Extension and validation of the pendulum model for longitudinal solar prominence oscillations

Context. Longitudinal oscillations in prominences are common phenomena on the Sun. These can be used to infer geometry and intensity of filament magnetic field. Previous theoretical studies longitudinal made two simplifying assumptions: uniform gravity semicircular dips supporting flux tubes. However, is not realistic semicircular. Aims. Our aim understand effects including nonuniform solar explore validity pendulum model with different flux-tube geometries. Methods. We first derived equation describing motion plasma along tube gravity, yielding corrections original model. also computed full numerical solutions for normal modes compared them new approximation. Results. find that introduces a significant modification found cut-off period; i.e., cannot have period longer than 167 min. In addition, considering geometries, depends almost exclusively radius curvature at bottom dip. Conclusions. conclude significantly modifies important prominence seismology, because inferred values minimum magnetic-field strength differ substantially from those old we corrected quite robust still valid noncircular dips.