Modelling stellar atmospheres becomes increasingly demanding as more accurate observations draw a more complex picture of how real stars look like. What could be called a normal star becomes ...increasingly rare because of, e.g., significant deviations from the classical solar abundance pattern and clear evidence for stratification of elements in the atmospheres as well as surface inhomogeneities (spots) causing further severe deviations from “standard” atmospheres. We describe here a new code for calculating LTE plane-parallel stellar model atmospheres for early and intermediate type of stars which has been written in Compaq Fortran 95 and can be compiled for Windows and Linux/UNIX computer platforms. The code is based on modified atlas9 subroutines (Kurucz) and on spectrum synthesis codes written by V. Tsymbal with the main modifications of input physics concerning the block for opacity calculation. Each line contributing to opacity is taken into account for modelling the atmosphere, similar to synthetic spectrum calculations. This approach, which we call the line-by-line (LL) technique, avoids problems resulting from statistical methods (ODF, OS) and allows to calculate complex models with abundances which are not simply scaled from a standard pattern (usually the solar abundances) and which can be even depth dependent. Stratification is considered in this context as an empirical input parameter which has to be derived from observations. Due to the implemented numerical methods, mainly in the opacity calculation module, our code produces model atmospheres with modern PCs in a time comparable to that required by classical routines.
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The stellar parameters of RR Lyrae stars vary considerably over a pulsation cycle, and their determination is crucial for stellar modelling. We present a detailed spectroscopic analysis of the ...pulsating star RR Lyr, the prototype of its class, over a complete pulsation cycle, based on high-resolution spectra collected at the 2.7-m telescope of McDonald Observatory. We used simultaneous photometry to determine the accurate pulsation phase of each spectrum and determined the effective temperature, the shape of the depth-dependent microturbulent velocity, and the abundance of several elements, for each phase. The surface gravity was fixed to 2.4. Element abundances resulting from our analysis are stable over the pulsation cycle. However, a variation in ionization equilibrium is observed around minimum radius. We attribute this mostly to a dynamical acceleration contributing to the surface gravity. Variable turbulent convection on time-scales longer than the pulsation cycle has been proposed as a cause for the Blazhko effect. We test this hypothesis to some extent by using the derived variable depth-dependent microturbulent velocity profiles to estimate their effect on the stellar magnitude. These effects turn out to be wavelength dependent and much smaller than the observed light variations over the Blazhko cycle: if variations in the turbulent motions are entirely responsible for the Blazhko effect, they must surpass the scales covered by the microturbulent velocity. This work demonstrates the possibility of a self-consistent spectroscopic analysis over an entire pulsation cycle using static atmosphere models, provided one takes into account certain features of a rapidly pulsating atmosphere.
Context. High-resolution spectra of some chemically peculiar stars clearly demonstrate the presence of strong abundance gradients in their atmospheres. However, these inhomogeneities are usually ...ignored in the standard scheme of model atmosphere calculations, breaking the consistency between model structure and spectroscopically derived abundance pattern. Aims. In this paper we present the first empirical self-consistent stellar atmosphere model of the roAp star HD 24712 with stratification of chemical elements included, and which is derived directly from the observed profiles of spectral lines without time-consuming simulations of physical mechanisms responsible for these anomalies. Methods. We used the LLmodels stellar model atmosphere code and DDAFIT minimization tool for analysis of chemical element stratification and construction of a self-consistent atmospheric model. Empirical determination of Pr and Nd stratification in the atmosphere of HD 24712 is based on NLTE line formation for Pr II/III and Nd II/III with the use of the DETAIL code. Results. Based on an iterative procedure of stratification analysis and subsequent re-calculation of model atmosphere structure, we constructed a self-consistent model of HD 24712, i.e. the model whose temperature-pressure structure is consistent with the results of the stratification analysis. It is shown that stratification of chemical elements leads to considerable changes in model structure compared to the non-stratified homogeneous case. We find that accumulation of rare earth elements (REE) allows for the inverse temperature gradient to be present in the upper atmosphere of the star with a maximum temperature increase of about 600 K. Conclusions.
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Context. Chemically peculiar A-type (Ap) stars are a subgroup of the CP2 stars that exhibit anomalous overabundances of numerous elements, e.g. Fe, Cr, Sr, and rare earth elements. The pulsating ...subgroup of Ap stars, the roAp stars, present ideal laboratories to observe and model pulsational signatures, as well as the interplay of the pulsations with strong magnetic fields and vertical abundance gradients. Aims. Based on high-resolution spectroscopic observations and observed stellar energy distributions, we construct a self-consistent model atmosphere for the roAp star 10 Aquilae (HD 176232). It accounts for modulations of the temperature-pressure structure caused by vertical abundance gradients. We demonstrate that such an analysis can be used to determine precisely the fundamental atmospheric parameters required for pulsation modelling. Methods. Average abundances were derived for 56 species. For Mg, Si, Ca, Cr, Fe, Co, Sr, Pr, and Nd, vertical stratification profiles were empirically derived using the DDAFit minimisation routine together with the magnetic spectrum synthesis codeSynthmag. Model atmospheres were computed with the LLmodels code, which accounts for the individual abundances and stratification of chemical elements. Results. For the final model atmosphere, Teff = 7550 K and log (g) = 3.8 were adopted. While Mg, Si, Co, and Cr exhibit steep abundance gradients, Ca, Fe, and Sr showed much wider abundance gradients between logτ5000 = −1.5 and 0.5. Elements Mg and Co were found to be the least stratified, while Ca and Sr showed strong depth variations in abundance of up to ≈ 6 dex.
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Context. Historically, stellar model atmospheres with scaled solar abundances (for all elements heavier then helium) have been widely used for analysis of the atmospheres of chemically peculiar (CP) ...stars. However, in reality, atmospheres of CP stars demonstrate a variety of abundances, not necessarily scaled to the solar composition. Aims. We study the effects of individual abundance patterns on the model atmospheres of CP stars. The main purpose is to conduct a systematic homogenous study to explore the abundance parameter space occupied by these stars. Methods. We calculated a grid of the model atmospheres of A and B stars ({\log g=4.0}) for different effective temperatures ({T_{\rm eff}=8000}, 9500, 11 000, 13 000, 15 000, 20 000 K) and chemical compositions. We used the LLMODELS code to compute model atmospheres with individual abundance patterns, varying the following elements: C, Mg, Si, Ca, Ti, Cr, Mn, Fe, Ni, Sr, Eu and He. We compared the computational results for these peculiar model atmospheres with those of reference model atmospheres of the solar chemical composition. Results. We present a homogeneous study of model atmosphere temperature structure, energy distribution, photometric indices in the u\upsilon by\beta and \Delta a systems, hydrogen line profiles, and the abundance determination procedure as it applies to CP stars. In particular, we found that Si, Cr and Fe are the main elements to influence model atmospheres of CP stars, and thus to be considered in order to assess the adequacy of model atmospheres with scaled solar abundances in application to CP stars. We provide a theoretical explanation of the robust property of the \Delta a photometric system to recognize CP stars with peculiar Fe content. Also, the results of our numerical tests using model atmospheres with one or several elements overabundant (Si and Fe by +1 dex, Cr by +2 dex) suggest that the uncertainty of abundance analysis in the atmospheres of CP stars using models with scaled abundances is less than \pm0.25 dex. If the same homogeneous models are used for the abundance stratification analysis then we find that the uncertainty of the value of the vertical abundance gradient is within an 0.4 dex error bar. Conclusions. Model atmospheres with individual abundance patterns should be used in order to match the actual anomalies of CP stars and minimize analysis errors.
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Aims. We simulate the light variability of the Ap star ε UMa using the observed surface distributions of Fe, Cr, Ca, Mn, Mg, Sr, and Ti obtained with the help of the Doppler imaging technique. ...Methods. Using all photometric data available, we specified light variations of ε UMa modulated by its rotation from far UV to IR. We employed the LLmodels stellar model atmosphere code to predict the light variability in different photometric systems. Results. The rotational period of ε UMa is refined to 5ḍ088631(18). It is shown that the observed light variability can be explained as a result of the redistribution of radiative flux from the UV spectral region to the visual caused by the inhomogeneous surface distribution of chemical elements. Among seven mapped elements, only Fe and Cr contribute significantly to the amplitude of the observed light variability. In general, we find very good agreement between theory and observations. We confirm the important role of Fe and Cr in determining the magnitude of the well-known depression around 5200 Å by analyzing the peculiar a-parameter. Finally, we show that the abundance spots of considered elements cannot explain the observed variabilities in near UV and β index, which probably have other causes. Conclusions. The inhomogeneous surface distribution of chemical elements can explain most of the observed light variability of the A-type CP star ε UMa.
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Context. For asteroseismic modelling, analysis of the high-accuracy light curves delivered by the Kepler satellite mission needs support by ground-based, multi-colour and spectroscopic observations. ...Aims. We determine the fundamental parameters of SPB and β Cep candidate stars observed by the Kepler satellite mission and estimate the expected types of non-radial pulsators. Methods. We compared newly obtained high-resolution spectra with synthetic spectra computed on a grid of stellar parameters assuming LTE, and checked for NLTE effects for the hottest stars. For comparison, we determined Teff independently from fitting the spectral energy distribution of the stars obtained from the available photometry. Results. We determine Teff, log g, microturbulent velocity, vsini, metallicity, and elemental abundance for 14 of the 16 candidate stars. Two stars are spectroscopic binaries. No significant influence of NLTE effects on the results could be found. For hot stars, we find systematic deviations in the determined effective temperatures from those given in the Kepler Input Catalogue. The deviations are confirmed by the results obtained from ground-based photometry. Five stars show reduced metallicity, two stars are He-strong, one is He-weak, and one is Si-strong. Two of the stars could be β Cep/SPB hybrid pulsators, four SPB pulsators, and five more stars are located close to the borders of the SPB instability region.
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Magnetic Doppler imaging is currently the most powerful method of interpreting high-resolution spectropolarimetric observations of stars. This technique has provided the very first maps of stellar ...magnetic field topologies reconstructed from time series of full Stokes vector spectra, revealing the presence of small-scale magnetic fields on the surfaces of Ap stars. These studies were recently criticised by Stift et al., who claimed that magnetic inversions are not robust and are seriously undermined by neglecting a feedback on the Stokes line profiles from the local atmospheric structure in the regions of enhanced metal abundance. We show that Stift et al. misinterpreted published magnetic Doppler imaging results and consistently neglected some of the most fundamental principles behind magnetic mapping. Using state-of-the-art opacity sampling model atmosphere and polarized radiative transfer codes, we demonstrate that the variation of atmospheric structure across the surface of a star with chemical spots affects the local continuum intensity but is negligible for the normalized local Stokes profiles except for the rare situation of a very strong line in an extremely Fe-rich atmosphere. For the disc-integrated spectra of an Ap star with extreme abundance variations, we find that the assumption of a mean model atmosphere leads to moderate errors in Stokes I but is negligible for the circular and linear polarization spectra. Employing a new magnetic inversion code, which incorporates the horizontal variation of atmospheric structure induced by chemical spots, we reconstructed new maps of magnetic field and Fe abundance for the bright Ap star α2 CVn. The resulting distribution of chemical spots changes insignificantly compared to the previous modelling based on a single model atmosphere, while the magnetic field geometry does not change at all. This shows that the assertions by Stift et al. are exaggerated as a consequence of unreasonable assumptions and extrapolations, as well as methodological flaws and inconsistencies of their analysis. Our discussion proves that published magnetic inversions based on a mean stellar atmosphere are highly robust and reliable, and that the presence of small-scale magnetic field structures on the surfaces of Ap stars is indeed real. Incorporating horizontal variations of atmospheric structure in Doppler imaging can marginally improve reconstruction of abundance distributions for stars showing very large iron overabundances. But this costly technique is unnecessary for magnetic mapping with high-resolution polarization spectra.
Context. Chemically peculiar (CP) stars are unique natural laboratories for the investigation of the microscopic diffusion processes of chemical elements. The element segregation under the influence ...of gravity and radiation pressure leads to the appearance of strong abundance gradients in the atmospheres of CP stars. Consequently, the atmospheric temperature-pressure structure of these objects could deviate significantly from the atmospheres of normal stars with homogeneous abundances. Aims. In this study we performed a self-consistent, empirical model atmosphere study of the brightest rapidly oscillating Ap star alpha Cir. We account for chemical stratification in the model atmosphere calculations and assess the importance of non-uniform vertical element distribution on the model structure, energy distribution and hydrogen line profiles. Methods. For the chemical stratification analysis we use the DDAFIT minimization tool in combination with a magnetic spectrum synthesis code. The model atmospheres with inhomogeneous vertical distributions of elements are calculated with the LLMODELS stellar model atmosphere code. Results. Based on an iterative procedure of the chemical abundance analysis of 52 ions of 35 elements, stratification modeling of 4 elements (Si, Ca, Cr and Fe) and subsequent re-calculations of the atmospheric structure, we derived a new model atmosphere of alpha Cir which is consistent with the inferred atmospheric chemistry of the star. We find T-eff = 7500 K, log g = 4.1, and demonstrate that chemical stratification has a noticeable impact on the model structure and modifies the formation of the hydrogen Balmer lines. At the same time, the energy distribution appears to be less sensitive to the presence of large abundance gradients. Conclusions. Our spectroscopically determined T-eff of alpha Cir agrees with the fundamental effective temperature of this star. This shows that temperatures inferred in detailed spectroscopic analyses of cool magnetic CP stars are not affected by a large systematic bias.
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Context. There is still a debate about the nature of the mechanism that causes the pulsation excitation of the rapidly oscillating Ap stars that oscillate above the highest theoretically acoustic ...frequency. HD 24712 is a good test case for such a study because it is bright, its parallax accurately determined, and its frequency spectrum is well known. Aims. Visible long-baseline interferometry is a unique technique for measuring accurate angular diameters of targets as small as the brightest roAp stars, and thus estimating accurate radii by a method as independent as possible of atmosphere models. Methods. We used the visible spectrograph VEGA at the CHARA long-baseline optical array to observe HD 24712, and we derived its limb-darkened diameter. We also estimated its bolometric flux from spectroscopic data in the literature and determined its radius, luminosity, and effective temperature. Results. We determined a limb-darkened angular diameter of 0.335 + or - 0.009 mas for HD 24712 and derived a radius of R= 1.772 + or - 0.057 R sub(?), a luminosity of L= 7.2 + or - 1.8 L sub(?), and an effective temperature of T sub(eff)= 7235 + or - 280 K, which is in very close agreement with the values provided by the self-consistent stratified model developed for this star. We used these fundamental parameters to set HD 24712 in the Hertzsprung-Russell diagram. Its position is marginally consistent with the region where high radial order modes are predicted to be excited by the kappa-mechanism. Conclusions. We conclude that oscillations in this star are most likely not driven by the kappa-mechanism.
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