Extinction curves, extinction laws, and the failure of interstellar dust models

Abstract

The interpretation of ultraviolet Galactic interstellar extinction curves is obscured today by accumulated assumptions, such as a purported link between the 2200 A bump and metallicity, that are not firmly supported by observations. In this paper I define extinction curves as the ratio F*/F0 of the near-infrared-to-ultraviolet spectrum of a reddened star to that of the same star without intervening material, rather than in terms of a magnitude difference, and revisit their observed properties. Special attention is given to the connection that Galactic extinction curves with a 2200 A bump retain with the ultraviolet extrapolation of the exponential extinction law defined by their near-infrared-to-optical segment. This connection leads to the classification of all extinction curves into three types. A graphical representation of these types together with their underlying exponential extinction laws demonstrates that interstellar extinction curves can be interpreted in two ways. Either they result from the mixing of distinct extinction laws associated with different particles, as traditionally assumed, or Galactic ultraviolet curves with a bump are not extinction laws proper but instead deviate from a universal exponential extinction law owing to an additional contribution from coherently forward-scattered starlight. Given the observational constraints on the interpretation of extinction curves, such as their dependence on just two parameters, and the fact that bump-like extinction curves are barely observed outside the Galaxy, the latter interpretation emerges as the only logically consistent one.

Figures (2)

• Figure 1: Observed ultraviolet extinction curve types. All extinction curves fall into one of three categories according to the relationship they maintain in the ultraviolet with the exponential extinction law describing their optical part, represented here by the gray exponential lines. Type I (left panel) and Type II (left and upper right panels) curves remain closely associated with the optical exponential law, either throughout the ultraviolet spectrum (Type I) or down to the bump region only (Type II). Type III curves (bottom right panel), the most common type in the Galaxy, clearly diverge from the optical exponential law, remaining above it except at the bump position (Section \ref{['bump']}). Gray shaded areas highlight the difference between observed extinction curves and their optical extinction laws and may reflect either a change in extinction law or an additional contribution of forward-scattered starlight (Section \ref{['explaw']}). High-redshift extinction curves are almost exclusively featureless Type I curves. In the Galaxy, Types I and II are observed only at extremely low reddening or when local extinction dominates. The examples shown here have reddening values $E(B-V)\sim 0.05$ and 0.17 mag (Type I), 0.3 mag (Type II), and 0.45 mag (Type III). The exponential laws are $e^{-1.1E(B-V)/\lambda^{1.4}}$ (see Section \ref{['expec']}).
• Figure 2: Type II extinction curves produced by local dust. Left: Ultraviolet extinction curves of the shell star AB Aur (HD 31293, $E(B-V)\simeq 0.2$; sitko81). With the exception of one case, all extinction curves derived by Sitko et al. remain close to the optical exponential law up to the bump, as illustrated here by the extinction curve toward AB Aur. Right: Ultraviolet extinction curve of Wolf-Rayet star MR 119, affected by strong local extinction garmany84. Although Garmany et al. did not explicitly derive the extinction curve, they noted that applying a standard extinction correction to their Wolf-Rayet sample would yield a far-ultraviolet thermal turnover redder than observed, implying that circumstellar ultraviolet extinction must be substantially stronger than predicted by standard models. The extinction curve of MR 119 closely follows the gray exponential line corresponding to the exponential extinction law $e^{-1.1\times 1.15/\lambda^{1.4}}$ down to the bump region, and displays a much stronger pre-bump extinction than expected for a normal Galactic field star, such as the Type III star HD 229196 ($E(B-V)\simeq 1$; upper gray dotted curve).