The Effect of Gravitational Stratification on Kink Oscillations in Curved Coronal Loops

TL;DR

This study investigates how gravitational stratification influences kink oscillation frequencies in curved coronal loops, revealing that local Alfvén frequency approximations can effectively predict these frequencies for seismological applications.

Contribution

It provides a detailed numerical analysis of gravitational stratification effects on kink oscillations, highlighting the accuracy of local Alfvén frequency estimates for different polarizations and harmonics.

Findings

Vertically polarized fundamental mode frequency deviates by about 18% from WKB approximation.

Horizontally polarized fundamental mode frequency deviates by about 7% from WKB approximation.

WKB approximation reliably estimates frequencies for first overtones and certain polarizations.

Abstract

Kink oscillation frequency is a key parameter for coronal seismology. It is still unclear how gravitational stratification affects the kink frequency in curved coronal loops. This work aims to investigate the effect of gravitational stratification on the frequency of kink oscillations in curved coronal loops and discuss their seismological potential. We conduct numerical computations within the ideal MHD framework to study different kink polarizations and harmonics in a curved, gravitationally stratified coronal loop. The oscillation frequencies derived from the Lagrangian displacement are compared with the WKB approximation. For the vertically polarized fundamental mode, the oscillation frequency deviates from the WKB approximation by about 18\% in the current numerical setup. Nevertheless, the oscillation frequency closely matches the local Alfv\'en frequency near the loop apex. On the other hand, the frequency of the horizontally polarized fundamental mode exhibits only a 7\% deviation in our current model from the WKB approximation and closely matches the local Alfv\'en frequency near one quarter of the loop. For the first overtones, the frequencies for both polarizations can be well described by the WKB approximation. The frequency of vertically polarized fundamental kink modes can be predicted by the local Alfv\'en frequency near the loop apex. In contrast, the WKB approximation remains highly reliable for estimating the frequency of horizontally polarized fundamental modes and first overtones, which is also well described by the local Alfv\'en frequency near one quarter of the loop. These results therefore pave the way for spatially dependent coronal seismology, enabling, e.g., the probing of magnetic field strength at different locations along a coronal loop.