Normal modes of transverse coronal loop oscillations from numerical simulations. I. Method and test case

Abstract

<p><em>[eng] The purpose of this work is to develop a procedure to obtain the normal modes of a coronal loop from time-dependent</em></p><p><em>numerical simulations with the aim of better understanding observed transverse loop oscillations. To achieve this goal,</em></p><p><em>in this paper we present a new method and test its performance with a problem for which the normal modes can be</em></p><p><em>computed analytically. In a follow-up paper, the application to the simulations of Rial et al. is tackled. The method</em></p><p><em>proceeds iteratively and at each step consists of (i) a time-dependent numerical simulation followed by (ii) the Complex</em></p><p><em>Empirical Orthogonal Function (CEOF) analysis of the simulation results. The CEOF analysis provides an</em></p><p><em>approximation to the normal mode eigenfunctions that can be used to set up the initial conditions for the numerical</em></p><p><em>simulation of the following iteration, in which an improved normal mode approximation is obtained. The iterative</em></p><p><em>process is stopped once the global difference between successive approximate eigenfunctions is below a prescribed</em></p><p><em>threshold. The equilibrium used in this paper contains material discontinuities that result in one eigenfunction with a</em></p><p><em>jump across these discontinuities and two eigenfunctions whose normal derivatives are discontinuous there. After six</em></p><p><em>iterations, the approximations to the frequency and eigenfunctions are accurate to ~0.7% except for the eigenfunction</em></p><p><em>with discontinuities, which displays a much larger error at these positions.</em></p>