3D INVERSION OF CHROMOSPHERIC STRUCTURES

This thesis addresses the challenge of inferring the magnetic field vector in chromospheric plasma,a longstanding issue in solar astrophysics.This research aims at developing new numerical tools to improve the efficiency and accuracy of the magnetic field inference in the solar atmosphere.The information on the solar magnetic field is encoded in thepolarization of the electromagnetic radiation emerging from the Sun.This polarization is sensitive to the magnetic field via the Zeemanand Hanle effects. Our most powerful tools for magnetic fielddiagnosis are inversion techniques. Generally, these techniques consistof two parts, a forward solver capable of solving the radiation transfer(RT) problem, and an optimizer to find the physical parameters (such as temperature, velocity, and themagnetic field, among others) that,when fed into the forward solver, fit a given set of data. The first research problem we have tackled in this thesis is theacceleration of inversion techniques based on the Zeeman effect inchromospheric lines. Except in the deepest layers of the solarphotosphere, spectral lines in the Sun form outside of LocalThermodynamic Equilibrium (NLTE). The RT problem under NLTE conditionsis both non-linear and non-local and its solution is computationallyexpensive, especially when compared with the linear and local LTEproblem. The RT problem, and thus the forward solver, is the clearbottleneck of these inversion techniques. We have leveraged thepotential of machine learning techniques, specifically Graph NeuralNetworks (GNNs), to completely bypass the solution of the RT problem.By training and applying the network to the Ca ii line at8542 A we have demonstrated that a GNN can not only provide anaccurate enough set of populations in NLTE, thus reducing the RTproblem to a single and fast forward solution of the RT equation, butthe resulting inversion code is about 1000 faster when compared tothe traditional method which solves the detailed RT problem. Our second objective has been assessing the impact of some of theapproximations usually considered in the study of solar filaments andprominences. Most of the studies on the magnetic field of thesestructures is based on the analysis of the spectro-polarimetricprofiles of He i triplets at 10830 A and D3 at 5876 A, whichshow scattering polarization signals and features of both Hanle and Zeemaneffects. Due to the particularities of their formation, they areoften interpreted by means of a constant property slab modelneglecting RT effects. However, it is not rare to infer opticalthickness of unity and larger for the slab in the He i10830 A triplet. We have studied the impact of RT effects andof the differential illumination between the triplet componentsin the He i 10830 A triplet in a constant property slabmodel. We have demonstrated that, for optical depths of order unityand above along the normal of the slab, RT effects have a significantimpact on the emerging scattering polarization. We have also assessedhow RT effects can impact the reliability of the inferred magneticfield, which can potentially result in the misinterpretation of itsstrength in an order of magnitude in the worst case scenarios. Finally, we have tackled the problem of the inversion ofspectro-polarimetric data in prominences considering RT effects infull 3D. To this end we have developed an atomic module for thesolution of the statistical equilibrium equations and the calculationof the RT coefficients for the He i 10830 A triplet, accounting for quantum interference and differentialillumination. This module is part of the POLARIS code, a 3D inversioncode that we have developed during this thesis and that is capableof inverting spectro-polarimetric data in full 3D by solving anunconstrained minimization problem with a meshfree approach. Due totime constraints, we have only been able to include preliminaryresults of its application to spectro-polarimetric data in thisthesis. Nevertheless, these results seem really promising, and thisresearch will be continued and completed in the near future.