4 DIB measurement methods

Central wavelengths, equivalent widths and full widths at half maximum were measured in the spectra of the three reddened stars (BD+63$^{\circ }$ 1964, BD+40$^{\circ }$ 4220, and HD 183143) using the IRAF (Image Reduction and Analysis Facility) software package. Equivalent widths were obtained by integration of the pixel intensities within the region:

$$W = \sum_{i}\left(1-\frac{I_{i}}{C_{i}}\right)$$

where I_i is the intensity at pixel i and C_i is the continuum level at pixel i. The central wavelength was estimated by calculating:

$$\lambda_{\rm c} = \frac{\sum_{i} \lambda_{i}(I_{i} - C_{i})^{\frac{3}{2}}}{\sum_{i}(I_{i} - C_{i})^{\frac{3}{2}}}$$

where $\lambda_{i}$ is the wavelength of pixel i. Alternatively a Gaussian profile can be fitted to the feature, resulting in the additional estimation of the full width at half maximum. Accurately defining the continuum level, which is especially important in measuring medium-broad to broad DIBs, involves fitting a polynomial to the continuum and dividing it out of the spectrum. Error estimates, using a model based on the Poisson statistics of the data, were also obtained using the IRAF package. An error estimate model is fit to the data using as input a constant $\sigma$ estimated from the statistics of the spectrum. A number of simulations are created in which random Gaussian noise is added to the noise-free spectrum using the pixel sigmas from the noise model. The model fitting is done for each simulation and the absolute deviation of each fitted parameter to the noise-free model parameter is recorded. The error estimate for each parameter is then calculated as that deviation, inside which contains 68.3$\%$ (1 $\sigma$) of the parameter estimates.

The wavelengths of absorption bands of certain known molecular, atomic and ionic species (Ca II, Ca I, CH and CH⁺) residing in the line of sight towards BD+63$^{\circ }$ 1964 were measured and the shift in wavelength between those lines and their values recorded in the laboratory was calculated. The sodium lines at 5890 Å and 5895 Å were saturated and so were not included in these calculations. Under ideal conditions the velocity shift would be identical for all lines. However the presence of at least two main clouds of similar column densities and of different velocities (the velocity difference between two substructures in the molecular absorption line was measured to be $\sim$8 km s^-1) in the line of sight of BD+63$^{\circ }$ 1964 and the resulting two-component structure of the interstellar lines limited the estimation of the correct wavelength to an accuracy of $\sim$0.05 Å. The average central wavelengths of the interstellar lines were measured and an average of the velocity shift of 19.5 $\pm$ 0.5 km s^-1 was obtained based upon these measurements. The DIBs' measured wavelengths were then shifted by this amount to provide reliable laboratory wavelengths.