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NASA NTRS2016

Suppression of Heating of Coronal Loops Rooted in Opposite Polarity Sunspot Umbrae

EUV observations of active region (AR) coronae reveal the presence of loops at different temperatures. To understand the mechanisms that result in hotter or cooler loops, we study a typical bipolar AR, near solar disk center, which has moderate overall magnetic twist and at least one fully developed sunspot of each polarity. From AIA 193 and 94 Å images we identify many clearly discernible coronal loops that connect plage or a sunspot of one polarity to an opposite-polarity plage region. The AIA 94 Å images show dim regions in the umbrae of the spots. To see which coronal loops are rooted in a dim umbral area, we performed a non-linear force‐free field (NLFFF) modeling using photospheric vector magnetic field measurements obtained with the Heliosesmic Magnetic Imager (HMI) onboard SDO. The NLFFF model, validated by comparison of calculated model field lines with observed loops in AIA 193 and 94 Å, specifies the photospheric roots of the model field lines. Some model coronal magnetic field lines arch from the dim umbral area of the positive-polarity sunspot to the dim umbral area of a negative-polarity sunspot. Because these coronal loops are not visible in any of the coronal EUV and X-ray images of the AR, we conclude they are the coolest loops in the AR. This result suggests that the loops connecting opposite polarity umbrae are the least heated because the field in umbrae is so strong that the convective braiding of the field is strongly suppressed.

sunspot↗

NASA NTRS1985

Thermal stability of static coronal loops: Part 1: Effects of boundary conditions

The linear stability of static coronal-loop models undergoing thermal perturbations was investigated. The effect of conditions at the loop base on the stability properties of the models was considered in detail. The question of appropriate boundary conditions at the loop base was considered and it was concluded that the most physical assumptions are that the temperature and density (or pressure) perturbations vanish there. However, if the base is taken to be sufficiently deep in the chromosphere, either several chromospheric scale heights or several coronal loop lengths in depth, then the effect of the boundary conditions on loop stability becomes negligible so that all physically acceptable conditions are equally appropriate. For example, one could as well assume that the velocity vanishes at the base. The growth rates and eigenmodes of static models in which gravity is neglected and in which the coronal heating is a relatively simple function, either constant per-unit mass or per-unit volume were calculated. It was found that all such models are unstable with a growth rate of the order of the coronal cooling time. The physical implications of these results for the solar corona and transition region are discussed.

Antiochos, S. K.↗

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 NTRS1983

MHD stability of incompressible coronal loops with radiative energy loss

Previous studies of the magnetohydrodynamic (MHD) stability of solar coronal loops have not taken into account the effects of radiative energy loss in the energy equation. However, since coronal loops continuously lose energy by radiation and heat conduction, it is important to understand how these energy loss mechanisms affect MHD stability. We investigate the problem assuming that a magnetic loop has cylindrical geometry. As a first step, stability is studied for a localized mode, and the result is applied to a specific equilibrium. We find that the radiative energy loss effect not only changes the growth rate of ideally unstable modes, but also alters the stability boundary predicted by ideal MHD theory.

An, C.-H.↗

NASA NTRS2016

Suppression of Heating of Coronal Loops Rooted in Opposite Polarity Sunspot Umbrae

sunspots↗

NASA NTRS1979

Thermal instabilities in magnetically confined plasmas - Solar coronal loops

The thermal stability of confined solar coronal structures ('loops') is investigated, following both normal mode and a new, global instability analysis. It is demonstrated that: (1) normal mode analysis shows modes with size scales comparable to that of loops to be unstable, but to be strongly affected by the loop boundary conditions; (2) a global analysis, based upon variation of the total loop energy losses and gains, yields loop stability conditions for global modes dependent upon the coronal loop heating process, with magnetically coupled heating processes giving marginal stability. The connection between the present analysis and the minimum flux corona of Hearn is also discussed.

Habbal, S. R.↗

NASA NTRS2008

Explaining Warm Coronal Loops

One of the great mysteries of coronal physics that has come to light in the last few years is the discovery that warn (- 1 INK) coronal loops are much denser than expected for quasi-static equilibrium. Both the excess densities and relatively long lifetimes of the loops can be explained with bundles of unresolved strands that are heated impulsively to very high temperatures. Since neighboring strands are at different stages of cooling, the composite loop bundle is multi-thermal, with the distribution of temperatures depending on the details of the "nanoflare storm." Emission hotter than 2 MK is predicted, but it is not clear that such emission is always observed. We consider two possible explanations for the existence of over-dense warm loops without corresponding hot emission: (1) loops are bundles of nanoflare heated strands, but a significant fraction of the nanoflare energy takes the form of a nonthermal electron beam rather then direct plasma heating; (2) loops are bundles of strands that undergo thermal nonequilibrium that results when steady heating is sufficiently concentrated near the footpoints. We present numerical hydro simulations of both of these possibilities and explore the observational consequences, including the production of hard X-ray emission and absorption by cool material in the corona.

Klimchuk, James A.↗

NASA NTRS1984

MHD stability of compressible coronal loops with radiative energy loss

The effect of radiative energy loss on the stability of compressible plasma in coronal loops is studied. By taking the limit as poloidal wavenumber m approaches infinity, stability conditions for local modes are derived. It was found that the radiation effect can trigger MHD instabilities of coronal loops which are in ideally marginally stable states. Compressibility is a stabilizing effect for ideal MHD local modes because the compression of magnetic field lines exerts a restoring force by increasing magnetic pressure. Compression of plasma induces two modes in a radiatively unstable plasma, magnetosonic and condensation modes. Compressibility affects the stability of ideally stable (or unstable) coronal plasmas through magnetosonic modes, which are a stabilizing (destabilizing) effect for ideally stable (unstable) plasmas. For coronal plasmas in ideally marginally stable states, condensation as well as magnetosonic modes can trigger MHD instability. Because of these two modes, the effect of radiation on compressible coronal plasmas is more destabilizing than it is on incompressible plasmas when the plasmas are in ideal MHD unstable or marginally stable states.

An, C.-H.↗

NASA NTRS1990

Effects of plasma mass flow on Alfven wave phase mixing in coronal loops

Ground-based and space observations suggest that flow phenomena are intrinsic to the solar corona loops. The present analysis addresses flow effects on Alfven wave behavior in coronal loops. The effect of flow on the shear Alfven wave continuum and the associated damping process resulting from phase-mixing is investigated. Flow Doppler-shifts the Alfven wave continuum, thus displacing the range of frequencies for optimum heating. The present study explores Alfven resonance effects on surface waves propagating along coronal loops that are under the influence of flow. Coupling to the Alfven resonance leads to damping of the surface waves. The damping rate in the presence of sub-Alfvenic flows is computed. Flow increases the damping rate of certain modes, thus enhancing the heating effectiveness of those modes. Therefore, these calculations suggest that flow is potentially an important ingredient for an accurate evaluation of heating the solar corona by dissipation of Alfven waves via phase-mixing.

Peredo, M.↗

NASA NTRS2012

Coronal Loop Evolution Observed with AIA and Hi-C

Despite much progress toward understanding the dynamics of the solar corona, the physical properties of coronal loops are not yet fully understood. Recent investigations and observations from different instruments have yielded contradictory results about the true physical properties of coronal loops. In the past, the evolution of loops has been used to infer the loop substructure. With the recent launch of High Resolution Coronal Imager (Hi-C), this inference can be validated. In this poster we discuss the first results of loop analysis comparing AIA and Hi-C data. We find signatures of cooling in a pixel selected along a loop structure in the AIA multi-filter observations. However, unlike previous studies, we find that the cooling time is much longer than the draining time. This is inconsistent with previous cooling models.

Mulu-Moore, Fana↗

NASA NTRS1983

The stability of coronal loops - Finite-length and pressure-profile limits

Results are described from a quickly converging, necessary-and-sufficient, MHD-stability test for coronal-loop models. The primary stabilizing influence arises from magnetic line tying at the photosphere, and this end conditions requires a series expansion of possible loop excitations. The stability boundary is shown to quickly approach a limit as the number of terms increases, providing a critical length for the loop in proportion to its transverse magnetic scale. Several models of force-free-field profiles are tested and the stability behavior of a localized current channel, embedded in an external current-free region, is shown to be superior to that of other, broader, current profiles. Pressure-gradient effects, leading to increased or decreased stability, are shown to be amplified by line tying. Long loops must either conduct low net current, or exhibit an axial-field reversal coexisting with a low-pressure core. The limits on stability depend on the magnetic aspect ratio, the plasma-to-magnetic pressure ratio, and the field orientation at the loop edge. Applications of these results to the structure of coronal loops are described.

Einaudi, G.↗

NASA NTRS2014

MHD Modeling of Coronal Loops: the Transition Region Throat

Context. The expansion of coronal loops in the transition region may considerably influence the diagnostics of the plasma emission measure. The cross-sectional area of the loops is expected to depend on the temperature and pressure, and might be sensitive to the heating rate. Aims. The approach here is to study the area response to slow changes in the coronal heating rate, and check the current interpretation in terms of steady heating models. Methods. We study the area response with a time-dependent 2D magnetohydrodynamic (MHD) loop model, including the description of the expanding magnetic field, coronal heating and losses by thermal conduction, and radiation from optically thin plasma. We run a simulation for a loop 50 Mm long and quasi-statically heated to about 4 millikelvin. Results. We find that the area can change substantially with the quasi-steady heating rate, e.g., by approx. 40% at 0.5 millikelvin as the loop temperature varies between 1 millikelvin and 4 millikelvin, and, therefore, affects the interpretation of the differential emission measure vs. temperature (DEM(T)) curves.

magnetohydrodynamics (MHD)↗

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 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 NTRS1987

The plasma and magnetic field properties of coronal loops observed at high spatial resolution

Two data sets are analyzed in order to improve understanding of the plasma and magnetic field properties of active region coronal loops. Each set consists of coaligned, high spatial resolution soft X-ray, microwave, and magnetogram images that are used to compare observations of coronal loops and their feet in the photosphere and to constrain possible microwave emission mechanisms. The loops are found to have plasma parameters typical of quiescent active region loops. Each loop has a compact microwave source with peak brightness temperature T(b) = 1-2.5 x 10 to the 6th K cospatial with or near the loop apex. No complete loops are imaged in microwaves. The loop emission observed at 4.9 GHz is best described by fourth harmonic gyroresonance emission from a dipole loop model, but with less field variation along the loop than in the models of Holman and Kundu (1985).

Webb, D. F.↗

NASA NTRS1999

On Heating Large Bright Coronal Loops by Magnetic Microexplosions at their Feet

In previous work, by registering Yohkoh SXT coronal X-ray images with MSFC vector magnetograms, we found that: (1) many of the larger bright coronal loops rooted at one or both ends in an active region are rooted around magnetic islands of included polarity, (2) the core field encasing the neutral line encircling the island is strongly sheared, and (3) this sheared core field is the seat of frequent microflares. This suggests that the coronal heating in these extended bright loops is driven by many small explosive releases of stored magnetic energy from the sheared core field at their feet, some of which magnetic microexplosions also produce the microflare heating in the core fields. In this paper, we show that this scenario is feasible in terms of the energy Abstract: required for the observed coronal heating and the magnetic energy available in the observed sheared core fields. In a representative active region, from the X-ray and vector field data, we estimate the coronal heating consumption by a selected typical large bright loop, the coronal heating consumption by a typical microflare at the foot of this loop, the frequency of microflares at the foot, and the available magnetic energy in the microflaring core field. We find that: (1) the rate of magnetic energy release to power the microflares at the foot (approx. 6 x 10(ext 25)erg/s) is enough to also power the coronal heating in the body of the extended loop (approx. 2 x l0(exp 25 erg/s), and (2) there is enough stored magnetic energy in the sheared core field to sustain the microflaring and extended loop heating for about a day, which is a typical time for buildup of neutral-line magnetic shear in an active region. This work was funded by the Solar Physics Branch of NASA's Office of Space Science through the SR&T Program and the SEC Guest Investigator Program.

Moore, Ronald L↗

NASA NTRS2024

Exploring Standing and Reflected Slow-mode Waves in Flaring Coronal Loops: A Parametric Study Using 2.5D MHD Modeling

Abstract Recent observations of reflected propagating and standing slow-mode waves in hot flaring coronal loops have spurred our investigation into their underlying excitation and damping mechanisms. To understand these processes, we conduct 2.5D magnetohydrodynamic (MHD) simulations using an arcade active region model that includes a hot and dense loop. Our simulations allow for in-depth parametric investigations complementing and expanding our previous 3D MHD modeling results. We excite these waves using a large-amplitude, flow pulse applied at one footpoint of the loop in two distinct models as motivated by observations from the Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA). The first model (Model 1) incorporates classical compressive viscosity coefficient, while the second model (Model 2) adopts a 10-times enhanced viscosity coefficient. We obtain the following major results: (1) Our 2.5D MHD simulations reinforce previous conclusions derived from 1D and 3D MHD models that significantly enhanced viscosity is crucial for the rapid excitation of standing slow waves with damping times consistent with observations by Wang et al. (2015). (2)We uncover that nonlinearity in Model 1 delays the conversion of a reflected propagating wave into a standing wave. In contrast, Model 2 exhibits a much weak influence of nonlinearity on the excitation time of standing waves, thanks to the suppression of these effects by enhanced viscosity. (3) Our results reveal that the transverse temperature structure holds more influence on wave behavior than the density structure. In Model 1, increased loop temperature contrast significantly enhances wave trapping within the structure, mitigating the impact of temperature-dependent viscous damping. Conversely, in Model 2, the impact of temperature structure on wave behavior weakens in comparison to the effect of viscosity. (4) Model 1 displays evident nonlinear coupling to the fast and kink magnetoacoustic waves and pronounced wave leakage into the corona. Model 2 exhibits significantly weaker effects in this regard. Analyzing three observed wave events by SDO/AIA aligns with Model 2 predictions, providing further support for the substantial viscosity increase. Our 2.5D study unravels the complex interplay of wave-flow phenomena and nonlinear processes in coronal loops, extending our previous 1D modeling results to incorporate more realistic loop geometry. This provides insights into scenarios where 3D effects may be neglected, thereby enhancing our understanding of the intricate dynamics of the solar corona.

Tongjiang Wang↗

NASA NTRS1987

Heating of coronal loops by phase-mixid shear Alfven waves

The dissipation of shear Alfven waves in a coronal loop driven externally by an incident wave in the subcoronal region is investigated. The phase mixing of these incident shear Alfven waves serves as the dissipation mechanism in the corona. The wave solution found by Heyvaerts and Priest (1983) for coronal holes is used to compute the total energy deposited in a loop. The energy deposited is shown to depend upon the magnetic diffusivity nu(m) and viscosity nu(v), contrary to the conclusion of authors who assumed that coronal loops are perfect resonators. The energy deposited in a three-layer model is computed for incident waves with periods of five minutes or five seconds. For a five-minute period, almost no energy is deposited, especially for small loops. For a five-second period, a substantial amount of energy is deposited in the loop, but not enough to account for the heating of small loops.

Abdelatif, Toufik E.↗