Selection of ThAr lines for wavelength calibration of VLT/UVES
Below is a description of how I've selected ThAr lines from the original literature line-lists in order to produce a better wavelength calibration of UVES. However, the algorithms can easily be applied to other spectrographs. If you'd like me to produce a catalogue for your spectrograph of interest then "all" I need is a ThAr spectrum from that spectrograph (covering your wavelength range of interest).

0. Paper
A paper describing the selection procedure and results has been accepted by MNRAS. A copy of the most up-to-date version is on astro-ph. If you use any information or results from this paper or this web page, including the final ThAr line-list, I would appreciate you citing the paper. The current bibliographic information can be found on my publications page.

1. Here's all the important data files and spectra
I wrote the text below before I wrote the paper. Although the latter is more detailed and has been refereed, the following text might still be helpful as a quick reference or because the links might point you more directly to the file above that you're most interested in. The text below will also be updated in future if and when anything changes.

2. Synthesis of existing Th and Ar line-lists
Before selecting which ThAr lines are to be used to calibrate UVES, we first require a list of the absolute laboratory wavelengths for as many features appearing in the UVES ThAr lamp spectrum as possible. Most features, especially below 6000 Angstroms, are either known to be due to Th or are unidentified (but probably due to Th), while ~10% of the features are from Ar and <1% are from "contaminant" species such as MgI, CaII, NaI, FeI etc. The Th and Ar lines and even some of the contaminant lines are catalogued in various atlases derived from painstaking (but usually rather old) laboratory work. These atlases provide our starting point. However, every ThAr lamp gives a somewhat different spectrum and there are always additional lines which cannot be found in any atlas, even as "unidentified" lines. These are probably due to additional contaminant ions and molecular species in the lamp. This means that our knowledge of the ThAr spectrum from any given lamp is, at best, incomplete and this necessitates the selection procedure detailed in the next section.

There is no single atlas of the ThAr spectrum covering the whole wavelength range of UVES (~3030-10540 Angstroms). However, there is one atlas of Th lines only which does cover this range, Palmer & Engleman (1983; hereafter PE83). The PE83 absolute velocity precision varies from about 15 to 120 m/s depending on the line intensity. PE83 identify a large number of ThI, II and III lines in their spectrum but there is left a large number of unidentified lines which are probably due to Th. Furthermore, on comparison with real ThAr lamp spectra, one notices that there are still several thousand lines which cannot be accounted for by Ar or contaminant species.

Very recently, Lovis et al. (2007, in preparation; hereafter L07) used a large library of spectra from the highly stable HARPS spectrograph on the 3.6-m ESO telescope to improve the situation, at least over the wavelength range 3780-6915 Angstroms. They identified in their spectra lines from the PE83 list which showed no positional variations with time and obtained line positions to within an RMS of about 5-10 m/s. Thus, while bootstrapping their overall wavelength scale to that of PE83, they were able to correct the wavelengths of individual PE83 lines, especially weaker lines, due to their large statistical gain. Moreover, they were able to measure the wavelengths of ALL other features in their ThAr spectra, again at the ~5-10 m/s precision level. They removed from their list lines which saturated their CCD, (very few) lines which appeared in the PE83 catalogue but which were too weak for them to detect and, most importantly, they removed lines which were either closely blended with other lines or were observed to change position with time. The latter indicates either that the line experiences significant shifts with changing lamp pressure or current or that the line is actually a blend and that the relative intensities of the blended lines vary with changing lamp conditions.

The L07 catalogue ranges from 3780 to 6915 Angstroms. Thus, the PE83 line list is used for Th and contaminant lines outside this range. However, to ensure that the maximum number of lines are used to calibrate UVES and to properly select which lines are most useful (i.e. to reject blends) it is desirable to use the known Ar lines as well. Three useful Ar line-lists exist - Norlen (1973; hereafter N73), Whaling et al. (1995; hereafter W95) and Whaling (2002; hereafter W02) - each of which has different advantages and disadvantages. N73 contains both ArI and ArII whereas W95 contains ArII lines and W02 contains ArI lines. The sensitivity of the N73 experiment was worse than W95 and W02 and so fewer lines are listed. The velocity precision achieved by N73 for the ArI lines is better than that of W02 but the ArII lines of W95 should be more precise than N73's. Finally, there is a calibration difference such that the Whaling wavenumbers are larger than the Norlen ones by a factor of SNW = [1 + 6.8x10^{-8}]. Whaling's calibration should be more reliable and so we choose to use the Whaling calibration scale in synthesising the Argon line-lists.

The different lists of ArI and ArII lines are combined in the following ways. We do not consider the ArIII lines from W95 since there are very few of them and since their wavelengths tend to be sensitive to the pressure and current in the ThAr lamp. After combining the L07, PE83, N73, W95 and W02 lists in the above way we obtain the file LovisC+PalmerB+WhalingW+NorlenG_v3000-v11000.dat, hereafter referred to as LPWN. The format of the file is the same as that of the final ThAr line list which is described in Section 4. One difference is the intensity measures reported. Note from the above that the intensity scales for each species (e.g. ThI, ArI, ArII) are different and that the relative intensities of lines from different species depend on many factors, such as lamp pressure and current and the relative partial pressures of Th and Ar gas used. In LPWN we keep the original intensity measures described above.

3. ThAr line selection
One should not simply use the above line-list, LPWN, to calibrate UVES spectra because of the potential for line-blending. The FTS spectra of PE83, N73, W95 and W02 and the HARPS spectra of L07 all have resolving powers R >= 120,000 whereas the UVES resolving power is typically 35,000-70,000 and possibly as high as 110,000. Therefore, a major part of the line-selection that follows is the rejection of "close" blends. The concept of "close" clearly depends on the relative intensities of the blended lines and so it is necessary to put all lines in the above list onto the one intensity scale typical of measured UVES ThAr spectra. Furthermore, since there are always additional unknown lines in measured ThAr spectra, a given ThAr line can only be used for calibration if it is measured to be reliable in the UVES ThAr spectrum. For these reasons we have constructed a UVES ThAr spectrum for use in the line selection process.

3.1 UVES ThAr spectrum
ThAr spectra taken with a 0.6 arcsecond slit and no CCD rebinning were retrieved from the ESO VLT archive. Several exposures were used, each taken in a different standard UVES wavelength setting (346, 437, 580, 600, 760 and 860nm) so that complete wavelength coverage was achieved, with the exception of three small echelle order gaps redwards of 1000nm (1008.443-1008.593nm, 1025.242-1025.695nm & 1042.610-1043.376nm). The UVES pipeline was used to extract and wavelength calibrate the data. Several modifications to the pipeline, described here, were made to improve object extraction and wavelength calibration. The data were re-dispersed to a log-linear wavelength scale using UVES_popler, code specifically written to re-disperse and combine multiple wavelength setting data from UVES. Overlapping regions of spectra were cut away so that only one raw exposure contributed to the final spectrum over echelle-order scales. No effort was made to flux calibrate the final spectrum and the blaze-function of the echelle grating was still evident in the data. However, our results from the intensity re-scaling in the next section demonstrate that this is a minor consideration. The final spectrum has a resolving power of R ~ 70,000 and the log-linear dispersion is set to 1.75 km/s.

3.2 ThAr selection algorithm
The above line-list, LPWN, is treated as the input catalogue to the following algorithm for selecting a final list for calibration of UVES. We make three passes through the algorithm, altering the line list used to calibrate the UVES ThAr spectrum and other parameters specified below. All plots below pertain to the final pass through the algorithm.
  1. UVES ThAr spectrum calibration: The above procedure for constructing the UVES ThAr spectrum requires an input line-list for the wavelength calibration stage. At the first pass we use the line-list provided by ESO with the UVES pipeline (thargood_2.tfits, pipeline_thar.dat). At the second and third passes the output from the previous pass through the algorithm is used.
  2. Gaussian fitting: Each line in the input list LPWN is searched for and fitted with a Gaussian. The fit includes the 13 pixels centred on the pixel with maximum intensity. A first-guess continuum is defined by averaging the first and last 2 pixels in the window. A first-guess continuum slope is defined by taking the difference between the average of the last 2 and first two pixels. A first-guess intensity is defined as the maximum intensity minus the continuum level. A first-guess width is defined by taking the velocity difference between the first and last pixels which have intensities below the continuum plus half the first-guess intensity. The first-guess central velocity is calculated as the intensity weighted velocity of the 3 central pixels. A 5-parameter Gaussian fit is performed and the best-fit parameters used in subsequent steps. The initial guesses and Gaussian fitting procedure is identical to that used in the UVES pipeline (see modifications made to pipeline).
  3. Intensity re-scaling: The different Th and Ar atlases combined above have different intensity scales. Furthermore, one would not expect to find the same relative intensities for lines of different ionic species (e.g. ArI and ArII) in the laboratory and astronomical spectra since the ThAr lamps used will have had different operating conditions (e.g. pressure, current etc.). We therefore aim to place all lines from the different ionic species (ThI, II & II, ArI & II, XX 0 & 1) from each different intensity scale ("L", "P", "N" & "W") on a single intensity scale directly related to the UVES ThAr spectrum. First, any pairs of lines within 13 km/s of each other are removed from the input line list LPWN. For each category of line - that is, one of "ThI L", "ThI P", "ThII L", "ThII P", "ThIII L", "ThIII P", "ArI L", "ArI N", "ArI W", "ArII L", "ArII N", "ArII W", "XX 0 L", "XX 0 P" or "XX 1 L" - the median ratio of the measured and expected intensities of remaining lines, alpha, is defined as the scale-factor. All lines from this category are then scaled to the UVES intensity scale by multiplying their listed intensities by alpha. Two examples of this process are shown in Fig. 1. Figure 2 shows all lines from all categories placed on the UVES intensity scale.


    Figure 1: Examples of the intensity scaling procedure. Measured and expected intensities for unblended lines from each category (e.g. "ThI L", "ThI P") are compared to derive the scale-factor, alpha. All lines from that category are then scaled to the UVES intensity scale using alpha.


    Figure 2: Lines from all categories placed on the UVES intensity scale. The red points are lines from the initial list which satisfy the blending criteria defined in step 4 of the ThAr selection algorithm. The black points are lines satisfying all selection criteria and constitute the final ThAr line-list. Here, Ilist refers to the re-scaled listed intensities.

  4. Blend removal: If, when Gaussian-fitting a single line, another weaker blending line is present but ignored in the fit then the centroid returned from the fit will be shifted towards the blending line. The magnitude of the shift will depend not only on the velocity separation between the two lines, dvsep, but also on the relative intensities of the two lines, I2/I1. When the two lines are not resolved from one another, it is easy to approximate the velocity shift. The new centroid wavelength can be approximated by the intensity weighted mean wavelength of the two blended lines,

    and so the velocity shift due to the blending line is

    However, if the two lines are further apart and are partially resolved, it is not clear how dvc will depend on dvsep and I2/I1. Figure 3 (right) shows the results of a numerical experiment where two blended lines are varied in relative intensity and separation and fitted with a single Gaussian with similar initial guesses as in step 2. A by-eye fit to the contours of constant velocity shift gives the following relationship:

    The first term on the right-hand-side is just the previous equation and applies when dvsep is small with respect to sigmav = FWHM/2.355. We therefore reject lines from the input line-list LPWN which have blending lines within 13 km/s with relative intensities greater than that predicted by the above equation to produce shifts greater than a tolerance of 40 m/s. This tolerance is roughly equal to the overall wavelength calibration residuals achievable with the UVES pipeline using the final ThAr list.


    Figure 3: Removal of strongly blended lines from the list. Right/Bottom: The shift in the centroid of a synthetic Gaussian due to blending with a weaker line. Both lines have widths typical of those seen in our UVES ThAr spectrum. The black dashed lines are contours equally spaced in the logarithm of the shift. The solid red line is a simple "fit" to these contours at a velocity tolerance of 40 m/s (see above equations). All lines with weaker lines more than 13 km/s away are safe from velocity shifts greater than ~40 m/s and this is marked with the vertical dashed red line. Left/Top: Pairs of lines in the input line-list LPWN with the same solid red line from the right-hand panel.

  5. Removal of weak lines: If ThAr lines appear weak in the UVES lamp spectrum then the UVES pipeline's line-identification algorithm can fail or yield a false identification. The amount of velocity information in weak lines is also too small to be useful in calibrating the wavelength scale of UVES. We therefore reject any lines with measured intensities (above the measured continuum) less than 4 times the measured continuum level.
  6. FWHM selection: Any additional unknown features in the UVES ThAr spectrum can cause blending with the remaining lines from the two selection steps above. The next three steps aim to reject those lines which are effected in this way. The first of these steps is to remove lines whose widths are clearly inconsistent with the instrumental resolution, in this case R ~ 70,000 or FWHM ~ 4.3 km/s. Figure 4 shows the distribution of FWHM for all lines surviving the previous two selection steps. After visual inspection of the lines lying away from the main cluster around FWHM ~ 4.3 km/s it was clear that lines wider than ~ 5.3 km/s and narrower than ~ 3.5 km/s should be removed. Lines were fitted as too wide when blended with other unknown features or where saturation of the CCD occurred. Lines were fitted as too narrow usually when they were very weak.


    Figure 4: The FWHM distribution of the lines surviving the previous selection steps. The structure seen in the main congregation of points is due to slightly differing resolutions in the different exposures from different wavelength settings.

  7. High slope rejection: One of the improvements made to the UVES pipeline was the addition of a continuum slope parameter to the Gaussian fitting of ThAr lines during the wavelength calibration. If a line is close to a strong, previously unknown feature in the UVES ThAr spectrum then a large slope (relative to the line's intensity) might be needed to fit the line properly. Since these unknown features probably vary with lamp conditions, one might regard lines fitted with large continuum slopes as best avoided when calibrating the wavelength scale of UVES. Figure 5 shows the distribution of the absolute velocity difference, dvs, between two Gaussian fits - one made including the slope parameter, the other made with the slope fixed to zero - with continuum slope normalised by the line intensity. Visual inspection of lines with dvs greater than 80 m/s showed that some of them have large asymmetries which are probably due to close blends with unknown features. Therefore, all lines with dvs >= 80 m/s are rejected.


    Figure 5: Distribution of the absolute velocity difference between the centroids of two Gaussian fits - one made including the slope parameter, the other made with the slope fixed to zero - with the continuum slope. A conservative cut is made at dvs = 80 m/s to reject lines which might be effected by additional unknown features in the UVES ThAr spectrum.

  8. Large residual rejection: As a final selection step we reject lines surviving all previous selection steps which are fitted at wavelengths at some variance with those expected from the input line list LPWN. In the first pass through the selection algorithm we do not apply this criterion because of possible inaccuracies in the ThAr line-list supplied with the UVES pipeline. In the second pass we reject lines which are fitted at positions more than 0.25 km/s away from the expected position. In the third pass we reduce this parameter to 0.15 km/s.

4. Results
The ThAr line-list formed after the third pass through the selection algorithm, referred to as the final list, is available as an ASCII file, thar_MM201006.dat, and as a TFITS file suitable for use with the UVES pipeline, thar_MM201006.tfits. The latter has some additional lines added from LPWN at the beginning and end of the file to satisfy some requirements of the UVES pipeline. However, these lines are not used in the calibration. The TFITS file should replace the thargood_2.tfits file provided with the UVES pipeline. The first column of thar_MM201006.dat is the wavenumber, omegai, in cm-1 [lambdavac = 1x108/omegai] for each line, i. The second column is the air-wavelength computed from lambdavac using the Edlen (1966) formula for the dispersion of air at 15 degrees C and atmospheric pressure (see Murphy et al. 2001 for detailed discussion). The third column is the logarithm (base 10) of the original listed intensity scaled to the intensity scale of the UVES ThAr spectrum (described above). The fourth and fifth columns provide the line identification when available. If the line is unidentified then "XX" is used as the element designation and an ionization level of either "0" or "1" is given. The final column identifies the source of the wavenumber and which intensity scale the line was originally on: "L" indicates L07, "P" indicates PE83, "N" indicates N73 while "W" indicates W95 or W02. For "XX" lines in L07 the ionization is given as "0" if the unidentified line appears in PE83 and as "1" if L07 claim the line was previously unknown.

The initial input list LPWN contains 13903 lines while the final list contains just 3070. For comparison, the line-list supplied with the UVES pipeline contains 2387 lines over the wavelength range covered by UVES. So, although a large number of lines are rejected in the selection algorithm, there are certainly enough remaining lines to provide a reliable calibration of the UVES wavelength scale. Figure 6 (left) shows the distribution of lines with wavelength in bins which approximate the size of extracted UVES echelle orders. Compared to the initial input list, the distribution of lines is quite uniform. This is mainly because of the rejection of close blends. Note also that there are always more than ~20 useful lines per UVES echelle order in the final list. This is enough to supply a reliable and accurate wavelength calibration solution. Figure 6 (right) shows the distribution of lines at each step of the third pass through the selection algorithm. None of the steps after the rejection of blends removes lines in a strongly wavelength-dependent manner, as expected. Figure 7 (left) shows the contribution from Th, Ar and unidentified lines in the initial input list LPWN and Fig. 7 (right) shows the composition of the final list. One notices the strong decrease in the fraction of unidentified lines through the selection algorithm. This is because most of the unidentified lines are those newly discovered by L07, many of which are quite weak and/or blended at the UVES resolution.


Figure 6: Histograms showing the expected number of lines per echelle order for different line-lists. Left/Top: Comparison of the initial line-list with the list after close blends have been removed. Also a comparison of the final line-list with that provided with the UVES pipeline. Right/Bottom: The reduction of the line-list through the various selection stages.


Figure 7: Histograms showing the contributions from Th, Ar and unidentified lines to the initial (left/top) and final (right/bottom) ThAr line-lists.

We have used the final list to calibrate the UVES ThAr spectrum a final time and the resulting spectrum is available as a FITS file, thar_spec_MM201006.fits, and an ASCII file thar_spec_MM201006.dat. The former is readable with IRAF and the formats of both files are fully explained in the documentation for UVES_popler. In extracting and wavelength calibrating the spectrum with the UVES pipeline, we noted an improvement in the wavelength calibration residuals of more than a factor of 3: Using the version of the UVES pipeline distributed by ESO (i.e. without the modifications described here) and the line-list provided with the UVES pipeline, wavelength calibration residuals of about 140 m/s were acheived for the unbinned ThAr frames discuss above. In our final calibration using the final ThAr line-list, we achieved wavelength calibration residuals 40 m/s over the entire wavelength range without losing too many lines; an average of >=15 lines were utilized per echelle order by the wavelength calibration software.

To demonstrate the strong advantage of using the new line-list (thar_MM201006.dat, thar_MM201006.tfits) in preference to the one distributed by ESO with the UVES pipeline (thargood_2.tfits, pipeline_thar.dat), we have also reduced the same raw ThAr exposures used above with the unmodified UVES pipeline and the thargood_2.tfits line-list. We use the new line-list to trace any distortions of the wavelength scale and the results are plotted in Fig. 8. The ThAr lines in the spectrum are fitted in the same manner as described above (Section 3.2, step 2) and the residual between the fitted wavelength and the wavelength listed in thar_MM201006.dat is calculated. The mean of the residuals shows strong, statistically significant variations with wavelength. For example, the difference between the mean residual at 6000 and 6300 Angstroems is about 75m/s!


Figure 8: Distortions of the wavelength scale introduced by the ESO UVES pipeline and ThAr line-list. A ThAr spectrum was reduced using the original UVES pipeline, without modifications, and its accompanying line-list and the ThAr lines are fitted with Gaussians. The residual between the fitted wavelengths and those expected based on our final line-list, thar_MM201006.dat are plotted versus the wavelength. The structure in the residuals is traced by the green line which is calculated by taking the mean in bins which cover approximately two echelle orders.

References
Edlen B., 1966, Metrologia, 2, 71
Palmer B.A., Engleman R., 1983, Atlas of the Thorium Spectrum, Sinoradzky H. (ed.), Los Alamos National Laboratory
Lovis et al., 2007, A&A, accepted, astro-ph/0703412
Minnhagen L., 1973, J. Opt. Soc. Am., 63, 1185
Murphy M. T., Webb J. K., Flambaum V. V., Churchill C. W., Prochaska J. X., 2001, Mon. Not. Roy. Soc., 327, 1223
Norlen G., 1973, Physica Scripta, 8, 249
Whaling et al., 1995, J. Quant. Spectrosc. Radiat. Transfer, 53, 1
Whaling et al., 2002, J. Res. Natl. Inst. Stand. Technol., 107, 149
De Cuyper J.-P., Hensberge H., 1998, Astron. Astrophys. Supp. Ser., 128, 409
Last updated: 20th October, 2006 by Michael Murphy