Similarities and Differences Between Non-linear Force-Free Fields Produced by Evolution and Extrapolation Techniques

Abstract Non-Linear Force-Free Fields (NLFFF) play a key role in our understanding of the nature and evolution of coronal magnetic fields. Two of the most common methods for their construction are the “extrapolation” and “evolution” approaches. The aim of the present paper is to compare results from these two approaches when they have the same vector magnetic field on the bottom boundary. To begin with a NLFFF evolution simulation of AR10977 is carried out to produce a time series of the vector field at the lower boundary covering the full life-span of the active region. Next at eight unique times in this time series, NLFFF extrapolations are constructed using the simulated vector boundary data. The resulting 3D coronal magnetic fields are then compared. During the early stages in the lifetime of AR10977, when the coronal magnetic field is composed of simply connected field lines, both NLFFF approaches produce a high level of agreement as long as the full vector field is injected into the extrapolation. When injection is limited to only strong field locations, a poorer agreement is found. In contrast, once a flux rope has formed during the later stages in the lifetime of the active region poor agreement is found between the two approaches, regardless of how the boundary information is injected in the extrapolations. This indicates that once a flux rope has formed through flux cancellation and risen into the corona the information held within the boundary vector field is insufficient to capture the complexity of the 3D coronal magnetic field. This result is also supported by the poor agreement that arises when comparing the relative magnetic helicity between the two modelling approaches. While the present study considers one extrapolation approach, it is important to repeat the study using alternative extrapolation methods that exist in the published literature.