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NASA NTRS1989

Magnetohydrodynamic waves and particle acceleration in a coronal loop

A model is presented for the acceleration of electrons in a flaring solar coronal loop. It is suggested that the primary energy release event in the flare establishes a spectrum of MHD waves within the loop which accelerate electrons by wave-particle resonant interactions. The nature of the MHD oscillations are described and numerical and analytic solution of the dispersion relation are examined. It is found that the behavior of a particle depends on whether or not it is in resonance with the wave spectrum. Resonant particles follow chaotic trajectories and can diffuse in velocity space between wave effective potentials, thereby gaining energy.

De La Beaujardiere, Jean-Francois↗

NASA NTRS1992

Development of magnetohydrodynamic turbulence in coronal loops

It is proposed that a stationary spectrum of magnetohydrodynamic turbulence is generated in solar coronal loops by the interweaving of magnetic field lines driven by the turbulent velocity field in the convective region. Starting from the set of incompressible magnetohydrodynamic equations, two ordinary differential equations describing the stationary turbulent energy spectrum and the frequency of direct energy cascade for a given kinetic energy spectrum of the subphotospheric convective motions are derived. An estimate of the typical dissipation length scale, at which magnetic energy efficiently heats the plasma by Joule dissipation is obtained. The impact of recent results of two-dimensional magnetohydrodynamic numerical simulations on the coronal heating problem is also discussed.

Gomez, Daniel O.↗

NASA NTRS1981

Numerical studies of the energy balance in coronal loops

A numerical method is applied to treat the energy balance of quasi-static solar coronal loops, which have been observed to persist for periods much greater than the radiative cooling time. The quasi-static loop model employed takes into account gravity, density-, temperature- or position-dependent energy input, an accurate form of the radiative losses and variable loop cross-sectional area, under assumptions of energy input by coronal heating balanced by radiative and conductive losses, an optically thin plasma, energy conduction along the field lines only and hydrostatic equilibrium. Computations of an emission measure function for various distributions of the energy input and loop geometries are then presented which show that little information on the location of the energy input may be gained from spectral line intensity measurements integrated over a single loop.

Underwood, J. H.↗

NASA NTRS2003

Automated Coronal Loop Identification Using Digital Image Processing Techniques

The results of a master thesis project on a study of computer algorithms for automatic identification of optical-thin, 3-dimensional solar coronal loop centers from extreme ultraviolet and X-ray 2-dimensional images will be presented. These center splines are proxies of associated magnetic field lines. The project is pattern recognition problems in which there are no unique shapes or edges and in which photon and detector noise heavily influence the images. The study explores extraction techniques using: (1) linear feature recognition of local patterns (related to the inertia-tensor concept), (2) parametric space via the Hough transform, and (3) topological adaptive contours (snakes) that constrains curvature and continuity as possible candidates for digital loop detection schemes. We have developed synthesized images for the coronal loops to test the various loop identification algorithms. Since the topology of these solar features is dominated by the magnetic field structure, a first-order magnetic field approximation using multiple dipoles provides a priori information in the identification process. Results from both synthesized and solar images will be presented.

Lee, Jong K.↗

NASA NTRS2004

Automated Detection of Solar Loops by the Oriented Connectivity Method

An automated technique to segment solar coronal loops from intensity images of the Sun s corona is introduced. It exploits physical characteristics of the solar magnetic field to enable robust extraction from noisy images. The technique is a constructive curve detection approach, constrained by collections of estimates of the magnetic fields orientation. Its effectiveness is evaluated through experiments on synthetic and real coronal images.

Lee, Jong Kwan↗

NASA NTRS1991

On the transport and acceleration of solar flare particles in a coronal loop

The turbulent environment of a flaring solar coronal loop directly affects the population of particles to be accelerated or already accelerated. Under the assumption of a uniform turbulent MHD wave field within the loop, the behavior of a particle distribution as it interacts with the turbulence is discussed, including particle precipitation to the footpoints of the loop and the evolution of the energy distribution as the particles undergo second-order stochastic acceleration. Two cases are discussed in detail: (1) particles spatially diffusing within the loop and precipitating with minimal acceleration in the short time scale of an impulsive event and (2) particles diffusing in both real and momentum space in a long duration event. Collisional losses due to ambient electrons are included. The gamma-ray flare of June 3, 1982 is modeled, and good agreement is obtained between predicted and observed time profiles if the loop length is 100,000 km with an intrinsic spatial diffusion time of 100-450 s. It follows that the production of high-energy neutrons and pi mesons extends over a time scale of 1000 s as observed.

Ryan, James M.↗

NASA NTRS1980

Physical properties of individual coronal loops in a solar active region observed in the XUV

The physical properties of individual coronal loops in a solar active region observed in the XUV by the slitless objective grating spectroheliograph on board Skylab are investigated. Spectroheliograms of the normal active loop region McMath 12378 reveal three distinctive structural groups of loops in different temperature ranges, namely (1) small compact and smaller loops at temperatures of about 2,000,000 K observed in Fe XV and Fe XVI; (2) large Ne VII and Mg IX loops at temperatures from 500,000 to 1,000,000 K; and (3) chromospheric ribbons in He II and H alpha. The temperature of the active region is found to be uniform at about 2,000,000 K in the loops and background while loop density is found to be 3.5 x 10 to the 9th/cu cm in the loops and 2.5 x 10 to the 9th/cu cm in the surrounding background. Significant changes in the active region are observed in 24 h, although the gross temperature density structures of many loops do not show changes in 7 min. Gas pressure within the coronal loops is found to be about 40% greater than that of the background plasma. The observed loop parameters are noted to be consistent with flux-limited models of density enhancement in magnetic flux tubes and thus no esoteric heating function is required.

Cheng, C.-C.↗

NASA NTRS2017

Invisibility of Solar Active Region Umbra-to-Umbra Coronal Loops: New Evidence that Magnetoconvection Drives Solar-Stellar Coronal Heating

Coronal heating generally increases with increasing magnetic field strength: the EUV/X-ray corona in active regions is 10--100 times more luminous and 2--4 times hotter than that in quiet regions and coronal holes, which are heated to only about 1.5 MK, and have fields that are 10--100 times weaker than that in active regions. From a comparison of a nonlinear force-free model of the three-dimensional active region coronal field to observed extreme-ultraviolet loops, we find that (1) umbra-to-umbra coronal loops, despite being rooted in the strongest magnetic flux, are invisible, and (2) the brightest loops have one foot in an umbra or penumbra and the other foot in another sunspot's penumbra or in unipolar or mixed-polarity plage. The invisibility of umbra-to-umbra loops is new evidence that magnetoconvection drives solar-stellar coronal heating: evidently, the strong umbral field at both ends quenches the magnetoconvection and hence the heating. Our results from EUV observations and nonlinear force-free modeling of coronal magnetic field imply that, for any coronal loop on the Sun or on any other convective star, as long as the field can be braided by convection in at least one loop foot, the stronger the field in the loop, the stronger the coronal heating.

Tiwari, Sanjiv K.↗

NASA NTRS1981

Adiabatic and nonadiabatic processes in thermal models of solar hard X-ray bursts

The temporal evolution of thermal-bremsstrahlung-emitting material at the top of a solar coronal loop under various processes is examined as a model of solar hard X-ray bursts. The behavior of emission measure and temperature with time is analyzed for the hot plasma confined in a segment at the top of a loop, taking into account the effects or the time variation of the confining toroidal magnetic field, the longitudinal expansion of the source through the motion of a pair of collisionless conduction fronts and unspecified heating or cooling processes. Analytic expressions for the behavior of the toroidal magnetic field and the heating rate necessary to reproduce a given behavior of emission measure and temperature with time are obtained in terms of the initial magnetic field strength and density of the heated region and a characteristic longitudinal expansion time. Results are applied to observations of two impulsive solar hard X-ray bursts, and it is shown that the contribution of heating is negligible after the first few seconds of the events, although significant nonadiabatic heating occurs early in the events.

Emslie, A. G.↗

NASA NTRS1989

Nonlinear twist-kink instability of a coronal loop

Three-dimensional magnetoinductive particle simulations are used to demonstrate that the mechanical twisting motion applied to a magnetized plasma column induces a current aligned to the external magnetic field direction, pinches the plasma and magnetic fields, and stores the energy in poloidal magnetic fields. As the twist motion continues, the field lines locally begin to wrap around the plasma more than one revolution. A strong MHD instability sets in that is a mixture of kink and ballooning modes, releasing the magnetic energy and causing destruction of coherent column structure and flows of turbulent plasma. A similar episode ensues, exhibiting relaxation oscillations. The buildup of poloidal fields and structure and its sudden release driven by the twist motion may be a model for the solar coronal loop dynamics which exhibits a slow energy buildup with some photospheric motion and a sudden energy release by flares.

Zaidman, E. G.↗

NASA NTRS1980

Resonant electrodynamic heating of stellar coronal loops: An LRC circuit analogue

The electrodynamic coupling of stellar coronal loops to underlying beta velocity fields. A rigorous analysis revealed that the physics can be represented by a simple yet equivalent LRC circuit analogue. This analogue points to the existence of global structure oscillations which resonantly excite internal field line oscillations at a spatial resonance within the coronal loop. Although the width of this spatial resonance, as well as the induced currents and coronal velocity field, explicitly depend upon viscosity and resistivity, the resonant form of the generalized electrodynamic heating function is virtually independent of irreversibilities. This is a classic feature of high quality resonators that are externally driven by a broad band source of spectral power. Applications to solar coronal loops result in remarkable agreement with observations.

Ionson, J. A.↗

NASA NTRS2023

The F-CHROMA Grid of 1D RADYN Flare Models

Context. Solar flares are the result of the sudden release of magnetic energy in the corona. Much of this energy goes into accelerating charged particles to high velocity. These particles travel along the magnetic field and the energy is dissipated when the density gets high enough, primarily in the solar chromosphere. Modelling this region is difficult because the radiation energy balance is dominated by strong, optically thick spectral lines. Aims. Our aim is to provide the community with realistic simulations of a flaring loop with an emphasis on the detailed treatment of the chromospheric energy balance. This will enable a detailed comparison of existing and upcoming observations with synthetic observables from the simulations, thereby elucidating the complex interactions in a flaring chromosphere. Methods. We used the 1D radiation hydrodynamics code RADYN to perform simulations of the effect of a beam of electrons injected at the apex of a solar coronal loop. A grid of models was produced, varying the total energy input, the steepness, and low-energy cutoff of the beam energy spectrum. Results. The full simulation results for a grid of models are made available online. Some general properties of the simulations are discussed.

hydrodynamics↗

NASA NTRS1984

A unified theory of electrodynamic coupling in coronal magnetic loops - The coronal heating problem

The coronal heating problem is studied, and it is demonstrated that Ionson's (1982) LRC approach results in a unified theory of coronal heating which unveils a variety of new heating mechanisms and which links together previously proposed mechanisms. Ionson's LRC equation is rederived, focusing on various aspects that were not clarified in the original article and incorporating new processes that were neglected. A parameterized heating rate is obtained. It is shown that Alfvenic surface wave heating, stochastic magnetic pumping, resonant electrodynamic heating, and dynamical dissipation emerge as special cases of a much more general formalism. This generalized theory is applied to solar coronal loops and it is found that active region and large scale loops are underdamped systems. Young active region loops and (possibly) bright points are found to be overdamped systems.

Ionson, J. A.↗

NASA NTRS2023

Role of Small-Scale Impulsive Events in Heating the X-Ray Bright Points of the Quiet Sun

Small-scale impulsive events, known as nanoflares, are thought to be one of the prime candidates that can keep the solar corona hot at its multimillion-Kelvin temperature. Individual nanoflares are difficult to detect with the current generation of instruments; however, their presence can be inferred through indirect techniques such as Differential Emission Measure (DEM) analysis. Here, we employ this technique to investigate the possibility of nanoflare heating of the quiet corona during the minimum of solar cycle 24. We estimate the DEM of disk-integrated quiet Sun and X-ray bright points (XBP) using the observations from XSM on board the Chandrayaan-2 orbiter and AIA on board the Solar Dynamic Observatory. XBPs are found to be the dominant contributor to disk-integrated X-rays, with a radiative flux of ∼2 × 10 5 erg cm −2 s −1 . XBPs consist of small-scale loops associated with bipolar magnetic fields. We simulate such XBP loops using the EBTEL hydrodynamic code. The lengths and magnetic field strengths of these loops are obtained through a potential field extrapolation of the photospheric magnetogram. Each loop is assumed to be heated by random nanoflares having an energy that depends on the loop properties. The composite nanoflare energy distribution for all the loops has a power-law slope close to −2.5. The simulation output is then used to obtain the integrated DEM. It agrees remarkably well with the observed DEM at temperatures above 1 MK, suggesting that the nanoflare distribution, as predicted by our model, can explain the XBP heating.

Solar coronal heating↗

DOE OSTI2021

Change-point Detection and Image Segmentation for Time Series of Astrophysical Images

Many astrophysical phenomena are time-varying, in the sense that their intensity, energy spectrum, and/or the spatial distribution of the emission suddenly change. This paper develops a method for modeling a time series of images. Under the assumption that the arrival times of the photons follow a Poisson process, the data are binned into 4D grids of voxels (time, energy band, and x-y coordinates), and viewed as a time series of non-homogeneous Poisson images. The method assumes that at each time point, the corresponding multiband image stack is an unknown 3D piecewise constant function including Poisson noise. It also assumes that all image stacks between any two adjacent change points (in time domain) share the same unknown piecewise constant function. The proposed method is designed to estimate the number and the locations of all of the change points (in time domain), as well as all of the unknown piecewise constant functions between any pairs of the change points. The method applies the minimum description length principle to perform this task. A practical algorithm is also developed to solve the corresponding complicated optimization problem. Simulation experiments and applications to real data sets show that the proposed method enjoys very promising empirical properties. Applications to two real data sets, the XMM observation of a flaring star and an emerging solar coronal loop, illustrate the usage of the proposed method and the scientific insight gained from it.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1979

The energetics of resistive magnetic tearing

A new treatment of the energetics of resistive magnetic tearing is presented. This instability is the only known field-reconnection mechanism which develops in time, and is thus a primary candidate for a number of astrophysical 'flare' processes occurring in stressed magnetic fields. The tearing process is elucidated by a subdivision into magnetic regions of different characteristics: first, as dominated by resistive or highly conductive dynamics, and then by function as a source or sink of the energy flux. Matching conditions between these zones provide a determination of the growth rate and its physical-parameter dependence. The observable plasma energy outputs, due mainly to two distinct magnetically driven acceleration mechanisms, are estimated and their directive spatial properties shown. Finally, the generality of resistive tearing is demonstrated by an application of the previous considerations to realistic sheared-field configurations, including the case of a solar coronal loop, for which flare-instability thresholds and energy-deposition sites are described.

Van Hoven, G.↗

NASA NTRS1981

Closed coronal structures. II - Generalized hydrostatic model

Numerical computations of stationary solar coronal loop atmospheres are used to extend earlier analytical work. Two classes of loops are examined, namely symmetric loops with a temperature maximum at the top but now having a length greater than the pressure scale height and loops which have a local temperature minimum at the top. For the first class, new scaling laws are found which relate the base pressure and loop length to the base heating, the heating deposition scale height, and the pressure scale height. It is found that loops for which the length is greater than about two to three times the pressure scale height do not have stable solutions unless they have a temperature minimum at the top. Computed models with a temperature inversion at the top are permitted in a wider range of heating deposition scale height values than are loops with a temperature maximum at the top. These results are discussed in relation to observations showing a dependence of prominence formation and stability on the state of evolution of magnetic structures, and a general scenario is suggested for the understanding of loop evolution from emergence in active regions through the large-scale structure phase to opening in coronal holes.

Serio, S.↗

NASA NTRS1981

Stability of a diffuse linear pinch with axial boundaries

A formulation of the stability behavior of a finite-length pinch is presented. A general initial perturbation is expressed as a uniformly convergent sum over a complete discrete k set. A variational calculation is then performed, based on the energy principle, in which the end-boundary conditions appear as constraints. The requisite Lagrange multipliers mutually couple the elemental periodic excitations. The resulting extended form of delta-W still admits a proper second-variation treatment so that the minimization and stability considerations of Newcomb remain applicable. Comparison theorems are discussed as is the relevance of this end-effect model to the stability of solar coronal loops.

Einaudi, G.↗