Spectra of standing kink waves in loops and the effects of the lower solar atmosphere

¹ Centre for mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
² Solar-Terrestrial Centre of Excellence – SIDC, Royal Observatory of Belgium, Ringlaan -3- Av. Circulaire, 1180 Brussels, Belgium
³ School of Earth and Space Sciences, Peking University, Beijing 100871, PR China

^⋆ Corresponding author; kostas.karampelas@kuleuven.be

Received: 27 September 2024
Accepted: 15 December 2024

Abstract

Context. Understanding the effects of the lower solar atmosphere on the spectrum of standing kink oscillations of coronal loops, in both the decaying and decayless regime, is essential for developing more advanced tools for coronal seismology.

Aims. We aim to reveal the effects of the chromosphere on the spatial profiles and frequencies of the standing kink modes, create synthetic emission maps to compare with observations, and study the results using spatial and temporal coronal seismology techniques.

Methods. We excited transverse oscillations in a 3D straight flux tube using (a) a broadband footpoint driver, (b) a sinusoidal velocity pulse, and (c) an off-centre Gaussian velocity pulse, using the PLUTO code. The flux tube is gravitationally stratified, with footpoints embedded in chromospheric plasma. Using the FoMo code, we created synthetic observations of our data in the Fe IX 17.1 nm line and calculated the spectra with the Automatic Northumbria University Wave Tracking code. We also numerically solved the generalised eigenvalue system for the 1D wave equation to determine the effects of the stratification on the kink modes of our system.

Results. The synthetic observations of the loops perturbed by the velocity pulses show a single dominant mode that our 1D analysis reveals to be the third harmonic of the system. For the broadband driver, the synthetic emission shows multiple frequency bands, associated with both the loop and the driver. Finally, using seismological techniques, we highlight the possibility of misidentifying the observed third, sixth, and ninth harmonics with the first, second, and third harmonics of the coronal part of the loop. Unless more advanced techniques of spatial seismology are used with many data points from observations along the entire loop length, this misidentification can result in overestimating the mean magnetic field by a factor equal to the period ratio of the fundamental over the third harmonic.

Conclusions. For longer coronal loops it is easy to misidentify the detected standing kink modes for lower-order modes of the system, which can have important seismological implications. To prevent these errors and properly constrain the value of the estimated mean magnetic field, additional observations of the loops footpoints using transition region and chromospheric lines are necessary.