The effects of magnetic-field geometry on longitudinal oscillations of solar prominences: Cross-sectional area variation for thin tubes

Abstract

Context. Solar prominences are subject to both field-aligned (longitudinal) and transverse oscillatory motions, as evidenced by an increasing number of observations. Large-amplitude longitudinal motions provide valuable information on the geometry of the filamentchannel magnetic structure that supports the cool prominence plasma against gravity. Our pendulum model, in which the restoring force is the gravity projected along the dipped field lines of the magnetic structure, best explains these oscillations. However, several factors can influence the longitudinal oscillations, potentially invalidating the pendulum model. Aims. The aim of this work is to study the influence of large-scale variations in the magnetic field strength along the field lines, i.e., variations of the cross-sectional area along the flux tubes supporting prominence threads. Methods. We studied the normal modes of several flux tube configurations, using linear perturbation analysis, to assess the influence of different geometrical parameters on the oscillation properties. Results. We found that the influence of the symmetric and asymmetric expansion factors on longitudinal oscillations is small. Conclusions. We conclude that the longitudinal oscillations are not significantly influenced by variations of the cross-section of the flux tubes, validating the pendulum model in this context.

Large-amplitude Longitudinal Oscillations Triggered by the Merging of Two Solar Filaments: Observations and Magnetic Field Analysis

“…Luna et al (2016b) found that the oscillations are dependent chiefly on the radius of curvature of the magnetic field and not other details of the field line geometry. Luna et al (2016a) found that there is no coupling between longitudinal motion and transverse motions in 2D numerical simulations. All these results indicate the robustness of the pendulum model for explanation and analysis of LALOs.…”

“…Thus, we find that that the periodicities in the system we analyze range from 54 ± 1 to 69 ± 2 minutes. According to the model of ; ; Luna et al (2016a), the period of the longitudinal fundamental mode is determined by the relation…”

Prominence oscillations

“…The agreement found between the numerical results and the Luna and Karpen (2012) theoretical model provides with a tool to determine the curvature radius of the magnetic field lines and, therefore, to perform filament seismology. On the other hand, Luna et al (2016a) have studied the influence of cross-sectional area variations along a flux tube, which contains a prominence thread and is surrounded by the hot corona, on the longitudinal oscillations. These authors have found that these variations do not affect in a significant way to the oscillations, which validates the pendulum model (Luna and Karpen 2012;Luna et al 2012a).…”

Gravitational instability of solar prominence threads I. Curved magnetic fields without dips

“…This work is in progress and is addressed in part II as a continuation of the present paper part I. Another future improvement to the model is the implementation of the variation of the cross-sectional area along the tube, allowing us to incorporate a truly 3D effect in the calculation of the equilibrium and the corresponding eigenfrequencies (see Luna et al 2016a). An et al (1988) and Wu et al (1990) investigated the effects of plasma injection on the formation of the Kippenhahn-Schlüter model of prominence in optimum conditions.…”