No unique solution to the seismological problem of standing kink magnetohydrodynamic waves

¹ Instituto de Astrofísica de Canarias, 38205 La Laguna, Tenerife, Spain
e-mail: iarregui@iac.es
² Departmento de Astrofísica, Universidad de La Laguna, 38206 La Laguna, Tenerife, Spain
³ Centre for Mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven Celestijnenlaan 200B bus 2400, 3001 Leuven, Belgium
e-mail: marcel.goossens@kuleuven.be

Received: 10 July 2018
Accepted: 8 December 2018

Abstract

The aim of this paper is to point out that the classic seismological problem using observations and theoretical expressions for the periods and damping times of transverse standing magnetohydrodynamic waves in coronal loops is better referred to as a reduced seismological problem. “Reduced” emphasises the fact that only a small number of characteristic quantities of the equilibrium profiles can be determined. Reduced also implies that there is no unique solution to the full seismological problem. Even the reduced seismological problem does not allow a unique solution. Bayesian inference results support our mathematical arguments and offer insight into the relationship between the algebraic and the probabilistic inversions.