N H in the columndensity range N H =(1 ∼ × cm − . τ also shows agood linear relation with N H but with systematic devi-ations as described above.Figure 10 replicates Figure 9 but for E ( B − V ) ratherthan τ . Although the sample used here is small, thesefigures demonstrate clearly that the ratio E ( B − V )/ N H is more stable than τ / N H over the range of columndensities and sightlines covered by our analysis. In fact,with N H corrected for optical depth effects, our data arecompatible with a constant value for E ( B − V )/ N H , upto N H =30 × cm − . On the other hand, we have ob-served an increase of τ / N H with N H which we suggestmay be due to an increase of the dust emissivity (anincrease of r and/or κ without affecting significantlythe dust absorption cross-section). While we are unfor-tunately unable to follow how these relations evolve athigher A V and in molecular gas, our results neverthelesssuggest that the E ( B − V ) maps of Green et al. (2018) area more reliable proxy for N H than the current release of Planck τ in low-to-moderate column density regimes. OH ABUNDANCE RATIO X OH The rotational lines of CO are widely used to probe thephysical properties of H clouds, but in diffuse molecularregimes where CO is not detectable in emission, otherspecies and transitions must be considered as alternativetracers of H . Among these, the ground-state main linesof OH are a promising dark gas tracer; they are readilydetectable in translucent/diffuse molecular clouds (e.g.Magnani & Siskind 1990; Barriault et al. 2010), and sinceOH is considered as a precursor molecule necessary for0 Hiep Nguyen et al. (2018)the formation of CO in diffuse regions (Black & Dalgarno1977; Barriault et al. 2010), it is expected to be abundantin low-CO density/abundance regimes.The utility of OH as a tracer of CO-dark H dependson our ability to constrain the OH/H abundance ra-tio, X OH = N OH / N H . From an observational perspec-tive, this requires good estimates of both the OH and H column densities, the latter of which often cannot be ob-served directly. Many efforts (both modeling and obser-vational) have been devoted to deriving X OH in differentenvironmental conditions, which we summarize below: • Astrochemical models by Black & Dalgarno (1977)found X OH ∼ − for the case of ζ Ophiuchi cloud. •
19 comprehensive models of diffuse interstellarclouds with n H from 250 to 1000 cm − , T k from20 to 100K and A V from 0.62 to 2.12 mag (vanDishoeck & Black 1986) found OH/H abundancesfrom 1.6 × − to 2.9 × − . • The OH abundance with respect to H from chemi-cal models of diffuse clouds was found to vary from7.8 × − to 8.3 × − with A V =(0.1 −
1) mag, T K =(50 − n =(50 − − (Viala 1986). • ratios between 5.3 × − and 2.5 × − . • From OH observations towards high-latitudeclouds using the 43m NRAO telescope, Magnaniet al. (1988) derived X OH values between 4.8 × − to 4 × − in the range of A V =(0.4 − N H =9.4 × A V . However, we notethat the excitation temperatures of the OH mainlines were assumed to be equal, T ex , =T ex , ,likely resulting in overestimation of N OH (seeCrutcher 1979; Dawson et al. 2014). • Andersson & Wannier (1993) obtained an OHabundance of ∼ − from models of halos arounddark molecular clouds. • Combining N OH data from Roueff (1996) and Fe-lenbok & Roueff (1996) with measurements of N H from Savage et al. (1977, using UV absorption),Rachford et al. (2002, using UV absorption) andJoseph et al. (1986, using CO emission), Liszt &Lucas (2002) find X OH =(1.0 ± × − towarddiffuse clouds. • Weselak et al. (2010) derived OH abundances of(1.05 ± × − from absorption line observa-tions of 5 translucent sightlines, with molecularhydrogen column densities N H measured throughUV absorption by (Rachford et al. 2002, 2009). • Xu et al. (2016) report that X OH decreases from8 × − to 1 × − across a boundary regionof the Taurus molecular cloud, over the rangeAv=0.4 − N H was obtained from an in-tegration of A V -based estimates of the H volumedensity (assuming N H =9.4 × A V ). • Recently, Rugel et al. (2018) report a median X OH ∼ × − from THOR Survey observationsof OH absorption in the first Milky Way quadrant,with N H estimated from CO(1-0).Overall, while model calculations tend to produce somevariation in the OH abundance ratio over different partsof parameter space (8 × − to 4 × − ), observationally-determined measurements of X OH cluster fairly tightlyaround 10 − , with some suggestion that this may de-crease for denser sightlines.In this paper we determine our own OH abundances,using the MS dataset to provide N OH and N HI ; thenemploying τ and E ( B − V ) (along with our own con-version factors) to compute molecular hydrogen columndensities as N H = ( N H − N HI ). We note that since thisdust-based estimate of N H cannot be decomposed invelocity space, the OH abundances are determined inan integrated fashion for each sightline, and not on acomponent-by-component basis. While CO was detectedalong all but one sightline, it was not detected towardsall velocity components, meaning that our abundancesare generally computed for a mixture of CO-dark andCO-bright H (for further details see Li et al. 2018).The OH column densities derived in Section 3 arederived from direct measurements of T ex and τ . Thismeans that they should be accurate compared to meth-ods that rely on assumptions about these variables (seee.g. Crutcher 1979; Dawson et al. 2014). In computing N H we assume that the linear correlations (deduced from τ , E ( B − V ) and N HI towards 34 atomic sightlines) stillhold in molecular regions. In this manner, estimates ofthe OH/H abundance ratio can be obtained within arange of visual extinction A V =(0.25 − N H thatis either negative or consistent with zero to within themeasurement uncertainties; these are excluded from theanalysis.Figure 11 shows N OH and X OH as functions of N H .We find N OH increases approximately linearly with N H ,and the OH/H abundance ratio is approximately con-sistent for the two methods, with no evidence of andsystematic trends with increasing column density. Dif-ferences arise due to the overestimation of N H derivedfrom τ along dense sightlines compared to N H from E ( B − V ). As discussed in Section 4, σ varies by upto a factor of 2 in the range N H =(1 ∼ × cm − ,whereas the ratio (cid:104) N H / E ( B − V ) (cid:105) is quite constant. Themean and standard deviation of the X OH distribution de-duced from E ( B − V ) is (0.9 ± × − , which is closeto the canonical value of ∼ × − , and double the X OH from τ , (0.5 ± × − . We regard the higher valueas more reliable. CONCLUSIONS
We have combined accurate, opacity-corrected H i col-umn densities from the Arecibo Millennium Survey and21-SPONGE with thermal dust data from the Planck satellite and the new E ( B − V ) maps of Green et al.(2018). We have also made use of newly published Mil-lennium Survey OH data and information on CO de-tections from Li et al. (2018). In combination, thesedatasets allow us to select reliable subsamples of purely-atomic (or partially-molecular) sightlines, and hence as-ust-Gas Scaling Relations 11 N H [10 cm − ] − N OH [ c m − ] N H from E(B − V)N H from τ N H [10 cm − ] − X OH [ − ] X OH from E(B − V)X OH from τ Fig. 11.—
Left: N OH as a function of N H obtained from the two N H proxies, E ( B − V ) (blue) and τ (red). Right: X OH derivedfrom the two proxies as a function of N H . sess the impact of H i opacity on the scaling relations com-monly used to convert dust data to total proton columndensity N H . They also allow us to make new measure-ments of the OH/H abundance ratio, which is essentialin interpreting the next generation of OH datasets. Ourkey conclusions are as follows:1. H i opacity effects become important above N HI > × cm − ; below this value the optically thinassumption may usually be considered reliable.2. Along purely atomic sightlines with N H = N HI =(1–30) × cm − , the dust opacity, σ = τ / N H , is ∼ N H =5 × cm − ). We haveargued that this rise is likely due to the evolution of dustgrains in the atomic ISM, although large-scale systemat-ics in the Planck data cannot be definitively ruled out. Failure to account for H i opacity can cause an additionalapparent rise of the order of ∼ N H / E ( B − V ) ratio of (9.4 ± × cm − mag − . Thisis consistent with Lenz et al. (2017) and Liszt (2014a),but 60% higher than the canonical value from Bohlinet al. (1978).4. Our results suggest that N H derived from the E ( B − V ) map of Green et al. (2018) is more reliablethan that obtained from the τ map of PLC2014a inlow-to-moderate column density regimes.5. We measure the OH/H abundance ratio, X OH ,along a sample of 16 molecular sightlines. We find X OH ∼ × − , with no evidence of a systematic trendwith column density. Since our sightlines include bothCO-dark and CO-bright molecular gas components, thissuggests that OH may be used as a reliable proxy for H over a broad range of molecular regimes. ACKNOWLEDGMENTS
JRD is the recipient of an Australian ResearchCouncil (ARC) DECRA Fellowship (project numberDE170101086). N.M.-G. acknowledges the support of theARC through Future Fellowship FT150100024. LB ac-knowledges the support from CONICYT grant PFB06.We are indebted to Professor Mark Wardle for provid-ing us with valuable advice and support. We gratefullyacknowledge discussions with Dr. Cormac Purcell andAnita Petzler. Finally, we thank the anonymous refereefor comments and criticisms which allowed us to improvethe paper.This research has made use of the NASA/IPAC In-frared Science Archive, which is operated by the JetPropulsion Laboratory, California Institute of Technol-ogy, under contract with the National Aeronautics andSpace Administration.
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APPENDIX
APPENDIX A: LOCATIONS OF ATOMIC SIGHTLINES
50 55 60757677 τ [ − ]
165 166−35−34−33
CTA21
238 240 242656667
P1117 + 14
235 240737475
50 55 60757677 E ( B − V )[ m a g ]
165 166−35−34−33 238 240 242656667 235 240737475 −2 −2 −2
36 38 40596061 τ [ − ]
38 40 42575859
198 200 202525354
188 190 192535455
36 38 40596061 E ( B − V )[ m a g ]
38 40 42575859 198 200 202525354 188 190 192535455 −2 −2 −2 −2 Fig. 12.—
See Figure 5 for details.
156 158 160−49−48−47 τ [ − ]
186 187 188−8−7−6
P0531 + 19
200 201 202293031
P0820 + 22
197 198 199252627
156 158 160−49−48−47 E ( B − V )[ m a g ]
186 187 188−8−7−6 200 201 202293031 197 198 199252627 −2 −2
128 130−50−49−48 τ [ − ]
186 187 188−12−11−10
163 164 165−35−34−33
174 176−46−45−44
128 130−50−49−48 E ( B − V )[ m a g ]
186 187 188−12−11−10 163 164 165−35−34−33 174 176−46−45−44
177 178 179 180−32−31−30 τ [ − ]
288 290 292636465
209 210 211161718
DW0742 + 10
190 191 192121314
177 178 179 180−32−31−30 E ( B − V )[ m a g ]
288 290 292636465 209 210 211161718 190 191 192121314 −2 −2 −2 Fig. 13.—
See Figure 5 for details. ust-Gas Scaling Relations 15
212 213 214 215333435 τ [ − ]
212 213 214 215323334
60 65 70 75808182
275 280 285747576
212 213 214 215333435 E ( B − V )[ m a g ]
212 213 214 215323334 60 65 70 75808182 275 280 285747576 −2 −2 −2 −2
320 322.5 325686970 τ [ − ]
232 234555657
50 55 60 65808182
207 208 209212223
320 322.5 325686970 E ( B − V )[ m a g ]
232 234555657 50 55 60 65808182 207 208 209212223 −2 −2 −2 −2
260 270 280828384 τ [ − ]
350 352 354606162
260 270 280828384 E ( B − V )[ m a g ]
350 352 354606162 −2 −2 Fig. 14.—
See Figure 5 for details.
APPENDIX B: LOCATIONS OF OH SIGHTLINES
176 177 178−20−19−18 τ [ − ] P0428 + 20
85 86 87 88−39−38−37
187 188 189−101
185 186 187345
176 177 178−20−19−18 E ( B − V )[ m a g ]
85 86 87 88−39−38−37 187 188 189−101 185 186 187345 ×10 ×10 ×10
177 178 179−11−10−9 τ [ − ]
177 178 179 180−14−13−12
170 171 172−9−8−7
181 182 183−29−28−27
177 178 179−11−10−9 E ( B − V )[ m a g ]
177 178 179 180−14−13−12 170 171 172−9−8−7 181 182 183−29−28−27 ×10 ×10
118 120−54−53−52 τ [ − ]
62 63 64−7−6−5
170 172−46−45−44
180 181 182 183−6−5−4
T0526 + 24
118 120−54−53−52 E ( B − V )[ m a g ]
62 63 64−7−6−5 170 172−46−45−44 180 181 182 183−6−5−4 ×10 Fig. 15.—
See Figure 5 for details. ust-Gas Scaling Relations 17
206 207 208012 τ [ − ]
186 187 188 189−35−34−33
170 171 172−13−12−11
68 69 70−5−4−3
206 207 208012 E ( B − V )[ m a g ]
186 187 188 189−35−34−33 170 171 172−13−12−11 68 69 70−5−4−3 ×10 ×10 ×10
42 43 44 458910 τ [ − ]
212 213 214293031
201 202 203−1012
T0629 + 10
42 43 44 458910 E ( B − V )[ m a g ]
212 213 214293031 201 202 203−1012 ×10 ×10 Fig. 16.—
See Figure 5 for details. T A B L E P a r a m e t e r s f o r O H m a i n l i n e s S o u r c e l / b O H ( ) O H ( ) τ V l s r ∆ V T e x N ( O H ) τ V l s r ∆ V T e x N ( O H )( N a m e )( o )( k m s − )( k m s − )( K )( c m − )( k m s − )( k m s − )( K )( c m − ) C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . . . ± . - . ± . . ± . . ± . . ± . . ± . - . ± . . ± . . ± . . ± . C . . . ± . - . ± . . ± . . ± . . ± . . ± . - . ± . . ± . . ± . . ± . C . . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . - . ± . . ± . . ± . . ± . . ± . - . ± . . ± . . ± . . ± . C . - . . ± . - . ± . . ± . . ± . . ± . . ± . - . ± . . ± . . ± . . ± . C . . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . . - . . ± . - . ± . . ± . . ± . . ± . . ± . - . ± . . ± . . ± . . ± . C . - . . ± . - . ± . . ± . . ± . . ± . . ± . - . ± . . ± . . ± . . ± . C . . . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . C . . . . ± . - . ± . . ± . . ± . . ± . . ± . - . ± . . ± . . ± . . ± . C . . . . ± . - . ± . . ± . . ± . . ± . . ± . - . ± . . ± . . ± . . ± . G . + . . . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . G . + . . . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . G . + . . . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . G . + . . . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . G . + . . . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . G . + . . . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . P + . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . P + . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . T + . - . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . T + . . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . T + . . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . T + . . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . T + . . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . T + . . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . T + . . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . T + . . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . T + . . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . ust-Gas Scaling Relations 19 TABLE 234 atomic sightlines
Sources(Name) l/b ( o ) N HI (10 cm − ) N ∗ HI (10 cm − ) σ τ (OH )(10 − ) N H2 (upper limit) * (10 cm − ) τ (10 − ) E ( B − V )(10 − mag)3C33 129.4/-49.3 3.25 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± * Estimated from OH(1667) 3 σ detection limits using T ex =3.5 K, FWHM=1 km/s and N OH / N H =10 −7