Photospheric response to a flare

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Nugget
Number: 332
1st Author: Mike Wheatland
2nd Author:
Published: 17 September 2018
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Introduction

Solar flares involve sudden conversion of magnetic energy into other forms in the solar corona. In particular, flares accelerate large numbers of electrons to 10-100 keV, producing hard-X-ray emission in the low solar atmosphere. Flares introduce sudden and permanent changes in the photospheric magnetic field. Vector magnetogram observations show that the predominant change is in the horizontal magnetic field (parallel to the photosphere), which tends to increase along a flaring neutral line. By definition the neutral line marks the change of polarity of the field, dividing outward from inward domains. Flares can also produce sudden photospheric motion, strikingly illustrated by the rotation of a sunspot in response to a flare (Refs. [1,2]) an event which was likened to "the tail wagging the dog" (Ref. [3]). The sunspot was observed to differentially rotate as the flare ribbons swept across it. Figures 1 and 2 show photospheric data for this event.

Figure 1: Changes in the vertical component of the magnetic field (left) and the vertical electric current density (right) in the flare SOL2015-06-22, using HMI data from the SDO space observatory. The rotating sunspot reported by Ref. [1] is in the box. The electric current density is observed to suddenly increase close to the neutral line (black), coincident with the flare.
Figure 2: The vector change in the horizontal magnetic field for the SDO/HMI data shown in Figure 1. The horizontal field increases over a broad region along the neutral line. The largest changes are about 1000 gauss.

The photospheric field changes are interpreted as the photospheric response to coronal magnetic restructuring due to magnetic reconnection. Here we consider a simple 2D model for the changes in the field and flows introduced at the photosphere, in terms of a large-amplitude shear Alfvén wave impacting the photosphere (Ref. [4]).

Large amplitude shear Alfvén wave model

We consider a simple 2D model in which the photosphere is the z = 0 plane, and the x-axis is directed away from the neutral line. Figure 3 illustrates the model. A large-amplitude shear Alfvén wave is assumed to propagate downwards at the coronal Alfvén speed A1, introducing shear field and flow components By = B1 and vy = v1, respectively, behind a front. The wave front is assumed to be obliquely oriented to the photosphere, so that the changes are introduced first close to the neutral line, and then further away. The wave is partially reflected and partially transmitted at the photospheric boundary. The wave propagates at a lower Alfvén spee vA2 in the sub-photosphere. Behind the reflected and transmitted fronts, there are new shear components By = B2 and vy = v2.

The MHD equations and continuity imply the relationships:

Failed to parse (PNG conversion failed;

check for correct installation of latex, dvips, gs, and convert): \nabla \times \mathbf{B} = \mu \mathbf{J} + \mu \epsilon \frac{\partial \mathbf{E}}{\partial t}.


so that in the limit of a very dense photosphere, B2 ➝ 2B1 and v2 ➝ 0.

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