Structure Of Solar Corona Research Articles

Prediction of Solar Coronal Structures Using Fourier Neural Operators Based on the Solar Photospheric Magnetic Field Observation

AbstractThis paper constructs the structures of the solar corona (SC) using Fourier neural operators (FNO) based on solar photospheric magnetic field observation. The purpose is to learn the mapping between two infinite‐dimensional function spaces, which takes the photospheric magnetic field as input and the magnetohydrodynamic (MHD) solar wind plasma parameters as output, from a finite collection of input‐output pairs. The FNO‐SC model is established using MHD simulated results of 36 Carrington rotations (CRs) from 2008, 2009, and 2020. The performance of the FNO‐SC model is tested for 6 CRs during various phases of the solar activity such as descending, minimum, and ascending phases to generate the 3D structures of the SC. With the MHD simulations as references, the average structure similarity index measure (SSIM) value for the magnetic field topology from 1 to 3Rs is around 0.88. From 1 to 20Rs, the SSIM values for the number density and radial speed surpass 0.9. Relative to OMNI observations, the mean absolute percentage error for the radial speed generated from the FNO‐SC model does not exceed 0.25. These results indicate that the FNO‐SC model effectively captures the solar coronal structures typical of the periods investigated, by recovering the MHD simulations as well as the observations. The FNO‐SC model is further trained with enriched data from the maximum phase to assess the capability of modeling such a situation. The FNO‐SC model costs 48.7 s for a single CR prediction, and thus facilitates real‐time space weather forecasting.

Complete X-ray census of M dwarfs in the solar neighborhood

Context. X-ray emission is the most sensitive diagnostic of magnetic activity in M dwarfs and, hence, of the dynamo in low-mass stars. Moreover it is crucial for quantifying the influence of the stellar irradiation on the evolution of planet atmospheres. Aims. We have embarked in a systematic study of the X-ray emission in a volume-limited sample of M dwarf stars to explore the full range of activity levels present in their coronae. We look to obtain a better understanding of the conditions in their outer atmospheres and their possible impact on the circumstellar environment. Methods. Based on a recent catalog of Gaia objects within 10 pc from the Sun, we identified all its stars with spectral types between M0 and M4 and we carried out a systematic search for X-ray measurements of this sample. To this end, we used both archival data from ROSAT, XMM-Newton, and the ROentgen Survey with an Imaging Telescope Array (eROSITA) on board the Russian Spektrum-Roentgen-Gamma mission, as well as our own dedicated XMM-Newton observations. To make inferences on the properties of the M dwarf corona, we compared the range of their observed X-ray emission levels to the flux radiated by the Sun from different types of magnetic structures: coronal holes, background corona, active regions, and cores of active regions. In this work, we focus on the properties of stars with the faintest X-ray emission. Results. At the current state of our project, with more than 90% of the 10 pc M dwarf sample observed in the X-ray, there is only one star that has had no detections: GJ 745 A. With an upper limit luminosity of log Lx (erg s−1) < 25.4 and an X-ray surface flux of log FX,SURF (erg cm−2 s−1) < 3.6, GJ 745 A defines the lower boundary of the X-ray emission level for M dwarfs. Together with its proper motion companion (GJ 745 B), it is the only star in this volume-complete sample located in the range of X-ray surface flux that corresponds to the faintest solar coronal structures, namely: coronal holes. The fact that the ultra-low X-ray emission level of GJ 745 B (log Lx (erg s−1) = 25.6 and log FX,SURF (erg cm−2 s−1) = 3.8) is entirely attributed to flaring activity indicates that while its corona is dominated by “holes,” at least one magnetically active structure is present. This structure determines the total X-ray brightness and the coronal temperature of the star.

A New Numerical Implementation for Solar Coronal Modeling by an HLL Generalized Riemann Problem Solver

In this paper, we employ a Harten–Lax–van Leer (HLL) generalized Riemann problem (HLL-GRP) solver within the framework of a finite volume method to model 3D solar coronal structures for the first time. Based on the rotational invariance of magnetohydrodynamics (MHD) equations, the HLL-GRP solver is successfully implemented into 3D MHD simulations. To constrain the divergence of the magnetic field, the locally divergence-free weighted-least-squares-based essentially nonoscillatory reconstruction and the properly discretized Godunov–Powell source term are applied. To keep density and pressure positive, a positivity-preserving limiter is added to the reconstructed polynomials of density and pressure. We first test a 3D blast wave problem to preliminarily validate the effectiveness of the proposed scheme on Cartesian structured grid. Then, we further run our code on a six-component grid to numerically study the steady-state coronal structures of Carrington rotation 2218 during the solar minimum phase. A comparison with the two-stage Runge–Kutta scheme is performed for both the 3D blast wave problem and solar coronal problem. Numerical results of large-scale solar coronal structures are basically consistent with the observational characteristics, indicating the robustness of the proposed model.

Implicit Solar Coronal Magnetohydrodynamic (MHD) Modeling with a Low-dissipation Hybridized AUSM-HLL Riemann Solver

In this paper, we develop a 3D implicit single-fluid magnetohydrodynamic (MHD) model to simulate the steady-state solar corona with a wide range of Mach numbers and low plasma β. We employ a low-dissipation advection upstream splitting method (AUSM) to calculate the convective flux in the regions of low Mach numbers for a high resolution, and hybridize the AUSM with Harten-Lax-van Leer Riemann solver in the regions of high Mach numbers to improve the solver’s robustness. The inner boundary condition of no backflow is implemented by numerical flux. A reconstruction method based on the divergence-free radial basis function is adopted to enhance the divergence-free constraint of magnetic field. Also, an anisotropic thermal conduction term is considered; the positivity-preserving reconstruction method is used to prevent the presence of negative thermal pressure and plasma density, and the implicit lower-upper symmetric Gauss Seidel method is implemented for a better convergence rate. After establishing the implicit solar wind MHD model, we employ it to simulate steady-state solar coronal structures in Carrington rotations 2177 and 2212. The simulations demonstrate that the MHD model’s computational efficiency is desirable, and the modeled results are basically in agreement with the solar coronal observations and the mapped in situ measurements from the OMNI archive. Consequently, this implicit MHD model is promising to simulate a complex plasma environment with high-intensity magnetic field and wide-ranging Mach numbers.

Enhanced phase mixing of torsional Alfvén waves in stratified and divergent solar coronal structures – II. Non-linear simulations

ABSTRACT We use magnetohydrodynamic (MHD) simulations to detect the non-linear effects of torsional Alfvén wave propagation in a potential magnetic field with exponentially divergent field lines, embedded in a stratified solar corona. In Paper I, we considered solutions to the linearized governing equations for torsional Alfvén wave propagation and showed, using a finite difference solver we developed named WiggleWave, that in certain scenarios wave damping is stronger than what would be predicted by our analytical solutions. In this paper, we consider whether damping would be further enhanced by the presence of non-linear effects. We begin by deriving the non-linear governing equations for torsional Alfvén wave propagation and identifying the terms that cause coupling to magnetosonic perturbations. We then compare simulation outputs from an MHD solver called Lare3d, which solves the full set of non-linear MHD equations, to the outputs from WiggleWave to detect non-linear effects such as: the excitation of magnetosonic waves by the Alfvén wave, self-interaction of the Alfvén wave through coupling to the induced magnetosonic waves, and the formation of shock waves higher in the atmosphere caused by the steepening of these compressive perturbations. We suggest that the presence of these non-linear effects in the solar corona would lead to Alfvén wave heating that exceeds the expectation from the phase mixing alone.

Enhanced phase mixing of torsional Alfvén waves in stratified and divergent solar coronal structures – Paper I. Linear solutions

ABSTRACT We derive a corrected analytical solution for the propagation and enhanced phase mixing of torsional Alfvén waves, in a potential magnetic field with exponentially divergent field lines, embedded in a stratified solar corona. Further we develop a code named TAWAS that calculates the analytic solution describing torsional Alfvén waves using idl software language. We then use TAWAS to demonstrate that both our correction to the analytic solution and the inclusion of wave reflection have a significant impact on Alfvén wave damping. We continue to utilize TAWAS by performing a parameter study in order to identify the conditions under which enhanced phase mixing is strongest. We find that phase mixing is the strongest for high frequency Alfvén waves in magnetic fields with highly divergent field lines and without density stratification. We then present a finite difference solver, Wigglewave, which solves the linearized evolution equations for the system directly. Comparing solutions from TAWAS and Wigglewave we see that our analytical solution is accurate within the limits of the WKB approximation but under-reports the wave damping, caused by enhanced phase mixing, beyond the WKB limit. Both TAWAS and Wigglewave solve the linearized governing equations and not the complete non-linear magnetohydrodynamics (MHD) equations. Paper II will consider simulations that solve the full MHD equations including important non-linear effects.

The Solar Line Emission Dopplerometer project

Observations of the dynamics of solar coronal structures are necessary to investigate space weather phenomena and global heating of the corona. The profiles of high temperature lines emitted by the hot plasma are usually integrated by narrow band filters or recorded by classical spectroscopy. We present in this paper details of a new transportable instrument (under construction) for imaging spectroscopy: the Solar Line Emission Dopplerometer (SLED). It uses the Multi-channel Subtractive Double Pass (MSDP) technique, which combines the advantages of both filters and narrow slit spectrographs, i.e. high temporal, spatial and spectral resolutions. The SLED will measure at high cadence (1 Hz) the line-of-sight velocities (Doppler shifts) of hot coronal loops, in the forbidden lines of FeX 637. nm and FeXIV 530.3 nm. It will follow the dynamics of fast evolving events of solar activity such as flares or Coronal Mass Ejections (CMEs), and also study coronal heating by short period waves. Observations will be performed with the coronagraph at the Lomnicky Stit Observatory (LSO, in Slovakia) or during total eclipses. The SLED will also observe the dynamics of solar prominences in Halpha 656.3 nm or HeD3 587.6 nm lines when mounted on the Bialkow coronagraph (near Wroclaw, Poland). It is fully compatible with polarimetric measurements by various techniques.

Thermodynamic evolution of a sigmoidal active region with associated flares

ABSTRACT Active regions often show S-shaped structures in the corona called sigmoids. These are highly sheared and twisted loops formed along the polarity inversion line. They are considered to be one of the best pre-eruption signatures for CMEs. Here, we investigate the thermodynamic evolution of an on-disc sigmoid observed during 2015 December 24–28. For this purpose, we have employed Emission Measure (EM) and filter-ratio techniques on the observations recorded by the Atmospheric Imaging Assembly (AIA) on-board the Solar Dynamics Observatory (SDO) and X-ray Telescope (XRT) on-board Hinode. The EM analysis showed multithermal plasma along the sigmoid and provided a peak temperature of ∼10–12.5 MK for all observed flares. The sigmoidal structure showed emission from Fe xviii (93.93 Å) and Fe xxi (128.75 Å) lines in the AIA 94 and 131 Å channels, respectively. Our results show that the hot plasma is often confined to very hot strands. The temperature obtained from the EM analysis was found to be in good agreement with that obtained using the XRT, AIA, and GOES filter-ratio methods. These results provide important constraints for the thermodynamic modelling of sigmoidal structures in the core of active regions. Moreover, this study also benchmarks different techniques available for temperature estimation in solar coronal structures.

Torsional waves with force-free magnetic fields in solar plasma structures

ABSTRACT The aim here is to model torsional waves in homogeneous and expanding twisted flux tubes of solar coronal magnetic plasma structures. For the sake of simplicity, a force-free condition applicable to solar magnetic structures is presented to determine the existing three-dimensional equilibrium magnetic fields. The determined magnetic field is implemented to study the effects of the magnetic twist parameter on the eigenvalues and eigenfunctions of torsional waves. Solenoidal and force-free conditions are applied to find the three-dimensional components of the magnetic field with respect to the numerical flux function. The obtained differential equation is linear where the technique of the separation of variables is implemented in order to solve it. The equilibrium magnetic field components and appropriate vector potential are extracted. Using the provided components in the magnetohydrodynamic theory, a differential equation that governs the frequency dependence of the torsional wave is obtained, whereby the differential transform method is solved. Both eigenvalues and eigenfunctions of torsional waves are calculated numerically. The obtained values for the frequency of the fundamental mode and its first harmonic, together with appropriate functions, exhibit a fine consistency with observations, with regards to the ratio of ω2/ω1, which is estimated to be around 2. At a fixed distance from the tube axis, the ratio increases with the increase of the twist parameter. The higher the applied twist parameter, the more variations of the ω2/ω1 ratio are observed. We cannot find significant variations of the eigenfunctions of torsional waves due to the twist parameter. The consistency between analytical results and observations proves adequate for implementing a force-free equilibrium magnetic field subject to conditions in solar plasma structures regarding torsional wave propagation.

Shear-driven Transition to Isotropically Turbulent Solar Wind Outside the Alfvén Critical Zone

Abstract Motivated by prior remote observations of a transition from striated solar coronal structures to more isotropic “flocculated” fluctuations, we propose that the dynamics of the inner solar wind just outside the Alfvén critical zone, and in the vicinity of the first surface, is powered by the relative velocities of adjacent coronal magnetic flux tubes. We suggest that large-amplitude flow contrasts are magnetically constrained at lower altitude but shear-driven dynamics are triggered as such constraints are released above the Alfvén critical zone, as suggested by global magnetohydrodynamic (MHD) simulations that include self-consistent turbulence transport. We argue that this dynamical evolution accounts for features observed by Parker Solar Probe (PSP) near initial perihelia, including magnetic “switchbacks,” and large transverse velocities that are partially corotational and saturate near the local Alfvén speed. Large-scale magnetic increments are more longitudinal than latitudinal, a state unlikely to originate in or below the lower corona. We attribute this to preferentially longitudinal velocity shear from varying degrees of corotation. Supporting evidence includes comparison with a high Mach number three-dimensional compressible MHD simulation of nonlinear shear-driven turbulence, reproducing several observed diagnostics, including characteristic distributions of fluctuations that are qualitatively similar to PSP observations near the first perihelion. The concurrence of evidence from remote sensing observations, in situ measurements, and both global and local simulations supports the idea that the dynamics just above the Alfvén critical zone boost low-frequency plasma turbulence to the level routinely observed throughout the explored solar system.

Hyperbolic Cell-centered Finite Volume Method for Obtaining Potential Magnetic Field Solutions

Abstract A hyperbolic cell-centered finite volume solver (HCCFVS) is proposed to obtain the potential magnetic field solutions prescribed by the solar observed magnetograms. By introducing solution gradients as additional unknowns and adding a pseudo-time derivative, HCCFVS transforms the second-order Poisson equation into an equivalent first-order pseudo-time-dependent hyperbolic system. Thus, instead of directly solving the Poisson equation, HCCFVS obtains the solution to the Poisson equation by achieving the steady-state solution to this first-order hyperbolic system. The code is established in Fortran 90 with Message Passing Interface parallelization. To preliminarily demonstrate the effectiveness and accuracy of the code, two test cases with exact solutions are first performed. The numerical results show its second-order convergence. Then, the code is applied to numerically solve the solar potential magnetic field problem. The solutions demonstrate the capability of HCCFVS to adequately handle the solar potential field problem, and thus it can provide a promising method of solving the same problem, except for the spherical harmonic expansion and the iterative finite difference method. Finally, by using the potential magnetic fields from HCCFVS and the spherical harmonic expansion as initial inputs, we make a comparative study on the steady-state solar corona in Carrington rotation 2098 to reaffirm the HCCFVS’s performance. Both simulations show that their modeled results are similar and capture the large-scale solar coronal structures. The average relative divergence errors, controlled by solving the Poisson equation in the projection method with HCCFVS for both simulations, are kept at an acceptable level.

Ideal MHD instabilities for coronal mass ejections: interacting current channels and particle acceleration

We review and discuss insights on ideal magnetohydrodynamic (MHD) instabilities that can play a role in destabilizing solar coronal flux rope structures. For single flux ropes, failed or actual eruptions may result from internal or external kink evolutions, or from torus unstable configurations. We highlight recent findings from 3D magnetic field reconstructions and simulations where kink and torus instabilities play a prominent role. For interacting current systems, we critically discuss different routes to coronal dynamics and global eruptions, due to current channel coalescence or to tilt-kink scenarios. These scenarios involve the presence of two nearby current channels and are clearly distinct from the popular kink or torus instability. Since the solar corona is pervaded with myriads of magnetic loops -- creating interacting flux ropes typified by parallel or antiparallel current channels as exemplified in various recent observational studies -- coalescence or tilt-kink evolutions must be very common for destabilizing adjacent flux rope systems. Since they also evolve on ideal MHD timescales, they may well drive many sympathetic eruptions witnessed in the solar corona. Moreover, they necessarily lead to thin current sheets that are liable to reconnection. We review findings from 2D and 3D MHD simulations for tilt and coalescence evolutions, as well as on particle acceleration aspects derived from computed charged particle motions in tilt-kink disruptions and coalescing flux ropes. The latter were recently studied in two-way coupled kinetic-fluid models, where the complete phase-space information of reconnection is incorporated.

Damping of slow magnetoacoustic oscillations by the misbalance between heating and cooling processes in the solar corona

Context. Rapidly decaying slow magnetoacoustic waves are regularly observed in the solar coronal structures, offering a promising tool for a seismological diagnostics of the coronal plasma, including its thermodynamical properties. Aims. The effect of damping of standing slow magnetoacoustic oscillations in the solar coronal loops is investigated accounting for field-aligned thermal conductivity and a wave-induced misbalance between radiative cooling and some unspecified heating rates. Methods. The non-adiabatic terms were allowed to be arbitrarily large, corresponding to the observed values. The thermal conductivity was taken in its classical form, and a power-law dependence of the heating function on the density and temperature was assumed. The analysis was conducted in the linear regime and in the infinite magnetic field approximation. Results. The wave dynamics is found to be highly sensitive to the characteristic timescales of the thermal misbalance. Depending on certain values of the misbalance, timescales three regimes of the wave evolution were identified, namely the regime of a suppressed damping, enhanced damping in which the damping rate drops down to observational values, and acoustic over-stability. The specific regime is determined by the dependences of the radiative cooling and heating functions on thermodynamical parameters of the plasma in the vicinity of the perturbed thermal equilibrium. Conclusions. The comparison of the observed and theoretically derived decay times and oscillation periods allows us to constrain the coronal heating function. For typical coronal parameters, the observed properties of standing slow magnetoacoustic oscillations could be readily reproduced with a reasonable choice of the heating function.

Large-Scale Magnetostatic Structures in the Solar Corona and a Model of the Polar Coronal Hole

A method for the theoretical calculation of large-scale magnetoplasma solar coronal structures with a rotational symmetry in the spherical coordinate system is presented. The method makes it possible to obtain analytical solutions for equilibrium spatial distributions of pressures, densities, and temperatures in any preset axisymmetrical magnetic configuration. The obtained solution is used to plot model polar coronal holes via the introduction of a small power correction in the force free distribution of the magnetic field for subpolar region. The thermodynamic parameters of the coronal hole represented in this model are close to the observed values.

Sausage oscillations in a plasma cylinder with a surface current

Linear sausage oscillations of a cylinder embedded in a plasma with an azimuthal magnetic field, created by a current on the surface of the cylinder, are studied. Such a plasma configuration could be applied to modelling flaring loops, and magnetic ropes in coronal mass ejections. The plasma is assumed to be cold everywhere. Dispersion relations demonstrate that the lowest radial harmonic of the sausage mode is in the trapped regime for all values of the parallel wave number. In the long-wavelength limit, phase and group speeds of this mode are equal to the Alfvén speed in the external medium. It makes the oscillation period to be determined by the ratio of the parallel wavelength, e.g. double the length of an oscillating loop, to the external Alfvén speed, allowing for its seismological estimations. The application of the results obtained to the interpretation of long-period (longer than a minute) oscillations of emission intensity detected in solar coronal structures, gives reasonable estimations of the external Alfvén speed. Cutoff values of the parallel wavenumber for higher radial harmonics are determined analytically. Implications of this finding to the observational signatures of fast magnetoacoustic wave trains guided by cylindrical plasma non-uniformities are discussed.

The Analysis of Total Solar Eclipse Pictures on August 21, 2017 at Wyoming, USA

Total Solar Eclipse has become a magnet for everyone, especially scientists. That’s because every eclipse will have their own characteristics. Even using simple instrument such as digital camera, tripod, tele lens, and solar filter, the eclipse pictures obtained. The digital picture of solar corona taken several times with different shutter speed to get the best solar corona composite with radial blur procedure and stacking technique. From that editing procedure, the structure of solar corona can be analyzing and also the maximum height of solar corona determined which is 502513.53 km or equal with 0.72 times radius of the sun.

APPARENT CROSS-FIELD SUPERSLOW PROPAGATION OF MAGNETOHYDRODYNAMIC WAVES IN SOLAR PLASMAS

In this paper we show that the phase mixing of continuum Alfv\'{e}n waves and/or continuum slow waves in magnetic structures of the solar atmosphere as, e.g., coronal arcades, can create the illusion of wave propagation across the magnetic field. This phenomenon could be erroneously interpreted as fast magnetosonic waves. The cross-field propagation due to phase mixing of continuum waves is apparent because there is no real propagation of energy across the magnetic surfaces. We investigate the continuous Alfv\'{e}n and slow spectra in 2D Cartesian equilibrium models with a purely poloidal magnetic field. We show that apparent superslow propagation across the magnetic surfaces in solar coronal structures is a consequence of the existence of continuum Alfv\'{e}n waves and continuum slow waves that naturally live on those structures and phase mix as time evolves. The apparent cross-field phase velocity is related to the spatial variation of the local Alfv\'{e}n/slow frequency across the magnetic surfaces and is slower than the Alfv\'{e}n/sound velocities for typical coronal conditions. Understanding the nature of the apparent cross-field propagation is important for the correct analysis of numerical simulations and the correct interpretation of observations.

Coexisting fast and slow propagating waves of the extreme-UV intensity in solar coronal plasma structures

Context. From 06:15 UT to 08:15 UT on 2011 June 2, a toroidal filament located at the joint of two active regions, 11226 and 11227, appeared to perform two eruptions. During this phenomenon, fast and slow magnetoacoustic waves were detected to propagate simultaneously along a funnel coronal loop system of AR 11227. Aims. We aim to understand the relationship between fast and slow magnetoacoustic waves during their propagations and measure their properties, such as the propagating speed, path, amplitude, and period observed in the extreme ultraviolet (EUV) wavebands. Methods. We analyse time sequences of EUV images acquired by the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory. By creating time-distance maps along selected directions, we measure the speeds and localisation of EUV intensity waves in different EUV wavebands. We determine the periods of the waves with wavelet analysis. Results. The fast and slow magnetoacoustic waves, apparently propagating along the same path, are found to have different properties. Their apparent propagation speeds, travel distances, and periods are about 900 km s-1 and 100 km s-1, 145 Mm and 36 Mm, and 2 min and 3 min, respectively.

The High-Resolution Coronal Imager (Hi-C)

The High-Resolution Coronal Imager (Hi-C) was flown on a NASA sounding rocket on 11 July 2012. The goal of the Hi-C mission was to obtain high-resolution (≈ 0.3 – 0.4′′), high-cadence (≈ 5 seconds) images of a solar active region to investigate the dynamics of solar coronal structures at small spatial scales. The instrument consists of a normal-incidence telescope with the optics coated with multilayers to reflect a narrow wavelength range around 19.3 nm (including the Fe xii 19.5-nm spectral line) and a 4096×4096 camera with a plate scale of 0.1′′ pixel−1. The target of the Hi-C rocket flight was Active Region 11520. Hi-C obtained 37 full-frame images and 86 partial-frame images during the rocket flight. Analysis of the Hi-C data indicates the corona is structured on scales smaller than currently resolved by existing satellite missions.

New energy and helicity bounds for knotted and braided magnetic fields

In this article we present a review of some of the author's most recent results in topological magnetohydrodynamics (MHD), with an eye to possible applications to astrophysical flows and solar coronal structures. First, we briefly review basic work on magnetic helicity and linking numbers, and fundamental relations with magnetic energy and average crossing numbers of magnetic systems in ideal conditions. In the case of magnetic knots, we focus on the relation between their groundstate energy and topology, discussing the energy spectrum of tight knots in terms of ropelength. We compare this spectrum with the one given by considering the bending energy of such idealized knots, showing that curvature information provides a rather good indicator of magnetic energy contents. For loose knots far from equilibrium we show that inflexional states determine the transition to braid form. New lower bounds for tight knots and braids are then established. We conclude with results on energy-complexity relations for systems in presence of dissipation.