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The determination of the three-dimensional (3D) geometry of coronal features is important for understanding the magnetic structuring of the solar atmosphere. In this context, the length of a coronal loop, which is subject to standing transverse oscillations, is a crucial parameter in coronal seismology for the correct estimation of the phase speed of the wave and, consequently, of the Alfvén speed and coronal magnetic-field strength. Simultaneous space-based observations of the solar corona from different vantage points, e.g. one from the Solar Dynamics Observatory (SDO) and the second from the Solar TErrestrial RElations Observatory (STEREO), have permitted the reconstruction of the geometry of coronal loops. Nisticò, Verwichte, and Nakariakov ( Entropy 15 , 4520, 2013 ) proposed a method based on principal component analysis for fitting an ensemble of 3D points that sample a coronal loop. This method was shown to retrieve easily the main geometric parameters that define a loop, such as the loop axes and the loop plane. In this article, an extension of that work is presented that includes a Python tool for performing geometric triangulation of coronal features seen by two different observers.

Coronal loops are bright, filamentary structures formed by thermal plasmas constrained by the sun’s magnetic field. Studying coronal loops provides insights into magnetic fields and their role in coronal heating processes. We propose a new automatic coronal loop detection method to optimize the problem of existing algorithms in detecting low-intensity coronal loops. Our method employs a line-Gaussian filter to enhance the contrast between coronal loops and background pixels, facilitating the detection of low-intensity ones. Following the detection of coronal loops, each loop is extracted using a method based on approximate local direction. Compared with the classical automatic detection method, Oriented Coronal Curved Loop Tracing (OCCULT), and its improved version, OCCULT-2, the proposed method demonstrates superior accuracy and completeness in loop detection. Furthermore, testing with images from the Transition Region and Coronal Explorer (TRACE) at 173 Å, the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO) at 193 Å, and the High-Resolution Coronal Imager (Hi-C) at 193 Å and 172 Å confirms the robust generalization capabilities of our method. Statistical analysis of the cross-section width of coronal loops shows that most of the loop widths are resolved in Hi-C images.

We study the non-reflective propagation of kink waves in inhomogeneous magnetic-flux tubes. We use the thin-tube and zero-beta plasma approximations. The wave equation with the variable velocity is reduced to the Euler–Poisson–Darboux equation. This equation contains one dimensionless parameter. There are two infinite sequences of this parameter, one monotonically increasing and the other monotonically decreasing, when exact analytical solutions for the Euler–Poisson–Darboux equation can be obtained. For the monotonically increasing sequences the Euler–Poisson–Darboux equation becomes the equation describing spherically symmetric waves in multi-dimensional spaces. The general results are applied to kink-wave propagation in coronal magnetic loops. We consider a coronal magnetic loop of a half-circular shape. We find that for a fixed loop height there is a one-parametric family of dependences of the loop cross-sectional radius on the coordinate along the loop corresponding to the non-reflective kink-wave propagation.

The excitation and damping of the transversal coronal loop oscillations and quantitative relation between damping time, damping property (damping time per period), oscillation amplitude, dissipation mechanism and the wake phenomena are investigated. The observed time series data with the Atmospheric Imaging Assembly (AIA) telescope on NASA’s Solar Dynamics Observatory (SDO) satellite on 2015 March 2, consisting of 400 consecutive images with 12 s cadence in the 171 Å pass band is analyzed for evidence of transversal oscillations along the coronal loops by the Lomb–Scargle periodgram. In this analysis signatures of transversal coronal loop oscillations that are damped rapidly were found with dominant oscillation periods in the range of P = 12.25 – 15.80 min. Also, damping times and damping properties of the transversal coronal loop oscillations at dominant oscillation periods are estimated in the range of τ d = 11.76 – 21.46 min and τ d / P = 0.86 – 1.49 , respectively. The observational results of this analysis show that damping properties decrease slowly with increasing amplitude of the oscillation, but the periods of the oscillations are not sensitive functions of the amplitude of the oscillations. The order of magnitude of the damping properties and damping times are in good agreement with previous findings and the theoretical prediction for damping of kink mode oscillations by the dissipation mechanism. Furthermore, oscillations of the loop segments attenuate with time roughly as t − α and the magnitude values of α for 30 different segments change from 0.51 to 0.75.

Magnetoacoustic waves are actively used as a means of diagnosing plasma parameters and processes occurring in it. In this paper, we study the problem of the evolution of a weak perturbation specified at the base of a coronal loop. The analysis is carried out under the assumption that the plasma is in a strong magnetic field, such that the evolution of slow magnetoacoustic and entropy modes can be described within the framework of gas dynamics equations with a high degree of accuracy. The spectrum of the waves in question is assumed to be such that the main source of dispersion and dissipation of the waves is the thermal conduction of the medium. Within the framework of the specified approximations, an exact solution to the boundary value problem for the linear evolution equation is found using the Fourier method and Duhamel’s principle. The obtained exact analytical solution can be used to interpret the observation results, as well as numerical modeling of slow magnetoacoustic and entropy waves in the solar corona.

We study kink and fluting waves in expanding and twisted magnetic flux tubes. We use the thin-tube and zero-beta plasma approximations. The equilibrium magnetic field is force free with a constant proportionality coefficient between the electrical current and the magnetic field. We derive the equation governing the kink and fluting waves in a tube. Using this equation we study the propagation of kink waves in a particular case of a magnetic tube homogeneous in the axial direction. We show that while there is only one propagating kink wave with the phase speed equal to the kink speed in an untwisted tube, in a twisted tube there are two wave modes, accelerated and decelerated. The phase speed of the accelerated wave exceeds the kink speed, while the phase speed of the decelerated wave is less than the kink speed. We also show that the standing modes are defined by the same eigenvalue problem as that in the case of an untwisted tube. Hence, the frequencies of the standing-wave modes are not affected by the twist. This implies that the seismological results based on the observation of the standing-wave mode frequencies remain valid when the twist is taken into account. The only effect of twist is the variation of the direction of polarisation of the coronal magnetic-loop displacement along the loop. As a result, an apparent node can be detected near the loop apex if only one component of the loop displacement is observed. This can lead to an incorrect conclusion that the observed coronal loop kink oscillation was the first overtone, while in fact it was the fundamental mode.

The imaging telescope on board the Transition Region and Coronal Explorer (TRACE) spacecraft observed the decaying transversal oscillations of a long [(130 ± 6) × 10$^6$ meters], thin [diameter (2.0 ± 0.36) × 10$^6$ meters], bright coronal loop in the 171 angstrom Fe$^{IX}$ emission line. The oscillations were excited by a solar flare in the adjacent active region. The decay time of the oscillations is 14.5 ± 2.7 minutes for an oscillation with a frequency 3.90 ± 0.13 millihertz. The coronal dissipation coefficient is estimated to be eight to nine orders of magnitude larger than the theoretically predicted classical value. The larger dissipation coefficient may solve existing difficulties with wave heating and reconnection theories.

The photometry of eclipse white-light (W-L) images showing a moving blob is interpreted for the first time together with observations from space with the PRoject for On Board Autonomy (PROBA-2) mission (ESA). An off-limb event seen with great details in W-L was analyzed with the SWAP imager ( Sun Watcher using Active pixel system detector and image Processing ) working in the EUV near 174 Å. It is an elongated plasma blob structure of 25 Mm diameter moving above the east limb with coronal loops under. Summed and co-aligned SWAP images are evaluated using a 20-h sequence, in addition to the 11 July, 2010 eclipse W-L images taken from several sites. The Atmospheric Imaging Assembly (AIA) instrument on board the Solar Dynamics Observatory (SDO) recorded the event suggesting a magnetic reconnection near a high neutral point; accordingly, we also call it a magnetic plasmoid. The measured proper motion of the blob shows a velocity up to 12 km s − 1 . Electron densities of the isolated condensation (cloud or blob or plasmoid) are photometrically evaluated. The typical value is 10 8 cm − 3 at r = 1.7 R ⊙ , superposed on a background corona of 10 7 cm − 3 density. The mass of the cloud near its maximum brightness is found to be 1.6 × 10 13  g, which is typically 0.6 × 10 − 4 of the overall mass of the corona. From the extrapolated magnetic field the cloud evolves inside a rather broad open region but decelerates, after reaching its maximum brightness. The influence of such small events for supplying material to the ubiquitous slow wind is noticed. A precise evaluation of the EUV photometric data, after accurately removing the stray light, suggests an interpretation of the weak 174 Å radiation of the cloud as due to resonance scattering in the Fe IX/X lines.

The heating of the solar chromosphere and corona to the observed high temperatures, imply the presence of ongoing heating that balances the strong radiative and thermal conduction losses expected in the solar atmosphere. It has been theorized for decades that the required heating mechanisms of the chromospheric and coronal parts of the active regions, quiet-Sun, and coronal holes are associated with the solar magnetic fields. However, the exact physical process that transport and dissipate the magnetic energy which ultimately leads to the solar plasma heating are not yet fully understood. The current understanding of coronal heating relies on two main mechanism: reconnection and MHD waves that may have various degrees of importance in different coronal regions. In this review we focus on recent advances in our understanding of MHD wave heating mechanisms. First, we focus on giving an overview of observational results, where we show that different wave modes have been discovered in the corona in the last decade, many of which are associated with a significant energy flux, either generated in situ or pumped from the lower solar atmosphere. Afterwards, we summarise the recent findings of numerical modelling of waves, motivated by the observational results. Despite the advances, only 3D MHD models with Alfvén wave heating in an unstructured corona can explain the observed coronal temperatures compatible with the quiet Sun, while 3D MHD wave heating models including cross-field density structuring are not yet able to account for the heating of coronal loops in active regions to their observed temperature.

The Sun’s outer atmosphere is heated to temperatures of millions of degrees, and solar plasma flows out into interplanetary space at supersonic speeds. This paper reviews our current understanding of these interrelated problems: coronal heating and the acceleration of the ambient solar wind. We also discuss where the community stands in its ability to forecast how variations in the solar wind (i.e., fast and slow wind streams) impact the Earth. Although the last few decades have seen significant progress in observations and modeling, we still do not have a complete understanding of the relevant physical processes, nor do we have a quantitatively precise census of which coronal structures contribute to specific types of solar wind. Fast streams are known to be connected to the central regions of large coronal holes. Slow streams, however, appear to come from a wide range of sources, including streamers, pseudostreamers, coronal loops, active regions, and coronal hole boundaries. Complicating our understanding even more is the fact that processes such as turbulence, stream-stream interactions, and Coulomb collisions can make it difficult to unambiguously map a parcel measured at 1 AU back down to its coronal source. We also review recent progress—in theoretical modeling, observational data analysis, and forecasting techniques that sit at the interface between data and theory—that gives us hope that the above problems are indeed solvable.