[en] 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 decomposition (PTD) of the evolving magnetic field vector with Doppler and horizontal plasma velocities. Our current, more comprehensive method, which we dub the 'PTD-Doppler-FLCT Ideal' (PDFI) technique, can now incorporate Doppler velocities from non-normal viewing angles. It uses the 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 (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 (θ = 0) and less than 25% and 10% errors, respectively, at large viewing angles (θ < 60°). We compare our results with other inversion methods at zero viewing angle and find that our method's 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.

[en] The zero point of measured photospheric Doppler shifts is uncertain for at least two reasons: instrumental variations (from, e.g., thermal drifts); and the convective blueshift, a known correlation between intensity and upflows. Accurate knowledge of the zero point is, however, useful for (1) improving estimates of the Poynting flux of magnetic energy across the photosphere, and (2) constraining processes underlying flux cancellation, the mutual apparent loss of magnetic flux in closely spaced, opposite-polarity magnetogram features. We present a method to absolutely calibrate line-of-sight (LOS) velocities in solar active regions (ARs) near disk center using three successive vector magnetograms and one Dopplergram coincident with the central magnetogram. It exploits the fact that Doppler shifts measured along polarity inversion lines (PILs) of the LOS magnetic field determine one component of the velocity perpendicular to the magnetic field, and optimizes consistency between changes in LOS flux near PILs and the transport of transverse magnetic flux by LOS velocities, assuming that ideal electric fields govern the magnetic evolution. Previous calibrations fitted the center-to-limb variation of Doppler velocities, but this approach cannot, by itself, account for residual convective shifts at the limb. We apply our method to vector magnetograms of AR 11158, observed by the Helioseismic and Magnetic Imager aboard the Solar Dynamics Observatory, and find clear evidence of offsets in the Doppler zero point in the range of 50-550 m s^–1. In addition, we note that a simpler calibration can be determined from an LOS magnetogram and Dopplergram pair from the median Doppler velocity among all near-disk-center PIL pixels. We briefly discuss shortcomings in our initial implementation, and suggest ways to address these. In addition, as a step in our data reduction, we discuss the use of temporal continuity in the transverse magnetic field direction to correct apparently spurious fluctuations in resolution of the 180° ambiguity.

[en] How much electromagnetic energy crosses the photosphere in evolving solar active regions (ARs)? With the advent of high-cadence vector magnetic field observations, addressing this fundamental question has become tractable. In this paper, we apply the “PTD-Doppler-FLCT-Ideal” (PDFI) electric field inversion technique of Kazachenko et al. to a 6-day vector magnetogram and Doppler velocity sequence from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory to find the electric field and Poynting flux evolution in NOAA 11158, which produced an X2.2 flare early on 2011 February 15. We find photospheric electric fields ranging up to 2 V cm⁻¹. The Poynting fluxes range from [−0.6 to 2.3] × ${10}^{10}\mathrm{e}\mathrm{r}\mathrm{g}$ cm⁻² s⁻¹, mostly positive, with the largest contribution to the energy budget in the range of $[{10}^9-<!--\; ???\; -->{10}^{10}]$ erg cm⁻² s⁻¹. Integrating the instantaneous energy flux over space and time, we find that the total magnetic energy accumulated above the photosphere from the initial emergence to the moment before the X2.2 flare to be $E=10.6\times <!--\; ??\; -->{10}^{32}\mathrm{e}\mathrm{r}\mathrm{g}$, which is partitioned as 2.0×10³²erg and $8.6\times <!--\; ??\; -->{10}^{32}\mathrm{e}\mathrm{r}\mathrm{g}$, respectively, between free and potential energies. Those estimates are consistent with estimates from preflare nonlinear force-free field extrapolations and the Minimum Current Corona estimates, in spite of our very different approach. This study of photospheric electric fields demonstrates the potential of the PDFI approach for estimating Poynting fluxes and opens the door to more quantitative studies of the solar photosphere and more realistic data-driven simulations of coronal magnetic field evolution.

[en] We estimated photospheric velocities by separately applying the Fourier Local Correlation Tracking and Differential Affine Velocity Estimator methods to 2708 co-registered pairs of SOHO/MDI magnetograms, with nominal 96 minute cadence and ∼2'' pixels, from 46 active regions (ARs) from 1996 to 1998 over the time interval τ₄₅ when each AR was within 45⁰ of disk center. For each magnetogram pair, we computed the reprojected, average estimated radial magnetic field, B-tilde_R; and each tracking method produced an independently estimated flow field, u. We then quantitatively characterized these magnetic and flow fields by computing several extensive and intensive properties of each; extensive properties scale with AR size, while intensive properties do not depend directly on AR size. Intensive flow properties included moments of speeds, horizontal divergences, and radial curls; extensive flow properties included sums of these properties over each AR, and a crude proxy for the ideal Poynting flux, S_R=Σ|u|B-tilde_R². Several quantities derived from B-tilde_R were also computed, including: Φ, the total unsigned flux; R, a measure of the unsigned flux near strong-field polarity inversion lines; and ΣB-tilde_R². Next, using correlation and discriminant analysis, we investigated the associations between these properties and flares from the GOES flare catalog, when averaged over both τ₄₅ and shorter time windows of 6 and 24 hr. Our AR sample included both flaring and flare-quiet ARs; the latter did not flare above GOES C1.0 level during τ₄₅. Among magnetic properties, we found R to be most strongly associated with flare flux. Among extensive flow properties, the proxy Poynting flux, S_R , was most strongly associated with flare flux, at a level comparable to that of R. All intensive flow properties studied were more poorly associated with flare flux than these extensive properties. Past flare activity was also associated with future flare occurrence. The largest coefficients of determination from correlations with flare flux that we performed are ∼0.25, implying no single variable that we considered can explain the majority of variability in average flare flux.

[en] Recent efforts coupling our Sun-to-Earth magnetohydrodynamics (MHD) model and lower-corona magnetofrictional (MF) model are described. Our Global Heliospheric MHD (GHM) model uses time-dependent three-component magnetic field data from the lower-corona MF model as time-dependent boundary values. The MF model uses data-assimilation techniques to introduce the vector magnetic field data from the Solar Dynamics Observatory/Helioseismic and Magnetic Imager, hence as a whole this simulation coupling structure is driven with actual observations. The GHM model employs a newly developed interface boundary treatment that is based on the concept of characteristics, and it properly treats the interface boundary sphere set at a height of the sub-Alfvénic lower corona (1.15 R _⊙ in this work). The coupled model framework numerically produces twisted nonpotential magnetic features and consequent eruption events in the solar corona in response to the time-dependent boundary values. The combination of our two originally independently developed models presented here is a model framework toward achieving further capabilities of modeling the nonlinear time-dependent nature of magnetic field and plasma, from small-scale solar active regions to large-scale solar wind structures. This work is a part of the Coronal Global Evolutionary Model project for enhancing our understanding of Sun–Earth physics to help improve space weather capabilities.

[en] Knowledge of electric fields in the photosphere is required to calculate the electromagnetic energy flux through the photosphere and set up boundary conditions for data-driven magnetohydrodynamic (MHD) simulations of solar eruptions. Recently, the PDFI_SS method for inversions of electric fields from a sequence of vector magnetograms and Doppler velocity measurements was improved to incorporate spherical geometry and a staggered-grid description of variables. The method was previously validated using synthetic data from anelastic MHD (ANMHD) simulations. In this paper, we further validate the PDFI_SS method, using approximately 1 hr long MHD simulation data of magnetic flux emergence from the upper convection zone into the solar atmosphere. We reconstruct photospheric electric fields and calculate the Poynting flux, and we compare those to the actual values from the simulations. We find that the accuracy of the PDFI_SS reconstruction is quite good during the emergence phase of the simulated ephemeral active region evolution and decreases during the shearing phase. Analyzing our results, we conclude that the more complex nature of the evolution (compared to the previously studied ANMHD case) that includes the shearing evolution phase is responsible for the obtained accuracy decrease.

[en] Solar active region (AR) 12192 of 2014 October hosts the largest sunspot group in 24 years. It is the most prolific flaring site of Cycle 24 so far, but surprisingly produced no coronal mass ejection (CME) from the core region during its disk passage. Here, we study the magnetic conditions that prevented eruption and the consequences that ensued. We find AR 12192 to be “big but mild”; its core region exhibits weaker non-potentiality, stronger overlying field, and smaller flare-related field changes compared to two other major flare-CME-productive ARs (11429 and 11158). These differences are present in the intensive-type indices (e.g., means) but generally not the extensive ones (e.g., totals). AR 12192's large amount of magnetic free energy does not translate into CME productivity. The unexpected behavior suggests that AR eruptiveness is limited by some relative measure of magnetic non-potentiality over the restriction of background field, and that confined flares may leave weaker photospheric and coronal imprints compared to their eruptive counterparts

[en] We describe the PDFI_SS software library, which is designed to find the electric field at the Sun’s photosphere from a sequence of vector magnetogram and Doppler velocity measurements and estimates of horizontal velocities obtained from local correlation tracking using the recently upgraded Fourier Local Correlation Tracking code. The library, a collection of FORTRAN subroutines, uses the “PDFI” technique described by Kazachenko et al., but modified for use in spherical, Plate Carrée geometry on a staggered grid. The domain over which solutions are found is a subset of the global spherical surface, defined by user-specified limits of colatitude and longitude. Our staggered grid approach, based on that of Yee, is more conservative and self-consistent compared to the centered, Cartesian grid used by Kazachenko et al. The library can be used to compute an end-to-end solution for electric fields from data taken by the HMI instrument aboard NASA’s SDO mission. This capability has been incorporated into the HMI pipeline processing system operating at SDO’s Joint Science Operations Center. The library is written in a general and modular way so that the calculations can be customized to modify or delete electric field contributions, or used with other data sets. Other applications include “nudging” numerical models of the solar atmosphere to facilitate assimilative simulations. The library includes an ability to compute “global” (whole-Sun) electric field solutions. The library also includes an ability to compute potential magnetic field solutions in spherical coordinates. This distribution includes a number of test programs that allow the user to test the software.

[en] The Coronal Global Evolutionary Model (CGEM) provides data-driven simulations of the magnetic field in the solar corona to better understand the build-up of magnetic energy that leads to eruptive events. The CGEM project has developed six capabilities. CGEM modules (1) prepare time series of full-disk vector magnetic field observations to (2) derive the changing electric field in the solar photosphere over active-region scales. This local electric field is (3) incorporated into a surface flux transport model that reconstructs a global electric field that evolves magnetic flux in a consistent way. These electric fields drive a (4) 3D spherical magnetofrictional (SMF) model, either at high resolution over a restricted range of solid angles or at lower resolution over a global domain to determine the magnetic field and current density in the low corona. An SMF-generated initial field above an active region and the evolving electric field at the photosphere are used to drive (5) detailed magnetohydrodynamic (MHD) simulations of active regions in the low corona. SMF or MHD solutions are then used to compute emissivity proxies that can be compared with coronal observations. Finally, a lower-resolution SMF magnetic field is used to initialize (6) a global MHD model that is driven by an SMF electric field time series to simulate the outer corona and heliosphere, ultimately connecting Sun to Earth. As a demonstration, this report features results of CGEM applied to observations of the evolution of NOAA Active Region 11158 in 2011 February.