3 The line list

The list is given as Table 1 available in electronic form via anonymous ftp at the CDS and UAO ftp servers (see earlier footnote). It contains data for 4891 spectral lines. The data columns in the table are:

1. Packed parameter of form Z + 0.01(Z-N), where Z is the atomic number and N is the number of electrons.

2. Air Wavelength (Å).

3. Lower level J quantum number.

4. Upper level J quantum number.

5. Lower level energy (eV).

6. Upper level energy (eV).

7. Lower level energy (cm^-1).

8. Lower level series limit (cm^-1).

9. Upper level energy (cm^-1).

10. Upper level series limit (cm^-1).

11. Lower level l quantum number.

12. Upper level l quantum number.

13. Cross-section $\sigma$ for v=10000 m s^-1 (a.u.).

14. Velocity parameter $\alpha$.

15. Log of line width (FWHM) per perturber at $T= \hspace*{5mm} 10000$ K (rad s^-1 cm³).

16. Temperature dependence exponent $(1-\alpha)/2$.

A short sample of the data between 5327.0 and 5329.5 Å is presented in Table 2. We show later the effects on synthesis of this region.

  

Table 2: Sample of Table 1 for the region 5327.0 to 5329.5 Å

The broadening data from the list is incorporated into VALD which provides various tools for intelligent retrieval of atomic data, which can be accessed at http://www.astro.univie.ac.at/~vald. The list is currently known as "VALD 2: VanderWaals'' under the VALD-2 referencing system, and under the current default configuration for VALD is always used when available. Under VALD-2, for reasons of continuity, the value returned is the logarithm of the full line width at 10000 K, and there is no indication of the temperature dependence. Many spectrum synthesis programs use this value assuming the line width is proportional to T^0.3 which is the result from the Unsöld theory ([1955]) using the van der Waals interaction. This would correspond to a velocity parameter of $\alpha=0.4$ in the Anstee & O'Mara theory as the cross-section is related to temperature by

$$\sigma \propto T^{\frac{1-\alpha}{2}}.$$ (1)

Calculations have usually found $\alpha$ to be somewhat lower (between 0.2 and 0.4), implying a slightly stronger dependence on temperature, typically of the form T^0.38. However approximation to T^0.3 usually has only a small effect on the line shape.

In a future version of VALD, users will be able to choose either the current format or to obtain both the line broadening cross-section and the velocity parameter.

3.1 List analysis

We now briefly present some analysis designed to demonstrate the overall impact of the new data.

Data were extracted from VALD using the default configuration but not including this list. That is, the best data otherwise available in VALD. These values otherwise in VALD are those from the Kurucz CDROM line lists, which were mostly computed from the Unsöld theory (some have been corrected with better calculations such as the Mg b lines discussed later). These values were then compared with the values provided by our new list.

Some 583 lines did not previously have data for broadening by neutral hydrogen available in VALD. For those lines where data were previously available we compared the line widths per perturber at 10000 K. Figures 2 and 3 show the ratio of the new width to the previous VALD line widths, plotted against $\log(gf)$ and excitation respectively. The data show a general increase in the value for the broadening. On average, the line width increases by a factor 1.88 (standard deviation 0.79) when excluding lines with no previous data.

Figure 2: Comparison of the new data with that otherwise available in VALD. The ratio of the two line widths at 10000 K is plotted against the $\log(gf)$ value from VALD

Figure 3: Comparison of the new data with that otherwise available in VALD. The ratio of the two line widths at 10000 K is plotted against the lower level excitation. Points on the x axis represent lines for which data were not previously available in VALD

In Fig. 2 the most noticeable feature is the apparent "banding'' of the data into three groups. The largest of these groups is the band between the ratios of 1 and 2. There is then a band at higher ratios and a rather small group with ratios less than unity. In Fig. 3, we see that the upper band almost completely consists of lines of higher excitation. The most logical explanation for this is that the calculations using the Anstee & O'Mara theory treat better the states of higher quantum number l, which are often more excited, than the Unsöld theory which makes no distinction between angular momentum states. In Fig. 4, we show the ratio plotted against the transition type, and this plot supports this explanation. It shows that the upper band primarily consists of transitions with upper p- and d- states while the middle and lower bands are almost exclusively lines with upper s-states. It also supports the effect first found by Carter ([1949]) for neutral iron lines in the solar spectrum, that for a given binding energy of the optical electron in the upper state of the transition, lines with an upper s-state are broadened more strongly than those with an upper p-state. Although in Fig. 4 there is no line selection on the basis of the binding energy of the optical electron, lines with a transition index of 2 which correspond to transitions with an upper s-state are generally more strongly enhanced than lines with a transition index of 1 which correspond to lines with an upper p-state. In the specific case of iron lines Anstee et al. ([1997]) have shown that the new line broadening theory accounts quantitatively for the Carter effect whereas conventional van der Waals theory predicts only a very slight effect which does not match the solar spectrum.

Figure 4: Comparison of the new data with that otherwise available in VALD. The ratio of the two line widths at 10000 K is plotted against the transition type indicated by $2 l_{{\rm lower}}+l_{{\rm upper}}$ where $l_{{\rm lower}}$ and $l_{{\rm upper}}$ are the lower and upper state l quantum numbers. Hence 1 corresponds to s-p, 2 to p-s, 4 to p-d, 5 to d-p, 7 to d-f and 8 to f-d. The lack of lines with index 5 and above actually reflects that data were often not previously available for these lines in VALD

Figure 5: Plot showing the two bluest lines of the Ca II infrared triplet. Synthetic spectra are shown for VALD with new data (full) and without (dashed) compared to observed (double line) flux spectra (NSO/Kitt Peak Data)

Figure 6: Plot showing synthetic spectra for the region around the strong line of Fe at 5328 Å. Synthetic spectra are shown for VALD with new data (full) and without (dashed) compared to observed (double line) flux spectra (NSO/Kitt Peak Data)

The relatively small number of lines making the band with ratios less than unity in Fig. 2 also requires comment. As we see in Fig. 4, this band results almost entirely from s-p transitions. We identified the lines with ratios of less than 0.9 and tried to determine the reason for the result. Notably the Mg b lines were among these lines. This particular case is explained by the fact that the data in the Kurucz lists for these lines is a corrected value as described by Castelli et al. ([1997]), not the Unsöld theory result. The remainder of the lines in this band were all lines of V, Cr, Mn, Fe or Co. We checked a number of these lines and found that they are double electron excitations with highly excited parent configurations. We assume that our taking into account these effects is responsible for the differences with the Kurucz calculations.

3.2 Impact on spectral synthesis

To further demonstrate the impact of the new data we have selected two spectral regions as examples, and compared synthesis using VALD data in the case where the new list is included with that where the new data is not included. The data have been tested against the solar spectrum in previous papers, hence our aim here is merely to show examples of how the new list effects VALD.

For our synthesis we use the SYNTH code of Piskunov ([1992]) which assumes LTE. We use the Holweger & Müller ([1974]) model atmosphere.

Figures 5 and 6 show two examples of the difference made by inclusion of the new data. In each case we used meteoritic abundances for elements (Grevesse et al. [1996]). The Ca II triplet example was chosen as an example where the data makes quite a large positive impact to the VALD data for an important spectral region. The Fe I 5328 Å line region was chosen as example of the impact on a reasonably complex region of the spectrum containing lines of varying strengths. We performed similar comparisons for a number of regions and believe these examples to be representative of the general effect.

In the synthesis of the Fe I 5328 Å region, for the Cr I lines at 5328.3 Å and 5329.1 Å we needed to adjust the wavelengths slightly from those in VALD to match observations. Also, the $\log(gf)$ of the Ti I line at 5328.7 Å needed to be reduced. Both plots show a general improvement using the new data, compared to observation. The fits support the assumption of equality between solar and meteoritic abundances and the new line broadening data within the errors of the analysis.

As part of the transition to VALD-3, we plan to systematically assess the accuracy of spectral lines visible on the Sun by synthesizing the whole spectrum and verifying line identification, accuracy of the central wavelengths, oscillator strengths, broadening parameters and presence of NLTE effects. This project will provide an additional input for the continuation of this work by creating a list of lines that require better quality damping constants.