“Solar” oscillator strength scale and determination of the LTE silicon abundance in the solar atmosphere

Abstract

We determine LTE abundance of silicon from 65 lines of Si I using one-dimensional semiempirical models of the solar atmosphere HOLMUL, MACKKL, and VAL,C. Our list of lines is considerably larger than lists used earlier. We confirm the reliability of the oscillator strength scale of E.A. Gurtovenko and R.I. Kostik for Si I lines that was based on the fitting to the observed solar equivalent widths. It is shown that this scale is displaced by +0.073 dex and −0.026 dex from experimental scales derived by Becker et al. and Garz, respectively. The difference between “solar” and experimental oscillator strength scales hardly depends on their lower excitation potentials, wavelengths, and equivalent widths. This difference can be interpreted as a total error caused by the choice of the one-dimensional model of atmosphere, the neglect of NLTE effects, the ignoring of the granulation, errors of the van der Waals damping constant, the microturbulence velocity, and the observed equivalent width. We study the effect of changes in various input parameters on the obtained LTE abundance of silicon and show that both the experimental scale of Becker et al. and the displaced “solar” scale produce almost the same silicon abundance. A total root-mean-square error of the abundance, which is caused by errors in equivalent widths and the microturbulence velocity, is 0.02 dex. The use of the semiclassical theory of Anstee, Barklem, and O’Mara for the description of the van der Waals damping constant leads to the emergence of a correlation of the abundance obtained from Si I lines with the equivalent width. There is no such correlation when using the classical Unsold approximation with an enhancement factor E = 1.5. On average, differences in abundances obtained using the mentioned approximations do not exceed 0.03 dex. At E = 1.5, the LTE silicon abundance calculated using the HOLMUL model with “solar” oscillator strengths referred to the experimental scale of Becker et al. is equal to 7.594 ± 0.015, whereas the LTE silicon abundance calculated using the VAL,C model is 7.623 ± 0.021.