Exploring transverse oscillations in the solar corona with a reconstructed magnetic field

¹ Department of Physics, Shahid Beheshti University, 1983969411 Tehran, Iran

^⋆ Corresponding author: nasiri@iasbs.ac.ir

Received: 29 July 2024
Accepted: 9 April 2025

Abstract

Context. The vast majority of activities and interactions within the solar corona are significantly influenced by its magnetic field. Although the investigation of the coronal magnetic field has attracted great attention, the observational evidence is not enough to decide on its structure and strengths. One may employ a magnetogram to reconstruct an appropriate magnetic field satisfying the coronal conditions. Here we use the Lagrange multiplier method to optimise a non-linear force-free field in a computational box using the photospheric magnetogram as its lower base. The hydromagnetic oscillations in the presence of the magnetic field are studied in this computational box.

Aims. Coronal seismology allows researchers to estimate the magnetic field strength in the solar corona by analysing oscillations in coronal loops. However, one may take another approach and try to calculate the energies and frequencies using a reconstructed magnetic field. This research considers the solar corona oscillations assuming a reconstructed non-linear force-free magnetic field. The energy induced by the perturbed magnetic field as well as the plasma particles’ motions may enhance the flaring capability. We show that these energies are comparable with the magnetic free energy already known as the flaring agent.

Methods. We use the Lagrange multiplier technique to reconstruct a magnetic field in the solar corona, using an artificial magnetogram that faithfully represents the required conditions in the solar corona. By a small displacement of a fluid element from its equilibrium position, we solve the linearised force equations to obtain the normal modes of transverse oscillations. Our computational box includes an active region where we assume a strong magnetic field along the z-direction, with negligible x and y components. This allows one to achieve considerable simplicity in mathematical manipulations and numerical calculations. Due to coronal conditions, the gravity and pressure forces are neglected and the Lorentz force is considered as the only dominant force acting on the medium.

Results. To reconstruct a force-free and divergence-free magnetic field, one may possibly reduce the angle between the magnetic field and the current density vector. The corresponding Lorentz force is the only acting agent capable of exciting the transverse modes in the medium. In other words, the gravity and pressure modes are not excited while the corresponding forces are disregarded. The oscillation frequencies are calculated as the eigenvalues of the linearised eigenvalue problem. The perturbed kinetic and magnetic energies are calculated for excited oscillation modes which are comparable with the unperturbed free magnetic energy. The results calculated for the semi-analytical (L&L) model are in agreement with those obtained by our method.

Conclusions. The non-linear force-free magnetic field is reconstructed in a computational box using an artificial magnetogram obtained by the semi-analytical method. Usually, researchers use the data obtained by oscillations to estimate the coronal magnetic field. However, one may use the magnetic field reconstructed using the magnetogram observations, which is more or less close to the real magnetic field, to study the possible coronal oscillations. To do this, a perturbation is induced in the coronal magnetised plasma and the resulting oscillation modes are studied. The only exciting Lorentz force gives rise to the transverse Alfvén wave propagation. The energy of the perturbed configuration is calculated and compared with the unperturbed case.