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

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

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&

Rebuilding the Cepheid Distance Scale I: A Global Analysis of Cepheid Mean Magnitudes

We develop a statistical method for using multicolor photometry to determine distances using Cepheid variables including the effects of temperature, extinction, and metallicity and apply it to UBVRIJHK photometry of 694 Cepheids in 17 galaxies. We derive homogeneous distance, extinction and uncertainty estimates for four models, starting from the standard extragalactic method and then adding the physical effects of temperature distributions, extinction distributions, requiring positive definite extinctions, and metallicity. While we find general agreement with published distances when we make similar systematic assumptions, there is a clear problem in the standard distances because they require Cepheids with negative extinctions, particularly in low metallicity galaxies, unless the mean LMC extinction exceeds E(B-V) > 0.25. The problem can be explained by the physically expected metallicity dependence of the Cepheid distance scale, where metal-poor Cepheids are hotter and fainter than metal-rich Cepheids. For V and I we found that the mean magnitude change is -0.14 +/- 0.14 mag/dex and the mean color change is 0.13 +/- 0.04 mag/dex, with the change in color dominating the change in distance. The effect on Type Ia supernova estimates of the Hubble constant is dramatic because most were found in the metal poor galaxies with the bluest Cepheids. The Type Ia Multi-color Light Curve Shape (MLCS) method estimate for H_0 formally rises from 69 +/- 8 km/s Mpc to 80 +/- 6 km/s Mpc with the metallicity correction.Comment: 54 pages, 7 figures, 4 tables, submitted to Ap

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

Spectropolarimetric multi line analysis of stellar magnetic fields

In this paper we study the feasibility of inferring the magnetic field from polarized multi-line spectra using two methods: The pseudo line approach and The PCA-ZDI approach. We use multi-line techniques, meaning that all the lines of a stellar spectrum contribute to obtain a polarization signature. The use of multiple lines dramatically increases the signal to noise ratio of these polarizations signatures. Using one technique, the pseudo-line approach, we construct the pseudo-line as the mean profile of all the individual lines. The other technique, the PCA-ZDI approach proposed recently by Semel et al. (2006) for the detection of polarized signals, combines Principle Components Analysis (PCA) and the Zeeman Do ppler Imaging technique (ZDI). This new method has a main advantage: the polarized signature is extracted using cross correlations between the stellar spectra nd functions containing the polarization properties of each line. These functions are the principal components of a database of synthetic spectra. The synthesis of the spectra of the database are obtained using the radiative transfer equations in LTE. The profiles built with the PCA-ZDI technique are denominated Multi-Zeeman-Signatures. The construction of the pseudo line as well as the Multi-Zeeman-Signatures is a powerful tool in the study of stellar and solar magnetic fields. The information of the physical parameters that governs the line formation is contained in the final polarized profiles. In particular, using inversion codes, we have shown that the magnetic field vector can be properly inferred with both approaches despite the magnetic field regime.Comment: Accepted for publication in Astronomy and Astrophysic