What can be learned from the seismology of a coronal loop using only a handful of frequencies?

¹ School of Mathematics and Statistics, The University of Sheffield, S3 7RH, UK
e-mail: R.Jain@sheffield.ac.uk
² JILA and Department of Astrophysical and Planetary Sciences, University of Colorado at Boulder, CO 80309-0440, USA
e-mail: hindman@lcd.colorado.edu

Received: 1 July 2012
Accepted: 1 August 2012

Abstract

Context. Transverse oscillating loops in the solar corona have been observed and the frequencies for a couple of low-order modes measured. These frequencies have been used as a diagnostic tool to investigate the internal properties of such oscillating loops. In particular, the density and magnetic field profiles along the loop are estimated by comparing the measured frequencies with those of a reference model. In this paper, we argue that only the kink speed may be assessed directly and there is no diagnostic capability for density or magnetic field independent of the wave speed. Further, with just a handful of measured frequencies available, only broad spatial averages of the kink speed may be obtained. We demonstrate using a frequency inversion procedure that with only two frequencies as inputs, at best one can assess the mean and the contrast of the kink speed along the loop. One requires access to the frequencies of many mode orders to perform inversions that offer kink speed determinations with high spatial resolution.

Aims. We suggest a rigorous mathematical formalism that describes the information content of the measured mode frequencies and we present a method to infer the kink speed within a coronal loop by inverting those frequencies.

Methods. We consider a single magnetic coronal loop and by using perturbation theory, relate its eigenfrequencies to the loop’s physical properties.

Results. We derive the sensitivity kernels that describe how each eigenfrequency contain the information about the kink speed and density along the loop.

Conclusions. We conclude that the eigenfrequencies contain information primarily about the kink speed, and do not strongly depend on the density. Therefore, all loop models with the same kink speed profile (but different density and magnetic field profiles) are seismically indistinguishable. To acheive the spatial resolution neccessary to uncover the non-uniform nature of the coronal loop, it is necessary to do inversion of many measured frequencies. Making inferences about the density stratification and magnetic field varying along the loop requires supplemental observations that are non-seismic in nature.