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Register a new userForce-Free Field Reconstructions Enhanced by Chromospheric Magnetic Field Data
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3D picture of the coronal magnetic field remains an outstanding problem in solar physics, particularly, in active regions. Nonlinear force-free field reconstructions that employ routinely available full-disk photospheric vector magnetograms represent state-of-the-art coronal magnetic field modeling. Such reconstructions, however, suffer from an inconsistency between a force-free coronal magnetic field and non-force-free photospheric boundary condition, from which the coronal reconstruction is performed. In this study we focus on integrating the additional chromospheric and / or coronal magnetic field data with the vector photospheric magnetograms with the goal of improving the reliability of the magnetic field reconstructions. We develop a corresponding modification of the available optimization codes described in Fleishman et al. (2017) and test their performance using a full-fledged MHD model obtained from the Bifrost code by performing a `voxel-by-voxel comparison between the reconstructed and the model magnetic fields. We demonstrate that adding even an incomplete set of chromospheric magnetic field data can measurably improve the reconstruction of the coronal magnetic field, greatly improve reconstructions of the magnetic connectivity and of the coronal electric current.
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Force-free extrapolations are widely used to study the magnetic field in the solar corona based on surface measurements. The extrapolations assume that the ratio of internal energy of the plasma to magnetic energy, the plasma-beta is negligible. Despite the widespread use of this assumption observations, models, and theoretical considerations show that beta is of the order of a few percent to more than 10%, and thus not small. We investigate what consequences this has for the reliability of extrapolation results. We use basic concepts starting with the force and the energy balance to infer relations between plasma-beta and free magnetic energy, to study the direction of currents in the corona with respect to the magnetic field, and to estimate the errors in the free magnetic energy by neglecting effects of the plasma (beta<<1). A comparison with a 3D MHD model supports our basic considerations. If plasma-beta is of the order of the relative free energy (the ratio of the free magnetic energy to the total magnetic energy) then the pressure gradient can balance the Lorentz force. This is the case in the solar corona, and therefore the currents are not properly described. In particular the error in terms of magnetic energy by neglecting the plasma is of the order of the free magnetic energy, so that the latter can not be reliably determined by an extrapolation. While a force-free extrapolation might capture the magnetic structure and connectivity of the coronal magnetic field, the derived currents and free magnetic energy are not reliable. Thus quantitative results of extrapolations on the location and amount of heating in the corona (through current dissipation) and on the energy storage of the magnetic field (e.g. for eruptive events) are limited.
Extrapolations of solar photospheric vector magnetograms into three-dimensional magnetic fields in the chromosphere and corona are usually done under the assumption that the fields are force-free. The field calculations can be improved by preprocessing the photospheric magnetograms. We compare two preprocessing methods presently in use, namely the methods of Wiegelmann et al. (2006) and Fuhrmann et al. (2007). The two preprocessing methods were applied to a recently observed vector magnetogram. We examine the changes in the magnetogram effected by the two preprocessing algorithms. Furthermore, the original magnetogram and the two preprocessed magnetograms were each used as input data for nonlinear force-free field extrapolations by means of two different methods, and we analyze the resulting fields. Both preprocessing methods managed to significantly decrease the magnetic forces and magnetic torques that act through the magnetogram area and that can cause incompatibilities with the assumption of force-freeness in the solution domain. Both methods also reduced the amount of small-scale irregularities in the observed photospheric field, which can sharply worsen the quality of the solutions. For the chosen parameter set, the Wiegelmann et al. method led to greater changes in strong-field areas, leaving weak-field areas mostly unchanged, and thus providing an approximation of the magnetic field vector in the chromosphere, while the Fuhrmann et al. method weakly changed the whole magnetogram, thereby better preserving patterns present in the original magnetogram. Both preprocessing methods raised the magnetic energy content of the extrapolated fields to values above the minimum energy, corresponding to the potential field. Also, the fields calculated from the preprocessed magnetograms fulfill the solenoidal condition better than those calculated without preprocessing.
Aims. We analyze observational data from 4 instruments to study the correlations between chromospheric emission, spanning the heights from the temperature minimum region to the middle chromosphere, and photospheric magnetic field. Methods: The data consist of radio images at 3.5 mm from the Berkeley-Illinois-Maryland Array (BIMA), UV images at 1600 A from TRACE, Ca II K-line filtergrams from BBSO, and MDI/SOHO longitudinal photospheric magnetograms. For the first time interferometric millimeter data with the highest currently available resolution are included in such an analysis. We determine various parameters of the intensity maps and correlate the intensities with each other and with the magnetic field. Results: The chromospheric diagnostics studied here show a pronounced similarity in their brightness structures and map out the underlying photospheric magnetic field relatively well. We find a power law to be a good representation of the relationship between photospheric magnetic field and emission from chromospheric diagnostics at all wavelengths. The dependence of chromospheric brightness on magnetic field is found to be different for network and internetwork regions.
We present observations and magnetic field models of an intermediate filament present on the Sun in August 2012, associated with a polarity inversion line that extends from AR 11541 in the east into the quiet sun at its western end. A combination of SDO/AIA, SDO/HMI, and GONG H alpha data allow us to analyse the structure and evolution of the filament from 2012 August 4 23:00 UT to 2012 August 6 08:00 UT when the filament was in equilibrium. By applying the flux rope insertion method, nonlinear force-free field models of the filament are constructed using SDO/HMI line-of-sight magnetograms as the boundary condition at the two times given above. Guided by observed filament barbs, both modelled flux ropes are split into three sections each with a different value of axial flux to represent the non-uniform photospheric field distribution. The flux in the eastern section of the rope increases by 4$times$10$^{20}$ Mx between the two models, which is in good agreement with the amount of flux cancelled along the internal PIL of AR 11541, calculated to be 3.2$times$10$^{20}$ Mx. This suggests that flux cancellation builds flux into the filaments magnetic structure. Additionally, the number of field line dips increases between the two models in the locations where flux cancellation, the formation of new filament threads and growth of the filament is observed. This suggests that flux cancellation associated with magnetic reconnection forms concave-up magnetic field that lifts plasma into the filament. During this time, the free magnetic energy in the models increases by 0.2$times$10$^{31}$ ergs.
We investigate the plasma and magnetic environment of active region NOAA 11261 on 2 August 2011 around a GOES M1.4 flare/CME (SOL2011-08-02T06:19). We compare coronal emission at (extreme) ultraviolet and X-ray wavelengths, using SDO AIA and RHESSI images, in order to identify the relative timing and locations of reconnection-related sources. We trace flare ribbon signatures at ultraviolet wavelengths, in order to pin down the intersection of previously reconnected flaring loops at the lower solar atmosphere. These locations are used to calculate field lines from 3D nonlinear force-free magnetic field models, established on the basis of SDO HMI photospheric vector magnetic field maps. With this procedure, we analyze the quasi-static time evolution of the coronal model magnetic field previously involved in magnetic reconnection. This allows us, for the first time, to estimate the elevation speed of the current sheets lower tip during an on-disk observed flare, as a few kilometers per second. Comparison to post-flare loops observed later above the limb in STEREO EUVI images supports this velocity estimate. Furthermore, we provide evidence for an implosion of parts of the flaring coronal model magnetic field, and identify the corresponding coronal sub-volumes associated to the loss of magnetic energy. Finally, we spatially relate the build up of magnetic energy in the 3D models to highly sheared fields, established due to dynamic relative motions of polarity patches within the active region.
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