Doppler imaging of chemical spots on magnetic Ap/Bp stars

Numerical tests and assessment of systematic errors

Department of Physics and Astronomy, Uppsala University, Box 516, 75120 Uppsala, Sweden
e-mail: oleg.kochukhov@physics.uu.se

Received: 21 September 2016
Accepted: 10 November 2016

Abstract

Context. Doppler imaging (DI) is a powerful spectroscopic inversion technique that enables conversion of a line profile time series into a two-dimensional map of the stellar surface inhomogeneities. DI has been repeatedly applied to reconstruct chemical spot topologies of magnetic Ap/Bp stars with the goal of understanding variability of these objects and gaining an insight into the physical processes responsible for spot formation.

Aims. In this paper we investigate the accuracy of chemical abundance DI and assess the impact of several different systematic errors on the reconstructed spot maps.

Methods. We have simulated spectroscopic observational data for two different Fe spot distributions with a surface abundance contrast of 1.5 dex in the presence of a moderately strong dipolar magnetic field. We then reconstructed chemical maps using different sets of spectral lines and making different assumptions about line formation in the inversion calculations.

Results. Our numerical experiments demonstrate that a modern DI code successfully recovers the input chemical spot distributions comprised of multiple circular spots at different latitudes or an element overabundance belt at the magnetic equator. For the optimal reconstruction based on half a dozen spectral intervals, the average reconstruction errors do not exceed ~0.10 dex. The errors increase to about 0.15 dex when abundance distributions are recovered from a few and/or blended spectral lines. Ignoring a 2.5 kG dipolar magnetic field in chemical abundance DI leads to an average relative error of 0.2 dex and maximum errors of 0.3 dex. Similar errors are encountered if a DI inversion is carried out neglecting a non-uniform continuum brightness distribution and variation of the local atmospheric structure. None of the considered systematic effects lead to major spurious features in the recovered abundance maps.

Conclusions. This series of numerical DI simulations proves that inversions based on one or two spectral lines with simplifying assumptions of the non-magnetic radiative transfer and a single model atmosphere are generally reliable provided that the stellar magnetic field is not much stronger than 2–3 kG and the recovered spot map has a contrast of at least ~0.3 dex. In the light of these findings, we assess magnetic field strengths of several dozen Ap/Bp stars previously studied with DI methods, concluding that the vast majority of the published chemical spot maps are unaffected by the systematic errors addressed in this paper.