Milan S. Dimitrijević and Nenad Milovanović 11th Serbian Conference on Spectral Line Shapes in Astrophysics August, 21-25, 2017 Šabac, Serbia CALCULATION OF STARK BROADENING PARAMETERS OF S II MULTIPLETS AND STELLAR MODELS ANALYSIS Milan S. Dimitrijević and Nenad Milovanović Astronomical Observatory Belgrade, Serbia

Astrophysical importance: XI SCSLSA August, 21-25, 2017, Šabac, Serbia STARK BROADENING DATA Astrophysical importance: 1. Analysis and modeling of stellar spectra 2. Analysis, modeling and diagnostics of stellar plasma 3. Abundances determination 4. Stellar opacity calculations 5. Stellar luminosity calculations 6. Nuclear processes in stellar interiors

XI SCSLSA August, 21-25, 2017, Šabac, Serbia Stark broadening of spectral lines is the dominant pressure broadening mechanism in hot, early-type, stars and white dwarf atmospheres. This type of broadening might also be important in interstellar molecular and ionized hydrogen clouds and in cooler stars such as solar type ones for transitions involving higher principal quantum numbers. The Stark broadening mechanism is also important for the investigation, analysis, and modeling of B-type, and particularly A-type, stellar atmospheres, as well as for DA, DB, DO white dwarf atmospheres.

XI SCSLSA August, 21-25, 2017, Šabac, Serbia Maximum (top line) and minimum (bottom line) of the ratio of the equivalent widths with and without Stark broadening (EWSt/EW0) for different types of stars (Popović L.Č., Simić S., Milovanović N., Dimitrijević M.S. Astrophysical Journal Supplement Series, 135 (2001) 109.)

XI SCSLSA August, 21-25, 2017, Šabac, Serbia The electron-impact broadening data are needed for various problems in astrophysics and physics, as e.g. for diagnostic and modeling of laboratory and stellar plasma, investigation of its physical properties and for abundance determination. These investigations provide us with useful information for modeling of stellar evolution. As an example, the abundances study in stellar atmospheres provides evidences for the chemical composition of the stellar primordial cloud, processes occurring within the stellar interior, and the dynamical processes in stellar atmosphere.

XI SCSLSA August, 21-25, 2017, Šabac, Serbia Advanced calculations of the Stark broadening parameters using the strong-coupling quantum-mechanical method is so complicated that only a limited number of data for spectral lines originating from low-lying transitions was calculated adequately.

XI SCSLSA August, 21-25, 2017, Šabac, Serbia Within semiclassical perturbation method the full width at half-intensity maximum (FWHM - W) and the shift (d) of an isolated line, from the transition between the initial level i and the final level f, with perturbation levels i' and f' is expressed as where N and v are the electron density and the velocity of perturbers, respectively, f(v) is the Maxwellian distribution of electron velocities, and ρ the impact parameter of the free electron colliding with the emitter.

and the elastic contribution to the width is given by XI SCSLSA August, 21-25, 2017, Šabac, Serbia The inelastic cross-section σii'(v) (respectively, σff'(v)), can be expressed by an integration of the transition probability Pjj'(ρ,v) (j=i, f and j'=i', f'), over the impact parameter ρ as and the elastic contribution to the width is given by Here, σel is the elastic cross-section, while φp(r -4) and φq(r -3), are phase shifts due to the polarization and quadripolar potential, respectively.

Sahal-Brechot S. Astronomy and Astrophysics, 1 (1969) 91. XI SCSLSA August, 21-25, 2017, Šabac, Serbia Griem H.R. Spectral Line Broadening by Plasmas, New York and London, Academic Press (1978). Sahal-Brechot S. Astronomy and Astrophysics, 1 (1969) 91. Sahal-Brechot S. Astronomy and Astrophysics, 2 (1969) 322. Dimitrijević M.S., Sahal-Brechot S., Bomier V. Astronomy and Astrophysics Supplement Series, 89 (1991) 581. Sahal-Brechot S. Astronomy and Astrophysics, 35 (1974) 319. Sahal-Brechot S. Astronomy and Astrophysics, 245 (1991) 322. Fleurier C., Sahal-Brechot S., Chapelle J. J. Quant. Spectrosc. Radiat. Transfer, 17 (1977) 595. Dimitrijević M.S., Sahal-Brechot S. Phys. Scr., 54 (1996) 50. Sahal-Brechot S., Dimitrijević M.S., Ben Nessib N. Atoms, 2 (2014) 225.

P I isoelectronic sequence ground state: [Ne]3s23p3 3So3/2 XI SCSLSA August, 21-25, 2017, Šabac, Serbia Ionized sulfur (S II) P I isoelectronic sequence ground state: [Ne]3s23p3 3So3/2 ionization energy: 23.32 eV (188 200 cm-1) Energy levels for these calculations have been taken from NIST Atomic Spectra Database Levels Data, while for the needed oscillator strengths, Bates-Damgard method has been used together with the tables of Oertel and Shomo.

XI SCSLSA August, 21-25, 2017, Šabac, Serbia Electron-, proton-, and helium-ion-impact broadening parameters for S II multiplets. Calculated wavelengths (λ) and parameters C are given. This parameter, when divided with corresponding Stark width, gives an estimate for the maximal perturber density for which the line may be treated as isolated. Perturber density is 1021 m-3.   Multiplet T (kK) Electrons Protons Ionized Helium width (Å) shift (10-1 Å) width (10-1 Å) (10-2 Å) width shift (10-2 Å) 3p23d 4F - 3p2(3P)4p 4Do λ=5606.11 Å C=0.63∙1020 5 0.836 0.558 0.400 0.126 0.507 0.125 10 0.651 0.407 0.598 0.268 0.703 0.255 20 0.513 0.346 0.743 0.474 0.804 0.420 30 0.454 0.247 0.803 0.581 0.860 0.512 50 0.406 0.227 0.875 0.747 0.922 0.627 100 0.365 0.199 0.950 0.911 0.967 0.751 3p24s 4P - λ=5428.64 Å C=0.77∙1020 1.070 -1.890 0.337 -0.866 0.431 -0.799 0.808 -1.350 -0.156 0.607 -1.330 0.615 -1.030 0.656 -0.230 0.701 -1.950 0.549 -0.925 0.713 -0.264 0.752 -2.180 0.496 -0.821 0.784 -0.307 0.815 -2.520 -0.648 0.867 -0.367 0.863 -3.010 Experimental widths Multiplet T (kK) width (Å) Acc. 3p23d 4F - 3p2(3P)4p 4Do   λ=5606.11 Å 11.6 0.77 C+ 23.5 0.38 3p24s 4P - λ=5428.64 Å 0.69 B+ 0.46 Konjević N., Wiese W.L. JPCRD, 5 (1976) 259.

XI SCSLSA August, 21-25, 2017, Šabac, Serbia Stark widths (FWHM) (thinner lines) and Doppler width (thicker line) for S II 3p23d 4F - 3p2(3P)4p 4Do (λ=5606.11 Å) as a function of atmospheric layer temperatures. Stark widths are shown for 8 atmospheric models with effective temperatures Teff = 7000 - 30000 K, corresponding to spectral classes (Sp) from F0 to B0, log g = 4 and turbulent velocity vt = 0 km/s.

XI SCSLSA August, 21-25, 2017, Šabac, Serbia Stark widths (FWHM) (thinner lines) and Doppler width (thicker line) for S II 3p23d 4F - 3p2(3P)4p 4Do (λ=5606.11 Å) as a function of atmospheric layer temperatures. Stark widths are shown for 7 values of model gravity log g = 2 - 5, Teff = 10000 K and vt = 0 km/s.

XI SCSLSA August, 21-25, 2017, Šabac, Serbia servo.aob.rs

XI SCSLSA August, 21-25, 2017, Šabac, Serbia

11th Serbian Conference on Spectral Line Shapes in Astrophysics August, 21-25, 2017, Šabac, Serbia

XI SCSLSA August, 21-25, 2017, Šabac, Serbia

XI SCSLSA August, 21-25, 2017, Šabac, Serbia

XI SCSLSA August, 21-25, 2017, Šabac, Serbia

Thank you! Milan S. Dimitrijević web: mdimitrijevic.aob.rs XI SCSLSA August, 21-25, 2017, Šabac, Serbia Milan S. Dimitrijević web: mdimitrijevic.aob.rs email: mdimitrijevic@aob.rs Nenad Milovnović web: nmilovanovic.aob.rs email: nmilovanovic@aob.rs Thank you!