Nonlinear deconvolution with deblending: a new analyzing technique for spectroscopy

Context. Spectroscopy data in general often deals with an entanglement of spectral line properties, especially in the case of blended line profiles, independently of how high the quality of the data may be. In stellar spectroscopy and spectropolarimetry, where atomic transition parameters are usually known, the use of multi-line techniques to increase the signal-to-noise ratio of observations has become common practice. These methods extract an average line profile by means of either least squares deconvolution (LSD) or principle component analysis (PCA). However, only a few methods account for the blending of line profiles, and when they do, they assume that line profiles add linearly. Aims. We abandon the simplification of linear line-adding for Stokes I and present a novel approach that accounts for the nonlinearity in blended profiles, also illuminating the process of a reasonable deconvolution of a spectrum. Only the combination of those two enables us to treat spectral line variables independently, constituting our method of nonlinear deconvolution with deblending (NDD). The improved interpretation of a common line profile achieved compensates for the additional expense in calculation time, especially when it comes to the application to (Zeeman) doppler imaging (ZDI). Methods. By examining how absorption lines of different depths blend with each other and describing the effects of line-adding in a mathematically simple, yet physically meaningful way, we discover how it is possible to express a total line depth in terms of a (nonlinear) combination of contributing individual components. Thus, we disentangle blended line profiles and underlying parameters in a truthful manner and strongly increase the reliability of the common line patterns retrieved. Results. By comparing different versions of LSD with our NDD technique applied to simulated atomic and molecular intensity spectra, we are able to illustrate the improvements provided by our method to the interpretation of the recovered mean line profiles. As a consequence, it is possible for the first time to retrieve an intrinsic line pattern from a molecular band, offering the opportunity to fully include them in a NDD-based ZDI. However, we also show that strong line broadening deters the existence of a unique solution for heavily blended lines such as in molecular bandheads.