Numerical Simulations Of Solar Filament Oscillations And The Formation Of Threads

Solar Filaments are important phenomena in the solar atmosphere.They appear as the well-known bright prominences when observed on the solar limb,but appear as long filaments when observed against the solar disk.Filaments appear to be composed of numerous fibril-like structures,called filament threads.Since the typical temperature of solar filaments is two orders lower and their density is two orders higher than the neigh-boring corona,they are considered to be supported by the local Lorentz force against the gravity,and the place where magnetic field can provide this kind of upward Lorentz force is called magnetic dips.Through recent theoretical and observational works,we have known a lot about solar filaments,including the magnetic field,thread structures,formation,oscillation,eruption and so on.But the non-linear physics involved in the dynamics of filaments makes the research full of challenges.In this paper,with filament oscillations,we try to tackle some important problems with numerical simulations.Filament oscillations can be divided into longitudinal ones,whose direction is par-allel to the local magnetic field,of the filament,and transverse ones,whose direction is perpendicular to the filament axis.Longitudinal oscillations of solar filaments have been observed and explored for 16 years.Previous studies are mainly based on one-dimensional rigid flux tube model with a single magnetic dip.However,it has been noted that there might be two magnetic dips,and hence two threads,along one mag-netic field line.Therefore,longitudinal oscillations in such a configuration would be affected by the thread-thread interaction so that departure from the traditional pendulum model is expected.Following previous work,we investigate the kinematics of the fil-ament longitudinal oscillations when two threads are magnetically connected,which is done by numerically solving one-dimensional radiative hydrodynamic equations.Two different types of perturbations are considered,and the new features resulting from the interaction of the two filament threads are investigated.We find that even with the in-clusion of the thread-thread interaction,the oscillation period is modified weakly,by at most 20%compared to the traditional pendulum model with one thread.However,the damping timescale is significantly affected by the thread-thread interaction.Hence,the thread-thread interaction might be an important factor when considering the damping of longitudinal oscillations where two threads are magnetically connected.Solar prominences are subject to many kinds of perturbations during their lifetime,and oscillate frequently.The study of prominence oscillations provides an alternative way to investigate their internal magnetic and thermal structures because the character-istics of the oscillations depend on their interplay with the solar corona.Based on pre-vious works,we perform three-dimensional(3D)ideal magnetohydrodynamic(MHD)simulations of prominence oscillations,with the aim to compare the oscillation periods with those predicted by various simplified models and to examine the restoring force.We find that the longitudinal oscillation has a period of about 49 minutes,which is in accordance with the pendulum model where the field-aligned component of gravity serves as the restoring force.In contrast,the horizontal transverse oscillation has a pe-riod of about 10 minutes and the vertical transverse oscillation has a period of about 14 minutes,and both of them can be nicely fitted with a two-dimensional slab model.We also find that the magnetic tension force dominates most of the time in transverse oscillations,except during the first minute when magnetic pressure overwhelms.Although such 3D simulations provide us some information about filament oscil-lations,further study requires an improved resolution,the fine structure of filaments,i.e.,filament threads,can be resolved.Then,we should first know the detailed mech-anism of the formation of filament threads.Different from previous theories based on MHD instabilities,we proposed a brand new model to explain the formation of fila-ment threads.This model is based on the randomized energy deposition at the foot-points of the filament,so that the filament threads are automatically formed.A 2D simulation based on the evaporation-condensation model is done to demonstrate the idea.Simulation results show that the typical scale of the thread structures is similar to the observations.Whereas the whole filament body is relatively stable,each of the threads is in full dynamics,and the well-known contour-streaming flows are obtained from our simulation.The velocities got from the H? time-slice diagram is also simi-lar to observations.At the same time,we can detect some longitudinal oscillations of filament threads from our results.These results provide some useful information for future quantitative investigations of filament oscillations.