An inversion approach to retrieve the vector magnetic field from scattering polarization in strong solar resonance lines

¹ Istituto ricerche solari Aldo e Cele Daccò (IRSOL), Faculty of Informatics, Università della Svizzera italiana (USI), 6605 Locarno, Switzerland
² Euler Institute, Università della Svizzera italiana (USI), 6900 Lugano, Switzerland
³ Institute for Solar Physics (KIS), Georges-Khöler-Allee 401a, 79110 Freiburg, Germany
⁴ Faculty of Mathematics, University of Belgrade, Studentski Trg 16, 11000 Belgrade, Serbia
⁵ Astronomical Observatory, Volgina 7, 11060 Belgrade, Serbia

^★ Corresponding author: gioele.janett@irsol.usi.ch

Received: 12 June 2025
Accepted: 11 July 2025

Abstract

Context. Inferring the weak magnetic field present in the outer layers of the solar atmosphere is a long-standing challenge in modern solar physics. Spectropolarimetric diagnostic techniques based on the Zeeman effect are ineffective in this context, highlighting the need for alternative approaches.

Aims. Our goal is to develop a novel inference method that fits a depth-dependent vector magnetic field in a solar model atmosphere to observations of Hanle and Zeeman signals from strong resonance lines, including partial frequency redistribution (PRD) effects.

Methods. We assumed that the thermal stratification of the atmosphere is given, and we used an efficient radiative transfer forward engine tailored to strong resonance lines, while accounting for PRD, scattering polarization, and the Hanle and Zeeman effects. By formulating the inverse problem as a nonlinear least-squares problem, we applied an efficient iterative optimization algorithm that enables an efficient retrieval of the searched magnetic field vector through fast computation of the Jacobian.

Results. We tested this inversion approach by inverting synthetic Stokes profiles of the Ca I line at 4227 Å. We successfully retrieved the original height-dependent vector magnetic and bulk velocity fields in different 1D plane-parallel models. We considered both semi-empirical models and models extracted from a snapshot of a 3D MHD simulation of the solar atmosphere.

Conclusions. Our proposed inversion tool has demonstrated its reliability and promise for inverting vector magnetic fields in strong solar resonance lines that exhibit scattering polarization. Future plans include testing the approach in more complex scenarios, featuring intricate magnetic field structures. This assessment paves the way for applying our inversion tool to new spectropolarimetric observations.