Synopsis and Motivation

Synopsis

CLEDB aims to invert coronal magnetic field information from observations of polarized light. The algorithm takes arrays of one or two sets of SpectroPolarimetric Stokes IQUV observations sobs_in along with their header metadata information. The data and metadata are pre-processed, and optimal corresponding sets of databases resulting from forward calculations are selected and read from disk storage.

The data processing is split into two branches, based on the available polarized coronal Stokes observations:

  • 1-line branch: 4 input IQUV observations (one coronal emission line).

  • 2-line branch: 8 input I1Q1U1V1I2Q2U2V2 observations (two coronal emission lines).

    or

  • 2-line branch: 6 input I1Q1U1I2Q2U2 observations (two coronal emission lines without Stokes V).

Spectroscopic analysis products are computed for each line for both 1-line or 2-line branches that include a spectral dimension.

The 1-line branch employs analytical approximations to calculate line of sight (LOS) integrated magnetic field products, while the 2-line branch offers access to additional magnetic field products. The 2-line setup benefits from more degrees of freedom allowing us to break degeneracies intrinsic in the inversion. Thus, the 2-line algorithm branch performs a \({\chi}^2\) fitting between the observation and a forward-modeled database to recover full 3D vector magnetic field components. The 8 component IQUV fit will result in sets of two times degenerate solutions, while the 6 component IQUD fit will recover two sets of sets (4 total) degenerate solutions. The IQUD setup needs access to additional information recovered from Doppler oscillation analysis in order to constrain the solution.

The databases are generated via forward modeling of combinations of input magnetic field and geometric parameters. In this setup, databases are used as a static input with respect to the inversion scheme and should not be computed dynamically for each observation.

Motivation for the CLEDB approach

By utilizing 2-line observations, we can recover the 3D magnetic field information for single point voxel using a \({\chi}^2\) fitting approach. Theoretically, we can employ the CLE (Coronal Line Emission) spectral synthesis code to generate forward-model calculations. About 107-109 atomic plasma and magnetic configurations are needed in order to satisfy a reasonable solution resolution criteria. Directly forward modeling such solutions for one pixel/voxel in a dynamic fashion would be time consuming. Such a calculation has execution times in the order of 5-10 hours, on a single CPU thread when using a fast implementation of the Fortran CLE code.

Building a static database (via the CLEDB_BUILD module of our algorithm) to store the vast set of synthetic Stokes observations, along with the input plasma and magnetic field configurations responsible for producing polarized emission, proved to be a significantly more feasible approach.

Additionally, the database theoretical calculations gain intrinsic access to otherwise un-observable input parameters (e.g. atomic alignment \({\sigma}_0^2\), intrinsic magnetic field angles \({\vartheta}\), \({\varphi}\) etc.) that can be used to break inherent degeneracies encountered when attempting analytical inversions (as for example occurring in the 1-line branch implementation). The dimensionality of the problem at hand can be further reduced by 1-2 orders of magnitude by using native symmetries when building and querying databases. Detailed discussions on the physics aspects of dimensionality reduction and degeneracy breaking effects can be found in the sources below.

List of Relevant Publications

Academic journal papers that helped fundament, build and justify CLEDB:

  1. Paraschiv & Judge, SolPhys, 2022 covered the scientific justification of the algorithm, and the setup of the CLEDB inversion.

  2. Judge, Casini, & Paraschiv, ApJ, 2021 discussed the importance of scattering geometry when solving for coronal magnetic fields.

  3. Ali, Paraschiv, Reardon, & Judge, ApJ, 2022 performed a spectroscopic exploration of the infrared regions of the emission lines available for inversion with CLEDB.

  4. Dima & Schad, ApJ, 2020 discussed potential degeneracies in using certain line combinations. The one-line CLEDB inversion directly utilizes the methods and results described in this work.

  5. Schiffmann, Brage, Judge, Paraschiv & Wang, ApJ, 2021 performed large-scale Lande g factor calculations for our ions of interest and discusses degeneracies in context of their results.

  6. Casini & Judge, ApJ, 1999 and Judge & Casini, ASP proc., 2001 described the theoretical line formation process implemented by CLE, the coronal forward synthesis Fortran code that is currently utilized by CLEDB.