Novel framework for the three-dimensional NLTE inverse problem

Abstract

The inversion of spectropolarimetric observations of the solar upper atmosphere is one of the most challenging goals in solar physics. If we account for all relevant ingredients of the spectral line formation process, such as the three-dimensional (3D) radiative transfer out of local thermodynamic equilibrium (NLTE), the task becomes extremely computationally expensive. Instead of generalizing 1D methods to 3D, we have developed a new approach to the inverse problem. In our meshfree method, we do not consider the requirement of 3D\,NLTE consistency as an obstacle, but as a natural regularization with respect to the traditional pixel-by-pixel methods. This leads to more robust and less ambiguous solutions. We solve the 3D\,NLTE inverse problem as an unconstrained global minimization problem that avoids repetitive evaluations of the $\Lambda$ operator. Apart from the 3D\,NLTE consistency, the method allows us to easily include additional conditions of physical consistency such as the zero divergence of the magnetic field. Stochastic ingredients make the method less prone to ending up within the local minima of the loss function. Our method is capable of solving the inverse problem faster by several orders of magnitude than by using grid-based methods. The method can provide accurate and physically consistent results if sufficient computing time is available, along with approximate solutions in the case of very complex plasma structures or limited computing time.

arXiv comment18 pages, 13 figures, accepted for publication in A&A

References in corpus (20)

• The stellar atmosphere simulation code Bifrost
• An Open Source, Massively Parallel Code for Non-LTE Synthesis and Inversion of Spectral Lines and Zeeman-induced Stokes Profiles
• Advanced Forward Modeling and Inversion of Stokes Profiles Resulting from the Joint Action of the Hanle and Zeeman Effects
• STiC -- A multi-atom non-LTE PRD inversion code for full-Stokes solar observations
• Inversion of the radiative transfer equation for polarized light
• Spatially coupled inversion of spectro-polarimetric image data I: Method and first results
• Radiative diagnostics in the solar photosphere and chromosphere
• PORTA: A three-dimensional multilevel radiative transfer code for modeling the intensity and polarization of spectral lines with massively parallel computers
• Stokes Inversion based on Convolutional Neural Networks
• Sparse inversion of Stokes profiles. I. Two-dimensional Milne-Eddington inversions
• A novel investigation of the small-scale magnetic activity of the quiet Sun via the Hanle effect in the Sr I 4607 Å line
• Three-dimensional radiative transfer simulations of the scattering polarization of the hydrogen Ly$\alpha$ line in a MHD model of the chromosphere-corona transition region
• The Hanle and Zeeman polarization signals of the solar Ca II 8542 Å line
• Recent advancements in the EST project
• The effects of three-dimensional radiative transfer on the resonance polarization of the Ca I 4227 $\mathring{\mathrm{A}}$ line
• Numerical solutions to linear transfer problems of polarized radiation II. Krylov methods and matrix-free implementation
• Near optimal angular quadratures for polarised radiative transfer
• Numerical solutions to linear transfer problems of polarized radiation I. Algebraic formulation and stationary iterative methods
• Improved near optimal angular quadratures for polarised radiative transfer in 3D MHD models
• Long characteristics vs. short characteristics in 3D radiative transfer simulations of polarized radiation

Cited by in corpus (6)

• Exploring spectropolarimetric inversions using neural fields. Solar chromospheric magnetic field under the weak-field approximation
• Magnetic field diagnostics of prominences with the Mg II k line: 3D Stokes inversions versus traditional methods
• The He I 10830 A line: Radiative transfer and differential illumination effects
• The uncertainty of magnetic fields in 3D non-local thermodynamic equilibrium inversions
• Accelerating 3D Non-LTE Synthesis with Graph Neural Networks
• Irregular grids for 3D NLTE radiative transfer in stellar atmospheres