Magnetic field modeling of the solar atmosphere

The atmospheric layers of the Sun are magnetically coupled to the solar interior by a magnetic field, generated in the convection zone by the action of a hydromagnetic dynamo. Once created, strong toroidal fields buoyantly rise towards the visible solar surface (the photosphere) and expand into the solar atmosphere. Continuously, electric currents are induced and magnetic energy is stored, driven by the motion of the magnetic field line foot points relative to the ambient magnetic field. Abrupt reconfigurations of the magnetic field in the outer solar atmosphere (the chromosphere and corona), driven by resistive instabilities, lead to the release of previously stored magnetic energy. Impressive consequences of such reconfigurations of localized magnetic fields in the solar atmosphere are solar flares and coronal mass ejections (CMEs). They are usually associated with locations where bundles of magnetic field lines emerge from or re-enter the visible solar surface (active regions). During a CME, immense masses of magnetized plasma are released with velocities of hundreds to thousands of kilometers per second. During flares, sudden enhancements of electromagnetic radiation are observed, caused by accelerated particles and excessive heating of the upper solar atmospheric layers. Moreover, flares and CMEs are the major source of the "space weather" at Earth. The lack of routine direct measurements of magnetic fields in the chromosphere and corona is nowadays compensated by the usage of reconstruction methods. These approximate the magnetic field in those layers indirectly, based on routinely performed, direct measurements of the magnetic field at photospheric levels. By the use of one of the most sophisticated static equilibrium model approach, the pre- and post-eruptive coronal magnetic field can be approximated in a realistic way. Based on resulting the 3D model fields, we will be able to study the temporal evolution of related quantities, for instance the magnetic energy and relative helicity, in the course of eruptions. The proposed project aims to investigate the storage and release processes of magnetic energy during solar eruptions with unprecedented spatial and temporal resolution. It is aimed to disentangle the temporal and spatial scales on which the magnetic field and associated quantities evolve during solar eruptions. Additionally, the temporal and spatial associations of the coronal magnetic field and the flare-related emission signatures is to be investigated. Moreover, we aim to localize the coronal site of the changing magnetic topology and systematically investigate the role of the magnetic helicity in the course of flares with and without associated CME.

The main aim of this project was to investigate the physical processes of solar eruptions. Solar eruptions occur due to abrupt reconfigurations of the magnetic field (magnetic reconnection) in the outer solar atmosphere (the chromosphere and corona). Impressive consequences of such magnetic field reconfigurations within localized volumes in the solar atmosphere are flares (sudden dramatic enhancement of the emitted electromagnetic radiation) and coronal mass ejections (CMEs; immense masses of magnetized plasma expelled to interplanetary space). In their course, previously stored magnetic energy is violently released. We used sophisticated numerical methods to reconstruct the threedimensional coronal magnetic field, in order to compensate for the lack of direct measurements of the coronal magnetic field. As an input, we used routine measurements of the magnetic field on the visible solar surface (the photosphere) at a high spatial and temporal cadence. Based on the resulting three-dimensional magnetic field models, we were able to study relevant physical quantities for eruptive and non-eruptive (CME-less) flares, as well as to analyze the temporal and spatial relationship of the magnetic field and observed coronal emission in the solar corona.The main results obtained within this project are the following: 1) Sheared and/or twisted magnetic field configurations are recognized in the form of localized bright structures in coronal intensity images as they represent locations where electric currents are dissipated. The latter are induced and stored in the corona by corresponding characteristic motions of the photospheric plasma. 2) Magnetic field structures that are involved in magnetic reconnection can be unambiguously identified via enhanced hard X-ray emission observed in localized regions. 3) The flaring corona is composed of a mix of small-scale volumes, locally dominated by magnetic energy release or storage. During the impulsive phase, flare-induced losses of magnetic energy are located at successively higher heights in the atmosphere. 4) The magnetic fields emanating from locations populated by flare ribbons (low-atmosphere footpoints of newly reconnected magnetic fields) are capable of monitoring the approximate location of the reconnection site in the solar corona, as a function of height and time. 5) The large-scale coronal magnetic field may serve as a strong confinement, capable of resulting in failed eruptions (CME-less flares). 6) During confined flares, magnetic fields may be subject to multiple magnetic reconnection processes, as suggested by the observation of repeated brightenings at localized positions along the flare ribbons.