Force-Free Field Modeling of Twist and Braiding-Induced Magnetic Energy in an Active-Region Corona

Abstract

The theoretical concept that braided magnetic field lines in the solar corona may dissipate a sufficient amount of energy to account for the brightening observed in the active-region corona, has been substantiated by highresolution observations only recently. From the analysis of coronal images obtained with the High Resolution Coronal Imager, first observational evidence of the braiding of magnetic field lines was reported by Cirtain et al.(2013) (hereafter CG13). We present nonlinear force-free reconstructions of the associated coronal magnetic field based on vector SDO/HMI magnetograms. We deliver estimates of the free magnetic energy associated to a braided coronal structure. Our model results suggest (∼ 100 times) more free energy at the braiding site than analytically estimated by CG13, strengthening the possibility of the active-region corona being heated by field line braiding. We were able to assess the coronal free energy appropriately by using vector field measurements and attribute the lower energy estimate of CG13 to the underestimated (by a factor of 10) azimuthal field strength. We also quantify the increase of the overall twist of a flare-related flux rope which had been claimed by CG13. From our models we find that the overall twist of the flux rope increased by about half a turn within twelve minutes. Unlike another method, to which we compare our results to, we evaluate the winding of the flux rope's constituent field lines around each other purely based on their modeled coronal 3D field line geometryto our knowledge for the first time.

Observable Signatures of Energy Release in Braided Coronal Loops

“…These factors and our simplified geometry can explain to some extent the differences between the observed and modeled braids. For example, the braided structure "1" in Cirtain et al (2013) is described as having a "pinched" region (red arrow in Figure 1), and its net twist is found to increase with time (Cirtain et al 2013;Thalmann et al 2014), neither of which are the case in our simulation. Despite these differences, it is encouraging to note that the Fe XII emission intensities are comparable to those observed by Hi-C, perhaps indicating that the free energy (degree of field line tangling) we considered is not too unrealistic.…”

“…Hi-C images, with a spatial resolution of about 150 km and a cadence of 5 s, were obtained using a narrow passband filter centered at 193 Å, which is emitted by Fe XII at about 1.5 MK (Cirtain et al 2013). Thalmann et al (2014) constructed a nonlinear force-free field and verified the presence of these braided structures, also finding that these braided loops were rather low lying compared with other coronal loops (see also Del Zanna 2013). The large braided loop, numbered "1" in Cirtain et al (2013), was very dynamic and produced more than 10 subflares -in many cases triggered externally due to interaction with an erupting coronal loop from underneath-over 4 hours of Solar Dynamics Observatory/Atmospheric Imaging Assembly (Lemen et al 2012) observations .…”

The magnetic field in the solar atmosphere

“…Such braiding is a measure of how often different field lines cross each other in space Berger and Asgari-Targhi 2009 and is supported by MHD models (Gudiksen and Nordlund 2005;Rappazzo et al 2008;van Ballegooijen et al 2011). These braided small-scale field structures efficiently heat the coronal environment by the dissipation of electric currents, where oppositely directed magnetic fields are found in close vicinity to each other (Parker 1983, see also Cirtain et al 2013;Thalmann et al 2014). The sub-surface dynamics controlling the temporal evolution of the coronal magnetic field, also launch waves propagating upwards.…”

Magnetic Helicity, Tilt, and Twist

“…Such sudden acquisitions of half twists may be observable. For example, a recent force-free modelling of an active region corona using vector SDO/HMI magnetograms (Thalmann et al 2014) displays an apparent increase of a half turn twist in a flux rope.…”