Coronal Loops Research Articles

Kink Waves in Twisted and Expanding Magnetic Tubes

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 Sun’s Alfvén Surface: Recent Insights and Prospects for the Polarimeter to Unify the Corona and Heliosphere (PUNCH)

The solar wind is the extension of the Sun’s hot and ionized corona, and it exists in a state of continuous expansion into interplanetary space. The radial distance at which the wind’s outflow speed exceeds the phase speed of Alfvénic and fast-mode magnetohydrodynamic (MHD) waves is called the Alfvén radius. In one-dimensional models, this is a singular point beyond which most fluctuations in the plasma and magnetic field cannot propagate back down to the Sun. In the multi-dimensional solar wind, this point can occur at different distances along an irregularly shaped “Alfvén surface.” In this article, we review the properties of this surface and discuss its importance in models of solar-wind acceleration, angular-momentum transport, MHD waves and turbulence, and the geometry of magnetically closed coronal loops. We also review the results of simulations and data-analysis techniques that aim to determine the location of the Alfvén surface. Combined with recent perihelia of Parker Solar Probe, these studies seem to indicate that the Alfvén surface spends most of its time at heliocentric distances between about 10 and 20 solar radii. It is becoming apparent that this region of the heliosphere is sufficiently turbulent that there often exist multiple (stochastic and time-dependent) crossings of the Alfvén surface along any radial ray. Thus, in many contexts, it is more appropriate to use the concept of a topologically complex “Alfvén zone” rather than one closed surface. This article also reviews how the Polarimeter to Unify the Corona and Heliosphere (PUNCH) mission will measure the properties of the Alfvén surface and provide key constraints on theories of solar-wind acceleration.

A Method for Estimating the Spatial Period of Energy Release in Solar Flares

A method for estimating the spatial period of energy release in solar flares is proposed toanalyze the present-day satellite observations of arcades of flare coronal loops. The method is based on theapplication of a Fourier analysis to the difference images of flare arcades in the far ultraviolet. The operationof the method is demonstrated with the observations of the Bastille Day flare from the TRACE spacecraftin the 171 ˚A channel. The mean spatial period of energy release in the Bastille Day flare determined bythe proposed method is 5–8 Mm, in good agreement with the scenario for the development of thermalinstability of the preflare current layer in solar flares.

Small-Scale Upflows in a Coronal Hole – Tracked from the Photosphere to the Corona

Coronal transients are known as sources of coronal upflows. With the commissioning of Solar Orbiter, it became apparent that coronal small-scale features are even more frequent than previously estimated. It was found that even small coronal features seen by Solar Orbiter can produce visible upflows. Therefore, it is important to study the plasma flows on small scales better and understand their atmospheric driving mechanisms.In this article, we present the results from a two-week coordinated multi-spacecraft observation campaign with Hinode, IRIS, and the GREGOR telescope. We identify a small region of coronal upflows with Doppler velocities of up to 16.5 km s−1. The upflows are located north of a coronal bright point in a coronal hole. We study the corona, the transition region, the chromosphere and the photospheric magnetic field to find evidence of underlying mechanisms for the coronal upflow. We find a complex photospheric magnetic field with several small mixed polarities that are the footpoints of different loops. Flux emergence and cancellation are observed at the constantly changing footpoints of the coronal loops. Reconnection of loops can be identified as the driver of the coronal upflow. Furthermore, the impact of the coronal activity triggers plasma flows in the underlying layers. This work highlights that frequent small coronal features can cause considerable atmospheric response and ubiquitously produce plasma upflows that potentially feed into the solar wind.

Morphological evidence for nanoflares heating warm loops in the solar corona

Context. Nanoflares are impulsive energy releases that occur due to magnetic reconnection in the braided coronal magnetic field, which is a potential mechanism for heating the corona. However, there are still sporadic observations of the interchange of braiding structure segments and footpoints inside coronal loops, which is predicted to be the morphological evolution of the reconnecting magnetic bundles in the nanoflare picture. Aims. This work aims to detect the evolutions of the pairs of braiding strands within the apparent single coronal loops observed in Atmospheric Imaging Assembly (AIA) images. Methods. The loop strands were detected on two kinds of upsampled AIA 193 Å images, which were obtained by upscaling the point spread function matched AIA images via bicubic interpolation and were generated using a super-resolution convolutional neural network. The architecture of the network is designed to map the AIA images to unprecedentedly high spatial resolution coronal images taken by the High-resolution Coronal Imager (Hi-C) during its brief flight. Results. At times, pairs of separate strands that appear braided together later evolved into pairs of almost parallel strands with completely exchanged parts. These evolutions offer morphological evidence that magnetic reconnections between the braiding strands have taken place, which is further supported by the appearance of transient hot emissions containing significant high-temperature components (T > 5 MK) at the footpoints of the braiding structures. Conlusions. The brief appearances of the two rearranging strands support the idea that magnetic reconnections have occurred within what appears to be a single AIA loop.

Steadiness of Coronal Heating

The EUI instrument on the Solar Orbiter spacecraft has obtained the most stable, high-resolution images of the solar corona from its orbit with a perihelion near 0.4 au. A sequence of 360 images obtained at 17.1 nm, between 2022 October 25 19:00 and 19:30 UT, is scrutinized. One image pixel corresponds to 148 km at the solar surface. The widely held belief that the outer atmosphere of the Sun is in a continuous state of magnetic turmoil is pitted against the EUI data. The observed plasma variations appear to fall into two classes. By far the dominant behavior is a very low amplitude variation in brightness (1%) in the coronal loops, with larger variations in some footpoint regions. No hints of observable changes in magnetic topology are associated with such small variations. The larger-amplitude, more rapid, rarer, and less well organized changes are associated with flux emergence. It is suggested therefore that while magnetic reconnection drives the latter, most of the active corona is heated with no evidence of a role for large-scale (observable) reconnection. Since most coronal emission-line widths are subsonic, the bulk of coronal heating, if driven by reconnection, can only be of tangentially discontinuous magnetic fields, with angles below about 0.5c S /c A ∼ 0.3β, with β the plasma beta parameter (∼0.01) and c S and c A the sound and Alfvén speeds, respectively. If heated by multiple small flare-like events, then these must be ≲1021 erg, i.e., picoflares. But processes other than reconnection have yet to be ruled out, such as viscous dissipation, which may contribute to the steady heating of coronal loops over active regions.

Estimations of Elemental Abundances during Solar Flares Observed in Soft X-Rays by the MinXSS-1 CubeSat Mission

Solar flares are complex phenomena emitting all types of electromagnetic radiation and accelerating particles on timescales of minutes, converting magnetic energy to thermal, radiative, and kinetic energy through magnetic reconnections. As a result, local plasma can be heated to temperatures in excess of 20 MK. During the soft X-ray (SXR) solar flare peak, the elemental abundance of low first ionization potential elements are typically observed to be depleted from coronal values. We explored the abundance variations using disk-integrated solar spectra from the Miniature X-ray Solar Spectrometer CubeSat-1 (MinXSS-1). MinXSS-1 is sensitive to the 1–12 keV energy range with an effective 0.25 keV FWHM resolution at 5.9 keV. During the year-long mission of MinXSS-1, between 2016 May and 2017 May, 21 flares with intermittent data downlinks were observed ranging from C to M class. We examine the time evolution of temperature, volume emission measure, and elemental abundances of Fe, Ca, Si, S, and Ar with CHIANTI spectral models near the peak SXR emission times observed in the MinXSS-1 data. We determined the average absolute abundance of A(Fe) = 7.81, A(Ca) = 6.84, A(S) = 7.28, A(Si) = 7.90, and A(Ar) = 6.56. These abundances are depleted from coronal values during the SXR peak compared to nonflaring times. The elemental abundance values that are depleted from their coronal values are consistent with the process of chromospheric evaporation, in which the lower atmospheric plasma fills the coronal loops.

First Results for Solar Soft X-Ray Irradiance Measurements from the Third-generation Miniature X-Ray Solar Spectrometer

Three generations of the Miniature X-ray Solar Spectrometer (MinXSS) have flown on small satellites with the goal “to explore the energy distribution of soft X-ray (SXR) emissions from the quiescent Sun, active regions, and during solar flares, and to model the impact on Earth’s ionosphere and thermosphere.” The primary science instrument is the Amptek X123 X-ray spectrometer that has improved with each generation of the MinXSS experiment. This third-generation MinXSS-3 has a higher energy resolution and larger effective area than its predecessors and is also known as the Dual-zone Aperture X-ray Solar Spectrometer (DAXSS). It was launched on the INSPIRESat-1 satellite on 2022 February 14, and INSPIRESat-1 has successfully completed its 6 month prime mission. The INSPIRESat-1 is in a dawn–dusk, Sun-synchronous orbit and therefore has had 24 hr coverage of the Sun during most of its mission so far. The rise of Solar Cycle 25 has been observed by DAXSS. This paper introduces the INSPIRESat-1 DAXSS solar SXR observations, and we focus the science results here on a solar occultation experiment and multiple flares on 2022 April 24. One key flare result is that the reduction of elemental abundances appears greatest during the flare impulsive phase, thus highlighting the important role of chromospheric evaporation during flares to inject warmer plasma into the coronal loops. Furthermore, these results are suggestive that the amount of chromospheric evaporation is related to flare temperature and intensity.

Fleeting Small-scale Surface Magnetic Fields Build the Quiet-Sun Corona

Arch-like loop structures filled with million Kelvin hot plasma form the building blocks of the quiet-Sun corona. Both high-resolution observations and magnetoconvection simulations show the ubiquitous presence of magnetic fields on the solar surface on small spatial scales of ∼100 km. However, the question of how exactly these quiet-Sun coronal loops originate from the photosphere and how the magnetic energy from the surface is channeled to heat the overlying atmosphere is a long-standing puzzle. Here we report high-resolution photospheric magnetic field and coronal data acquired during the second science perihelion of Solar Orbiter that reveal a highly dynamic magnetic landscape underlying the observed quiet-Sun corona. We found that coronal loops often connect to surface regions that harbor fleeting weaker, mixed-polarity magnetic field patches structured on small spatial scales, and that coronal disturbances could emerge from these areas. We suggest that weaker magnetic fields with fluxes as low as 1015 Mx and/or those that evolve on timescales less than 5 minutes are crucial to understanding the coronal structuring and dynamics.

Beyond small-scale transients: A closer look at the diffuse quiet solar corona

Aims. Within the quiet Sun corona imaged at 1 MK, much of the field of view consists of diffuse emission that appears to lack the spatial structuring that is so evident in coronal loops or bright points. Our aim is to determine if these diffuse regions are categorically different in terms of their intensity fluctuations and spatial configuration from the better-studied dynamic coronal features. Methods. We analyzed a time series of observations from Solar Orbiter’s High Resolution Imager in the extreme ultraviolet to quantify the characterization of the diffuse corona at high spatial and temporal resolutions. We then compared this to the dynamic features within the field of view, mainly a coronal bright point. Results. We find that the diffuse corona lacks visible structuring, such as small embedded loops, and that this is persistent over the 25 min duration of the observation. The intensity fluctuations of the diffuse corona, which are within ±5%, are significantly smaller in comparison to the coronal bright point; however, the total intensity observed in the diffuse corona is on the same order as the bright point. Conclusions. It seems inconsistent with our data that the diffuse corona is a composition of small loops or jets or that it is driven by discrete small heating events that follow a power-law-like distribution. We speculate that small-scale processes such as magnetohydrodynamic turbulence might be energizing the diffuse regions, but at this point we cannot offer a conclusive explanation for the nature of this feature.

Measuring local physical parameters in coronal loops with spatial seismology

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.

Coronal energy release by MHD avalanches

Context. A possible key element for large-scale energy release in the solar corona is a magnetohydrodynamic (MHD) kink instability in a single twisted magnetic flux tube. An initial helical current sheet progressively fragments in a turbulent way into smaller-scale sheets. Dissipation of these sheets is similar to a nanoflare storm. Since the loop expands in the radial direction during the relaxation process, an unstable loop can disrupt nearby stable loops and trigger an MHD avalanche. Aims. Exploratory investigations have been conducted in previous works with relatively simplified loop configurations. In this work, we address a more realistic environment that comprehensively accounts for most of the physical effects involved in a stratified atmosphere typical of an active region. The questions we investigate are whether the avalanche process will be triggered, with what timescales, and how will it develop as compared with the original, simpler approach. Methods. We used three-dimensional MHD simulations to describe the interaction of magnetic flux tubes, which have a stratified atmosphere with chromospheric layers, a thin transition region to the corona, and a related transition from high-β to dlow-β regions. The model also includes the effects of thermal conduction and of optically thin radiation. Results. Our simulations address the case where one flux tube amongst a few is twisted at the footpoints faster than its neighbours. We show that this flux tube becomes kink unstable first in conditions in agreement with those predicted by analytical models. It then rapidly affects nearby stable tubes, instigating significant magnetic reconnection and dissipation of energy as heat. In turn, the heating brings about chromospheric evaporation as the temperature rises up to about 107 K, close to microflare observations. Conclusions. This work confirms, in more realistic conditions, that avalanches are a viable mechanism for the storing and release of magnetic energy in plasma confined in closed coronal loops as a result of photospheric motions.

A New Insight into the Linear Theory of Magnetoacoustic Waves in the Homogeneous Flux Tubes with an Abrupt Boundary

An important and interesting issue is brought to notice in the standard linear theory of the magnetoacoustic waves in the homogeneous magnetic flux tubes with an abrupt magnetic boundary, which are representative of the coronal, chromospheric, and photospheric loops of the solar atmosphere. It is shown that the dispersion relation given for the magnetoacoustic waves of such flux tubes by the linear standard theory is generally inapplicable because it does not take into account the electrodynamic boundary condition and the applicability is only restricted to the case β = 0, where β is the usual plasma parameter given by the ratio of the thermodynamic gas pressure to the magnetic pressure. This issue is then addressed, which gives us new insight into the standard linear theory of such modes, and a new dispersion relation is obtained, which is generally applicable i.e., for all β and would reduce to the earlier expression as a special case for β = 0. Finally a comparison is drawn between the dispersion curves described by the newly derived dispersion relation and its previous counterpart.

The Effect of Mass Flow on Slow MHD Oscillations of Curved Solar Coronal Loops

The Effect of Mass Flow on Slow MHD Oscillations of Curved Solar Coronal Loops

Modeling of Transverse Oscillations Driven by p-modes in Short Coronal Loops

Recent observations have revealed two types of decayless transverse oscillations in short coronal loops: one with short periods scaling with loop lengths, and the other with longer periods that exhibit a peak at around 5 minutes in the period distribution. To understand such a difference in period, we work in the framework of ideal MHD and model a short coronal loop embedded in an atmosphere with density stratification from the chromosphere to the corona. An inclined p-mode-like driver with a period of 5 minutes is launched at one loop footpoint. It is discovered that two types of decayless transverse oscillations can be excited in the loop. We interpret the 5 minutes periodicity as being directly driven by the footpoint driver, while the others, with periods of several tens of seconds, are regarded as kink eigenmodes of different harmonics. Therefore, our simulation shows that both types of decayless oscillations found in observations can be excited by p-modes in one short coronal loop. This study extends our understanding of ubiquitous decayless transverse oscillations in the corona. Furthermore, it suggests that p-modes could be an important energy source for coronal heating by driving decayless transverse oscillations.

Magnetic Fields in Solar Plage Regions: Insights from High-sensitivity Spectropolarimetry

Plage regions are patches of concentrated magnetic field in the Sun’s atmosphere where hot coronal loops are rooted. While previous studies have shed light on the properties of plage magnetic fields in the photosphere, there are still challenges in measuring the overlying chromospheric magnetic fields, which are crucial to understanding the overall heating and dynamics. Here, we utilize high-sensitivity, spectropolarimetric data obtained by the 4 meter Daniel K. Inouye Solar Telescope to investigate the dynamic environment and magnetic field stratification of an extended, decaying plage region. The data show strong circular polarization signals in both plage cores and surrounding fibrils. Notably, weak linear polarization signals clearly differentiate between plage patches and the fibril canopy, where they are relatively stronger. Inversions of the Ca II 8542 Å spectra show an imprint of the fibrils in the chromospheric magnetic field, with typical field strength values ranging from ∼200 to 300 G in fibrils. We confirm the weak correlation between field strength and cooling rates in the lower chromosphere. Additionally, we observe supersonic downflows and strong velocity gradients in the plage periphery, indicating dynamical processes occurring in the chromosphere. These findings contribute to our understanding of the magnetic field and dynamics within plages, emphasizing the need for further research to explore the expansion of magnetic fields with height and the three-dimensional distribution of heating rates in the lower chromosphere.

Comparison of damping models for kink oscillations of coronal loops

ABSTRACT Kink oscillations of solar coronal loops are of intense interest due to their potential for diagnosing plasma parameters in the corona. The accurate measurement of the kink oscillation damping time is crucial for precise seismological diagnostics, such as the transverse density profile, and for the determination of the damping mechanism. Previous studies of large-amplitude rapidly decaying kink oscillations have shown that both an exponential damping model and a generalized model (consisting of Gaussian and exponential damping patterns) fit observed damping profiles sufficiently well. However, it has recently been shown theoretically that the transition from the decaying regime to the decayless regime could be characterized by a superexponential damping model. In this work, we reanalyse a sample of decaying kink oscillation events, and utilize the Markov chain Monte Carlo Bayesian approach to compare the exponential, Gaussian–exponential, and superexponential damping models. It is found that in 7 out of 10 analysed oscillations, the preferential damping model is the superexponential one. In two events, the preferential damping is exponential, and in one it is Gaussian–exponential. This finding indicates the plausibility of the superexponential damping model. The possibility of a non-exponential damping pattern needs to be taken into account in the analysis of a larger number of events, especially in the estimation of the damping time and its associated empirical scalings with the oscillation period and amplitude, and in seismological inversions.

Exploring source region of 3-min slow magnetoacoustic waves observed in coronal fan loops rooted in sunspot umbra

ABSTRACT Sunspots host various oscillations and wave phenomena like umbral flashes, umbral oscillations, running penumbral waves, and coronal waves. All fan loops rooted in sunspot umbra constantly show a 3-min period propagating slow magnetoacoustic waves in the corona. However, their origin in the lower atmosphere is still unclear. In this work, we studied these oscillations in detail along a clean fan loop system rooted in active region AR 12553 for a duration of 4 h on 2016 June 16 observed by Interface Region Imaging Spectrograph and Solar Dynamics Observatory. We traced foot-points of several fan loops by identifying their locations at different atmospheric heights from the corona to the photosphere. We found presence of 3-min oscillations at foot-points of all the loops and at all atmospheric heights. We further traced origin of these waves by utilizing their amplitude modulation characteristics while propagating in the solar atmosphere. We found several amplitude modulation periods in the range of 9–14, 20–24, and 30–40 min of these 3-min waves at all heights. Based on our findings, we interpret that 3-min slow magnetoacoustic waves propagating in coronal fan loops are driven by 3-min oscillations observed at the photospheric foot-points of these fan loops in the umbral region. We also explored any connection between 3- and 5-min oscillations observed at the photospheric foot-points of these loops and found them to be weakly coupled. Results provide clear evidence of magnetic coupling of the solar atmosphere through propagation of 3-min waves along fan loops at different atmospheric heights.

30-min decayless kink oscillations in a very long bundle of solar coronal plasma loops

The energy balance in the corona of the Sun is the key to the long-standing coronal heating dilemma, which could be potentially revealed by observational studies of decayless kink oscillations of coronal plasma loops. A bundle of very long off-limb coronal loops with the length of 736pm 80 Mm and a lifetime of about 2 days are found to exhibit decayless kink oscillations. The oscillations are observed for several hours. The oscillation amplitude is measured at 0.3–0.5 Mm, and the period at 28–33 min. The existence of 30-min periodicity of decayless kink oscillations indicates that the mechanism compensating the wave damping is still valid in such a massive plasma structure. It provides important evidence for the non-resonant origin of decayless kink oscillations with 2–6 min periods, i.e., the lack of their link with the leakage of photospheric and chromospheric oscillations into the corona and the likely role of the broadband energy sources. Magnetohydrodynamic seismology based on the reported detection of the kink oscillation, with the assistance of the differential emission measure analysis and a background coronal model provides us with a comprehensive set of plasma and magnetic field diagnostics, which is of interest as input parameters of space weather models.

Variation of temperature and non-thermal velocity with height in fan loops

ABSTRACT We study the variation of temperature and non-thermal velocity with height in fan loops. For this purpose, we have used the observations recorded by the Extreme Ultraviolet Imaging Spectrometer onboard Hinode. We have employed the emission measure (EM)-loci method to estimate the temperatures of different coronal fan loops and then compute the non-thermal velocities using the obtained temperatures in Si vii 275.35 Å and Fe viii 185.21 Å lines. The EM-loci analysis provides nearly iso-thermal temperature along the fan loops. We obtain the peak temperatures in the range $\log \, T(K)$ = 5.85–5.95 for fan loops, and the subtraction of thermal broadening gives the non-thermal velocities in the range ≈5–15 and 11–29 km s−1 for Si vii 275.35 Å and Fe viii 185.21 Å, respectively. Our method provides quantitative accuracy in the measurement of non-thermal velocity, which is an important parameter in understanding the dynamics of heating of the solar atmosphere.