3.2 Using a R-Dependent Mean Curve

If the value of R has been measured along a sightline of interest, or if some general information is available about the dust grain environment (e.g., dense region or diffuse region?), then the uncertainties in dereddening can be reduced somewhat by adopting an R-dependent extinction curve computed at the appropriate value of R. For the original 29 sightlines used by CCM, the standard deviation of the individual observed extinction curves minus the computed R-dependent curves is about a factor of 2 smaller than when the individual curves are compared to the average Galactic (R = 3.1) curve. Thus the uncertainties in a dereddened energy distribution can be estimated using eq. 1 and adopting 0.5 times the _k(-V) values from Table 1. If R is poorly measured or only estimated from environmental factors, then allowance must be made for this in the error analysis.

Using an appropriate R-dependent curve can slightly improve the accuracy of results from ironing out the 2175 Å bump. The values of ²_m(-V) can be estimated as above in Section 3.1, using the same value of _{E (B-V)} 20% and 0.5 x _k(-V) from Table 1. The resultant values of ²_m(-V) are about 85% as large as those listed in the last column of Table 1. The gain from using the R-dependent curves is only marginal because the normalized bump heights are highly variable and not correlated with R.

It is important to note that, even when R and E (B - V) are well-determined, the use of an R-dependent extinction curve only reduces - but does not eliminate - the wavelength dependent dereddening error. The standard deviation of the observed vs. R-dependent curves does not go to zero, even for the sample of 29 sightlines used by CCM to define the R-dependence, because the UV/optical curves are not really a one-parameter family dependent only on R. Curves derived for different sightlines with the same values of R show a wide range of properties, including differences in the strengths of the bump and the far-UV rise. Thus, as noted by CCM, the CCM formula reproduces a general trend, but does not provide particularly good fits to individual extinction curves, even when the value of R is well-determined.

Apart from this intrinsic scatter around the mean R relation, the accuracy of the CCM results is limited in the IR/optical region due to bandpass effects with the broadband Johnson filters used to measure the extinction. As a result, CCM tends to overestimate the level of extinction in the near-IR and blue-visible. In the Appendix, a new derivation of the R-dependence of IR-through-UV extinction is presented. This corrects for the systematic bandpass effects in CCM, but is still plagued by the same uncertainties caused by the ``cosmic'' scatter of extinction properties around the mean R relation.