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NASA NTRS1993

Coronal heating by the resonant absorption of Alfven waves - Importance of the global mode and scaling laws

Numerical simulations of the MHD equations for a fully compressible, low-beta, resistive plasma are used to study the resonance absorption process for the heating of coronal active region loops. Comparisons with more approximate analytic models show that the major predictions of the analytic theories are, to a large extent, confirmed by the numerical computations. The simulations demonstrate that the dissipation occurs primarily in a thin resonance layer. Some of the analytically predicted features verified by the simulations are (a) the position of the resonance layer within the initial inhomogeneity; (b) the importance of the global mode for a large range of loop densities; (c) the dependence of the resonance layer thickness and the steady-state heating rate on the dissipation coefficient; and (d) the time required for the resonance layer to form. In contrast with some previous analytic and simulation results, the time for the loop to reach a steady state is found to be the phase-mixing time rather than a dissipation time. This disagreement is shown to result from neglect of the existence of the global mode in some of the earlier analyses. The resonant absorption process is also shown to behave similar to a classical driven harmonic oscillator.

Steinolfson, Richard S.↗
NASA NTRS1982

Energy balance of stellar coronae. I - Methods and examples. II - Effect of coronal heating

Simplified models of magnetically open coronal regions are computed, with the aim of fulfilling appropriate boundary conditions at the base of the atmosphere, at the critical point, and at infinity. The models are determined by the stellar mass and radius and by the amount and location of coronal heating, and this dependence is analyzed in terms of pressure, temperature, characteristic heights, energy losses, mass loss, and asymptotic behavior. The results are used to classify the magnetically open coronal regions according to the energy loss mechanism that dominates in the region between the base and the critical point, and it is shown that more complicated heating mechanisms may be replaced by the presented exponential heating law, provided that the damping length is suitably chosen.

Hammer, R.↗
NASA NTRS1997

Neutral-Line Magnetic Shear and Enhanced Coronal Heating in Solar Active Regions

By examining the magnetic structure at sites in the bright coronal interiors of active regions that are not flaring but exhibit persistent strong coronal heating, we establish some new characteristics of the magnetic origins of this heating. We have examined the magnetic structure of these sites in five active regions, each of which was well observed by both the Yohkoh SXT and the Marshall Space Flight Center Vector Magnetograph and showed strong shear in its magnetic field along part of at least one neutral line (polarity inversion). Thus, we can assess whether this form of nonpotential field structure in active regions is a characteristic of the enhanced coronal heating and vice versa. From 27 orbits' worth of Yohkoh SXT images of the five active regions, we have obtained a sample of 94 persistently bright coronal features (bright in all images from a given orbit), 40 long (greater than or approximately equals 20,000 km) neutral-line segments having strong magnetic shear throughout (shear angle greater than 45 deg), and 39 long neutral-line segments having weak magnetic shear throughout (shear angle less than 45 deg). From this sample, we find that: (1) all of our persistently bright coronal features are rooted in magnetic fields that are stronger than 150 G; (2) nearly all (95%) of these enhanced coronal features are rooted near neutral lines (closer than 10,000 km); (3) a great majority (80%) of the bright features are rooted near strong-shear portions of neutral lines; (4) a great majority (85%) of long strong-shear segments of neutral lines have persistently bright coronal features rooted near them; (5) a large minority (40%) of long weak-shear segments of neutral lines have persistently bright coronal features rooted near them; and (6) the brightness of a persistently bright Coronal feature often changes greatly over a few hours. From these results, we conclude that most persistent enhanced heating of coronal loops in active regions: (1) requires the presence of a polarity inversion in the magnetic field near at least one of the loop footpoints; (2) is greatly aided by the presence of strong shear in the core magnetic field along that neutral line; and (3) is controlled by some variable process that acts in this magnetic environment. We infer that this variable process is low-lying reconnection accompanying flux cancellation.

Falconer, D. A.↗
NASA NTRS2019

The Role of Magnetic Helicity in Coronal Heating

One of the greatest challenges in solar physics is understanding the heating of the Sun's corona. Most theories for coronal heating postulate that free energy in the form of magnetic twist/stress is injected by the photosphere into the corona where the free energy is converted into heat either through reconnection or wave dissipation. The magnetic helicity associated with the twist/stress, however, is expected to be conserved and appear in the corona. In previous works, we showed that the helicity associated with the small-scale twists undergoes an inverse cascade via stochastic reconnection in the corona and ends up as the observed large-scale shear of filament channels. Our "helicity condensation" model accounts for both the formation of filament channels and the observed smooth, laminar structure of coronal loops. In this paper, we demonstrate, using helicity- and energy-conserving numerical simulations of a coronal system driven by photospheric motions, that the model also provides a natural mechanism for heating the corona. We show that the heat generated by the reconnection responsible for the helicity condensation process is sufficient to account for the observed coronal heating. We study the role that helicity injection plays in determining coronal heating and find that, crucially, the heating rate is only weakly dependent on the net helicity preference of the photospheric driving. Our calculations demonstrate that motions with 100% helicity preference are least efficient at heating the corona; those with 0% preference are most efficient. We discuss the physical origins of this result and its implications for the observed corona.

Knizhnik, K. J.↗
NASA NTRS1998

An Assessment of Magnetic Conditions for Strong Coronal Heating in Solar Active Regions by Comparing Observed Loops with Computed Potential Field Lines

We report further results on the magnetic origins of coronal heating found from combining coronal images with photospheric magnetograms. Here, for two complementary active regions, we compare the measured photospheric magnetic roots, extrapolated potential fields, and the distribution of bright coronal loops, to examine the global nonpotentiality of bright extended coronal loops and the three-dimensional structure of the magnetic field at their feet and to assess the role of these magnetic conditions in the strong coronal heating in these loops.

Falconer, D. A.↗
NASA NTRSDate not supplied

Application of EUV and SXR Spectra from the EUNIS Sounding Rocket to Solar Coronal Heating

The nanoflare model is among the most actively investigated approaches to the longstanding problem of solar coronal heating. According to this model, the ~2 MK corona is heated by numerous tiny impulsive heating events, each of which is too small to be detected individually. Evidence for nanoflares is faint emission from small amounts of plasma at flare-like temperatures (4-10 MK) in non-flaring regions. The Extreme Ultraviolet Normal Incidence Spectrograph (EUNIS) sounding rocket instrument was designed to investigate coronal heating by observing emission lines of Fe XVIII, whose maximum ionization fraction occurs at temperatures around 7.1 MK, and Fe XIX (8.9 MK). Although expected to be faint, emission from hot plasma to which these lines are sensitive provides compelling evidence for the nanoflare model. EUNIS observes spectral line emission at 92-115 A in 3rd order, 277-344 A in 1st order, and 530-640 A in 1st order. These wavebands include lines from Fe XVIII and Fe XIX, as well as lines from ions formed over a wide range of lower temperatures (0.1-3.5 MK). We present preliminary results for a quiescent solar active region observed during the flight of 2021 May 18.

ultraviolet radiation↗
NASA NTRS1999

Microflaring in Low-Lying Core Fields and Extended Coronal Heating in the Quiet Sun

We have previously reported analyses of Yohkoh SXT data examining the relationship between the heating of extended coronal loops (both within and stemming from active regions) and microflaring in core fields lying along neutral lines near their footpoints (J. G. Porter, D. A. Falconer, and R. L. Moore 1998, in Solar Jets and Coronal Plumes, ed. T. Guyenne, ESA SP-421, and references therein). We found a surprisingly poor correlation of intensity variations in the extended loops with individual microflares in the compact heated areas at their feet, despite considerable circumstancial evidence linking the heating processes in these regions. Now, a study of Fe XII image sequences from SOHO EIT show that similar associations of core field structures with the footpoints of very extended coronal features can be found in the quiet Sun. The morphology is consistent with the finding of Wang et al. (1997, ApJ 484, L75) that polar plumes are rooted at sites of mixed polarity in the magnetic network. We find that the upstairs/downstairs intensity variations often follow the trend, identified in the active region observations, of a weak correspondence. Apparently much of the coronal heating in the extended loops is driven by a type of core field magnetic activity that is "cooler" than the events having the coronal signature of microflares, i.e., activity that results in little heating within the core fields themselves. 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.

Porter, Jason G.↗
NASA NTRS1980

Magnetic fields and coronal heating

General considerations concerning the scaling properties of magnetic-field-related coronal heating mechanisms are used to build a two-parameter model for the heating of closed coronal regions. The model predicts the way in which coronal temperature and electron density are related to photospheric magnetic field strength and the size of the region, using the additional constraint provided by the scaling law of Rosner, Tucker, and Vaiana. The model duplicates the observed scaling of total thermal energy content with total longitudinal flux; it also predicts a relation between the coronal energy density (or pressure) and the longitudinal field strength modified by the region scale size.

Golub, L.↗
NASA NTRS2008

Coronal Heating and Structure

The existence of the Sun's million-degree corona is one of the oldest and most challenging problems in all space physics. It is generally accepted that the solar magnetic field is responsible for both the heating and the structure of coronal plasma, but the physical mechanisms are still not clearly understood. Gene Parker has made many seminal contributions to solving the coronal heating problem, in particular, his widely-used nano-flare model. Parker argued that in closed field regions the complex motions of the photosphere must lead to the formation of fine-scale electric currents in the corona and, consequently, to continual bursts of magnetic reconnection. We discuss the implications of these ideas for understanding the observed features of the corona. We show that the type of reconnection proposed by Parker may well account for all the well-known observations of both the closed and open field corona, and we discuss the implications of our results for upcoming NASA missions. This work was supported by the NASA HTP and TR&T programs.

Antiochos, Spiro K.↗
NASA NTRS2022

Observational Signatures of Coronal Heating in Magnetohydrodynamic Simulations without Radiation or a Lower Atmosphere

It is extremely difficult to simulate the details of coronal heating and also make meaningful predictions of the emitted radiation. Thus, testing realistic models with observations is a major challenge. Observational signatures of coronal heating depend crucially on radiation, thermal conduction, and the exchange of mass and energy with the transition region and chromosphere below. Many magnetohydrodynamic simulation studies do not include these effects, opting instead to devote computational resources to the magnetic aspects of the problem. We have developed a simple method of accounting approximately for the missing effects. It is applied to the simulation output ex post facto and therefore may be a valuable tool for many studies. We have used it to predict the emission from a model corona that is driven by vortical boundary motions meant to represent photospheric convection. We find that individual magnetic strands experience short-term brightenings, both scattered throughout the computational volume and in localized clusters. The former may explain the diffuse component of the observed corona, while the latter may explain bright coronal loops. Several observed properties of loops are reproduced reasonably well: width, lifetime, and quasi-circular cross section (aspect ratio not high). Our results lend support to the idea that loops are multistranded structures heated by "storms" of nanoflares.

James A. Klimchuk↗
NASA NTRS2008

Coronal Heating and the Need for High-Resolution Observations

Despite excellent progress in recent years in understanding coronal heating, there remain many crucial questions that are still unanswered. Limitations in the observations are one important reason. Both theoretical and observational considerations point to the importance of small spatial scales, impulsive energy release, strong dynamics, and extreme plasma nonuniformity. As a consequence, high spatial resolution, broad temperature coverage, high temperature fidelity, and sensitivity to velocities and densities are all critical observational parameters. Current instruments lack one or more of these properties, and this has led to considerable ambiguity and confusion. In this talk, I will discuss recent ideas about coronal heating and emphasize that high spatial resolution observations, especially spectroscopic observations, are needed to make major progress on this important problem.

Klimchuk, James A.↗
NASA NTRS1998

Coronal Heating by Magnetic Explosions

We build a case for the persistent strong coronal heating in active regions and the pervasive quasi-steady heating of the corona in quiet regions and coronal holes being driven in basically the same way as the intense transient heating in solar flares: by explosions of sheared magnetic fields in the cores of initially closed bipoles. We begin by summarizing the observational case for exploding sheared core fields being the drivers of a wide variety of flare events, with and without coronal mass ejections. We conclude that the arrangement of an event's flare heating, whether there is a coronal mass ejection, and the time and place of the ejection relative to the flare heating are all largely determined by four elements of the form and action the magnetic field: (1) the arrangement of the impacted, interacting bipoles participating in the event, (2) which of these bipoles are active (have sheared core fields that explode) and which are passive (are heated by injection from impacted active bipoles), (3) which core field explodes first, and (4) which core-field explosions are confined within the closed field of their bipoles and which ejectively open their bipoles.

Moore, Ronald L.↗
NASA NTRS1981

Dependence of open stellar coronal regions on coronal heating

Models of open regions in hot stellar coronae are presented. For a given star these regions depend on the total amount phi sub Mo of coronal heating and on the characteristic length (L) over which this energy is dissipated. The height of the temperature maximum is mainly determined by L. The coronal temperature, the mass loss rate, and the relative fraction of wind energy losses increase strongly with L as long as L is much smaller than the stellar radius. For large L, however, these quantities are only weak functions of L, while they still increase with increasing phi sub Mo. Thus, if the heating occurs close to the stellar surface, the open coronal regions are cool, and most of the energy is used for radiation. Extended coronal heating, on the other hand, leads to hot coronal regions with small base pressure and predominating energy losses due to stellar wind (for large phi sub Mo and/or outward thermal conduction (for small phi sub Mo).

Hammer, R.↗
NASA NTRS2020

Transition Region Contribution to AIA Observations in the Context of Coronal Heating

We investigate the ratio of coronal and transition region intensity in coronal loops observed by the AtmosphericImaging Assembly(AIA)on the Solar Dynamics Observatory(SDO). Using Enthalpy-based Thermal Evolution ofLoops(EBTEL)hydrodynamic simulations, we model loops with multiple lengths and energyfluxes heatedrandomly by events drawn from power-law distributions with different slopes and minimum delays between eventsto investigate how each of these parameters influences observable loop properties. We generate AIA intensitiesfrom the corona and transition region for each realization. The variations within and between models generatedwith these different parameters illustrate the sensitivity of narrowband imaging to the details of coronal heating.We then analyze the transition region and coronal emission from a number of observed active regions andfindbroad agreement with the trends in the models. In both models and observations, the transition region brightness issignificant, often greater than the coronal brightness in all six“coronal”AIA channels. We also identify an inverserelationship, consistent with heating theories, between the slope of the differential emission measure(DEM)coolward of the peak temperature and the observed ratio of coronal to transition region intensity. These resultshighlight the use of narrowband observations and the importance of properly considering the transition region ininvestigations of coronal heating

S J Schonfeld↗
NASA NTRS2023

Coronal Heating as Determined by the Solar Flare Frequency Distribution Obtained by Aggregating Case Studies

Flare frequency distributions represent a key approach to addressing one of the largest problems in solar and stellar physics: determining the mechanism that counterintuitively heats coronae to temperatures that are orders of magnitude hotter than the corresponding photospheres. It is widely accepted that the magnetic field is responsible for the heating, but there are two competing mechanisms that could explain it: nanoflares or Alfvén waves. To date, neither can be directly observed. Nanoflares are, by definition, extremely small, but their aggregate energy release could represent a substantial heating mechanism, presuming they are sufficiently abundant. One way to test this presumption is via the flare frequency distribution, which describes how often flares of various energies occur. If the slope of the power law fitting the flare frequency distribution is above a critical threshold, α = 2 as established in prior literature, then there should be a sufficient abundance of nanoflares to explain coronal heating. We performed >600 case studies of solar flares, made possible by an unprecedented number of data analysts via three semesters of an undergraduate physics laboratory course. This allowed us to include two crucial, but nontrivial, analysis methods: preflare baseline subtraction and computation of the flare energy, which requires determining flare start and stop times. We aggregated the results of these analyses into a statistical study to determine that α = 1.63 ± 0.03. This is below the critical threshold, suggesting that Alfvén waves are an important driver of coronal heating.

Astrostatistics distributions↗
NASA NTRS2008

The Foggy EUV Corona and Coronal Heating by MHD Waves from Explosive Reconnection Events

In 0.5 arcsec/pixel TRACE coronal EUV images, the corona rooted in active regions that are at the limb and are not flaring is seen to consist of (1) a complex array of discrete loops and plumes embedded in (2) a diffuse ambient component that shows no fine structure and gradually fades with height. For each of two not-flaring active regions, found that the diffuse component is (1) approximately isothermal and hydrostatic and (2) emits well over half of the total EUV luminosity of the active-region corona. Here, from a TRACE Fe XII coronal image of another not-flaring active region, the large sunspot active region AR 10652 when it was at the west limb on 30 July 2004, we separate the diffuse component from the discrete loop component by spatial filtering, and find that the diffuse component has about 60% of the total luminosity. If under much higher spatial resolution than that of TRACE (e. g., the 0.1 arcsec/pixel resolution of the Hi-C sounding-rocket experiment proposed by J. W. Cirtain et al), most of the diffuse component remains diffuse rather being resolved into very narrow loops and plumes, this will raise the possibility that the EUV corona in active regions consists of two basically different but comparably luminous components: one being the set of discrete bright loops and plumes and the other being a truly diffuse component filling the space between the discrete loops and plumes. This dichotomy would imply that there are two different but comparably powerful coronal heating mechanisms operating in active regions, one for the distinct loops and plumes and another for the diffuse component. We present a scenario in which (1) each discrete bright loop or plume is a flux tube that was recently reconnected in a burst of reconnection, and (2) the diffuse component is heated by MHD waves that are generated by these reconnection events and by other fine-scale explosive reconnection events, most of which occur in and below the base of the corona where they are seen as UV explosive events, EUV blinkers, and type II spicules. These MHD waves propagate across field lines and dissipate, heating the plasma in the field between the bright loops and plumes.

Moore, Ron L.↗
NASA NTRS2013

Coronal Heating Observed with Hi-C

The recent launch of the High‐Resolution Coronal Imager (Hi‐C) as a sounding rocket has offered a new, different view of the Sun. With approx 0.3" resolution and 5 second cadence, Hi‐C reveals dynamic, small‐scale structure within a complicated active region, including coronal braiding, reconnection regions, Alfven waves, and flows along active region fans. By combining the Hi‐C data with other available data, we have compiled a rich data set that can be used to address many outstanding questions in solar physics. Though the Hi‐C rocket flight was short (only 5 minutes), the added insight of the small‐scale structure gained from the Hi‐C data allows us to look at this active region and other active regions with new understanding. In this talk, I will review the first results from the Hi‐C sounding rocket and discuss the impact of these results on the coronal heating problem.

Winebarger, Amy R.↗
NASA NTRS2003

Exploration of the Characteristics of the Time Variable Component of the Coronal Heating Process

By coordinating coronal SOHO observations in white light, ultraviolet, extreme ultraviolet, with radio occultation measurements, and complementing these with modeling, two break-throughs were achieved from this funding: (1) The discovery that minor ions are accelerated much faster than protons in the fast solar wind, and (2) that the imprint of coronal density structures is carried outwards from the Sun into the solar wind. Three refereed papers and one invited review, published in the proceedings of the conference, resulted from this funding. A summary of each is given.

Wagner, William↗