Variations of Interstellar Gas-to-dust Ratios at High Galactic Latitudes

Interstellar dust at high Galactic latitudes can influence astronomical foreground subtraction, produce diffuse scattered light, and soften the UV spectra of quasars. In a sample of 94 sight lines toward quasars at high latitude and low extinction, we evaluate the interstellar “gas-to-dust ratio” N H/E(B − V), using hydrogen column densities (H i and H2) and far-IR (FIR) estimates of dust reddening. In the Galactic plane, this ratio is 6.0 ± 0.2 (in units of 1021 cm−2 mag−1). On average, recent Planck estimates of E(B − V) in low-reddening sight lines are 12% higher than those from Schlafly & Finkbeiner, and N H I exhibits significant variations when measured at different radio telescopes. In a sample of 51 quasars with measurements of both H i and H2 and 0.01 ≤ E(B − V) ≲ 0.1, we find mean ratios 10.3 ± 0.4 (gas at all velocities) and 9.2 ± 0.3 (low-velocity only) using Planck E(B − V) data. High-latitude H2 fractions are generally small (2%–3% on average), although nine of 39 sight lines at ∣b∣ ≥ 40° have f H2 of 1%–17%. Because FIR-inferred E(B − V) is sensitive to modeled dust temperature T d and emissivity index β, 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 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.


Introduction
This paper examines measures of the interstellar "gas-to-dust ratio", N H /E(B − V ), found from the total column density of atomic and molecular hydrogen, N H = N HI + 2N 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 (Lyα and H 2 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 × 10 21 cm −2 mag −1 , hereafter quoted in standard units of 10 21 cm −2 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 ± 1.01 (1σ 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(Sota et al. , 2014)).For a subset of 21 stars at E(B − V ) ≤ 0.25 mag, the mean ratio was N H /E(B − V ) = 5.83.A FUSE survey of 38 translucent sight lines with A V ≈ 0.5-4.7 mag (Rachford et al. 2009) found a mean ratio of 5.94, and several large compilations of UV measurements found 6.12 (Gudennavar et al. 2012) and 6.2 (Liszt & Gerin 2023).We conclude that the interstellar medium (ISM) in the Galactic disk has a consistent mean gas-to-dust ratio of ∼ 6 × 10 21 cm −2 mag −1 to an accuracy of 3-4% and with 17% dispersion.
However, recent estimates of the gas-to-dust ratio at high Galactic latitudes find 35-45% higher values, using N 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 might be expected, as dust settles gravitationally to the disk or is blown into the low halo, where it can be sputtered by hot gas.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 andSchlafly &Finkbeiner 2011) hereafter denoted SFD98 and SF11 and available on the IPAC/IRSA reddening website 1 .In sight lines at latitudes |b| > 20 • and low reddening, 0.015 < E(B − V ) < 0.075, Liszt (2014a,b) found a mean ratio N HI /E(B − V ) = 8.3, with H I from the Leiden-Argentina-Bonn (LAB) survey (Kalberla et al. 1995) at 36 ′ resolution and E(B−V ) from SFD98.Lenz et al. (2017) found a mean ratio of 8.8, using H I from the HI4PI survey (HI4PI Collaboration et al. 2016) at 16 ′ resolution and E(B − V ) from SF11.They only considered atomic gas with N HI < 4 × 10 20 cm −2 and local standard of rest velocities |V LSR | < 90 km s −1 .Lenz et al. (2017) noted that the values obtained with the SFD98 maps are somewhat higher than the 8.3 value obtained by Liszt (2014b), who did not use the 12% SF11 correction to the SFD98 calibration.Liszt & Gerin (2023) quoted a mean high-latitude ratio of 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 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 H 2 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 H 2 data.Errors in measurements of N HI can result from telescope beam sizes, stray radiation 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 HI in surveys with radio telescopes whose beam sizes range from 36 ′ to 9 ′ , 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 • .Indeed, 78 lie at |b| ≥ 40 • .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 HI , N H2 , selective extinction E(B − V ), and their uncertainties.We examine the measurements used to construct N 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 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 gasto-dust ratios at |b| > 30 • .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 H and E(B − V ), which are almost certainly much larger than the small values (≤ 5%) commonly listed in observational tables.

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 H 2 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 H 2 in the Galactic disk, the highlatitude measurements of the dust-to-gas ratio (Liszt 2014a,b;Lenz et al. 2017) used 21-cm emission for N 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 ) ≲ 0.04 mag.Toward high-latitude quasars, reddening uncertainties often dominate the propagated errors in the ratio N H /E(B − V ).However, we also found cases in which measurements of N HI differ by 10-30% among different telescopes with a range of beam sizes.
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 SF11 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 Survey 2 .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 ′ .We query this map using the IPAC/IRSA website, which provides 1σ variances averaged over neighboring 5 ′ pixels around each line of sight.We also downloaded the original SFD98 map projected into a HEALPix grid of N side = 2048 and applied the re-calibration correction factor3 .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 ) ≤ 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 ) ≤ 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).
2 The 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 NHI/E(B − V ) = 8.2, using pixels in a revised reddening map (Schlafly et al. 2014) based on Pan-STARRS1 optical photometry of 500 million stars.

Atomic Hydrogen (N 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, H 2 , 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 ′ (HI4PI Collaboration et al. 2016).We use two related data products: (a) the N HI map computed by integrating the H I spectra over the entire velocity range of |V LSR | < 600 km s −1 ; and (b) the N HI map obtained by Lenz et al. (2017) who integrated over low-velocity gas, |V LSR | < 90 km s −1 excluding HVC emission, and masked out regions with N HI > 4 × 10 20 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 side = 1024.Liszt (2014a,b) used H I column densities from the LAB survey (36 ′ beam), and Lenz et al. (2017) used the HI4PI survey (16.1 ′ ).For the H I column densities and 21-cm spectra presented by Wakker et al. (2003) the beams range from 35 ′ in the Leiden-Dwingeloo Survey (Hartmann & Burton 1997) to 16.1 ′ 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 µm) and Planck (5 ′ at 350-857 µm).With its 9.1 ′ beam and avoidance of stray radiation 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 HI from data taken in the LAB survey, owing to a "spurious broad component" with N HI ≈ 5 × 10 19 cm −2 .
In Table 2 we compare N HI measured by radio telescopes with various beam sizes toward 36 AGN in common with those tabulated by Wakker et al. (2011).The column densities in Table 1 (from Wakker et al. 2003) are higher on average by +0.059 (dex) in log N HI relative to those from GBT. Columns from the GB 140-ft are higher by +0.017 (dex), and those from the HI4PI survey are higher by +0.023 (dex).Quoted measurement errors in log N HI are typically ± 0.01-0.03.We consider differences ∆ log N HI ≥ 0.050 to be discrepant and highlight them in boldface.Figure 3 shows the differences in N HI between HI4PI and Wakker et al. (2003).Although the average offset differences are comparable to the quoted errors on log N 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 HI could arise from calibration, stray-radiation contamination, or smallscale 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.

Molecular Hydrogen (N H2 )
Of the 94 quasars in our survey, 55 quasars (group 1) have both H I and H 2 column densities.The H 2 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), andFox et al. (2005).Notes on overlapping H 2 data from these surveys and corrections for specific sight lines are provided in Appendix B. In most of the 55 sight lines, the H 2 column densities are much smaller than those of H I. In 30 of the 39 AGN sight lines at latitudes |b| ≥ 40 • , the molecular fraction f H2 ≡ 2N H2 /N H ranges between 3 × 10 −6 and 5 × 10 −4 , often making H 2 a negligible contributor to the total N H in sight lines with column densities below the atomic-to-molecular transition at log N H ≈ 20.38 ± 0.13 seen at high latitude (Gillmon et al. 2006).However, nine sight lines at |b| ≥ 40 • have f H2 > 0.01 (range 1-17%) and are listed in Table 3, together with log N H and E(B − V ).These 9 sight lines have E(B − V ) = 0.02-0.06(SF11 scale), which is below the observed H I-to-H 2 transition at E(B − V ) ≈ 0.08-0.10seen in low-latitude surveys (Bohlin et al. 1978;Shull et al. 2021).Shifts in the transition to lower N H toward high-latitude quasars are influenced by lower gas metallicities, lower dust content, and reduced far-UV (H 2 -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| ≥ 40 • with E(B −V ) < 0.056, the H 2 contributions could be small in most cases.However, 17 of the 39 sight lines have column densities log N H ≈ 20.25-20.67,near or above the H I-to-H 2 transition.Thus, some of the group-2 sample would likely require corrections (1% to 10%) for undetected H 2 .In our Tables, we separate the two groups (55 and 39 AGN) and conduct independent statistical analyses.

Reddening Maps
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 µm map.The final optical depth map has a 5 ′ beam size and is provided at HEALPix N side = 2048 resolution.We multiply the optical depth map at 353 GHz by the conversion factor 1.49 × 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 HI maps from HI4PI and Lenz et al. (2017) we smooth the reddening maps to 16.1 ′ 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 , 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 solidstate 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 (β), where emissivity ϵ(ν) ∝ ν β .Combining the scaling of dust radiance R ∝ τ 353 T 4+β d ∝ T 3+β d with the observed anti-correlation (β ∝ T −α d ), we find that radiance is sensitive to small changes in the two parameters (α, β), Table 4 shows the dust parameters adopted in several FIR papers.Over the range of indices, β = 1.6 ± 0.2, adopted in the 2016 Planck-GNILC study and with α = 2/3, the radiance factor would change by a factor of 2.3 about R 0 .Table 5 lists 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 1σ variance σ(T d ) = 0.213 K (1.2% in group 1).The correspondence between FIR flux and reddening is good, with 10% variance σ(I/E) = 5.63 MJy sr −1 mag −1 in the distribution of I(100 µm)/E(B − V ).However, because of the sensitivity of the modeled dust column density to T d and β, 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 (1σ variances).For these reasons, we are suspicious of the accuracy of the ratios N H /E(B − V ) for AGN sight lines with E(B − V ) ≲ 0.04.In the next section, we examine these issues statistically for various sub-samples.

Survey Results
Table 1 presented the gas column densities, inferred E(B − V ), and corresponding ratio N 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 H 2 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 H2 with those of atomic hydrogen N HI to arrive at the total hydrogen column density N H = N HI + 2N H2 .Columns 9 and 10 in Table 1 list dust-to-gas ratios for gas at all velocities and for low-velocity gas only.
In Section 3.1 we discuss the statistical changes of excluding these sight lines in modified subsamples (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.

Gas-to-Dust Ratios for QSO Sub-samples
Table 6 shows mean values of the ratios N 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 H 2 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 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 H 2 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 ) ≤ 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 ) ≤ 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 , β) 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 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 H /E(B − V ).For example, PG 1626+554 has log N 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 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 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.

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 LSR | ≥ 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 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. 2001aRichter et al. , 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 LSR | ≥ 90 km s −1 ), IVCs (|V LSR | = 30-90 km s −1 ), and low-velocity gas.In the first group of 55 AGN sight lines with both H I and H 2 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 1206.500Å absorption line found large sky-covering fractions, f c = 0.81 ± 0.05 (Shull et al. 2009) and f c = 0.77 ± 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 H 2 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 emission 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.Similar depletion measurements have been seen in the Leading Arm of the Magellanic Stream (Richter et al. 2018).

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 (ℓ, b) (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 (β) compared to the rest of the high-latitude sky.It shows up in the reddening difference map because SFD98 assumed a constant β, 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 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 cm −2 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).

Summary and Conclusions
The goal of our study was to assess the accuracy and reliability of measurements of the gas-todust ratio N 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 sp ≈ (1 Gyr)(10 −3 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, H 2 ) 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, H 2 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 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 ) ≤ 0.04.From sub-samples of the 94 AGN, examining the measurements N HI , N 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 ) ≤ 0.02 and 12% higher for 81 AGN with E(B − V ) ≤ 0.04.
• Measurements with the GBT 100 m telescope exhibit N HI lower by 4.0-4.5% on average compared to the NRAO 140 ft at Green Bank and the HI4PI survey.In several sight lines, GBT measured N HI lower by 10-30%.
• Including H 2 in the total N H = N HI +2N H2 increases N H by 2-3% on average at high latitude, with four sight lines exhibiting f H2 of 7% to 17%.
• Excluding high velocity gas (HVCs) decreases N 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 subsample, three points show the shifts that occur when one uses different reddening maps (SF11 vs. Planck-GN) or sight lines with values of N 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 • would be expected to show higher gasto-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 H 2 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 ) ≤ 0.04.A comparison of H I column densities obtained from different radio telescopes (Table 2) found differences in N 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 β.Appendix C demonstrated the sensitivity of dust radiance to β 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 • 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.In the Galactic disk, the mean ratio N H /E(B − V ) of interstellar gas-to-dust in the Galactic disk has been determined as 6.0 ± 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;Liszt & Gerin 2023).For 51 quasars at high Galactic latitude, with both H I and H 2 and 0.01 ≤ E(B − V ) ≲ 0.1 (Planck-GN scale), we find mean ratios 10.3 ± 0.4 (gas at all velocities) and 9.2 ± 0.3 (low-velocity).
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. Owing to uncertainties in both numerator N 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 HI differed by 0.05-0.12(dex) in 21-cm observations at various radio telescopes.Compared to data from the GBT 100 m (9.1 ′ beam), the average values of log N HI were higher by +0.017 (GB-140 ft, 21 ′ beam), +0.023 (HI4PI, 16 ′ beam), and +0.059 Wakker et al. (2003).

5.
Values of E(B − V ) at |b| > 30 • 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 ) ≤ 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 "Bmodes" in polarized emission.Variations in log N HI measurements and FIR-inferred E(B − V ) and propagated errors in the numerator and denominator result in large, asymmetric errors in N 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 HI to reddening and extinction.

A. Error Propagation in the Ratio N H /E(B-V)
Errors in the gas-to-reddening ratio N H /E(B − V ) arise from uncertainties in measurements of three quantities: log N HI , log N H2 , and E B−V , where N H ≡ N HI + 2N H2 .Because log N = (ln N/2.303), we have σ log N H = (σ ln N H /2.303) = (σ N H /2.303 N H ). The propagated errors on log N H give the weighted formula, Similarly, propagated errors in N H /E(B − V ) lead to We can use this expression to evaluate which errors dominate uncertainty in the gas-to-reddening ratios discussed in this paper.Next, consider a moderately reddened quasar, Mrk 1095 with log N HI = 20.969±0.07,log N H2 = 18.76 +0.21  −0.31 , and E(B − V ) = 0.1099.The IPAC/IRSA tables quote an error of ±0.0017 (1.5%) on E(B − V ) (from SF11), but we suggest a larger systematic error of ±0.02 (18%).From these, we find log N H = 20.974±0.069and σ ratio /ratio = 0.24, so that N H /E(B −V ) = (6.8±1.6)×10 21cm −2 mag −1 .Errors on this ratio are dominated by uncertainties in both log N 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 ) = 0.0161 ± 0.0006 (SFD98), 0.0138 ± 0.0005 (SF11), 0.0197 ± 0.0063 (Planck-DL), and 0.0154 ± 0.0002 (Planck-GN).The column densities are log N HI = 20.388±0.05,log N H2 = 14.42±0.09,and log N H = 20.338±0.048.The gas-to-dust ratios (15.8, 11.1, 14.1)are given 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.
The observed determinations of the β-index (Table 4) illustrate the difficulties in dust modeling.An early study (Planck Collaboration XXIV 2011) used β = 1.8, noting compatibility with the FIRAS spectrum of the diffuse ISM.Subsequent Planck papers found β ≈ 1.6 for high-latitude sight lines.Their mean and 1σ variance were β = 1.59 ± 0.12 (Planck Collaboration XI 2014) and β = 1.63 ± 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 Here τ 353 is the dust optical depth at ν 0 = 353 GHz, the frequency at which the emissivity index is normalized.In the MBB formulation, with 2 ) in the Rayleigh-Jeans limit, the dust optical depth τ 353 ∝ T −1 d .Because of the sensitivity of dust emissivity to temperature, it is useful to understand how the inferred radiance depends on the assumed index β.Several papers (see Figure 16 in Planck Collaboration XI 2014) found an anti-correlation between β obs and T obs .A possible explanation is that when dust emits more efficiently it acquires a lower temperature.Martin et al. (2012) proposed an approximate relation, (β/1.8)≈ (T d /17.9 K) −2/3 , based on 100-500 µm Galactic-plane data from Paradis et al. (2010).The latter paper fitted to a general relation, β ∝ T −α d and α ≈ 4/3 (with substantial scatter).We adopt the formulation (β/β 0 ) = (T d /T 0 ) −α , where T 0 and β 0 are fiducial parameters chosen at the center of the distributions.Combining the scaling of R ∝ τ 353 T 4+β d ∝ T 3+β d with the anti-correlation (T d ∝ β −1/α ) between dust emission index and dust temperature, we find that radiance is quite sensitive to changes in these indices (α and β), For the range of emission indices, β = 1.6±0.2,adopted in the 2016 Planck-GN study (and α = 2/3) the radiance factor changes by a factor of 2.3 about 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" Ratios a    (Wakker et al. 2003).Values of log N HI for NGC 1068 are correct; they were incorrectly transcribed in Gillmon et al. (2006).The first 55 AGN also have H 2 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 HI ) for all velocities (Wakker et al. 2003), and column 6 gives H I excluding HVCs and most IVCs.Column 7 gives H 2 column densities, and column 8 gives values of N H = N HI + 2N H2 at all velocities.The last three columns present ratios N H /E(B − V ) in units 10 21 cm −2 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).
b Column 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 H 2 detected in absorption they likely contain dust.The gas-to-dust ratios for these sight lines are computed with N HI that includes the IVCs, marked with asterisks (Column 10).Most high-latitude sight lines exhibit ratios higher than the mean value, ⟨N H /E(B − V )⟩ ≈ 6 × 10 21 cm −2 mag −1 , measured toward OB stars in the Galactic disk (Bohlin et al. 1978;Shull et al. 2021).
We have annotated several sight lines in which N 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.

Fig. 1 .
Fig. 1.-Polar projection maps of the ratio N H /E(B − V ) between N HI from HI4PI for low-velocity gas with |V LSR | ≤ 90 km s −1 and E(B − V ) from SF11 (top) and Planck-GN (bottom).Locations of the 94 quasars are shown as white circles.Both reddening maps are smoothed to the HI4PI resolution of 16 ′ .Northern Galactic hemisphere is on the left, southern hemisphere on the right.Galactic longitude ℓ = 0 • is at the bottom and ℓ = 180 • at the top of each map.Longitude increases clockwise for northern hemisphere and counterclockwise for southern hemisphere, meeting at ℓ = 270 • .Color scale at bottom shows gas-to-dust ratio in units 10 21 cm −2 mag −1 .The linear scale covers the 1 st and 99 th percentiles of the distribution of ratios of the top panel.White circles mark of 94 AGN.

Fig. 3 .
Fig. 3.-Differences in N HI (at all velocities, in units of 10 20 cm −2 ) between HI4PI values (HI4PI Collaboration et al. 2016) and those from Wakker et al. (2003) from our Table1.These are plotted versus N HI (in units of 10 21 cm −2 ) from Table1.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 HI .We have annotated several sight lines in which N HI from HI4PI is considerably lower than that inWakker 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.

Fig. 4 .
Fig. 4.-Distribution of ratios of E(B − V ) from Planck-GN and SF11.Values are from full sample (94 AGN), with nine QSOs behind HVC Complex C plotted in red.These include 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 ) ≲ 0.04.The plotted errors are likely under-estimated owing to systematic effects in FIR modeling.

Fig. 6 .
Fig. 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 (ℓ, b) = (260 − 330 • , 80 − 84 • ) is Markkanen's Cloud(Markkanen 1979) with a discrepant dust emissivity spectral index β, as noted in Planck Collaboration XI (2014).Many IVCs also appear in these difference plots (see Section 3.3).

Fig. 7 .
Fig. 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 HI comes from HI4PI survey for gas at |V LSR | ≤ 90 km s −1 .Reddening maps are smoothed to the HI4PI resolution (16 ′ ).In the label box, SFD-S11 refers to the standard 0.86 recalibration, and SFD-0.884refers 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 (1σ) variance in the Shull et al. (2021) survey of 129 stars within 5 kpc.

Fig. 8 .
Fig. 8.-Summary of mean ratios N H /E(B − V ) from our primary sample (group 1, 55 AGN) with both H I and H 2 measurements, and secondary sample (group 2, 39 AGN) with only H I. Modified samples exclude sight lines with uncertain reddening E(B − V ) < 0.01 (see Table6).Ratios are shown for two reddening maps (SF11 and Planck-GNILC) and for gas at low velocity and all velocities (including HVCs and IVCs).Nine sight lines through HVC Complex C with elevated ratios (low dust content) are a subset of the primary sample.The horizontal dotted line shows the mean ratio of N HI /E(B − V ) = 8.8 at high latitude found byLenz et al. (2017).
Fig. 8.-Summary of mean ratios N H /E(B − V ) from our primary sample (group 1, 55 AGN) with both H I and H 2 measurements, and secondary sample (group 2, 39 AGN) with only H I. Modified samples exclude sight lines with uncertain reddening E(B − V ) < 0.01 (see Table6).Ratios are shown for two reddening maps (SF11 and Planck-GNILC) and for gas at low velocity and all velocities (including HVCs and IVCs).Nine sight lines through HVC Complex C with elevated ratios (low dust content) are a subset of the primary sample.The horizontal dotted line shows the mean ratio of N HI /E(B − V ) = 8.8 at high latitude found byLenz et al. (2017).

Table 2 .
Comparison of H I Column Densities a