NLTE formation of the solar spectrum of silicon: Abundance of silicon in a three-dimensional model of the solar atmosphere

We investigated the NLTE formation of the solar spectrum of neutral silicon using 3D hydrodynamic model of the solar atmosphere and realistic atomic model. We show that, within the intergranular region, combined action of the deficit in the source function and excess in opacity due to the overpopulation of the lower Si I levels leads to a considerably higher increase in the central depth D and equivalent width W of these lines as compared to the granules. We have fitted silicon abundances A _W and A _D from the equivalent widths W and central depths D for 65 Si I lines using a 3D model. We show that a total error in the calculated silicon abundance due to neglecting NLTE and 3D effects, as well as the uncertainty in the van der Waals broadening constant γ₆, turns out to be ?0.1 dex. Using a semiclassical theory by Anstee, Barklem, and O’Mara in calculating γ₆ yields a fair coincidence between the values of A _W and A _D , because the average difference A _W — A _D does not exceed 0.01 dex for both NLTE and LTE. When applying the Unsold’s approximation in calculating γ₆ with an enhancement factor E = 1.5, the abundances A _W and A _D proved to be in disagreement with one another. We analyzed the “solar” oscillator strength scale by Gurtovenko and Kostik, as well as the experimental one by Garz and Becker et al. We show that using “solar” oscillator strengths log gfw leads to a minimum trend with the equivalent widths for NLTE abundances A _W , A _D , their difference A _W — A _D , and standard deviations. The NLTE abundance of silicon obtained using solar oscillator strength scale by Gurtovenko and Kostik is A _W ^NTLE = 7.549 ± 0.016. This value is in good agreement with the value of silicon abundance recommended by Grevesse and Sauval for the CI chondrite meteorites.