2.1 Cross-Correlation Tools

  A cross-correlation analysis offers both a convenient and efficient method of determining wavelength shifts for a series of test spectra with respect to a reference spectrum. This is largely because it utilizes the aggregate signal contained in the spectrum. No pre-conditions are required in terms of the shapes or positions of individual spectral features. Thus, the presence of practical problems such as line blending or continuum placement do not degrade the accuracy of the solution as long as these as errors are independent of wavelength. Even a limited signal-to-noise ratio will decrease the precision of the result, but it does not introduce a bias. To implement the cross-correlation analysis we used the IUEDAC IDL routine CRSCOR. This program is itself a ``wrapper" for a small IDL collection of programs. It computes the cross (auto) correlation function according to its definition: that is, by shifting iteratively a test spectrum with respect to the reference by a series of regularly spaced wavelength increments and computing the sum of the product of the flux differences of the shifted and unshifted spectrum at each pixel within a specified wavelength or velocity range. This maximum of this function is located by least-squares polynomial fitting. For echelle data the natural unit is velocity, and so the pixel shift produced by the program is converted to km s<sup>-1</sup> as an output option. As implemented, CRSCOR truncates the start and ending wavelengths of the spectral array to the same values, thereby avoiding the generation of any false ``noise" due to wrap-around of shifted arrays. The program interpolates the test spectrum to the wavelength grid of the reference template to accommodate subpixel wavelength shifts. This step also facilitates comparisons with spectra from other instruments. To test these interpolations we cross-correlated several test spectra against copies of themselves by using a similar (but not identical) set of wavelengths from other observations of the same target. This comparison tests the accuracy of interpolating spectra observed at discrete wavelengths. We found that interpolations to one set of wavelengths produce false shifts of always less than ± 1.0 km s^-1.

Our procedure was to run CRSCOR iteratively for each echelle order and to evaluate the net shift of the order as a whole wavelength segment. In our procedures we took care to screen the data for known pathologies of the IUE cameras. For example, fluxes near the edges of the order (particularly the long-wavelength end for the SWP camera) were avoided because the noise is high and also because systematic errors can be large in the blaze ``ripple correction" (Gonzalez-Riestra et al. 1998). Such errors often mean sloped continua, which can lead to a small bias in line centroid positions. We also excluded small groups of pixels with negative data quality flags (usually associated with instrumental ``reseaux") because their fluxes are generally meaningless. In these cases, we interpolated the fluxes from neighboring pixels. This step has the effect of adding incrementally to random noise but does not introduce a random shift unless the interpolated regions in the two spectra being compared are extensive and have different slopes. Apart from specific tests on zero-point shifts of interstellar line systems ($\S$4. ) discussed below, we did not exclude interstellar lines from our cross-correlations. Although these lines are formed in a velocity frame shifted from the photospheric lines, the resulting wavelength shift can be assumed to be the same for different instruments because the cross-correlation routine does not distinguish between features formed in various velocity frames. For example, we did not have to exclude ``wind" lines because the shifts from orders including these lines did not differ noticeably from shifts of adjacent orders.

In comparing IUE spectra with spectra from the HST GHRS and STIS instruments, we convolved the HST data by gaussian broadenings to make their resolutions equivalent to IUE spectra. When all these steps were carried out, we experimented with CRSCOR in an interactive mode for the investigations discussed in $\S$ 4. After finding that shifts arising from unflagged data pathologies are rare, we automated the program in order to compare large groups of spectra efficiently.