E(B – V), N(H I), and N(H₂)

We consider the structure of the N(H I)-E(B – V) relationship when H I is measured in the 21 cm radio line and E(B – V) is defined by far-IR dust-derived measures. We derive reddening-dependent corrections to N(H I) based on interferometric absorption measurements over the past 30 yr that follow a single power-law relationship ∫τ(H I)dv=14.07 km s⁻¹ E(B – V)^1.074 at 0.02 ≲ E(B – V) ≲ 3 mag. Corrections to 21 cm line-derived H I column densities are too small to have had any effect on the ratio N(H I)/E(B – V) = 8.3 × 10²¹ cm^–2 mag^–1 we derived at 0.015 ≲ E(B – V) ≲ 0.075 mag and |b| ≥ 20°; they are also too small to explain the break in the slope of the N(H I)-E(B – V) relation at E(B – V) ≳ 0.1 mag that we demonstrated around the Galaxy at |b|≥20°. The latter must therefore be attributed to the onset of H₂ formation and we show that models of H₂ formation in a low-density diffuse molecular gas can readily explain the inflected N (H I) – E(B – V) relationship. Below |b| = 20° N(H I)/E(B – V) measured at 0.015 ≲ E(B – V) ≲ 0.075 mag increases steadily down to |b| = 8° where sightlines with small E(B – V) no longer occur. By contrast, the ratio N(H I)/E(B – V) measured over all E(B – V) declines to N(H I)/E(B – V) = 5-6 × 10²¹ cm^–2 mag^–1 at |b| ≲ 30°, perhaps providing an explanation of the difference between our results and the gas/reddening ratios measured previously using stellar spectra.