On the Number of Independent Parameters of Interstellar Extinction Curves

Abstract

Abstract The number of independent parameters that ultraviolet interstellar extinction curves depend on has never been decisively clarified, yet the issue is critical for the comprehension and modeling of interstellar extinction observations. Cardelli, Clayton, & Mathis (CCM89) concluded that normalized extinction curves rely on only one parameter, but E. Fitzpatrick and others consider this finding at most a first-order approximation favored by uncertainties in measurement. However, the multiparameter fits successively introduced by Fitzpatrick & Massa were intended to give the best possible analytical representation of extinction curves, not to investigate their degrees of freedom. A deeper examination of these fits and of the CCM89 conclusion shows that they do not necessarily conflict. Fitzpatrick & Massa’s parameterization of extinction curves and the large database (nearly 600 directions) published by Krelowski & Strobel are used in this paper to show that, within the precision allowed by the data, E(λ − V) correlates tightly with E(B − V) for all λ within the near-infrared to far-ultraviolet spectrum. This correlation confirms the relationships that led to the CCM89 fit and calls into question the reliability of today’s interstellar dust models, which all need at least seven parameters (reddening included) to fit observed ultraviolet extinction curves.