Zeeman component decomposition for recovering common profiles and magnetic fields

Context. High resolution spectropolarimetric data contain information about the region where atomic and/or molecular lines form. Existing multi-line techniques assuming similarities in shapes of line profiles can extract generalized Stokes signatures from noisy spectra. However, the interpretability of these signatures is limited by the commonly employed weak-field and weak-line approximations. On the other hand, inversion techniques based on realistic polarized radiative transfer can interpret complicated individual line profiles but still unable to handle the informative wealth of broad-band spectra. Aims. We present a new method, Zeeman component decomposition (ZCD), which combines the versatility of an unconstrained line profile resulting from a multi-line analysis with the radiative transfer physics implying that one profile constitutes all Stokes parameters. We show that the ZCD is capable of inferring a common Zeeman component profile as well as a reliable magnetic field vector from noisy broad-band spectra. Methods. We employ an analytic polarized radiative transfer solution describing formation of polarized line profiles in a Milne-Eddington atmosphere. The ZCD is built as a nonlinear inversion procedure with a number of free parameters, namely an unconstrained line profile, the line central depths, and the magnetic field parameters |B|, γ and χ. The procedure is applied to all Stokes parameters simultaneously. We carefully analyse blending of line profiles and Zeeman components and obtain practical analytical expressions. By comparing the anomalous Zeeman splitting with the commonly used triplet approximation, we obtain an estimate of the error, helping us to identify the cases where the simplification is not applicable. Results. We demonstrate the capabilities of the ZCD by applying it to simulated Stokes I,V, and full I,Q,U,V spectra. The first test shows that the ZCD outperforms standard multi-line techniques in finding common line profiles for noisy polarization spectra and, in addition, consistently recovers the line-of-sight magnetic field. Trials with I,Q,U,V spectra demonstrate the ability of the ZCD to work with noisy linear polarization spectra and recover the magnetic field parameters in realistic scenarios.