Arved Sapar

Modelling of mercury isotope separation in CP stellar atmospheres: Results and problems

Abstract Formation of anomalous isotope abundances in the atmospheres of chemically peculiar (CP) stars can be explained by light-induced drift (LID). This effect is additional to the radiative acceleration and appears due to systematic asymmetry of radiative flux in partly overlapping isotopic spectral line profiles. LID causes levitation of an isotope with a red-shifted spectral line and sinking of an isotope with a blue-shifted line, generating thus diffusive separation of isotopes. We have studied diffusion of mercury as a typical well-studied isotope-rich heavy metal. Our model computations show that in mercury-rich quiescent atmospheres of CP stars LID causes levitation of the heavier mercury isotopes and sinking of the lighter ones. Precise quantitative modelling of the process of isotope separation demands very high-resolution computations and the high-precision input data, including data on hyperfine and isotopic splitting of spectral lines, adequate line profiles and impact cross-sections. Presence of microturbulence and weak stellar winds can essentially reduce the effect of radiative-driven diffusion.

SMART – a computer program for modelling stellar atmospheres

Program SMART (Spectra and Model Atmospheres by Radiative Transfer) has been composed for modelling atmospheres and spectra of hot stars (O, B and A spectral classes) and studying different physical processes in them (Sapar & Poolaae 2003, Sapar et al. 2007). Line-blanketed models are computed assuming plane-parallel, static and horizontally homogeneous atmosphere in radiative, hydrostatic and local thermodynamic equilibrium. Main advantages of SMART are its shortness, simplicity, user friendliness and flexibility for study of different physical processes. SMART successfully runs on PC both under Windows and Linux.

A Pan-Spectral Method of Abundance Determination

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.

Analytical solutions for saturated P Cygni type profiles

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.

Diffusional Separation of Calcium Isotopes in Chemically Peculiar Stellar Atmospheres

Abstract Diffusional separation of calcium isotopes in the atmospheres of hot chemically peculiar stars is studied. In addition to the usual radiative acceleration effect, the light-induced drift is taken into account. We propose that microturbulence in stable stellar atmospheres is generated by the interaction between plasma particles and radiative flux. Formulae for the microturbulent velocity and microturbulence diffusion coefficient are derived. Data on isotopic and hyperfine splitting of the calcium spectral lines have been collected as an input file. The equilibrium Ca isotope concentrations are found in model computations, iteratively correcting the radiative acceleration values. The general picture of Ca isotope stratification is found to be similar to our previous results obtained for Hg isotopes: dominating overabundance of the heaviest isotope. Diffusional stratification of Ca isotope concentrations in atmospheres of late B and early A spectral types are computed and visualized in figures. The isotope abundances on the inner boundary surface were fixed to be the solar ones. The computed Ca II infrared triplet line profiles are compared with the observed line profiles in a high-dispersion spectrum of HD 175640.

A New High-Precision Correction Method of Temperature Distribution in Model Stellar Atmospheres

Abstract The main features of the temperature correction methods, suggested and used in modeling of plane-parallel stellar atmospheres, are discussed. The main features of the new method are described. Derivation of the formulae for a version of the Unsöld-Lucy method, used by us in the SMART (Stellar Model Atmospheres and Radiative Transport) software for modeling stellar atmospheres, is presented. The method is based on a correction of the model temperature distribution based on minimizing differences of flux from its accepted constant value and on the requirement of the lack of its gradient, meaning that local source and sink terms of radiation must be equal. The final relative flux constancy obtainable by the method with the SMART code turned out to have the precision of the order of 0.5 %. Some of the rapidly converging iteration steps can be useful before starting the high-precision model correction. The corrections of both the flux value and of its gradient, like in Unsöld-Lucy method, are unavoidably needed to obtain high-precision flux constancy. A new temperature correction method to obtain high-precision flux constancy for plane-parallel LTE model stellar atmospheres is proposed and studied. The non-linear optimization is carried out by the least squares, in which the Levenberg-Marquardt correction method and thereafter additional correction by the Broyden iteration loop were applied. Small finite differences of temperature (δT/T = 10−3) are used in the computations. A single Jacobian step appears to be mostly sufficient to get flux constancy of the order 10−2 %. The dual numbers and their generalization – the dual complex numbers (the duplex numbers) – enable automatically to get the derivatives in the nilpotent part of the dual numbers. A version of the SMART software is in the stage of refactorization to dual and duplex numbers, what enables to get rid of the finite differences, as an additional source of lowering precision of the computed results.

New Methods in Modeling of Hot Stellar Atmospheres

Abstract 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 θ = T/Teff and β = P/P(Teff) it has been shown that for hot convection-free stellar atmospheres the curves log θ versus log β 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 = Teff and for Teff > 5000 K) can be described in the same manner by curves log θ versus log β 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(Teff), 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 Unsöld-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 Unsöld-Lucy method. The precision estimators as criteria of the modeling algorithms self-consistency and of the computational precision level have been proposed and used.

Analytical solutions for saturated P cygni type profiles II: General case

As in the first part of the present study (Sapar et al., 2002) we use the β-law for velocity of stellar wind and the Sobolev approximation for radiative transfer. Here we have succeeded to derive general and relatively simple analytical formulae in elementary functions for saturated P Cygni type line profiles if parameter 2β is arbitrary positive integer (in the first part we studied the cases 2β ≤ 4). The four terms obtained describe contributions to the line profile due to isotropic and anisotropic parts of optical thickness in the source function of the light-scattering layer followed by isotropic and anisotropic parts of multiple scattering. The limits of acceptability of the Sobolev approximation for β-law have been discussed and specified.

Expression of Turbulence and the Variability of Stellar Winds in Resonance Line Profiles

Observations suggest that supersonic turbulent velocities are generated in stellar winds by instabilities. We treat these velocities as thermal velocity distributions (i.e., Gaussian functions) with higher equivalent temperatures in the radial direction. We derived a general frequency redistribution function assuming coherent photon scattering in the rest frame of each particle for turbulence and partially coherent thermal scattering of photons. In such a scattering layer, the source function grows with optical depth. We found the source function, the emergent scattered radiation intensity at the outer and inner surfaces of the layer, and the increased radiative acceleration in the stellar wind due to the transfer of photon momentum by the prevalence of backscattering (i.e., due to the recoil effect). This effect explains the wide, dark plateaus seen in resonance line profiles and approximately doubles the momentum transfer to the stellar wind. Collisions of high-speed clumps produce superionization and large high-speed clumps are seen as narrow absorption components (NACs).

Stellar wind of χ2 from its resonance lines

K e y words: stars: atmospheres, circumstellar matter, stellar wind techniques: spectroscopic line: profiles