Nonlinear force-free field (NLFFF) models are thought to be viable tools for investigating the structure, dynamics and evolution of the coronae of solar active regions. In a series of NLFFF modeling studies, we have found that NLFFF models are successful in application to analytic test cases, and relatively successful when applied to numerically constructed Sun-like test cases, but they are less successful in application to real solar data. Different NLFFF models have been found to have markedly different field line configurations and to provide widely varying estimates of the magnetic free energy in the coronal volume, when applied to solar data. NLFFF models require consistent, forcefree vector magnetic boundary data. However, vector magnetogram observations sampling the photosphere, which is dynamic and contains significant Lorentz and buoyancy forces, do not satisfy this requirement, thus creating several major problems for force-free coronal modeling efforts. In this article, we discuss NLFFF modeling of NOAA Active Region 10953 using Hinode/SOT-SP, Hinode/XRT, STEREO/SECCHI-EUVI, and SOHO/MDI observations, and in the process illustrate the three such issues we judge to be critical to the success of NLFFF modeling: (1) vector magnetic field data covering larger areas are needed so that more electric currents associated with the full active regions of interest are measured, (2) the modeling algorithms need a way to accommodate the various uncertainties in the boundary data, and (3) a more realistic physical model is needed to approximate the photosphere-to-corona interface in order to better transform the forced photospheric magnetograms into adequate approximations of nearly force-free fields at the base of the corona. We make recommendations for future modeling efforts to overcome these as yet unsolved problems.

Knowledge regarding the coronal magnetic field is important for the understanding of many phenomena, like flares and coronal mass ejections. Because of the low plasma beta in the solar corona, the coronal magnetic field is often assumed to be force-free and we use photospheric vector magnetograph data to extrapolate the magnetic field into the corona with the help of a nonlinear force-free optimization code. Unfortunately, the measurements of the photospheric magnetic field contain inconsistencies and noise. In particular, the transversal components (say B x and B y ) of current vector magnetographs have their uncertainties. Furthermore, the magnetic field in the photosphere is not necessarily force free and often not consistent with the assumption of a force-free field above the magnetogram. We develop a preprocessing procedure to drive the observed nonforce-free data towards suitable boundary conditions for a force-free extrapolation. As a result, we get a data set which is as close as possible to the measured data and consistent with the force-free assumption.

No abstract

The magnetic field of the Sun is the underlying cause of the many diverse phenomena combined under the heading of solar activity. Here we describe the magnetic field as it threads its way from the bottom of the convection zone, where it is built up by the solar dynamo, to the solar surface, where it manifests itself in the form of sunspots and faculae, and beyond into the outer solar atmosphere and, finally, into the heliosphere. On the way it, transports energy from the surface and the subsurface layers into the solar corona, where it heats the gas and accelerates the solar wind.

The space mission STEREO will provide images from two viewpoints. An important aim of the STEREO mission is to get a 3D view of the solar corona. We develop a program for the stereoscopic reconstruction of 3D coronal loops from images taken with the two STEREO spacecraft. A pure geometric triangulation of coronal features leads to ambiguities because the dilute plasma emissions complicates the association of features in image 1 with features in image 2. As a consequence of these problems the stereoscopic reconstruction is not unique and multiple solutions occur. We demonstrate how these ambiguities can be resolved with the help of different coronal magnetic field models (potential, linear and non-linear force-free fields). The idea is that, due to the high conductivity in the coronal plasma, the emitting plasma outlines the magnetic field lines. Consequently the 3D coronal magnetic field provides a proxy for the stereoscopy which allows to eliminate inconsistent configurations. The combination of stereoscopy and magnetic modelling is more powerful than one of these tools alone. We test our method with the help of a model active region and plan to apply it to the solar case as soon as STEREO data become available.Comment: 18 pages, 5 figure

Context. The heating of the solar corona by small heating events requires an increasing number of such events at progressively smaller scales, with the bulk of the heating occurring at scales that are currently unresolved. Aims. The goal of this work is to study the smallest brightening events observed in the extreme-UV quiet Sun. Methods. We used commissioning data taken by the Extreme Ultraviolet Imager (EUI) on board the recently launched Solar Orbiter mission. On 30 May 2020, the EUI was situated at 0.556 AU from the Sun. Its High Resolution EUV telescope (HRI EUV , 17.4 nm passband) reached an exceptionally high two-pixel spatial resolution of 400 km. The size and duration of small-scale structures was determined by the HRI EUV data, while their height was estimated from triangulation with simultaneous images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) mission. This is the first stereoscopy of small-scale brightenings at high resolution. Results. We observed small localised brightenings, also known as 'campfires', in a quiet Sun region with length scales between 400 km and 4000 km and durations between 10 sec and 200 sec. The smallest and weakest of these HRI EUV brightenings have not been previously observed. Simultaneous observations from the EUI High-resolution Lyman-α telescope (HRI Lya ) do not show localised brightening events, but the locations of the HRI EUV events clearly correspond to the chromospheric network. Comparisons with simultaneous AIA images shows that most events can also be identified in the 17.1 nm, 19.3 nm, 21.1 nm, and 30.4 nm pass-bands of AIA, although they appear weaker and blurred. Our differential emission measure (DEM) analysis indicated coronal temperatures peaking at log T ≈ 6.1 − 6.15. We determined the height for a few of these campfires to be between 1000 and 5000 km above the photosphere. Conclusions. We find that 'campfires' are mostly coronal in nature and rooted in the magnetic flux concentrations of the chromospheric network. We interpret these events as a new extension to the flare-microflare-nanoflare family. Given their low height, the EUI 'campfires' could stand as a new element of the fine structure of the transition region-low corona, that is, as apexes of small-scale loops that undergo internal heating all the way up to coronal temperatures.

Context. The measured solar photospheric magnetic field vector is extrapolated into the solar corona under the assumption of a force-free plasma. In the generic case this problem is nonlinear. Aims. We aim to improve an algorithm for computing the nonlinear force-free coronal magnetic field. We are in particular interested to incorporate measurement errors and to handle lacking data in the boundary conditions. Methods. We solve the nonlinear force-free field equations by minimizing a functional. Within this work we extend the functional by an additional term, which allows us to incorporate measurement errors and treat regions with lacking observational data. We test the new code with the help of a well known semi-analytic test case. We compare coronal magnetic field extrapolations from ideal boundary conditions and boundary conditions where the transversal magnetic field information is lacking or has a poor signal-to-noise ratio in weak field regions. Results. For ideal boundary conditions the new code gives the same result as the old code. The advantage of the new approach, which includes an error matrix, is visible only for non-ideal boundary conditions. The force-free and solenoidal conditions are fulfilled significantly better and the solutions agrees somewhat better with the exact solution. The new approach also relaxes the boundary and allows a deviation from the boundary data in poor signal-to-noise ratio areas. Conclusions. The incorporation of measurement errors in the updated extrapolation code significantly improves the quality of nonlinear force-free field extrapolation from imperfect boundary conditions.

No abstract