Time Evolution of Coronal Magnetic Helicity in the Flaring Active Region NOAA 10930

TL;DR

This study investigates the evolution of coronal magnetic helicity in NOAA 10930 before and after an X3.4 flare, revealing a strong correlation between coronal helicity and surface injection, and suggesting flare involvement with helicity interactions.

Contribution

It provides a detailed analysis of the 3D magnetic helicity evolution in a flaring active region, combining coronal reconstructions with surface flux measurements, which is a novel integrated approach.

Findings

Coronal helicity correlates well with surface helicity injection.

The active region's coronal helicity was approximately -4.3×10^43 Mx^2 before the flare.

Positive helicity injections occurred alongside negative helicity buildup prior to the flare.

Abstract

To study the three-dimensional (3D) magnetic field topology and its long-term evolution associated with the X3.4 flare of 2006 December 13, we investigate the coronal relative magnetic helicity in the flaring active region (AR) NOAA 10930 during the time period of December 8-14. The coronal helicity is calculated based on the 3D nonlinear force-free magnetic fields reconstructed by the weighted optimization method of Wiegelmann, and is compared with the amount of helicity injected through the photospheric surface of the AR. The helicity injection is determined from the magnetic helicity flux density proposed by Pariat et al. using Solar and Heliospheric Observatory/Michelson Doppler Imager magnetograms. The major findings of this study are the following. (1) The time profile of the coronal helicity shows a good correlation with that of the helicity accumulation by injection through the surface. (2) The coronal helicity of the AR is estimated to be -4.3$\times$10$^{43}$ Mx$^{2}$ just before the X3.4 flare. (3) This flare is preceded not only by a large increase of negative helicity, -3.2$\times$10$^{43}$ Mx$^{2}$, in the corona over ~1.5 days but also by noticeable injections of positive helicity though the photospheric surface around the flaring magnetic polarity inversion line during the time period of the channel structure development. We conjecture that the occurrence of the X3.4 flare is involved with the positive helicity injection into an existing system of negative helicity.