Numerical modelling of surface abundance distributions in ApBp star atmospheres constitutes a challenging astrophysical problem. This paper is intended to deepen our understanding of how atomic ...diffusion affects the atmospheric structure of magnetic ApBp stars, and in particular how time-dependent calculations may be compared to the alternative method of estimating equilibrium stratifications. Our numerical calculations – with the stellar atmosphere adjusted self-consistently to the abundance profiles – show that final stationary solutions of the time-dependent diffusion problem (constant particle flux throughout the stellar atmosphere) are seemingly at variance with equilibrium stratifications (zero particle flux). In this work, we will provide some understanding of the origin of these differences and try to elucidate the as yet little explored behaviour of time-dependent atomic diffusion. To this purpose, we assess the influence of the boundary condition at the bottom of the atmosphere, we investigate how the stratifications depend on magnetic field angle and strength, and we have a look at possible interactions between different chemical elements. Based on a grid of atmospheric models and stratifications reflecting dipolar magnetic geometries, we also present predicted line profiles for different oblique rotator models. Finally, we shortly discuss the consequences of our findings for the interpretation of abundance maps of magnetic ApBp stars.
ABSTRACT
We present time-dependent atomic diffusion calculations for Ca, Cr, and Fe in a stellar magnetic atmosphere including an anisotropic wind. For three different models of mass-loss rates (or ...wind), we obtain a 3D description of the entire atmosphere. In two of these models, the mass-loss rate varies according to the magnetic field inclination, the assumed field geometry being non-axisymmetric. When the dipolar component of the magnetic field dominates, we find that ring-like abundance structures will be prominent. Spot-like distributions can also exist according to the field geometry. Abundance distributions turn out to be highly sensitive to the mass-loss model. The results are discussed and compared to an observational model of a real chemically peculiar star (θ Aurigae) that features parameters close to those of the model we have adopted for our calculations.
Aims.
For the observational modelling of horizontal abundance distributions and of magnetic geometries in chemically peculiar (CP) stars, Zeeman Doppler mapping (ZDM) has become the method of choice. ...Comparisons between abundance maps obtained for CP stars and predictions from numerical simulations of atomic diffusion have always proved unsatisfactory. This study is intended to explore the reasons for the discrepancies.
Methods.
We cast a cold eye (evoking the epitaph on Nobel laureate W.B. Yeats’ gravestone:
Cast a cold Eye / On Life, on Death. / Horseman, pass by
) on essential assumptions underlying ZDM, in particular, the formulae governing the magnetic field geometry, but also the regularisation functionals.
Results.
Recognising that the observed strong magnetic fields in most well-mapped stars require the field geometry to be force free, we show that the formulae used so far to describe the magnetic geometry do not meet this condition. It follows that the published magnetic maps and the abundance maps of these stars are all spurious.
Conclusions.
To obtain observational constraints for the modelling of atomic diffusion, the use in ZDM of the correct formulae for force-free or potential magnetic fields is paramount. Extensive simulations are required to quantify the effects of chemical stratifications and of regularisation functions on the recovered magnetic and abundance maps.
Abstract
Numerical models for the atmospheres of magnetic ApBp stars have in the past dealt only with centred dipole magnetic field geometries. These models include atomic diffusion that stratifies ...the abundances of metals according to the local magnetic field strength and the direction with respect to the surface normal. The magnetic variations with rotational phase of most well observed stars, however, reveal that this assumption is far too simplistic. In this work, we establish for the first time a three-dimensional model with abundance stratifications arising from atomic diffusion of 16 metals, adopting a non-axisymmetric magnetic field geometry inspired by the configuration derived for a real ApBp star. We find that the chemical elements are distributed in complex patterns in all three dimensions, far from the simple rings that have been proposed as the dominant abundance structures from calculations that assume a perfectly centred dipolar magnetic geometry.
Time-dependent diffusion in stellar atmospheres Alecian, G.; Stift, M. J.; Dorfi, E. A.
Monthly notices of the Royal Astronomical Society,
December 2011, Letnik:
418, Številka:
2
Journal Article
Recenzirano
Odprti dostop
The chemical peculiarities of Ap stars are due to abundance stratifications produced by atomic diffusion in their outer layers. Theoretical models can predict such stratifications, but so far only ...provide equilibrium solutions which correspond to the maximum depth-dependent abundances for each element that can be supported by the radiation field. However, these stratifications are actually built up through a non-linear, time-dependent process which has never been modelled for realistic stellar atmospheres.
Here, we present the first numerical simulations of time-dependent diffusion. We solve the continuity equation after having computed, as accurately as possible, atomic diffusion velocities (with and without a magnetic field) for a simplified fictitious - but still realistic - chemical element: cloudium. The direct comparison with existing observations is not the immediate aim of this work but rather a general understanding of how the stratification build-up proceeds in time and space. Our results raise serious questions as to the relevance of equilibrium solutions and reinforce the suspicion that certain accumulations of chemical elements might prove unstable.
Abstract
We present the chemical abundance analysis of 19 upper main-sequence stars of the young open cluster NGC 6250 (log t ∼ 7.42 yr). This work is part of a project aimed at setting ...observational constraints on the theory of atomic diffusion in stellar photospheres, by means of a systematic study of the abundances of the chemical elements of early F-, A- and late B-type stars of well-determined age. Our data set consists of low-, medium- and high-resolution spectra obtained with the Fibre Large Array Multi Element Spectrograph (FLAMES) instrument of the ESO Very Large Telescope (VLT). To perform our analysis, we have developed a new suite of software tools for the chemical abundance analysis of stellar photospheres in local thermodynamical equilibrium. Together with the chemical composition of the stellar photospheres, we have provided new estimates of the cluster mean radial velocity, proper motion, refined the cluster membership, and we have given the stellar parameters including masses and fractional age. We find no evidence of statistically significant correlation between any of the parameters, including abundance and cluster age, except perhaps for an increase in Ba abundance with cluster age. We have proven that our new software tool may be successfully used for the chemical abundance analysis of large data sets of stellar spectra.
Context. Theoretical modelling of abundance stratifications and surface distributions of chemical elements in Ap stars constitutes a major challenge. The atomic diffusion model provides the most ...appropriate framework in which to understand these abundance anomalies. Aims. We present theoretical 2D stratifications of 16 metals in upper main sequence chemically peculiar stars, with and without magnetic fields to provide a reference point for further theoretical and observational studies. Methods. We used our code CaratStrat to compute a large grid of stratifications (equilibrium solutions in LTE) for plane-parallel $T_{\rm eff}$ = 8500, 10 000, 12 000, and 14 000 K stellar atmospheres. By interpolation, we constructed bi-dimensional cuts through these stellar atmospheres, which are permeated by a dipolar magnetic field of strength 20 kG at the magnetic pole. We also provide vertical (1D) stratifications of metals in non-magnetic stars (HgMn). Results. We present a large number of 2D and 1D stratifications, mostly as online material. We discuss in detail the case of Fe for the Teff = 8500 K model in the printed version, and compare it with stratifications derived from observed spectra.
ABSTRACT
Elemental abundances have been found – both empirically and theoretically – to be stratified in the magnetic atmospheres of many chemically peculiar (CP) stars, but these findings are rarely ...if ever taken into account for example in (Zeeman) Doppler mapping, resulting in a disturbing problem of self‐consistency. Such a lack of self‐consistency is also present in many studies of atomic diffusion which have usually been based on vertically homogeneous atmospheric models. In this paper we go one step further in our modelling of diffusion in magnetic CP star atmospheres and discuss self‐consistent equilibrium stratifications of elements, in particular of Fe. In an iterative approach, the atmospheric structure is adjusted to the latest stratification profiles of the various elements until zero particle flux throughout the atmosphere is achieved. It can be shown that the resulting stratifications are different from those calculated with vertically homogeneous atmospheres – mainly on account of the change in temperature structure – and that the unphysical behaviour resulting from the latter atmospheres may be avoided. An important finding concerns the mutual interaction between the various elements, leading to stratification profiles that differ substantially depending on whether e.g. Fe alone is allowed to diffuse or whether other elements may diffuse too. This presentation ends with a discussion of these interactions in the context of time‐dependent diffusion calculations.
Empirical abundance maps derived with the help of Zeeman Doppler mapping are found to be at variance with the predictions of numerical models of atomic diffusion in magnetic atmospheres of ApBp ...stars. Although theory has often been made responsible for this lack of agreement, direct spectral synthesis based on the published abundance maps reveals that all the chemical inhomogeneities claimed for HD 3980 are entirely spurious, and those of HD 50773 to a large extent. In the former case, this is shown to be due to the neglect of a strong magnetic field, and in the latter case, due to noisy spectra in combination with considerable rotational broadening and ensuing strong line blending. Doppler maps for other magnetic ApBp stars could be affected by similar problems. It is also pointed out that the patchy, extreme overabundances in HD 3980 cannot be reconciled with the theory of stellar atmospheres.
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