Giuseppe Nisticò

Brouwer-Zadeh posets and three-valued Ł ukasiewicz posets

Abstract This paper is a study of the structure of Brouwer-Zadeh (or BZ-) poset, i.e. a poset endowed with two non-usual orthocomplementations. These two orthocomplementations allow definition of two unary operators which can be considered as algebraic counterparts of the necessity and possibility operators of modal logic. A construction of how to induce a three-valued BZ-poset from a BZ-poset is given. The examples of the BZ-lattice of all generalized characteristic functionals on a reference space and of the BZ-poset of all generalized orthogonal projections on a Hilbert space are dealt with.

Decaying and decayless transverse oscillations of a coronal loop

Aims. We investigate kink oscillations of loops observed in an active region with the Atmospheric Imaging Assembly (AIA) instrument on board the Solar Dynamics Observatory (SDO) spacecraft before and after a flare. Methods. The oscillations were depicted and analysed with time-distance maps, extracted from the cuts taken parallel or perpendicular to the loop axis. Moving loops were followed in time with steadily moving slits. The period of oscillations and its time variation were determined by best-fitting harmonic functions. Results. We show that before and well after the occurrence of the flare, the loops experience low-amplitude decayless oscillations. The flare and the coronal mass ejection associated to it trigger large-amplitude oscillations that decay exponentially in time. The periods of the kink oscillations in both regimes (about 240 s) are similar. An empirical model of the phenomenon in terms of a damped linear oscillator excited by a continuous low-amplitude harmonic driver and by an impulsive high-amplitude driver is found to be consistent with the observations.

Decay-less kink oscillations in coronal loops

Context: Kink oscillations of coronal loops in an off-limb active region are detected with the Imaging Assembly Array (AIA) instruments of the Solar Dynamics Observatory (SDO) at 171 A. Aims: We aim to measure periods and amplitudes of kink oscillations of different loops and to determinate the evolution of the oscillation phase along the oscillating loop. Methods: Oscillating coronal loops were visually identified in the field of view of SDO/AIA and STEREO/EUVI-A: the loop length was derived by three-dimensional analysis. Several slits were taken along the loops to assemble time-distance maps. We identified oscillatory patterns and retrieved periods and amplitudes of the oscillations. We applied the cross-correlation technique to estimate the phase shift between oscillations at different segments of oscillating loops. Results: We found that all analysed loops show low-amplitude undamped transverse oscillations. Oscillation periods of loops in the same active region range from 2.5 to 11 min, and are different for different loops. The displacement amplitude is lower than 1 Mm. The oscillation phase is constant along each analysed loop. The spatial structure of the phase of the oscillations corresponds to the fundamental standing kink mode. We conclude that the observed behaviour is consistent with the empirical model in terms of a damped harmonic resonator affected by a non-resonant continuously operating external force.

Decayless low-amplitude kink oscillations: a common phenomenon in the solar corona?

We investigate the decayless regime of coronal kink oscillations recently discovered in the Solar Dynamics Observatory (SDO)/AIA data. In contrast to decaying kink oscillations that are excited by impulsive dynamical processes, this type of transverse oscillations is not connected to any external impulsive impact, such as a flare or CME, and does not show any significant decay. Moreover the amplitude of these decayless oscillations is typically lower than that of decaying oscillations. The aim of this research is to estimate the prevalence of this phenomenon and its characteristic signatures. We analysed 21 active regions (NOAA 11637--11657) observed in January 2013 in the 171 A channel of SDO/AIA. For each active region we inspected six hours of observations, constructing time-distance plots for the slits positioned across pronounced bright loops. The oscillatory patterns in time-distance plots were visually identified and the oscillation periods and amplitudes were measured. We also estimated the length of each oscillating loop. Low-amplitude decayless kink oscillations are found to be present in the majority of the analysed active regions. The oscillation periods lie in the range from 1.5 to 10~minutes. In two active regions with insufficient observation conditions we did not identify any oscillation patterns. The oscillation periods are found to increase with the length of the oscillating loop. The considered type of coronal oscillations is a common phenomenon in the corona. The established dependence of the oscillation period on the loop length is consistent with their interpretation in terms of standing kink waves.

Observation of a high-quality quasi-periodic rapidly propagating wave train using SDO/AIA

Context. We present a new event of quasi-periodic wave trains observed in EUV wavebands that rapidly propagate away from an active region after a flare. Aims. We measured the parameters of a wave train observed on 7 December 2013 after an M1.2 flare, such as the phase speeds, periods and wavelengths, in relationship to the local coronal environment and the energy sources. Methods. We compared our observations with a numerical simulation of fast magnetoacoustic waves that undergo dispersive evolution and leakage in a coronal loop embedded in a potential magnetic field. Results. The wave train is observed to propagate as several arc-shaped intensity disturbances for almost half an hour, with a speed greater than 1000 km s-1 and a period of about 1 min. The wave train followed two different patterns of propagation, in accordance with the magnetic structure of the active region. The oscillatory signal is found to be of high-quality, i.e. there is a large number (10 or more) of subsequent wave fronts observed. The observations are found to be consistent with the numerical simulation of a fast wave train generated by a localised impulsive energy release. Conclusions. Transverse structuring in the corona can efficiently create and guide high-quality quasi-periodic propagating fast wave trains.

A statistical study of decaying kink oscillations detected using SDO/AIA

Context. Despite intensive studies of kink oscillations of coronal loops in the last decade, a large-scale statistically significant investigation of the oscillation parameters has not been made using data from the Solar Dynamics Observatory (SDO). Aims. We carry out a statistical study of kink oscillations using extreme ultraviolet imaging data from a previously compiled catalogue. Methods. We analysed 58 kink oscillation events observed by the Atmospheric Imaging Assembly (AIA) on board SDO during its first four years of operation (2010–2014). Parameters of the oscillations, including the initial apparent amplitude, period, length of the oscillating loop, and damping are studied for 120 individual loop oscillations. Results. Analysis of the initial loop displacement and oscillation amplitude leads to the conclusion that the initial loop displacement prescribes the initial amplitude of oscillation in general. The period is found to scale with the loop length, and a linear fit of the data cloud gives a kink speed of Ck = (1330 ± 50) km s −1 . The main body of the data corresponds to kink speeds in the range Ck = (800−3300) km s −1 . Measurements of 52 exponential damping times were made, and it was noted that at least 21 of the damping profiles may be better approximated by a combination of non-exponential and exponential profiles rather than a purely exponential damping envelope. There are nine additional cases where the profile appears to be purely non-exponential and no damping time was measured. A scaling of the exponential damping time with the period is found, following the previously established linear scaling between these two parameters.

Damping profile of standing kink oscillations observed by SDO/AIA

Aims: Strongly damped standing and propagating kink oscillations are observed in the solar corona. This can be understood in terms of mode coupling, which causes the wave energy to be converted from the bulk transverse oscillation to localised, unresolved azimuthal motions. The damping rate can provide information about the loop structure, and theory predicts two possible damping profiles. Methods: We used the recently compiled catalogue of decaying standing kink oscillations of coronal loops to search for examples with high spatial and temporal resolution and sufficient signal quality to allow the damping profile to be examined. The location of the loop axis was tracked, detrended, and fitted with sinusoidal oscillations with Gaussian and exponential damping profiles. Results: Using the highest quality data currently available, we find that for the majority of our cases a Gaussian profile describes the damping behaviour at least as well as an exponential profile, which is consistent with the recently developed theory for the damping profile due to mode coupling.

Coronal loop seismology using damping of standing kink oscillations by mode coupling

Context. Kink oscillations of solar coronal loops are frequently observed to be strongly damped. The damping can be explained by mode coupling on the condition that loops have a finite inhomogeneous layer between the higher density core and lower density background. The damping rate depends on the loop density contrast ratio and inhomogeneous layer width. Aims. The theoretical description for mode coupling of kink waves has been extended to include the initial Gaussian damping regime in addition to the exponential asymptotic state. Observation of these damping regimes would provide information about the structuring of the coronal loop and so provide a seismological tool. Methods. We consider three examples of standing kink oscillations observed by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) for which the general damping profile (Gaussian and exponential regimes) can be fitted. Determining the Gaussian and exponential damping times allows us to perform seismological inversions for the loop density contrast ratio and the inhomogeneous layer width normalised to the loop radius. The layer width and loop minor radius are found separately by comparing the observed loop intensity profile with forward modelling based on our seismological results. Results. The seismological method which allows the density contrast ratio and inhomogeneous layer width to be simultaneously determined from the kink mode damping profile has been applied to observational data for the first time. This allows the internal and external Alfven speeds to be calculated, and estimates for the magnetic field strength can be dramatically improved using the given plasma density. Conclusions. The kink mode damping rate can be used as a powerful diagnostic tool to determine the coronal loop density profile. This information can be used for further calculations such as the magnetic field strength or phase mixing rate.

Coronal loop seismology using damping of standing kink oscillations by mode coupling II. additional physical effects and Bayesian analysis

Context. The strong damping of kink oscillations of coronal loops can be explained by mode coupling. The damping envelope depends on the transverse density profile of the loop. Observational measurements of the damping envelope have been used to determine the transverse loop structure which is important for understanding other physical processes such as heating. Aims. The general damping envelope describing the mode coupling of kink waves consists of a Gaussian damping regime followed by an exponential damping regime. Recent observational detection of these damping regimes has been employed as a seismological tool. We extend the description of the damping behaviour to account for additional physical effects, namely a time-dependent period of oscillation, the presence of additional longitudinal harmonics, and the decayless regime of standing kink oscillations. Methods. We examine four examples of standing kink oscillations observed by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). We use forward modelling of the loop position and investigate the dependence on the model parameters using Bayesian inference and Markov Chain Monte Carlo (MCMC) sampling. Results. Our improvements to the physical model combined with the use of Bayesian inference and MCMC produce improved estimates of model parameters and their uncertainties. Calculation of the Bayes factor also allows us to compare the suitability of different physical models. We also use a new method based on spline interpolation of the zeroes of the oscillation to accurately describe the background trend of the oscillating loop. Conclusions. This powerful and robust method allows for accurate seismology of coronal loops, in particular the transverse density profile, and potentially reveals additional physical effects.

Dynamics of a multi-thermal loop in the solar corona

Context. We present an observation of a long-living multi-thermal coronal loop, visible in different extreme ultra-violet wavebands of SDO/AIA in a quiet-Sun region close to the western solar limb. Aims. Analysis of persistent kink displacements of the loop seen in different bandpasses that correspond to different temperatures of the plasma allows sub-resolution structuring of the loop to be revealed. Methods. A vertically oriented slit is taken at the loop top, and time-distance maps are made from it. Loop displacements in time-distance maps are automatically tracked with the Gaussian fitting technique and fitted with a sinusoidal function that is “guessed”. Wavelet transforms are further used in order to quantify the periodicity variation in time of the kink oscillations. Results. The loop strands are found to oscillate with the periods ranging between 3 and 15 min. The oscillations are observed in intermittent regime with temporal changes in the period and amplitude. The oscillations are different at three analysed wavelengths. Conclusions. This finding suggests that the loop-like threads seen at different wavelengths are not co-spatial, hence that the loop consists of several multi-thermal strands. The detected irregularity of the oscillations can be associated with a stochastic driver acting at the footpoints of the loop.