Reconstructing Highly-twisted Magnetic Fields
- PDF / 1,335,867 Bytes
- 15 Pages / 439.37 x 666.142 pts Page_size
- 93 Downloads / 204 Views
Reconstructing Highly-twisted Magnetic Fields Victor M. Demcsak1 · Michael S. Wheatland1 Alpha Mastrano1 · Kai E. Yang1
·
Received: 19 January 2020 / Accepted: 3 August 2020 / Published online: 26 August 2020 © Springer Nature B.V. 2020
Abstract We investigate the ability of a nonlinear force-free code to calculate highlytwisted magnetic field configurations using the Titov and Démoulin (Astron. Astrophys. 351:707, 1999) equilibrium field as a test case. The code calculates a force-free field using boundary conditions on the normal component of the field in the lower boundary, and the normal component of the current density over one polarity of the field in the lower boundary. The code can also use the current density over both polarities of the field in the lower boundary as a boundary condition. We investigate the accuracy of the reconstructions with increasing flux-rope surface twist number Nt , achieved by decreasing the sub-surface line current in the model. We find that the code can approximately reconstruct the Titov– Démoulin field for surface twist numbers up to Nt ≈ 8.8. This includes configurations with bald patches. We investigate the ability to recover bald patches, and more generally identify the limitations of our method for highly-twisted fields. The results have implications for our ability to reconstruct coronal magnetic fields from observational data. Keywords Active regions · Magnetic fields · Corona · Models
1. Introduction A solar flare is an explosive release of magnetic energy, characterized by impulsive brightening in an active region on the Sun. The coronal magnetic field responsible for a flare cannot be measured directly, however, it can be reconstructed using boundary conditions provided by vector magnetograms (DeRosa et al., 2009). Detailed knowledge of the coronal field is needed to understand the physics of solar flares and eruptions. The coronal magnetic field can be modeled as a nonlinear force free field (NLFFF). The force-free equation (∇ × B) × B = 0 may be rewritten ∇ × B = αB,
B V.M. Demcsak
[email protected]
1
Sydney Institute for Astronomy, School of Physics, The University of Sydney, NSW 2006, Australia
(1)
116
Page 2 of 15
V.M. Demcsak et al.
where α is the force-free parameter. Taking the divergence of Equation 1 and applying the divergence-free condition ∇ ·B =0
(2)
B · ∇α = 0,
(3)
gives
which means that the gradient of α is everywhere perpendicular to the magnetic field. Many numerical methods to solve the NLFFF equations have been developed. There are three main types. The first is the Grad–Rubin approach (Grad and Rubin, 1958), which has been implemented by Amari, Boulmezaoud, and Mikic (1999), Wheatland (2007) and Amari, Boulmezaoud, and Aly (2006). The second is the magnetofrictional method (Valori et al., 2010), and the third is the optimization method (Wheatland, Sturrock, and Roumeliotis, 2000; Wiegelmann and Inhester, 2010; Wiegelmann et al., 2012). A hybrid optimization/Grad–Rubin approach appears in Amari and Aly (2010). This pape
Data Loading...
