Numerical Simulations Of Solar Filament Longitudinal Oscillations In Weak Magnetic Field

Solar filaments are dense and cool plasma embedded in the hot tenuous corona.They appear as dark elongated structures in the Ha monochrome images of the solar disk.Filaments are also called prominences when appearing above the solar limb.The eruption of filaments is often associated with solar flares and coronal mass ejections,therefore,the research on filaments is crucial for understanding the physical mecha-nisms of solar eruptions.High-resolution observations revealed that a filament is com-posed of a bunch of thin threads.The direction of each filament thread is along the local magnetic field.Since the magnetic structure of solar filaments can hardly be measured directly,the observations and research on filament threads provide an indispensable approach for the understanding of the coronal magnetic field.With early low-resolution observations,it was thought that filaments are static,be-ing held in equilibrium under the combination of gravity and magnetic Lorentz force.However,high-resolution observations indicate that filaments are never static,and their threads are always dynamic,with some materials draining down to the chromosphere and some chromospheric material replenishing the filament.Except that a small amount of filaments are formed through siphon flows from one footpoint to the other of a mag-netic loop where magnetic dips are not necessary,most filaments are situated in a stable or metastable state,supported by either a normal-polarity magnetic dip(e.g.,a sheared arcade)or an inverse-polarity magnetic dip(e.g.,a flux rope).Subject to the ubiquitous perturbations in the solar atmosphere,filament materials are often pushed to deviate from the equilibrium position,and start to oscillate,and filament oscillation was once proposed to be one of the possible precursors of solar eruptions.Filament oscillations were generally classified into large-amplitude and small-amplitude oscillations.How-ever,a more physical classification would be longitudinal oscillations versus transverse oscillations,where the restoring force is the field-aligned component of gravity for the former and magnetic Lorentz force for the latter.This thesis is focused on filament longitudinal oscillations.In this thesis,using the open-source code MPI-AMRVAC,we explore the dynam-ics of filament longitudinal oscillations in the case of weak magnetic field.The nu-merical code is equipped with adaptive mesh refinement and can be parallelized with Message Passing Interface.We performed two-dimensional(2D)radiation magneto-hydrodynamic simulations and compared the numerical results with the case of one-dimensional(1D)radiation hydrodynamic counterparts.The main results can be sum-marized as follows:(1)With the weak magnetic field,we found that the oscillation period decreases as the oscillation decays.In order to understand the period variation,we conducted force anal-ysis in detail,and it revealed that the gas pressure gradient plays completely different roles in the non-adiabatic case and the adiabatic case.In the adiabatic case,the pres-sure gradient is presented mainly as a restoring force,leading to a slightly shorter period of the longitudinal oscillation compared to the theoretical prediction of the pendulum model.On the contrary,in the non-adiabatic case,the pressure gradient behaves more like a viscous resistance,leading to a shorter decay time of the filament oscillation.(2)With both radiation and heat conduction included,the decay time of the filament longitudinal oscillation decreases from 113 minutes in the 1D case to 34 minutes in the 2D case.In 2D simulations,we examine the velocity perpendicular to the magnetic field,and conclude that in a weak magnetic field,the longitudinal oscillation excites transverse oscillation.The vertical perturbation caused by the transverse oscillation produces outward fast-mode waves,dissipating the kinetic energy of the filament,This is a multi-dimensional effect.Hence we propose that wave leakage is an important decay mechanism for filament longitudinal oscillations.(3)Within the 2D magnetohydrodynamic framework,the decay time of the filament longitudinal oscillation is 211 minutes in the adiabatic case and 34 minutes in the non-adiabatic case.Due to the presence of radiation and heat conduction,the increased gradient of either the temperature or the pressure during the oscillation is reduced by the non-adiabatic terms.The phase of the pressure gradient is altered to produce stronger resistance.Therefore,the decay time in the non-adiabatic longitudinal oscillation is shorter than in the adiabatic case.Such a result indicates that non-adiabatic processes,such as radiation and heat conduction,are the primary decay mechanism for filament longitudinal oscillations.These results well reconcile the discrepancies between previous 1D numerical sim-ulations and observations,and provide important clues for coronal seismology in the weak magnetic field case.