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

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

The Hubble Space Telescope Extragalactic Distance Scale Key Project. X. The Cepheid Distance to NGC 7331

The distance to NGC 7331 has been derived from Cepheid variables observed with HST/WFPC2, as part of the Extragalactic Distance Scale Key Project. Multi-epoch exposures in F555W (V) and F814W (I), with photometry derived independently from DoPHOT and DAOPHOT/ALLFRAME programs, were used to detect a total of 13 reliable Cepheids, with periods between 11 and 42 days. The relative distance moduli between NGC 7331 and the LMC, imply an extinction to NGC 7331 of A_V = 0.47+-0.15 mag, and an extinction-corrected distance modulus to NGC 7331 of 30.89+-0.14(random) mag, equivalent to a distance of 15.1 Mpc. There are additional systematic uncertainties in the distance modulus of +-0.12 mag due to the calibration of the Cepheid Period-Luminosity relation, and a systematic offset of +0.05+-0.04 mag if we applied the metallicity correction inferred from the M101 results of Kennicutt et al 1998.Comment: To be published in The Astrophysical Journal, 1998 July 1, v501 note: Figs 1 and 2 (JPEG files) and Fig 7 (multipage .eps file) need to be viewed/printed separatel

Morphologic and Molecular Features of Hepatocellular Adenoma with Gadoxetic Acid-enhanced MR Imaging

Purpose To evaluate the diagnostic performance of imaging features of gadoxetic acid-enhanced magnetic resonance (MR) imaging to differentiate among hepatocellular adenoma (HCA) subtypes by using the histopathologic results of the new immunophenotype and genotype classification and to correlate the enhancement pattern on the hepatobiliary phase (HBP) with the degrees of expression of organic anion transporting polypeptide (OATP1B1/3), multidrug resistance-associated protein 2 (MRP) (MRP2), and MRP 3 (MRP3) transporters. Materials and Methods This retrospective study was approved by the institutional review board, and the requirement for informed consent waived. MR imaging findings of 29 patients with 43 HCAs were assessed by two radiologists independently then compared with the histopathologic analysis as the standard of reference. Receiver operating characteristic curves and Spearman rank correlation coefficient were used to test the diagnostic performance of gadoxetic acid-enhanced MR imaging features, which included the retention or washout at HBP and degree of transporter expression. Interreader agreement was assessed by using the κ statistic with 95% confidence interval. Results The area under the curve for the diagnosis of inflammatory HCA was 0.79 (95% confidence interval: 0.64, 0.90); for the steatotic type, it was 0.90 (95% confidence interval: 0.77, 0.97); and for the β-catenin type, it was 0.87 (95% confidence interval: 0.74, 0.95). There were no imaging features that showed a significant statistical correlation for the diagnosis of unclassified HCAs. On immunohistochemical staining, OATP1B1/3 expression was the main determinant for the retention, whereas MRP3 was the key determinant for washout of gadoxetic acid at HBP (P < .001). MRP2 appeared to have no role. Conclusion Gadoxetic acid-enhanced MR imaging features may suggest the subtype of HCA. The degree of OATP1B1/3 and MRP3 expression correlated statistically with gadoxetic acid retention and washout, respectively, in the HBP. (©) RSNA, 2015 Online supplemental material is available for this article