Draft version May 31, 2018Preprint typeset using LATEX style emulateapj v. 12/16/11

DUST-GAS SCALING RELATIONS AND OH ABUNDANCE IN THE GALACTIC ISM

Hiep Nguyen1,2, J. R. Dawson1,2, M.-A. Miville-Deschenes3,4, Ningyu Tang5, Di Li5,6,7, Carl Heiles8, Claire E.Murray9, Snezana Stanimirovic10, Steven J. Gibson11, N. M. McClure-Griffiths12, Thomas Troland13, L.

Bronfman14, R. Finger15

Draft version May 31, 2018

ABSTRACT

Observations of interstellar dust are often used as a proxy for total gas column density NH. 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) Hi column densities and newly-published OH data from the Arecibo Millennium survey and 21-SPONGE, we confirm linear corre-lations between dust optical depth τ353, reddening E(B−V )and the total proton column density NH

in the range (1–30)×1020cm−2, along sightlines with no molecular gas detections in emission. Wederive an NH/E(B−V ) ratio of (9.4±1.6)×1021cm−2mag−1 for purely atomic sightlines at |b|>5◦,which is 60% higher than the canonical value of Bohlin et al. (1978). We report a ∼40% increase inopacity σ353=τ353/NH, when moving from the low column density (NH<5×1020cm−2) to moderatecolumn density (NH>5×1020cm−2) regime, and suggest that this rise is due to the evolution of dustgrains in the atomic ISM. Failure to account for Hi opacity can cause an additional apparent rise inσ353, of the order of a further ∼20%. We estimate molecular hydrogen column densities NH2

fromour derived linear relations, and hence derive the OH/H2 abundance ratio of XOH∼1×10−7 for allmolecular sightlines. Our results show no evidence of systematic trends in OH abundance with NH2

in the range NH2∼(0.1−10)×1021cm−2. This suggests that OH may be used as a reliable proxy forH2 in this range, which includes sightlines with both CO-dark and CO-bright gas.Subject headings: ISM: clouds — ISM: molecules — ISM: dust, reddening, extinction.

1. INTRODUCTION

Observations of neutral hydrogen in the interstellarmedium (ISM) have historically been dominated by tworadio spectral lines: the 21 cm line of atomic hydrogen(Hi) and the microwave emission from carbon monox-ide (CO), particularly the CO(J=1–0) line. The for-

1 Department of Physics and Astronomy and MQ Re-search Centre in Astronomy, Astrophysics and Astrophoton-ics, Macquarie University, NSW 2109, Australia. Email: van-hiep.nguyen@hdr.mq.edu.au

2 Australia Telescope National Facility, CSIRO Astronomyand Space Science, PO Box 76, Epping, NSW 1710, Australia

3 Institut d’Astrophysique Spatiale, CNRS, Univ. Paris-Sud,Universite Paris-Saclay, Bat. 121, 91405, Orsay Cedex, France

4 Laboratoire AIM, Paris-Saclay, CEA/IRFU/DAp - CNRS -Universite Paris Diderot, 91191, Gif-sur-Yvette Cedex, France

5 National Astronomical Observatories, CAS, Beijing 100012,China

6 Key Laboratory of Radio Astronomy, Chinese Academy ofScience

7 University of Chinese Academy of Sciences, Beijing 100049,China

8 Department of Astronomy, University of California, Berke-ley, 601 Campbell Hall 3411, Berkeley, CA 94720-3411

9 Space Telescope Science Institute, 3700 San Martin Drive,Baltimore, MD 21218, USA

10 Department of Astronomy, University of Wisconsin-Madison, 475 North Charter Street, Madison, WI 53706, USA

11 Department of Physics and Astronomy, Western KentuckyUniversity, Bowling Green, KY 42101, USA

12 Research School of Astronomy and Astrophysics, AustralianNational University, Canberra, ACT 2611, Australia

13 Department of Physics and Astronomy, University of Ken-tucky, Lexington, Kentucky 40506

14 Departamento de Astronomıa, Universidad de Chile, Casilla36, Santiago de Chile, Chile

15 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 (H2),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 Hi 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 fromHi 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), Cii 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 Hi could account for almost all the miss-ing gas mass (Fukui et al. 2015), CO-dark H2 is generallyexpected to be a major constituent, particularly in theenvelopes of molecular clouds (e.g. Lee et al. 2015). Indiffuse molecular regions, H2 is effectively self-shielded,

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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 H2 in such environments. Indeed Herschel observa-tions of Cii suggest that between 20–75% of the H2 inthe Galactic Plane may be CO-dark (Pineda et al. 2013).

For the atomic medium, the mass of warm Hi can becomputed directly from measured line intensities underthe optically thin assumption. However, cold Hi withspin temperature Ts . 100K suffers from significant op-tical depth effects, leading to an underestimation of thetotal column density. This difficulty is generally ad-dressed by combining Hi absorption and emission profilesobserved towards (and immediately adjacent to) bright,compact continuum background sources. Such studiesfind that the optically thin assumption underestimatesthe true Hi 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 andH2 absorption in stellar spectra to calibrate the relation-ship between total Hydrogen column density NH, andthe color excess E(B−V ). Similar work was carried outby comparing X-ray absorption with optical extinction,AV (Reina & Tarenghi 1973, Gorenstein 1975). Bohlinet al’s value of NH/E(B−V )=5.8×1021cm−2mag−1 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 NH than Hi 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 NH (as measured by Hi and CO)is typically found in the range AV =0.3−2.7 mag (PlanckCollaboration et al. 2011, 2014a,b; Martin et al. 2012),consistent with the range where CO-dark H2 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 Hi opacity; (3) in-sufficient sensitivity for CO detection. It has also beenimpossible to rule out remaining systematic effects in thePlanck data or bias in the estimate of τ353 introduced bythe choice of the modified black-body model.

In this study, we examine the correlations betweenaccurately-derived Hi column densities and dust-basedproxies for NH. We make use of opacity-corrected Hicolumn 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 H2. Observationally, they appear to reside inthe same environments, as evidenced by tight relationsbetween their column densities (Weselak & Kre lowski2014). Theoretically, the synthesis of OH is driven bythe ions O+ and H+

3 but requires H2 as the precursor;once H2 becomes available, OH can be formed efficientlythrough the charge-exchange chemical reactions initiatedby cosmic ray ionization (van Dishoeck & Black 1986).Here we combine Hi, OH and dust datasets to obtain newmeasurements of the abundance ratio, XOH=NOH/NH2

– a key quantity for the interpretation of OH datasets.The structure of this article is as follows. In Section

2, the observations, the data processing techniques andcorrections on Hi are briefly summarized. In Section 3,the results from OH observations are discussed. Section4 discusses the relationship between τ353, E(B−V ) andNH in the atomic ISM. We finally estimate the OH/H2

abundance ratio in Section 5, before concluding in Sec-tion 6.

2. DATASETS

In this study, we use the all-sky optical depth(τ353) 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), Hi 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).

2.1. Hi and OH

Hi data from the Millennium Arecibo 21-CentimeterAbsorption-Line Survey (hereafter MS) was taken to-wards 79 strong radio sources (typically S & 2 Jy) us-ing the Arecibo L-wide receiver. The two main lines ofground state OH at 1665.402 and 1667.359 MHz wereobserved simultaneously towards 72 positions, and OHabsorption was detected along 19 of these sightlines (seealso Li et al. 2018). The observations are described indetail by HT03. Briefly, their so-called Z16 observa-tion pattern consists of one on-source absorption spec-trum towards the background radio source and 16 off-source emission spectra with the innermost positions at1.0 HPBW and the outermost positions at

√2 HPBW

from the central source. The off-source “expected” emis-sion spectrum, the emission profile we would observe inthe absence of the continuum source, is then estimatedby modeling the 17-point measurements. In this work weuse the published values of HT03 for the total Hi columndensity, NHI (scaled as described below), and use the off-source (expected) MS emission profiles to compute the

Dust-Gas Scaling Relations 3

Hi 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 ηb=0.5 (Heiles et al.2001), appropriate if the OH is not extended comparedto the Arecibo beam size of 3′.

In order to increase the source sample, we also use Hidata 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.

2.1.1. Hi 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 Hi. 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 ∼1.14. A possible explanationfor this difference lies in the fact that (in contrast to 21-SPONGE) the MS did not apply a main beam efficiency.

To bring the MS dataset in-line with LAB, HI4PIand 21-SPONGE, one might assume that both the on-source and off-source spectra must be rescaled, and theopacity-corrected column densities recomputed accord-ing to the method of HT03 (or equivalent). However,NHI 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 ofNHI 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:

TONB (v) = (Tbg + Tc)e−τv + Ts(1− e−τv ) + Trx (1)

TOFFB (v) = Tbge

−τv + Ts(1− e−τv ) + Trx, (2)

where TOFFB (v) and TON

B (v) are the main beam tempera-tures of the off-source spectrum and on-source spectrum,respectively. Ts is the spin temperature, τv is the opticaldepth, Trx is the receiver temperature (∼25 K), and Tc isthe main-beam temperature of the continuum source, ob-tained from the line-free portions of the on-source spec-

trum. Tbg 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 forτv and Ts:

e−τv =TON

B (v)− TOFFB (v)

Tc, (3)

Ts =TOFF

B (v)− Tbge−τv − Trx

1− e−τv. (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 Ts must be recomputed. This is doneon a component-by-component basis from the tabu-lated Gaussian fit parameters for peak optical depth, τ0,peak brightness temperature (scaled by 1.14), and thelinewidth ∆v. The corrected NHI is obtained from

NHI

[1018 cm−2]= 1.94 · τ0 ·

Ts

[K]· ∆v

[km s−1], (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.

2.1.2. NHI vs N∗HI

We show in Figure 2 the correlation between NHI

and N∗HI towards all 93 positions. While opti-cally thin Hi column density is comparable with thetrue column density in diffuse/low-density regions withNHI.5×1020cm−2, opacity effects start to become ap-parent above ∼5×1020cm−2.

If a linear fit is performed to the data, the ra-tio f=NHI/N

∗HI may be described as a function of

log(N∗HI/1020) with a slope of (0.19±0.02) and an in-tercept of (0.89±0.02) (see also Lee et al. 2015). Alter-natively, a simple isothermal correction to the opticallythin N∗HI data with Ts∼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 lowNHI plateau, NHI<5×1020cm−2, below which N∗HI≈NHI.While a single component with a constant spin temper-ature is a poor physical description of interstellar Hi, itcan provide a reasonable (if crude) correction for opacity.

2.2. 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 12CO, 13CO, andC18O were observed with the Delingha 13.7m telescopein China. 12CO(J=2–1) data for 45 sources and J=3–2data for 8 sources with strong 12CO 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.

4 Hiep Nguyen et al. (2018)

3C132

2×10−9 3×10−6 5×10−3

Fig. 1.— Locations of all 93 sightlines considered in this study, overlaid on the map of dust optical depth τ353. Squares show Hiabsorption 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 Hi 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.

100 101 102

NHI [1020cm−2]

1.0

1.5

2.0

2.5

3.0

NHI/N

∗ HI

NHI (ON/OFF method from MS & 21−SPONGE)

Same as black, but for the 34 atomic sightlines

NHI (Ts∼144K)

Fig. 2.— The ratio f=NHI/N∗HI as a function of opacity-

corrected NHI along 93 sightlines from the MS and 21-SPONGEsurveys. Circles show accurate NHI 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 NHI obtained from N∗HI assuming a single isother-mal component of Ts∼144 K. The vertical dashed line is plot-ted at NHI=5×1020cm−2, the horizontal dashed line marks whereNHI=N

∗HI.

2.3. Dust

To trace the total gas column density NH we usepublicly-available all-sky maps of the 353 GHz dust opti-cal depth (τ353) from the Planck satellite. The τ353 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 Healpix16 for-mat (Gorski 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′.4-13′.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 release17.

3. 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, Tex, 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 Tex.

16 http : //healpix.sourceforge.net17 http://argonaut.skymaps.info/usage

Dust-Gas Scaling Relations 5

The radiative transfer equations for the on-source andoff-source (expected) spectra are identical to those for Hi,given above in Equations (1) and (2). All terms and theirmeanings are identical, with the exception that the spintemperature, Ts is replaced by Tex. Tbg 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

Tbg = 2.7 + Tbg,408(νOH/408)−2.8, (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:

TOFFB (v) = Tbg + Trx. (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 deriveTex and τv for each of the OH lines, as shown in Equa-tions (3) and (4) for the case of Hi.

We fit each OH opacity spectrum (cf. Equation 3) witha set of Gaussian profiles to obtain the peak optical depth(τ0,n), central velocity (v0,n) and FWHM (∆vn) of eachcomponent, n. Equation (4) is then used to calculate ex-citation temperature spectra. Examples of e−τv , TOFF

B ,and Tex spectra are shown in Figure 3, together withtheir associated Gaussian fits. It can be seen that theTex spectra are approximately flat within the FWHM ofeach Gaussian component. We therefore compute an ex-citation temperature for each component from the meanTex in the range v0,n ±∆v/2.

Figure 4 compares the τ0 and Tex 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, NOH, inde-pendently from both the 1667 and 1665 MHz lines via:

NOH,1667

[1014 cm−2]= 2.39 · τ1667 ·

Tex,1667

[K]· ∆v1667

[km s−2], (8)

NOH,1665

[1014 cm−2]= 4.30 · τ1665 ·

Tex,1665

[K]· ∆v1665

[km s−2], (9)

where the constants include Einstein A-coefficients ofA1667 = 7.778× 10−11s−1 and A1665 = 7.177× 10−11s−1

for the OH main lines (Destombes et al. 1977). Allvalues of τ0, Tex and NOH are tabulated in Table 1.

Fig. 3.— Example of OH 1667 MHz e−τv (top), expected TOFFB

(middle), and Tex (bottom) spectra for the source P0428+20. TheFWHM of the Gaussian fits to the absorption profile are used todefine the range over which Tex is computed for each component,shown as white regions in the bottom panel.

10−2 10−1

τLi(2018)

10−2

10−1

τ

100 101

TexLi(2018) [K]

100

101

Tex

[K]

Fig. 4.— Comparison between derived values of the peak opticaldepth τ (left panel), and Tex (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.

4. 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 NH. Specifically, we consider dust optical depth at353 GHz, τ353, and reddening, E(B−V ), with datasetssourced as described in Section 2.3. When these quanti-ties are used as proxies forNH, a single linear relationshipbetween the measured quantity and NH is typically as-sumed. In this work, our Hi 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

6 Hiep Nguyen et al. (2018)

22 23 2428

29

30

τ 353

[10−

6 ]3C348

197 198 199−16

−15

−14

3C142.1

189 190 191

−28

−27

−263C120

38 39 40

17

18

194C13.65

22 23 2428

29

30

E(B−

V)[m

ag]

197 198 199−16

−15

−14

189 190 191

−28

−27

−26

38 39 40

17

18

19

4

6

8

10

12

0.080.100.120.140.160.18

20

40

60

80

100

0.10.20.30.40.50.60.70.8

101520253035

0.15

0.20

0.25

0.30

0.35

46810121416

0.080.100.120.140.160.180.200.22

Fig. 5.— Example maps of the immediate vicinity of 4 “purely atomic” sightlines towards background radio sources. Dust maps (3×3degrees in Galactic coordinates) are adopted from Planck collaboration 2014 (τ353, 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 WCO(1−0) from the

all-sky extension to the maps of Dame et al. (2001) (T. Dame, private communication). The base level is at 0.25 K kms−1, 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 τ353/NH and E(B−V )/NH

along a sample of purely atomic sightlines for which NH

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 NOH<1×1013cm−2 (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 H2, and note that allbut one of them lie outside the Galactic plane (|b|>10◦).Figure 5 shows example maps of the immediate vicinityof 4 of these sightlines in τ353 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, NH is therefore taken to beequal to NHI, the opacity-corrected Hi column density, asderived along sightlines with no molecular gas detectedin emission.

4.1. NH from dust optical depth τ353

We adopt the all-sky map of dust optical depth τ353

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:

Iν = τ353Bν(Tdust)( ν

353

)βdust

. (10)

Here, τ353, dust temperature, Tdust, and spectral index,βdust, are the three free parameters, and Bν(Tdust) is thePlanck function for dust at temperature Tdust 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:

τ353 =I353

B353(Tdust)= κ353rµmHNH = σ353NH , (11)

where σ353 is the dust opacity, κ353 is the dust emissivitycross-section per unit mass (cm2g−1), r is the dust-to-gasmass ratio, µ is the mean molecular weight and mH isthe mass of a hydrogen atom.

Figure 6 shows the correlation between NH and τ353.A tight linear trend can be seen with a Pearson co-efficient of 0.95. The value of σ353 from the orthog-onal distance regression (Boggs & Rogers 1990) linearfit is (7.9±0.6)×10−27cm2H−1 (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 Hi data fromLAB, (6.6±1.7)×10−27cm2H−1. Note that here we havequoted the PLC2014a measurement made towards lowNHI positions, because the lack of any Hi opacity cor-rection in that work makes this value the most reliable.However, our fit is consistent with all of σ353 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 §4.3.

In order to examine the possible contribution of molec-ular gas toNH along the 34 atomic sightlines, we estimateupper limits on NH2 from the 3σ OH detection limits us-ing an abundance ratio of XOH=10−7 (see Section 5).These values are tabulated in Table 1, and the resultingupper limits on NH are shown as gray triangles in Figure6. As expected, the σ353 obtained from the fit to theseupper limits is lower, at (6.4±0.3)×10−27cm2H−1. How-ever, while some molecular gas may indeed be present atlow levels, these limits should be considered as extreme

Dust-Gas Scaling Relations 7

upper bounds on the true molecular column density. Thisis particularly true for the most diffuse sightlines withthe lowest column density (NHI<5×1020cm−2), wherethe observational upper limits may appear to raise NH

by up to ∼50%. Molecules are not expected to be well-shielded at such low columns (and indeed even CNM islargely absent along these sightlines in our data). Evenfor higher column density datapoints, it can be readilyseen from Figures 5 and 12–14 that all sightlines consid-ered in this analysis lie well away from even the faintestoutskirts of CO-bright molecular gas complexes. We alsonote that the deviations from the linear fit that will bediscussed in more detail below could not be removed byany selective addition of molecular gas at levels up tothese limits.

100 101

NH [1020cm−2]

100

101

τ353[10−6]

Linear fit

PLC2014a

Fukui et al. (2015)Upper limit with NH2 from OH detection limits

Fig. 6.— τ353 vs NH along the 34 purely atomic sightlines de-scribed in the text. Grey triangles indicate the upper limits for NHalong these 34 atomic sightlines with NH2

estimated from the 3σ

OH detection limits using an abundance ratio NOH/NH2=10−7.

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 τ353 map).τ353 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 σ353

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 ∼1.5), by restrictingtheir fit to only the warmest dust temperatures, underthe assumption that these most reliably select for gen-uinely optically thin Hi. They then applied this factor tothe Planck τ353 map (excluding |b|<15◦ and CO-brightsightlines) to estimate NHI, assuming that the contri-bution from CO-dark H2 was negligible. This resultedin NHI values ∼2–2.5 times higher than under the op-tically thin assumption, and motivated their hypothesisthat significantly more optically thick Hi exists than isusually assumed. However, we find that while the σ353 ofFukui et al. (2015) may be a good fit to some sightlinesin the very low NHI regime (.3×1020cm−2), it overes-timates NHI at larger column densities by ∼50%. In-deed, as will be discussed below, σ353 is not expectedto remain constant as dust evolves. This (combinedwith some contribution from CO-dark H2) may recon-cile the apparent discrepancy between their findings andabsorption/emission-based measurements of the opacity-corrected Hi column.

100 101

NH [10−2cm−2]

100

101

E(B

−V)[10−2mag]

Linear fitUpper limit with NH2 from OH detection limits

Fig. 7.— Correlation between NH and dust reddening E(B−V )from Green et al. (2018) along 34 atomic sightlines. Grey trian-gles indicate the upper limits for NH along these 34 atomic sight-lines, with NH2

estimated from the 3σ OH detection limits using

an abundance ratio NOH/NH2=10−7. 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.

4.2. NH from dust reddening E(B−V )

Reddening caused by the absorption and scattering oflight by dust grains is defined as:

E(B−V ) =AVRV

= 1.086κVRV

rµmHNH (12)

where AV is the dust extinction, RV is an empirical co-efficient correlated with the average grain size and allother symbols are defined as before. In the Milky Way,RV 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 〈NH/E(B−V )〉=5.8×1021cm−2mag−1

(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 H2 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 Hi 21cm data have found significantlyhigher values (PLC2014a; Liszt 2014a; Lenz et al. 2017).

Here we use the all-sky map of E(B−V ) from Greenet al. (2018) to estimate the ratio NH/E(B−V ) for oursample of purely atomic sightlines, at |b|>5◦. The resultsare shown in Figure 7. It can be seen that E(B−V ) andNH are strongly linearly correlated, with a Pearson co-efficient of 0.93. The ratio obtained from the linear fitis NH/E(B−V )=(9.4±1.6)×1021cm−2mag−1 (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):NH/E(B−V )=8.8×1021 cm−2 mag−1 (no uncertainty isgiven in that work). These authors compared opticallythin Hi column density from HI4PI Collaboration et al.(2016) with various estimates of E(B−V ) from Schlegel

8 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 NH<4×1020cm−2, where it seems safeto assume that the 21 cm emission is optically thin.Our value is also close to Liszt (2014a), who findNHI/E(B−V )=8.3×1021 cm−2 mag−1 (also given with-out uncertainty) for |b|≥20◦ and 0.015.E(B−V ).0.075,by comparing Hi 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′). However, Liszt (2014a)did apply an empirical correction factor to account forHi 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 NHI relation at low NHI and therefore increase thevalue of NHI/E(B−V ) artificially. Because we are ableto accurately probe a large column density range (upto 3×1021 cm−2), we would naively expect our estimateof NH/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 NH/E(B−V ) ratio.

Despite minor differences between these three studies,it is clear that they point at a NHI/E(B−V ) value of(∼8–9)×1021cm−2mag−1. 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 ifNH is replaced with upper limits (as discussed in §4.1),NH/E(B−V ) climbs yet higher, leaving this key conclu-sion unaffected.

4.3. Disentangling the effects of grain evolution anddark gas on σ353

A number of studies have used the correlation betweenτ353 and NH, 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 thatτ353 and NH are in general linearly correlated only ifσ353 is a constant. However, it is recognized that σ353 issensitive to grain evolution, and significant variations inthe ratio NH/τ353 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 σ353 may relate to a change in dust propertiesvia κ353, and/or a variation in the dust-to-gas ratio r,but may also include a contribution due to the presence

100 101 102

NH[1020cm−2]

4

6

8

10

12

14

16

18

σ353=

τ353/N

H[10−27cm

2H

−1]

This work

XCO=1×1020 (PLC2014a)

XCO=2×1020 (PLC2014a)

XCO=3×1020 (PLC2014a)

Fig. 8.— Dust opacity σ353 versus total column density NHalong the 34 purely atomic sightlines presented in this work (redpoints), overlaid on σ353 derived for the whole sky at 30′ reso-lution from PLC2014a. Here, blue points assume an X-factor ofXCO=1.0×1020, black assume XCO=2.0×1020, and violet assumeXCO=3.0×1020. The grey envelope is the standard deviation ofthese all-sky measurements for XCO=2.0×1020. The red and blackdashed lines show respectively the constant σ353 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 estimatedNH.

PLC2014a presented the variation in σ353 with NH at30′ resolution over the entire sky. In that work, NH wasderived from (N∗HI+XCOWCO), thus dark gas (both op-tically thick Hi and CO-dark H2) was unaccounted for.We reproduce their data in Figure 8. It can be seenthat σ353 is roughly flat and at a minimum in a nar-row, low-column density range NH=(1−3)×1020cm−2,then increases linearly untilNH=15×1020cm−2, by whichpoint it is almost a factor of 2 higher. It then re-mains approximately constant for the canonical value ofXCO=2.0×1020cm−2K−1km−1s. A key issue for dark gasstudies is disentangling how much of the initial rise inσ353 is due to changing grain properties, and how muchis due to the contribution of unseen material, whetherit be opaque Hi or diffuse H2. (Note also the upturn inσ353 seen at the lowest NH, which may be due to thepresence of unaccounted-for protons in the warm ionizedmedium.)

The column density range probed by our purelyatomic sightlines, NH=(1∼30)×1020cm−2 well samplesthe range where σ353 undergoes its first linear increase.Dark gas is also fully accounted for in our data, sinceHi is opacity-corrected, and no molecular gas is detectedin emission along these sightlines. To quantify the ef-fect of ignoring Hi opacity on σ353 we compare σ353 de-duced from the true, opacity-corrected NHI with that de-duced under the optically thin assumption. The resultsare shown in Figure 9. In low column density regions(NH<5×1020cm−2), each σ353 pair from NHI and N∗HIare comparable. However, at higher column densities(NH>5×1020cm−2) σ353 from true NHI is systematicallylower than that measured from N∗HI. On average, σ353

obtained from optically thin Hi column density increasesby ∼1.6 when going from low to high column densityregions; whereas σ353 from true NHI increases by ∼1.4.This suggests that if Hi opacity is not explicitly correctedfor, it can account for around one third (1/3) of the in-

Dust-Gas Scaling Relations 9

100 101

NH [1020cm−2]

4

6

8

10

12

14

σ353=

τ353/N

H[10−27cm

2H

−1] NH = N∗

HI

NH = NHI

Fig. 9.— Dust opacity σ353 versus total column density NHalong the 34 purely atomic sightlines presented in this workusing true NHI (red) and N∗HI (black) as the total gas col-

umn density NH. The vertical line is at 5×1020cm−2. Thelarge datapoints are the average values for the low-density(NH<5×1020cm−2) and high-density (NH>5×1020cm−2) regions(error bars on these points are the standard error on the mean).Note that two datapoints, one black (σ353=27.2×10−27cm2H−1)and one red (σ353=16.1×10−27cm2H−1), at NH=18.2×1020cm−2

are not shown, but are included in the averages.

crease of σ353 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 σ353 is a function ofthe dust-to-gas mass ratio, r, and the dust emissivitycross-section, κ353, 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 σ353 observed hereare due to an increase of the dust mass (i.e., r) or to achange in the dust emission properties (i.e., κ353). 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 σ353 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 κ353. Alter-natively, it is possible that this systematic variation ofτ353/NH 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 τ353. Neither of these explanations can be ruled out.

Figure 8 shows σ353 as a function of NH superim-posed on the results from PLC2014a. It can be seenthat we observe a similar rise in σ353 in the column den-sity range (∼5−30)×1020cm−2, but less extreme. In par-ticular, most of our data points in the higher columndensity range (NH>5×1020cm−2) are found below thePLC2014a trend, which is derived from the mean valuesof σ353 over the whole sky in NH bins. This is true evenif we use N∗HI rather than NHI to derive σ353, indicat-ing that optically thick Hi alone cannot shift our data-points high enough for a perfect match. This is consistentwith the fact that we are examining purely atomic sight-

100 101

NH [1020cm−2]

1

2

E(B

−V)/

NH[10−22magcm

2H

−1]

NH = N∗HI

NH = NHI

Fig. 10.— The ratio E(B−V )/NH as a function of NH alongthe 34 purely atomic sightlines presented in this work, using trueNHI (red) and N∗HI (black) as the total gas column density NH.

The dashed line is at 5×1020cm−2. The large datapoints are theaverage values for the low-density (NH<5×1020cm−2) and high-density (NH>5×1020cm−2) 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 (nH . 10–100 cm−3;a mixture of WNM and CNM), whereas the sample inPLC2014a includes molecular gas in the NH bins, pre-sumably with a higher κ353. However, in diffuse regionswith NH<5×1020cm−2, the mean value of σ353 from oursample is comparable with that from PLC2014a.

4.4. E(B−V ) as the more Reliable Proxy for NH?

We have seen that along 34 atomic sightlines E(B−V )shows a tight linear correlation with NH in the columndensity range NH=(1∼30)×1020cm−2. τ353 also shows agood linear relation with NH but with systematic devi-ations as described above.

Figure 10 replicates Figure 9 but for E(B−V ) ratherthan τ353. Although the sample used here is small, thesefigures demonstrate clearly that the ratio E(B−V )/NH

is more stable than τ353/NH over the range of columndensities and sightlines covered by our analysis. In fact,with NH corrected for optical depth effects, our data arecompatible with a constant value for E(B−V )/NH, upto NH=30×1020cm−2. On the other hand, we have ob-served an increase of τ353/NH with NH which we suggestmay be due to an increase of the dust emissivity (anincrease of r and/or κ353 without affecting significantlythe dust absorption cross-section). While we are unfor-tunately unable to follow how these relations evolve athigher AV and in molecular gas, our results neverthelesssuggest that the E(B−V ) maps of Green et al. (2018) area more reliable proxy for NH than the current release ofPlanck τ353 in low-to-moderate column density regimes.

5. OH ABUNDANCE RATIO XOH

The rotational lines of CO are widely used to probe thephysical properties of H2 clouds, but in diffuse molecularregimes where CO is not detectable in emission, otherspecies and transitions must be considered as alternativetracers of H2. 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 for

10 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 H2 dependson our ability to constrain the OH/H2 abundance ra-tio, XOH=NOH/NH2

. From an observational perspec-tive, this requires good estimates of both the OH and H2

column densities, the latter of which often cannot be ob-served directly. Many efforts (both modeling and obser-vational) have been devoted to deriving XOH in differentenvironmental conditions, which we summarize below:

• Astrochemical models by Black & Dalgarno (1977)found XOH∼10−7 for the case of ζ Ophiuchi cloud.

• 19 comprehensive models of diffuse interstellarclouds with nH from 250 to 1000 cm−3, Tk from20 to 100K and AV from 0.62 to 2.12 mag (vanDishoeck & Black 1986) found OH/H2 abundancesfrom 1.6×10−8 to 2.9×10−7.

• The OH abundance with respect to H2 from chemi-cal models of diffuse clouds was found to vary from7.8×10−9 to 8.3×10−8 with AV =(0.1−1) mag,TK=(50−100) K, n=(50−1000) cm−3 (Viala 1986).

• 6 model calculations (that differ in depletion fac-tors of heavy elements and cosmic ray ionizationrate) by Nercessian et al. (1988) towards moleculargas in front of the star HD 29647 in Taurus foundOH/H2 ratios between 5.3×10−8 and 2.5×10−6.

• From OH observations towards high-latitudeclouds using the 43m NRAO telescope, Magnaniet al. (1988) derived XOH values between 4.8×10−7

to 4×10−6 in the range of AV =(0.4−1.1) mag as-suming that NH2

=9.4×1020AV . However, we notethat the excitation temperatures of the OH mainlines were assumed to be equal, Tex,1665=Tex,1667,likely resulting in overestimation of NOH (seeCrutcher 1979; Dawson et al. 2014).

• Andersson & Wannier (1993) obtained an OHabundance of ∼10−7 from models of halos arounddark molecular clouds.

• Combining NOH data from Roueff (1996) and Fe-lenbok & Roueff (1996) with measurements of NH2

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 XOH=(1.0±0.2)×10−7 towarddiffuse clouds.

• Weselak et al. (2010) derived OH abundances of(1.05±0.24)×10−7 from absorption line observa-tions of 5 translucent sightlines, with molecularhydrogen column densities NH2

measured throughUV absorption by (Rachford et al. 2002, 2009).

• Xu et al. (2016) report that XOH decreases from8×10−7 to 1×10−7 across a boundary regionof the Taurus molecular cloud, over the rangeAv=0.4−2.7 mag. NH2

was obtained from an in-tegration of AV -based estimates of the H2 volumedensity (assuming NH2=9.4×1020AV ).

• Recently, Rugel et al. (2018) report a medianXOH∼1.3×10−7 from THOR Survey observationsof OH absorption in the first Milky Way quadrant,with NH2 estimated from 13CO(1-0).

Overall, while model calculations tend to produce somevariation in the OH abundance ratio over different partsof parameter space (8×10−9 to 4×10−6), observationally-determined measurements of XOH cluster fairly tightlyaround 10−7, 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 NOH and NHI; thenemploying τ353 and E(B−V ) (along with our own con-version factors) to compute molecular hydrogen columndensities as NH2

= 12 (NH−NHI). We note that since this

dust-based estimate of NH2cannot be decomposed in

velocity 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 H2 (for further details see Li et al. 2018).

The OH column densities derived in Section 3 arederived from direct measurements of Tex 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 computingNH we assume that the linear correlations (deduced fromτ353, E(B−V ) andNHI towards 34 atomic sightlines) stillhold in molecular regions. In this manner, estimates ofthe OH/H2 abundance ratio can be obtained within arange of visual extinction AV =(0.25−4.8) mag. We notethat of our 19 OH-bright sightlines, 5 produce NH2 thatis either negative or consistent with zero to within themeasurement uncertainties; these are excluded from theanalysis.

Figure 11 shows NOH and XOH as functions of NH2.

We find NOH increases approximately linearly with NH2 ,and the OH/H2 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 NH derivedfrom τ353 along dense sightlines compared to NH fromE(B−V ). As discussed in Section 4, σ353 varies by upto a factor of 2 in the range NH=(1∼30)×1020cm−2,whereas the ratio 〈NH/E(B−V )〉 is quite constant. Themean and standard deviation of the XOH distribution de-duced from E(B−V ) is (0.9±0.6)×10−7, which is closeto the canonical value of ∼1×10−7, and double the XOH

from τ353, (0.5±0.3)×10−7. We regard the higher valueas more reliable.

6. CONCLUSIONS

We have combined accurate, opacity-corrected Hi col-umn densities from the Arecibo Millennium Survey and21-SPONGE with thermal dust data from the Plancksatellite 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-

Dust-Gas Scaling Relations 11

100 101 102

NH2 [1020cm−2]

10−1

100

101N

OH[1014cm

−2]

NH2 from E(B− V)

NH2 from τ353

100 101 102

NH2 [1020cm−2]

10−1

100

101

XOH[10−7]

XOH from E(B− V)

XOH from τ353

Fig. 11.— Left: NOH as a function of NH2obtained from the twoNH proxies, E(B−V ) (blue) and τ353 (red). Right: XOH derivedfrom the two proxies as a function of NH2

.

sess the impact of Hi opacity on the scaling relations com-monly used to convert dust data to total proton columndensity NH. They also allow us to make new measure-ments of the OH/H2 abundance ratio, which is essentialin interpreting the next generation of OH datasets. Ourkey conclusions are as follows:

1. Hi opacity effects become important aboveNHI>5×1020cm−2; below this value the optically thinassumption may usually be considered reliable.

2. Along purely atomic sightlines with NH=NHI=(1–30)×1020cm−2, the dust opacity, σ353=τ353/NH, is∼40%higher for moderate-to-high column densities than low(defined as above and belowNH=5×1020cm−2). 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 Hi opacity can cause an additionalapparent rise of the order of ∼20%.

3. For purely atomic sightlines, we measure aNH/E(B−V ) ratio of (9.4±1.6)×1021cm−2mag−1. 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 NH derived from theE(B−V ) map of Green et al. (2018) is more reliablethan that obtained from the τ353 map of PLC2014a inlow-to-moderate column density regimes.

5. We measure the OH/H2 abundance ratio, XOH,along a sample of 16 molecular sightlines. We findXOH∼1×10−7, 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 H2

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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Dust-Gas Scaling Relations 13

APPENDIX

APPENDIX A: LOCATIONS OF ATOMIC SIGHTLINES

50 55 60

75

76

77

τ 353[10−

6 ]

3C293

165 166−35

−34

−33

CTA21

238 240 242

65

66

67P1117+14

235 240

73

74

753C264.0

50 55 60

75

76

77

E(B−

V)[m

ag]

165 166−35

−34

−33

238 240 242

65

66

67

235 240

73

74

75

0.250.500.751.001.251.501.752.00

2.0

2.5

3.0

3.5

4.0×10−2

681012141618

0.100.120.140.160.180.20

246810121416

2.0

2.5

3.0

3.5

4.0

×10−2

0.5

1.0

1.5

2.0

2.5

2.0

2.5

3.0

3.5

4.0×10−2

36 38 4059

60

61

τ 353

[10−

6 ]

3C310

38 40 4257

58

59

3C315

198 200 202

52

53

543C234

188 190 192

53

54

55

3C236

36 38 4059

60

61

E(B−

V)[m

ag]

38 40 4257

58

59

198 200 202

52

53

54

188 190 192

53

54

55

1.01.52.02.53.03.54.04.5

3

4

5

6

×10−2

1.52.02.53.03.54.04.5

3

4

5

6

7×10−2

0.51.01.52.02.53.0

2.5

3.0

3.5

4.0

×10−2

0.5

1.0

1.5

2.0

2.5

1.752.002.252.502.753.003.253.503.75

×10−2

Fig. 12.— See Figure 5 for details.

14 Hiep Nguyen et al. (2018)

156 158 160

−49

−48

−47

τ 353[10−

6 ]3C64

186 187 188

−8

−7

−6

P0531+19

200 201 202

29

30

31P0820+22

197 198 19925

26

27

3C192

156 158 160

−49

−48

−47

E(B−

V)[m

ag]

186 187 188

−8

−7

−6

200 201 202

29

30

31

197 198 19925

26

27

4

6

8

10

12

0.070.080.090.100.110.120.130.14

20253035404550

0.250.300.350.400.450.500.55

234567

3.253.503.754.004.254.504.755.005.25×10−2

2

3

4

5

6

3.54.04.55.05.56.0

×10−2

128 130

−50

−49

−48

τ 353

[10−

6 ]

3C33

186 187 188

−12

−11

−103C138

163 164 165

−35

−34

−333C79

174 176−46

−45

−44

3C78

128 130

−50

−49

−48

E(B−

V)[m

ag]

186 187 188

−12

−11

−10

163 164 165

−35

−34

−33

174 176−46

−45

−44

2

4

6

8

10

12

0.030.040.050.060.070.080.090.100.11

20

30

40

50

60

0.200.250.300.350.400.450.50

5.07.510.012.515.017.520.022.5

0.100.120.140.160.180.200.220.24

5.07.510.012.515.017.520.0

0.080.100.120.140.160.180.200.220.24

177 178 179 180

−32

−31

−30

τ 353[10−

6 ]

3C98

288 290 29263

64

65

3C273

209 210 211

16

17

18DW0742+10

190 191 19212

13

14

3C172.0

177 178 179 180

−32

−31

−30

E(B−

V)[m

ag]

288 290 29263

64

65

209 210 211

16

17

18

190 191 19212

13

14

10

15

20

25

30

35

0.15

0.20

0.25

0.30

0.35

12345678

2.0

2.5

3.0

3.5

4.0

×10−2

1.01.52.02.53.03.54.04.5

2.42.62.83.03.23.43.6

×10−2

3456789

3.03.54.04.55.05.56.06.5×10−2

Fig. 13.— See Figure 5 for details.

Dust-Gas Scaling Relations 15

212 213 214 215

33

34

35τ 3

53[10−

6 ]3C208.1

212 213 214 21532

33

34

3C208.0

60 65 70 75

80

81

82

4C32.44

275 280 285

74

75

763C272.1

212 213 214 215

33

34

35

E(B−

V)[m

ag]

212 213 214 21532

33

34

60 65 70 75

80

81

82

275 280 285

74

75

76

2345678

2.53.03.54.04.55.05.56.06.5×10−2

2345678

3.03.54.04.55.05.56.06.5×10−2

0.250.500.751.001.251.501.75

2

3

4

5

6

×10−2

0.51.01.52.02.53.03.54.0

3

4

5

6

7

×10−2

320 322.5 325

68

69

70

τ 353

[10−

6 ]

4C07.32

232 23455

56

57

3C245

50 55 60 65

80

81

823C286

207 208 209

21

22

23

3C190.0

320 322.5 325

68

69

70

E(B−

V)[m

ag]

232 23455

56

57

50 55 60 65

80

81

82

207 208 209

21

22

23

1.01.52.02.53.03.54.0

2.53.03.54.04.55.0

×10−2

123456

2.5

3.0

3.5

4.0

4.55.0×10−2

0.250.500.751.001.251.501.752.00

1.752.002.252.502.753.003.25

×10−2

1.52.02.53.03.5

2.753.003.253.503.754.004.254.50×10−2

260 270 28082

83

84

τ 353

[10−

6 ]

3C274.1

350 352 354

60

61

623C298

260 270 28082

83

84

E(B−

V)[m

ag]

350 352 354

60

61

62

1234567

2.02.53.03.54.04.55.05.5×10−2

0.751.001.251.501.752.002.25

2.502.753.003.253.503.754.004.25

×10−2

Fig. 14.— See Figure 5 for details.

16 Hiep Nguyen et al. (2018)

APPENDIX B: LOCATIONS OF OH SIGHTLINES

176 177 178−20

−19

−18

τ 353[10−

6 ]

P0428+20

85 86 87 88

−39

−38

−373C454.3

187 188 189

−1

0

1

4C22.12

185 186 187

3

4

5

3C154

176 177 178−20

−19

−18

E(B−

V)[m

ag]

85 86 87 88

−39

−38

−37

187 188 189

−1

0

1

185 186 187

3

4

5

0.4

0.6

0.8

1.0

1.2

1.4×102

0.4

0.6

0.8

1.0

1.2

2

4

6

8

10

12

0.040.050.060.070.080.090.100.110.12

1

2

3

4

5×102

0.81.01.21.41.61.82.02.2

0.4

0.6

0.8

1.0

×102

0.4

0.6

0.8

1.0

177 178 179

−11

−10

−9

τ 353

[10−

6 ]

3C133

177 178 179 180−14

−13

−12

3C132

170 171 172−9

−8

−7

3C131

181 182 183−29

−28

−27

3C109

177 178 179

−11

−10

−9

E(B−

V)[m

ag]

177 178 179 180−14

−13

−12

170 171 172−9

−8

−7

181 182 183−29

−28

−27

0.51.01.52.02.53.03.5

×102

0.4

0.6

0.8

1.0

1.2

2025303540455055

0.300.350.400.450.500.550.600.65

0.500.751.001.251.501.752.002.25

×102

0.4

0.6

0.8

1.0

1.2

1.4

20

30

40

50

60

0.2

0.3

0.4

0.5

0.6

118 120−54

−53

−52

τ 353[10−

6 ]

3C18

62 63 64

−7

−6

−5

3C409

170 172

−46

−45

−44

3C75

180 181 182 183

−6

−5

−4T0526+24

118 120−54

−53

−52

E(B−

V)[m

ag]

62 63 64

−7

−6

−5

170 172

−46

−45

−44

180 181 182 183

−6

−5

−4

5101520253035

0.060.080.100.120.140.160.180.200.22

2030405060708090

0.4

0.6

0.8

1.0

1.2

5.07.510.012.515.017.520.022.525.0

0.10

0.15

0.20

0.25

0.30

0.40.60.81.01.21.41.6

×102

0.50.60.70.80.91.01.1

Fig. 15.— See Figure 5 for details.

Dust-Gas Scaling Relations 17

206 207 2080

1

2

τ 353

[10−

6 ]3C167

186 187 188 189−35

−34

−33

3C105

170 171 172−13

−12

−11

3C123

68 69 70−5

−4

−3

3C410

206 207 2080

1

2

E(B−

V)[m

ag]

186 187 188 189−35

−34

−33

170 171 172−13

−12

−11

68 69 70−5

−4

−3

0.40.60.81.01.21.4

×102

0.4

0.6

0.8

1.0

1.2

152025303540

0.200.250.300.350.400.45

0.5

1.0

1.5

2.0

2.5×102

0.4

0.6

0.8

1.0

1.2

0.500.751.001.251.501.752.002.25

×102

0.60.81.01.21.41.61.8

42 43 44 458

9

10

τ 353[10−

6 ]

4C13.67

212 213 21429

30

31

3C207

201 202 203−1

0

1

2T0629+10

42 43 44 458

9

10

E(B−

V)[m

ag]

212 213 21429

30

31

201 202 203−1

0

1

2

0.20.40.60.81.01.21.4

×102

0.4

0.6

0.8

1.0

2

4

6

8

10

0.030.040.050.060.070.080.090.10

1

2

3

4

5

6×102

0.500.751.001.251.501.752.002.252.50

Fig. 16.— See Figure 5 for details.

18 Hiep Nguyen et al. (2018)T

AB

LE

1P

aram

eters

for

OH

main

lin

es

Source

l/b

OH

(1665)

OH

(1667)

τVlsr

∆V

Tex

N(OH

)τ

Vlsr

∆V

Tex

N(OH

)

(Nam

e)

(o)

(kms−

1)

(kms−

1)

(K)

(1014cm

−2)

(kms−

1)

(kms−

1)

(K)

(1014cm

−2)

3C

105

187.6

/-3

3.6

0.0

156±

0.0

003

8.1

4±

0.0

10.9

5±

0.0

34.6

5±

1.8

60.2

9±

0.1

20.0

265±

0.0

004

8.1

7±

0.0

10.9

4±

0.0

23.9

5±

0.9

50.2

3±

0.0

6

3C

105

187.6

/-3

3.6

0.0

062±

0.0

003

10.2

2±

0.0

20.9

3±

0.0

68.5±

4.8

90.2

1±

0.1

20.0

104±

0.0

004

10.2

5±

0.0

20.9

6±

0.0

47.6

6±

3.4

10.1

8±

0.0

8

3C

109

181.8

/-2

7.8

0.0

023±

0.0

003

9.1

5±

0.1

11.0

3±

0.2

618.2

8±

27.0

60.1

8±

0.2

70.0

036±

0.0

004

9.2

4±

0.0

50.7

5±

0.1

224.5

8±

8.7

0.1

6±

0.0

6

3C

109

181.8

/-2

7.8

0.0

036±

0.0

003

10.4

5±

0.0

70.9

8±

0.1

513.9

7±

5.4

10.2

1±

0.0

90.0

053±

0.0

004

10.5

5±

0.0

41.0

2±

0.1

13.6

3±

4.4

80.1

8±

0.0

6

3C

123

170.6

/-1

1.7

0.0

191±

0.0

007

3.6

5±

0.0

61.1

9±

0.1

110.9

2±

3.2

61.0

5±

0.3

30.0

348±

0.0

009

3.7

1±

0.0

41.2

2±

0.0

710.9

2±

2.6

91.1±

0.2

8

3C

123

170.6

/-1

1.7

0.0

431±

0.0

023

4.4

3±

0.0

10.5

3±

0.0

38.0

6±

0.7

80.7

8±

0.0

90.0

919±

0.0

029

4.4

6±

0.0

0.5

3±

0.0

17.7±

0.6

50.8

9±

0.0

8

3C

123

170.6

/-1

1.7

0.0

337±

0.0

008

5.3

7±

0.0

10.9

1±

0.0

311.5

9±

4.3

1.5

3±

0.5

70.0

784±

0.0

009

5.4

7±

0.0

10.9

2±

0.0

18.7

9±

2.5

71.5±

0.4

4

3C

131

171.4

/-7

.80.0

065±

0.0

005

4.5

5±

0.0

20.5

6±

0.0

512.5

2±

3.5

90.1

9±

0.0

60.0

117±

0.0

004

4.6

4±

0.0

10.7

8±

0.0

46.9

6±

1.9

80.1

5±

0.0

4

3C

131

171.4

/-7

.80.0

073±

0.0

006

6.8

1±

0.0

62.9

1±

0.2

38.9

4±

4.5

40.8

2±

0.4

20.0

089±

0.0

005

5.8

4±

0.0

30.6

7±

0.0

811.0

4±

2.0

70.1

6±

0.0

4

3C

131

171.4

/-7

.80.0

166±

0.0

007

6.5

9±

0.0

10.4

2±

0.0

25.6

9±

0.8

50.1

7±

0.0

30.0

319±

0.0

007

6.5

5±

0.0

10.4

5±

0.0

25.9

9±

0.8

40.2±

0.0

3

3C

131

171.4

/-7

.80.0

521±

0.0

007

7.2

3±

0.0

0.5

5±

0.0

15.9

1±

0.6

40.7

2±

0.0

80.0

927±

0.0

005

7.2

2±

0.0

0.6

5±

0.0

15.9

8±

0.3

40.8

5±

0.0

5

3C

132

178.9

/-1

2.5

0.0

033±

0.0

003

7.8

2±

0.0

40.9±

0.1

15.5

5±

6.2

30.1

9±

0.0

80.0

056±

0.0

003

7.7

9±

0.0

20.7

9±

0.0

623.5

6±

2.1

70.2

5±

0.0

3

3C

133

177.7

/-9

.90.1

008±

0.0

01

7.6

6±

0.0

0.5

3±

0.0

4.4

7±

0.4

41.0

1±

0.1

0.2

132±

0.0

014

7.6

8±

0.0

0.5

2±

0.0

3.2

5±

0.2

70.8

5±

0.0

7

3C

133

177.7

/-9

.90.0

149±

0.0

01

7.9

4±

0.0

21.2

2±

0.0

47.0

8±

3.0

80.5

5±

0.2

40.0

333±

0.0

013

7.9

6±

0.0

11.2

3±

0.0

24.1

7±

0.9

90.4±

0.1

3C

154

185.6

/4.0

0.0

266±

0.0

006

-2.3

2±

0.0

20.7

4±

0.0

32.6

9±

1.9

30.2

3±

0.1

60.0

429±

0.0

006

-2.3

4±

0.0

10.7

1±

0.0

22.5

7±

0.7

50.1

9±

0.0

5

3C

154

185.6

/4.0

0.0

1±

0.0

006

-1.3

9±

0.0

40.8

3±

0.0

95.2±

5.2

80.1

8±

0.1

90.0

181±

0.0

005

-1.3

4±

0.0

20.9

4±

0.0

54.4

6±

1.7

90.1

8±

0.0

7

3C

154

185.6

/4.0

0.0

038±

0.0

005

2.2

3±

0.0

71.1

4±

0.1

75.8

3±

6.5

60.1

1±

0.1

20.0

054±

0.0

004

2.1

9±

0.0

51.5

7±

0.1

30.5

4±

8.6

90.0

1±

0.1

7

3C

167

207.3

/1.2

0.0

106±

0.0

019

18.4

6±

0.1

21.4

9±

0.3

54.7

5±

17.9

50.3

2±

1.2

20.0

09±

0.0

018

17.7

7±

0.1

51.7

6±

0.4

94.5

9±

9.5

70.1

7±

0.3

6

3C

18

118.6

/-5

2.7

0.0

031±

0.0

003

-8.5

2±

0.1

12.6

4±

0.2

710.9

2±

14.8

80.3

8±

0.5

20.0

06±

0.0

003

-8.3

4±

0.0

52.6

1±

0.1

49.2±

6.0

40.3

4±

0.2

3

3C

18

118.6

/-5

2.7

0.0

056±

0.0

004

-7.8

2±

0.0

20.6

7±

0.0

76.4

5±

3.7

0.1±

0.0

60.0

079±

0.0

004

-7.8

5±

0.0

10.6±

0.0

44.8

3±

1.6

0.0

5±

0.0

2

3C

207

213.0

/30.1

0.0

15±

0.0

002

4.5

5±

0.0

10.7

6±

0.0

12.9

4±

1.5

50.1

4±

0.0

80.0

266±

0.0

002

4.5

5±

0.0

0.7

7±

0.0

12.4

8±

0.4

60.1

2±

0.0

2

3C

409

63.4

/-6

.10.0

058±

0.0

011

14.5

9±

0.2

71.6

8±

0.3

511.3

1±

8.5

30.4

7±

0.3

80.0

055±

0.0

015

14.6

8±

0.3

31.5

2±

0.4

7.8

3±

11.7

30.1

6±

0.2

4

3C

409

63.4

/-6

.10.0

204±

0.0

025

15.4±

0.0

10.8

9±

0.0

53.1

8±

2.3

10.2

5±

0.1

80.0

275±

0.0

032

15.4

2±

0.0

10.8

6±

0.0

40.6

2±

1.0

0.0

3±

0.0

6

3C

410

69.2

/-3

.80.0

044±

0.0

006

6.3

2±

0.0

41.8

9±

0.1

513.4

1±

11.2

20.4

7±

0.4

0.0

079±

0.0

005

6.3

8±

0.0

22.3

2±

0.0

96.4±

5.2

50.2

8±

0.2

3

3C

410

69.2

/-3

.80.0

089±

0.0

006

6.2

1±

0.0

10.6

5±

0.0

48.4

6±

2.4

0.2

1±

0.0

60.0

193±

0.0

005

6.2

6±

0.0

10.8

1±

0.0

23.8

1±

1.2

80.1

4±

0.0

5

3C

410

69.2

/-3

.80.0

044±

0.0

003

10.7±

0.0

30.7

1±

0.0

710.0

6±

5.8

90.1

3±

0.0

80.0

085±

0.0

002

10.7

1±

0.0

20.8

1±

0.0

44.1

5±

3.0

90.0

7±

0.0

5

3C

410

69.2

/-3

.80.0

054±

0.0

002

11.6

7±

0.0

30.8

4±

0.0

74.8

3±

4.6

60.0

9±

0.0

90.0

115±

0.0

002

11.6

8±

0.0

20.8

2±

0.0

32.9

3±

3.0

0.0

7±

0.0

7

3C

454.3

86.1

/-3

8.2

0.0

023±

0.0

001

-9.6

7±

0.0

31.6±

0.0

94.6

3±

12.3

60.0

7±

0.1

90.0

044±

0.0

001

-9.5

4±

0.0

11.2

5±

0.0

48.1

3±

6.0

60.1±

0.0

8

3C

75

170.3

/-4

4.9

0.0

071±

0.0

005

-10.3

6±

0.0

41.3±

0.1

23.4

5±

5.4

10.1

4±

0.2

10.0

14±

0.0

008

-10.3

6±

0.0

31.2

2±

0.0

93.5

1±

1.5

60.1

4±

0.0

6

4C

13.6

743.5

/9.2

0.0

464±

0.0

043

4.8

5±

0.0

51.1±

0.1

210.4

3±

2.7

72.2

8±

0.6

90.0

567±

0.0

057

4.8

9±

0.0

51.1

2±

0.1

410.3

4±

2.1

31.5

5±

0.4

4C

22.1

2188.1

/0.0

0.0

058±

0.0

01

-2.8

4±

0.0

70.7

9±

0.1

96.5

4±

7.0

30.1

3±

0.1

40.0

102±

0.0

011

-2.7

3±

0.0

40.7

8±

0.1

26.7

2±

2.3

20.1

3±

0.0

5

4C

22.1

2188.1

/0.0

0.0

172±

0.0

012

-1.7

8±

0.0

20.5

6±

0.0

55.0

7±

2.1

20.2

1±

0.0

90.0

354±

0.0

013

-1.7

8±

0.0

10.5

4±

0.0

33.7

8±

0.7

40.1

7±

0.0

3

G196.6

+0.2

196.6

/0.2

0.0

044±

0.0

005

3.2

6±

0.1

11.9

4±

0.2

710.8

2±

12.2

20.4±

0.4

60.0

062±

0.0

005

3.4±

0.0

92.3

8±

0.2

28.8

5±

8.6

0.3

1±

0.3

G197.0

+1.1

197.0

/1.1

0.0

126±

0.0

005

4.8

3±

0.0

41.8

8±

0.0

96.9

4±

3.8

20.7±

0.3

90.0

191±

0.0

01

4.7

3±

0.0

41.6

5±

0.1

4.8±

2.1

70.3

6±

0.1

6

G197.0

+1.1

197.0

/1.1

0.0

059±

0.0

009

7.4

6±

0.0

50.6

5±

0.1

10.3

1±

10.5

80.0±

0.1

70.0

078±

0.0

015

7.3

4±

0.0

60.6

5±

0.1

41.6

1±

5.8

70.0

2±

0.0

7

G197.0

+1.1

197.0

/1.1

0.0

049±

0.0

005

17.0

1±

0.1

22.4

7±

0.2

810.9

9±

9.9

0.5

7±

0.5

20.0

081±

0.0

034

16.2

6±

0.1

70.9

1±

0.3

6.4

5±

2.9

50.1

1±

0.0

8

G197.0

+1.1

197.0

/1.1

0.0

052±

0.0

015

17.5

9±

0.0

30.2

5±

0.0

89.8

7±

1.8

10.0

5±

0.0

30.0

127±

0.0

013

17.3

8±

0.2

1.4

6±

0.3

55.4

6±

4.3

50.2

4±

0.2

G197.0

+1.1

197.0

/1.1

0.0

237±

0.0

01

32.0

1±

0.0

10.5

7±

0.0

34.7

5±

1.9

20.2

7±

0.1

10.0

43±

0.0

017

32.0

1±

0.0

10.5

4±

0.0

23.9

6±

1.0

40.2

2±

0.0

6

P0428+

20

176.8

/-1

8.6

0.0

014±

0.0

002

3.6±

0.0

81.0

1±

0.1

913.4

8±

7.8

0.0

8±

0.0

50.0

029±

0.0

003

3.5

4±

0.0

30.6

9±

0.0

84.4

5±

9.9

80.0

2±

0.0

5

P0428+

20

176.8

/-1

8.6

0.0

075±

0.0

002

10.7±

0.0

21.0

9±

0.0

413.4

9±

3.4

50.4

7±

0.1

20.0

136±

0.0

002

10.7±

0.0

11.1±

0.0

212.7

2±

1.6

20.4

5±

0.0

6

T0526+

24

181.4

/-5

.20.0

172±

0.0

073

7.5

5±

0.2

91.9±

1.1

313.7±

15.6

51.9

1±

2.5

90.0

43±

0.0

102

7.5

6±

0.1

42.4

3±

0.7

510.1

9±

7.5

2.5

2±

2.1

T0629+

10

201.5

/0.5

0.0

043±

0.0

022

0.1

6±

0.0

0.6

5±

0.4

4.1

6±

2.9

70.0

5±

0.0

50.0

103±

0.0

035

0.3

5±

0.0

1.1

8±

0.4

13.2

5±

1.9

30.0

9±

0.0

7

T0629+

10

201.5

/0.5

0.0

387±

0.0

074

3.1

4±

0.1

31.1±

0.0

3.8

5±

0.4

70.7±

0.1

60.0

577±

0.0

113

3.0

7±

0.1

41.1±

0.0

4.5

4±

0.5

50.6

8±

0.1

6

T0629+

10

201.5

/0.5

0.0

169±

0.0

015

1.4

6±

0.0

71.3

9±

0.2

62.1

9±

2.1

10.2

2±

0.2

20.0

281±

0.0

029

1.5

1±

0.0

81.2

3±

0.2

52.9±

0.9

10.2

4±

0.0

9

T0629+

10

201.5

/0.5

0.1

607±

0.0

104

3.6±

0.0

10.6

1±

0.0

23.8

3±

0.3

51.5

9±

0.1

90.2

536±

0.0

154

3.6±

0.0

10.6

5±

0.0

34.7

2±

0.6

41.8

4±

0.2

9

T0629+

10

201.5

/0.5

0.0

811±

0.0

02

4.6

2±

0.0

10.7

6±

0.0

36.4

3±

0.9

71.6

8±

0.2

70.1

553±

0.0

037

4.6

1±

0.0

10.6

7±

0.0

36.6

2±

1.0

11.6

3±

0.2

6

T0629+

10

201.5

/0.5

0.0

747±

0.0

018

6.0

9±

0.0

21.0

6±

0.0

55.4

4±

1.5

81.8

4±

0.5

40.1

165±

0.0

03

6.0

6±

0.0

21.1

7±

0.0

76.5

2±

1.6

72.1±

0.5

5

T0629+

10

201.5

/0.5

0.0

367±

0.0

031

7.0±

0.0

20.4

9±

0.0

64.3

6±

0.6

80.3

3±

0.0

70.0

631±

0.0

056

7.0±

0.0

20.5±

0.0

64.2±

0.3

0.3

1±

0.0

5

T0629+

10

201.5

/0.5

0.0

174±

0.0

018

7.9±

0.0

50.8

3±

0.1

33.4

4±

1.6

70.2

1±

0.1

10.0

307±

0.0

03

7.9

1±

0.0

50.8

2±

0.1

33.6

5±

1.2

10.2

2±

0.0

8

Dust-Gas Scaling Relations 19

TABLE 234 atomic sightlines

Sources(Name)

l/b

(o)

NHI

(1020cm−2)

N∗HI

(1020cm−2)

στ (OH1667)

(10−4)

NH2(upper limit)*

(1020cm−2)

τ353

(10−6)

E(B−V )

(10−2 mag)

3C33 129.4/-49.3 3.25±0.0 3.2±0.1 12.14 0.6 2.16±0.07 3.54±0.423C142.1 197.6/-14.5 25.11±2.6 19.6±0.8 10.55 0.52 21.53±0.72 21.71±0.813C138 187.4/-11.3 22.9±1.1 19.9±0.3 5.02 0.25 21.63±0.81 17.47±0.593C79 164.1/-34.5 10.86±1.2 9.8±0.8 37.03 1.84 9.23±0.37 12.67±0.783C78 174.9/-44.5 11.69±0.5 10.3±0.2 13.25 0.66 12.45±0.63 14.64±1.073C310 38.5/60.2 4.29±0.1 4.0±0.1 16.19 0.8 3.48±0.15 2.75±0.533C315 39.4/58.3 5.48±0.4 4.7±0.0 12.96 0.64 3.98±0.09 5.63±0.263C234 200.2/52.7 1.84±0.0 1.9±1.1 12.66 0.63 0.78±0.03 1.64±0.563C236 190.1/54.0 1.38±0.0 1.3±1.2 10.72 0.53 0.7±0.03 2.04±0.493C64 157.8/-48.2 7.29±0.2 6.9±0.8 33.12 1.65 6.55±0.35 9.01±0.36P0531+19 186.8/-7.1 27.33±0.7 25.4±0.3 6.37 0.32 20.75±0.62 20.54±1.3P0820+22 201.4/29.7 4.82±0.2 4.8±1.1 7.09 0.35 3.73±0.11 2.56±0.43C192 197.9/26.4 4.56±0.1 4.5±0.1 20.66 1.03 3.38±0.08 4.05±0.533C98 179.8/-31.0 12.7±0.5 11.3±1.3 12.26 0.61 13.72±0.41 17.73±1.023C273 289.9/64.4 2.35±0.0 2.3±0.1 21.0 1.04 1.3±0.09 1.98±0.41DW0742+10 209.8/16.6 2.77±0.0 2.8±0.9 8.01 0.4 1.6±0.03 1.99±0.253C172.0 191.2/13.4 8.89±0.2 8.6±1.1 13.02 0.65 5.66±0.08 4.7±0.523C293 54.6/76.1 1.46±0.1 1.5±1.1 6.24 0.31 1.31±0.09 2.83±0.753C120 190.4/-27.4 18.17±2.1 10.7±0.1 28.29 1.41 29.26±1.08 22.74±1.03CTA21 166.6/-33.6 10.97±0.4 10.0±0.8 27.35 1.36 10.39±0.44 13.3±0.96P1117+14 240.4/65.8 1.79±0.0 1.8±0.3 15.0 0.75 1.5±0.04 2.73±0.543C264.0 237.0/73.6 1.97±0.0 2.0±0.4 6.29 0.31 1.64±0.08 2.88±0.343C208.1 213.6/33.6 3.15±0.1 3.2±0.2 18.67 0.93 3.12±0.04 2.93±0.433C208.0 213.7/33.2 3.41±0.1 3.5±0.2 19.69 0.98 3.38±0.07 4.37±0.474C32.44 67.2/81.0 1.23±0.0 1.3±0.6 9.88 0.49 0.81±0.02 1.94±0.293C272.1 280.6/74.7 2.82±0.0 2.8±0.3 10.24 0.51 1.73±0.28 2.43±0.314C07.32 322.2/68.8 2.43±0.0 2.4±0.3 30.7 1.53 2.32±0.06 4.3±0.413C245 233.1/56.3 2.39±0.0 2.4±0.2 11.36 0.56 2.22±0.06 2.71±0.363C348 23.0/29.2 6.56±0.2 6.0±0.1 16.51 0.82 5.7±0.15 9.8±0.333C286 56.5/80.7 2.33±0.1 2.4±2.7 7.13 0.35 0.81±0.05 2.75±0.744C13.65 39.3/17.7 10.56±0.2 9.9±0.1 20.01 0.99 11.8±0.39 15.63±0.63C190.0 207.6/21.8 3.21±0.0 3.4±0.9 17.57 0.87 2.41±0.03 1.96±0.423C274.1 269.9/83.2 2.74±0.0 2.6±0.1 13.13 0.65 2.34±0.02 2.64±0.423C298 352.2/60.7 2.39±0.4 2.6±0.1 10.69 0.53 1.3±0.07 1.97±0.39

*Estimated from OH(1667) 3σ detection limits using Tex=3.5 K, FWHM=1 km/s and NOH/NH2=10−7 (see Section 5).