Photospheric Electric Fields and Energy Fluxes in the Eruptive Active Region NOAA 11158

From RHESSI Wiki

Jump to: navigation, search

Number: 261
1st Author: Maria Kazachenko
2nd Author:
Published: 14 September 2015
Next Nugget: GOES photometry
Previous Nugget: RHESSI and General Relativity
List all



Flares, CMEs, and other forms of spontaneous solar energy release - including RHESSI's hard X-ray and gamma-ray bursts - seem to require the gradual build-up of free energy in the solar corona. We are sure that this must come from the gradual transport of energy from the interior to the corona, but in the form of plasma effects rather than electromagnetic radiation (light waves). This is describable as a form of Poynting flux, but one that flows at the Alfvén speed rather than the speed of light. To estimate the Poynting flux one needs information about both the magnetic field in the plasma, and also the electric field - this latter is especially tricky.

The advent of high-cadence vector magnetic field and Doppler velocity measurements from e.g. HMI/SDO, SOT/Hinode and SOLIS, have made the estimation of electric fields in the solar photosphere possible. The calculation of the electric field from magnetic and Doppler data is critically important for various quantitative studies of the solar atmosphere. First, if we know both electric and magnetic field vectors in the photosphere, we can estimate both the Poynting flux of magnetic energy and the flux of relative magnetic helicity entering the corona. Second, knowledge of electric and magnetic fields enables the driving of time-dependent simulations of the coronal magnetic field. This is the goal of the Coronal Global Evolutionary Model (CGEM, Ref. [4]).

A particular active region, NOAA 11158, has attracted particular attention. This region produced excellent observations over a wide range of wavelengths, and produced the first X-class flare of Cycle 24: SOL2011-02-15 and a flood of interesting literature.

Method and Data

We have recently improved the electric field inversion methods introduced in Ref. [1] to create a comprehensive technique for calculating photospheric electric fields from vector magnetogram image sequences. The new method, which we dubbed the PDFI (an abbreviation for PTD-Doppler-FLCT-Ideal technique, where PTD and FLCT stand for Poloidal-Toroidal Decomposition and Fourier Local Correlation Tracking, respectively), has been systematically tested for accuracy and robustness, using synthetic data from simulations (see Ref. [2]). Here we take the next step forward, and apply the PDFI technique directly to observations.

The flare-productive active region (AR) NOAA 11158 was observed by the Solar Dynamics Observatory nearly continuously for a six-day period over 2011 February 10–16, right from its first emergence (see the Bz-snapshots in Figure 1; these show the vertical component of the solar magnetic field at the photosphere). We used this sequence of 770 vector magnetic field and velocity measurements to derive the temporal evolution of electric fields E and Poynting fluxes S during these six days.

Figure 1: (A)–(D): HMI vertical magnetic field (Bz) maps at four different times in the evolution of NOAA 11158. Panel (E): positive/negative vertical magnetic fluxes during the 6-day interval. Diamonds indicate the times of images on the left. An X2.2 flare is marked with the dashed line.


To describe the photospheric electric fields E and energy fluxes S in NOAA 11158, we use two approaches: we first show the spatial distribution of the B, E and S fields at two times, before and after the X2.2 flare; we then analyze their temporal spatially integrated evolution over six days of observations. For more details of the analysis see Ref. [5].

Magnetic Field: preflare vs postflare

Figure 2. Horizontal (arrows) and vertical (grayscale) components of the magnetic field in NOAA 11158 at preflare (top left) and postflare times (bottom left), and the difference image between the two (right panel). The blue and red colors correspond to horizontal fields in areas of positive and negative Bz.

Pre- and post-flare snapshots of the vertical magnetic field (Figure 2) show that the horizontal magnetic field close to the photospheric inversion line (PIL) increased by over 300 G during the X2.2 flare (see arrows), while the vertical magnetic field remained nearly constant, consistent with the field implosion scenario. The PIL separates the regions of opposite Bz orientation, i.e. up and down. On the difference image (right panel) we also notice two circular patterns, directed counter-clockwise in negative and clockwise in positive polarities, implying that the field connecting those polarities becomes less twisted during the flare.

Electric Field: preflare vs postflare

Figure 3. Horizontal (arrows) and vertical (grayscale) components of the electric field at preflare (top left) and postflare times (bottom left), and the difference image between the two (right panel). The blue and red colors correspond to horizontal fields in areas of positive and negative Ez.

We find the photospheric electric field vector, ranging from -2 to 2 V/cm, to increase its magnitude by up to 0.5 V/cm at the PIL and 1 V/cm away from the PIL during the flare (Figure 3). The horizontal component is mostly concentrated along the PIL, while the vertical component is largest at the PIL and in the sunspots’ penumbrae. The presence of a nonzero Ez is related to changes in the vertical current, which is mostly concentrated close to the main PIL (Ref. [3])

Poynting Flux: preflare vs postflare

Figure 4. Horizontal (arrows) and vertical (background) Poynting vector field components at preflare (top left) and postflare times (bottom left), and the difference image between the two (right panel). The blue and red colors correspond to Sh in positive and negative areas of the background Sz. The range of the background Sz is [-1, 1] 1010 erg cm-2s-1 in the left panels and [-0.4, 0.4] 1010 erg cm-2s-1 in the right panel.

We find the photospheric Poynting ranging from [-0.6 to 2.3] 1010 erg cm-2s-1 with majority of the energy flux moving upward into corona. More than half of the total energy input rate is injected from within the range of Sz = [109, 1010 ] erg cm-2s-1, while the rest of the energy is injected in the range of [108, 109 ] erg cm-2s-1. The strongest Poynting flux is concentrated at the PIL.

Six-day Evolution of Vertical Energy Flux

Integrating the Poynting flux in time and spatially over the NOAA 11158, we find the total magnetic energy before the flare to be E=[10.6+-3.1] 1032 erg. In spite of a very different approach, it is consistent within the uncertainty with the total energies from DAVE4VM, MCC and NLFFF method estimates and larger than the coronal NLFFF estimates.


This study is the first application of the PDFI electric field inversion technique to photospheric vector magnetic field and Doppler measurements. We find that the total amount of energy injected through the photosphere before the flare estimated by the PDFI method is consistent with estimates from other approaches, in spite of differing techniques. This agreement is very promising, implying that the PDFI technique is not only capable of describing the coronal energy and helicity budget, but can also provide instantaneous estimates of energy and helicity transferred through the photosphere. We believe that both the derived dataset of PDFI electric fields and the PDFI method itself will be useful to the science community for analysis of the evolution and spatial distribution of the photospheric electric fields, fluxes of energy and helicity, and their relationships with flare activity. In addition, PDFI electric fields can be used as time-dependent boundary conditions for data-driven models of coronal magnetic field evolution. The dataset of magnetic and electric fields and Poynting fluxes in NOAA 11158 is available for downloading on our website.


[1] "Estimating Electric Fields from Vector Magnetogram Sequences"

[2] "A Comprehensive Method of Estimating Electric Fields from Vector Magnetic Field and Doppler Measurements"

[3] "A Spatio-temporal Description of the Abrupt Changes in the Photospheric Magnetic and Lorentz-Force Vectors During the 15 February 2011 X2.2 Flare"

[4] "The Coronal Global Evolutionary Model: Using HMI Vector Magnetogram and Doppler Data to Model the Buildup of Free Magnetic Energy in the Solar Corona"

[5] "Photospheric Electric Fields and Energy Fluxes in the Eruptive Active Region NOAA 11158"

Personal tools