The recondite intricacies of Zeeman Doppler mapping

We present a detailed analysis of the reliability of abundance and magnetic maps of Ap stars obtained by Zeeman Doppler mapping (ZDM). It is shown how they can be adversely affected by the assumption of a mean stellar atmosphere instead of appropriate "local" atmospheres corresponding to the actual abundances in a given region. The essenceof the difficulties was already shown by Chandrasekhar's picket-fence model. The results obtained with a suite of Stokes codes written in the Ada programming language and based on modern line-blanketed atmospheres are described in detail. We demonstrate that the high metallicity values claimed to have been found in chemically inhomogeneous Ap star atmospheres would lead to local temperature structures, continuum and line intensities, and line shapes that differ significantly from those predicted by a mean stellar atmosphere. Unfortunately, past applications of ZDM have consistently overlooked the intricate aspects of metallicity with their all-pervading effects. The erroneous assumption of a mean atmosphere for a spotted star can lead to phase-dependent errors of uncomfortably large proportions at varying wavelengths both in the Stokes I and V profiles, making precise mapping of abundances and magnetic field vectors largely impossible. The relation between core and wings of the H_beta line changes, too, with possible repercussions on the determination of gravity and effective temperature. Finally, a ZDM analysis of the synthetic Stokes spectra of a spotted star reveals the disturbing differences between the respective abundance maps based on a mean atmosphere on the one hand, and on appropriate "local" atmospheres on the other. We then discuss what this all means for published ZDMresults. Our discussion makes it clear that realistic local atmospheres must be used, especially if credible small-scale structures are to be obtained.Comment: Accepted for publication in MNRA

Modelling the incomplete Paschen-Back effect in the spectra of magnetic Ap stars

We present first results of a systematic investigation of the incomplete Paschen-Back effect in magnetic Ap stars. A short overview of the theory is followed by a demonstration of how level splittings and component strengths change with magnetic field strength for some lines of special astrophysical interest. Requirements are set out for a code which allows the calculation of full Stokes spectra in the Paschen-Back regime and the behaviour of Stokes I and V profiles of transitions in the multiplet 74 of FeII is discussed in some detail. It is shown that the incomplete Paschen-Back effect can lead to noticeable line shifts which strongly depend on total multiplet strength, magnetic field strength and field direction. Ghost components (which violate the normal selection rule on J) show up in strong magnetic fields but are probably unobservable. Finally it is shown that measurements of the integrated magnetic field modulus $H_s$ are not adversely affected by the Paschen-Back effect, and that there is a potential problem in (magnetic) Doppler mapping if lines in the Paschen-Back regime are treated in the Zeeman approximation.Comment: 8 pages, 10 figures, to appear in MNRA

Multiline Zeeman Signatures Through Line Addition

In order to get a significant Zeeman signature in the polarised spectra of a magnetic star, we usually 'add' the contributions of numerous spectral lines; the ultimate goal is to recover the spectropolarimetric prints of the magnetic field in these line additions. Here we want to clarify the meaning of these techniques of line addition; in particular, we try to interpret the meaning of the 'pseudo-line' formed during this process and to find out why and how its Zeeman signature is still meaningful. We create a synthetic case of line addition and apply well tested standard solar methods routinely used in the research on magnetism in our nearest star. The results are convincing and the Zeeman signatures well detected; Solar methods are found to be quite efficient also for stellar observations. We statistically compare line addition with least-squares deconvolution and demonstrate that they both give very similar results as a consequence of the special statistical properties of the weights. The Zeeman signatures are unequivocally detected in this multiline approach. We may anticipate the outcome that magnetic field detection is reliable well beyond the weak-field approximation. Linear polarisation in the spectra of solar type stars can be detected when the spectral resolution is sufficiently high.Comment: 8 pages, accepted for publication in A&

Radiative diffusion in stellar atmospheres: diffusion velocities

The present paper addresses some of the problems in the buildup of element stratification in stellar magnetic atmospheres due to microscopic diffusion, in particular the redistribution of momentum among the various ionisation stages of a given element and the calculation of diffusion velocities in the presence of inclined magnetic fields. We have considerably modified and extended our CARAT code to provide radiative accelerations, not only from bound-bound but also from bound-free transitions. In addition, our code now computes ionisation and recombination rates, both radiative and collisional. These rates are used in calculating the redistribution of momentum among the various ionisation stages of the chemical elements. A careful comparison shows that the two different theoretical approaches to redistribution that are presently available lead to widely discrepant results for some chemical elements, especially in the magnetic case. In the absence of a fully satisfactory theory of redistribution, we propose to use the geometrical mean of the radiative accelerations from both methods. Diffusion velocities have been calculated for 28 chemical elements in a T_eff = 12000K, log g = 4.00 stellar magnetic atmosphere with solar abundances. Velocities and resulting element fluxes in magnetic fields are discussed; rates of abundance changes are analysed for systematic trends with field strength and field direction. Special consideration is given to the Si case and our results are confronted in detail with well-known results derived more than two decades ago.Comment: To be published in Astronomy & Astrophysics (accepted 02/03/2006

Modelling element distributions in the atmospheres of magnetic Ap stars

In recent papers convincing evidence has been presented for chemical stratification in Ap star atmospheres, and surface abundance maps have been shown to correlate with the magnetic field direction. Radiatively driven diffusion in magnetic fields is among the processes responsible for these inhomogeneities. Here we explore the hypothesis that equilibrium stratifications can, in a number of cases, explain the observed abundance maps and vertical distributions of the various elements. The investigation of equilibrium stratifications in stellar atmospheres with temperatures from 8500K to 12000K and fields up to 10 kG reveals considerable variations in the vertical distribution of the 5 elements studied (Mg, Si, Ca, Ti, Fe), often with zones of large over- or under-abundances and with indications of other competing processes (such as mass loss). Horizontal magnetic fields can be very efficient in helping the accumulation of elements in higher layers. A comparison between our calculations and the vertical abundance profiles and surface maps derived by magnetic Doppler imaging reveals that equilibrium stratifications are in a number of cases consistent with the main trends inferred from observed spectra. However, it is not clear whether such equilibrium solutions will ever be reached during the evolution of an Ap star.Comment: 7 pages, 6 figures, the paper will be published in Astronomy & Astrophysics, on November 200