On Determining Extinction from Reddening

The influence of shifts in effective wavelengths on ratios of total to selective extinction is examined, primarily to determine how to evaluate the Galactic extinction of extragalactic bodies in a way that minimizes systematic errors. In the process, a new procedure is developed for evaluating the Galactic or extragalactic extinction of any source in any filter from any index of reddening. The amount of dust along a sightline is quantified by the optical depth at 1 μm, which has the advantage of being roughly equal numerically to E(B-V). The optical depth can be derived iteratively from a color excess using an appropriate spectral energy distribution (SED) for the reddening probe, and a monochromatic law of reddening which delivers a value of AV/E(B-V) characteristic of the obscuring medium when applied to the spectrum of a reference source for which this ratio is known. Knowledge of the optical depth then facilitates the determination of the extinction of any source in any filter without concern as to the shape of the spectrum of the probe. The ratio of total to selective extinction for stars and galaxies is synthesized for a variety of filter combinations in order to examine variations with type, tilt, optical depth, and redshift. For this purpose, representative integrated SEDs spanning the space ultraviolet to the near-infrared are constructed for galaxy types E, Sab, Sbc, Scd, and Im, all at well-defined inclinations. In addition, an algorithm to adjust the shapes of the SEDs for tilt is developed. Along the main sequence, the classical ratio of total to selective extinction, AV/E(B-V), increases by 23% from O5 to M6. At late types, there are differences as high as 17% between evolved and unevolved stars. Along the Hubble sequence, AV/E(B-V) decreases by 5% from E to Im. The value for elliptical galaxies falls near the locus for the main sequence, not the giant branch. Correlated against B-I, AV/E(B-V) for star-forming galaxies is systematically lower than for stars of the same color by up to 5%. It increases much more rapidly with tilt than with the optical depth of Galactic dust, although neither dependence is strong. For both stars and galaxies, AV/E(B-V) varies dramatically with the redshift. Changes of 16% for a Type Ia supernovae and 22% for a Cepheid are seen out to z = 0.4. For elliptical galaxies, a variation of 30% can be expected out to z = 1, the precise form of which being dependent upon the ultraviolet excess. Even infrared ratios of total to selective extinction, such as AH/E(B-V), change significantly with color and redshift because of differential shifts in the effective wavelengths of B and V. As a gauge of reddening, E(V-I) is greatly preferable to E(B-V), because it is much less sensitive to color and redshift, yet more sensitive to the optical depth of dust. A demonstration is given on how to quantify upper limits to Galactic extinction which should be placed on studies of high-redshift supernovae, to reduce the redshift dependence of extinction corrections to a range that is insignificant compared with residuals supporting accelerated universal expansion. When the new technique for evaluating extinction corrections is applied to Cepheids in M31, distances for fields at different radii become less dispersed, confirming that the period-luminosity relation is not very sensitive to metallicity. However, the discrepancy between the Cepheid and maser distances to NGC 4258 cannot be attributed to the method of handling the extinction.