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Register a new userDetermination of transport coefficients by coronal seismology of flare-induced slow-mode waves: Numerical parametric study of 1D loop model
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Recent studies of a flaring loop oscillation event on 2013 December 28 observed by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) have revealed the suppression of thermal conduction and significant enhancement of compressive viscosity in hot ($sim$10 MK) plasma. In this study we aim at developing a new coronal seismology method for determining the transport coefficients based on a parametric study of wave properties using a 1D nonlinear MHD loop model in combination with the linear theory. The simulations suggest a two-step scheme: we first determine the effective thermal conduction coefficient from the observed phase shift between temperature and density perturbations as this physical parameter is insensitive to the unknown viscosity; then from the loop model with the obtained thermal conduction coefficient, we determine the effective viscosity coefficient from the observed decay time using the parametric modeling. With this new seismology technique we are able to quantify the suppression of thermal conductivity by a factor of about 3 and the enhancement of viscosity coefficient by a factor of 10 in the studied flaring loop. Using the loop model with these refined transport coefficients, we study the excitation of slow magnetoacoustic waves by launching a flow pulse from one footpoint. The simulation can self-consistently produce the fundamental standing wave on a timescale in agreement with the observation.
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Standing slow-mode waves have been recently observed in flaring loops by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO). By means of the coronal seismology technique transport coefficients in hot ($sim$10 MK) plasma were determined by Wang et al.(2015, Paper I), revealing that thermal conductivity is nearly suppressed and compressive viscosity is enhanced by more than an order of magnitude. In this study we use 1D nonlinear MHD simulations to validate the predicted results from the linear theory and investigate the standing slow-mode wave excitation mechanism. We first explore the wave trigger based on the magnetic field extrapolation and flare emission features. Using a flow pulse driven at one footpoint we simulate the wave excitation in two types of loop models: model 1 with the classical transport coefficients and model 2 with the seismology-determined transport coefficients. We find that model 2 can form the standing wave pattern (within about one period) from initial propagating disturbances much faster than model 1, in better agreement with the observations. Simulations of the harmonic waves and the Fourier decomposition analysis show that the scaling law between damping time ($tau$) and wave period ($P$) follows $taupropto{P^2}$ in model 2, while $taupropto{P}$ in model 1. This indicates that the largely enhanced viscosity efficiently increases the dissipation of higher harmonic components, favoring the quick formation of the fundamental standing mode. Our study suggests that observational constraints on the transport coefficients are important in understanding both, the wave excitation and damping mechanisms.
Rapidly decaying long-period oscillations often occur in hot coronal loops of active regions associated with small (or micro-) flares. This kind of wave activity was first discovered with the SOHO/SUMER spectrometer from Doppler velocity measurements of hot emission lines, thus also often called SUMER oscillations. They were mainly interpreted as global (or fundamental mode) standing slow magnetoacoustic waves. In addition, increasing evidence has suggested that the decaying harmonic type of pulsations detected in light curves of solar and stellar flares are likely caused by standing slow-mode waves. The study of slow magnetoacoustic waves in coronal loops has become a topic of particular interest in connection with coronal seismology. We review recent results from SDO/AIA and Hinode/XRT observations that have detected both standing and reflected intensity oscillations in hot flaring loops showing the physical properties (e.g., oscillation periods, decay times, and triggers) in accord with the SUMER oscillations. We also review recent advances in theory and numerical modeling of slow-mode waves focusing on the wave excitation and damping mechanisms. MHD simulations in 1D, 2D and 3D have been dedicated to understanding the physical conditions for the generation of a reflected propagating or a standing wave by impulsive heating. Various damping mechanisms and their analysis methods are summarized. Calculations based on linear theory suggest that the non-ideal MHD effects such as thermal conduction, compressive viscosity, and optically thin radiation may dominate in damping of slow-mode waves in coronal loops of different physical conditions. Finally, an overview is given of several important seismological applications such as determination of transport coefficients and heating function.
In this work, we report our multi-wavelength observations of the transverse oscillation of a large scale coronal loop with a length of 350 Mm. The oscillation was induced by a blowout coronal jet, which was related to a circular ribbon flare (CRF) in AR 12434 on 2015 October 16. We aim to determine the physical parameters in the coronal loop, including the Alfven speed and magnetic field strength. The jet induced kink oscillation was observed in extreme-ultraviolet (EUV) wavelengths by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). Line of sight magnetograms were observed by the Helioseismic and Magnetic Imager (HMI) on board SDO. We took several slices along the loop to assemble time-distance diagrams, and used an exponentially decaying sine function to fit the decaying oscillation. The initial amplitude, period, and damping time of kink oscillation were obtained. Coronal seismology of the kink mode was applied to estimate the Alfven speed and magnetic field strength in the oscillating loop. In addition, we measured the magnetic field of the loop through non-linear force free field (NLFFF) modeling using the flux rope insertion method. The oscillation is most pronounced in AIA 171 and 131. The oscillation is almost in phase along the loop with a peak initial amplitude of 13.6 Mm, meaning that the oscillation belong to the fast standing kink mode. The oscillation lasts for 3.5 cycles with an average period of 462 s and average damping time of 976 s. The values of t/P lie in the range of 1.5-2.5. Based on coronal seismology, the Alfven speed in the oscillating loop is estimated to be 1210 km. Two independent methods are applied to calculate the magnetic field strength of the loop, resulting in 30043 G using the coronal seismology and 21123 G using the NLFFF modeling, respectively.
Using full three-dimensional magnetohydrodynamic numerical simulations, we study the effects of magnetic field sigmoidity or helicity on the properties of the fundamental kink oscillation of solar coronal loops. Our model consists of a single denser coronal loop, embedded in a plasma with dipolar force-free magnetic field with a constant alpha-parameter. For the loop with no sigmoidity, we find that the numerically determined oscillation period of the fundamental kink mode matches the theoretical period calculated using WKB theory. In contrast, with increasing sigmoidity of the loop, the actual period is increasingly smaller than the one estimated by WKB theory. Translated through coronal seismology, increasing sigmoidity results in magnetic field estimates which are increasingly shifting towards higher values, and even surpassing the average value for the highest alpha value considered. Nevertheless, the estimated range of the coronal magnetic field value lies within the mimimal/maximal limits, proving the robustness coronal seismology. We propose that the discrepancy in the estimations of the absolute value of the force-free magnetic field could be exploited seismologically to determine the free energy of coronal loops, if averages of the internal magnetic field and density can be reliably estimated by other methods.
EIT waves are freely-propagating global pulses in the low corona which are strongly associated with the initial evolution of coronal mass ejections (CMEs). They are thought to be large-amplitude, fast-mode magnetohydrodynamic waves initially driven by the rapid expansion of a CME in the low corona. An EIT wave was observed on 6 July 2012 to impact an adjacent trans-equatorial loop system which then exhibited a decaying oscillation as it returned to rest. Observations of the loop oscillations were used to estimate the magnetic field strength of the loop system by studying the decaying oscillation of the loop, measuring the propagation of ubiquitous transverse waves in the loop and extrapolating the magnetic field from observed magnetograms. Observations from the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory (SDO/AIA) and the Coronal Multi-channel Polarimeter (CoMP) were used to study the event. An Empirical Mode Decomposition analysis was used to characterise the oscillation of the loop system in CoMP Doppler velocity and line width and in AIA intensity. The loop system was shown to oscillate in the 2nd harmonic mode rather than at the fundamental frequency, with the seismological analysis returning an estimated magnetic field strength of ~5.5+/-1.5 G. This compares to the magnetic field strength estimates of ~1-9 G and ~3-9 G found using the measurements of transverse wave propagation and magnetic field extrapolation respectively.
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