Bernd Inhester

A Critical Assessment of Nonlinear Force-Free Field Modeling of the Solar Corona for Active Region 10953

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, force-free 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 paper, 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 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.

The solar magnetic field

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 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.

How to deal with measurement errors and lacking data in nonlinear force-free coronal magnetic field modelling?

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.

Comparing magnetic field extrapolations with measurements of magnetic loops

We compare magnetic field extrapolations from a photospheric magnetogram with the observationally inferred struc- ture of magnetic loops in a newly developed active region. This is the first time that the reconstructed 3D-topology of the magnetic field is available to test the extrapolations. We compare the observations with potential fields, linear force-free fields and non-linear force-free fields. This comparison reveals that a potential field extrapolation is not suitable for a reconstruction of the magnetic field in this young, developing active region. The inclusion of field-line-parallel electric currents, the so called force-free approach, gives much better results. Furthermore, a non-linear force-free computation reproduces the observations better than the linear force-free approximation, although no free parameters are available in the former case.

First View of the Extended Green-Line Emission Corona At Solar Activity Minimum Using the Lasco-C1 Coronagraph on Soho

The newly developed C1 coronagraph as part of the Large-Angle Spectroscopic Coronagraph (LASCO) on board the SOHO spacecraft has been operating since January 29, 1996. We present observations obtained in the first three months of operation. The green-line emission corona can be made visible throughout the instruments full field of view, i.e., from 1.1 R⊙ out to 3.2 R⊙ (measured from Sun center). Quantitative evaluations based on calibrations cannot yet be performed, but some basic signatures show up even now: (1) There are often bright and apparently closed loop systems centered at latitudes of 30° to 45° in both hemispheres. Their helmet-like extensions are bent towards the equatorial plane. Farther out, they merge into one large equatorial ‘streamer sheet’ clearly discernible out to 32 R⊙. (2) At mid latitudes a more diffuse pattern is usually visible, well separated from the high-latitude loops and with very pronounced variability. (3) All high-latitude structures remain stable on time scales of several days, and no signature of transient disruption of high-latitude streamers was observed in these early data. (4) Within the first 4 months of observation, only one single ‘fast’ feature was observed moving outward at a speed of 70 km s-1 close to the equator. Faster events may have escaped attention because of data gaps. (5) The centers of high-latitude loops are usually found at the positions of magnetic neutral lines in photospheric magnetograms. The large-scale streamer structure follows the magnetic pattern fairly precisely. Based on our observations we conclude that the shape and stability of the heliospheric current sheet at solar activity minimum are probably due to high-latitude streamers rather than to the near-equatorial activity belt.

How Should One Optimize Nonlinear Force-Free Coronal Magnetic Field Extrapolations from SDO/HMI Vector Magnetograms?

The Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) provides photospheric vector magnetograms with a high spatial and temporal resolution. Our intention is to model the coronal magnetic field above active regions with the help of a nonlinear force-free extrapolation code. Our code is based on an optimization principle and has been tested extensively with semianalytic and numeric equilibria and applied to vector magnetograms from Hinode and ground-based observations. Recently we implemented a new version which takes into account measurement errors in photospheric vector magnetograms. Photospheric field measurements are often affected by measurement errors and finite nonmagnetic forces inconsistent for use as a boundary for a force-free field in the corona. To deal with these uncertainties, we developed two improvements: i) preprocessing of the surface measurements to make them compatible with a force-free field, and ii) new code which keeps a balance between the force-free constraint and deviation from the photospheric field measurements. Both methods contain free parameters, which must be optimized for use with data from SDO/HMI. In this work we describe the corresponding analysis method and evaluate the force-free equilibria by how well force-freeness and solenoidal conditions are fulfilled, by the angle between magnetic field and electric current, and by comparing projections of magnetic field lines with coronal images from the Atmospheric Imaging Assembly (SDO/AIA). We also compute the available free magnetic energy and discuss the potential influence of control parameters.

Observations of a rotating macrospicule associated with an X-ray jet

Aims. We attempt to understand the driving mechanism of a macrospicule and its relationship with a coronal jet. Methods. We study the dynamics of a macrospicule and an associated coronal jet captured by multi-spacecraft observations. Doppler velocities in both the macrospicule and the coronal jet are determined by EIS and SUMER spectra. Their temporal evolution is studied using X-ray and He II λ304 images. Results. A blueshift of -120 ± 15 km s -1 is detected on one side of the macrospicule, while a redshift of 50 ± 6 km s -1 is found at the base of the other side. The inclination angle of the macrospicule inferred from a stereoscopic analysis with STEREO suggests that the measured Doppler velocities can be attributed to a rotating motion of the macrospicule rather than a radial flow or an expansion. Conclusions. The macrospicule is driven by the unfolding motion of a twisted magnetic flux rope, while the associated X-ray jet is a radial outflow.

Factors Related to the Origin of a Gradual Coronal Mass Ejection Associated with an Eruptive Prominence on 1998 June 21-22

We present observations of a coronal mass ejection (CME) associated with an eruptive prominence during 1998 June 21-22 by LASCO (Large Angle Spectroscopic Coronagraph) aboard SOHO (Solar and Heliospheric Observatory). Various features in the three-part structured, white-light CME as observed by LASCO-C2 and C3 coronagraphs were compared with features in the other wavelengths, for example, in Fe XIV and Fe X emission lines obtained from LASCO C1, in Hα from Helio-Research and at 17 GHz obtained from Nobeyama Radioheliograph. We have investigated conditions in several data sets to understand the eruptive and the pre-eruptive scenario of the CME. The CME and the eruptive prominence accelerate up to ~20 R☉ and then decelerate to the velocity of the ambient slow solar wind. The analysis clearly shows that this particular CME is a typical case of a very slow or gradual CME for which it is difficult to define an exact onset time. The CME could be tracked for about 30 hours until it crossed a distance of 30 R☉ and disappeared from the field of view of the LASCO-C3 coronagraph. The height-time profiles of various features of this CME suggest that the leading edge of the CME and the top of the prominence or the core follow similar pattern, implying a common driver for both the CME and the eruptive prominence. The observations provide strong evidence that the CME and the prominence eruption resulted from a common cause which is the global restructuring of the magnetic field in the corona in an extensive volume of space near and including the CME. The restructuring in turn was a consequence of newly emerging flux regions near and within the neighboring active regions close to the base of the CME.

FIRST STEREOSCOPIC CORONAL LOOP RECONSTRUCTIONS FROM STEREO SECCHI IMAGES

We present the first reconstruction of the three-dimensional shape of magnetic loops in an active region from two different vantage points based on simultaneously recorded images. The images were taken by the two EUVI telescopes of the SECCHI instrument on board the recently launched STEREO spacecraft when the heliocentric separation of the two space probes was 12°. We demonstrate that these data allow us to obtain a reliable three-dimensional reconstruction of sufficiently bright loops. The result is compared with field lines derived from a coronal magnetic field model extrapolated from a photospheric magnetogram recorded nearly simultaneously by SOHO MDI. We attribute discrepancies between reconstructed loops and extrapolated field lines to the inadequacy of the linear force-free field model used for the extrapolation.

Direct determination of the local ionospheric hall conductance distribution from two-dimensional electric and magnetic field data

From two-dimensional ground magnetic and ionospheric electric field observations it should in principle be possible to estimate the two-dimensional distribution of the ionospheric conductance. In the past this was achieved using auroral zone data by modeling the ionospheric conductances on a trial-and-error basis until the observed magnetic variations were reproduced. No information about the existence or the uniqueness of the solution was available this way. We have developed a method to directly deduce the Hall conductance distribution ΣH from ground magnetic and ionospheric electric field observations based upon some assumption for the ratio of the Hall to the Pedersen conductivity. In general, the solutions are shown not to be unique because for a specific solution the value of ΣH on certain parts of the boundary of the two-dimensional domain has to be specified. However, in many situations, especially in the presence of strong and isolated field-aligned currents, these boundary values become less influential, and the solution can be shown to be practically unique over a large area of the domain. In some cases, a rather restrictive relation between the electric field and the equivalent height-integrated current density is shown to hold that could be used to cross-check the quality of the observations. As a specific example, we apply our formalism to the observation of a Harang discontinuity obtained in northern Scandinavia simultaneously by the STARE coherent radar system and the IMS Scandinavian Magnetometer Array.