Least-squares deconvolution of the stellar intensity and polarization spectra

Context. Least-squares deconvolution (LSD) is a powerful method of extracting high-precision average line profiles from the stellar intensity and polarization spectra. This technique is widely used for detection, characterization, and detailed mapping of the temperature, magnetic, and chemical abundance structures on the surfaces of stars.
Aims: Despite its common usage, the LSD method is poorly documented and has never been tested with 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 of 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.
Methods: We have developed an improved, multiprofile version of LSD (iLSD) and have extended the deconvolution procedure to linear polarization analysis taking into account anomalous Zeeman splitting of spectral lines. The iLSD method is applied to the theoretical Stokes parameter spectra computed for a wide wavelength interval containing all relevant spectral lines. We test various methods of interpreting the mean profiles, investigating how coarse approximations of the multiline technique translate into errors of the derived parameters.
Results: 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 (intensity) variation with abundance and Stokes Q (linear polarization) variation with magnetic field. At the same time, the Stokes V (circular polarization) LSD spectra closely resemble the profile of a properly chosen synthetic line for the magnetic field strength up to 1 kG. The longitudinal field estimated from the Stokes V LSD profile is accurate to within 10% for the field strength below 5 kG and to within a few percent for the fields weaker than 1 kG. Our iLSD technique offers clear advantages over the standard LSD method in the individual analysis of different chemical elements.
Conclusions: 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.