Least squares deconvolution of the stellar intensity and polarization spectra

TL;DR

This paper critically examines the least squares deconvolution (LSD) technique for stellar spectra, improves its implementation, and evaluates its accuracy in interpreting magnetic fields and elemental abundances.

Contribution

It provides a detailed analysis of LSD assumptions, introduces an improved multiprofile version, and offers guidelines for better interpretation of LSD profiles in stellar magnetic studies.

Findings

LSD profiles do not always behave like real spectral lines.

Stokes V LSD spectra reliably indicate magnetic field strength up to 1 kG.

Interpreting LSD profiles as real lines can lead to errors outside limited parameter ranges.

Abstract

Least squares deconvolution (LSD) is a powerful method of extracting high-precision average line profiles from the stellar intensity and polarization spectra. Despite its common usage, the LSD method is poorly documented and has never been tested using realistic synthetic spectra. In this study we revisit the key assumptions of the LSD technique, clarify its numerical implementation, discuss possible improvements and give recommendations how to make LSD results understandable and reproducible. We also address the problem of interpretation of the moments and shapes of the LSD profiles in terms of physical parameters. We have developed an improved, multiprofile version of LSD and have extended the deconvolution procedure to linear polarization analysis taking into account anomalous Zeeman splitting of spectral lines. This code is applied to the theoretical Stokes parameter spectra. We test various methods of interpreting the mean profiles, investigating how coarse approximations of the multiline technique translate into errors of the derived parameters. We find that, generally, the Stokes parameter LSD profiles do not behave as a real spectral line with respect to the variation of magnetic field and elemental abundance. This problem is especially prominent for the Stokes I variation with abundance and Stokes Q variation with magnetic field. At the same time, the Stokes V LSD spectra closely resemble profile of a properly chosen synthetic line for the magnetic field strength up to 1 kG. We conclude that the usual method of interpreting the LSD profiles by assuming that they are equivalent to a real spectral line gives satisfactory results only in a limited parameter range and thus should be applied with caution. A more trustworthy approach is to abandon the single-line approximation of the average profiles and apply LSD consistently to observations and synthetic spectra.