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Register a new userCompressive oscillations in hot coronal loops: Are sloshing oscillations and standing slow waves independent?
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Employing high-resolution EUV imaging observations from SDO/AIA, we analyse a compressive plasma oscillation in a hot coronal loop triggered by a C-class flare near one of its foot points as first studied by Kumar et al. We investigate the oscillation properties in both the 131{,}{AA} and 94{,}{AA} channels and find that what appears as a pure sloshing oscillation in the 131{,}{AA} channel actually transforms into a standing wave in the 94{,}{AA} channel at a later time. This is the first clear evidence of such transformation confirming the results of a recent numerical study which suggests that these two oscillations are not independent phenomena. We introduce a new analytical expression to properly fit the sloshing phase of an oscillation and extract the oscillation properties. For the AIA 131{,}{AA} channel, the obtained oscillation period and damping time are 608$pm$4{,}s and 431$pm$20{,}s, respectively during the sloshing phase. The corresponding values for the AIA 94{,}{AA} channel are 617$pm$3{,}s and 828$pm$50{,}s. During the standing phase that is observed only in the AIA 94{,}{AA} channel, the oscillation period and damping time have increased to 791$pm$5{,}s and 1598$pm$138{,}s, respectively. The plasma temperature obtained from the DEM analysis indicates substantial cooling of the plasma during the oscillation. Considering this, we show that the observed oscillation properties and the associated changes are compatible with damping due to thermal conduction. We further demonstrate that the absence of a standing phase in the 131{,}{AA} channel is a consequence of cooling plasma besides the faster decay of oscillation in this channel.
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The analysis of a hot loop oscillation event using SOHO/SUMER, GOES/SXI, and RHESSI observations is presented. Damped Doppler shift oscillations were detected in the Fe XIX line by SUMER, and interpreted as a fundamental standing slow mode. The evolution of soft X-ray emission from GOES/SXI and hard X-ray sources from RHESSI suggests that the oscillations of a large loop are triggered by a small flare, which may be produced by interaction (local reconnection) of this large loop with a small loop at its footpoint. This study provides clear evidence supporting our early conjecture that the slow-mode standing waves in hot coronal loops are excited by impulsive heating (small or microflares) at the loops footpoint.
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.
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.
We investigate the nature of transverse kink oscillations of loops expanding through the solar corona and how can oscillations be used to diagnose the plasma parameters and the magnetic field. In particular, we aim to analyse how the temporal dependence of the loop length (here modelling the expansion) will affect the P1 /P2 period ratio of transverse loop oscillations. Due to the uncertainty of the loops shape through its expansion, we discuss separately the case of the loop that maintains its initial semi-circular shape and the case of the loop that from a semi-circular shape evolve into an elliptical shape loop. The equations that describe the oscillations in expanding flux tube are complicated due to the spatial and temporal dependence of coefficients. Using the WKB approximation we find approximative values for periods and their evolution, as well as the period ratio. For small values of time (near the start of the expansion) we can employ a regular perturbation method to find approximative relations for eigenfunctions and eigenfrequencies. Using simple analytical and numerical methods we show that the period of oscillations are affected by the rising of the coronal loop. The change in the period due to the increase in the loops length is more pronounced for those loops that expand into a more structured (or cooler corona). The deviation of periods will have significant implications in determining the degree of stratification in the solar corona. The effect of expansion on the periods of oscillations is considerable only in the process of expansion of the loop but not when it reached its final stage.
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.
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