Fast inversion of Zeeman line profiles using central moments

II. Stokes V moments and determination of vector magnetic fields

¹ LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris Diderot, Sorbonne Paris Cité, 5 place Jules Janssen, 92195 Meudon, France
e-mail: Pierre.Mein@obspm.fr
² National Solar Observatory, Sacramento Peak, PO Box 62, Sunspot, NM 88349, USA
³ Observatoire de Paris, 5 place Jules Janssen, 92195 Meudon, France
⁴ UMR 6525 H. Fizeau, Université de Nice Sophia Antipolis, CNRS, Observatoire de la Côte d’Azur, Campus Valrose, 06108 Nice, France

Received: 30 January 2015
Accepted: 30 March 2016

Abstract

Context. In the case of unresolved solar structures or stray light contamination, inversion techniques using four Stokes parameters of Zeeman profiles cannot disentangle the combined contributions of magnetic and nonmagnetic areas to the observed Stokes I.

Aims. In the framework of a two-component model atmosphere with filling factor f, we propose an inversion method restricting input data to Q , U, and V profiles, thus overcoming ambiguities from stray light and spatial mixing.

Methods. The V-moments inversion (VMI) method uses shifts S_V derived from moments of V-profiles and integrals of Q², U², and V² to determine the strength B and inclination ψ of a magnetic field vector through least-squares polynomial fits and with very few iterations. Moment calculations are optimized to reduce data noise effects. To specify the model atmosphere of the magnetic component, an additional parameter δ, deduced from the shape of V-profiles, is used to interpolate between expansions corresponding to two basic models.

Results. We perform inversions of HINODE SOT/SP data for inclination ranges 0 <ψ< 60° and 120 <ψ< 180° for the 630.2 nm Fe i line. A damping coefficient is fitted to take instrumental line broadening into account. We estimate errors from data noise. Magnetic field strengths and inclinations deduced from VMI inversion are compared with results from the inversion codes UNNOFIT and MERLIN.

Conclusions. The VMI inversion method is insensitive to the dependence of Stokes I profiles on the thermodynamic structure in nonmagnetic areas. In the range of Bf products larger than 200 G, mean field strengths exceed 1000 G and there is not a very significant departure from the UNNOFIT results because of differences between magnetic and nonmagnetic model atmospheres. Further improvements might include additional parameters deduced from the shape of Stokes V profiles and from large sets of 3D-MHD simulations, especially for unresolved magnetic flux tubes.