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Context. Coronal loop oscillations can be triggered by solar eruptions, for example, and are observed frequently by the Atmospheric Imaging Assembly (AIA) on board Solar Dynamics Observatory (SDO). The Helioseismic and Magnetic Imager (HMI) on board SDO offers us the opportunity to measure the photospheric vector magnetic field and carry out solar...
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... in the vicinity of a given initial value, we use a seeking algorithm to obtain the final oscillation period satisfying the boundary conditions. The final results are shown in Table 2, in which the observed values P obs , analytical solutions P anl , numerical solutions with the semi-circle loop geometry P sc and the numerical solutions with the real loop geometry P real are compared. The deviation from P obs is provided in the parentheses following the calculated periods. ...Context 2
... the two complicated factors, the inclination and loop geometry, were considered in the governing equations. The results showed that the coronal loop geometry has an significant influence on the periods (Table 2). A loop with different paths and the same magnetic and density distribution would have markedly different oscillation periods. ...Context 3
... in the vicinity of a given initial value, we use a seeking algorithm to obtain the final oscillation period satisfying the boundary conditions. The final results are shown in Table 2, in which the observed values P obs , analytical solutions P anl , numerical solutions with the semi-circle loop geometry P sc , and the numerical solutions with the real loop geometry P real are compared. The deviation from P obs is provided in the parentheses following the calculated periods. ...Context 4
... the two complicated factors, the inclination and loop geometry, were considered in the governing equations. The results show that the coronal loop geometry has a significant influence on the periods (Table 2). A loop with different paths and the same magnetic and density distribution would have markedly different oscillation periods. ...Citations
... The solid line represents the radiation function computed with the CHIANTI atomic database, and the dashed line denotes a piecewise power-law function that serves as an approximation of the realistic CHIANTI function. implies a large cross-sectional expansion of coronal loops (e.g., Asgari-Targhi & van Ballegooijen 2012;Chen et al. 2022), observations typically demonstrate a less-than-expected expansion for the loops: they either keep a roughly constant cross section or just exhibit a modest cross-sectional expansion (e.g., ...
Recent coronal loop modeling has emphasized the importance of combining both Coulomb collisions and turbulent scattering to characterize field-aligned thermal conduction, which invokes a hybrid loop model. In this work, we generalize the hybrid model by incorporating a nonuniform heating and cross section that are both formulated by a power-law function of temperature. Based on the hybrid model solutions, we construct scaling laws that relate loop-top temperature ( T a ) and heating rate ( H a ) to other loop parameters. It is found that the loop-top properties for turbulent loops are additionally power-law functions of the turbulent mean free path ( λ T ), with the functional forms varying from situation to situation, depending on the specification of the heating and/or areal parameters. More importantly, both a sufficiently footpoint-concentrated heating and a cross-sectional expansion with height can effectively weaken (strengthen) the negative (positive) power-law dependence of T a ( H a ) on λ T . The reason lies in a notable reduction of heat flux by footpoint heating and/or cross-sectional expansion in the turbulence-dominated coronal part, where turbulent scattering introduces a much weaker dependence of the conduction coefficient on temperature. In this region, therefore, the reduction of the heat flux predominately relies on a backward flattening of the temperature gradient. Through numerical modeling that incorporates more realistic conditions, this scenario is further consolidated. Our results have important implications for solar active region (AR) loops. With the factors of nonuniform heating and cross section taken into account, AR loops can bear relatively stronger turbulence while still keeping a physically reasonable temperature for nonflaring loops.
... In order to detect harmonic signals, several methods such as direct or residual sine/cosine harmonic fitting, the fast Fourier transform (FFT), periodogram, and the wavelet transform are used to determine harmonic-order periods (Verwichte et al. 2004;De Moortel & Brady 2007;van Doorsselaere et al. 2009;Guo et al. 2015;Duckenfield et al. 2019;Chen et al. 2022). We use a combined damped sine harmonic model to fit the profile. ...
... The amplitude C is magnified 5 times. Chen et al. 2022). There are two reasons that might result in the large difference between our calculation and other studies. ...
We present the observations of multimode kink waves and a narrow quasiperiodic fast-propagating (QFP) wave train in association with a jet on 2011 December 11. The jet impinged on a loop, which excited a propagating kink mode transitioning into a standing kink mode and also excited a QFP wave train away from the jet. Motion magnification is used to fit the higher harmonic standing wave oscillation profile with three periods at three different spatial locations. The periods have the ratio 6:3:2. The ratio of the fundamental mode to the second harmonic of the standing wave is about 1.95, suggesting that the magnetic field strength variation effect is strong enough to cancel out the density stratification. The differential emission measure is used to estimate the loop’s plasma property at these three points, and it found the density and the temperature are roughly constant. The magnetic field strength, B = 51 ± 16 G, is derived by the coronal seismology using the fundamental kink mode. It is striking to find that the the ratio of the second harmonic to the third harmonic of the kink wave coincides with that of the periods of the QFP wave train, and the ratio of periods is about 1.5 in both cases. We propose that the excitation of the high-order harmonics and the QFP wave train could be the nonlinear response of the steep density-gradient plasma interacting with electromagnetic field in the southwest foot region. This region, like a resonator, might play an important role in energy reservoir capture and act as a frequency filter to generate propagating waves of particular frequencies.
Loops are fundamental structures in the magnetized atmosphere of the Sun. Their physical properties are crucial for understanding the nature of the solar atmosphere. Transition region loops are relatively dynamic and their physical properties have not yet been fully understood. With spectral data of the line pair of O iv 1399.8 Å and 1401.2 Å ( T max = 1.4 × 10 5 K) of 23 transition region loops obtained by IRIS, we carry out the first systematic analyses to their loop lengths ( L ), electron densities ( n e ), and effective temperatures. We found electron densities, loop lengths, and effective temperatures of these loops are in the ranges of 8.9 × 10 ⁹ –3.5 × 10 ¹¹ cm ⁻³ , 8–30 Mm, and 1.9 × 10 ⁵ –1.3 × 10 ⁶ K, respectively. At a significant level of 90%, regression analyses show that the relationship between electron densities and loop lengths is n e [cm ⁻³ ] ∝ ( L [Mm]) −0.78±0.42 , while the dependences of electron densities on effective temperatures and that on the line intensities are not obvious. These observations demonstrate that transition region loops are significantly different than their coronal counterparts. Further studies on the theoretical aspect based on the physical parameters obtained here are of significance for understanding the nature of transition region loops.
Context. The method of spatial seismology can be applied to the amplitude profile of transverse coronal loop oscillations to constrain the distributions of physical parameters, such as the loop density, magnitude of the magnetic field, and so on.
Aims. We intend to develop and apply a practical spatial seismology technique to detect physical parameters of plasma and validate its effectiveness by comparing it with other methods.
Methods. A spatial seismology inversion was conducted by numerically optimizing a parametric dynamic model of the loop’s density stratification and magnetic field variation to best fit the measured amplitude profile of the loop.
Results. The spatial seismology inversion technique developed here was applied to a transverse coronal loop oscillation that occurred on 2013 April 11, whose oscillation amplitude profile of both the fundamental mode and first overtone was reported in previous work. The consistency between the time domain analysis and spatial seismology has been verified. Meanwhile, we accounted for the asymmetric profile of the fundamental mode by forward modeling and we derived the magnetic field distribution by inverse modeling, which is coincident with that of the extrapolated one. In addition, spatial seismology inversion was applied to the transverse oscillation event on 2022 March 30 to obtain the distribution of the loop’s density and magnetic field, which are compared with the results derived from the differential emission measure (DEM) diagnostics and the direct potential field extrapolation.
Conclusions. Spatial seismology inversion can be used as an effective method to independently measure various physical parameters, for example the density and magnetic field of coronal loops, which are consistent with the results obtained by DEM diagnostics and potential field extrapolation.
