In the present study we had three main aims. First to study the possibility of reducing the initial model atmosphere data to short analytical polynomials. The second was to use as the depth variable the logarithm of the local gas pressure instead the Rosseland mean. The third aim was to check the applicability of the derived formulae and proposed computation methods to obtain high precision self-consistent results in modeling hot plane-parallel stellar atmospheres. Introducing the dimensionless (reduced) local quantities theta = T/T-eff and beta = P/P(T-eff) it has been shown that for hot convection-free stellar atmospheres the curves log theta versus log beta reduce an initial grid of models to simple polynomials and bring forth some general features of the model stellar atmospheres. Even for stellar atmospheres having the convective zones in the deeper atmospheric layers, the outer part of the atmosphere (up to T = T-eff and for T-eff > 5000 K) can be described in the same manner by curves log theta versus log as for the hotter stars. Iterative modeling of any hot stellar atmosphere can be started from these formulae (obtained for solar abundances), using rational polynomial ratios for P(T-eff), obtaining from these data the needed T versus P dependence. To check suitability of the formulae, the iterative correction of the model stellar atmospheres has been carried out by the traditional Unsold-Lucy method and by the novel least squares optimization based on Levenberg-Marquardt method, followed by Broyden correction loop. It has been shown that the flux constancy obtained by it is almost 2 dex higher than obtained by the Unsold-Lucy method. The precision estimators as criteria of the modeling algorithms self-consistency and of the computational precision level have been proposed and used.
We present formulae suitable for computing LID acceleration and corresponding diffusive segregation of isotopes in atmospheres of CP stars.
We propose a new method for determination of element abundances in stellar atmospheres aimed for the automatic processing of high-quality stellar spectra. The pan-spectral method is based on weighted cumulative line-widths \(Q_\lambda = \int_{\lambda _0 }^\lambda {\left| {\frac{{dR_\lambda }}{{dZ}}} \right|} (1 - R_\lambda )d\lambda \), where R λ is residual flux and Z is abundance of studied element. Difference in quantities Q λ found from synthetic and observed spectra gives a correction to the initial abundance. Final abundances are then found by rapidly converging iterations. Calculations can be made for many elements simultaneously and do not demand supercomputers.
The high-precision analytical expression of the Holtsmark line profile function is found for the intermediate region of its argument in addition to the former known polynomial coefficients obtained by the use of series expansions. By numerical computations it was found that for high-precision results 30 members of series expansion are due to use in computations. For the intermediate region the best fit approximation as a ratio of polynomials has been obtained. The relative error of these expressions in the region of their validity is less than 10(-7). The twice integrated formula for convolution of Stark, Doppler and Lorentz profile functions has been used. By the use of general series expansions the analytical series expressions for corresponding three line profile function ingredients of hydrogenic particles have been derived at small and large arguments of the Holtsmark line profile function. For the intermediate argument values, however, the line profile is to be found using a numerical integration scheme.
Main theoretical formulae and some computational results of evolutionary segregation of Hg isotopes due to light-induced drift in the atmospheres of chemically peculiar stars have been represented.
A short review is given of a new compact FORTRAN code "SMART" developed for modeling radiative transfer, and for the study of physical processes in stellar atmospheres. The main structural units and specific features of the codes are described. For the computation of NLTE state-populations, a simulation of the physical process of time-relaxation to the nonequilibrium state is used.
Analytical formulae for single P Cygni type saturated resonance line profiles in stellar winds have been derived. The limbdarkening and presence of underlying intrinsic atmospheric profile have been ignored. The Sobolev approximation for radiative transfer has been used and the general velocity law has been specified by widely used β parameter. The analytical formulae for the saturated resonance line profiles can be found for cases when 2β is an integer. The formulae for 2β = 1,2, 3 and 4 have been found by us. Also the formulae for calculating the line profiles in the cases of external and internal sharp truncation (cutoff) of the scattering shell have been given. Some characteristic line profiles have been presented. It has been shown that the turbulence-generated isotropic dominant backscattering of radiation in stellar winds generates wide dark plateaux in the blue wings of spectral lines, and the slopes of plateaux are shaped by turbulence.
Analytical formulae for singlet P Cyg-type saturated line profiles are derived for velocity laws with beta = 1/2 and beta = 1.
It is shown that deviations from LTE in electron populations of the ionization and excitation states can be estimated by simple formulae.These formulae are applied to study the deviations from LTE in the ionization degrees and in the upper state populations of the resonance lines in the model stellar atmospheres.
Main theoretical formulae and some computational results of evolutionary segregation of Hg isotopes due to light-induced drift in the atmospheres of chemically peculiar stars have been represented.
