Han Uitenbroek
NSO/Sacramento Peak

The solar abundance value that has been used for the past decades (log A_F = 4.56 on a scale where log A_H = 12.00), was determined by Hall and Noyes^[1] based on dated theoretical values of the energy levels and oscillator strengths of the HF molecule, which is the only fluoride compound that produces observable lines in the visible part of the solar spectrum. The HF molecule has a relatively low dissociation energy of 5.87 eV, causing it to be only significantly present in the solar atmosphere in the cool umbrae of sunspots. Therefore, the solar fluorine abundance has to be determined by fitting profiles of HF lines to those observed in umbral spectra, as indeed was done by Hall and Noyes. Because of the fragility of the HF molecule special care has to be taken to choose the right temperature model for fluorine abundance determination.

Recently, new values of the parameters for HF rotation-vibration lines became available via the HITRAN data base^[2], prompting an effort to verify the solar fluorine abundance determination with these improved molecular data. We have undertaken such an effort (see Ref [3]), based on the solar umbral atlas from Ref [4], and using radiative equilibrium models of Kurucz with different effective temperatures to accurately update the solar fluorine abundance.

Figure 1 | Comparison of observed OH line spectrum (diamonds) with calculated spectra from models with different effective temperatures, approximately representative of a sunspot umbra. The Fe I line at 1564.8nm is completely split by the magnetic field of 2500 G. The sigma components of the latter line are significantly broadened because the FTS instrument had relatively large aperture sampling different magnetic field strengths. The width of the OH lines is less affected because of the small Lande g factors of these molecular lines.

To determine the proper effective temperature corresponding to the umbral atlas we first fitted lines of the OH molecule, which are strongly temperature dependent, at 1.5 micron. The results are shown in Fig. 1. Clearly the atmosphere with an effective temperature of 4250K comes closest to reproducing the observed OH lines, in particular the weaker ones, which form at the same heights as the HF line we wish to reproduce. Next we varied the fluorine abundance in the T_eff = 4250 K model until we best fit the 8 HF lines in the umbral atlas. The results for one of the lines, the R 9 line, is shown in Fig. 2, where the atlas is plotted in light-blue diamonds and the model spectrum in the solid black curve. We take the Zeeman splitting of the OH lines as well as the HF lines into account in these modeling efforts, even though typical Lande g factors are only of order 0.1.

Figure 2 | Best fit of the HF R 9 line (solid black) compared with the umbral atlas (blue diamonds). Lines to the left are first overtone vibration-rotation lines of CO.

The new solar abundance for the best fit is log A_F = 4.40 +/- 0.25, is fortunately only slightly lower than the old value determined by Hall and Noyes, and is very close to the abundance value determined in chondrite meteorites of log A_F = 4.42.

References

[1] Hall, D. N. B., & Noyes, R. W. 1969, ApJ Lett, 4, 143
[2] Rothman, L. S., Gordon, I. E., Babikov, Y., et al. 2013, JQSRT, 130, 4R
[3] Maiorca, E., Uitenbroek, H., Uttenthaler, S., Randich, S., Busso, M., & Magrini, L. 2014, ApJ, 788, 149
[4] Wallace, Hinkle, & Livingston 1981, in “Sunspot Umbral Spectra in the Region 4000 to 8640 cm^-1 (1.16 to 2.50 microns)”, NSO Technical Report #01-001