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Longitudinal oscillations in prominences are common phenomena on the Sun.These oscillations can be used to infer the geometry and intensity of thefilament magnetic field. Previous theoretical studies of longitudinaloscillations made two simplifying assumptions: uniform gravity andsemi-circular dips on the supporting flux tubes. However, the gravity is notuniform and realistic dips are not semi-circular. To understand the effects ofincluding the nonuniform solar gravity on longitudinal oscillations, andexplore the validity of the pendulum model with different flux-tube geometries.We first derive the equation describing the motion of the plasma along the fluxtube including the effects of nonuniform gravity, yielding corrections to theoriginal pendulum model. We also compute the full numerical solutions for thenormal modes, and compare them with the new pendulum approximation. We havefound that the nonuniform gravity introduces a significant modification in thependulum model. We have also found a cut-off period, i.e. the longitudinaloscillations cannot have a period longer than 167 minutes. In addition,considering different tube geometries, the period depends almost exclusively onthe radius of curvature at the bottom of the dip. We conclude that nonuniformgravity significantly modifies the pendulum model. These corrections areimportant for prominence seismology, because the inferred values of the radiusof curvature and minimum magnetic-field strength differ substantially fromthose of the old model. However, we find that the corrected pendulum model isquite robust and is still valid for non-circular dips.

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