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Register a new userEstimating Electric Fields from Vector Magnetogram Sequences
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Determining the electric field (E-field) distribution on the Suns photosphere is essential for quantitative studies of how energy flows from the Suns photosphere, through the corona, and into the heliosphere. This E-field also provides valuable input for data-driven models of the solar atmosphere and the Sun-Earth system. We show how Faradays Law can be used with observed vector magnetogram time series to estimate the photospheric E-field, an ill-posed inversion problem. Our method uses a poloidal-toroidal decomposition (PTD) of the time derivative of the vector magnetic field. The PTD solutions are not unique; the gradient of a scalar potential can be added to the PTD E-field without affecting consistency with Faradays Law. We present an iterative technique to determine a potential function consistent with ideal MHD evolution; but this E-field is also not a unique solution to Faradays Law. Finally, we explore a variational approach that minimizes an energy functional to determine a unique E-field, similar to Longcopes Minimum Energy Fit. The PTD technique, the iterative technique, and the variational technique are used to estimate E-fields from a pair of synthetic vector magnetograms taken from an MHD simulation; and these E-fields are compared with the simulations known electric fields. These three techniques are then applied to a pair of vector magnetograms of solar active region NOAA AR8210, to demonstrate the methods with real data.
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Photospheric electric fields, estimated from sequences of vector magnetic field and Doppler measurements, can be used to estimate the flux of magnetic energy (the Poynting flux) into the corona and as time-dependent boundary conditions for dynamic models of the coronal magnetic field. We have modified and extended an existing method to estimate photospheric electric fields that combines a poloidal-toroidal (PTD) decomposition of the evolving magnetic field vector with Doppler and horizontal plasma velocities. Our current, more comprehensive method, which we dub the {bf P}TD-{bf D}oppler-{bf F}LCT {bf I}deal (PDFI) technique, can now incorporate Doppler velocities from non-normal viewing angles. It uses the texttt{FISHPACK} software package to solve several two-dimensional Poisson equations, a faster and more robust approach than our previous implementations. Here, we describe systematic, quantitative tests of the accuracy and robustness of the PDFI technique using synthetic data from anelastic MHD (texttt{ANMHD}) simulations, which have been used in similar tests in the past. We find that the PDFI method has less than $1%$ error in the total Poynting flux and a $10%$ error in the helicity flux rate at a normal viewing angle $(theta=0$) and less than $25%$ and $10%$ errors respectively at large viewing angles ($theta<60^circ$). We compare our results with other inversion methods at zero viewing angle, and find that our methods estimates of the fluxes of magnetic energy and helicity are comparable to or more accurate than other methods. We also discuss the limitations of the PDFI method and its uncertainties.
The availability of vector magnetogram sequences with sufficient accuracy and cadence to estimate the time derivative of the magnetic field allows us to use Faradays law to find an approximate solution for the electric field in the photosphere, using a Poloidal-Toroidal Decomposition (PTD) of the magnetic field and its partial time derivative. Without additional information, however, the electric field found from this technique is under-determined -- Faradays law provides no information about the electric field that can be derived the gradient of a scalar potential. Here, we show how additional information in the form of line-of-sight Doppler flow measurements, and motions transverse to the line-of-sight determined with ad-hoc methods such as local correlation tracking, can be combined with the PTD solutions to provide much more accurate solutions for the solar electric field, and therefore the Poynting flux of electromagnetic energy in the solar photosphere. Reliable, accurate maps of the Poynting flux are essential for quantitative studies of the buildup of magnetic energy before flares and coronal mass ejections.
Context. High resolution magnetic field measurements are routinely done only in the solar photosphere. Higher layers like the chromosphere and corona can be modeled by extrapolating the photospheric magnetic field upward. In the solar corona, plasma forces can be neglected and the Lorentz force vanishes. This is not the case in the upper photosphere and chromosphere where magnetic and non-magnetic forces are equally important. One way to deal with this problem is to compute the plasma and magnetic field self-consistently with a magnetohydrostatic (MHS) model. Aims. We aim to derive the magnetic field, plasma pressure and density of AR11768 by applying the newly developed extrapolation technique to the SUNRISE/IMaX data. Methods. An optimization method is used for the MHS modeling. The initial conditions consist of a nonlinear force-free field (NLFFF) and a gravity-stratified atmosphere. Results. In the non-force-free layer, which is spatially resolved by the new code, Lorentz forces are effectively balanced by the gas pressure gradient force and the gravity force. The pressure and density are depleted in strong field regions, which is consistent with observations. Denser plasma, however, is also observed at some parts of the active region edges. In the chromosphere, the fibril-like plasma structures trace the magnetic field nicely. Bright points in SUNRISE/SuFI 3000 {$AA$} images are often accompanied by the plasma pressure and electric current concentrations. In addition, the average of angle between MHS field lines and the selected chromospheric fibrils is $11.8^circ$, which is smaller than those computed from the NLFFF model ($15.7^circ$) and linear MHS model ($20.9^circ$). This indicates that the MHS solution provides a better representation of the magnetic field in the chromosphere.
The minimum-energy configuration for the magnetic field above the solar photosphere is curl-free (hence, by Amperes law, also current-free), so can be represented as the gradient of a scalar potential. Since magnetic fields are divergence free, this scalar potential obeys Laplaces equation, given an appropriate boundary condition (BC). With measurements of the full magnetic vector at the photosphere, it is possible to employ either Neumann or Dirichlet BCs there. Historically, the Neumann BC was used with available line-of-sight magnetic field measurements, which approximate the radial field needed for the Neumann BC. Since each BC fully determines the 3D vector magnetic field, either choice will, in general, be inconsistent with some aspect of the observed field on the boundary, due to the presence of both currents and noise in the observed field. We present a method to combine solutions from both Dirichlet and Neumann BCs to determine a hybrid, least-squares potential field, which minimizes the integrated square of the residual between the potential and actual fields. This has advantages in both not overfitting the radial field used for the Neumann BC, and maximizing consistency with the observations. We demonstrate our methods with SDO/HMI vector magnetic field observations of AR 11158, and find that residual discrepancies between the observed and potential fields are significant, and are consistent with nonzero horizontal photospheric currents. We also analyze potential fields for two other active regions observed with two different vector magnetographs, and find that hybrid potential fields have significantly less energy than the Neumann fields in every case --- by more than 10^(32) erg in some cases. This has major implications for estimates of free magnetic energy in coronal field models, e.g., non-linear force-free field extrapolations.
We developed a flare prediction model using machine learning, which is optimized to predict the maximum class of flares occurring in the following 24 h. Machine learning is used to devise algorithms that can learn from and make decisions on a huge amount of data. We used solar observation data during the period 2010-2015, such as vector magnetogram, ultraviolet (UV) emission, and soft X-ray emission taken by the Solar Dynamics Observatory and the Geostationary Operational Environmental Satellite. We detected active regions from the full-disk magnetogram, from which 60 features were extracted with their time differentials, including magnetic neutral lines, the current helicity, the UV brightening, and the flare history. After standardizing the feature database, we fully shuffled and randomly separated it into two for training and testing. To investigate which algorithm is best for flare prediction, we compared three machine learning algorithms: the support vector machine (SVM), k-nearest neighbors (k-NN), and extremely randomized trees (ERT). The prediction score, the true skill statistic (TSS), was higher than 0.9 with a fully shuffled dataset, which is higher than that for human forecasts. It was found that k-NN has the highest performance among the three algorithms. The ranking of the feature importance showed that the previous flare activity is most effective, followed by the length of magnetic neutral lines, the unsigned magnetic flux, the area of UV brightening, and the time differentials of features over 24 h, all of which are strongly correlated with the flux emergence dynamics in an active region.
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