5. Improved Th and Ar input wavelengths

The improved Th and Ar input wavelengths for moderately high resolutions in astronomy are given in the electronic appendix of this paper, as ASCII tables. A sample page of the principal table is shown in Table 5 (click here). In addition to the original laboratory wavelength and the resolution-dependent improved blend wavelengths, it contains additional information giving the user freedom in the choice of his selection limits. However, no corrections are given for heavily blended lines, as such corrections are intrinsically uncertain. Restricted tables, listing only the resolution-dependent blend wavelength of preselected lines together with the laboratory wavelength and the emitting ion of the principal component, are also available; a sample page is given in Table 6 (click here). Lines that are in principle useful but intrinsically weak, and mixed Th-Ar blends giving results too dependent on the relative strength of the Ar versus Th components were removed from these ready-to-use lists.

 

Table 5:  Sample page of the principal table for the "standard" case of the Ar-to-Th line strength ratio (see Table 1 (click here)), showing the laboratory wavelength [Å] (Col. 1), the emitting ion (Col. 2) and the relative intensity in log-scale (Col. 3) of the principal component; the resolution-dependent blend wavelengths [Å] (Cols. 5-9), and their corresponding displacement [pix] and discretisation stability parameter s [pix] (Cols. 10-20). The headers of Cols. 5-9 refer to /pixel-scale and the headers of Cols. 10-20 refer to /pixel-scale

 

maincomp ion

4686.1946 4686.1946 ThI

4690.6235 4690.6219 ThI

4694.0914 4694.0914 ThII

4698.2248 4698.2248 Th

4703.9895 4703.9898 ThI

4726.8683 4726.8683 ArII

4732.0543 4732.0532 ArII

4735.9064 4735.9058 ArII

4739.6784 4739.6764 ThI

Table 6:  Sample page of the restricted table for pixel-scale , giving the blend wavelength [Å] (Col. 1), the laboratory wavelength (Col. 2) and the emitting ion (Col. 3) of the principal component

Considerations that might influence the user's selection choice are e.g.

• the calibration accuracy of interest for the specific problem; as a rule of thumb, no lines should be included with a computed displacement exceeding the aimed local wavelength accuracy, and intrinsically useful but too noisy lines should not be used (user defined S/N cut-off of faint lines).
• the change of detector sensitivity with wavelength and through one spectral order. An even distribution of the calibrator lines over the frame is the best guarantee for an optimal local accuracy. Nowhere lower quality data should degrade nearby high quality data (locally defined S/N cut-off). As this aspect of the selection depends very specifically on the observing conditions, it must necessarily be the concern of the user if one wants to obtain the highest possible accuracy.
• the difference between the centering algorithm used and the one applied in our calculations. The sensitivity of centering methods to asymmetry depends on the algorithm, and hence the measured blend wavelength depends on the algorithm. (e.g. the centre of gravity is much more sensitive than a gaussian fit to the asymmetries at the edges of the fit interval.) The use of a different fit interval will change the predicted wavelengths for those few cases where a strongly blending line (or line wing) is near the edge of the interval.
• the difference in observed and assumed line width. Broader calibration lines lead to an increase of bias in the wider blends. For the weak blends of interest here, significant differences in predicted position may occur for blends composed of components separated by more than two pixels if the PSF is at least 25% broader than assumed in our computations. Thus, differences in line width or in centering algorithm both require a more stringent selection of the wider blends.
• the observed Ar-to-Th line strength ratio. The fact that the principal table contains results for two different Ar-to-Th line strengths and the relative strengths of all lines (for comparison with ones observations) permits to evaluate the risk of using specific mixed blends. Note that the fraction of potentially useful Th-Ar features sensitive to the Ar-to-Th ratio is small (Sect. 3); a "fast and safe" solution is to disregard them always.

The user can make a final check on the selection and line centering procedure for a particular lamp spectrum by inspecting the residuals between the measured line positions and the ones predicted by his calibration model (assuming the latter model is precise). The residuals for a given line on different frames should not correlate with discretisation (i.e., with the sub-pixel position of the line centre), and its average value over all frames should not deviate significantly from 0. A correlation with discretisation for completely unblended lines indicates that the line centering procedure contains (implicit) invalid assumptions about the PSF. This may also lead to an offset from 0 when not all discretisations are evenly sampled in the set of frames. Blended lines are expected to give rise to residuals that correlate with discretisation to the extent described by the parameter s in our tables. Significant offsets from 0 may hint to biased theoretical wavelengths. Such outliers, if any, should be rare (as argued in Sect. 3) after application of the proposed "cleaned" calibrator lists and thus easily recognizable.