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NASA NTRS2001

Characteristics of the Time Variable Component of the Coronal Heating Process

The goal of the proposed study was to explore the non-steady nature of the coronal heating processes and its manifestations in the inner corona and interplanetary space by coordinating coronal SOHO observations in white light, ultraviolet, and extreme ultraviolet, with complementary radio occultation measurements during an unprecedented and rare coincidence of a total solar eclipse with the superior conjunction of a planetary spacecraft, Galileo, in February 1998. In addition, radio occultation measurements by the Mars Global Surveyor spacecraft in May 1998 spanned the inner heliosphere observed by coronal SOHO instruments and probing it to within 0.5 R(sub S), above the solar surface. Inferences of physical properties derived from these simultaneous observations were subsequently used in solar wind model computations to yield the range of plasma parameters characteristic of the fast and slow solar wind.

Habbal, Shadia R.↗
NASA NTRS1981

On the theory of coronal heating mechanisms

The present state-of-the-art of two classes of theories of coronal heating is examined: (1) heating by acoustic processes in the 'nonmagnetic' parts of the atmosphere (the shock-wave theory is an example); and (2) heating by electrodynamic processes in the magnetic regions of the corona (beta much less than 1) either by MHD waves or current heating in regions with high electric current densities (flare-type heating). It is concluded that the mechanism of the heating of the solar chromosphere and corona remains an open question, especially in explaining detailed atmospheric structures. The acoustic theory might be correct with little modification for most of the chromosphere, but as soon as the atmosphere shows a high degree of structure as in the corona and transition layer the magnetic field must play a dominant role. It appears that the current heating theories have a small range of applicability, while the MHD-wave theories are the most promising.

Kuperus, M.↗
NASA NTRS2007

Coronal Heating, Weak MHD Turbulence, and Scaling Laws

Long-time high-resolution simulations of the dynamics of a coronal loop in Cartesian geometry are carried out, within the framework of reduced magnetohydrodynamics (RMHD), to understand coronal heating driven by the motion of field lines anchored in the photosphere. We unambiguously identify MHD anisotropic turbulence as the physical mechanism responsible for the transport of energy from the large scales, where energy is injected by photospheric motions, to the small scales, where it is dissipated. As the loop parameters vary, different regimes of turbulence develop: strong turbulence is found for weak axial magnetic fields and long loops, leading to Kolmogorov-like spectra in the perpendicular direction, while weaker and weaker regimes (steeper spectral slopes of total energy) are found for strong axial magnetic fields and short loops. As a consequence we predict that the scaling of the heating rate with axial magnetic field intensity B, which depends on the spectral index of total energy for given loop parameters, must vary from B3/2 for weak fields to B2 for strong fields at a given aspect ratio. The predicted heating rate is within the lower range of observed active region and quiet-Sun coronal energy losses.

corona↗
NASA NTRS2001

Coronal Heating and the Magnetic Flux Content of the Network

Previously, from analysis of SOHO coronal images in combination with Kitt Peak magnetograms, we found that the quiet corona is the sum of two components: the large-scale corona and the coronal network. The large-scale corona consists of all coronal-temperature (T approximately 10(exp 6) K) structures larger than supergranules (greater than approximately 30,000 kilometers). The coronal network (1) consists of all coronal-temperature structures smaller than supergranules, (2) is rooted in and loosely traces the photospheric magnetic network, (3) has its brightest features seated on polarity dividing lines (neutral lines) in the network magnetic flux, and (4) produces only about 5% of the total coronal emission in quiet regions. The heating of the coronal network is apparently magnetic in origin. Here, from analysis of EIT coronal images of quiet regions in combination with magnetograms of the same quiet regions from SOHO/MDI and from Kitt Peak, we examine the other 95% of the quiet corona and its relation to the underlying magnetic network. We find: (1) Dividing the large-scale corona into its bright and dim halves divides the area into bright "continents" and dark "oceans" having spans of 2-4 supergranules. (2) These patterns are also present in the photospheric magnetograms: the network is stronger under the bright half and weaker under the dim half. (3) The radiation from the large-scale corona increases roughly as the cube root of the magnetic flux content of the underlying magnetic network. In contrast, the coronal radiation from an active region increases roughly linearly with the magnetic flux content of the active region. We assume, as is widely held, that nearly all of the large-scale corona is magnetically rooted in the network. Our results suggest that either the coronal heating in quiet regions has a large non-magnetic component, or, if the heating is predominantly produced via the magnetic field, the mechanism is significantly different than in active regions.

Falconer, D. A.↗
NASA NTRS2001

Coronal Heating and the Magnetic Flux Content of the Network

Previously, from analysis of SOHO/EIT coronal images in combination with Kitt Peak magnetograms (Falconer et al 1998, ApJ, 501, 386-396), we found that the quiet corona is the sum of two components: the e-scale corona and the coronal network. The large-scale corona consists of all coronal-temperature (T approx. 10(exp 6) K) structures larger than supergranules (>approx.30,000 km). The coronal network (1) consists of all coronal-temperature structures smaller than supergranules, (2) is rooted in and loosely traces the photospheric magnetic network, (3) has its brightest features seated on polarity dividing fines (neutral lines) in the network magnetic flux, and (4) produces only about 5% of the total coronal emission in quiet regions. The heating of the coronal network is apparently magnetic in origin. Here, from analysis of EIT coronal images of quiet regions in combination with magnetograms of the same quiet regions from SOHO/MDI and from Kitt Peak, we examine the other 95% of the quiet corona and its relation to the underlying magnetic network. We find: (1) Dividing the large-scale corona into its bright and dim halves divides the area into bright "continents" and dark "oceans" having spans of 2-4 supergranules. (2) These patterns are also present in the photospheric magnetograms: the network is stronger under the bright half and weaker under the dim half. (3) The radiation from the large-scale corona increases roughly as the cube root of the magnetic flux content of the underlying magnetic network. In contrast, Fisher et A (1998, ApJ, 508, 985-998) found that the coronal radiation from an active region increases roughly linearly with the magnetic flux content of the active region. We assume, as is widely held, that nearly all of the large-scale corona is magnetically rooted in the network. Our results, together with the result of Fisher et al (1999), suggest that either the coronal heating in quiet regions has a large non-magnetic component, or, if the heating is predominantly produced via the magnetic field, the mechanism is significantly different than in active regions. This work is funded by NASA's Office of Space Science through the Solar Physics Supporting Research and Technology Program and the Sun-Earth Connection Guest Investigator Program.

Falconer, D. A.↗
NASA NTRS1990

Episodic coronal heating

A study is made of the observational consequences of the hypothesis that there is no steady coronal heating, the solar corona instead being heated episodically, such that each short burst of heating is followed by a long period of radiative cooling. The form of the resulting contribution to the differential emission measure (DEM), and to a convenient related function (the differential energy flux, DEF) is calculated. Observational data for the quiet solar atmosphere indicate that the upper branch of the DEM, corresponding to temperatures above 100,000 K, can be interpreted in terms of episodic energy injection at coronal temperatures.

Sturrock, P. A.↗
NASA NTRS2011

Understanding Coronal Heating with Emission Measure Distributions

It is widely believed that the cross-field spatial scale of coronal heating is small, so that the fundamental plasma structures (loop strands) are spatially unresolved. We therefore must appeal to diagnostic techniques that are not strongly affected by spatial averaging. One valuable observable is the emission measure distribution, EM(T), which indicates how much material is present at each temperature. Using data from the Extreme-ultraviolet Imaging Spectrograph on the Hinode mission, we have determined emission measure distributions in the cores of two active regions. The distributions have power law slopes of approximately 2.4 coolward of the peak. We compare these slopes, as well as the amount of emission measure at very high temperature, with the predictions of a series of models. The models assume impulsive heating (nanoflares) in unresolved strands and take full account of non equilibrium ionization. A variety of nanoflare properties and initial conditions are considered. We also comment on the selection of spectral lines for upcoming missions like Solar Orbiter.

Klimchik, James A.↗
NASA NTRS1991

The phase mixing of Alfven waves, coordinated modes, and coronal heating

Phase mixing has been a popular theoretical mechanism invoked to dissipate the photospheric plane shear Alfven waves hypothesized to penetrate up into the coronal hole and solar wind, thereby maintaining the expanding coronal gas at 1.5 million K and serving as the principal energy source for the solar wind. However, phase mixing requires an ignorable coordinate, which is not available in the presumably filamentary coronal hole. The filamentary density and temperature of the coronal hole couple the waves into a coordinated mode with a unique phase velocity omega/k, which provides the other popular theoretical mechanism, viz, resonant absorption where the local Alfven speed C is equal to omega/k. This provides coronal heating at radial distances O(10 solar radii), where it serves to accelerate the solar wind to high velocity. But it does not provide the principal heat input in the first 1-2 solar radii, required by Withbroe's (1988) analysis of the observed structure of the coronal hole.

Parker, E. N.↗
NASA NTRSDate not supplied

Study of Coronal Heating in Solar Active Regions Using Wide-Field Imaging Spectroscopy: Hinode EIS Slot Observations

Understanding the frequency of heating events that keep the coronal plasma at several million Kelvin above the photospheric temperature of~ 6000K, is one of the most important problems in solar astrophysics. Spectroscopic observations of the Sun in the extreme ultraviolet (EUV) indicate that the coronal plasma reaches temperatures from 1 to 5 MK in active regions. It is also established that temperature in active regions can vary strongly with time and, moreover, contain sub-regions that evolve and develop separately. Tracking the spatio-temporal evolution of temperature requires continuous observation of the entire active region via imaging and spectroscopy. Traditional slit imaging spectroscopy probes plasma heating in solar active regions through observations of diagnostic emission lines and the resulting data are spectrally pure. Here, imaging is performed through rastering process, which severely limits co-temporal observations and often can be slow to miss events that evolve at other portions of the active region. In contrast, wide-field imaging spectroscopy offer simultaneous coverage of a large field of view as well as obtain spectral information in the same direction. This data suffers from spatial-spectral confusion, and are called spectroheliograms. Using the state-of-the-art inversion techniques that are developed recently, now spectroheliogram data can be unfolded to yield spectrally pure maps of large fields over long duration of observations. We use wide slit data, usually referred as ‘slot’, from the EUV Imaging Spectrometer (EIS) onboard Hinode satellite, focusing on active region observations. Here, we present our study of coronal heating in an active region using a long duration Hinode EIS slot observation.

Active region heating↗
NASA NTRS2010

SDO/AIA Light Curves and Implications for Coronal Heating: Model Predictions

It seems largely agreed that many coronal loops---those observed at a temperature of about 1 MK---are bundles of unresolved strands that are heated by storms of impulsive nanoflares. The nature of coronal heating in hotter loops and in the very important but largely ignored diffuse component of active regions is much less clear. Is it also impulsive or is it quasi steady? The spectacular new data from the Atmospheric Imaging Assembly (AIA) telescopes on the Solar Dynamics Observatory (SDO) offer an excellent opportunity to address this question. We analyze the light curves of coronal loops and the diffuse corona in 6 different AIA channels and compare them with the predicted light curves from theoretical models. Light curves in the different AIA channels reach their peak intensities with predictable orderings as a function the nanoflare storm properties. We show that while some sets of light curves exhibit clear evidence of cooling after nanoflare storms, other cases are less straightforward to interpret. Complications arise because of line-of-sight integration through many different structures, the broadband nature of the AIA channels, and because physical properties can change substantially depending on the magnitude of the energy release. Nevertheless, the light curves exhibit predictable and understandable patterns. This presentation emphasizes the modeling aspects of our study. A companion presentation emphasizes the observations.

Klimchuk, James A.↗
NASA NTRS1994

On the relation between coronal heating, flux tube divergence, and the solar wind proton flux and flow speed

A one-fluid solar wind model is used to investigate some relations between coronal heating, the flux tube divergence near the Sun, and the solar wind proton flux and flow speed. The effects of energy addition to the supersonic region of the flow are also studied. We allow for a mechanical energy flux that heats the corona, and an Alfven wave energy flux that adds energy, mainly to the supersonic flow, both as momentum and as heat. We find that the mechanical energy flux determines the solar wind mass flux, and in order to keep an almost constant proton flux at the orbit of Earth with changing flow geometry, that the mechanical energy flux must vary linearly with the magnetic field in the inner corona. This thermally driven wind generally has a low asymptotic flow speed. When Alfven waves are added to the thermally driven flow, the asymptotic flow speed is increased and is determined by the ratio of the Alfven wave and the mechanical energy fluxes at the coronal base. Flow speeds characteristic of recurrent high-speed solar wind streams can be obtained only when the Alfven wave energy flux, deposited in the supersonic flow, is larger than the mechanical energy flux heating the corona.

Sandbaek, Onulf↗
NASA NTRS1981

OSO 8 observational limits to the acoustic coronal heating mechanism

An improved analysis of time-resolved line profiles of the C IV resonance line at 1548 A has been used to test the acoustic wave hypothesis of solar coronal heating. It is shown that the observed motions and brightness fluctuations are consistent with the existence of acoustic waves. Specific account is taken of the effect of photon statistics on the observed velocities, and a test is devised to determine whether the motions represent propagating or evanescent waves. It is found that on the average about as much energy is carried upward as downward such that the net acoustic flux density is statistically consistent with zero. The statistical uncertainty in this null result is three orders of magnitue lower than the flux level needed to heat the corona.

Bruner, E. C., Jr.↗
NASA NTRS1999

Nonthermal Linewidths from Serts: Implications for Coronal Heating Models

Observations from Solar Extreme-ultraviolet Research Telescope and Spectrograph (SERTS) are used to determine the nonthermal velocity in the corona for active and quiet Sun regions in 1991 and 1993. A nonthermal velocity of 20-30 km/s is obtained in all solar structures observed at both observing times. These observations can be used to constrain coronal heating models. The idea that magnetic reconnection could provide energy to heat the non-transient corona is not supported by the data.

Davila, Joseph M.↗
NASA NTRS1993

The distribution of flare parameters and implications for coronal heating

Assuming that solar hard X-ray flares are caused by bremsstrahlung from a distribution of accelerated electrons impinging on a thick target, we determine the relationship between the total flare energy released in the corona and observable flare parameters. It is shown that for the more numerous smaller flares to be energetically more important than larger ones, there must be an anticorrelation between observed flux and one or more of the photon spectral index, the total flare duration, the ratio of the total energy that goes into heating the corona to the energy that goes into acceleration of electrons, and the reciprocal of the low-energy cutoff of the accelerated electron spectrum. Using a new statistical test which properly takes account of data truncation due to observational selection effects, we find that neither spectral index nor duration show an anticorrelation with flux in ISEE 3/ICE hard X-ray data. Using a nonparametric method, we obtain single distributions of peak flux, spectral index, duration, and fluence, corrected for selection biases. The functional forms of these distributions do not support coronal heating by numerous small flares without very specific behavior by yet unobserved parameters.

Lee, Theodore T.↗
NASA NTRS1986

Cascade model of coronal heating

It is suggested that the quasi-static evolution of coronal magnetic structures is characterized by a cascade of magnetic energy to smaller length scales. This cascade process takes place on a time scale t sub b determined entirely by the photospheric motions. The Ohmic heating rate E sub H in the statistically stationary state was estimated using observational data on the diffusivity of photospheric motions; E sub H turned out to be too small by a factor of 40 when compared with observed coronal energy losses. However, given the fact that the theoretical estimate is based on a rather uncertain extrapolation to the diffusive regime, current heating cannot be ruled out as a viable mechanism of coronal heating.

Vanballegooijen, A. A.↗
NASA NTRS1995

Coronal heating by the resonant absorption of Alfven waves: Wavenumber scaling laws.

The importance of global modes in coronal loop heating is well established. In the present work the scaling of the global-mode resonant heating rate with the perturbation wavenumbers is studied with the numerical solution of the linearized time-dependent MHD equations for a full compressible, low-beta, resistive plasma using an implicit integration scheme. The numerical simulations demonstrate that the dissipation on inhomogeneties in the background Alfven speed occurs in narrow resonant layer with the highest heating rate at the global-mode frequency. The global-mode heating rate H (sub r) was found to scale as H (Sub r) approximately k (sub y) (exp 1.03) when k (sub z) = 0.1, and as H (sub r) approximately k (sub y) (exp -1.93) when k (sub z) = 0.75, where k (sub y) and k (sub z) are the wavenumbers in the perpendicular and parallel to the magnetic field directions, respectively, while the dependence of H (sub r) on k (sub z) is more complex. The quality factor Q of the MHD resonance cavity scales as Q approximately k (sub y) (exp -1.8) for k (sub z) = 0.75 and as Q approximately k (sub y) (exp -1.46) for k (sub z) = 0.1. The numerically determined heating rate scaling, the global-mode fequency, and the quality factor are in good agreement with the analytical linear theory. The magnitude of the perturbed velocities was found to decrease with k (sub y). Assuming typical coronal loop parameters (B (sub 0) = 100-200 G, upsilon (sub A) = 2000-4000 km/s), the Alfven waves can supply the required heating to a low-Q loops.

Ofman, L.↗