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

TL;DR

This study investigates how gravitational stratification influences kink oscillations in curved coronal loops using 3D ideal MHD simulations. By comparing numerically obtained kink frequencies with the WKB approximation, it reveals a polarization-dependent deviation: vertical fundamental modes differ by about $18\%$ from $P_{\rm WKB}$ yet align with the local Alfvén frequency near the loop apex, while horizontal fundamental modes deviate by about $7\%$ and align near a quarter-loop location; first overtones for both polarizations are well described by WKB. The results demonstrate that different locations along a loop are probed by the two polarizations, enabling spatially dependent coronal seismology and potential magnetic-field profiling, provided that local densities are known. They also show that period ratios can diagnose density scale height, but magnetic-field inhomogeneity must be included for reliable inferences, underscoring the need for careful modeling in stratified, curved-loop seismology.

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 Alfvén 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 Alfvén 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 Alfvén 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 Alfvén 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.

Figures (8)

• Figure 1: 3D rendering of the density-enhanced loop. The left panel shows the initial state before relaxation, and the right panel shows the relaxed state.
• Figure 2: Temporal evolution of $v_{\rm v}$ for the vertically polarized fundamental kink oscillations. The black, blue, and green lines represent $v_{\rm v}$ of fluid parcels initially located at the loop apex ($[x_0,y_0,z_0]=[0,0,70]$ Mm), at one quarter of the loop ($[x_1,y_1,z_1]=[59.4,0,49.4]$ Mm), and at the opposite quarter of the loop ($[x_2,y_2,z_2]=[-59.4,0,49.4]$ Mm), respectively. The black and blue dashed line designate $v_{\rm v}$ measured at the fixed position $[x_0,y_0,z_0]$ and $[x_1,y_1,z_1]$.
• Figure 3: Similar to Figure \ref{['fig_v_v']}, but for the horizontal polarized fundamental kink oscillations.
• Figure 4: Temporal evolution of $v_{\rm v}$ for the vertically polarized first overtones of kink oscillations. The black, blue, and green lines represent $v_{\rm v}$ of fluid parcels initially located at the loop apex ($[x_0,y_0,z_0]=[0,0,70]$ Mm), at one quarter of the loop ($[x_1,y_1,z_1]=[59.4,0,49.4]$ Mm), and at the opposite quarter of the loop ($[x_2,y_2,z_2]=[-59.4,0,49.4]$ Mm), respectively.
• Figure 5: Similar to Figure \ref{['fig_v_v_1st']}, but for the horizontal first overtones of kink oscillations.