The effect of gravitational stratification on kink oscillations in curved coronal loops

Context. 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. Aims. 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. Methods. We conducted numerical computations within the ideal magnetohydrodynamic framework to study different kink polarizations and harmonics in a curved, gravitationally stratified coronal loop. The oscillation frequencies derived from the Lagrangian displacement were compared with the Wentzel-Kramers-Brillouin (WKB) approximation. Results. 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. Conclusions. 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, for example, the probing of magnetic field strength at different locations along a coronal loop.