Magnetic Field Extrapolations in the Corona: Success and Future Improvements

TL;DR

This review discusses the methods and assumptions behind magnetic field extrapolation techniques used to model the solar corona's magnetic structure, highlighting successes and areas for future improvement.

Contribution

It provides a comprehensive summary of current extrapolation methods, their physical assumptions, and compares results with multi-wavelength observations, outlining future directions.

Findings

Extrapolation techniques effectively model coronal magnetic fields.

Comparison with observations validates some models, revealing limitations.

Physical assumptions influence the accuracy of magnetic field reconstructions.

Abstract

The solar atmosphere being magnetic in nature, the understanding of the structure and evolution of the magnetic field in different regions of the solar atmosphere has been an important task over the past decades. This task has been made complicated by the difficulties to measure the magnetic field in the corona, while it is currently known with a good accuracy in the photosphere and/or chromosphere. Thus, to determine the coronal magnetic field, a mathematical method has been developed based on the observed magnetic field. This is the so-called magnetic field extrapolation technique. This technique relies on two crucial points: (i) the physical assumption leading to the system of differential equations to be solved, (ii) the choice and quality of the associated boundary conditions. In this review, I summarise the physical assumptions currently in use and the findings at different scales in the solar atmosphere. I concentrate the discussion on the extrapolation techniques applied to solar magnetic data and the comparison with observations in a broad range of wavelengths (from hard X-rays to radio emission).