Coronal kink oscillations and photospheric driving

Kink oscillations of coronal loops have been widely studied, both observationally and theoretically, over the past few decades. It has been shown that the majority of observed driven coronal loop oscillations appear to damp with either exponential or Gaussian profiles and a range of mechanisms have been proposed to account for this. However, some driven oscillations seem to evolve in manners which cannot be modeled with purely Gaussian or exponential profiles, with amplification of oscillations even being observed on occasions. Recent research has shown that incorporating the combined effects of coronal loop expansion, resonant absorption, and cooling can cause significant deviations from Gaussian and exponential profiles in damping profiles, potentially explaining increases in oscillation amplitude through time in some cases. In this article, we analyze 10 driven kink oscillations in coronal loops to further investigate the ability of expansion and cooling to explain complex damping profiles. Our results do not rely on fitting a periodicity to the oscillations meaning complexities in both temporal (period changes) and spatial (amplitude changes) can be accounted for in an elegant and simple way. Furthermore, this approach could also allow us to infer some important diagnostic information (such as, for example, the density ratio at the loop foot-points) from the oscillation profile alone, without detailed measurements of the loop and without complex numerical methods. Our results imply the existence of correlations between the density ratio at the loop foot-points and the amplitudes and periods of the oscillations. Finally, we compare our results to previous models, namely purely Gaussian and purely exponential damping profiles, through the calculation of χ2 values, finding the inclusion of cooling can produce better fits in some cases. The current study indicates that thermal evolution should be included in kink-mode oscillation models in the future to help us to better understand oscillations that are not purely Gaussian or exponential.

Ever since their detection two decades ago, standing kink oscillations in coronal loops have been extensively studied both observationally and theoretically. Almost all driven coronal loop oscillations (e.g., by flares) are observed to damp through time often with Gaussian or exponential profiles. Intriguingly, however, it has been shown theoretically that the amplitudes of some oscillations could be modified from Gaussian or exponential profiles if cooling is present in the coronal loop systems. Indeed, in some cases the oscillation amplitude can even increase through time. In this article, we analyse a flare-driven coronal loop oscillation observed by the Solar Dynamics Observatory's Atmospheric Imaging Assembly (SDO/AIA) in order to investigate whether models of cooling can explain the amplitude profile of the oscillation and whether hints of cooling can be found in the intensity evolution of several SDO/AIA filters. During the oscillation of this loop system, the kink mode amplitude appears to differ from a typical Gaussian or exponential profile with some hints being present that the amplitude increases. The application of cooling coronal loop modelling allowed us to estimate the density ratio between the loop and the background plasma, with a ratio of between 2.05-2.35 being returned. Overall, our results indicate that consideration of the thermal evolution of coronal loop systems can allow us to better describe oscillations in these structures and return more accurate estimates of the physical properties of the loops (e.g., density, scale height, magnetic field strength).

The transverse structure of coronal loops plays a key role in the physics but the small transverse scales can be difficult to observe directly. For wider loops the density profile may be estimated by forward modelling of the transverse intensity profile. The transverse density profile may also be estimated seismologically using kink oscillations in coronal loops. The strong damping of kink oscillations is attributed to resonant absorption and the damping profile contains information about the transverse structure of the loop. However, the analytical descriptions for damping by resonant absorption presently only describe the behaviour for thin inhomogeneous layers. Previous numerical studies have demonstrated that this thin boundary approximation produces poor estimates of the damping behaviour in loops with wider inhomogeneous layers. Both the seismological and forward modelling approaches suggest loops have a range of layer widths and so there is a need for a description of the damping behaviour that accurately describes such loops. We perform a parametric study of the damping of standing kink oscillations by resonant absorption for a wide range of inhomogeneous layer widths and density contrast ratios, with a focus on the values most relevant to observational cases. We describe the damping profile produced by our numerical simulations without prior assumption of its shape and compile our results into a lookup table which may be used to produce accurate seismological estimates for kink oscillation observations.

Decayless kink oscillations of solar coronal loops are studied in terms of a low-dimensional model based on a randomly driven Rayleigh oscillator with coefficients experiencing random fluctuations. The model considers kink oscillations as natural modes of coronal loops, decaying by linear resonant absorption. The damping is counteracted by random motions of the loop footpoints and the interaction of the loop with external quasi-steady flows with random fluctuations. In other words, the model combines the self-oscillatory and randomly driven mechanisms for the decayless behaviour. The random signals are taken to be of the stationary red noise nature. In the noiseless case, the model has an asymptotically stationary oscillatory solution, i.e. a kink self-oscillation. It is established that the kink oscillation period is practically independent of noise. This finding justifies the seismological estimations of the kink and Alfvén speeds, and the magnetic field in an oscillating loop by kink oscillations, based on the observed oscillation period. The oscillatory patterns are found to be almost harmonic. Noisy fluctuations of external flows modulate the amplitude of the almost monochromatic oscillatory pattern symmetrically, while random motions of the loop footpoints cause antisymmetric amplitude modulation. Such modulations are also consistent with the observed behaviour.

A series of events featuring decaying Transverse Coronal Loop Oscillations is examined utilizing high‐resolution observations from the Atmospheric Imaging Assembly on board Solar Dynamic Observatory and Extreme Ultraviolet Imager from Solar Terrestrial Relations Observatory twin spacecrafts, A (ahead) and B (behind). We used two distinct methods, coronal seismology and extrapolations, independently to assess the coronal magnetic field values within oscillating loops. For the coronal seismology, we performed stereoscopic tracing of coronal loops to obtain an accurate measurement of their lengths. Subsequently, we estimated the oscillation parameters such as amplitude, period, phase, and damping time. Using the periods of oscillations and loop lengths, we calculated average magnetic field values within the oscillating coronal loops, ranging from 12 to 146 G. On the other hand, we performed non‐linear extrapolations to match field lines with the coronal loops, resulting magnetic field values between 54 and 187 G. Our findings indicate that extrapolated field lines exhibited slightly higher values than those obtained through coronal seismology, though both methods provided reasonable estimates of the magnetic field strengths in the analyzed coronal loops.

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 magneto-seismology (SMS). Aims. By applying SMS, we aim to verify the consistency between the observed period and the one derived from the information of coronal density, magnetic field, and loop geometry, that is, the shape of the loop axis. Methods. We analysed the data of three coronal loop oscillation events detected by SDO/AIA and SDO/HMI. First, we obtained oscillation parameters by fitting the observational data. Second, we used a differential emission measure (DEM) analysis to diagnose the temperature and density distribution along the coronal loop. Subsequently, we applied magnetic field extrapolation to reconstruct the three-dimensional magnetic field and then, finally, used the shooting method to compute the oscillation periods from the governing equation. Results. The average magnetic field determined by magnetic field extrapolation is consistent with that derived by SMS. A new analytical solution is found under the assumption of exponential density profile and uniform magnetic field. The periods estimated by combining the coronal density and magnetic field distribution and the associated loop geometry are closest to the observed ones, and are more realistic than when the loop geometry is regarded as being semi-circular or having a linear shape. Conclusions. The period of a coronal loop is sensitive to not only the density and magnetic field distribution but also the loop geometry.

We introduce a new method for the investigation of low-amplitude transverse oscillations of solar plasma non-uniformities, such as coronal loops, individual strands in coronal arcades, jets, prominence fibrils, polar plumes, and other contrast features, observed with imaging instruments. The method is based on the two-dimensional dual tree complex wavelet transform (DT$\mathbb{C}$WT). It allows us to magnify transverse, in the plane-of-the-sky, quasi-periodic motions of contrast features in image sequences. The tests performed on the artificial data cubes imitating exponentially decaying, multi-periodic and frequency-modulated kink oscillations of coronal loops showed the effectiveness, reliability and robustness of this technique. The algorithm was found to give linear scaling of the magnified amplitudes with the original amplitudes provided they are sufficiently small. Also, the magnification is independent of the oscillation period in a broad range of the periods. The application of this technique to SDO/AIA EUV data cubes of a non-flaring active region allowed for the improved detection of low-amplitude decay-less oscillations in the majority of loops.

\n Transverse oscillations of coronal magnetic loops are routinely observed\nduring the space missions. Since the first observation these oscillations\nwere interpreted in terms of kink oscillations of magnetic tubes. Sometimes \ncollective oscillations of two or more coronal loops are observed. This\nmakes the development of theory of collective oscillations of a few parallel \nmagnetic tubes desirable. Another reason for the development of this\ntheory is that there are evidences that at least some coronal loops are \nnot monolithic but consist of many thin magnetic threads. In this paper\nthe linear theory of kink oscillations of two parallel magnetic tubes\nwith the density varying along the tubes is developed. The asymptotic\nmethod is used to derive the system of equations governing the collective\nkink oscillations of two tubes. This system is used to study the effect\nof density variation on the eigenfrequencies of collective oscillations.\nThe implication of the obtained results on coronal seismology is \ndiscussed. \n\n

Here, we present a study of the phenomena of decayless kink oscillations in a system of active-region (AR) coronal loops. Using high-resolution observations from two different instruments, namely the Extreme Ultraviolet Imager (EUI) on board Solar Orbiter and the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory, we follow these AR loops for an hour each on three consecutive days. Our results show significantly more resolved decayless waves in the higher resolution EUI data compared with the AIA data. Furthermore, the same system of loops exhibits many of these decayless oscillations on Day 2, while we detect very few oscillations on Day 3 , and find none at all on Day 1. Analysis of photospheric magnetic field data reveals that, most of the time, these loops were rooted in sunspots, where supergranular flows are generally absent. This suggests that supergranular flows, which are often invoked as drivers of decayless waves, are not necessarily driving such oscillations in our observations. Similarly, our findings also cast doubt on other possible drivers of these waves, such as a transient driver or mode conversion of longitudinal waves near the loop footpoints. In conclusion, our analysis suggests that none of the commonly suspected sources proposed to drive decayless oscillations in active-region loops seem to be operating in this event, and therefore the search for that elusive wave driver needs to continue.

The cross sections of solar coronal loops are suggested to be rarely circular. We examine linear kink oscillations in straight, density-enhanced, magnetic cylinders with elliptical cross sections by solving the three-dimensional magnetohydrodynamic equations from an initial-value-problem perspective. Motivated by relevant eigenmode analyses, we distinguish between two independent polarizations, one along the major axis (the M-modes) and the other along the minor one (the m-modes). We find that, as happens for coronal loops with circular cross sections, the apparent damping of the transverse displacement of the loop axis is accompanied by the accumulation of transverse Alfvénic motions and the consequent development of small scales therein, suggesting the robustness of the concepts of resonant absorption and phase mixing. In addition, two stages can in general be told apart in the temporal evolution of the loop displacement: a Gaussian time dependence precedes an exponential one. For the two examined density ratios between loops and their surroundings, the periods of the M-modes (m-modes) tend to increase (decrease) with the major-to-minor-half-axis ratio, and the damping times in the exponential stage for the M-modes tend to exceed their m-mode counterparts. This is true for the two transverse profiles we examine. However, the relative magnitudes of the damping times in the exponential stage for different polarizations depend on the specification of the transverse profile or the density contrast. The applications of our numerical findings are discussed in the context of coronal seismology.

The extreme-ultraviolet (EUV) imagers onboard the planned Solar Dynamics Observatory (SDO) and Solar Orbiter (SO) will offer us the best chance yet of using observations of post-flare loop oscillations to probe the fine structure of the corona. Recently developed magnetohydrodynamic (MHD) wave theory has shown that the properties of loop oscillations depend on their plasma fine structure. Up to this point, many studies have concentrated solely on the effect of plasma density stratification on coronal loop oscillations. In this paper we develop MHD wave theory which models the effect of an inhomogeneous magnetic field on coronal loop oscillations. The results have the potential to be used in testing the efficacy of photospheric magnetic field extrapolations and have important implications regarding magneto-seismology of the corona.

A recent study by Nakariakov et al. pointed out that the dispersion relation of MHD sausage mode oscillations has been incorrectly applied to coronal loops, neglecting the highly dispersive nature of the phase speed and the long-wavelength cutoff of the wave number. In the light of these new insights we revisit previous observations that have been interpreted in terms of MHD sausage mode oscillations in coronal loops and come to the following conclusions: (1) Fast sausage MHD mode oscillations require such a high electron density imposed by the wave number cutoff that they can only occur in flare loops; (2) In the previously reported radio observations ($\nu \approx 100$ MHz to 1 GHz) with periods of $P\approx 0.5-5$ s, the fast sausage MHD mode oscillation is likely to be confined to a small segment (corresponding to a high harmonic node) near the apex of the loop, rather than involving a global oscillation over the entire loop length. The recent microwave and soft X-ray observations of fast periods ($P\approx 6-17$ s) by Asai et al. and Melnikov et al., however, are consistent with fast sausage MHD oscillations at the fundamental harmonic.

The solar atmosphere is filled with clusters of hot small-scale loops commonly known as coronal bright points (CBPs). These ubiquitous structures stand out in the Sun by their strong X-ray and/or extreme-ultraviolet (EUV) emission for hours to days, which makes them a crucial piece when solving the solar coronal heating puzzle. In addition, they can be the source of coronal jets and small-scale filament eruptions. Here we present a novel 3D numerical model using the Bifrost code that explains the sustained CBP heating for several hours. We find that stochastic photospheric convective motions alone significantly stress the CBP magnetic field topology, leading to important Joule and viscous heating concentrated around the CBP’s inner spine at a few megameters above the solar surface. We also detect continuous upflows with faint EUV signals resembling observational dark coronal jets and small-scale eruptions when Hα fibrils interact with the reconnection site. We validate our model by comparing simultaneous CBP observations from the Solar Dynamics Observatory (SDO) and the Swedish 1‐m Solar Telescope (SST) with observable diagnostics calculated from the numerical results for EUV wavelengths as well as for the Hα line using the Multi3D synthesis code. Additionally, we provide synthetic observables to be compared with Hinode, Solar Orbiter, and the Interface Region Imaging Spectrograph (IRIS). Our results constitute a step forward in the understanding of the many different facets of the solar coronal heating problem.

Context. Heating of the solar corona by nanoflares, which are small transient events in which stored magnetic energy is dissipated by magnetic reconnection, may occur as the result of the nonlinear phase of the kink instability (Hood et al. 2009). Because of the high temperatures reached through these reconnection events, thermal conduction cannot be ignored in the evolution of the kink instability. Aims. To study the effect of thermal conduction on the nonlinear evolution of the kink instability of a coronal loop. To assess the efficiency of loop heating and the role of thermal conduction, both during the kink instability and for the long time evolution of the loop. Methods. Numerically solve the 3D nonlinear magnetohydrodynamic equations to simulate the evolution of a coronal loop that is initially in an unstable equilibrium. The initial state has zero net current. A comparison is made of the time evolution of the loop with thermal conduction and without thermal conduction. Results. Thermal conduction along magnetic field lines reduces the local temperature. This leads to temperatures that are an order of magnitude lower than those obtained in the absence of thermal conductivity. Consequently, different spectral lines are activated with and without the inclusion of thermal conduction, which have consequences for observations of solar corona loops. The conduction process is also important on the timescale of the fast magnetohydrodynamic phenomena. It reduces the kinetic energy released by an order of magnitude. Conclusions. Thermal conduction plays an essential role in the kink instability of coronal loops and cannot be ignored in the forward modelling of such loops.

Aims. We construct a new analytical model of a solar coronal loop that is embedded in a gravitationally stratified and magnetically confined atmosphere. On the basis of this analytical model, we devise a numerical model of solar coronal loops. We adopt it to perform the numerical simulations of its vertical kink oscillations excited by an external driver. Methods. Our model of the solar atmosphere is constructed by adopting a realistic temperature distribution and specifying the curved magnetic field lines that constitute a coronal loop. This loop is described by 2D, ideal magnetohydro- dynamic equations that are numerically solved by the FLASH code. Results. The vertical kink oscillations are excited by a periodic driver in the vertical component of velocity, acting at the top of the photosphere. For this forced driver with its amplitude 3 km/s, the excited oscillations exhibit about 1.2 km/s amplitude in their velocity and the loop apex oscillates with its amplitude in displacement of about 100 km. Conclusions. The newly devised analytical model of the coronal loops is utilized for the numerical simulations of the vertical kink oscillations, which match well with the recent observations of decay-less kink oscillations excited in solar loops. The model will have further implications on the study of waves and plasma dynamics in coronal loops, revealing physics of energy and mass transport mechanisms in the localized solar atmosphere.