Fast inversion of Zeeman line profiles using central moments

Abstract

Context. Many inversion techniques derive vector magnetic fields and other parameters of the solar atmosphere from Stokes profiles with an iterative process. Aims. We propose a new inversion method, using functions derived from central moments (ICM), to determine magnetic field vectors with very few iterations. Methods. Two quantities A 1 and A 2 that combine moments of profiles I ± S (S = Q, U, V) are proposed. They are nearly linear functions of the longitudinal and transverse components of the magnetic field, and lead to estimates of the field components through a least-squares polynomial fit. A third quantity A D can be used to interpolate between expansions that correspond to two basic models. Exponents β 1 and β 2 in the moment expressions are adjusted to minimize the sensitivity to data noise. Results. Inversion coefficients are computed for magnetic fields up to 3000 G in the case of the 630.2 Fe i line by forward modeling in two selected 1D model atmospheres (FALC and MALTM). After inversion of synthetic profiles computed with four models at disk center (FALA, FALC, FALF, MALTM), the mean standard deviations with respect to the input fields do not exceed 5 G for both components over the full range 0-3000 G. A comparison of ICM results with inversion by the UNNOFIT code of profiles observed with THEMIS/MTR shows good agreement. The typical computing time for a solar map of 100 000 points is less than 30 s. Conclusions. The ICM inversions are almost insensitive to thermodynamic properties and solve for vector magnetic fields in a wide range of solar conditions, ranging from plage to spot, with very little computational effort. They are, therefore, extremely suitable for large data sets. Further improvements should take into account instrumental profiles and effects of limited spatial resolution by using filling factors. Extensions using more parameters and models with large departures from the Milne Eddington approximation could also be considered.

Inversion of the radiative transfer equation for polarized light

“…Oriented to its extensive use with the data coming from the Helioseismic and Magnetic Imager (Graham et al, 2003) aboard the Solar Dynamics Observatory, presented VFISV (Very Fast Inversion of the Stokes Vector), a new ME code but with several further approximations and simplifying assumptions to make it significantly faster than other available codes. Mein et al (2011) presented an alternative inversion code in which, with a significant number of simplifying assumptions on top of the ME approximation (such Stokes I profiles being Gaussians and magneto-optical effects being almost negligible), some moments of the Stokes profiles are used to retrieve the vector magnetic field and the LOS velocity. In 2012, a significant step forward was provided by van Noort, who combined spectral information with the known spatial degradation effects on two-dimensional maps to obtain a consistent restoration of the atmosphere across the whole field of view.…”

Fast inversion of Zeeman line profiles using central moments

“…For weak fields, algorithms using central moments (Semel 1967;Uitenbroek 2003;Criscuoli et al 2013) can provide measurements of magnetic field components. In a previous paper (Paper I; Mein et al 2011), we extended the inversion by moment calculations of I±S profiles to the general case of any magnetic field strength.…”