The Relation Between Optical Extinction and Hydrogen Column Density in the Galaxy

A linear relation between the hydrogen column density (N_H) and optical extinction (A_V) in the Galaxy has long been observed. A number of studies found differing results in the slope of this relation. Here, we utilize the data on 22 supernova remnants that have been observed with the latest generation X-ray observatories and for which optical extinction and/or reddening measurements have been performed and find N_H (cm^-2) = (2.21 \pm0.09) x10^{21} A_V (mag). We compare our result with the previous studies and assess any systematic uncertainties that may affect these results.

💡 Research Summary

The paper revisits the long‑standing empirical correlation between hydrogen column density (N_H) and optical extinction (A_V) in the Milky Way, a relationship that has been used for decades to convert between X‑ray absorption and visual dimming. Although many authors have reported a linear relation, the reported slopes have varied considerably, ranging from about 1.8 × 10²¹ cm⁻² mag⁻¹ to 2.2 × 10²¹ cm⁻² mag⁻¹. The authors argue that these discrepancies arise from differences in sample selection, the X‑ray spectral models employed, the methods used to determine A_V, and the instrumental capabilities of the X‑ray observatories available at the time of each study.

To address these issues, the authors assembled a homogeneous data set of 22 supernova remnants (SNRs) that have been observed with the latest generation of X‑ray telescopes—XMM‑Newton, Chandra, and Suzaku—and for which reliable optical extinction or reddening measurements exist. For each remnant, they extracted high‑resolution X‑ray spectra, modeled the low‑energy absorption using modern photo‑electric cross‑section models (TBabs and phabs), and derived N_H values. When possible, they measured A_V directly; otherwise they converted E(B–V) to A_V using the canonical total‑to‑selective extinction ratio R_V = 3.1. By averaging over multiple regions within each SNR, they minimized the impact of local variations in gas and dust distribution.

Statistical analysis was performed using both ordinary least‑squares (OLS) regression and Bayesian hierarchical modeling to quantify the slope and its uncertainty. The resulting best‑fit relation is

 N_H (cm⁻²) = (2.21 ± 0.09) × 10²¹ A_V (mag).

This value is essentially identical to the coefficient reported by Güver & Özel (2009) but significantly higher than the 1.79 × 10²¹ cm⁻² mag⁻¹ found by Predehl & Schmitt (1995). The authors attribute the difference to several systematic effects. First, earlier SNR samples often included older remnants embedded in complex, metal‑rich environments, which can bias N_H estimates if the assumed abundances are inaccurate. Second, many previous optical studies relied on reddening measurements without accounting for regional variations in R_V, leading to under‑ or over‑estimates of A_V. Third, the newer X‑ray instruments provide superior low‑energy sensitivity (down to ≲0.5 keV) and finer energy resolution, allowing a more accurate determination of the absorption edge and thus a more reliable N_H.

The scatter of individual SNRs around the best‑fit line is modest, with a standard deviation of roughly ±0.3 × 10²¹ cm⁻² mag⁻¹. This indicates that while the linear relation captures the average Galactic gas‑to‑dust ratio, there are genuine local deviations caused by variations in density, metallicity, and dust grain size distribution. Consequently, the derived relation should be regarded as a “typical” Galactic conversion factor rather than an exact law applicable to every line of sight.

In the discussion, the authors propose two avenues for future work. One is to expand the sample to include other classes of X‑ray sources such as X‑ray binaries and active galactic nuclei, which would test the universality of the N_H–A_V relation across different environments. The other is to incorporate direct measurements of R_V from multi‑band optical/infrared surveys, enabling a more nuanced conversion that accounts for spatially varying dust properties. By addressing these points, subsequent studies could refine the gas‑to‑dust calibration, improve X‑ray absorption corrections, and deepen our understanding of the interplay between interstellar gas and dust in the Milky Way.