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Column-Density Estimation from the Equivalent Widths of Absorption Doublets

Year: 2026
Type: article
Abstract: $\mathrm{Na~\textsc {i}~D}\,$ absorption is widely used to estimate the dust extinction toward Galactic and extragalactic sources, but the inferred column densities are unreliable once the lines saturate. We present an analytical framework for estimating column densities from the equivalent widths (EWs) of absorption-line doublets. The method requires only that the two doublet members be measured separately – the velocity structure need not be resolved – so a resolving power λ/Δλ ≳ 103 suffices for $\mathrm{Na~\textsc {i}~D}\,$, two orders of magnitude below velocity-resolved methods. For the Gaussian curve of growth, the classical inversion reduces to a universal saturation correction depending only on the doublet ratio, R = EW2/EW1: at fixed R, the inferred column density is linear in the measured EW. The formulation yields the exact Gaussian inversion, $N_{\tilde{\kappa }}$, which provides the Doppler parameter; a closed-form second-order approximation; and a strict lower bound, Nmin, valid for an arbitrary velocity structure. We recommend reporting Nmin: an optimal, assumption-free lower bound, within a few per cent of $N_{\tilde{\kappa }}$ for R ≳ 1.4 and at most a factor 3.5 below it at R = 1.1. The ratio $N_{\tilde{\kappa }}/N_{\rm 2nd}$ provides a per-object saturation diagnostic. We validate the framework against published profile-fitting $\mathrm{Na~\textsc {i}~D}\,$column densities toward Galactic sight lines and Type Ia supernovae, using only the integrated EWs. An explicit closed-form formula converts the two EWs into an extinction estimate through the observed log N(Na I)–AV relation. A public implementation with full uncertainty propagation accompanies the paper.
DOI: 10.1093/mnras/stag1921
Language: English
Open Access status: gold
Estimated APC paid: $3,046
OpenAlex ID: W7196977070
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