# Dust-Gas Scaling Relations and OH Abundance in the Galactic ISM

Hiep Nguyen11affiliation: Department of Physics and Astronomy and MQ Research
Centre in Astronomy, Astrophysics and Astrophotonics, Macquarie University,
NSW 2109, Australia. Email<EMAIL_ADDRESS>22affiliation:
Australia Telescope National Facility, CSIRO Astronomy and Space Science, PO
Box 76, Epping, NSW 1710, Australia , J. R. Dawson11affiliation: Department of
Physics and Astronomy and MQ Research Centre in Astronomy, Astrophysics and
Astrophotonics, Macquarie University, NSW 2109, Australia. Email: van-
<EMAIL_ADDRESS>22affiliation: Australia Telescope National
Facility, CSIRO Astronomy and Space Science, PO Box 76, Epping, NSW 1710,
Australia , M.-A. Miville-Deschênes33affiliation: Institut d’Astrophysique
Spatiale, CNRS, Univ. Paris-Sud, Université Paris-Saclay, Bât. 121, 91405,
Orsay Cedex, France 44affiliation: Laboratoire AIM, Paris-Saclay, CEA/IRFU/DAp
- CNRS - Université Paris Diderot, 91191, Gif-sur-Yvette Cedex, France ,
Ningyu Tang55affiliation: National Astronomical Observatories, CAS, Beijing
100012, China , Di Li55affiliation: National Astronomical Observatories, CAS,
Beijing 100012, China 66affiliation: Key Laboratory of Radio Astronomy,
Chinese Academy of Science 77affiliation: University of Chinese Academy of
Sciences, Beijing 100049, China , Carl Heiles88affiliation: Department of
Astronomy, University of California, Berkeley, 601 Campbell Hall 3411,
Berkeley, CA 94720-3411 , Claire E. Murray99affiliation: Space Telescope
Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA , Snežana
Stanimirović1010affiliation: Department of Astronomy, University of Wisconsin-
Madison, 475 North Charter Street, Madison, WI 53706, USA , Steven J.
Gibson1111affiliation: Department of Physics and Astronomy, Western Kentucky
University, Bowling Green, KY 42101, USA , N. M. McClure-
Griffiths1212affiliation: Research School of Astronomy and Astrophysics,
Australian National University, Canberra, ACT 2611, Australia , Thomas
Troland1313affiliation: Department of Physics and Astronomy, University of
Kentucky, Lexington, Kentucky 40506 , L. Bronfman1414affiliation: Departamento
de Astronomía, Universidad de Chile, Casilla 36, Santiago de Chile, Chile , R.
Finger1515affiliation: Astronomy Department, Universidad de Chile, Camino El
Observatorio 1515, 1058 Santiago, Chile

###### Abstract

Observations of interstellar dust are often used as a proxy for total gas
column density $N_{\mathrm{H}}$. By comparing Planck thermal dust data
(Release 1.2) and new dust reddening maps from Pan-STARRS 1 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 correlations between dust optical depth $\tau_{353}$, reddening
$E(B{-}V)$and the total proton column density $N_{\mathrm{H}}$ in the range
(1–30)$\times$1020cm-2, along sightlines with no molecular gas detections in
emission. We derive an $N_{\mathrm{H}}$/$E(B{-}V)$ ratio of
(9.4$\pm$1.6)$\times$1021cm-2mag-1 for purely atomic sightlines at $|b|$$>$5∘,
which is 60% higher than the canonical value of Bohlin et al. (1978). We
report a $\sim$40% increase in opacity
$\sigma_{353}$=$\tau_{353}$/$N_{\mathrm{H}}$, when moving from the low column
density ($N_{\mathrm{H}}$$<$5$\times$1020cm-2) to moderate column density
($N_{\mathrm{H}}$$>$5$\times$1020cm-2) regime, and suggest that this rise is
due to the evolution of dust grains in the atomic ISM. Failure to account for
Hi opacity can cause an additional apparent rise in $\sigma_{353}$, of the
order of a further $\sim$20%. We estimate molecular hydrogen column densities
$N_{\mathrm{H}_{2}}$ from our derived linear relations, and hence derive the
OH/H2 abundance ratio of $X_{\mathrm{OH}}$$\sim$1$\times$10-7 for all
molecular sightlines. Our results show no evidence of systematic trends in OH
abundance with $N_{\mathrm{H}_{2}}$ in the range
$N_{\mathrm{H}_{2}}$$\sim$(0.1$-$10)$\times$1021cm-2. This suggests that OH
may be used as a reliable proxy for H2 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 interstellar medium (ISM) have
historically been dominated by two radio spectral lines: the 21 cm line of
atomic hydrogen (Hi) and the microwave emission from carbon monoxide (CO),
particularly the CO(J=1–0) line. The former provides direct measurements of
the warm neutral medium (WNM), and the cold neutral medium (CNM) which is the
precursor to molecular clouds. The latter is widely used as a proxy for
molecular hydrogen (H2), often via the use of an empirical ‘X-factor’, (e.g.
Bolatto et al. 2013). The processes by which CNM and molecular clouds form
from warm atomic gas sows the seeds of structure into clouds, laying the
foundations for star formation. Being able to observationally track the ISM
through this transition is of key importance.

However, there is strong evidence for gas not seen in either Hi or CO. This
undetected material is often called “dark gas”, following Grenier et al.
(2005). These authors found an excess of diffuse gamma-ray emission from the
Local ISM, with respect to the expected flux due to cosmic ray interactions
with the gas mass estimated from Hi and CO. Similar conclusions have been
reached using many different tracers, including $\gamma$-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; Reach et al. 1994; Douglas & Taylor 2007;
Planck Collaboration et 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 emission 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 missing gas mass (Fukui et al., 2015), CO-dark H2
is generally expected to be a major constituent, particularly in the envelopes
of molecular clouds (e.g. Lee et al., 2015). In diffuse molecular regions, H2
is effectively self-shielded, but CO is typically photodissociated (Tielens &
Hollenbach, 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 tracer of H2 in such environments. Indeed Herschel
observations of Cii suggest that between 20–75% of the H2 in the Galactic
Plane may be CO-dark (Pineda et al., 2013).

For the atomic medium, the mass of warm Hi can be computed directly from
measured line intensities under the optically thin assumption. However, cold
Hi with spin temperature $T_{s}$ $\lesssim$ 100K suffers from significant
optical depth effects, leading to an underestimation of the total column
density. This difficulty is generally addressed by combining Hi absorption and
emission profiles observed towards (and immediately adjacent to) bright,
compact continuum background sources. Such studies find that the optically
thin assumption underestimates the true Hi column by no more than a few 10%
along most 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 regions may be much higher (Bihr et al., 2015).

Since dust and gas are generally well mixed, absorption due to dust grains has
been widely used as a proxy for total gas column density. Early work (e.g.
Savage & Jenkins 1972, Bohlin et al. 1978) observed Lyman-$\alpha$ and H2
absorption in stellar spectra to calibrate the relationship between total
Hydrogen column density $N_{\mathrm{H}}$, and the color excess $E(B{-}V)$.
Similar work was carried out by comparing X-ray absorption with optical
extinction, $A_{V}$ (Reina & Tarenghi 1973, Gorenstein 1975). Bohlin et al’s
value of $N_{\mathrm{H}}$/$E(B{-}V)$=5.8$\times$1021cm-2mag-1 has become a
widely accepted standard.

Dust emission is also a powerful tool, and requires no background source
population. The dust emission spectrum in the bulk of the ISM peaks in the
FIR-to-millimeter range, and arises mostly from large grains in thermal
equilibrium with the ambient local radiation field (Draine 2003, Draine & Li
2007). It has long been recognized that FIR dust emission could potentially be
a better tracer of $N_{\mathrm{H}}$ 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 a linear correlation with
$N_{\mathrm{H}}$ (as measured by Hi and CO) is typically found in the range
$A_{V}$=0.3$-$2.7 mag (Planck Collaboration et al. 2011, 2014a, 2014b; 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 grains across the gas phases; (2)
underestimation of the total gas column due to significant cold Hi opacity;
(3) insufficient sensitivity for CO detection. It has also been impossible to
rule out remaining systematic effects in the Planck data or bias in the
estimate of $\tau_{353}$ introduced by the choice of the modified black-body
model.

In this study, we examine the correlations between accurately-derived Hi
column densities and dust-based proxies for $N_{\mathrm{H}}$. We make use of
opacity-corrected Hi column densities derived from two surveys: the Arecibo
Millennium Survey (MS, Heiles & Troland, 2003b, hereafter HT03), and 21-SPONGE
(Murray et al. 2015), both of which used on-/off-source measurements towards
extragalactic radio continuum sources to derive accurate physical properties
for the atomic ISM. We also make use of archival OH data from the Millennium
Survey, recently published for the first time in a companion paper, Li et al.
(2018). OH is an effective tracer of diffuse molecular regions (Wannier et al.
1993; Liszt & Lucas 1996; Barriault et al. 2010; Allen et al. 2012, 2015; Xu
et al. 2016; Li et al. 2018), and has recently been surveyed at high
sensitivity in parts of the Galactic Plane (Dawson et al., 2014; Bihr et al.,
2015). There exists both theoretical and observational evidence for the close
coexistence of interstellar OH and H2. Observationally, they appear to reside
in the same environments, as evidenced by tight relations between their column
densities (Weselak & Krełowski, 2014). Theoretically, the synthesis of OH is
driven by the ions O+ and H${}_{3}^{+}$ but requires H2 as the precursor; once
H2 becomes available, OH can be formed efficiently through the charge-exchange
chemical reactions initiated by cosmic ray ionization (van Dishoeck & Black,
1986). Here we combine Hi, OH and dust datasets to obtain new measurements of
the abundance ratio, $X_{\mathrm{OH}}$=$N_{\mathrm{OH}}$/$N_{\mathrm{H}_{2}}$
– 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 and corrections on Hi are briefly summarized.
In Section 3, the results from OH observations are discussed. Section 4
discusses the relationship between $\tau_{353}$, $E(B{-}V)$ and
$N_{\mathrm{H}}$ in the atomic ISM. We finally estimate the OH/H2 abundance
ratio in Section 5, before concluding in Section 6.

##  2\. Datasets

In this study, we use the all-sky optical depth ($\tau_{353}$) map of the dust
model data measured by Planck/IRAS (Planck Collaboration et al. 2014a –
hereafter PLC2014a), the reddening $E(B{-}V)$ all-sky map from Green et al.
(2018), Hi data from both the 21-SPONGE Survey (Murray et al. 2015) and the
Millennium Survey (Heiles & Troland 2003a, HT03), OH data from the Millennium
Survey (Li et al., 2018), CO data from the Delingha 14m Telescope, the Caltech
Submillimeter Observatory (CSO) and the IRAM 30m telescope (Li et al., 2018).

###  2.1. Hi and OH

Hi data from the Millennium Arecibo 21-Centimeter Absorption-Line Survey
(hereafter MS) was taken towards 79 strong radio sources (typically S
$\gtrsim$ 2 Jy) using the Arecibo L-wide receiver. The two main lines of
ground state OH at 1665.402 and 1667.359 MHz were observed simultaneously
towards 72 positions, and OH absorption was detected along 19 of these
sightlines (see also Li et al., 2018). The observations are described in
detail by HT03. Briefly, their so-called Z16 observation pattern consists of
one on-source absorption spectrum towards the background radio source and 16
off-source emission spectra with the innermost positions at 1.0 HPBW and the
outermost positions at $\sqrt{2}$ HPBW from the central source. The off-source
“expected” emission spectrum, the emission profile we would observe in the
absence of the continuum source, is then estimated by modeling the 17-point
measurements. In this work we use the published values of HT03 for the total
Hi column density, $N_{\mathrm{HI}}$ (scaled as described below), and use the
off-source (expected) MS emission profiles to compute the Hi column density
under the optically thin assumption, $N^{*}_{\mathrm{HI}}$, where required. We
compute OH column densities ourselves, as described in Section 3. All OH
emission and absorption spectra are scaled to a main-beam temperature scale
using a beam efficiency of $\eta_{b}$=0.5 (Heiles et al., 2001), appropriate
if the OH is not extended compared to the Arecibo beam size of $3^{\prime}$.

In order to increase the source sample, we also use Hi data from the Very
Large Array (VLA) 21-SPONGE Survey, which observed 30 continuum sources,
including 16 in-common with the Millennium Survey sample (Murray et al. 2015).
21-SPONGE used on-source absorption data from the VLA, combining them with
off-source emission profiles observed with Arecibo. Murray et al. (2015)
report an excellent agreement between the optical depths measured by the two
surveys, demonstrating that the single dish Arecibo absorption profiles are
not significantly contaminated with resolved 21 cm emission. Note that in this
work we have used an updated scaling of the 21-SPONGE emission profiles, which
applies a beam efficiency factor of 0.94 to the Arecibo spectra. The total
number of unique sightlines presented in this work is therefore 93. The
locations of all observed sources in Galactic coordinates are presented in
Figure 1. Where sources were observed in both the MS and 21-SPONGE, we use the
MS data.

####  2.1.1 Hi Intensity Scale Corrections

We check our $N^{*}_{\mathrm{HI}}$ against the Leiden-Argentine-Bonn survey
(LAB, Hartmann & Burton, 1997; Kalberla et al., 2005) and the HI4PI survey
(HI4PI Collaboration et al., 2016). Both are widely regarded as a gold
standard in the absolute calibration of Galactic Hi. We find that the
optically thin column densities derived from 21-SPONGE are consistent with LAB
and HI4PI. However, the MS values are systematically lower than both LAB and
HI4PI by a factor of $\sim$1.14. A possible explanation for 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, HI4PI and 21-SPONGE, one might
assume that both the on-source and off-source spectra must be rescaled, and
the opacity-corrected column densities recomputed according to the method of
HT03 (or equivalent). However, $N_{\mathrm{HI}}$ may in fact be obtained from
the tabulated values of HT03, with no need to perform a full reanalysis of the
data. For warm components, the tabulated values of $N_{\mathrm{HI}}$ are
simply scaled by 1.14 – appropriate since these were originally computed
directly from the the integrated off-source (expected) profiles under the
optically thin assumption. For cold components, we recall that the radiative
transfer equations for the on-source and off-source (expected) spectra in the
MS dataset are given by:

$T_{\mathrm{B}}^{\mathrm{ON}}(v)=(T_{\mathrm{bg}}+T_{\mathrm{c}})e^{-\tau_{v}}+T_{\mathrm{s}}(1-e^{-\tau_{v}})+T_{\mathrm{rx}}$
(1)
$T_{\mathrm{B}}^{\mathrm{OFF}}(v)=T_{\mathrm{bg}}e^{-\tau_{v}}+T_{\mathrm{s}}(1-e^{-\tau_{v}})+T_{\mathrm{rx}},$
(2)

where $T_{\mathrm{B}}^{\mathrm{OFF}}(v)$ and $T_{\mathrm{B}}^{\mathrm{ON}}(v)$
are the main beam temperatures of the off-source spectrum and on-source
spectrum, respectively. $T_{\mathrm{s}}$ is the spin temperature, $\tau_{v}$
is the optical depth, $T_{\mathrm{rx}}$ is the receiver temperature ($\sim$25
K), and $T_{\mathrm{c}}$ is the main-beam temperature of the continuum source,
obtained from the line-free portions of the on-source spectrum.
$T_{\mathrm{bg}}$ is the continuum background brightness temperature including
the 2.7 K isotropic radiation from CMB and the Galactic synchrotron background
at the source position. Equations (1) and (2) may be solved for $\tau_{v}$ and
$T_{\mathrm{s}}$:

$e^{-\tau_{v}}=\frac{T_{\mathrm{B}}^{\mathrm{ON}}(v)-T_{\mathrm{B}}^{\mathrm{OFF}}(v)}{T_{\mathrm{c}}},$
(3)
$T_{\mathrm{s}}=\frac{T_{\mathrm{B}}^{\mathrm{OFF}}(v)-T_{\mathrm{bg}}e^{-\tau_{v}}-T_{\mathrm{rx}}}{1-e^{-\tau_{v}}}.$
(4)

From Equation (3), it is clear that optical depth is unchanged by any
rescaling, which will affect both the numerator and denominator of the
expression identically. Only $T_{s}$ must be recomputed. This is done on a
component-by-component basis from the tabulated Gaussian fit parameters for
peak optical depth, $\tau_{0}$, peak brightness temperature (scaled by 1.14),
and the linewidth $\Delta v$. The corrected $N_{\mathrm{HI}}$ is obtained from

$\frac{N_{\mathrm{HI}}}{[10^{18}~{}\mathrm{cm}^{-2}]}=1.94\cdot\tau_{0}\cdot\frac{T_{\mathrm{s}}}{[K]}\cdot\frac{\Delta
v}{[\mathrm{km~{}s}^{-1}]},$ (5)

where the factor 1.94 includes the usual constant 1.8224 and the 1.065 arising
from the integration over the Gaussian line profile.

Figure 1.— Locations of all 93 sightlines considered in this study, overlaid
on the map of dust optical depth $\tau_{353}$. Squares show Hi absorption
detections (93/93); red circles show OH absorption detections (19/72) and
black circles non-detections (51/72); red triangles show CO detections (19/44)
and black triangles non-detections (25/44). For purely atomic sightlines
(those with no molecular detection at the threshold discussed in Section 4),
the squares are colored red. Note that the absence of a symbol indicates that
the sightline was not observed in that particular tracer. The labeled
sightline towards 3C132 (far left) shows the single position detected in Hi
and OH but not detected in CO emissions. The “X” marker labels the center of
the Milky Way. Note that the symbols for a small number of sightlines entirely
overlap due to their proximity on the sky.

####  2.1.2 $N_{\mathrm{HI}}$ vs $N^{*}_{\mathrm{HI}}$

We show in Figure 2 the correlation between $N_{\mathrm{HI}}$ and
$N^{*}_{\mathrm{HI}}$ towards all 93 positions. While optically thin Hi column
density is comparable with the true column density in diffuse/low-density
regions with $N_{\mathrm{HI}}$$\lesssim$5$\times$1020cm-2, opacity effects
start to become apparent above $\sim$5$\times$1020cm-2.

If a linear fit is performed to the data, the ratio
$f$=$N_{\mathrm{HI}}$/$N^{*}_{\mathrm{HI}}$ may be described as a function of
log($N^{*}_{\mathrm{HI}}$/1020) with a slope of (0.19$\pm$0.02) and an
intercept of (0.89$\pm$0.02) (see also Lee et al., 2015). Alternatively, a
simple isothermal correction to the optically thin $N^{*}_{\mathrm{HI}}$ data
with $T_{\mathrm{s}}$$\sim$144 K also yields a good agreement with our
datapoints, as illustrated in Figure 2 (see also Liszt, 2014b). This approach
also better fits the low $N_{\mathrm{HI}}$ plateau,
$N_{\mathrm{HI}}$$<$5$\times$1020cm-2, below which
$N^{*}_{\mathrm{HI}}$$\approx$$N_{\mathrm{HI}}$. While a single component with
a constant spin temperature is a poor physical description of interstellar Hi,
it can provide a reasonable (if crude) correction for opacity.

Figure 2.— The ratio $f$=$N_{\mathrm{HI}}$/$N^{*}_{\mathrm{HI}}$ as a function
of opacity-corrected $N_{\mathrm{HI}}$ along 93 sightlines from the MS and
21-SPONGE surveys. Circles show accurate $N_{\mathrm{HI}}$ obtained via on-
and off-source observations (HT03; scaled as described in the text), with the
34 atomic sightlines (selection criteria described in Section 4) filled grey
and all other points filled black. Red triangles show $N_{\mathrm{HI}}$
obtained from $N^{*}_{\mathrm{HI}}$ assuming a single isothermal component of
$T_{\mathrm{s}}$$\sim$144 K. The vertical dashed line is plotted at
$N_{\mathrm{HI}}$=5$\times$1020cm-2, the horizontal dashed line marks where
$N_{\mathrm{HI}}$=$N^{*}_{\mathrm{HI}}$.

###  2.2. CO

As described in Li et al. (2018), a CO follow-up survey was conducted towards
44 of the sightlines considered in this work. The J=1–0 transitions of 12CO,
13CO, and C18O were observed with the Delingha 13.7m telescope in China.
12CO(J=2–1) data for 45 sources and J=3–2 data for 8 sources with strong 12CO
emission were taken with the 10.4m CSO on Mauna Kea, with further
supplementary data obtained by the IRAM 30m telescope. In this work we use CO
data solely to identify and exclude from some parts of the analysis positions
with detected CO-bright molecular gas – comprising 19 of the 44 observed
positions. These positions are identified in Figure 1.

###  2.3. Dust

To trace the total gas column density $N_{\mathrm{H}}$ we use publicly-
available all-sky maps of the 353 GHz dust optical depth ($\tau_{353}$) from
the Planck satellite. The $\tau_{353}$ map was obtained by a modified black-
body (MBB) fit to the first 15 months of 353, 545, and 857 GHz data, together
with IRAS 100 micron data (for details see PLC2014a). The angular resolution
of this dataset is 5 arcmin. In this work we use the R1.20 data release in
Healpix111$http://healpix.sourceforge.net$ format (Górski et al. 2005). For
dust reddening, we employ the newly-released all-sky 3D dust map of Green et
al. (2018) at an angular resolution of 3′.4-13′.7, which was derived from
2MASS and the latest Pan-STARRS 1 data photometry. In contrast to emission-
based dust maps that depend on the modeling of the temperature, optical depth,
and the shape of the emission spectrum, in maps based on stellar photometry
reddening values are more directly measured and not contaminated from zodiacal
light or large-scale structure. Here we convert the Green et al. (2018)
Bayestar17 dust map to $E(B{-}V)$ by applying a scaling factor of 0.884, as
described in the documentation accompanying the data
release222http://argonaut.skymaps.info/usage.

##  3\. OH Data Analysis

The Millennium Survey OH data consists of on-source and off-source ‘expected’
spectra for each of the OH lines. In our companion paper Li et al. (2018), we
use the method of HT03 to derive OH optical depths, excitation temperatures
and column densities. Namely, we obtain solutions for the excitation
temperature, $T_{\mathrm{ex}}$, and $\tau$ via Gaussian fitting (to both the
on-source and off-source spectra) that explicitly includes the appropriate
treatment of the radiative transfer. In the present work we use a simpler
channel-by-channel method for the derivation of $T_{\mathrm{ex}}$.

The radiative transfer equations for the on-source and off-source (expected)
spectra are identical to those for Hi, given above in Equations (1) and (2).
All terms and their meanings are identical, with the exception that the spin
temperature, $T_{\mathrm{s}}$ is replaced by $T_{\mathrm{ex}}$.
$T_{\mathrm{bg}}$ is the continuum background brightness temperature including
the 2.7 K isotropic radiation from CMB and the Galactic synchrotron background
at the source position. For consistency with HT03 and Li et al. (2018), we
estimate the synchrotron contribution at 1665.402 MHz and 1667.359 MHz from
the 408 MHz continuum map of Haslam et al. (1982), by adopting a temperature
spectral index of 2.8, such that

$T_{\mathrm{bg}}=2.7+T_{\mathrm{bg,408}}(\nu_{\mathrm{OH}}/408)^{-2.8},$ (6)

resulting in typical values of around 3.5 K. The background continuum
contribution from Galactic HII regions may be safely ignored, since the
continuum sources we observed are either at high Galactic latitudes or
Galactic Anti-Center longitudes. Thus, in line-free portions of the off-source
spectra:

$T_{\mathrm{B}}^{OFF}(v)=T_{\mathrm{bg}}+T_{\mathrm{rx}}.$ (7)

In the absence of information about the true gas distribution, we assume that
OH clouds cover fully both the continuum source and the main beam of the
telescope. We may therefore solve equations (1) and (2) to derive
$T_{\mathrm{ex}}$ and $\tau_{v}$ for each of the OH lines, as shown in
Equations (3) and (4) for the case of Hi.

We fit each OH opacity spectrum (cf. Equation 3) with a set of Gaussian
profiles to obtain the peak optical depth ($\tau_{0,n}$), central velocity
($v_{0,n}$) and FWHM ($\Delta v_{n}$) of each component, $n$. Equation (4) is
then used to calculate excitation temperature spectra. Examples of
$e^{-\tau_{v}}$, $T_{\mathrm{B}}^{\mathrm{OFF}}$, and $T_{\mathrm{ex}}$
spectra are shown in Figure 3, together with their associated Gaussian fits.
It can be seen that the $T_{\mathrm{ex}}$ spectra are approximately flat
within the FWHM of each Gaussian component. We therefore compute an excitation
temperature for each component from the mean $T_{\mathrm{ex}}$ in the range
$v_{0,n}\pm\Delta v/2$.

Figure 4 compares the $\tau_{0}$ and $T_{\mathrm{ex}}$ values obtained from
our method with those of Li et al. (2018), demonstrating that the two methods
generally return consistent results. Minor differences arise only for the most
complex sightlines through the Galactic Plane (G197.0+1.1, T0629+10) where the
spectra are not simple to analyze; however, even these points are mostly
consistent to within the errors.

We compute total OH column densities, $N_{\mathrm{OH}}$, independently from
both the 1667 and 1665 MHz lines via:

$\frac{N_{\mathrm{OH,1667}}}{[10^{14}~{}\mathrm{cm}^{-2}]}=2.39\cdot\tau_{1667}\cdot\frac{T_{\mathrm{ex,1667}}}{[K]}\cdot\frac{\Delta
v_{1667}}{[\mathrm{km~{}s}^{-2}]},$ (8)
$\frac{N_{\mathrm{OH,1665}}}{[10^{14}~{}\mathrm{cm}^{-2}]}=4.30\cdot\tau_{1665}\cdot\frac{T_{\mathrm{ex},1665}}{[K]}\cdot\frac{\Delta
v_{1665}}{[\mathrm{km~{}s}^{-2}]},$ (9)

where the constants include Einstein A-coefficients of $A_{1667}=7.778\times
10^{-11}s^{-1}$ and $A_{1665}=7.177\times 10^{-11}s^{-1}$ for the OH main
lines (Destombes et al. 1977). All values of $\tau_{0}$, $T_{\mathrm{ex}}$ and
$N_{\mathrm{OH}}$ are tabulated in Table 1.

Figure 3.— Example of OH 1667 MHz $e^{-\tau_{v}}$ (top), expected
$T_{\mathrm{B}}^{\mathrm{OFF}}$ (middle), and $T_{\mathrm{ex}}$ (bottom)
spectra for the source P0428+20. The FWHM of the Gaussian fits to the
absorption profile are used to define the range over which $T_{\mathrm{ex}}$
is computed for each component, shown as white regions in the bottom panel.
Figure 4.— Comparison between derived values of the peak optical depth $\tau$
(left panel), and $T_{\mathrm{ex}}$ (right panel) for both OH main lines, 1667
MHz (black) and 1665 MHz (gray), as obtained from our companion paper by Li et
al. (2018) and the present work. The dashed lines mark where the two values
are equal. Figure 5.— Example maps of the immediate vicinity of 4 “purely
atomic” sightlines towards background radio sources. Dust maps (3$\times$3
degrees in Galactic coordinates) are adopted from Planck collaboration 2014
($\tau_{353}$, Nside = 2048) and Green et al. 2018 ($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 typical sensitivity of CfA CO survey, and the other
contour levels are evenly spaced from the base to the maximum in each map
area. Equivalent maps for the remaining 30 purely atomic sightlines are given
in Appendix A and 19 OH-bright sightlines in Appendix B.

##  4\. Dust-Based Proxies for Total neutral gas
column density

In this section we will investigate the correlations between dust properties
and the total gas column density $N_{\mathrm{H}}$. Specifically, we consider
dust optical depth at 353 GHz, $\tau_{353}$, and reddening, $E(B{-}V)$, with
datasets sourced as described in Section 2.3. When these quantities are used
as proxies for $N_{\mathrm{H}}$, a single linear relationship between the
measured quantity and $N_{\mathrm{H}}$ is typically assumed. In this work, our
Hi dataset provides accurate (opacity-corrected) atomic column densities,
while complementary OH and CO data allow us to identify and exclude sightlines
with molecular gas (dark or not). We are therefore able to measure
$\tau_{353}$/$N_{\mathrm{H}}$ and $E(B{-}V)$/$N_{\mathrm{H}}$ along a sample
of purely atomic sightlines for which $N_{\mathrm{H}}$ is very well
constrained.

In the following, we consider 34/93 sightlines to be “purely atomic”. These
are defined as either (a) sightlines where CO and OH were observed and not
detected in emission (16/93); or (b) sightlines where CO was not observed but
OH was observed but not detected (18/93 sightlines). In both cases we require
that OH be undetected in the 1667 MHz line to a detection limit of
$N_{\mathrm{OH}}$$<$1$\times$1013cm-2 (see Li et al., 2018), which excludes
some positions with weaker continuum background sources. We may confidently
assume that these sightlines contain very little or no H2, and note that all
but one of them lie outside the Galactic plane ($|b|$$>$10∘). Figure 5 shows
example maps of the immediate vicinity of 4 of these sightlines in
$\tau_{353}$ and $E(B{-}V)$. Identical maps for the remaining 30 atomic
sightlines, as well as all 19 sightlines with OH detections (see also Section
5), are shown in the appendices.

In all following subsections, $N_{\mathrm{H}}$ is therefore taken to be equal
to $N_{\mathrm{HI}}$, the opacity-corrected Hi column density, as derived
along sightlines with no molecular gas detected in emission.

###  4.1.  $N_{\mathrm{H}}$ from dust optical depth $\tau_{353}$

We adopt the all-sky map of dust optical depth $\tau_{353}$ computed by
PLC2014a. This was derived from a MBB empirical fit to IRAS and Planck maps at
3000, 857, 545 and 353 GHz, described by the expression:

$I_{\nu}=\tau_{353}B_{\nu}(T_{\mathrm{dust}})\left(\frac{\nu}{353}\right)^{\beta_{\mathrm{dust}}}.$
(10)

Here, $\tau_{353}$, dust temperature, $T_{\mathrm{dust}}$, and spectral index,
$\beta_{\mathrm{dust}}$, are the three free parameters, and
$B_{\nu}(T_{\mathrm{dust}})$ is the Planck function for dust at temperature
$T_{\mathrm{dust}}$ which is, in this 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 then be written as:

$\tau_{353}=\frac{I_{353}}{B_{353}(T_{\mathrm{dust}})}=\kappa_{353}r\mu
m_{H}N_{H}=\sigma_{353}N_{H},$ (11)

where $\sigma_{353}$ is the dust opacity, $\kappa_{353}$ is the dust
emissivity cross-section per unit mass (cm2g-1), $r$ is the dust-to-gas mass
ratio, $\mu$ is the mean molecular weight and $m_{H}$ is the mass of a
hydrogen atom.

Figure 6 shows the correlation between $N_{\mathrm{H}}$ and $\tau_{353}$. A
tight linear trend can be seen with a Pearson coefficient of 0.95. The value
of $\sigma_{353}$ from the orthogonal distance regression (Boggs & Rogers,
1990) linear fit is (7.9$\pm$0.6)$\times$10-27cm2H-1 (the intercept is set to
0), where the quoted uncertainties are the 95% confidence limits estimated
from pair bootstrap resampling. This is consistent to within the uncertainties
with that obtained by PLC2014a based on all-sky Hi data from LAB,
(6.6$\pm$1.7)$\times$10-27cm2H-1. Note that here we have quoted the PLC2014a
measurement made towards low $N_{\mathrm{HI}}$ positions, because the lack of
any Hi opacity correction in that work makes this value the most reliable.
However, our fit is consistent with all of $\sigma_{353}$ values presented in
that work (which was based on the Planck R1.20 data release), to within the
quoted uncertainties.

Small systematic deviations from the linear fit, evident at the high and low
column density ends of the plot, are discussed further in $\S$4.3.

In order to examine the possible contribution of molecular gas to
$N_{\mathrm{H}}$ along the 34 atomic sightlines, we estimate upper limits on
$N_{\mathrm{H}_{2}}$ from the 3$\sigma$ OH detection limits using an abundance
ratio of $X_{\mathrm{OH}}$=$10^{-7}$ (see Section 5). These values are
tabulated in Table 1, and the resulting upper limits on $N_{\mathrm{H}}$ are
shown as gray triangles in Figure 6. As expected, the $\sigma_{353}$ obtained
from the fit to these upper limits is lower, at
(6.4$\pm$0.3)$\times$10-27cm2H-1. However, while some molecular gas may indeed
be present at low levels, these limits should be considered as extreme upper
bounds on the true molecular column density. This is particularly true for the
most diffuse sightlines with the lowest column density
($N_{\mathrm{HI}}$$<$5$\times$1020cm-2), where the observational upper limits
may appear to raise $N_{\mathrm{H}}$ by up to $\sim$50%. Molecules are not
expected to be well-shielded at such low columns (and indeed even CNM is
largely absent along these sightlines in our data). Even for higher column
density datapoints, it can be readily seen from Figures 5 and 12–14 that all
sightlines considered in this analysis lie well away from even the faintest
outskirts of CO-bright molecular gas complexes. We also note that the
deviations from the linear fit that will be discussed in more detail below
could not be removed by any selective addition of molecular gas at levels up
to these limits.

Figure 6.— $\tau_{353}$ vs $N_{\mathrm{H}}$ along the 34 purely atomic
sightlines described in the text. Grey triangles indicate the upper limits for
$N_{\mathrm{H}}$ along these 34 atomic sightlines with $N_{\mathrm{H}_{2}}$
estimated from the 3$\sigma$ OH detection limits using an abundance ratio
$N_{\mathrm{OH}}$/$N_{\mathrm{H}_{2}}$=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 Fukui et al. (2015). (Note that all these works use the same
$\tau_{353}$ map). $\tau_{353}$ error bars are from the uncertainty map of
PLC2014a; the shaded region represents the 95% confidence intervals for the
linear fit, estimated from pair bootstrap resampling.

We next compare our results with the dust opacity $\sigma_{353}$ derived by
Fukui et al. (2015) (plotted on Figure 6 as a dashed line). These authors
derived a smaller value than in the present work (by a factor of $\sim$1.5),
by restricting their fit to only the warmest dust temperatures, under the
assumption that these most reliably select for genuinely optically thin Hi.
They then applied this factor to the Planck $\tau_{353}$ map (excluding
$|b|$$<$15∘ and CO-bright sightlines) to estimate $N_{\mathrm{HI}}$, assuming
that the contribution from CO-dark H2 was negligible. This resulted in
$N_{\mathrm{HI}}$ values $\sim$2–2.5 times higher than under the optically
thin assumption, and motivated their hypothesis that significantly more
optically thick Hi exists than is usually assumed. However, we find that while
the $\sigma_{353}$ of Fukui et al. (2015) may be a good fit to some sightlines
in the very low $N_{\mathrm{HI}}$ regime ($\lesssim$3$\times$1020cm-2), it
overestimates $N_{\mathrm{HI}}$ at larger column densities by $\sim$50%.
Indeed, as will be discussed below, $\sigma_{353}$ is not expected to remain
constant as dust evolves. This (combined with some contribution from CO-dark
H2) may reconcile the apparent discrepancy between their findings and
absorption/emission-based measurements of the opacity-corrected Hi column.

###  4.2.  $N_{\mathrm{H}}$ from dust reddening $E(B{-}V)$

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

$\begin{split}E(B{-}V)=\frac{A_{V}}{R_{V}}=1.086\frac{\kappa_{V}}{R_{V}}r\mu
m_{\rm H}N_{\rm H}\end{split}$ (12)

where $A_{V}$ is the dust extinction, $R_{V}$ is an empirical coefficient
correlated with the average grain size and all other symbols are defined as
before. In the Milky Way, $R_{V}$ is typically assumed to be 3.1 (Schultz &
Wiemer, 1975), but it may vary between 2.5 and 6.0 along different sightlines
(Goodman et al., 1995; Draine, 2003).

The ratio
$\langle$$N_{\mathrm{H}}$/$E(B{-}V)$$\rangle$=5.8$\times$1021cm-2mag-1 (Bohlin
et al., 1978) is a widely-accepted standard, used in many fields of
astrophysics to connect reddening measurements to gas column density. This
value was derived from Lyman-${\alpha}$ and H2 line absorption measurements
toward 100 stars (see also Savage et al., 1977), and has been replicated over
the years via similar methodology (e.g. Shull & van Steenberg, 1985; Diplas &
Savage, 1994; Rachford et al., 2009). However, a number of recent works using
Hi 21cm data have found significantly higher values (PLC2014a; Liszt, 2014a;
Lenz et al., 2017).

Figure 7.— Correlation between $N_{\mathrm{H}}$ and dust reddening $E(B{-}V)$
from Green et al. (2018) along 34 atomic sightlines. Grey triangles indicate
the upper limits for $N_{\mathrm{H}}$ along these 34 atomic sightlines, with
$N_{\mathrm{H}_{2}}$ estimated from the 3$\sigma$ OH detection limits using an
abundance ratio $N_{\mathrm{OH}}$/$N_{\mathrm{H}_{2}}$=10-7. The errorbar on
$E(B{-}V)$ along each sightline is the standard deviation of the 20 Markov
Chain realisations of $E(B{-}V)$ at infinite distance; the shaded region
represents the 95% confidence intervals for the linear fit, estimated from
pair bootstrap resampling.

Here we use the all-sky map of $E(B{-}V)$ from Green et al. (2018) to estimate
the ratio $N_{\mathrm{H}}$/$E(B{-}V)$ for our sample of purely atomic
sightlines, at $|b|$$>$5∘. The results are shown in Figure 7. It can be seen
that $E(B{-}V)$ and $N_{\mathrm{H}}$ are strongly linearly correlated, with a
Pearson coefficient of 0.93. The ratio obtained from the linear fit is
$N_{\mathrm{H}}$/$E(B{-}V)$=(9.4$\pm$1.6)$\times$1021cm-2mag-1 (the intercept
is also set to be 0), where the quoted uncertainties are the 95% confidence
limits estimated from pair bootstrap resampling. This value is a factor of 1.6
higher than Bohlin et al. (1978).

The value obtained here is consistent with the estimate of Lenz et al. (2017):
$N_{\mathrm{H}}$/$E(B{-}V)$=8.8$\times 10^{21}$ cm-2 mag-1 (no uncertainty is
given in that work). These authors compared optically thin Hi column density
from HI4PI Collaboration et al. (2016) with various estimates of $E(B{-}V)$
from Schlegel 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) is only valid for $N_{\mathrm{H}}$$<$4$\times$1020cm-2, where it
seems safe to assume that the 21 cm emission is optically thin. Our value is
also close to Liszt (2014a), who find $N_{\mathrm{HI}}$/$E(B{-}V)$=8.3$\times
10^{21}$ cm-2 mag-1 (also given without uncertainty) for $|b|$$\geq$20∘ and
0.015$\lesssim$$E(B{-}V)$$\lesssim$0.075, by comparing Hi data from LAB and
$E(B{-}V)$ from Schlegel et al. (1998). The methodology used by these two
studies differs in a number of details. For instance, Liszt (2014a) did not
apply a gain correction to the Schlegel et al. (1998) map (whereas Lenz et al.
(2017) scaled it down by 12%), and did not smooth it to the LAB angular
resolution (30′). However, Liszt (2014a) did apply an empirical correction
factor to account for Hi opacity (albeit one whose effects on high-latitude
sightlines was small). These details may account for the difference between
the values obtained by these two otherwise similar studies.

We also note that, like the present work, these studies did not take into
account the potential contribution of dust associated with the diffuse warm
ionized gas (WIM). This would tend to produce a flattening of the $E(B{-}V)$
vs $N_{\mathrm{HI}}$ relation at low $N_{\mathrm{HI}}$ and therefore increase
the value of $N_{\mathrm{HI}}$/$E(B{-}V)$ artificially. Because we are able to
accurately probe a large column density range (up to 3$\times$1021 cm-2), we
would naively expect our estimate of $N_{\mathrm{H}}$/$E(B{-}V)$ to be less
affected by WIM bias than either Liszt (2014a) or Lenz et al. (2017) (which
would tend to have a greater effect on lower column datapoints). While more
work is needed to quantify the contribution of the WIM on dust
emission/absorption measurements at low $E(B{-}V)$, we consider it unlikely to
account for the difference between our work and historically lower
measurements of the $N_{\mathrm{H}}$/$E(B{-}V)$ ratio.

Despite minor differences between these three studies, it is clear that they
point at a $N_{\mathrm{HI}}$/$E(B{-}V)$ value of
($\sim$8–9)$\times$1021cm-2mag-1. This is 40–60% higher than the traditional
value of Bohlin et al. (1978), which has been used by most models of
interstellar dust as a reference point to set the dust-to-gas ratio (e.g.
Draine & Fraisse, 2009; Jones et al., 2013). We note that if $N_{\mathrm{H}}$
is replaced with upper limits (as discussed in §4.1),
$N_{\mathrm{H}}$/$E(B{-}V)$ climbs yet higher, leaving this key conclusion
unaffected.

###  4.3. Disentangling the effects of grain evolution and dark gas on
$\sigma_{353}$

A number of studies have used the correlation between $\tau_{353}$ and
$N_{\mathrm{H}}$, particularly with regards to the search for dark gas (e.g.
Planck Collaboration et al., 2011; Fukui et al., 2014, 2015; Reach et al.,
2015). It is clear that $\tau_{353}$ and $N_{\mathrm{H}}$ are in general
linearly correlated only if $\sigma_{353}$ is a constant. However, it is
recognized that $\sigma_{353}$ is sensitive to grain evolution, and
significant variations in the ratio $N_{\mathrm{H}}$/$\tau_{353}$ have been
observed, particularly when transitioning 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 variations in $\sigma_{353}$ may
relate to a change in dust properties via $\kappa_{353}$, and/or a variation
in the dust-to-gas ratio $r$, but may also include a contribution due to the
presence of dark gas, if this is unaccounted for in the estimated
$N_{\mathrm{H}}$.

PLC2014a presented the variation in $\sigma_{353}$ with $N_{\mathrm{H}}$ at
30′ resolution over the entire sky. In that work, $N_{\mathrm{H}}$ was derived
from ($N^{*}_{\mathrm{HI}}$+$X_{\mathrm{CO}}W_{\mathrm{CO}}$), thus dark gas
(both optically thick Hi and CO-dark H2) was unaccounted for. We reproduce
their data in Figure 8. It can be seen that $\sigma_{353}$ is roughly flat and
at a minimum in a narrow, low-column density range
$N_{\mathrm{H}}$=(1$-$3)$\times$1020cm-2, then increases linearly until
$N_{\mathrm{H}}$=15$\times$1020cm-2, by which point it is almost a factor of 2
higher. It then remains approximately constant for the canonical value of
$X_{\mathrm{CO}}$=2.0$\times$1020cm-2K-1km-1s. A key issue for dark gas
studies is disentangling how much of the initial rise in $\sigma_{353}$ is due
to changing grain properties, and how much is due to the contribution of
unseen material, whether it be opaque Hi or diffuse H2. (Note also the upturn
in $\sigma_{353}$ seen at the lowest $N_{\mathrm{H}}$, which may be due to the
presence of unaccounted-for protons in the warm ionized medium.)

Figure 8.— Dust opacity $\sigma_{353}$ versus total column density
$N_{\mathrm{H}}$ along the 34 purely atomic sightlines presented in this work
(red points), overlaid on $\sigma_{353}$ derived for the whole sky at 30′
resolution from PLC2014a. Here, blue points assume an X-factor of
$X_{\mathrm{CO}}$=1.0$\times$$10^{20}$, black assume
$X_{\mathrm{CO}}$=2.0$\times$$10^{20}$, and violet assume
$X_{\mathrm{CO}}$=3.0$\times$$10^{20}$. The grey envelope is the standard
deviation of these all-sky measurements for
$X_{\mathrm{CO}}$=2.0$\times$$10^{20}$. The red and black dashed lines show
respectively the constant $\sigma_{353}$ derived from the linear fit in
Section 4.1 and that obtained from PLC2014a for the low column-density regime.
Figure 9.— Dust opacity $\sigma_{353}$ versus total column density
$N_{\mathrm{H}}$ along the 34 purely atomic sightlines presented in this work
using true $N_{\mathrm{HI}}$ (red) and $N^{*}_{\mathrm{HI}}$ (black) as the
total gas column density $N_{\mathrm{H}}$. The vertical line is at
5$\times$1020cm-2. The large datapoints are the average values for the low-
density ($N_{\mathrm{H}}$$<$5$\times$1020cm-2) and high-density
($N_{\mathrm{H}}$$>$5$\times$1020cm-2) regions (error bars on these points are
the standard error on the mean). Note that two datapoints, one black
($\sigma_{353}$=27.2$\times$10-27cm2H-1) and one red
($\sigma_{353}$=16.1$\times$10-27cm2H-1), at
$N_{\mathrm{H}}$=18.2$\times$1020cm-2 are not shown, but are included in the
averages.

The column density range probed by our purely atomic sightlines,
$N_{\mathrm{H}}$=(1$\sim$30)$\times$1020cm-2 well samples the range where
$\sigma_{353}$ undergoes its first linear increase. Dark gas is also fully
accounted for in our data, since Hi is opacity-corrected, and no molecular gas
is detected in emission along these sightlines. To quantify the effect of
ignoring Hi opacity on $\sigma_{353}$ we compare $\sigma_{353}$ deduced from
the true, opacity-corrected $N_{\mathrm{HI}}$ with that deduced under the
optically thin assumption. The results are shown in Figure 9. In low column
density regions ($N_{\mathrm{H}}$$<$5$\times$1020cm-2), each $\sigma_{353}$
pair from $N_{\mathrm{HI}}$ and $N^{*}_{\mathrm{HI}}$ are comparable. However,
at higher column densities ($N_{\mathrm{H}}$$>$5$\times$1020cm-2)
$\sigma_{353}$ from true $N_{\mathrm{HI}}$ is systematically lower than that
measured from $N^{*}_{\mathrm{HI}}$. On average, $\sigma_{353}$ obtained from
optically thin Hi column density increases by $\sim$1.6 when going from low to
high column density regions; whereas $\sigma_{353}$ from true
$N_{\mathrm{HI}}$ increases by $\sim$1.4. This suggests that if Hi opacity is
not explicitly corrected for, it can account for around one third (1/3) of the
increase of $\sigma_{353}$ observed during the transition from diffuse to
dense atomic regimes. The remaining of two thirds (2/3) must arise due to
changes in dust properties.

From Equation 11, we see that $\sigma_{353}$ is a function of the dust-to-gas
mass ratio, $r$, and the dust emissivity cross-section, $\kappa_{353}$, which
depends on the composition and structure of dust grains. Given the
uncertainties on the efficiency of the physical processes involved in the
evolution of interstellar dust grains, it is difficult at this point to
conclude if the variations of $\sigma_{353}$ observed here are due to an
increase of the dust mass (i.e., $r$) or to a change in the dust emission
properties (i.e., $\kappa_{353}$). Using the dust model of Jones et al.
(2013), Ysard et al. (2015) suggest that most of the variations in the dust
emission observed by Planck in the diffuse ISM could be explained by
relatively small variations in the dust properties. That interpretation would
favor a scenario in which the increase of $\sigma_{353}$ from diffuse to
denser gas is caused by the growth of thin mantles via the accretion of atoms
and molecules from the gas phase. Even though this process would increase the
mass of grains (and therefore increase $r$) the change of the structure of the
grain surface would lead to a larger increase in $\kappa_{353}$.
Alternatively, it is possible that this systematic variation of
$\tau_{353}$/$N_{\mathrm{H}}$ could be due to residual large-scale systematic
effects in the Planck data, or to the fact that the modified black-body model
introduces a bias in the estimate of $\tau_{353}$. Neither of these
explanations can be ruled out.

Figure 8 shows $\sigma_{353}$ as a function of $N_{\mathrm{H}}$ superimposed
on the results from PLC2014a. It can be seen that we observe a similar rise in
$\sigma_{353}$ in the column density range ($\sim$5$-$30)$\times$1020cm-2, but
less extreme. In particular, most of our data points in the higher column
density range ($N_{\mathrm{H}}$$>$5$\times$1020cm-2) are found below the
PLC2014a trend, which is derived from the mean values of $\sigma_{353}$ over
the whole sky in $N_{\mathrm{H}}$ bins. This is true even if we use
$N^{*}_{\mathrm{HI}}$ rather than $N_{\mathrm{HI}}$ to derive $\sigma_{353}$,
indicating that optically thick Hi alone cannot shift our datapoints high
enough for a perfect match. This is consistent with the fact that we are
examining purely atomic sightlines, and likely happens because we are sampling
comparatively low number densities ($n_{H}\lesssim 10$–100 cm-3; a mixture of
WNM and CNM), whereas the sample in PLC2014a includes molecular gas in the
$N_{\mathrm{H}}$ bins, presumably with a higher $\kappa_{353}$. However, in
diffuse regions with $N_{\mathrm{H}}$$<$5$\times$1020cm-2, the mean value of
$\sigma_{353}$ from our sample is comparable with that from PLC2014a.

###  4.4. $E(B{-}V)$ as the more Reliable Proxy for $N_{\mathrm{H}}$?

We have seen that along 34 atomic sightlines $E(B{-}V)$ shows a tight linear
correlation with $N_{\mathrm{H}}$ in the column density range
$N_{\mathrm{H}}$=(1$\sim$30)$\times$1020cm-2. $\tau_{353}$ also shows a good
linear relation with $N_{\mathrm{H}}$ but with systematic deviations as
described above.

Figure 10 replicates Figure 9 but for $E(B{-}V)$ rather than $\tau_{353}$.
Although the sample used here is small, these figures demonstrate clearly that
the ratio $E(B{-}V)$/$N_{\mathrm{H}}$ is more stable than
$\tau_{353}$/$N_{\mathrm{H}}$ over the range of column densities and
sightlines covered by our analysis. In fact, with $N_{\mathrm{H}}$ corrected
for optical depth effects, our data are compatible with a constant value for
$E(B{-}V)$/$N_{\mathrm{H}}$, up to $N_{\mathrm{H}}$=30$\times$1020cm-2. On the
other hand, we have observed an increase of $\tau_{353}$/$N_{\mathrm{H}}$ with
$N_{\mathrm{H}}$ which we suggest may be due to an increase of the dust
emissivity (an increase of $r$ and/or $\kappa_{353}$ without affecting
significantly the dust absorption cross-section). While we are unfortunately
unable to follow how these relations evolve at higher $A_{V}$ and in molecular
gas, our results nevertheless suggest that the $E(B{-}V)$ maps of Green et al.
(2018) are a more reliable proxy for $N_{\mathrm{H}}$ than the current release
of Planck $\tau_{353}$ in low-to-moderate column density regimes.

Figure 10.— The ratio $E(B{-}V)$/$N_{\mathrm{H}}$ as a function of
$N_{\mathrm{H}}$ along the 34 purely atomic sightlines presented in this work,
using true $N_{\mathrm{HI}}$ (red) and $N^{*}_{\mathrm{HI}}$ (black) as the
total gas column density $N_{\mathrm{H}}$. The dashed line is at
5$\times$1020cm-2. The large datapoints are the average values for the low-
density ($N_{\mathrm{H}}$$<$5$\times$1020cm-2) and high-density
($N_{\mathrm{H}}$$>$5$\times$1020cm-2) regions (error bars on these points are
the standard error on the mean).

##  5\. OH abundance ratio $X_{\mathrm{OH}}$

The rotational lines of CO are widely used to probe the physical properties of
H2 clouds, but in diffuse molecular regimes where CO is not detectable in
emission, other species and transitions must be considered as alternative
tracers of H2. Among these, the ground-state main lines of OH are a promising
dark gas tracer; they are readily detectable in translucent/diffuse molecular
clouds (e.g. Magnani & Siskind, 1990; Barriault et al., 2010), and since OH is
considered as a precursor molecule necessary for the formation of CO in
diffuse regions (Black & Dalgarno, 1977; Barriault et al., 2010), it is
expected to be abundant in low-CO density/abundance regimes.

The utility of OH as a tracer of CO-dark H2 depends on our ability to
constrain the OH/H2 abundance ratio,
$X_{\mathrm{OH}}$=$N_{\mathrm{OH}}$/$N_{\mathrm{H}_{2}}$. From an
observational perspective, this requires good estimates of both the OH and H2
column densities, the latter of which often cannot be observed directly. Many
efforts (both modeling and observational) have been devoted to deriving
$X_{\mathrm{OH}}$ in different environmental conditions, which we summarize
below:

  * •

Astrochemical models by Black & Dalgarno (1977) found
$X_{\mathrm{OH}}$$\sim$$10^{-7}$ for the case of $\zeta$ Ophiuchi cloud.

  * •

19 comprehensive models of diffuse interstellar clouds with $n_{\mathrm{H}}$
from 250 to 1000 cm-3, $T_{\mathrm{k}}$ from 20 to 100K and $A_{V}$ from 0.62
to 2.12 mag (van Dishoeck & Black, 1986) found OH/H2 abundances from
1.6$\times$$10^{-8}$ to 2.9$\times$$10^{-7}$.

  * •

The OH abundance with respect to H2 from chemical models of diffuse clouds was
found to vary from 7.8$\times$$10^{-9}$ to 8.3$\times$$10^{-8}$ with
$A_{V}$=(0.1$-$1) mag, $T_{K}$=(50$-$100) K, $n$=(50$-$1000) cm-3 (Viala,
1986).

  * •

6 model calculations (that differ in depletion factors of heavy elements and
cosmic ray ionization rate) by Nercessian et al. (1988) towards molecular gas
in front of the star HD 29647 in Taurus found OH/H2 ratios between
5.3$\times$$10^{-8}$ and 2.5$\times$$10^{-6}$.

  * •

From OH observations towards high-latitude clouds using the 43m NRAO
telescope, Magnani et al. (1988) derived $X_{\mathrm{OH}}$ values between
4.8$\times$$10^{-7}$ to 4$\times$$10^{-6}$ in the range of $A_{V}$=(0.4$-$1.1)
mag assuming that $N_{\mathrm{H}_{2}}$=9.4$\times$$10^{20}$$A_{V}$. However,
we note that the excitation temperatures of the OH main lines were assumed to
be equal, Tex,1665=Tex,1667, likely resulting in overestimation of
$N_{\mathrm{OH}}$ (see Crutcher, 1979; Dawson et al., 2014).

  * •

Andersson & Wannier (1993) obtained an OH abundance of $\sim$$10^{-7}$ from
models of halos around dark molecular clouds.

  * •

Combining $N_{\mathrm{OH}}$ data from Roueff (1996) and Felenbok & Roueff
(1996) with measurements of $N_{\mathrm{H}_{2}}$ from Savage et al. (1977,
using UV absorption), Rachford et al. (2002, using UV absorption) and Joseph
et al. (1986, using CO emission), Liszt & Lucas (2002) find
$X_{\mathrm{OH}}$=(1.0$\pm$0.2)$\times$$10^{-7}$ toward diffuse clouds.

  * •

Weselak et al. (2010) derived OH abundances of
(1.05$\pm$0.24)$\times$$10^{-7}$ from absorption line observations of 5
translucent sightlines, with molecular hydrogen column densities
$N_{\mathrm{H}_{2}}$ measured through UV absorption by (Rachford et al., 2002,
2009).

  * •

Xu et al. (2016) report that $X_{\mathrm{OH}}$ decreases from 8$\times$10-7 to
1$\times$10-7 across a boundary region of the Taurus molecular cloud, over the
range Av=0.4$-$2.7 mag. $N_{\mathrm{H}_{2}}$ was obtained from an integration
of $A_{V}$-based estimates of the H2 volume density (assuming
$N_{\mathrm{H}_{2}}$=9.4$\times$$10^{20}$$A_{V}$).

  * •

Recently, Rugel et al. (2018) report a median
$X_{\mathrm{OH}}$$\sim$1.3$\times$$10^{-7}$ from THOR Survey observations of
OH absorption in the first Milky Way quadrant, with $N_{\mathrm{H}_{2}}$
estimated from 13CO(1-0).

Overall, while model calculations tend to produce some variation in the OH
abundance ratio over different parts of parameter space (8$\times$10-9 to
4$\times$10-6), observationally-determined measurements of $X_{\mathrm{OH}}$
cluster fairly tightly around $10^{-7}$, with some suggestion that this may
decrease for denser sightlines.

In this paper we determine our own OH abundances, using the MS dataset to
provide $N_{\mathrm{OH}}$ and $N_{\mathrm{HI}}$; then employing $\tau_{353}$
and $E(B{-}V)$ (along with our own conversion factors) to compute molecular
hydrogen column densities as
$N_{\mathrm{H}_{2}}$=$\frac{1}{2}(N_{\mathrm{H}}{-}N_{\mathrm{HI}})$. We note
that since this dust-based estimate of $N_{\mathrm{H}_{2}}$ cannot be
decomposed in velocity space, the OH abundances are determined in an
integrated fashion for each sightline, and not on a component-by-component
basis. While CO was detected along all but one sightline, it was not detected
towards all velocity components, meaning that our abundances are generally
computed for a mixture of CO-dark and CO-bright H2 (for further details see Li
et al., 2018).

The OH column densities derived in Section 3 are derived from direct
measurements of $T_{\mathrm{ex}}$ and $\tau$. This means that they should be
accurate compared to methods that rely on assumptions about these variables
(see e.g. Crutcher, 1979; Dawson et al., 2014). In computing $N_{\mathrm{H}}$
we assume that the linear correlations (deduced from $\tau_{353}$, $E(B{-}V)$
and $N_{\mathrm{HI}}$ towards 34 atomic sightlines) still hold in molecular
regions. In this manner, estimates of the OH/H2 abundance ratio can be
obtained within a range of visual extinction $A_{V}$=(0.25$-$4.8) mag. We note
that of our 19 OH-bright sightlines, 5 produce $N_{\mathrm{H}_{2}}$ that is
either negative or consistent with zero to within the measurement
uncertainties; these are excluded from the analysis.

Figure 11 shows $N_{\mathrm{OH}}$ and $X_{\mathrm{OH}}$ as functions of
$N_{\mathrm{H}_{2}}$. We find $N_{\mathrm{OH}}$ increases approximately
linearly with $N_{\mathrm{H}_{2}}$, and the OH/H2 abundance ratio is
approximately consistent for the two methods, with no evidence of and
systematic trends with increasing column density. Differences arise due to the
overestimation of $N_{\mathrm{H}}$ derived from $\tau_{353}$ along dense
sightlines compared to $N_{\mathrm{H}}$ from $E(B{-}V)$. As discussed in
Section 4, $\sigma_{353}$ varies by up to a factor of 2 in the range
$N_{\mathrm{H}}$=(1$\sim$30)$\times$1020cm-2, whereas the ratio
$\langle$$N_{\mathrm{H}}$/$E(B{-}V)$$\rangle$ is quite constant. The mean and
standard deviation of the $X_{\mathrm{OH}}$ distribution deduced from
$E(B{-}V)$ is (0.9$\pm$0.6)$\times$10-7, which is close to the canonical value
of $\sim$1$\times$10-7, and double the $X_{\mathrm{OH}}$ from $\tau_{353}$,
(0.5$\pm$0.3)$\times$10-7. We regard the higher value as more reliable.

Figure 11.— Left: $N_{\mathrm{OH}}$ as a function of
$N_{\mathrm{H}_{2}}$obtained from the two $N_{\mathrm{H}}$ proxies, $E(B{-}V)$
(blue) and $\tau_{353}$ (red). Right: $X_{\mathrm{OH}}$ derived from the two
proxies as a function of $N_{\mathrm{H}_{2}}$.

##  6\. Conclusions

We have combined accurate, opacity-corrected Hi column densities from the
Arecibo Millennium Survey and 21-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 Millennium Survey OH data and information on CO
detections from Li et al. (2018). In combination, these datasets allow us to
select reliable subsamples of purely-atomic (or partially-molecular)
sightlines, and hence assess the impact of Hi opacity on the scaling relations
commonly used to convert dust data to total proton column density
$N_{\mathrm{H}}$. They also allow us to make new measurements of the OH/H2
abundance ratio, which is essential in interpreting the next generation of OH
datasets. Our key conclusions are as follows:

1\. Hi opacity effects become important above
$N_{\mathrm{HI}}$$>$5$\times$1020cm-2; below this value the optically thin
assumption may usually be considered reliable.

2\. Along purely atomic sightlines with
$N_{\mathrm{H}}$=$N_{\mathrm{HI}}$=(1–30)$\times$1020cm-2, the dust opacity,
$\sigma_{353}$=$\tau_{353}$/$N_{\mathrm{H}}$, is $\sim$40% higher for
moderate-to-high column densities than low (defined as above and below
$N_{\mathrm{H}}$=5$\times$1020cm-2). We have argued that this rise is likely
due to the evolution of dust grains in the atomic ISM, although large-scale
systematics in the Planck data cannot be definitively ruled out. Failure to
account for Hi opacity can cause an additional apparent rise of the order of
$\sim$20%.

3\. For purely atomic sightlines, we measure a $N_{\mathrm{H}}$/$E(B{-}V)$
ratio of (9.4$\pm$1.6)$\times$1021cm-2mag-1. This is consistent with Lenz et
al. (2017) and Liszt (2014a), but 60% higher than the canonical value from
Bohlin et al. (1978).

4\. Our results suggest that $N_{\mathrm{H}}$ derived from the $E(B{-}V)$ map
of Green et al. (2018) is more reliable than that obtained from the
$\tau_{353}$ map of PLC2014a in low-to-moderate column density regimes.

5\. We measure the OH/H2 abundance ratio, $X_{\mathrm{OH}}$, along a sample of
16 molecular sightlines. We find $X_{\mathrm{OH}}$$\sim$1$\times 10^{-7}$,
with no evidence of a systematic trend with column density. Since our
sightlines include both CO-dark and CO-bright molecular gas components, this
suggests 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 Research Council (ARC) DECRA Fellowship
(project number DE170101086). N.M.-G. acknowledges the support of the ARC
through Future Fellowship FT150100024. LB acknowledges the support from
CONICYT grant PFB06. We are indebted to Professor Mark Wardle for providing us
with valuable advice and support. We gratefully acknowledge discussions with
Dr. Cormac Purcell and Anita Petzler. Finally, we thank the anonymous referee
for comments and criticisms which allowed us to improve the paper.

This research has made use of the NASA/IPAC Infrared Science Archive, which is
operated by the Jet Propulsion Laboratory, California Institute of Technology,
under contract with the National Aeronautics and Space Administration.

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##  Appendix A Appendix A: Locations of atomic sightlines

Figure 12.— See Figure 5 for details.

Figure 13.— See Figure 5 for details.

Figure 14.— See Figure 5 for details.

##  Appendix B Appendix B: Locations of OH sightlines

Figure 15.— See Figure 5 for details.

Figure 16.— See Figure 5 for details.

Table 1Parameters for OH main lines $Source$ | $l/b$ | OH(1665) | OH(1667)
---|---|---|---
$\tau$ | $V_{lsr}$ | $\Delta V$ | $T_{ex}$ | $N(OH)$ |  | $\tau$ | $V_{lsr}$ | $\Delta V$ | $T_{ex}$ | $N(OH)$
(Name) | $(^{o})$ |  | $(kms^{-1})$ | $(kms^{-1})$ | $(K)$ | $(10^{14}cm^{-2})$ |  |  | $(kms^{-1})$ | $(kms^{-1})$ | $(K)$ | $(10^{14}cm^{-2})$
3C105 | 187.6/-33.6 | 0.0156 $\pm$ 0.0003 | 8.14 $\pm$ 0.01 | 0.95 $\pm$ 0.03 | 4.65 $\pm$ 1.86 | 0.29 $\pm$ 0.12 |  | 0.0265 $\pm$ 0.0004 | 8.17 $\pm$ 0.01 | 0.94 $\pm$ 0.02 | 3.95 $\pm$ 0.95 | 0.23 $\pm$ 0.06
3C105 | 187.6/-33.6 | 0.0062 $\pm$ 0.0003 | 10.22 $\pm$ 0.02 | 0.93 $\pm$ 0.06 | 8.5 $\pm$ 4.89 | 0.21 $\pm$ 0.12 |  | 0.0104 $\pm$ 0.0004 | 10.25 $\pm$ 0.02 | 0.96 $\pm$ 0.04 | 7.66 $\pm$ 3.41 | 0.18 $\pm$ 0.08
3C109 | 181.8/-27.8 | 0.0023 $\pm$ 0.0003 | 9.15 $\pm$ 0.11 | 1.03 $\pm$ 0.26 | 18.28 $\pm$ 27.06 | 0.18 $\pm$ 0.27 |  | 0.0036 $\pm$ 0.0004 | 9.24 $\pm$ 0.05 | 0.75 $\pm$ 0.12 | 24.58 $\pm$ 8.7 | 0.16 $\pm$ 0.06
3C109 | 181.8/-27.8 | 0.0036 $\pm$ 0.0003 | 10.45 $\pm$ 0.07 | 0.98 $\pm$ 0.15 | 13.97 $\pm$ 5.41 | 0.21 $\pm$ 0.09 |  | 0.0053 $\pm$ 0.0004 | 10.55 $\pm$ 0.04 | 1.02 $\pm$ 0.1 | 13.63 $\pm$ 4.48 | 0.18 $\pm$ 0.06
3C123 | 170.6/-11.7 | 0.0191 $\pm$ 0.0007 | 3.65 $\pm$ 0.06 | 1.19 $\pm$ 0.11 | 10.92 $\pm$ 3.26 | 1.05 $\pm$ 0.33 |  | 0.0348 $\pm$ 0.0009 | 3.71 $\pm$ 0.04 | 1.22 $\pm$ 0.07 | 10.92 $\pm$ 2.69 | 1.1 $\pm$ 0.28
3C123 | 170.6/-11.7 | 0.0431 $\pm$ 0.0023 | 4.43 $\pm$ 0.01 | 0.53 $\pm$ 0.03 | 8.06 $\pm$ 0.78 | 0.78 $\pm$ 0.09 |  | 0.0919 $\pm$ 0.0029 | 4.46 $\pm$ 0.0 | 0.53 $\pm$ 0.01 | 7.7 $\pm$ 0.65 | 0.89 $\pm$ 0.08
3C123 | 170.6/-11.7 | 0.0337 $\pm$ 0.0008 | 5.37 $\pm$ 0.01 | 0.91 $\pm$ 0.03 | 11.59 $\pm$ 4.3 | 1.53 $\pm$ 0.57 |  | 0.0784 $\pm$ 0.0009 | 5.47 $\pm$ 0.01 | 0.92 $\pm$ 0.01 | 8.79 $\pm$ 2.57 | 1.5 $\pm$ 0.44
3C131 | 171.4/-7.8 | 0.0065 $\pm$ 0.0005 | 4.55 $\pm$ 0.02 | 0.56 $\pm$ 0.05 | 12.52 $\pm$ 3.59 | 0.19 $\pm$ 0.06 |  | 0.0117 $\pm$ 0.0004 | 4.64 $\pm$ 0.01 | 0.78 $\pm$ 0.04 | 6.96 $\pm$ 1.98 | 0.15 $\pm$ 0.04
3C131 | 171.4/-7.8 | 0.0073 $\pm$ 0.0006 | 6.81 $\pm$ 0.06 | 2.91 $\pm$ 0.23 | 8.94 $\pm$ 4.54 | 0.82 $\pm$ 0.42 |  | 0.0089 $\pm$ 0.0005 | 5.84 $\pm$ 0.03 | 0.67 $\pm$ 0.08 | 11.04 $\pm$ 2.07 | 0.16 $\pm$ 0.04
3C131 | 171.4/-7.8 | 0.0166 $\pm$ 0.0007 | 6.59 $\pm$ 0.01 | 0.42 $\pm$ 0.02 | 5.69 $\pm$ 0.85 | 0.17 $\pm$ 0.03 |  | 0.0319 $\pm$ 0.0007 | 6.55 $\pm$ 0.01 | 0.45 $\pm$ 0.02 | 5.99 $\pm$ 0.84 | 0.2 $\pm$ 0.03
3C131 | 171.4/-7.8 | 0.0521 $\pm$ 0.0007 | 7.23 $\pm$ 0.0 | 0.55 $\pm$ 0.01 | 5.91 $\pm$ 0.64 | 0.72 $\pm$ 0.08 |  | 0.0927 $\pm$ 0.0005 | 7.22 $\pm$ 0.0 | 0.65 $\pm$ 0.01 | 5.98 $\pm$ 0.34 | 0.85 $\pm$ 0.05
3C132 | 178.9/-12.5 | 0.0033 $\pm$ 0.0003 | 7.82 $\pm$ 0.04 | 0.9 $\pm$ 0.1 | 15.55 $\pm$ 6.23 | 0.19 $\pm$ 0.08 |  | 0.0056 $\pm$ 0.0003 | 7.79 $\pm$ 0.02 | 0.79 $\pm$ 0.06 | 23.56 $\pm$ 2.17 | 0.25 $\pm$ 0.03
3C133 | 177.7/-9.9 | 0.1008 $\pm$ 0.001 | 7.66 $\pm$ 0.0 | 0.53 $\pm$ 0.0 | 4.47 $\pm$ 0.44 | 1.01 $\pm$ 0.1 |  | 0.2132 $\pm$ 0.0014 | 7.68 $\pm$ 0.0 | 0.52 $\pm$ 0.0 | 3.25 $\pm$ 0.27 | 0.85 $\pm$ 0.07
3C133 | 177.7/-9.9 | 0.0149 $\pm$ 0.001 | 7.94 $\pm$ 0.02 | 1.22 $\pm$ 0.04 | 7.08 $\pm$ 3.08 | 0.55 $\pm$ 0.24 |  | 0.0333 $\pm$ 0.0013 | 7.96 $\pm$ 0.01 | 1.23 $\pm$ 0.02 | 4.17 $\pm$ 0.99 | 0.4 $\pm$ 0.1
3C154 | 185.6/4.0 | 0.0266 $\pm$ 0.0006 | -2.32 $\pm$ 0.02 | 0.74 $\pm$ 0.03 | 2.69 $\pm$ 1.93 | 0.23 $\pm$ 0.16 |  | 0.0429 $\pm$ 0.0006 | -2.34 $\pm$ 0.01 | 0.71 $\pm$ 0.02 | 2.57 $\pm$ 0.75 | 0.19 $\pm$ 0.05
3C154 | 185.6/4.0 | 0.01 $\pm$ 0.0006 | -1.39 $\pm$ 0.04 | 0.83 $\pm$ 0.09 | 5.2 $\pm$ 5.28 | 0.18 $\pm$ 0.19 |  | 0.0181 $\pm$ 0.0005 | -1.34 $\pm$ 0.02 | 0.94 $\pm$ 0.05 | 4.46 $\pm$ 1.79 | 0.18 $\pm$ 0.07
3C154 | 185.6/4.0 | 0.0038 $\pm$ 0.0005 | 2.23 $\pm$ 0.07 | 1.14 $\pm$ 0.17 | 5.83 $\pm$ 6.56 | 0.11 $\pm$ 0.12 |  | 0.0054 $\pm$ 0.0004 | 2.19 $\pm$ 0.05 | 1.57 $\pm$ 0.13 | 0.54 $\pm$ 8.69 | 0.01 $\pm$ 0.17
3C167 | 207.3/1.2 | 0.0106 $\pm$ 0.0019 | 18.46 $\pm$ 0.12 | 1.49 $\pm$ 0.35 | 4.75 $\pm$ 17.95 | 0.32 $\pm$ 1.22 |  | 0.009 $\pm$ 0.0018 | 17.77 $\pm$ 0.15 | 1.76 $\pm$ 0.49 | 4.59 $\pm$ 9.57 | 0.17 $\pm$ 0.36
3C18 | 118.6/-52.7 | 0.0031 $\pm$ 0.0003 | -8.52 $\pm$ 0.11 | 2.64 $\pm$ 0.27 | 10.92 $\pm$ 14.88 | 0.38 $\pm$ 0.52 |  | 0.006 $\pm$ 0.0003 | -8.34 $\pm$ 0.05 | 2.61 $\pm$ 0.14 | 9.2 $\pm$ 6.04 | 0.34 $\pm$ 0.23
3C18 | 118.6/-52.7 | 0.0056 $\pm$ 0.0004 | -7.82 $\pm$ 0.02 | 0.67 $\pm$ 0.07 | 6.45 $\pm$ 3.7 | 0.1 $\pm$ 0.06 |  | 0.0079 $\pm$ 0.0004 | -7.85 $\pm$ 0.01 | 0.6 $\pm$ 0.04 | 4.83 $\pm$ 1.6 | 0.05 $\pm$ 0.02
3C207 | 213.0/30.1 | 0.015 $\pm$ 0.0002 | 4.55 $\pm$ 0.01 | 0.76 $\pm$ 0.01 | 2.94 $\pm$ 1.55 | 0.14 $\pm$ 0.08 |  | 0.0266 $\pm$ 0.0002 | 4.55 $\pm$ 0.0 | 0.77 $\pm$ 0.01 | 2.48 $\pm$ 0.46 | 0.12 $\pm$ 0.02
3C409 | 63.4/-6.1 | 0.0058 $\pm$ 0.0011 | 14.59 $\pm$ 0.27 | 1.68 $\pm$ 0.35 | 11.31 $\pm$ 8.53 | 0.47 $\pm$ 0.38 |  | 0.0055 $\pm$ 0.0015 | 14.68 $\pm$ 0.33 | 1.52 $\pm$ 0.4 | 7.83 $\pm$ 11.73 | 0.16 $\pm$ 0.24
3C409 | 63.4/-6.1 | 0.0204 $\pm$ 0.0025 | 15.4 $\pm$ 0.01 | 0.89 $\pm$ 0.05 | 3.18 $\pm$ 2.31 | 0.25 $\pm$ 0.18 |  | 0.0275 $\pm$ 0.0032 | 15.42 $\pm$ 0.01 | 0.86 $\pm$ 0.04 | 0.62 $\pm$ 1.0 | 0.03 $\pm$ 0.06
3C410 | 69.2/-3.8 | 0.0044 $\pm$ 0.0006 | 6.32 $\pm$ 0.04 | 1.89 $\pm$ 0.15 | 13.41 $\pm$ 11.22 | 0.47 $\pm$ 0.4 |  | 0.0079 $\pm$ 0.0005 | 6.38 $\pm$ 0.02 | 2.32 $\pm$ 0.09 | 6.4 $\pm$ 5.25 | 0.28 $\pm$ 0.23
3C410 | 69.2/-3.8 | 0.0089 $\pm$ 0.0006 | 6.21 $\pm$ 0.01 | 0.65 $\pm$ 0.04 | 8.46 $\pm$ 2.4 | 0.21 $\pm$ 0.06 |  | 0.0193 $\pm$ 0.0005 | 6.26 $\pm$ 0.01 | 0.81 $\pm$ 0.02 | 3.81 $\pm$ 1.28 | 0.14 $\pm$ 0.05
3C410 | 69.2/-3.8 | 0.0044 $\pm$ 0.0003 | 10.7 $\pm$ 0.03 | 0.71 $\pm$ 0.07 | 10.06 $\pm$ 5.89 | 0.13 $\pm$ 0.08 |  | 0.0085 $\pm$ 0.0002 | 10.71 $\pm$ 0.02 | 0.81 $\pm$ 0.04 | 4.15 $\pm$ 3.09 | 0.07 $\pm$ 0.05
3C410 | 69.2/-3.8 | 0.0054 $\pm$ 0.0002 | 11.67 $\pm$ 0.03 | 0.84 $\pm$ 0.07 | 4.83 $\pm$ 4.66 | 0.09 $\pm$ 0.09 |  | 0.0115 $\pm$ 0.0002 | 11.68 $\pm$ 0.02 | 0.82 $\pm$ 0.03 | 2.93 $\pm$ 3.0 | 0.07 $\pm$ 0.07
3C454.3 | 86.1/-38.2 | 0.0023 $\pm$ 0.0001 | -9.67 $\pm$ 0.03 | 1.6 $\pm$ 0.09 | 4.63 $\pm$ 12.36 | 0.07 $\pm$ 0.19 |  | 0.0044 $\pm$ 0.0001 | -9.54 $\pm$ 0.01 | 1.25 $\pm$ 0.04 | 8.13 $\pm$ 6.06 | 0.1 $\pm$ 0.08
3C75 | 170.3/-44.9 | 0.0071 $\pm$ 0.0005 | -10.36 $\pm$ 0.04 | 1.3 $\pm$ 0.12 | 3.45 $\pm$ 5.41 | 0.14 $\pm$ 0.21 |  | 0.014 $\pm$ 0.0008 | -10.36 $\pm$ 0.03 | 1.22 $\pm$ 0.09 | 3.51 $\pm$ 1.56 | 0.14 $\pm$ 0.06
4C13.67 | 43.5/9.2 | 0.0464 $\pm$ 0.0043 | 4.85 $\pm$ 0.05 | 1.1 $\pm$ 0.12 | 10.43 $\pm$ 2.77 | 2.28 $\pm$ 0.69 |  | 0.0567 $\pm$ 0.0057 | 4.89 $\pm$ 0.05 | 1.12 $\pm$ 0.14 | 10.34 $\pm$ 2.13 | 1.55 $\pm$ 0.4
4C22.12 | 188.1/0.0 | 0.0058 $\pm$ 0.001 | -2.84 $\pm$ 0.07 | 0.79 $\pm$ 0.19 | 6.54 $\pm$ 7.03 | 0.13 $\pm$ 0.14 |  | 0.0102 $\pm$ 0.0011 | -2.73 $\pm$ 0.04 | 0.78 $\pm$ 0.12 | 6.72 $\pm$ 2.32 | 0.13 $\pm$ 0.05
4C22.12 | 188.1/0.0 | 0.0172 $\pm$ 0.0012 | -1.78 $\pm$ 0.02 | 0.56 $\pm$ 0.05 | 5.07 $\pm$ 2.12 | 0.21 $\pm$ 0.09 |  | 0.0354 $\pm$ 0.0013 | -1.78 $\pm$ 0.01 | 0.54 $\pm$ 0.03 | 3.78 $\pm$ 0.74 | 0.17 $\pm$ 0.03
G196.6+0.2 | 196.6/0.2 | 0.0044 $\pm$ 0.0005 | 3.26 $\pm$ 0.11 | 1.94 $\pm$ 0.27 | 10.82 $\pm$ 12.22 | 0.4 $\pm$ 0.46 |  | 0.0062 $\pm$ 0.0005 | 3.4 $\pm$ 0.09 | 2.38 $\pm$ 0.22 | 8.85 $\pm$ 8.6 | 0.31 $\pm$ 0.3
G197.0+1.1 | 197.0/1.1 | 0.0126 $\pm$ 0.0005 | 4.83 $\pm$ 0.04 | 1.88 $\pm$ 0.09 | 6.94 $\pm$ 3.82 | 0.7 $\pm$ 0.39 |  | 0.0191 $\pm$ 0.001 | 4.73 $\pm$ 0.04 | 1.65 $\pm$ 0.1 | 4.8 $\pm$ 2.17 | 0.36 $\pm$ 0.16
G197.0+1.1 | 197.0/1.1 | 0.0059 $\pm$ 0.0009 | 7.46 $\pm$ 0.05 | 0.65 $\pm$ 0.11 | 0.31 $\pm$ 10.58 | 0.0 $\pm$ 0.17 |  | 0.0078 $\pm$ 0.0015 | 7.34 $\pm$ 0.06 | 0.65 $\pm$ 0.14 | 1.61 $\pm$ 5.87 | 0.02 $\pm$ 0.07
G197.0+1.1 | 197.0/1.1 | 0.0049 $\pm$ 0.0005 | 17.01 $\pm$ 0.12 | 2.47 $\pm$ 0.28 | 10.99 $\pm$ 9.9 | 0.57 $\pm$ 0.52 |  | 0.0081 $\pm$ 0.0034 | 16.26 $\pm$ 0.17 | 0.91 $\pm$ 0.3 | 6.45 $\pm$ 2.95 | 0.11 $\pm$ 0.08
G197.0+1.1 | 197.0/1.1 | 0.0052 $\pm$ 0.0015 | 17.59 $\pm$ 0.03 | 0.25 $\pm$ 0.08 | 9.87 $\pm$ 1.81 | 0.05 $\pm$ 0.03 |  | 0.0127 $\pm$ 0.0013 | 17.38 $\pm$ 0.2 | 1.46 $\pm$ 0.35 | 5.46 $\pm$ 4.35 | 0.24 $\pm$ 0.2
G197.0+1.1 | 197.0/1.1 | 0.0237 $\pm$ 0.001 | 32.01 $\pm$ 0.01 | 0.57 $\pm$ 0.03 | 4.75 $\pm$ 1.92 | 0.27 $\pm$ 0.11 |  | 0.043 $\pm$ 0.0017 | 32.01 $\pm$ 0.01 | 0.54 $\pm$ 0.02 | 3.96 $\pm$ 1.04 | 0.22 $\pm$ 0.06
P0428+20 | 176.8/-18.6 | 0.0014 $\pm$ 0.0002 | 3.6 $\pm$ 0.08 | 1.01 $\pm$ 0.19 | 13.48 $\pm$ 7.8 | 0.08 $\pm$ 0.05 |  | 0.0029 $\pm$ 0.0003 | 3.54 $\pm$ 0.03 | 0.69 $\pm$ 0.08 | 4.45 $\pm$ 9.98 | 0.02 $\pm$ 0.05
P0428+20 | 176.8/-18.6 | 0.0075 $\pm$ 0.0002 | 10.7 $\pm$ 0.02 | 1.09 $\pm$ 0.04 | 13.49 $\pm$ 3.45 | 0.47 $\pm$ 0.12 |  | 0.0136 $\pm$ 0.0002 | 10.7 $\pm$ 0.01 | 1.1 $\pm$ 0.02 | 12.72 $\pm$ 1.62 | 0.45 $\pm$ 0.06
T0526+24 | 181.4/-5.2 | 0.0172 $\pm$ 0.0073 | 7.55 $\pm$ 0.29 | 1.9 $\pm$ 1.13 | 13.7 $\pm$ 15.65 | 1.91 $\pm$ 2.59 |  | 0.043 $\pm$ 0.0102 | 7.56 $\pm$ 0.14 | 2.43 $\pm$ 0.75 | 10.19 $\pm$ 7.5 | 2.52 $\pm$ 2.1
T0629+10 | 201.5/0.5 | 0.0043 $\pm$ 0.0022 | 0.16 $\pm$ 0.0 | 0.65 $\pm$ 0.4 | 4.16 $\pm$ 2.97 | 0.05 $\pm$ 0.05 |  | 0.0103 $\pm$ 0.0035 | 0.35 $\pm$ 0.0 | 1.18 $\pm$ 0.41 | 3.25 $\pm$ 1.93 | 0.09 $\pm$ 0.07
T0629+10 | 201.5/0.5 | 0.0387 $\pm$ 0.0074 | 3.14 $\pm$ 0.13 | 1.1 $\pm$ 0.0 | 3.85 $\pm$ 0.47 | 0.7 $\pm$ 0.16 |  | 0.0577 $\pm$ 0.0113 | 3.07 $\pm$ 0.14 | 1.1 $\pm$ 0.0 | 4.54 $\pm$ 0.55 | 0.68 $\pm$ 0.16
T0629+10 | 201.5/0.5 | 0.0169 $\pm$ 0.0015 | 1.46 $\pm$ 0.07 | 1.39 $\pm$ 0.26 | 2.19 $\pm$ 2.11 | 0.22 $\pm$ 0.22 |  | 0.0281 $\pm$ 0.0029 | 1.51 $\pm$ 0.08 | 1.23 $\pm$ 0.25 | 2.9 $\pm$ 0.91 | 0.24 $\pm$ 0.09
T0629+10 | 201.5/0.5 | 0.1607 $\pm$ 0.0104 | 3.6 $\pm$ 0.01 | 0.61 $\pm$ 0.02 | 3.83 $\pm$ 0.35 | 1.59 $\pm$ 0.19 |  | 0.2536 $\pm$ 0.0154 | 3.6 $\pm$ 0.01 | 0.65 $\pm$ 0.03 | 4.72 $\pm$ 0.64 | 1.84 $\pm$ 0.29
T0629+10 | 201.5/0.5 | 0.0811 $\pm$ 0.002 | 4.62 $\pm$ 0.01 | 0.76 $\pm$ 0.03 | 6.43 $\pm$ 0.97 | 1.68 $\pm$ 0.27 |  | 0.1553 $\pm$ 0.0037 | 4.61 $\pm$ 0.01 | 0.67 $\pm$ 0.03 | 6.62 $\pm$ 1.01 | 1.63 $\pm$ 0.26
T0629+10 | 201.5/0.5 | 0.0747 $\pm$ 0.0018 | 6.09 $\pm$ 0.02 | 1.06 $\pm$ 0.05 | 5.44 $\pm$ 1.58 | 1.84 $\pm$ 0.54 |  | 0.1165 $\pm$ 0.003 | 6.06 $\pm$ 0.02 | 1.17 $\pm$ 0.07 | 6.52 $\pm$ 1.67 | 2.1 $\pm$ 0.55
T0629+10 | 201.5/0.5 | 0.0367 $\pm$ 0.0031 | 7.0 $\pm$ 0.02 | 0.49 $\pm$ 0.06 | 4.36 $\pm$ 0.68 | 0.33 $\pm$ 0.07 |  | 0.0631 $\pm$ 0.0056 | 7.0 $\pm$ 0.02 | 0.5 $\pm$ 0.06 | 4.2 $\pm$ 0.3 | 0.31 $\pm$ 0.05
T0629+10 | 201.5/0.5 | 0.0174 $\pm$ 0.0018 | 7.9 $\pm$ 0.05 | 0.83 $\pm$ 0.13 | 3.44 $\pm$ 1.67 | 0.21 $\pm$ 0.11 |  | 0.0307 $\pm$ 0.003 | 7.91 $\pm$ 0.05 | 0.82 $\pm$ 0.13 | 3.65 $\pm$ 1.21 | 0.22 $\pm$ 0.08

Table 234 atomic sightlines Sources (Name) |  $l/b$ $(^{o})$ |  $N_{\mathrm{HI}}$ (1020cm-2) |  $N^{*}_{\mathrm{HI}}$ (1020cm-2) |  $\sigma_{\tau}$(OH1667) (10-4) |  $N_{\mathrm{H}_{2}}$(upper limit)**footnotemark:  (1020cm-2) |  $\tau_{353}$ (10-6) |  $E(B{-}V)$ (10-2 mag)
---|---|---|---|---|---|---|---
3C33 | 129.4/-49.3 | 3.25$\pm$0.0 | 3.2$\pm$0.1 | 12.14 | 0.6 | 2.16$\pm$0.07 | 3.54$\pm$0.42
3C142.1 | 197.6/-14.5 | 25.11$\pm$2.6 | 19.6$\pm$0.8 | 10.55 | 0.52 | 21.53$\pm$0.72 | 21.71$\pm$0.81
3C138 | 187.4/-11.3 | 22.9$\pm$1.1 | 19.9$\pm$0.3 | 5.02 | 0.25 | 21.63$\pm$0.81 | 17.47$\pm$0.59
3C79 | 164.1/-34.5 | 10.86$\pm$1.2 | 9.8$\pm$0.8 | 37.03 | 1.84 | 9.23$\pm$0.37 | 12.67$\pm$0.78
3C78 | 174.9/-44.5 | 11.69$\pm$0.5 | 10.3$\pm$0.2 | 13.25 | 0.66 | 12.45$\pm$0.63 | 14.64$\pm$1.07
3C310 | 38.5/60.2 | 4.29$\pm$0.1 | 4.0$\pm$0.1 | 16.19 | 0.8 | 3.48$\pm$0.15 | 2.75$\pm$0.53
3C315 | 39.4/58.3 | 5.48$\pm$0.4 | 4.7$\pm$0.0 | 12.96 | 0.64 | 3.98$\pm$0.09 | 5.63$\pm$0.26
3C234 | 200.2/52.7 | 1.84$\pm$0.0 | 1.9$\pm$1.1 | 12.66 | 0.63 | 0.78$\pm$0.03 | 1.64$\pm$0.56
3C236 | 190.1/54.0 | 1.38$\pm$0.0 | 1.3$\pm$1.2 | 10.72 | 0.53 | 0.7$\pm$0.03 | 2.04$\pm$0.49
3C64 | 157.8/-48.2 | 7.29$\pm$0.2 | 6.9$\pm$0.8 | 33.12 | 1.65 | 6.55$\pm$0.35 | 9.01$\pm$0.36
P0531+19 | 186.8/-7.1 | 27.33$\pm$0.7 | 25.4$\pm$0.3 | 6.37 | 0.32 | 20.75$\pm$0.62 | 20.54$\pm$1.3
P0820+22 | 201.4/29.7 | 4.82$\pm$0.2 | 4.8$\pm$1.1 | 7.09 | 0.35 | 3.73$\pm$0.11 | 2.56$\pm$0.4
3C192 | 197.9/26.4 | 4.56$\pm$0.1 | 4.5$\pm$0.1 | 20.66 | 1.03 | 3.38$\pm$0.08 | 4.05$\pm$0.53
3C98 | 179.8/-31.0 | 12.7$\pm$0.5 | 11.3$\pm$1.3 | 12.26 | 0.61 | 13.72$\pm$0.41 | 17.73$\pm$1.02
3C273 | 289.9/64.4 | 2.35$\pm$0.0 | 2.3$\pm$0.1 | 21.0 | 1.04 | 1.3$\pm$0.09 | 1.98$\pm$0.41
DW0742+10 | 209.8/16.6 | 2.77$\pm$0.0 | 2.8$\pm$0.9 | 8.01 | 0.4 | 1.6$\pm$0.03 | 1.99$\pm$0.25
3C172.0 | 191.2/13.4 | 8.89$\pm$0.2 | 8.6$\pm$1.1 | 13.02 | 0.65 | 5.66$\pm$0.08 | 4.7$\pm$0.52
3C293 | 54.6/76.1 | 1.46$\pm$0.1 | 1.5$\pm$1.1 | 6.24 | 0.31 | 1.31$\pm$0.09 | 2.83$\pm$0.75
3C120 | 190.4/-27.4 | 18.17$\pm$2.1 | 10.7$\pm$0.1 | 28.29 | 1.41 | 29.26$\pm$1.08 | 22.74$\pm$1.03
CTA21 | 166.6/-33.6 | 10.97$\pm$0.4 | 10.0$\pm$0.8 | 27.35 | 1.36 | 10.39$\pm$0.44 | 13.3$\pm$0.96
P1117+14 | 240.4/65.8 | 1.79$\pm$0.0 | 1.8$\pm$0.3 | 15.0 | 0.75 | 1.5$\pm$0.04 | 2.73$\pm$0.54
3C264.0 | 237.0/73.6 | 1.97$\pm$0.0 | 2.0$\pm$0.4 | 6.29 | 0.31 | 1.64$\pm$0.08 | 2.88$\pm$0.34
3C208.1 | 213.6/33.6 | 3.15$\pm$0.1 | 3.2$\pm$0.2 | 18.67 | 0.93 | 3.12$\pm$0.04 | 2.93$\pm$0.43
3C208.0 | 213.7/33.2 | 3.41$\pm$0.1 | 3.5$\pm$0.2 | 19.69 | 0.98 | 3.38$\pm$0.07 | 4.37$\pm$0.47
4C32.44 | 67.2/81.0 | 1.23$\pm$0.0 | 1.3$\pm$0.6 | 9.88 | 0.49 | 0.81$\pm$0.02 | 1.94$\pm$0.29
3C272.1 | 280.6/74.7 | 2.82$\pm$0.0 | 2.8$\pm$0.3 | 10.24 | 0.51 | 1.73$\pm$0.28 | 2.43$\pm$0.31
4C07.32 | 322.2/68.8 | 2.43$\pm$0.0 | 2.4$\pm$0.3 | 30.7 | 1.53 | 2.32$\pm$0.06 | 4.3$\pm$0.41
3C245 | 233.1/56.3 | 2.39$\pm$0.0 | 2.4$\pm$0.2 | 11.36 | 0.56 | 2.22$\pm$0.06 | 2.71$\pm$0.36
3C348 | 23.0/29.2 | 6.56$\pm$0.2 | 6.0$\pm$0.1 | 16.51 | 0.82 | 5.7$\pm$0.15 | 9.8$\pm$0.33
3C286 | 56.5/80.7 | 2.33$\pm$0.1 | 2.4$\pm$2.7 | 7.13 | 0.35 | 0.81$\pm$0.05 | 2.75$\pm$0.74
4C13.65 | 39.3/17.7 | 10.56$\pm$0.2 | 9.9$\pm$0.1 | 20.01 | 0.99 | 11.8$\pm$0.39 | 15.63$\pm$0.6
3C190.0 | 207.6/21.8 | 3.21$\pm$0.0 | 3.4$\pm$0.9 | 17.57 | 0.87 | 2.41$\pm$0.03 | 1.96$\pm$0.42
3C274.1 | 269.9/83.2 | 2.74$\pm$0.0 | 2.6$\pm$0.1 | 13.13 | 0.65 | 2.34$\pm$0.02 | 2.64$\pm$0.42
3C298 | 352.2/60.7 | 2.39$\pm$0.4 | 2.6$\pm$0.1 | 10.69 | 0.53 | 1.3$\pm$0.07 | 1.97$\pm$0.39
*Estimated from OH(1667) 3$\sigma$ detection limits using Tex=3.5 K, FWHM=1 km/s and $N_{\mathrm{OH}}$/$N_{\mathrm{H}_{2}}$=10-7 (see Section 5).