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We investigate the transverse oscillations of a line-tied multi-stranded coronal loop composed of several parallel cylindrical strands. First, the collective fast normal modes of the loop are found with the T-matrix theory. There is a huge quantity of normal modes with very different frequencies and a complex structure of the associated magnetic pressure perturbation and velocity field. The modes can be classified as bottom, middle, and top according to their frequencies and spatial structure. Second, the temporal evolution of the velocity and magnetic pressure perturbation after an initial disturbance are analyzed. We find complex motions of the strands. The frequency analysis reveals that these motions are a combination of low and high frequency modes. The complexity of the strand motions produces a strong modulation of the whole tube movement. We conclude that the presumed internal fine structure of a loop influences its transverse oscillations and so its transverse dynamics cannot be properly described by those of an equivalent monolithic loop.
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Determining the preferred spatial location of the energy input to solar coronal loops would be an important step forward towards a more complete understanding of the coronal heating problem. Following on from Sarkar & Walsh (2008) this paper presents a short 10e9 cm global loop as 125 individual strands, where each strand is modelled independently by a one-dimensional hydrodynamic simulation. The strands undergo small-scale episodic heating and are coupled together through the frequency distribution of the total energy input to the loop which follows a power law distribution with index ~ 2.29. The spatial preference of the swarm of heating events from apex to footpoint is investigated. From a theoretical perspective, the resulting emission measure weighted temperature profiles along these two extreme cases does demonstrate a possible observable difference. Subsequently, the simulated output is folded through the TRACE instrument response functions and a re-derivation of the temperature using different filter-ratio techniques is performed. Given the multi-thermal scenario created by this many strand loop model, a broad differential emission measure results; the subsequent double and triple filter ratios are very similar to those obtained from observations. However, any potential observational signature to differentiate between apex and footpoint dominant heating is possibly below instrumental thresholds. The consequences of using a broadband instrument like TRACE and Hinode-XRT in this way are discussed.
We report our multiwavelength observations of two homologous circular-ribbon flares (CRFs) in active region 11991 on 2014 March 5, focusing on the transverse oscillations of an extreme-ultraviolet (EUV) loop excited by the flares. The transverse oscillations are of fast standing kink-mode. The first-stage oscillation triggered by the C2.8 flare is decayless with lower amplitudes (310$-$510 km). The periods (115$-$118 s) in different wavelengths are nearly the same, indicating coherent oscillations. The magnetic field of the loop is estimated to be 65$-$78 G. The second-stage oscillation triggered by the M1.0 flare is decaying with larger amplitudes (1250$-$1280 km). The periods decreases from 117 s in 211 {AA} to 70 s in 171 {AA}, implying a decrease of loop length or an implosion after a gradual expansion. The damping time, being 147$-$315 s, increases with the period, so that the values of $tau/P$ are close to each other in different wavelengths. The thickness of the inhomogeneous layer is estimated to be $sim$0farcs45 under the assumption of resonant absorption. This is the first observation of the excitation of two kink-mode loop oscillations by two sympathetic flares. The results are important for understanding of the excitation of kink oscillations of coronal loops and hence the energy balance in the solar corona. Our findings also validate the prevalence of significantly amplified amplitudes of oscillations by successive drivers.
To investigate the excitation of kink oscillations in coronal loops and filaments, a C3.4 circular-ribbon flare (CRF) associated with a blowout jet in active region 12434 on 2015 October 16 is analyzed. The flare excited small-amplitude kink oscillation of a remote coronal loop. The oscillation lasted for $ge$4 cycles without significant damping. The amplitude and period are 0.3$pm$0.1 Mm and 207$pm$12 s. Interestingly, the flare also excited transverse oscillation of a remote filament. The oscillation lasted for $sim$3.5 cycles with decaying amplitudes. The initial amplitude is 1.7$-$2.2 Mm. The period and damping time are 437$-$475 s and 1142$-$1600 s. The starting times of simultaneous oscillations of coronal loop and filament were concurrent with the hard X-ray peak time. Though small in size and short in lifetime, the flare set off a chain reaction. It generated a bright secondary flare ribbon (SFR) in the chromosphere, remote brightening (RB) that was cospatial with the filament, and intermittent, jet-like flow propagating in the northeast direction. The loop oscillation is most probably excited by the flare-induced blast wave at a speed of $ge$1300 km s$^{-1}$. The excitation of the filament oscillation is more complicated. The blast wave triggers secondary magnetic reconnection far from the main flare, which not only heats the local plasma to higher temperatures (SFR and RB), but produces jet-like flow (i.e., reconnection outflow) as well. The filament is disturbed by the secondary magnetic reconnection and experiences transverse oscillation. The findings give new insight into the excitation of transverse oscillations of coronal loops and filaments.
The effects of finite amplitudes on the transverse oscillations of a quiescent prominence represented by a magnetic rope are investigated in terms of the model proposed by Kolotkov et al. 2016. We consider a weakly nonlinear case governed by a quadratic nonlinearity, and also analyse the fully nonlinear equations of motion. We treat the prominence as a massive line current located above the photosphere and interacting with the magnetised dipped environment via the Lorentz force. In this concept the magnetic dip is produced by two external current sources located at the photosphere. Finite amplitude horizontal and vertical oscillations are found to be strongly coupled between each other. The coupling is more efficient for larger amplitudes and smaller attack angles between the direction of the driver and the horizontal axis. Spatial structure of oscillations is represented by Lissajous-like curves with the limit cycle of a hourglass shape, appearing in the resonant case, when the frequency of the vertical mode is twice the horizontal mode frequency. A metastable equilibrium of the prominence is revealed, which is stable for small amplitude displacements, and becomes horizontally unstable, when the amplitude exceeds a threshold value. The maximum oscillation amplitudes are also analytically derived and analysed. Typical oscillation periods are determined by the oscillation amplitude, prominence current, its mass and position above the photosphere, and the parameters of the magnetic dip. The main new effects of the finite amplitude are the coupling of the horizontally and vertically polarised transverse oscillations (i.e. the lack of a simple, elliptically polarised regime) and the presence of metastable equilibria of prominences.
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.
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