# Variations of Interstellar Gas-to-Dust Ratios
at High Galactic Latitudes

J. Michael Shull  Department of Astrophysical and Planetary Sciences, CASA
University of Colorado, Boulder, CO 80309, USA  Georgia V. Panopoulou
Department of Space, Earth, & Environment,
Chalmers University of Technology, SE-412 93, Gothenburg, Sweden
<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Interstellar dust at high Galactic latitudes can influence astronomical
foreground subtraction, produce diffuse scattered light, and result in harder
(de-reddened) ultraviolet spectra of quasars. In a sample of 94 quasars at
high latitude and low extinction, we evaluate the interstellar “gas-to-dust
ratio” $N_{\rm H}/E(B-V)$, using hydrogen column densities (H I and H2) and
far-infrared estimates of dust reddening. In the Galactic plane, this ratio is
$6.0\pm 0.2$ (in units of $10^{21}~{}{\rm cm}^{-2}~{}{\rm mag}^{-1}$). In a
sub-sample of 51 quasars with measurements of both H I and H2 and $0.01\leq
E(B-V)\lesssim 0.1$, we find mean ratios $10.3\pm 0.4$ (gas at all velocities)
and $9.2\pm 0.3$ (low velocity only). Including H2 increases $N_{H}$ by $\sim
10$%, even at high latitude. On average, recent Planck estimates of $E(B-V)$
in low reddening sight lines are 12% higher than those from Schlafly &
Finkbeiner (2011), and $N_{\rm HI}$ exhibits significant variations when
measured at different radio telescopes. We also show that $E(B-V)$ is
sensitive to far-infrared modeled dust temperature $T_{d}$ and emissivity
index $\beta$. Consequently, gas-to-dust ratios have large, asymmetric errors
at low $E(B-V)$. The ratios are elevated in sight lines with high-velocity
clouds, which contribute $N_{\rm H}$ but little reddening. In Complex C, the
ratio decreases by 40% when high velocity gas is excluded. Decreases in dust
content are expected in low-metallicity gas above the Galactic plane,
resulting from grain destruction in shocks, settling to the disk, and thermal
sputtering in hot halo gas.

##  1 Introduction

This paper examines measures of the interstellar “gas-to-dust ratio”, $N_{\rm
H}/E(B-V)$, found from the total column density of atomic and molecular
hydrogen, $N_{\rm H}=N_{\rm HI}+2N_{\rm H2}$, and selective extinction
$E(B-V)$. In studies with the Copernicus satellite (Savage et al. 1977; Bohlin
et al. 1978) hydrogen column densities were measured with UV absorption lines
(Ly$\alpha$ and H2 Lyman/Werner bands). and $E(B-V)$ was obtained from stellar
photometry and spectral classification. Along 75 sight lines in the Galactic
disk, they found a mean ratio $5.8\times 10^{21}~{}{\rm cm}^{-2}~{}{\rm
mag}^{-1}$, hereafter quoted in standard units of $10^{21}~{}{\rm
cm}^{-2}~{}{\rm mag}^{-1}$. A recent survey with the FUSE satellite of sight
lines to 129 OB-stars within 5 kpc (Shull et al. 2021) found a mean value
$6.07\pm 1.01$ ($1\sigma$ variance in the distribution) using updated $E(B-V)$
from O-star photometry and spectral types from the Galactic O-star
Spectroscopic Survey (Sota et al. 2011, 2014). For a subset of 21 stars at low
reddening, $E(B-V)\leq 0.25$, the mean ratio was $N_{\rm H}/E(B-V)=5.83$. A
FUSE survey of 38 translucent sight lines with $A_{V}\approx$ 0.5–4.7
(Rachford et al. 2009) found a mean ratio of 5.94, and a heterogeneous
compilation of UV measurements (Gudennavar et al. 2012) found 6.12. We
conclude that the interstellar medium (ISM) in the Galactic disk has a
consistent mean gas-to-dust ratio of $\sim 6\times 10^{21}~{}{\rm
cm}^{-2}~{}{\rm mag}^{-1}$ to an accuracy of 3–4% and 17% dispersion.

However, recent estimates of the gas-to-dust ratio at high Galactic latitudes
find 35–45% higher values, using $N_{\rm HI}$ from 21-cm emission and $E(B-V)$
inferred from modeling far-infrared (FIR) emission as a tracer of the dust
column. Elevated ratios above the disk plane would be expected, as dust
settles to the disk or is elevated into the halo. Reductions in grain
abundance can also result from lower gas metallicities and grain disruption in
shocks. In the radio/FIR method, values of $E(B-V)$ were taken from two
studies (Schlegel et al. 1998 and Schlafly & Finkbeiner 2011) hereafter
denoted SFD98 and SF11 and available on the IPAC/IRSA reddening
website111https://irsa.ipac.caltech.edu/applications/DUST/docs/background.html.
In sight lines at latitudes $|b|>20^{\circ}$ and low reddening,
$0.015<E(B-V)<0.075$, Liszt (2014a,b) found a mean ratio $N_{\rm H}/E(B-V)$ =
8.3, with H I from the Leiden-Argentina-Bonn (LAB) survey (Kalberla et al.
1995) at $36^{\prime}$ resolution and $E(B-V)$ from SFD98. Lenz et al. (2017)
found a mean ratio of 8.8, with H I from the HI4PI survey (HI4PI Collaboration
et al. 2016) at $16^{\prime}$ resolution and $E(B-V)$ from SFD98. They only
considered atomic gas with $N_{\rm HI}<4\times 10^{20}~{}{\rm cm}^{-2}$ and
local standard of rest velocities $|V_{\rm LSR}|<90$ km s-1. The difference
between these ratios (8.3 and 8.8) likely results from different FIR
calibrations. Other surveys of the high-latitude mean ratio include Nguyen et
al. (2018), who found $9.14\pm 1.6$ and Liszt & Gerin (2023) who quoted 8.3.

The question arises whether the elevated gas-to-dust-ratios at high latitude
are real or the result of different methods and calibrations. To investigate
the reliability of the gas-to-dust ratio $N_{\rm H}/E(B-V)$ we examine
measurements of both the numerator and denominator, considering their
systematic uncertainties. Both Liszt (2014a,b) and Lenz et al. (2017) used
only H I, noting that corrections for H2 are normally small for $E(B-V)<0.08$.
This may not always be the case, as seen in our sample of quasar sight lines
with both H I and H2 data. Errors in measurements of $N_{\rm HI}$ can result
from telescope beam sizes, stray light removal, baseline determination and
calibration, and methods of integrating the 21-cm emission profile over
velocity. Following studies by Wakker et al. (2011), we have compared $N_{\rm
HI}$ in surveys with radio telescopes whose beam sizes range from
$36^{\prime}$ to $9^{\prime}$, including those from the Green Bank Telescope
and the HI4PI survey. We also assess the accuracy of FIR thermal emission
inferences of equivalent optical extinction. Several reddening maps have been
presented in the literature, exhibiting systematic differences (e.g., Lenz et
al. 2017; Chiang & Ménard 2019). For example, the reddening map presented in
Planck Collaboration XI (2014) has larger $E(B-V)$ at high Galactic latitude
compared to SF11 (Lenz et al. 2017; Casandjian et al. 2022). All of these
uncertainties result in large and asymmetric errors in the gas-to-dust ratio,
especially at low reddening.

Our data set includes sight lines to 94 quasars at high Galactic latitude,
most at $|b|>25\arcdeg$. Indeed, 78 lie at $|b|\geq 40\arcdeg$. Figure 1 shows
a polar projection of the quasar locations and ratios between H I column
density and two FIR-inferred $E(B-V)$ maps (see Section 2.3). The H I column
density has been computed within the same velocity range [-90, 90] km s-1 used
to derive the gas-to-dust ratio in Lenz et al. (2017). The spatial variation
of the ratio over the sky differs between the two reddening maps, indicating
systematic reddening uncertainties, probably arising from FIR modeling of dust
temperature and emissivity spectral index.

In Section 2 we discuss the sources of data used to evaluate the gas-to-dust
ratio, including column densities $N_{\rm HI}$, $N_{\rm H2}$, selective
extinction $E(B-V)$, and their uncertainties. We examine the measurements used
to construct $N_{\rm H}/E(B-V)$ ratios along the sight lines to 94 high-
latitude quasars. In particular, we explore uncertainties in 21-cm
measurements of $N_{\rm HI}$ from different radio telescopes and uncertainties
in inferring $E(B-V)$ from FIR emission and grain emissivity models. In
Section 3 we present data from our survey, which confirm previous observations
of elevated gas-to-dust ratios at $|b|>30\arcdeg$. However, we suggest large
uncertainties in the ratio. An important effect in elevated ratios is the
reduced dust content in Galactic high velocity clouds (HVCs) and some
intermediate velocity clouds (IVCs). In Section 4, we summarize our results
and their implications for astronomical foreground subtraction, diffuse
scattered light, and reddening corrections for the ultraviolet spectra of
quasars. We stress the importance of identifying the systematic uncertainties
in $\log N_{\rm H}$ and $E(B-V)$, which are almost certainly much larger than
the small values ($\leq 5$%) commonly listed in observational tables.

##  2 Data Compilation for Gas-to-Dust Ratios

Our full sample includes 94 quasars at high Galactic latitude (Table 1). The
first 55 quasars listed (group 1) have both H I and H2 column densities, a
primary sample that includes 47 sight lines with IVCs and 18 with HVCs. Nine
AGN lie behind Complex C (Figure 2), an extended structure of high-velocity
gas with metallicities 10–30% solar (Wakker et al. 1999; Collins et al. 2007;
Shull et al. 2011). We also analyzed 39 additional quasars (group 2 in Table
1) in which only H I column densities were available. In contrast to UV
studies of H I and H2 in the Galactic disk, the high-latitude measurements of
the dust-to-gas ratio (Liszt 2014a,b; Lenz et al. 2017) used 21-cm emission
for $N_{\rm HI}$ and FIR emission as a proxy for $E(B-V)$. As described in
Appendix A, these techniques can introduce systematic errors in the gas-to-
dust ratio, particularly when $E(B-V)\lesssim 0.04$ mag. Toward high-latitude
quasars, reddening uncertainties often dominate the propagated errors in the
ratio $N_{\rm H}/E(B-V)$. However, we also found cases in which measurements
of $N_{\rm HI}$ differ by 10–30% among different telescopes with a range of
beam sizes.

###  2.1 Atomic Hydrogen ($N_{\rm HI}$)

The H I column densities came from 21-cm spectra in several surveys. All 94
AGN appear in the H I compilation of Wakker et al. (2003), who published
velocity profiles from a variety of radio telescopes, primarily the Green Bank
140-ft (GB), 100-m Green Bank Telescope (GBT), Leiden-Dwingeloo Survey,
Effelsberg, and Villa Elisa. This 2003 paper has been used in many studies of
interstellar gas (metallicities, H2, and ionized phases) because it contains
velocity-component fits to the emission profiles. This allows to keep separate
accounts of low-velocity H I and HVCs and IVCs, when present. However,
Gaussian fitting can sometimes give spurious total column densities.

We also study these sight lines using the HI4PI all-sky survey, which combined
data from the Effelsberg and Parkes radio telescopes with an angular
resolution of $16^{\prime}$ (HI4PI Collaboration et al. 2016). We use two
related data products: (a) the $N_{\rm HI}$ map computed by integrating the H
I spectra over the entire velocity range of $|V_{\rm LSR}|<600$ km s-1; and
(b) the $N_{\rm HI}$ map obtained by Lenz et al. (2017) who integrated over
low-velocity gas, $|V_{\rm LSR}|<90$ km s-1 excluding HVC emission, and masked
out regions with $N_{\rm HI}>4\times 10^{20}~{}{\rm cm}^{-2}$. We refer to the
former as NHI–HI4PI(all) and the latter as NHI–HI4PI(90). Both maps are
provided in HEALPix with $N_{\rm side}=1024$.

Liszt (2014a,b) used H I column densities from the LAB survey ($36^{\prime}$
beam), and Lenz et al. (2017) used the HI4PI survey ($16.1^{\prime}$). For the
H I column densities and 21-cm spectra presented by Wakker et al. (2003) the
beams range from $35^{\prime}$ in the Leiden-Dwingeloo Survey (Hartmann &
Burton 1997) to $16.1^{\prime}$ with the Parkes Telescope and 9–10′ (GBT and
Effelsberg). A large beam could include small-scale H I, and velocity
component fitting could be more difficult. These should not be major issues at
high latitudes except in cases of small-scale structure. Nevertheless, there
is a potential mismatch to the resolutions of the space-borne telescopes: IRAS
(4–5′ at 100 $\mu$m) and Planck (5′ at 350–857 $\mu$m). With its
$9.1^{\prime}$ beam and avoidance of stray light due to its off-axis mount,
the GBT should provide reliable column densities. This was the conclusion in a
previous comparison (Wakker et al. 2011) who also identified 10% offset in
$N_{\rm HI}$ from data taken in the LAB survey, owing to a “spurious broad
component” with $N_{\rm HI}\approx 5\times 10^{19}~{}{\rm cm}^{-2}$.

In Table 2 we compare $N_{\rm HI}$ measured by radio telescopes with various
beam sizes toward 36 AGN in common with those tabulated by Wakker et al.
(2011). Our adopted column densities in Table 1 (from Wakker et al. 2003) are
higher on average by $+0.049$ dex in $\log N_{\rm HI}$ relative to those from
GBT. Columns from the GB 140-ft are higher by $+0.017$, and those from the
HI4PI survey are higher by $+0.019$. Quoted errors in $\log N_{\rm HI}$ (for
GB and GBT) are typically $\pm$ 0.01–0.03. We consider differences $\Delta\log
N_{\rm HI}\geq 0.050$ to be discrepant and highlight them in boldface. Figure
3 shows the differences in $N_{\rm HI}$ between HI4PI and Wakker et al.
(2003). Although the average offset differences are comparable to the quoted
errors on $\log N_{\rm HI}$, several AGN sight lines (e.g., 3C 273, Mrk 279,
Mrk 335, Mrk 1383, PG 1259+593, PG 0953+414, Ton S180) exhibit somewhat larger
offsets (0.05–0.12 dex). These include 5 of 32 sight lines measured by both
GBT and HI4PI.

Systematic errors in $N_{\rm HI}$ could arise from calibration, stray-light
contamination, or small-scale structure influenced by beam size. Integration
of antenna temperature over the 21-cm velocity profile could also result in
variations in the total column density. This may be the case in complex 21-cm
profiles such as Mrk 279 and PG 1259+593. Reducing the H I column densities by
12–15% would lower the gas-to-dust ratios, as would increasing $E(B-V)$ in low
reddening sight lines.

###  2.2 Molecular Hydrogen ($N_{\rm H2}$)

Of the 94 quasars in our survey, 55 quasars (group 1) have both H I and H2
column densities. The H2 column densities were measured by FUSE far-
ultraviolet (FUV) absorption-line spectra. With some survey overlap, these
came from 45 sight lines in Gillmon et al. (2006), 18 in Wakker (2006), and
one each from Richter et al. (2001b), Collins et al. (2003), and Fox et al.
(2005). Notes on overlapping H2 data from these surveys and corrections for
specific sight lines are provided in Appendix B. In most of the 55 sight
lines, the H2 column densities are smaller than those of H I. In 30 of the 38
AGN sight lines at latitudes $|b|\geq 40\arcdeg$, the molecular fraction
$f_{\rm H2}\equiv 2N_{\rm H2}/N_{\rm H}$ ranges between $3\times 10^{-6}$ and
$5\times 10^{-4}$, making H2 a negligible contributor to the total $N_{\rm
H}$. These 30 sight lines have column densities below the atomic-to-molecular
transition at $\log N_{\rm H}\approx 20.38\pm 0.13$ seen at high latitude
(Gillmon et al. 2006). Nine sight lines at $|b|\geq 40\arcdeg$ have $f_{\rm
H2}>0.01$ and are listed in Table 3, together with $\log N_{\rm H}$ and
$E(B-V)$. Most have $E(B-V)=$ 0.02–0.06, which is below the H I-to-H2
transition at $E(B-V)\approx$ 0.08–0.10 in low-latitude surveys (Bohlin et al.
1978; Shull et al. 2021). Shifts in the high-latitude transition to lower
$N_{\rm H}$ are influenced by lower gas metallicities, lower dust content, and
reduced far-UV (H2-dissociating) radiation fields; see Browning et al. (2003)
and Gillmon et al. (2006) for models.

We also analyzed 39 additional quasars (group 2 in Table 1) in which only H I
column densities were available. Because these AGN are all at $|b|\geq
40\arcdeg$ with $E(B-V)<0.056$, the H2 contributions could be small in most
cases. However, 17 of the 39 sight lines have column densities $\log N_{\rm
H}\approx$ 20.25–20.67, near or above the H I-to-H2 transition. Thus, some of
the group-2 sample would likely require corrections (1% to 10%) for undetected
H2. In our Tables, we separate the two groups (55 and 39 AGN) and conduct
independent statistical analyses.

###  2.3 Reddening Maps

We use two reddening maps based on previous modeling of the thermal dust
emission: (1) recalibration of the SFD98 map by SF11; (2) the map presented in
Planck Collaboration XLVIII (2016). The 2016 Planck map employed the GNILC
technique (Generalized Needlet Internal Linear Combination) which uses spatial
information from angular power spectra and diffuse component separation to
reduce contamination by cosmic infrared background radiation. These values are
preferred over those from Planck-DL (Planck Collaboration XXIX 2016). Values
of $E(B-V)$ for both SFD98 and SDF11 are available on the IPAC/IRSA reddening
website. Although that website quotes both values, we only list SF11 values,
which are 86% of SFD98 owing to re-calibration of colors using stars from the
Sloan Digital Sky Survey222The re-calibrated SF11 values of $E(B-V)$ are 86%
those of SFD98, but were not applied by Liszt (2014b). The 0.86 factor is less
than the conversion factor described in Section 2.2.1 of Lenz et al. (2017)
where 0.884 is for the Landolt-V filter, and 0.865 is for the CTIO-V filter.
Lenz et al. (2017) also noted a mean ratio of 8.2, using pixels in a revised
reddening map (Schlafly et al. 2014) based on Pan-STARRS1 optical photometry
of 500 million stars.. The SF11 study found that the SFD98 map needed a re-
calibration by a factor 0.86 (0.865 in their Table 6 for the CTIO-V filter).
The map has a FWHM of $6.1^{\prime}$. We query this map using the IPAC/IRSA
website, which provides $1\sigma$ variances averaged over neighboring
$5^{\prime}$ pixels around each line of sight. We also downloaded the original
SFD98 map projected into a HEALPix grid of $N_{\rm side}=2048$ and applied the
re-calibration correction factor333The map is provided on lambda.gsfc.nasa.gov
by Chiang (2023)..

The dust optical depth map presented in Planck Collaboration XLVIII (2016) was
obtained by modeling the Galactic thermal dust emission and separating
contributions from the Cosmic Infrared Background (CIB). The GNILC method was
applied to the Planck 2015 data and the IRAS $100~{}\mu$m map. The final
optical depth map has a $5^{\prime}$ beam size and is provided at HEALPix
$N_{\rm side}=2048$ resolution. We multiply the optical depth map at 353 GHz
by the conversion factor $1.49\times 10^{4}$ to obtain $E(B-V)$ in magnitudes.
Henceforth, we will refer to these techniques as Planck-GN, and the reddening
map as the GN map. When comparing to $N_{\rm HI}$ maps from HI4PI and Lenz et
al. (2017) we smooth the reddening maps to $16.1^{\prime}$ resolution to match
the H I data. As discussed in Appendix E of Planck Collaboration XI (2014),
the choice of filter used to compute $E(B-V)$ affects the conversion from dust
emission to reddening. The Planck team used the filter transmission of the
Johnson photometric system (M.-A. Miville-Deschênes, private communication).
The recalibration factor of SFD98 in this system is 0.884, as used in Lenz et
al. (2017).

Toward the AGN at high Galactic latitude and low extinction, the inferred
values of $E(B-V)$ have large uncertainties, and may in fact be
underestimated. For the quasars in our sample, the mean (FIR-inferred) values
from SFD98 and SF11 are low: $E(B-V)=0.030$ for group 1 (55 quasars) and 0.019
for group 2 (39 quasars). Figure 4 compares differences in $E(B-V)$ between
Planck-GN and SF11 values. On average, the Planck-GN values are 12% larger
than those from SF11 towards the AGN in our sample, including those for the
nine Complex C sight lines (plotted in red). Because of their improvement over
previous Planck products, we use the GN maps, which were recommended for
thermal dust science. The visual extinction is often estimated as
$A_{V}=R_{V}E(B-V)$, with a commonly adopted value of $R_{V}=3.1$. This adds
further systematic uncertainty, as Peek & Schiminovich (2013) found that no
single value of $R_{V}$ is valid over the entire high-latitude sky.

Using FIR emission from foreground dust to estimate the equivalent optical
reddening requires sophisticated models of the grain temperature and
emissivity (e.g., Draine & Li 2007; Compiègne et al. 2011; Hensley & Draine
2021) which depend on grain composition, size distribution, and solid-state
properties. In Appendix C we discuss the dependence of FIR (353 GHz) optical
depth and dust radiance on the dust temperature ($T_{d}$) and emissivity index
($\beta$), where emissivity $\epsilon(\nu)\propto\nu^{\beta}$. Combining the
scaling of dust radiance ${\cal R}\propto\tau_{353}T_{d}^{4+\beta}\propto
T_{d}^{3+\beta}$ with the observed anti-correlation ($\beta\propto
T^{-\alpha}$), we find that radiance is sensitive to small changes in the two
parameters ($\alpha$, $\beta$),

$\frac{{\cal R}}{{\cal
R}_{0}}=\left(\frac{\beta}{\beta_{0}}\right)^{-(3+\beta)/\alpha}\;.$ (1)

Table 4 shows the dust parameters adopted in several FIR papers. Over the
range of indices, $\beta=1.6\pm 0.2$, adopted in the 2016 Planck-GNILC study
and with $\alpha=2/3$, the radiance factor would change by a factor of 2.3
about ${\cal R}_{0}$. Table 5 lists the 100 $\mu$m surface brightness
$I(100~{}\mu$m), FIR-modeled dust temperature $T_{d}$, and inferred color
excess, $E(B-V)$ from SF11. The listed error bars are $1\sigma$ variances in
$E(B-V)$ over neighboring $5^{\prime}$ pixels. The true uncertainties are
likely much larger. Column 4 lists $I(100~{}\mu$m)/$E(B-V)$, with errors
propagated from relative errors on $I(100~{}\mu$m) and $E(B-V)$ added in
quadrature. Several AGN sight lines have large relative errors on $E(B-V)$ and
$I(100~{}\mu$m), with $I(100~{}\mu$m)/$E(B-V)$ uncertain by 10-15%. The
surface brightnesses typically range from 0.4–2 MJy sr-1, with mean values
1.61 MJy sr-1 (first group of 55) and 1.07 MJy sr-1 (second group of 39). The
mean dust temperatures are $\langle T_{d}\rangle=17.900~{}{\rm
K}\;(17.912,17.892)$ and the mean ratios are $\langle I(100~{}\mu{\rm
m})/E(B-V)\rangle=56.22~{}{\rm MJy~{}sr}^{-1}~{}{\rm
mag}^{-1}\;(56.24,56.20)$. Here, the first values are for all 94 quasars, and
the numbers in parentheses denote the means for groups 1 and 2. The uniformity
in mean dust temperatures is surprising, with $1\sigma$ variance
$\sigma(T_{d})=0.213~{}{\rm K}$ (1.2% in group 1). The correspondence between
FIR flux and reddening is good, with 10% variance $\sigma(I/E)=5.63~{}{\rm
MJy~{}sr}^{-1}~{}{\rm mag}^{-1}$ in the distribution of $I(100~{}\mu{\rm
m})/E(B-V)$. However, because of the sensitivity of the modeled dust column
density to $T_{d}$ and $\beta$, small changes can alter the inferred $E(B-V)$.

Given the uncertainties in the dust modeling, the systematic errors on
$E(B-V)$ are likely much larger than those quoted in the IPAC/IRSA tables
($1\sigma$ variances). There could also be intrinsic extinction from the local
environment of the AGN and its host galaxy (Gaskell et al. 2004). For these
reasons, we are suspicious of the accuracy of the ratios $N_{\rm H}/E(B-V)$
for AGN sight lines with $E(B-V)\lesssim 0.04$. In the next section, we
examine these issues statistically for various sub-samples.

##  3 Survey Results

Table 1 presented the gas column densities, inferred $E(B-V)$, and
corresponding ratio $N_{\rm H}/E(B-V)$. All 94 quasars are lightly reddened,
with $E(B-V)$ extending from 0.005 to 0.110 (SF11 scale). The first group of
55 quasars with both H I and H2 column densities has mean $E(B-V)=0.030$,
while the second group (H I only) has mean $E(B-V)=0.019$. The difference
likely arises from the somewhat higher latitudes in the second group. In group
1, we combine molecular hydrogen column densities $N_{\rm H2}$ with those of
atomic hydrogen $N_{\rm HI}$ to arrive at the total hydrogen column density
$N_{\rm H}=N_{\rm HI}+2N_{\rm H2}$. Columns 9 and 10 in Table 1 list dust-to-
gas ratios for gas at all velocities and for low-velocity gas only.

We investigated shifts in the gas-to-dust ratio when we use $E(B-V)$ from
Planck-GN (Planck Collaboration XLVIII 2016) instead of SF11. For the 48 AGN
sight lines with $E(B-V)\leq 0.02$, the GN reddenings are 15% higher than SF11
on average (15 are lower, 33 are higher). For the 81 AGN with $E(B-V)\leq
0.04$, the GN reddenings are 12% higher on average. Thus, using GN reddening
instead of SF11 would reduce the gas-to-dust ratios by 11–13%. For the 11
sight lines with $E(B-V)<0.01$, the ratio reductions are even larger. In Table
1, we highlight these uncertain sight lines in boldface (four in group 1,
seven in group 2). In Section 3.1 we discuss the statistical changes of
excluding these sight lines in modified sub-samples (51 in group 1 and 32 in
group 2). In Section 3.2, we compare the gas-to-dust ratios in sight lines
that contain HVCs and IVCs. In Section 3.3 we discuss Planck all-sky maps of
dust extinction and differences from earlier studies.

###  3.1 Gas-to-Dust Ratios for QSO Sub-samples

Table 6 shows mean values of the ratios $N_{\rm H}/E(B-V)$ for sub-samples of
the 94 high-latitude QSOs. The first group includes the 55 quasars for which
we have both H I and H2 column densities. The second group includes 39 quasars
with only H I. In each group, we list two mean ratios: one for all H I
velocity components fitted by Wakker et al. (2003) and a second for low-
velocity gas with $|V_{\rm LSR}|<90$ km s-1. Elevated ratios are evidence that
dust grains are deficient in high-velocity gas. For the 55 quasars, the mean
ratio using Planck-GN values of $E(B-V)$ is 11% higher than SF11. For the 39
quasars in group 2, the mean ratio for Planck-GN is 12% higher. In the low-
velocity statistics we excluded all HVCs and most of the IVCs, except for 17
IVCs in well-known structures containing H2 and included with low-velocity
gas. The two modified sub-samples in Table 6 omit the 11 sight lines with
highly uncertain $E(B-V)\leq 0.01$. The mean ratios of the sub-samples and
excluded sight lines are listed for comparison.

Figure 5 plots the 55 (group 1) individual gas-to-dust ratios vs. $E(B-V)$.
Some of the elevated ratios are unreliable because of large reddening
uncertainties at $E(B-V)\leq 0.04$. The two values of reddening in the
IPAC/IRSA tables (SFD98 and SF11) differ by 14% because of recalibration.
Systematic differences in $E(B-V)$ can arise because of FIR modeling
sensitivity to dust parameters ($T_{d}$, $\beta$) as discussed in Appendix C.
Gas-to-dust ratios appear high in HVCs because of low grain content, which
adds H I column density to the sight line without dust reddening. It remains
unclear whether the dust deficiency arises from low metallicity or grain
disruption in shocks (or both). Low dust content in HVCs and IVCs was also
noted in the Planck papers, for example Section 6.3 of Planck Collaboration
XXIV (2011), and in Figures 4 and 5 in Lenz et al. (2017) that illustrate the
dependence of $N_{\rm HI}/E(B-V)$ on H I velocity. Their range of ratios is
even larger than found here, probably due to different sky selections.

Complex C is a good example of HVC effects, demonstrating the importance of
keeping separate account of the high velocity gas. Table 7 shows the gas-to-
dust ratios for nine quasar sight lines passing through this gaseous
structure. The last four columns list the ratios derived for gas at all
velocities and then omitting H I in the HVCs. The ratios are shown for
$E(B-V)$ taken from both SF11 and Planck-GN. In both cases, the mean gas-to-
dust ratios drop 40% when one excludes HVCs. In Complex C, gas velocity is a
major factor in the elevated ratios.

Table 7 also illustrates differences in $E(B-V)$ estimates from SF11 and
Planck-GN among the Complex C sight lines. On average, the Planck-GN estimate
is 23% higher than SF11, over a range in SF11 reddening from $E(B-V)=0.0053$
to 0.0344. The three sight lines with $E(B-V)<0.010$ are likely quite
uncertain, resulting in large, asymmetric errors on $N_{\rm H}/E(B-V)$. For
example, PG 1626+554 has $\log N_{\rm H}=20.053$ (all velocities) and 19.936
(low-velocity gas) but with different values of $E(B-V)=0.0053$ (SF11) and
0.0137 (GN). Adopting the GN reddening instead of SF11 reduces $N_{\rm
H}/E(B-V)$ from 21.3 to 8.24 (all-velocities) and from 16.3 to 6.28 (low-
velocity gas). Similarly, toward Mrk 817, where $\log N_{\rm H}=20.085$ (all
velocities), $E(B-V)=0.0059$ (SF11), and 0.0115 (GN), the gas-to-dust ratio
drops by a factor of two, using GN instead of SF11.

###  3.2 Distinguishing Low-Velocity and High-Velocity Gas

Here we examine the possibility of different grain abundances in high velocity
gas. Specifically, we explore the dust-to-gas ratios after excluding HVCs and
some IVCs. To distinguish low-velocity gas from higher velocity clouds, we
tabulated the column densities of the velocity components and performed
statistics with and without HVC/IVC gas. This allowed us to assess whether
some of the gas is deficient in dust as a result of grain processing in
interstellar shocks (Draine & Salpeter 1979; Seab & Shull 1983; Jones et al.
1996; Slavin et al. 2004). The H I column densities in Table 1 (columns 5 and
6) were determined by summing the Gaussian component fits (Wakker et al. 2003)
in the 21-cm spectra.

Most of the HVCs (Wakker & van Woerden 1997) with velocities $|V_{\rm
LSR}|\geq 90$ km s-1 in the local standard of rest show no evidence for dust,
probably because of reduced metallicity or shock destruction of grains. In
some sight lines, HVCs provide a sizable portion of the 21-cm emission (Wakker
et al. 2003; Collins et al. 2007; Shull et al. 2011; Martin et al. 2015;
Panopoulou & Lenz 2020). IVCs have broadly been classified (Albert & Danly
2004) as having $|V_{\rm LSR}|$ between 20–90 km s-1. In recent surveys, the
IVC ranges were chosen as 30–90 km s-1 (Richter et al. 2003) and 40–90 km s-1
(Lehner et al. 2022). Located in the lower Galactic halo, IVCs display a
variety of physical conditions, with gas metallicities near solar values
(Wakker 2001; Richter et al. 2001a, 2003), but refractory element abundances
that suggest some grain disruption.

From the 21-cm spectra of our sample, we grouped the H I emission components
into three velocity categories: HVCs ($|V_{\rm LSR}|\geq 90$ km s-1), IVCs
($|V_{\rm LSR}|=$ 30–90 km s-1), and low-velocity gas. In the first group of
55 AGN sight lines with both H I and H2 data, we identified HVCs in 18 quasar
sight lines (33% coverage) and IVCs in 39 sight lines (73% coverage). In the
second group of 39 quasars with only H I data, we identified HVCs toward 3
quasars (8%) and IVCs toward 27 quasars (69%). The difference in HVC incidence
may be an effect of the higher Galactic latitudes of the AGN in group 2. Nine
of the quasars in group 1 were targeted to study HVC Complex C. In addition,
high-latitude absorbers may be more ionized, with spatial extents greater than
those seen in H I. Previous UV studies of IVC/HVC ionized gas in the strong Si
III 1206.500 Å absorption line found large sky-covering fractions,
$f_{c}=0.81\pm 0.05$ (Shull et al. 2009) and $f_{c}=0.77\pm 0.06$ (Richter et
al. 2017).

FIR emission has been observed in some IVCs (e.g., Planck Collaboration XXIV
2011; Planck Collaboration XI 2014), and the infrared cirrus was shown to
correlate with H2 absorption (Gillmon & Shull 2006). In our statistical
analysis of velocity effects, we included 17 strong IVCs with the low-velocity
gas. These sight lines are marked by asterisks in column 10 of Table 1. We
excluded all HVCs and most IVCs from the column densities of low velocity gas.
The excluded IVCs have velocities well separated from the low-velocity 21-cm
emission near the LSR. Included with the low-velocity gas were 10 of the 39
IVCs in group 1, and 7 of the 27 IVCs in group 2. They are all well-known
structures: eight sight lines through the Intermediate Velocity Arch (IV
Arch), three through the S1 cloud, four through IV18, and one each through
IV19 and IV26.

Planck Collaboration XXIV (2011) noted that IVCs had different FIR properties,
with different emission cross sections, often 50% lower compared to the low-
velocity clouds. There is also evidence for grain disruption in intermediate
velocity absorbers, including the “Routly-Spitzer effect” (Routly & Spitzer
1952) in which elevated Ca II/Na I ratios are observed at increasing cloud
velocity. Similar effects are observed in the rising abundances of refractory
elements (Si, Fe) with increasing cloud velocity (Shull et al. 1977). There
has been no strong evidence for dust in HVCs (e.g., Wakker & Boulanger 1986;
Désert et al. 1988) other than an unconfirmed claim of IR emission in one HVC
(Miville-Deschênes et al. 2005). Fox et al. (2023) reported indirect evidence
for some dust in Complex C, based on sub-solar differential abundance ratios
of refractory elements (Fe/S, Si/S, Al/S) relative to sulfur, which is assumed
to be undepleted.

###  3.3 All-Sky Maps

The sight lines through Complex C suggest that both low dust content and
uncertainties in FIR estimates of $E(B-V)$ could be responsible for some of
the elevated ratios along high latitude sight lines with low reddening. We
have compared the SF11 estimates of $E(B-V)$ to values from Planck
Collaboration XLVIII (2016) denoted here as Planck-GN. Polar projection maps
in Figure 6 illustrate the differences, which often track changes in the gas-
to-dust ratio in the maps of Figure 1. Features in the Northern Galactic
hemisphere that appear yellow in the GN ratio map correlate with locations of
IVCs, where both SFD98 and SF11 overestimate the total reddening compared to
Planck-GN. The bright feature in red near the North Galactic Pole at
($\ell,b)=(260-330\arcdeg,80-84\arcdeg)$ is Markkanen’s cloud (Markkanen
1979). This feature is also known as the North Galactic Pole Rift, seen in H I
(Puspitarini & Lallement 2012) and appearing as a foreground shadow in X-rays
(Snowden et al. 2015). This region is known (Planck Collaboration XI 2014) to
have a low dust emission spectral index ($\beta$) compared to the rest of the
high-latitude sky. It shows up in the reddening difference map because SFD98
assumed a constant $\beta$, whereas Planck-GN fit for the emission index.

Figure 7 shows three distributions of gas-to-dust ratios, using different
values of $E(B-V)$. The three colored curves show $N_{\rm HI}/E(B-V)$ for low-
velocity H I, with $E(B-V)$ taken from the SF11 re-calibration (blue), SFD
recalibrated with 0.884 (orange), and Planck-GN (green). We find mean ratios
of 9.3 (SF11) and 8.6 (Planck) in units of $10^{21}~{}{\rm cm}^{-2}~{}{\rm
mag}^{-1}$. The two vertical (dotted, dashed) lines show the mean high-
latitude ratios (8.8 and 8.2) quoted in Lenz et al. (2017). The two vertical
solid lines show the Galactic disk-plane values (5.8 and 6.07) from Bohlin et
al. (1978) and Shull et al. (2021).

##  4 Summary and Conclusions

The goal of our study was to assess the accuracy and reliability of
measurements of the gas-to-dust ratio $N_{\rm H}/E(B-V)$ toward high-latitude
extragalactic sources. Using radio/FIR techniques, past studies (Liszt
2014a,b; Lenz et al. 2017; Liszt & Gerin 2023) found 35–45% higher ratios than
established values in the Galactic disk plane. There are many astrophysical
processes that could segregate dust from gas (Hensley & Draine 2021; Shull et
al. 2021) to produce a deficit of interstellar dust grains above the disk
plane. Dust could settle to the disk, be radiatively elevated into the halo,
or be transported by supernova-driven outflows. Most HVCs exhibit little or no
evidence for dust, either because of low metallicity or shock destruction.
Dust elevated above the Galactic plane will come into contact with hot gas,
with grain sputtering lifetimes of $t_{\rm sp}\approx(1~{}{\rm
Gyr})(10^{-3}~{}{\rm cm}^{-3}/n_{e})$ at $10^{6.0-6.5}$ K.

Observations of gas and dust at high and low Galactic latitudes employ
different methods and calibrations. In the Galactic disk surveys, the hydrogen
(H I, H2) column densities were measured from UV absorption toward OB-type
stars, with $E(B-V)$ inferred from stellar photometry and intrinsic colors
assigned to spectral classification. Most high-latitude gas measurements
employ H I 21-cm emission toward extragalactic targets, and $E(B-V)$ is
inferred from models that convert FIR dust emission to the corresponding
optical extinction. In some cases, H2 measurements are available toward AGN,
but often not.

From our survey of 94 AGN, we confirm previous observations of elevated gas-
to-dust ratios at high Galactic latitude (Liszt 2014a,b; Lenz et al. 2017).
However, we found systematic uncertainties in measurements of both the
numerator $N_{\rm HI}$ and denominator $E(B-V)$ of the ratio. The different
ratios found with the two techniques are seen primarily at high latitudes and
in sight lines with $E(B-V)\leq 0.04$. From sub-samples of the 94 AGN,
examining the measurements $N_{\rm HI}$, $N_{\rm H2}$, and $E(B-V)$, we came
to several conclusions about offsets and uncertainties:

  * •

Values of $E(B-V)$ from Planck-GN generally exceed those from SF11 towards the
AGN in our sample. On average, we found their ratio (GN/SF11) to be 15% higher
for 48 AGN with $E(B-V)\leq 0.02$ and 12% higher for 81 AGN with $E(B-V)\leq
0.04$.

  * •

Measurements with the GBT 100 m telescope exhibit $N_{\rm HI}$ lower by
4.0–4.5% on average compared to the Green Bank 140 ft and the HI4PI survey. In
several sight lines, GBT measured $N_{\rm HI}$ lower by 10–30%.

  * •

Including H2 in total $N_{\rm H}=N_{\rm HI}+2N_{\rm H2}$ increases $N_{\rm H}$
by 10% on average at high latitude.

  * •

Excluding high velocity gas (HVCs) decreases $N_{\rm H}/E(B-V)$ by 15% on
average, and by 40% for nine sight lines through Complex C.

Figure 8 visually illustrates the mean gas-to-dust ratios in our sub-samples.
For each sub-sample, three points show the shifts that occur when one uses
different reddening maps (SF11 vs. Planck-GN) or sight lines with values of
$N_{\rm HI}$ at all velocities or just low velocity. Within formal
uncertainties, our dust-to-gas ratios are consistent with the 8.8 value from
Lenz et al. (2017) when we exclude the low-reddening sight lines, consider gas
at all velocities, and use Planck-GN reddening. The right-most points in each
triplet in Figure 8 (labeled SF11, low) are also consistent with Lenz et al.
(2017), but that sub-sample only considers low-velocity gas. There is also
good evidence that Planck-GN reddening maps are superior to SF11. The mean
ratio is sensitive to the AGN sample selection, implying once again that the
formal variation about the mean underestimates the systematic uncertainties.

As noted, surveys of extragalactic targets at $|b|>30^{\circ}$ would be
expected to show higher gas-to-dust ratios. However, it is important to assess
how much arises from reduced grain content, and how that deficiency occurs.
High ratios are clearly seen in sight lines with HVCs (18 of 55 of the AGN
sight lines in group 1). In this sample with both H I and H2 measurements, the
mean ratio drops by 15% when HVCs are excluded. Some of the anomalously high
ratios may result from under-estimated reddening when $E(B-V)\leq 0.04$. A
comparison of H I column densities obtained from different radio telescopes
(Table 2) found differences in $N_{\rm HI}$ between GB and GBT telescopes and
from the HI4PI survey, as well as from LAB, LDS, and Effelsberg measurements.
Uncertainties in $E(B-V)$ may be even larger, as converting FIR emission to
optical reddening requires precise modeling of dust temperature $T_{d}$ and
grain emissivity index $\beta$. Appendix C demonstrated the sensitivity of
dust radiance to $\beta$ and its anti-correlation with $T_{d}$. We also
discussed the accuracy of $E(B-V)$ in previous FIR studies (SFD98, SF11)
compared to values from FIR all-sky maps from the Planck Mission. Tabulated
values of $E(B-V)$ at $|b|>30\arcdeg$ have systematic uncertainties larger
than the variances listed on the IPAC/IRSA website. Given the sensitivity of
the FIR-derived values to grain parameters, the optical extinction may be
underestimated in high-latitude AGN sight lines.

We now summarize our survey results for the mean ratios of gas-to-dust,

  1. 1.

In the Galactic disk, the mean ratio $N_{\rm H}/E(B-V)$ of interstellar gas-
to-dust in the Galactic disk has been determined as $6.0\pm 0.2$ (in units of
$10^{21}$ cm-2 mag-1) by many studies (Bohlin et al. 1978; Shull et al. 2021;
Gudennavar et al. 2012; Widmark et al. 2023). For 51 quasars at high Galactic
latitude, with measurements of both H I and H2 and $0.01\leq E(B-V)\lesssim
0.1$ (SF11 scale), we find mean ratios $10.6\pm 0.4$ (gas at all velocities)
and $9.2\pm 0.3$ (low-velocity).

  2. 2.

A portion of the high gas-to-dust ratios likely arises from reduced grain
content in HVCs (and some IVCs) owing to low metallicity and shock destruction
of grains. For nine sight lines passing through Complex C, with mean
$E(B-V)=0.0151$ (SF11) and 0.0185 (GN), the ratio decreases by 40% when high
velocity gas is excluded.

  3. 3.

Owing to uncertainties in both numerator $N_{\rm HI}$ and denominator
$E(B-V)$, the gas-to-dust ratio has large and asymmetric errors. In a
comparison of 36 AGN sight lines, some values of $\log N_{\rm HI}$ differed by
0.05–0.12 in 21-cm observations at various radio telescopes. Compared to data
from the GBT 100 m ($9.1^{\prime}$ beam), the mean values of $\log N_{\rm HI}$
were higher by $+0.017$ (GB $21^{\prime}$ beam), $+0.019$ (HI4PI,
$16^{\prime}$ beam), and $+0.049$ (GB, Effelsberg, Villa Elisa) as tabulated
in Wakker et al. (2003).

  4. 4.

Elevated $N_{\rm H}/E(B-V)$ may also arise from uncertain FIR estimates of
$E(B-V)$, which are sensitive to dust temperature $T_{d}$ and emissivity index
$\beta$. With their observed anti-correlation,
$(\beta/\beta_{0})=(T_{d}/T_{0})^{-\alpha}$, dust radiance ${\cal R}\equiv\int
I_{\nu}\,d\nu$ depends sensitively on the emissivity index, ${\cal R}/{\cal
R}_{0}=(\beta/\beta_{0})^{-(3+\beta)/\alpha}$. For $\alpha\approx 2/3$ (Martin
et al. 2012) and $\beta=1.6\pm 0.2$ adopted in the 2016 Planck-GN study,
factor-of-two changes could occur in $E(B-V)$ from variations about the fitted
radiance ${\cal R}_{0}$.

  5. 5.

Values of $E(B-V)$ at $|b|>30\arcdeg$ from Planck-GN dust emission are
preferred over those from Planck-DL, SF11, or SFD98. On average, Planck-GN
reddening values are 12% higher than SF11 for $E(B-V)\leq 0.04$, with large
variations in the (GN/SF11) ratios of $E(B-V)$. An underestimate of reddening
at high latitudes and low $E(B-V)$ is consistent with an analysis of Planck
data (Casandjian et al. 2022), who also found excess dust at high latitude.

Reddening maps and variations in the gas-to-dust ratio are important for
studies of the ISM and many other areas of astrophysics. Owing to the steep
rise of selective extinction toward shorter wavelengths, the spectral slopes
of de-reddened UV spectra of AGN will be harder than found in composite
spectra (Stevans et al. 2014) which used IPAC/IRSA reddening tables. Reddening
maps will affect CMB foreground subtraction and derivation of cosmological
parameters, including “B-modes” in polarized emission. Variations in $\log
N_{\rm HI}$ measurements and FIR-inferred $E(B-V)$ and propagated errors in
the numerator and denominator result in large, asymmetric errors in $N_{\rm
H}/E(B-V)$. This suggests the need to obtain high-quality 21-cm observations
of a sample of high-latitude quasars to understand the source of offsets. It
would also be helpful to update the IPAC/IRSA reddening tables, frequently
used to convert measured $N_{\rm HI}$ to reddening and extinction.

We thank Bruce Draine, Charles Danforth, Bart Wakker, and Brandon Hensley for
helpful discussions. Jay Lockman kindly provided additional 21-cm data from
the Green Bank Telescope and expert advice on a number of AGN sight lines.
Marc-Antoine Miville-Deschênes provided the optical filter bandpasses used in
the Planck analysis. A portion of this study was supported by the New Horizons
Mission observational planning for observations of cosmic backgrounds at high
Galactic latitude. The authors also acknowledge Interstellar Institute’s
Program II6 and the Paris-Saclay University’s Institut Pascal for hosting
discussions that nourished the development of the ideas behind this work. Our
survey made use of the reddening website for IPAC/IRSA data of FIR emission
and modeled values of dust temperature $T_{d}$ and $E(B-V)$.

## References

  * (1)
  * (2) Albert, C. E., & Danly, L. 2004, in High Velocity Clouds, ASSL, 312, 73, ed. H. van Woerden, B. P. Wakker, U. J. Schwarz, K. S. de Boer (Dordrecht: Kluwer Acad. Publ.)
  * (3)
  * (4) Bohlin, R. C., Savage, B. D., & Drake, J. F. 1978, ApJ, 224, 132
  * (5)
  * (6) Browning, M. K., Tumlinson, J., & Shull, J. M. 2003, ApJ, 582, 810
  * (7)
  * (8) Casandjian, J.-M., Ballet, J., Grenier, I., & Remy, Q. 2022, ApJ, 940, 116
  * (9)
  * (10) Chiang, Y.-K. 2023, arXiv:2306.03926
  * (11)
  * (12) Chiang, Y.-K., & Ménard, B. 2019, ApJ, 870, 120
  * (13)
  * (14) Collins, J. A., Shull, J. M., & Giroux, M. L. 2003, ApJ, 585, 336
  * (15)
  * (16) Collins, J. A., Shull, J. M., & Giroux, M. L. 2007, ApJ, 657, 271
  * (17)
  * (18) Compiègne, M., Verstraete, L., Jones, A., et al. 2011, A&A, 525, A103
  * (19)
  * (20) Désert, F. X., Bazell, D., & Boulanger, F. 1988, ApJ, 334, 815
  * (21)
  * (22) Draine, B. T., & Li, A. 2007, ApJ, 657, 810
  * (23)
  * (24) Draine, B. T., & Salpeter, E. E. ApJ, 231, 438
  * (25)
  * (26) Fox, A. J., Savage, B. D., Wakker, B. P., et al. 2005, ApJ, 630, 332
  * (27)
  * (28) Fox, A. J., Cashman, F. H., Kriss, G. A., et al. 2023, ApJ, 946, L48
  * (29)
  * (30) Gaskell, C. M., Goosmann, R. W., Antonucci, R., et al. 2004, ApJ, 616, 147
  * (31)
  * (32) Gillmon, K., & Shull, J. M. 2006, ApJ, 636, 908
  * (33)
  * (34) Gillmon, K., Shull, J. M., Tumlinson, J., & Danforth, C. 2006, ApJ, 636, 891
  * (35)
  * (36) Górski, K. M., Hivon, E., Banday, A.J., et al. 2005 ApJ 622, 759
  * (37)
  * (38) Gudennavar, S. B., Bubbly, S. G., Preethi, K., & Murthy, J. 2012, ApJS, 199, 8
  * (39)
  * (40) Hartmann, D., & Burton, W. B. 1997, Atlas of Galactic Neutral Hydrogen (Cambridge: Cambridge University Press)
  * (41)
  * (42) Hensley, B. S., & Draine, B. T. 2021, ApJ, 906, 73
  * (43)
  * (44) HI4PI Collaboration, Ben Bekhti, N., Floer, L., et al. 2016, A&A, 594, A116
  * (45)
  * (46) Jones, A. P., Tielens, A. G. G. M., & Hollenbach, D. J. 1996, ApJ, 469, 740
  * (47)
  * (48) Kalberla, P. M. W., Burton, W. B., Hartmann, D., et al. 1995, A&A, 440, 775.
  * (49)
  * (50) Lehner, N., Howk, J. C., Marasco, A., & Fraternali, F. 2022, MNRAS, 513, 3228
  * (51)
  * (52) Lehner, N., Savage, B. D., Wakker, B. P. et al. 2006, ApJS, 164, 1
  * (53)
  * (54) Lenz, D., Hensley, B. S., & Doré, O. 2017, ApJ, 846, 38
  * (55)
  * (56) Liszt, H. 2014a, ApJ, 780, 10
  * (57)
  * (58) Liszt, H. 2014b, ApJ, 783, 17
  * (59)
  * (60) Liszt, H., & Gerin, M. 2023, ApJ, 943, 172
  * (61)
  * (62) Markkanen, T. 1979, A&A, 74, 201
  * (63)
  * (64) Martin, P. G., Blagrave, K. P. M., Lockman, F. J., et al. 2015, ApJ, 809, 153
  * (65)
  * (66) Martin, P. G., Roy, A., Bontemps, S., et al. 2012, ApJ, 751, 28
  * (67)
  * (68) Meisner, A. M., & Finkbeiner, D. P. 2015, ApJ, 798, 88
  * (69)
  * (70) Miville-Deschênes, M.-A., Boulanger, F., et al. 2005, ApJ, 631, L57
  * (71)
  * (72) Nguyen, H., Dawson, J. R., Miville-Deschênes, M.-A., et al. 2005, ApJ, 862, 49
  * (73)
  * (74) Panopoulou, G. V., & Lenz, D. 2020, ApJ, 902, 120
  * (75)
  * (76) Paradis, D., Veneziani, M., Noriega-Crespo, A., et al. 2010, A&A, 540, L8
  * (77)
  * (78) Peek, J. E. G., & Schiminovich, D. 2013, ApJ, 771, 68
  * (79)
  * (80) Planck Collaboration XXIV 2011, A&A, 536, A24
  * (81)
  * (82) Planck Collaboration XI 2014, A&A, 571, A11
  * (83)
  * (84) Planck Collaboration XXIX 2016, A&A, 586, A132 (Planck-DL)
  * (85)
  * (86) Planck Collaboration XLVIII 2016, A&A, 596, A109 (Planck-GN)
  * (87)
  * (88) Planck Collaboration IV 2020, A&A, 641, A4
  * (89)
  * (90) Puspitarini, L., & Lallement, R. 2012, A&A, 545, A21
  * (91)
  * (92) Rachford, B. L., Snow, T. P., Destree, J. D., et al. 2009, ApJS, 180, 125
  * (93)
  * (94) Routly, P. M., & Spitzer, L. 1952, 115, 227
  * (95)
  * (96) Richter, P., Nuza, S. E., Fox, A. J., et al. 2017, A&A, 607, A48
  * (97)
  * (98) Richter, P., Sembach, K. R., Wakker, B. P., et al. 2001a, ApJ, 559, 318
  * (99)
  * (100) Richter, P., Sembach, K. R., Wakker, B. P., & Savage, B. D. 2001b, ApJ, 562, L181
  * (101)
  * (102) Richter, P., Wakker, B. P., Savage, B. D., & Sembach, K. R. 2003, ApJ, 586, 230
  * (103)
  * (104) Savage, B. D., Bohlin, R. C., Drake, J. F., & Budich, W. 1977, ApJ, 216, 291
  * (105)
  * (106) Schlafly, E. F., & Finkbeiner, D. P. 2011, ApJ, 737, 103 (SF11)
  * (107)
  * (108) Schlafly, E. F., Green, G., Finkbeiner, D.P., et al. 2014, ApJ, 786, 29
  * (109)
  * (110) Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998, ApJ, 500, 525 (SFD98)
  * (111)
  * (112) Seab, C. G., & Shull, J. M. 1983, ApJ, 275, 652
  * (113)
  * (114) Shull, J. M., & Danforth, C. W. 2019, ApJ, 882, 180
  * (115)
  * (116) Shull, J. M., Danforth, C. W., & Anderson, K. L. 2021, ApJ, 911, 55
  * (117)
  * (118) Shull, J. M., Stevans, M., Danforth, C. W., et al. 2011, ApJ, 739, 105
  * (119)
  * (120) Shull, J. M., Jones, J. R., Danforth, C. W., & Collins, J. A. 2009, ApJ, 699, 754
  * (121)
  * (122) Shull, J. M., York, D. G., & Hobbs, L. M. 1977, ApJ, 211, L139
  * (123)
  * (124) Slavin, J. D., Dwek, E., & Jones, A. P. 2004, ApJ, 803, 7
  * (125)
  * (126) Snowden, S. L., Koutroumpa, D., Kuntz, K. D., et al. 2015, ApJ, 806, 120
  * (127)
  * (128) Sota, A., Maíz Apellániz, J., Walborn, N. R., et al. 2011, ApJS, 193, 24
  * (129)
  * (130) Sota, A., Maíz Apellániz, J., Morrell, N. I., et al. 2014, ApJS, 211, 10
  * (131)
  * (132) Stevans, M. L, Shull, J. M., Danforth, C. W., & Tilton, E. M. 2014, ApJ, 794, 75
  * (133)
  * (134) Wakker, B. P. 2001, ApJS, 136, 463
  * (135)
  * (136) Wakker, B. P. 2006, ApJS, 163, 282
  * (137)
  * (138) Wakker, B. P., & Boulanger, F. 1986, A&A, 170, 84
  * (139)
  * (140) Wakker, B. P., Howk, J. C., Savage, B. D., et al. 1999, Nature, 402, 388
  * (141)
  * (142) Wakker, B. P., Lockman, F. J., & Brown, J. M. 2011, ApJ, 728, 159
  * (143)
  * (144) Wakker, B. P., Savage, B. D., Sembach, K. D., et al. 2003, ApJS, 146, 1
  * (145)
  * (146) Wakker, B. P., & van Woerden, H. 1997, ARA&A, 35, 217
  * (147)
  * (148) Widmark, A., Korsmeier, M., & Linden, T. 2023, Phys. Rev. Lett., 130, 16 1002
  * (149)

##  Appendix A Error Propagation in the Ratio $N_{\rm H}$/E(B-V)

Errors in the gas-to-reddening ratio $N_{\rm H}/E(B-V)$ arise from
uncertainties in measurements of three quantities: $\log N_{\rm HI}$, $\log
N_{\rm H2}$, and $E_{B-V}$, where $N_{\rm H}\equiv N_{\rm HI}+2N_{\rm H2}$.
Because $\log N=(\ln N/2.303)$, we have $\sigma_{\log N_{H}}=(\sigma_{\ln
N_{H}}/2.303)=(\sigma_{N_{H}}/2.303\,N_{\rm H})$. The propagated errors on
$\log{\rm N}_{\rm H}$ give the weighted formula,

$\sigma^{2}_{\log N_{\rm H}}=\left(\frac{N_{\rm HI}}{N_{\rm
H}}\right)^{2}\sigma_{\log N_{\rm HI}}^{2}+\left(\frac{2N_{\rm H2}}{N_{\rm
H}}\right)^{2}\sigma_{\log N_{\rm H2}}^{2}\;.$ (A1)

Similarly, propagated errors in $N_{\rm H}/E(B-V)$ lead to

$\Bigl{(}\frac{\sigma_{\rm ratio}}{{\rm
ratio}}\Bigr{)}^{2}=\left(\frac{\sigma_{N_{H}}}{N_{H}}\right)^{2}+\left(\frac{\sigma_{E_{B-V}}}{E_{B-V}}\right)^{2}=\Bigl{[}2.303\,\sigma_{\log
N_{H}}\Bigr{]}^{2}+\Bigl{[}\frac{\sigma_{E_{B-V}}}{E_{B-V}}\Bigr{]}^{2}\;.$

We can use this expression to evaluate which errors dominate uncertainty in
the gas-to-reddening ratios discussed in this paper. Consider a typical
example of O-star data for HD 15137 (O9.5 II-IIIn) at $b=-7.58\arcdeg$ with
$\log N_{\rm HI}=21.24\pm 0.07$, $\log N_{\rm H2}=20.27\pm 0.05$, and
$E(B-V)=0.35\pm 0.03$. Here, the molecular fraction $f_{\rm H2}=0.186$, the
total hydrogen column density $\log N_{\rm H}=21.324\pm 0.058$, and the ratio
is $N_{\rm H}/E(B-V)=(6.02\pm 0.96)\times 10^{21}$ cm-2 mag-1 with uncertainty
$\sigma_{\rm ratio}/{\rm ratio}=0.159$ (16% errors). Errors on the ratio are
dominated by uncertainties in $\log N_{\rm HI}$ [0.07 dex or 17%] and $\log
N_{\rm H2}$ (0.05 dex or 12%) compared to 9% error on $E(B-V)$. Consider now
an O-star sight line with lower reddening, $E(B-V)=0.15\pm 0.03$ (20% error)
and column densities $\log N_{\rm HI}=21.00\pm 0.05$ and $\log N_{\rm
H2}=19.24\pm 0.10$. In this case, $\log N_{\rm H}=21.015\pm 0.048$ (12%
errors) and the ratio is $(6.90\pm 1.58)\times 10^{21}$ with 23% errors. In
this case, errors on $E(B-V)$ are more important.

Next, consider a moderately reddened quasar, Mrk 1095 with $\log N_{\rm
HI}=20.969\pm 0.07$, $\log N_{\rm H2}=18.76^{+0.21}_{-0.31}$, and
$E(B-V)=0.1099$. The IPAC/IRSA tables quote an error of $\pm 0.0017$ (1.5%) on
$E(B-V)$ (from SF11), but we suggest a larger systematic error of $\pm 0.02$
(18%). From these, we find $\log N_{\rm H}=20.974\pm 0.069$ and $\sigma_{\rm
ratio}/{\rm ratio}=0.24$, so that $N_{\rm H}/E(B-V)=(6.8\pm 1.6)\times
10^{21}$ cm-2 mag-1. Errors on this ratio are dominated by uncertainties in
both $\log N_{\rm HI}$ (17%) and $E(B-V)$ (18%)

As a final example, consider Mrk 279, a high-latitude quasar behind Complex C
with low reddening (see Table 7) variously quoted as $E(B-V)=0.0138\pm 0.0005$
(SF11), $0.0197\pm 0.0063$ (Planck-DL), and $0.0154\pm 0.0002$. The column
densities are $\log N_{\rm HI}=20.388\pm 0.05$, $\log N_{\rm H2}=14.42\pm
0.09$. and $\log N_{\rm H}=20.338\pm 0.048$. The gas-to-dust ratios (15.8,
11.1, 14.1) in the usual ($10^{21}$) units. The quoted relative errors on
$E(B-V)$ are inconsistent with the 26% dispersion among the three estimates;
systematic errors likely dominate the uncertainty on the ratio. Similar
uncertainties (and bias) are likely present in other lightly reddened
extragalactic sight lines.

##  Appendix B Notes on H2 for Individual AGN Sight Lines

In Table 1, we listed H2 column densities for the 55 sight lines in Group 1
based on several sources, primarily two 2006 FUSE surveys of high-latitude
quasars (Gillmon et al. 2006; Wakker 2006). We found generally good agreement,
but in several cases there were discrepancies. Table 1 includes H2 column
densities for 38 of the 45 AGN in Gillmon et al. (2006). For 9 other sight
lines (H1821+643, HE 0226-4110, Mrk 501, Mrk 817, NGC 1399, NGC 3310, NGC
3690, NGC 4214, PHL 1811) we adopted values from Wakker (2006), who analyzed
additional FUSE observations and generated smaller error bars. Wakker (2006)
also provided H2 data for 9 additional targets (H1821+643, HE 0226-4110, Mrk
279, Mrk 501, Mrk 817, Mrk 1383, NGC 985, PG 1116+215, Ton S210). Table 3 in
that paper also lists line widths (FWHM), which we translate to $b={\rm
FWHM}/1.665$ (assuming a Gaussian profile) to compare with curve-of-growth
Doppler parameters found by Gillmon et al. (2006). Below are notes on several
discrepancies and our reasons for the selected $N_{\rm H2}$.

Fairall 9. Richter et al. (2001b) detected H2 with $\log N_{\rm
H2}=16.40^{+0.28}_{-0.53}$ in the Magellanic Stream toward Fairall 9 at
$V_{\rm LSR}=+190$ km s-1. No H2 was seen at low velocity (Gillmon et al.
2006). We quote the high-velocity value, $\log N_{\rm H2}=16.40$ in Table 1.

H1821+643. Published H2 column densities and Doppler parameters differ between
two FUSE surveys: $\log N_{\rm H2}=17.91^{+0.13}_{-0.20}$ with
$b=1.7^{+0.8}_{-0.7}$ km s-1 (Gillmon et al. 2006) and $\log N_{\rm
H2}=15.99^{+0.16}_{-0.06}$ based on $b=4.3$ km s-1 inferred from FWHM = 7.2 km
s-1 quoted in Table 3 of Wakker (2006). The difference arises from the two
curve-of-growth $b$-values (or FWHM) fitted to the data. We adopted the lower
columns of Wakker (2006) because his higher Doppler parameter seemed more
plausible physically.

HE 0226-4110. Gillmon et al. (2006) quoted $\log N_{\rm H2}<14.29$, but Fox et
al. (2005) detected $\log N_{\rm H2}=14.58\pm 0.09$. Two subsequent analyses
quoted 14.54 (Lehner et al. 2006) and $14.56^{+0.15}_{-0.10}$ (Wakker 2006).
Summing the column densities $N(J)$ for $J=$ 0–3 in Table 3 of Wakker (2006),
we find $\log N_{\rm H2}=14.60\pm 0.14$, with propagation of errors on $N(J)$.
We use the latter value in Table 1.

MRC 2251-178. Gillmon et al. (2006) quoted $\log N_{\rm
H2}=14.54^{+0.23}_{-0.17}$, based on a detection in $J=1$ and an upper limit
in $J=0$. Wakker (2006) listed a total column density $\log N_{\rm
H2}=15.02^{+0.45}_{-0.23}$, but that included upper limits for column
densities in $J=$ 2–4, which should probably not be included in the total sum.
Instead, we adopt $\log N_{\rm H2}=14.87^{+0.23}_{-0.17}$ from the detected
column densities in $J=0$ and $J=1$.

Mrk 106. Gillmon et al. (2006) quoted $\log N_{\rm H2}=16.23^{+0.21}_{-0.15}$
with $b=14.9^{+3.5}_{-2.6}$ km s-1. Wakker (2006) quoted $\log N_{\rm
H2}=18.54^{+0.11}_{-0.10}$ with FWHM = 7.5 km s-1 ($b=4.5$ km s-1). We adopt
the smaller column density, since the high value in Wakker (2006) should
produce detectable damping wings. (However, the FUSE data do not have high
S/N.) Another argument for the lower value is that a large H2 column density
and high molecular fraction ($f_{\rm H2}\approx 0.03$) would be unlikely at
the estimated $E(B-V)\approx 0.0235$ (SF11).

Mrk 279. This target did not appear in Gillmon et al. (2006). Wakker (2006)
mentioned no low-velocity H2 absorption, but his Table 4 listed $\log N_{\rm
H2}=14.42\pm 0.09$ in the LLIV arch at $V_{\rm LSR}=-41$ km s-1. We quote the
latter (IVC) value in Table 1.

Mrk 501. We adopted the value $\log N_{\rm H2}=15.49^{+0.66}_{-0.24}$ from
Wakker (2006), as it was based on additional data than used by Gillmon et al.
(2006).

Mrk 817. We adopted the value $\log N_{\rm H2}=14.48^{+0.08}_{-0.07}$ from
Wakker (2006), as it was based on additional data than used by Gillmon et al.
(2006).

Mrk 876. Gillmon et al. (2006) quoted $\log N_{\rm H2}=16.58$ (low-velocity)
and 15.75 (IVC at $-33$ km s-1) both seen in $J=$ 0–3. The fitted Doppler
parameters were $b=7.3$ km s-1 and 5.7 km s-1 respectively. Wakker (2006)
found a much higher column density for the low-velocity component, $\log
N_{\rm H2}=18.07^{+0.22}_{-0.22}$ with FWHM = 7.6 km s-1 ($b=4.6$ km s-1), but
a similar value to Gillmon et al. (2006), $15.47^{+0.39}_{-0.13}$, for the IVC
component. We adopt the Gillmon et al. (2006) values, since the high value in
Wakker (2006) might produce detectable damping wings. (The FUSE data do not
have high S/N.) Such a large molecular fraction ($f_{\rm H2}\approx 0.014$)
would be unlikely at the estimated $E(B-V)\approx 0.0230$ (SF11).

Mrk 1383. We adopted the value $\log N_{\rm H2}=14.78^{+0.20}_{-0.14}$ from
Wakker (2006), as it was based on additional data than used by Gillmon et al.
(2006) and had smaller errors on $N(J)$.

NGC 985. The two FUSE surveys find similar values, $\log N_{\rm
H2}=16.05^{+1.95}_{-0.33}$ (Gillmon et al. 2006) and $\log N_{\rm
H2}=16.07^{+0.77}_{-0.24}$ (Wakker 2006). We list the latter value (smaller
errors).

PG 1116+215. Gillmon et al. (2006) quoted upper limits on low-velocity H2 in
$J=0$ and $J=1$, with $\log N(0)<13.78$ and $\log N(1)<13.93$. Wakker (2006)
quoted an iupper limit $\log N(0)<13.79$ but detected $\log
N(1)=13.82^{+0.20}_{-0.22}$ in the low-velocity component. He also quoted H2
detections in the S1 IVC (-44 km s-1) with $\log N_{\rm
H2}=15.27^{+0.44}_{-0.23}$. However, summing the column densities $N(J)$ for
$J=$ 0–3 in Wakker (2006), we find $\log N_{\rm H2}=16.01^{+0.38}_{-0.27}$,
with errors propagated $\log N(J)$. We quote the latter (IVC) value in Table
1.

Ton S210. The FUSE surveys find different values, $\log N_{\rm
H2}=16.57^{+1.18}_{-1.38}$ (Gillmon et al. 2006) with $b=4.4^{+5.6}_{-2.4}$ km
s-1 and $\log N_{\rm H2}=15.61^{+0.32}_{-0.20}$ (Wakker 2006) with FWHM = 7.3
km s-1 ($b=4.4$ km s-1). We list the latter in Table 1 (additional data
analyzed).

##  Appendix C Sensitivity of $E(B-V)$ Estimates to Dust Modeling

The FIR-inferred values of optical selective extinction $E(B-V)$ are derived
from a chain of computations and correlations with dust optical depth or
integrated emission intensity. Figure 14 of Lenz et al. (2017) is instructive,
showing systematic differences between reddening maps as a function of dust
temperature. The values from Planck Collaboration papers (2011, 2014, 2016,
2020) employ parameterized models of thermal dust emission based on a modified
blackbody (MBB) model with emissivity $\epsilon(\nu)\propto\nu^{\beta}$. The
parameters are based on assumed grain composition (e.g., graphite +
silicates), size distributions, and emission properties (e.g., Draine & Li
2007; Compiègne et al. 2011). Most past studies assumed a single-temperature
dust distribution, with $T_{d}\approx$ 16–23 K and $\beta\approx$ 1.5–2.0.
Meisner & Finkbeiner (2015) explored a two-component model with “hot dust”
($T_{d}\approx 16.2$ K, $\beta=1.67$) and “cold dust” ($T_{d}\approx 9.15$ K,
$\beta=2.70$).

The observed determinations of the $\beta$-index (Table 4) illustrate the
difficulties in dust modeling. An early study (Planck Collaboration XXIV 2011)
used $\beta=1.8$, noting compatibility with the FIRAS spectrum of the diffuse
ISM. Subsequent Planck papers found $\beta\approx 1.6$ for high-latitude sight
lines. Their mean and $1\sigma$ variance were $\beta=1.59\pm 0.12$ (Planck
Collaboration XI 2014) and $\beta=1.63\pm 0.17$ (Planck Collaboration XLVIII
2016). Several of these studies used a “dust radiance” method to estimate the
thermal dust emission in a MBB model, with radiance defined as

${\cal R}=\int
I_{\nu}\,d\nu=\int\tau_{353}\,B_{\nu}(T_{d})\left(\frac{\nu}{353~{}{\rm
GHz}}\right)^{\beta}\,d\nu\propto\tau_{353}\,T_{d}^{4+\beta}\;.$ (C1)

Here $\tau_{353}$ is the dust optical depth at $\nu_{0}=353$ GHz, the
frequency at which the emissivity index is normalized. In the MBB formulation,
with $\tau_{\nu}=I_{\nu}/B_{\nu}$ and $B_{\nu}(T_{d})=(2\nu^{2}T_{d}/c^{2})$
in the Rayleigh-Jeans limit, the dust optical depth $\tau_{353}\propto
T_{d}^{-1}$. Because of the sensitivity of dust emissivity to temperature, it
is useful to understand how the inferred radiance depends on the assumed index
$\beta$. Several papers (see Figure 16 in Planck Collaboration XI 2014) found
an anti-correlation between $\beta_{\rm obs}$ and $T_{\rm obs}$. A possible
explanation is that when dust emits more efficiently it acquires a lower
temperature.

Martin et al. (2012) proposed an approximate relation,
$(\beta/1.8)\approx(T_{d}/17.9~{}{\rm K})^{-2/3}$, based on 100–500 $\mu$m
Galactic-plane data from Paradis et al. (2010). The latter paper fitted to a
general relation, $\beta\propto T_{d}^{-\alpha}$ and $\alpha\approx 4/3$ (with
substantial scatter). We adopt the formulation
$(\beta/\beta_{0})=(T_{d}/T_{0})^{-\alpha}$, where $T_{0}$ and $\beta_{0}$ are
fiducial parameters chosen at the center of the distributions. Combining the
scaling of ${\cal R}\propto\tau_{353}T_{d}^{4+\beta}\propto T_{d}^{3+\beta}$
with the anti-correlation ($T_{d}\propto\beta^{-1/\alpha}$) between dust
emission index and dust temperature, we find that radiance is quite sensitive
to changes in these indices ($\alpha$ and $\beta$),

$\frac{{\cal R}}{{\cal
R}_{0}}=\left(\frac{\beta}{\beta_{0}}\right)^{-(3+\beta)/\alpha}\;.$ (C2)

For the range of emission indices, $\beta=1.6\pm 0.2$, adopted in the 2016
Planck-GN study (and $\alpha=2/3$) the radiance factor changes by a factor of
2.3 about ${\cal R}_{0}$. Over the range of adopted indices (Table 5) the
differences could be even larger.

Table 1: Data on 94 AGN Sight Lines and their “Gas-to-Dust” RatiosaaAGN sight lines surveyed in H I 21-cm emission. The first 55 AGN also have H2 column densities measured with FUSE ultraviolet spectra, with some survey duplications: 38 in Gillmon et al. (2006), 18 in Wakker (2006), 8 in Collins et al. (2003), one (Fairall 9) in Richter et al. (2001b) and one (HE 0226-4110) in both Fox et al. (2005) and Wakker et al. (2006). See Appendix B for more details. The next 39 AGN only have H I measurements. Columns 1–3 provide AGN name and Galactic coordinates. Column 4 gives the FIR-inferred $E(B-V)$ from SF11, as tabulated on the IRAC/IRSA website. Column 5 lists H I column densities ($\log N_{\rm HI}$) for all velocities (Wakker et al. 2003), and column 6 gives H I excluding HVCs and most IVCs. Column 7 gives H2 column densities, and column 8 gives values of $N_{H}=N_{\rm HI}+2N_{\rm H2}$ at all velocities. The last three columns present ratios $N_{H}/E(B-V)$ in units $10^{21}~{}{\rm cm}^{-2}~{}{\rm mag}^{-1}$. Column 9 presents ratios for gas at all velocities and SF11 reddening. Column 10 shows ratios for low-velocity gas (SF11 reddening) except when marked with an asterisk for inclusion of strong IVCs. Column 11 gives the all-velocities ratio, using $E(B-V)$ from Planck-GN. Ratios for 11 sight lines with $E(B-V)$ shown in boldface have uncertain $E(B-V)<0.01$ (SF11).  AGN Name | $\ell$ | $b$ | $E(B-V)$ | $\log N_{\rm HI}$bbColumn 5 lists low-velocity values after subtracting HVCs and most IVCs. Several sight lines pass through strong IVCs (IV Arch, IV18, IV19, IV26, S1) some of which are important contributors to the total H I (see notes in text). With H2 detected in absorption they likely contain dust. The gas-to-dust ratios for these sight lines are computed with NHI that includes the IVCs, marked with asterisks (Column 10). Most high-latitude sight lines exhibit ratios higher than the mean value, $\langle N_{H}/E(B-V)\rangle\approx 6\times 10^{21}$ cm-2 mag-1, measured toward OB stars in the Galactic disk (Bohlin et al. 1978; Shull et al. 2021).  | $\log N_{\rm HI}$bbColumn 5 lists low-velocity values after subtracting HVCs and most IVCs. Several sight lines pass through strong IVCs (IV Arch, IV18, IV19, IV26, S1) some of which are important contributors to the total H I (see notes in text). With H2 detected in absorption they likely contain dust. The gas-to-dust ratios for these sight lines are computed with NHI that includes the IVCs, marked with asterisks (Column 10). Most high-latitude sight lines exhibit ratios higher than the mean value, $\langle N_{H}/E(B-V)\rangle\approx 6\times 10^{21}$ cm-2 mag-1, measured toward OB stars in the Galactic disk (Bohlin et al. 1978; Shull et al. 2021).  | $\log N_{\rm H2}$bbColumn 5 lists low-velocity values after subtracting HVCs and most IVCs. Several sight lines pass through strong IVCs (IV Arch, IV18, IV19, IV26, S1) some of which are important contributors to the total H I (see notes in text). With H2 detected in absorption they likely contain dust. The gas-to-dust ratios for these sight lines are computed with NHI that includes the IVCs, marked with asterisks (Column 10). Most high-latitude sight lines exhibit ratios higher than the mean value, $\langle N_{H}/E(B-V)\rangle\approx 6\times 10^{21}$ cm-2 mag-1, measured toward OB stars in the Galactic disk (Bohlin et al. 1978; Shull et al. 2021).  | $\log N_{\rm H}$bbColumn 5 lists low-velocity values after subtracting HVCs and most IVCs. Several sight lines pass through strong IVCs (IV Arch, IV18, IV19, IV26, S1) some of which are important contributors to the total H I (see notes in text). With H2 detected in absorption they likely contain dust. The gas-to-dust ratios for these sight lines are computed with NHI that includes the IVCs, marked with asterisks (Column 10). Most high-latitude sight lines exhibit ratios higher than the mean value, $\langle N_{H}/E(B-V)\rangle\approx 6\times 10^{21}$ cm-2 mag-1, measured toward OB stars in the Galactic disk (Bohlin et al. 1978; Shull et al. 2021).  | RatioccWe list three values of $N_{H}/E(B-V)$, two with $E(B-V)$ from SF11 (columns 9 and 10) and one using Planck GN (column 11). Columns 9 and 11 include gas at all velocities, while column 10 uses gas at low velocities only. In 17 cases, noted by asterisks, we included strong IVCs with the low velocity gas.  | RatioccWe list three values of $N_{H}/E(B-V)$, two with $E(B-V)$ from SF11 (columns 9 and 10) and one using Planck GN (column 11). Columns 9 and 11 include gas at all velocities, while column 10 uses gas at low velocities only. In 17 cases, noted by asterisks, we included strong IVCs with the low velocity gas.  | GN-RatioccWe list three values of $N_{H}/E(B-V)$, two with $E(B-V)$ from SF11 (columns 9 and 10) and one using Planck GN (column 11). Columns 9 and 11 include gas at all velocities, while column 10 uses gas at low velocities only. In 17 cases, noted by asterisks, we included strong IVCs with the low velocity gas.
---|---|---|---|---|---|---|---|---|---|---
| (deg) | (deg) | (SF11) | (all-v) | (low-v) | (FUSE) | (total) | (all-v) | (low-v) | (all-v)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11)
3C 249.1 | 130.39 | 38.55 | $0.0301\pm 0.0020$ | 20.446 | 20.335 | $18.98^{+0.12}_{-0.14}$ | 20.475 | 9.92 | 7.82 | 7.48
3C 273 | 289.95 | 64.36 | $0.0179\pm 0.0004$ | 20.222 | 20.222 | $15.72^{+0.13}_{-0.09}$ | 20.222 | 9.32 | 9.32 | 8.02
ESO 141-G55 | 338.18 | -26.71 | $0.0944\pm 0.0062$ | 20.788 | 20.704 | $19.32^{+0.07}_{-0.07}$ | 20.817 | 6.95 | 5.80 | 7.05
Fairall 9 | 295.07 | -57.83 | $0.0217\pm 0.0011$ | 20.526 | 20.383 | $16.40^{+0.28}_{-0.53}$ | 20.526 | 15.5 | 11.1 | 15.5
H1821+643 | 94.00 | 27.42 | $0.0370\pm 0.0007$ | 20.584 | 20.570 | $15.99^{+0.16}_{-0.06}$ | 20.584 | 10.4 | 10.0 | 10.0
HE 0226-4110 | 253.94 | -65.77 | $0.0132\pm 0.0005$ | 20.272 | 20.272 | $14.60^{+0.14}_{-0.14}$ | 20.272 | 14.2 | 14.2 | 11.6
HE 1143-1810 | 281.85 | 41.71 | $0.0331\pm 0.0005$ | 20.506 | 20.496 | $16.54^{+1.32}_{-0.68}$ | 20.506 | 9.69 | 9.46 | 9.12
HS 0624+6907 | 145.71 | 23.35 | $0.0845\pm 0.0021$ | 20.898 | 20.798 | $19.82^{+0.09}_{-0.09}$ | 20.964 | 10.9 | 8.97 | 8.66
MRC 2251-178 | 46.20 | -61.33 | $0.0335\pm 0.0011$ | 20.415 | 20.407 | $14.54^{+0.23}_{-0.17}$ | 20.415 | 7.77 | 7.61 | 10.3
Mrk 9 | 158.36 | 28.75 | $0.0503\pm 0.0015$ | 20.677 | 20.639 | $19.36^{+0.09}_{-0.08}$ | 20.717 | 10.4 | 9.57 | 7.88
Mrk 106 | 161.14 | 42.88 | $0.0235\pm 0.0010$ | 20.453 | 20.349 | $16.22^{+0.21}_{-0.15}$ | 20.453 | 12.1 | 9.50 | 9.13
Mrk 116 | 160.53 | 44.84 | $0.0292\pm 0.0028$ | 20.505 | 20.429 | $19.09^{+0.08}_{-0.09}$ | 20.537 | 11.8 | 10.0 | 8.30
Mrk 205 | 125.45 | 41.67 | $0.0344\pm 0.0011$ | 20.508 | 20.405 | $16.53^{+0.13}_{-0.37}$ | 20.508 | 9.37 | 7.38 | 8.54
Mrk 209 | 134.15 | 68.08 | $0.0122\pm 0.0005$ | 20.052 | 20.006 | $<14.48$ | 20.052 | 9.24 | 8.30∗ | 8.35
Mrk 279 | 115.04 | 46.86 | $0.0138\pm 0.0005$ | 20.338 | 19.926 | $14.42^{+0.09}_{-0.09}$ | 20.338 | 15.8 | 6.11 | 14.2
Mrk 290 | 91.49 | 47.95 | $0.0120\pm 0.0008$ | 20.426 | 20.125 | $16.18^{+0.49}_{-0.39}$ | 20.426 | 22.2 | 11.1 | 16.4
Mrk 335 | 108.76 | -41.42 | $0.0305\pm 0.0031$ | 20.567 | 20.428 | $18.83^{+0.08}_{-0.08}$ | 20.583 | 12.5 | 9.23 | 9.56
Mrk 421 | 179.83 | 65.03 | $0.0130\pm 0.0011$ | 20.166 | 19.936 | $14.63^{+0.09}_{-0.10}$ | 20.166 | 11.3 | 6.64 | 11.5
Mrk 478 | 59.24 | 65.03 | $0.0111\pm 0.0009$ | 20.010 | 19.963 | $<14.56$ | 20.010 | 9.22 | 8.28 | 9.74
Mrk 501 | 63.60 | 38.86 | $0.0164\pm 0.0003$ | 20.314 | 20.242 | $15.49^{+0.66}_{-0.24}$ | 20.314 | 12.6 | 10.6 | 11.3
Mrk 509 | 35.97 | -29.86 | $0.0492\pm 0.0005$ | 20.613 | 20.577 | $17.87^{+0.31}_{-0.78}$ | 20.614 | 8.36 | 7.71 | 8.36
Mrk 817 | 100.30 | 53.48 | ${\bf 0.0059\pm 0.0002}$ | 20.085 | 19.950 | $14.48^{+0.08}_{-0.07}$ | 20.085 | 20.6 | 15.1∗ | 10.6
Mrk 876 | 98.27 | 40.38 | $0.0230\pm 0.0009$ | 20.424 | 20.210 | $16.58^{+1.96}_{-0.42}$ | 20.424 | 11.5 | 7.05 | 9.14
Mrk 1095 | 201.69 | -21.13 | $0.1099\pm 0.0017$ | 20.969 | 20.969 | $18.76^{+0.21}_{-0.31}$ | 20.975 | 8.62 | 8.62 | 9.96
Mrk 1383 | 349.22 | 55.12 | $0.0276\pm 0.0009$ | 20.547 | 20.547 | $14.78^{+0.20}_{-0.14}$ | 20.547 | 12.8 | 12.8 | 15.2
Mrk 1513 | 63.67 | -29.07 | $0.0370\pm 0.0017$ | 20.555 | 20.525 | $16.42^{+1.08}_{-0.26}$ | 20.555 | 9.70 | 9.06 | 7.98
MS 0700.7+6338 | 152.47 | 25.63 | $0.0448\pm 0.0014$ | 20.609 | 20.609 | $18.75^{+0.27}_{-0.68}$ | 20.620 | 9.31 | 9.31 | 8.48
NGC 985 | 180.84 | -59.49 | $0.0282\pm 0.0003$ | 20.522 | 20.522 | $16.07^{+0.77}_{-0.33}$ | 20.522 | 11.8 | 11.8 | 13.6
NGC 1068 | 172.10 | -51.93 | $0.0289\pm 0.0004$ | 20.436 | 20.416 | $18.13^{+0.13}_{-0.17}$ | 20.440 | 9.53 | 9.11 | 8.56
NGC 1399 | 236.72 | -53.63 | $0.0109\pm 0.0004$ | 20.196 | 20.196 | $<14.55$ | 20.196 | 14.4 | 14.4 | 10.7
NGC 1705 | 261.08 | -38.74 | ${\bf 0.0070\pm 0.0005}$ | 20.251 | 20.119 | $<14.17$ | 20.251 | 25.5 | 18.8 | 18.7
NGC 3310 | 156.60 | 54.06 | $0.0192\pm 0.0005$ | 20.150 | 19.888 | $19.14^{+0.22}_{-0.42}$ | 20.227 | 8.78 | 8.78∗ | 6.08
NGC 3690 | 141.91 | 55.41 | $0.0144\pm 0.0002$ | 19.994 | 19.758 | $<14.40$ | 19.994 | 6.85 | 6.47∗ | 6.37
NGC 4151 | 155.08 | 75.06 | $0.0237\pm 0.0011$ | 20.322 | 20.284 | $16.70^{+0.93}_{-0.31}$ | 20.322 | 8.86 | 8.86∗ | 11.3
NGC 4214 | 160.24 | 78.07 | $0.0187\pm 0.0003$ | 20.232 | 19.538 | $15.22^{+0.31}_{-0.19}$ | 20.232 | 9.12 | 9.12∗ | 11.2
NGC 4670 | 212.69 | 88.63 | $0.0128\pm 0.0003$ | 20.040 | 19.951 | $14.72^{+0.13}_{-0.16}$ | 20.040 | 8.56 | 6.98 | 9.79
NGC 7469 | 83.10 | -45.47 | $0.0599\pm 0.0015$ | 20.649 | 20.646 | $19.67^{+0.10}_{-0.10}$ | 20.732 | 9.00 | 8.94 | 7.59
NGC 7714 | 88.22 | -55.56 | $0.0451\pm 0.0002$ | 20.674 | 20.636 | $18.94^{+0.05}_{-0.05}$ | 20.690 | 10.9 | 10.0 | 8.20
PG 0804+761 | 138.28 | 31.03 | $0.0302\pm 0.0005$ | 20.588 | 20.545 | $18.66^{+0.14}_{-0.19}$ | 20.598 | 13.1 | 11.9 | 10.4
PG 0844+349 | 188.56 | 39.97 | $0.0314\pm 0.0007$ | 20.475 | 20.475 | $18.22^{+0.18}_{-0.28}$ | 20.480 | 9.62 | 9.62 | 11.3
PG 0953+414 | 179.79 | 51.71 | $0.0102\pm 0.0006$ | 20.087 | 20.004 | $15.03^{+0.11}_{-0.10}$ | 20.087 | 12.0 | 9.90 | 10.1
PG 1116+215 | 223.36 | 68.21 | $0.0193\pm 0.0001$ | 20.075 | 19.705 | $16.01^{+0.44}_{-0.33}$ | 20.075 | 6.16 | 6.16∗ | 14.1
PG 1211+143 | 267.55 | 74.32 | $0.0286\pm 0.0011$ | 20.421 | 20.249 | $18.38^{+0.15}_{-0.14}$ | 20.429 | 9.39 | 9.39∗ | 12.6
PG 1259+593 | 120.56 | 58.05 | ${\bf 0.0070\pm 0.0004}$ | 20.225 | 19.669 | $14.75^{+0.10}_{-0.12}$ | 20.225 | 24.0 | 11.2∗ | 19.5
PG 1302-102 | 308.59 | 52.16 | $0.0376\pm 0.0009$ | 20.502 | 20.368 | $15.62^{+1.41}_{-0.16}$ | 20.502 | 8.44 | 8.41 | 8.69
PG 1351+640 | 111.89 | 52.02 | $0.0177\pm 0.0003$ | 20.441 | 20.286 | $18.34^{+0.20}_{-0.11}$ | 20.448 | 15.9 | 11.2∗ | 18.0
PG 1626+554 | 84.51 | 42.19 | ${\bf 0.0053\pm 0.0005}$ | 20.053 | 19.936 | $15.14^{+0.54}_{-0.20}$ | 20.053 | 21.3 | 16.3 | 8.24
PHL 1811 | 47.46 | -44.81 | $0.0415\pm 0.0031$ | 20.592 | 20.592 | $19.36^{+0.07}_{-0.06}$ | 20.640 | 10.5 | 10.5 | 6.10
PKS 0405-12 | 204.93 | -41.76 | $0.0503\pm 0.0036$ | 20.537 | 20.537 | $15.79^{+0.25}_{-0.12}$ | 20.537 | 6.85 | 6.85 | 8.54
PKS 0558-504 | 257.96 | -28.57 | $0.0388\pm 0.0012$ | 20.675 | 20.526 | $15.44^{+0.18}_{-0.12}$ | 20.675 | 12.2 | 8.66 | 9.92
PKS 2005-489 | 350.37 | -32.60 | $0.0479\pm 0.0007$ | 20.655 | 20.600 | $15.07^{+0.10}_{-0.10}$ | 20.655 | 9.43 | 8.31 | 12.9
PKS 2155-304 | 17.73 | -52.25 | $0.0185\pm 0.0005$ | 20.123 | 20.123 | $14.17^{+0.11}_{-0.14}$ | 20.123 | 7.17 | 7.17 | 12.5
Ton S180 | 139.00 | -85.07 | $0.0123\pm 0.0002$ | 20.097 | 20.083 | $<14.37$ | 20.097 | 10.2 | 9.84 | 13.8
Ton S210 | 224.97 | -83.16 | $0.0144\pm 0.0004$ | 20.205 | 20.193 | $15.61^{+0.32}_{-0.20}$ | 20.205 | 11.1 | 10.8 | 12.8
VII Zw 118 | 151.36 | 25.99 | $0.0330\pm 0.0008$ | 20.558 | 20.558 | $18.84^{+0.10}_{-0.12}$ | 20.574 | 11.4 | 11.4 | 8.58
ESO350-IG38 | 328.06 | -82.85 | ${\bf 0.0096\pm 0.0001}$ | 20.201 | 20.157 | NA | 20.201 | 16.6 | 15.0 | 17.0
ESO572-G34 | 286.12 | 42.12 | $0.0340\pm 0.0004$ | 20.410 | 20.410 | NA | 20.410 | 7.56 | 7.56 | 6.54
HE 0238-1904 | 200.48 | -63.63 | $0.0272\pm 0.0011$ | 20.417 | 20.368 | NA | 20.417 | 9.61 | 8.58 | 8.97
Mrk 487 | 87.84 | 49.03 | $0.0120\pm 0.0003$ | 20.142 | 20.094 | NA | 20.142 | 11.6 | 10.3 | 8.66
NGC 4649 | 295.88 | 74.34 | $0.0226\pm 0.0006$ | 20.297 | 20.297 | NA | 20.297 | 8.77 | 8.77 | 12.2
HE 1228+0131 | 291.26 | 63.66 | $0.0162\pm 0.0014$ | 20.230 | 20.181 | NA | 20.230 | 10.5 | 9.37 | 10.1
HE 1326-0516 | 320.07 | 56.07 | $0.0256\pm 0.0006$ | 20.331 | 20.308 | NA | 20.331 | 8.37 | 7.94 | 7.88
HS 1102+3441 | 188.56 | 66.22 | $0.0197\pm 0.0012$ | 20.189 | 19.814 | NA | 20.189 | 7.85 | 7.85∗ | 9.33
Mrk 36 | 201.36 | 66.49 | $0.0250\pm 0.0012$ | 20.302 | 20.123 | NA | 20.302 | 8.01 | 5.31 | 8.79
Mrk 54 | 110.64 | 84.55 | $0.0129\pm 0.0004$ | 20.110 | 20.110 | NA | 20.110 | 10.0 | 10.0 | 8.96
Mrk 59 | 111.54 | 82.12 | ${\bf 0.0093\pm 0.0004}$ | 20.016 | 19.920 | NA | 20.016 | 11.2 | 11.2∗ | 8.16
Mrk 487 | 82.84 | 49.03 | $0.0120\pm 0.0003$ | 20.142 | 20.094 | NA | 20.094 | 11.6 | 10.3 | 9.33
Mrk 734 | 244.75 | 63.94 | $0.0267\pm 0.0011$ | 20.385 | 20.251 | NA | 20.385 | 9.09 | 9.09∗ | 9.79
Mrk 771 | 269.44 | 81.74 | $0.0233\pm 0.0003$ | 20.377 | 20.159 | NA | 20.377 | 10.2 | 6.19 | 6.12
Mrk 829 | 58.76 | 63.25 | $0.0108\pm 0.0003$ | 19.977 | 19.977 | NA | 19.977 | 8.79 | 8.79 | 7.99
Mrk 926 | 64.09 | -58.76 | $0.0354\pm 0.0007$ | 20.436 | 20.366 | NA | 20.436 | 7.70 | 6.56 | 10.9
Mrk 1502 | 123.75 | -50.18 | $0.0559\pm 0.0018$ | 20.669 | 20.669 | NA | 20.669 | 8.35 | 8.35 | 6.76
NGC 3504 | 204.60 | -66.04 | $0.0228\pm 0.0002$ | 20.294 | 19.628 | NA | 20.294 | 8.63 | 8.63∗ | 10.2
NGC 3991 | 185.68 | 77.20 | $0.0189\pm 0.0002$ | 20.217 | 19.966 | NA | 20.217 | 8.72 | 8.72∗ | 9.73
NGC 5548 | 31.96 | 70.50 | $0.0168\pm 0.0009$ | 20.203 | 20.203 | NA | 20.203 | 9.49 | 9.49 | 9.16
NGC 7496 | 347.84 | -63.80 | ${\bf 0.0084\pm 0.0001}$ | 20.133 | 20.114 | NA | 20.133 | 16.2 | 15.5 | 13.6
PG 0947+396 | 182.85 | 50.75 | $0.0162\pm 0.0006$ | 20.224 | 20.079 | NA | 20.224 | 10.3 | 7.40 | 9.01
PG 1001+291 | 200.09 | 53.20 | $0.0190\pm 0.0005$ | 20.249 | 19.801 | NA | 20.249 | 9.33 | 9.33∗ | 8.83
PG 1004+130 | 225.12 | 49.12 | $0.0331\pm 0.0005$ | 20.569 | 20.569 | NA | 20.569 | 11.2 | 11.2 | 9.21
PG 1048+342 | 190.60 | 63.44 | $0.0199\pm 0.0012$ | 20.202 | 19.958 | NA | 20.202 | 8.00 | 8.00∗ | 7.86
PG 1216+069 | 281.07 | 68.14 | $0.0186\pm 0.0007$ | 20.209 | 20.209 | NA | 20.209 | 8.69 | 8.69 | 8.01
PG 1307+085 | 316.79 | 70.71 | $0.0292\pm 0.0008$ | 20.341 | 20.324 | NA | 20.341 | 7.51 | 7.23 | 7.87
PG 1352+183 | 4.37 | 72.87 | $0.0159\pm 0.0006$ | 20.223 | 20.223 | NA | 20.223 | 10.5 | 10.5 | 10.7
PG 1402+261 | 32.96 | 73.46 | $0.0132\pm 0.0004$ | 20.158 | 20.158 | NA | 20.158 | 10.9 | 10.9 | 9.89
PG 1404+226 | 21.48 | 72.37 | $0.0190\pm 0.0003$ | 20.309 | 20.271 | NA | 20.309 | 10.7 | 9.82 | 9.96
PG 1411+442 | 83.83 | 66.35 | ${\bf 0.0084\pm 0.0012}$ | 19.880 | 19.857 | NA | 19.880 | 9.04 | 8.57 | 6.54
PG 1415+451 | 84.72 | 65.32 | ${\bf 0.0071\pm 0.0003}$ | 19.816 | 19.739 | NA | 19.816 | 9.23 | 7.72 | 6.14
PG 1444+407 | 69.90 | 62.72 | $0.0114\pm 0.0004$ | 20.031 | 19.866 | NA | 20.031 | 9.43 | 6.45 | 6.69
PG 2349-014 | 91.66 | -60.36 | $0.0234\pm 0.0004$ | 20.483 | 20.478 | NA | 20.483 | 13.0 | 12.9 | 9.37
SBS 0335-052 | 191.34 | -44.69 | $0.0402\pm 0.0015$ | 20.556 | 20.556 | NA | 20.556 | 8.94 | 8.94 | 7.40
SBS 1415+437 | 81.96 | 66.20 | ${\bf 0.0077\pm 0.0003}$ | 20.021 | 19.920 | NA | 20.021 | 13.6 | 10.8 | 9.39
Tol 0440-381 | 241.07 | -40.98 | $0.0130\pm 0.0005$ | 20.331 | 20.331 | NA | 20.331 | 16.5 | 16.5 | 13.0
Ton 1187 | 188.33 | 55.38 | ${\bf 0.0093\pm 0.0008}$ | 20.076 | 19.862 | NA | 20.076 | 12.8 | 7.83 | 12.0
vZ 1128 | 42.50 | 78.68 | $0.0117\pm 0.0005$ | 20.037 | 20.037 | NA | 20.037 | 9.30 | 9.30 | 9.36
Table 2: Comparison of H I Column DensitiesaaSample of 36 AGN sight lines surveyed in 21-cm emission at radio telescopes with different beam sizes. Columns 2–4 list H I column densities $\log N_{\rm HI}$ ($N_{\rm HI}$ in cm-2) from LAB, GB, GBT in Wakker et al. (2011). Additional GBT data in column 4 for Mrk 279, PG 1116+215, PG 1259+593, PKS 2155-304 were provided by Jay Lockman. Columns 5 and 6 list values for gas at all velocities (Wakker et al. 2003) and HI4PI survey. Telescope labels are: Leiden-Argentina-Bonn (LAB), Green Bank 140-ft (GB), 100-m Green Bank Telescope (GBT), Leiden-Dwingeloo Survey (LDS), Effelsberg (Eff), Villa Elisa (VE) with beam sizes: LAB ($36^{\prime}$), LDS ($35^{\prime}$), VE ($34^{\prime}$), GB ($21^{\prime}$), HI4PI ($16^{\prime}$), Eff ($9.7^{\prime}$), GBT ($9.1^{\prime}$). Columns 7, 8, and 9 show differences $\Delta\log N_{\rm HI}$ relative to GBT in measurements from GB, Wakker et al. (2003), and HI4PI, respectively. Values differing by more than 0.050 (dex) are highlighted in boldface. The mean differences from GBT are: $+0.017$ (GB), $+0.049$ (Wakker et al. 2003), and $+0.019$ (HI4PI).  AGN Name | $\log N_{\rm HI}$ | $\log N_{\rm HI}$ | $\log N_{\rm HI}$ | $\log N_{\rm HI}$ | $\log N_{\rm HI}$ | $\Delta\log N_{\rm HI}$ | $\Delta\log N_{\rm HI}$ | $\Delta\log N_{\rm HI}$
---|---|---|---|---|---|---|---|---
| (LAB) | (GB) | (GBT) | (Wak03) | (HI4PI) | (3)–(4) | (5)–(4) | (6)–(4)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
3C 249.1 | 20.400 | $20.431\pm 0.013$ | $20.414\pm 0.013$ | 20.446 (GB) | 20.452 | +0.017 | +0.032 | +0.038
3C 273 | 20.169 | $20.184\pm 0.021$ | $20.108\pm 0.032$ | 20.222 (GB) | 20.231 | +0.076 | +0.114 | +0.123
H1821+643 | 20.528 | … | $20.536\pm 0.011$ | 20.584 (Eff) | 20.549 | … | +0.048 | +0.013
HE 0226-4110 | 20.171 | … | … | 20.272 (VE) | 20.165 | … | … | …
HS 0624+6907 | 20.791 | … | $20.781\pm 0.024$ | 20.898 (Eff) | 20.802 | … | +0.117 | +0.021
MRC 2251-178 | 20.374 | $20.415\pm 0.016$ | $20.390\pm 0.014$ | 20.415 (GB) | 20.425 | +0.025 | +0.025 | +0.035
Mrk 205 | 20.436 | … | $20.463\pm 0.012$ | 20.508 (Eff) | 20.468 | … | +0.045 | +0.005
Mrk 279 | 20.128 | $20.216\pm 0.019$ | $20.193\pm 0.020$ | 20.338 (Eff) | 20.104 | +0.023 | +0.145 |  $-$0.089
Mrk 335 | 20.496 | $20.555\pm 0.015$ | $20.477\pm 0.015$ | 20.567 (GB) | 20.517 | +0.078 | +0.090 | +0.040
Mrk 478 | 19.916 | $19.913\pm 0.040$ | $19.927\pm 0.035$ | 20.010 (GB) | 19.956 | -0.014 | +0.083 | +0.029
Mrk 509 | 20.613 | $20.617\pm 0.013$ | $20.583\pm 0.012$ | 20.613 (GB) | 20.594 | +0.034 | +0.030 | +0.011
Mrk 771 | 20.415 | $20.357\pm 0.016$ | $20.327\pm 0.016$ | 20.377 (GB) | 20.355 | +0.030 | +0.050 | +0.028
Mrk 876 | 20.346 | $20.424\pm 0.013$ | $20.395\pm 0.015$ | 20.424 (Eff) | 20.372 | +0.029 | +0.029 |  $-$0.023
Mrk 926 | 20.413 | $20.417\pm 0.015$ | … | 20.436 (GB) | 20.458 | … | … | …
Mrk 1383 | 20.387 | $20.382\pm 0.017$ | $20.370\pm 0.017$ | 20.547 (GB) | 20.412 | +0.012 | +0.177 | +0.042
Mrk 1513 | 20.550 | $20.544\pm 0.013$ | $20.534\pm 0.013$ | 20.555 (GB) | 20.569 | +0.010 | +0.021 | +0.035
NGC 985 | 20.537 | $20.546\pm 0.014$ | $20.534\pm 0.015$ | 20.522 (GB) | 20.546 | +0.012 |  $-$0.012 | +0.012
NGC 5548 | 20.131 | $20.172\pm 0.022$ | $20.164\pm 0.021$ | 20.203 (GB) | 20.190 | +0.008 | +0.039 | +0.026
NGC 7469 | 20.654 | $20.643\pm 0.021$ | $20.637\pm 0.022$ | 20.649 (Eff) | 20.654 | +0.006 | +0.012 | +0.017
PG 0804+761 | 20.497 | $20.525\pm 0.016$ | $20.514\pm 0.017$ | 20.588 (Eff) | 20.524 | +0.011 | +0.074 | +0.010
PG 0953+414 | 19.997 | $20.039\pm 0.028$ | $19.995\pm 0.020$ | 20.087 (Eff) | 20.028 | +0.044 | +0.092 | +0.033
PG 1001+291 | 20.203 | $20.210\pm 0.019$ | $20.195\pm 0.019$ | 20.249 (GB) | 20.244 | +0.015 | +0.054 | +0.049
PG 1116+215 | 20.065 | $20.084\pm 0.035$ | $20.072\pm 0.020$ | 20.075 (Eff) | 20.086 | +0.012 | +0.003 | +0.014
PG 1211+143 | 20.413 | $20.410\pm 0.015$ | $20.413\pm 0.013$ | 20.421 (GB) | 20.425 |  $-$0.003 | +0.008 | +0.012
PG 1216+069 | 20.173 | $20.173\pm 0.026$ | $20.163\pm 0.021$ | 20.209 GB) | 20.182 | +0.010 | +0.046 | +0.019
PG 1259+593 | 19.983 | $20.168\pm 0.037$ | $20.247\pm 0.020$ | 20.225 (Eff) | 20.150 |  $-$0.079 |  $-$0.022 |  $-$0.097
PG 1302-102 | 20.497 | $20.485\pm 0.014$ | $20.455\pm 0.015$ | 20.502 (GB) | 20.494 | +0.030 | +0.047 | +0.039
PG 1351+640 | 20.301 | $20.401\pm 0.021$ | $20.419\pm 0.022$ | 20.441 (Eff) | 20.341 | -0.018 | +0.022 |  $-$0.078
PG 1444+407 | 20.008 | $20.037\pm 0.028$ | $20.022\pm 0.029$ | 20.031 (GB) | 20.036 | +0.015 | +0.009 | +0.014
PHL 1811 | 20.606 | … | $20.599\pm 0.019$ | 20.592 (LDS) | 20.628 | … |  $-$0.007 | +0.029
PKS 0405-12 | 20.508 | $20.531\pm 0.014$ | $20.509\pm 0.013$ | 20.537 (GB) | 20.541 | +0.022 | +0.028 | +0.032
PKS 2005-489 | 20.575 | … | … | 20.655 (VE) | 20.561 | … | … | …
PKS 2155-304 | 20.117 | $20.092\pm 0.026$ | $20.053\pm 0.020$ | 20.123 (Eff) | 20.102 | +0.039 | +0.070 | +0.049
Ton S180 | 20.104 | $20.035\pm 0.055$ | $20.031\pm 0.028$ | 20.097 (GB) | 20.122 | +0.004 | +0.066 | +0.091
Ton S210 | 20.129 | … | … | 20.205 (Eff) | 20.170 | … | … | …
VII Zw 118 | 20.543 | $20.564\pm 0.015$ | $20.539\pm 0.015$ | 20.558 (GB) | 20.576 | +0.025 | +0.019 | +0.037
Table 3: Nine AGN with Significant Molecular FractionsaaNine high-latitude AGN ($|b|\geq 40\arcdeg$) from group 1 with molecular fractions greater than 1%. Galactic latitudes ($b$), $E(B-V)$, and total hydrogen column densities $N_{\rm H}$ are from Table 1. Molecular fractions $f_{\rm H2}\equiv 2N_{\rm H2}/N_{\rm H}$ often exceed 1% when $\log N_{\rm H}>20.38\pm 0.13$, the atomic-to-molecular transition seen toward high-latitude AGN (Gillmon et al. 2006).  AGN Name | $b$ | $E(B-V)$ | $\log N_{\rm H}$ | $f_{\rm H2}$
---|---|---|---|---
|  | (SF11 mag) | ($N_{\rm H}$ cm-2) |
NGC 1068 | $-51.93$ | $0.0289\pm 0.0004$ | 20.440 | 0.0098
PG 1351+640 | $+52.02$ | $0.0177\pm 0.0003$ | 20.448 | 0.0156
PG 1211+143 | $+74.32$ | $0.0286\pm 0.0011$ | 20.429 | 0.0179
Mrk 335 | $-41.42$ | $0.0305\pm 0.0031$ | 20.583 | 0.0353
NGC 7714 | $-55.56$ | $0.0451\pm 0.0002$ | 20.690 | 0.0356
Mrk 116 | $+44.84$ | $0.0292\pm 0.0028$ | 20.537 | 0.0715
PHL 1811 | $-44.81$ | $0.0415\pm 0.0031$ | 20.640 | 0.105
NGC 3310 | $+54.06$ | $0.0192\pm 0.0005$ | 20.227 | 0.164
NGC 7469 | $-45.47$ | $0.0599\pm 0.0015$ | 20.732 | 0.173
Table 4: Dust Emission Model ParametersaaMean values of dust temperature $T_{d}$, with dispersion ($1\sigma$) in parentheses, and emissivity index ($\beta$) measured or assumed in a sample of FIR papers: Schlegel et al. (1998), Schlafly & Finkbeiner (2011), Casandjian et al. (2022), and four papers from the Planck Collaboration (listed in references). Meisner & Finkbeiner (2015) explored a two-temperature model with “hot dust” ($T_{2}\approx 16.2$ K, $\beta_{2}=1.67$) and “cold dust” ($T_{1}\approx 9.15$ K, $\beta_{1}=2.70$).  Paper | Data Set |  $T_{d}$ (K) | Index $\beta$ | Comments
---|---|---|---|---
SFD98 | IRAS/DIRBE | 18.2 | 2.0 | Calibrated on elliptical galaxies
SF11 | Recalibration | 18.2 | 2.0 | Calibrated on SDSS stars
Planck 2011 | Planck-HIFI | 17.9(0.9) | 1.78(0.18) | Anticorrelation $\beta\propto T_{d}^{-2/3}$
Planck 2014 | Planck-HIFI | 20.3(1.3) | 1.59(0.12) | Values at $|b|>15^{\circ}$
Planck 2016 | Planck-HIFI | 19.4(1.5) | 1.63(0.17) | Values at $|b|>20^{\circ}$ (353 GHz)
Planck 2020 | Planck HIFI | 19.6 | 1.55(0.05) | Polarized dust emission
Casandjian 2022 | IRAS/Planck | 20.2 | 1.4 | Excess dust at low $N_{\rm HI}$
Table 5: Far-IR, E(B-V), and Dust TemperaturesaaFIR data (SF11) used to estimate the extinction toward 94 AGN in Table 1. The first 55 quasars have both H I and H2 measurements; the next 39 have only H I. Columns 2 and 3 are the 100 $\mu$m surface brightness and FIR-inferred color excess, tabulated on the IPAC/IRSA website (https://irsa.ipac.caltech.edu/applications/DUST). Column 4 gives the ratio, $I(100~{}\mu$m)/$E(B-V)$, with errors found from the relative errors on $I(100~{}\mu$m) and $E(B-V)$ added in quadrature. Column 5 gives the modeled dust temperature $T_{d}$. Several AGN sight lines have large errors on $I(100~{}\mu$m) and $E(B-V)$ with their ratios uncertain by 10-15%. For PG 1411+442, the uncertainty is 20%.  AGN Name | $I(100~{}\mu$m) | $E(B-V)$ | $I(100)/E(B-V)$ | $T_{\rm d}$
---|---|---|---|---
| (MJy/sr) | (mag) | (MJy/sr/mag) | (K)
3C 249.1 | $1.66\pm 0.11$ | $0.0301\pm 0.0020$ | $55.0\pm 5.2$ | $17.861\pm 0.006$
3C 273 | $1.04\pm 0.03$ | $0.0179\pm 0.0004$ | $58.1\pm 2.1$ | $17.978\pm 0.013$
ESO 141-G55 | $5.09\pm 0.30$ | $0.0944\pm 0.0062$ | $53.9\pm 4.8$ | $17.861\pm 0.006$
Fairall 9 | $1.13\pm 0.06$ | $0.0217\pm 0.0011$ | $52.1\pm 3.7$ | $17.740\pm 0.011$
H1821+643 | $2.14\pm 0.03$ | $0.0370\pm 0.0007$ | $57.8\pm 1.4$ | $17.974\pm 0.019$
HE 0226-4110 | $0.75\pm 0.03$ | $0.0132\pm 0.0005$ | $56.7\pm 3.1$ | $17.939\pm 0.014$
HE 1143-1810 | $1.82\pm 0.03$ | $0.0331\pm 0.0005$ | $55.0\pm 1.2$ | $17.856\pm 0.010$
HS 0624+6907 | $3.53\pm 0.08$ | $0.0845\pm 0.0021$ | $41.8\pm 1.4$ | $17.278\pm 0.017$
MRC 2251-178 | $1.87\pm 0.06$ | $0.0335\pm 0.0011$ | $55.8\pm 2.6$ | $17.893\pm 0.004$
Mrk 9 | $2.40\pm 0.08$ | $0.0503\pm 0.0015$ | $47.7\pm 2.1$ | $17.550\pm 0.010$
Mrk 106 | $1.25\pm 0.05$ | $0.0235\pm 0.0010$ | $53.2\pm 3.1$ | $17.780\pm 0.009$
Mrk 116 | $1.68\pm 0.16$ | $0.0292\pm 0.0028$ | $57.5\pm 7.8$ | $17.966\pm 0.006$
Mrk 205 | $1.82\pm 0.06$ | $0.0344\pm 0.0011$ | $52.9\pm 2.4$ | $17.781\pm 0.009$
Mrk 209 | $0.68\pm 0.03$ | $0.0122\pm 0.0005$ | $55.3\pm 3.3$ | $17.876\pm 0.005$
Mrk 279 | $0.80\pm 0.03$ | $0.0138\pm 0.0005$ | $57.9\pm 3.0$ | $17.969\pm 0.005$
Mrk 290 | $0.66\pm 0.05$ | $0.0120\pm 0.0008$ | $55.0\pm 5.6$ | $17.871\pm 0.004$
Mrk 335 | $1.58\pm 0.16$ | $0.0305\pm 0.0031$ | $51.8\pm 7.4$ | $17.734\pm 0.013$
Mrk 421 | $0.73\pm 0.06$ | $0.0130\pm 0.0011$ | $56.0\pm 6.6$ | $17.893\pm 0.003$
Mrk 478 | $0.64\pm 0.06$ | $0.0111\pm 0.0009$ | $57.3\pm 7.1$ | $17.945\pm 0.005$
Mrk 501 | $0.87\pm 0.02$ | $0.0164\pm 0.0003$ | $53.0\pm 1.6$ | $17.782\pm 0.015$
Mrk 509 | $2.76\pm 0.03$ | $0.0492\pm 0.0005$ | $56.0\pm 0.8$ | $17.905\pm 0.005$
Mrk 817 | $0.34\pm 0.01$ | $0.0059\pm 0.0002$ | $57.2\pm 2.6$ | $17.948\pm 0.003$
Mrk 876 | $1.38\pm 0.06$ | $0.0230\pm 0.0009$ | $59.8\pm 2.3$ | $18.049\pm 0.006$
Mrk 1095 | $5.61\pm 0.11$ | $0.1099\pm 0.0017$ | $51.1\pm 1.3$ | $17.700\pm 0.005$
Mrk 1383 | $1.78\pm 0.06$ | $0.0276\pm 0.0009$ | $64.5\pm 3.0$ | $18.216\pm 0.009$
Mrk 1513 | $2.07\pm 0.09$ | $0.0370\pm 0.0017$ | $55.9\pm 3.8$ | $17.900\pm 0.013$
MS 0700.7+6338 | $1.87\pm 0.04$ | $0.0448\pm 0.0014$ | $41.8\pm 1.6$ | $17.273\pm 0.020$
NGC 985 | $1.60\pm 0.02$ | $0.0282\pm 0.0003$ | $56.7\pm 0.9$ | $17.931\pm 0.019$
NGC 1068 | $2.28\pm 0.02$ | $0.0289\pm 0.0004$ | $78.7\pm 1.3$ | $18.709\pm 0.017$
NGC 1399 | $0.60\pm 0.02$ | $0.0109\pm 0.0004$ | $54.8\pm 2.7$ | $17.541\pm 0.004$
NGC 1705 | $0.40\pm 0.03$ | $0.0070\pm 0.0005$ | $57.8\pm 6.0$ | $17.980\pm 0.002$
NGC 3310 | $1.12\pm 0.03$ | $0.0192\pm 0.0005$ | $58.3\pm 2.2$ | $17.992\pm 0.010$
NGC 3690 | $0.83\pm 0.02$ | $0.0144\pm 0.0002$ | $57.7\pm 1.6$ | $17.966\pm 0.010$
NGC 4151 | $1.45\pm 0.07$ | $0.0237\pm 0.0011$ | $61.3\pm 4.1$ | $18.103\pm 0.010$
NGC 4214 | $1.17\pm 0.02$ | $0.0187\pm 0.0003$ | $62.8\pm 1.5$ | $18.154\pm 0.014$
NGC 4670 | $0.75\pm 0.02$ | $0.0128\pm 0.0003$ | $58.6\pm 2.1$ | $18.013\pm 0.006$
NGC 7469 | $2.92\pm 0.07$ | $0.0599\pm 0.0015$ | $48.7\pm 1.7$ | $17.598\pm 0.024$
NGC 7714 | $2.19\pm 0.01$ | $0.0451\pm 0.0002$ | $48.5\pm 0.3$ | $17.588\pm 0.005$
PG 0804+761 | $1.61\pm 0.03$ | $0.0302\pm 0.0005$ | $53.3\pm 1.3$ | $17.793\pm 0.004$
PG 0844+349 | $1.72\pm 0.05$ | $0.0314\pm 0.0007$ | $54.6\pm 2.0$ | $17.848\pm 0.019$
PG 0953+414 | $0.57\pm 0.03$ | $0.0102\pm 0.0006$ | $55.7\pm 4.4$ | $17.898\pm 0.001$
PG 1116+215 | $1.13\pm 0.01$ | $0.0193\pm 0.0001$ | $58.5\pm 0.6$ | $18.001\pm 0.003$
PG 1211+143 | $1.76\pm 0.06$ | $0.0286\pm 0.0011$ | $61.6\pm 3.2$ | $18.118\pm 0.022$
PG 1259+593 | $0.41\pm 0.02$ | $0.0070\pm 0.0004$ | $58.6\pm 4.4$ | $17.995\pm 0.003$
PG 1302-102 | $2.38\pm 0.06$ | $0.0376\pm 0.0009$ | $63.2\pm 2.2$ | $18.172\pm 0.003$
PG 1351+640 | $1.15\pm 0.03$ | $0.0177\pm 0.0003$ | $65.0\pm 2.0$ | $18.237\pm 0.016$
PG 1626+554 | $0.29\pm 0.03$ | $0.0053\pm 0.0005$ | $55.3\pm 7.7$ | $17.877\pm 0.012$
PHL 1811 | $2.15\pm 0.15$ | $0.0415\pm 0.0031$ | $51.8\pm 5.3$ | $17.733\pm 0.012$
PKS 0405-12 | $2.74\pm 0.20$ | $0.0503\pm 0.0036$ | $54.6\pm 5.6$ | $17.845\pm 0.008$
PKS 0558-504 | $2.37\pm 0.07$ | $0.0388\pm 0.0012$ | $61.2\pm 2.6$ | $18.105\pm 0.007$
PKS 2005-489 | $2.94\pm 0.03$ | $0.0479\pm 0.0007$ | $61.4\pm 1.1$ | $18.108\pm 0.012$
PKS 2155-304 | $1.10\pm 0.03$ | $0.0185\pm 0.0005$ | $59.3\pm 2.3$ | $18.036\pm 0.010$
Ton S180 | $0.72\pm 0.02$ | $0.0123\pm 0.0002$ | $58.1\pm 1.9$ | $17.982\pm 0.002$
Ton S210 | $0.84\pm 0.03$ | $0.0144\pm 0.0004$ | $58.2\pm 2.6$ | $17.987\pm 0.003$
VII Zw 118 | $1.62\pm 0.04$ | $0.0330\pm 0.0008$ | $49.2\pm 1.7$ | $17.624\pm 0.008$
ESO350-IG38 | $0.55\pm 0.01$ | $0.0096\pm 0.0001$ | $57.8\pm 1.0$ | $17.969\pm 0.001$
ESO572-G34 | $1.87\pm 0.03$ | $0.0340\pm 0.0004$ | $54.9\pm 1.0$ | $17.862\pm 0.009$
HE 0238-1904 | $1.54\pm 0.06$ | $0.0272\pm 0.0011$ | $56.5\pm 3.2$ | $17.922\pm 0.063$
Mrk 487 | $0.67\pm 0.02$ | $0.0120\pm 0.0003$ | $55.8\pm 2.1$ | $17.894\pm 0.006$
NGC 4649 | $1.38\pm 0.04$ | $0.0226\pm 0.0006$ | $61.0\pm 2.4$ | $18.094\pm 0.012$
HE 1228+0131 | $0.95\pm 0.08$ | $0.0162\pm 0.0014$ | $54.5\pm 6.6$ | $18.017\pm 0.010$
HE 1326-0516 | $1.64\pm 0.04$ | $0.0256\pm 0.0006$ | $64.1\pm 2.2$ | $18.213\pm 0.006$
HS 1102+3441 | $1.11\pm 0.07$ | $0.0197\pm 0.0012$ | $56.5\pm 4.8$ | $17.925\pm 0.004$
Mrk 36 | $1.48\pm 0.07$ | $0.0250\pm 0.0012$ | $59.1\pm 4.0$ | $18.028\pm 0.002$
Mrk 54 | $0.73\pm 0.02$ | $0.0129\pm 0.0004$ | $56.7\pm 2.3$ | $17.928\pm 0.025$
Mrk 59 | $0.53\pm 0.02$ | $0.0093\pm 0.0004$ | $57.3\pm 3.5$ | $17.950\pm 0.005$
Mrk 487 | $0.67\pm 0.02$ | $0.0120\pm 0.0003$ | $55.8\pm 2.1$ | $17.894\pm 0.006$
Mrk 734 | $1.49\pm 0.06$ | $0.0267\pm 0.0011$ | $55.8\pm 3.2$ | $17.892\pm 0.004$
Mrk 771 | $1.24\pm 0.02$ | $0.0233\pm 0.0003$ | $53.3\pm 1.0$ | $17.794\pm 0.007$
Mrk 829 | $0.61\pm 0.01$ | $0.0108\pm 0.0003$ | $56.2\pm 2.0$ | $17.917\pm 0.004$
Mrk 926 | $2.07\pm 0.04$ | $0.0354\pm 0.0007$ | $58.5\pm 1.6$ | $17.997\pm 0.006$
Mrk 1502 | $2.55\pm 0.08$ | $0.0559\pm 0.0018$ | $45.6\pm 2.0$ | $17.455\pm 0.003$
NGC 3504 | $1.32\pm 0.01$ | $0.0228\pm 0.0002$ | $58.1\pm 0.7$ | $17.991\pm 0.008$
NGC 3991 | $1.06\pm 0.01$ | $0.0189\pm 0.0002$ | $56.1\pm 0.9$ | $17.901\pm 0.004$
NGC 5548 | $0.92\pm 0.05$ | $0.0168\pm 0.0009$ | $54.5\pm 4.1$ | $17.838\pm 0.005$
NGC 7496 | $0.47\pm 0.01$ | $0.0084\pm 0.0001$ | $55.9\pm 1.0$ | $17.887\pm 0.003$
PG 0947+396 | $0.92\pm 0.04$ | $0.0162\pm 0.0006$ | $56.9\pm 3.1$ | $17.943\pm 0.002$
PG 1001+291 | $1.08\pm 0.03$ | $0.0190\pm 0.0005$ | $57.1\pm 2.0$ | $17.924\pm 0.002$
PG 1004+130 | $1.87\pm 0.02$ | $0.0331\pm 0.0005$ | $56.6\pm 1.1$ | $17.928\pm 0.003$
PG 1048+342 | $1.13\pm 0.07$ | $0.0199\pm 0.0012$ | $56.8\pm 5.0$ | $17.933\pm 0.002$
PG 1216+069 | $1.01\pm 0.04$ | $0.0186\pm 0.0007$ | $54.4\pm 2.9$ | $17.845\pm 0.005$
PG 1307+085 | $1.58\pm 0.05$ | $0.0292\pm 0.0008$ | $54.0\pm 2.2$ | $17.823\pm 0.005$
PG 1352+183 | $0.90\pm 0.04$ | $0.0159\pm 0.0006$ | $56.7\pm 3.1$ | $17.931\pm 0.011$
PG 1402+261 | $0.74\pm 0.02$ | $0.0132\pm 0.0004$ | $56.1\pm 2.4$ | $17.907\pm 0.008$
PG 1404+226 | $1.12\pm 0.02$ | $0.0190\pm 0.0003$ | $58.7\pm 1.3$ | $18.007\pm 0.002$
PG 1411+442 | $0.48\pm 0.07$ | $0.0084\pm 0.0012$ | $56.5\pm 11.7$ | $17.927\pm 0.014$
PG 1415+451 | $0.40\pm 0.02$ | $0.0071\pm 0.0003$ | $56.9\pm 3.4$ | $17.928\pm 0.009$
PG 1444+407 | $0.63\pm 0.02$ | $0.0114\pm 0.0004$ | $55.0\pm 2.8$ | $17.855\pm 0.005$
PG 2349-014 | $1.33\pm 0.02$ | $0.0234\pm 0.0004$ | $56.9\pm 1.3$ | $17.921\pm 0.009$
SBS 0335-052 | $2.05\pm 0.07$ | $0.0402\pm 0.0015$ | $51.0\pm 2.7$ | $17.698\pm 0.012$
SBS 1415+437 | $0.45\pm 0.02$ | $0.0077\pm 0.0003$ | $58.6\pm 3.4$ | $18.007\pm 0.003$
Tol 0440-381 | $0.67\pm 0.03$ | $0.0130\pm 0.0005$ | $51.2\pm 2.9$ | $17.711\pm 0.012$
Ton 1187 | $0.52\pm 0.04$ | $0.0093\pm 0.0008$ | $56.0\pm 6.7$ | $17.894\pm 0.002$
vZ 1128 | $0.66\pm 0.03$ | $0.0117\pm 0.0005$ | $56.1\pm 3.3$ | $17.909\pm 0.002$
Table 6: Statistics of QSO Sub-samplesaaMean values of $E(B-V)$ and gas-to-dust ratios $\langle N_{\rm H}/E(B-V)\rangle$ in units $10^{21}~{}{\rm cm}^{-2}~{}{\rm mag}^{-1}$ for various sub-samples of the 94 quasars. The mean ratios are shown for gas at all velocities (columns 4 and 6) and low velocity only ($|V_{\rm LSR}|\leq 90$ km s-1) in column 5. Errors on the mean are evaluated as $\sigma/N^{1/2}$, where $\sigma$ is the variance in sample of $N$ targets. Ratios in columns 4 and 5 adopt $E(B-V)$ from SF11, while those in column 6 adopt Planck-GN. The primary group includes 55 QSOs with both H I and H2 measurements. In the secondary group of 39 QSOs with only H I, the mean ratios are 12% lower, reflecting the missing contribution from H2. In each group, the modified samples exclude sight lines with low (and uncertain) $E(B-V)<0.01$ from SF11. Nine quasars behind HVC Complex C (Table 7) are among the 55 targets with both H I and H2. Their elevated ratios exhibit large variations in FIR estimates of $E(B-V)$ from SF11 and Planck-GN. Sample | $N_{\rm QSO}$ | $\langle E(B-V)\rangle$ | $\langle N_{\rm H}/E(B-V)\rangle$ | $\langle N_{\rm H}/E(B-V)\rangle$ | $\langle N_{\rm H}/E(B-V)\rangle$
---|---|---|---|---|---
|  | (SF11) | (all vel/SF11) | (low vel/SF11) | (all vel/Pl-GN)
(1) | (2) | (3) | (4) | (5) | (6)
Primary (H I, H2) | 55 | 0.0295 | $11.53\pm 0.57$ | $9.66\pm 0.34$ | $10.59\pm 0.42$
Modified | 51 | 0.0313 | $10.64\pm 0.41$ | $9.22\pm 0.27$ | $10.30\pm 0.38$
Complex C | 9 | 0.0151 | $17.0\pm 5.2$ | $10.7\pm 3.5$ | $12.9\pm 4.3$
Low-E(B-V) | 4 | 0.0063 | 22.9 | 15.4 | 14.3
Secondary (H I) | 39 | 0.0192 | $10.20\pm 0.38$ | $9.37\pm 0.38$ | $9.27\pm 0.35$
Modified | 32 | 0.0219 | $9.66\pm 0.34$ | $9.03\pm 0.37$ | $9.02\pm 0.27$
Low-E(B-V) | 7 | 0.0084 | 12.7 | 10.9 | 10.4
Table 7: RatiosaaReddening values $E(B-V)$ and gas-to-dust ratios $N_{\rm H}/E(B-V)$ (in $10^{21}~{}{\rm cm}^{-2}~{}{\rm mag}^{-1}$) for gas at all velocities and low velocity only toward nine sight lines to quasars behind HVC Complex C (Figure 2). Columns 2 and 3 list $E(B-V)$ from SF11 and Planck-GN (Planck Collaboration XLVIII 2016), with their ratio in column (4). Columns 5 and 6 list gas-to-dust ratios $N_{\rm H}/E(B-V)$ based on SF11 reddening and gas at different velocities. Columns 7 and 8 list the ratios based on Planck-GN reddening. Mean values are listed at the bottom, spanning a range outside the errors. Mean values of $E(B-V)$ from Planck-GN are 22% higher than SF11, with most $E(B-V)$ ratios higher than SF11 values. Two sight lines have GN reddening 1.9–2.6 times larger than SF11, and only one of nine has a ratio less than 1.0. The mean low-velocity ($|V_{\rm LSR}|<90$ km s-1) gas-to-dust ratio is $\sim 60$% of that for gas at all velocities. in High-Velocity Cloud Complex-C  QSO | $E(B-V)$ | $E(B-V)$ |  $E$-Ratio | Ratio-all | Ratio-low | Ratio-all | Ratio-low
---|---|---|---|---|---|---|---
| (SF11) | (Pl-GN) | (GN/SF11) | (SF11) | (SF11) | (Pl-GN) | (Pl-GN)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8)
Mrk 205 | $0.0344\pm 0.0011$ | $0.0377\pm 0.0053$ | 1.10 | 9.37 | 7.38 | 8.54 | 6.73
Mrk 279 | $0.0138\pm 0.0005$ | $0.0154\pm 0.0002$ | 1.12 | 15.8 | 6.11 | 14.2 | 5.49
Mrk 290 | $0.0120\pm 0.0008$ | $0.0162\pm 0.0003$ | 1.35 | 22.2 | 11.1 | 16.4 | 8.21
Mrk 501 | $0.0164\pm 0.0003$ | $0.0183\pm 0.0004$ | 1.11 | 12.6 | 10.6 | 11.3 | 9.54
Mrk 817 | $0.0059\pm 0.0002$ | $0.0115\pm 0.0001$ | 1.95 | 20.6 | 15.1 | 10.6 | 7.75
Mrk 876 | $0.0230\pm 0.0009$ | $0.0291\pm 0.0006$ | 1.26 | 11.5 | 7.05 | 9.14 | 5.57
PG 1259+593 | $0.0070\pm 0.0004$ | $0.0086\pm 0.0001$ | 1.23 | 24.0 | 11.2 | 19.5 | 5.43
PG 1351+640 | $0.0177\pm 0.0003$ | $0.0156\pm 0.0001$ | 0.88 | 15.9 | 11.2 | 18.0 | 12.7
PG 1626+554 | $0.0053\pm 0.0005$ | $0.0137\pm 0.0002$ | 2.59 | 21.3 | 16.3 | 8.24 | 6.28
Mean values | 0.0151 | 0.0185 |  | 17.0 | 10.7 | 12.9 | 7.5

Figure 1: Polar projection maps of the ratio $N_{\rm H}/E(B-V)$ between
$N_{\rm HI}$ from HI4PI for gas with $|V_{\rm LSR}|\leq 90$ km s-1 and
$E(B-V)$ from SF11 (top) and Planck-GN (bottom). Both reddening maps are
smoothed to the HI4PI resolution of $16^{\prime}$. Northern Galactic
hemisphere is on the left, southern hemisphere on the right. Galactic
longitude $\ell=0\arcdeg$ is at the bottom and $\ell=180\arcdeg$ at the top of
each map. Longitude increases clockwise for northern hemisphere and
counterclockwise for southern hemisphere, meeting at $\ell=270\arcdeg$. Color
scale at bottom shows gas-to-dust ratio in units $10^{21}~{}{\rm
cm}^{-2}~{}{\rm mag}^{-1}$. The linear scale covers the $1^{\rm st}$ and
$99^{\rm th}$ percentiles of the distribution of ratios of the top panel.
White circles mark locations of 94 AGN.  Figure 2: Contours of H I column
density in Complex C from the Leiden-Dwingeloo Survey (Hartmann & Burton 1997)
plotted on a $0.5\deg$ grid ($35^{\prime}$ beam) with H I contours at 1, 3,
and $6\times 10^{19}~{}{\rm cm}^{-2}$. Locations of 8 of the 9 quasars in our
study (Table 5) are labeled; Mrk 205 ($\ell=125.45^{\circ}$,
$b=41.67^{\circ}$) lies just off the left side of the plot. Complex C extends
over $\sim 2000$ deg2 in the Northern Galactic sky, with metallicity along
these sight lines ranging from 0.1–0.3 solar (Collins et al. 2003, 2007).
Figure 3: Differences in $N_{\rm HI}$ (at all velocities, in units of
$10^{20}~{}{\rm cm}^{-2}$) between HI4PI values (HI4PI Collaboration et al.
2016) and those from Wakker et al. (2003) from our Table 1. These are plotted
versus $N_{\rm HI}$ (in units of $10^{21}~{}{\rm cm}^{-2}$) from Table 1. Red
points indicate nine sight lines passing through Complex C, an HVC with low
dust content where H I makes a significant contribution to total $N_{\rm HI}$.
We have annotated several sight lines in which $N_{\rm HI}$ from HI4PI is
considerably lower than that in Wakker et al. (2003). NGC 4214 is not shown,
because its internal H I (at $+295$ km s-1) is included in the HI4PI velocity
range.  Figure 4: Distribution of ratios of $E(B-V)$ from Planck-GN and SF11.
Values are from our full sample (94 AGN), with nine QSOs behind HVC Complex C
plotted in red. These include two outliers (PG 1626+554 and Mrk 817) with
anomalously high GN/SF11 ratios and very low $E(B-V)$. On average, the Planck-
GN values are 12% higher than SF11, with considerable dispersion about the
unweighted mean (red line), particularly in sight lines with $E(B-V)\lesssim
0.04$. The plotted errors are likely under-estimated owing to systematic
effects in FIR modeling.  Figure 5: Gas-to-dust ratios (in $10^{21}~{}{\rm
cm}^{-2}~{}{\rm mag}^{-1}$) of total hydrogen column density ($N_{\rm H}$ in
Table 1) for 55 AGN in our primary sample with both H I and H2. The FIR-
inferred $E(B-V)$ are plotted for both Planck-GN (blue circles) and SF11
(orange circles). Horizontal lines show the mean ratios of the two
distributions: 8.6 (blue solid line, Planck-GN), 9.3 (orange solid line,
SF11). Black dotted line shows the mean ratio 8.8 from Lenz et al. (2017).
Figure 6:  Polar projection maps showing the difference between $E(B-V)$ from
Planck-GN and values from SF11. These variations track changes in the gas-to-
dust ratio seen in the two ratio maps of Figure 1. For example, the red
feature towards ($\ell,b)=(260-330\arcdeg,80-84\arcdeg)$ is Markkanen’s Cloud
(Markkanen 1979) with a discrepant dust emissivity spectral index $\beta$, as
noted in Planck Collaboration XI (2014). Many IVCs also appear in these
difference plots (see Section 3.3).  Figure 7: Comparison of distributions of
gas-to-dust ratios over the high-latitude sky for three choices of reddening
map (SFD98, SF11, Planck-GN). Here $N_{\rm HI}$ comes from HI4PI survey for
gas at $|V_{\rm LSR}|\leq 90$ km s-1. Reddening maps are smoothed to the HI4PI
resolution ($16^{\prime}$). In the label box, SFD–S11 refers to the standard
0.86 recalibration, and SFD–0.884 refers to recalibration with the Johnson
bandpasses, consistent with Planck-GN analysis. Each histogram is normalized
to unit area. Vertical lines show mean ratios determined in previous papers:
5.8 (Bohlin et al. 1978) and 6.07 (Shull et al. 2021) toward stars in the
Galactic disk, and 8.8 and 8.2 quoted in Lenz et al. (2017) at high-latitude.
Grey wash shows the ($1\sigma$) variance in the Shull et al. (2021) survey of
129 stars within 5 kpc.  Figure 8: Summary of mean gas-to-dust ratios from our
primary sample (Group 1 of 55 AGN with both H I and H2 measurements) and
secondary sample (Group 2 of 39 AGN with only H I). Ratios are shown for two
reddening maps (SF11 and Planck-GN), including a distinction between gas at
low velocity and all velocities (including HVCs and IVCs). Modified samples
exclude sight lines with $E(B-V)<0.01$ (see Table 1). Nine sight lines through
HVC Complex C with elevated ratios (low dust content) are also included in the
primary sample (Group 1). The horizontal dotted line shows the mean high-
latitude ratio of 8.8 found by Lenz et al. (2017).