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NASA NTRS2012

Free Magnetic Energy and Coronal Heating

Previous work has shown that the coronal X-ray luminosity of an active region increases roughly in direct proportion to the total photospheric flux of the active region's magnetic field (Fisher et al. 1998). It is also observed, however, that the coronal luminosity of active regions of nearly the same flux content can differ by an order of magnitude. In this presentation, we analyze 10 active regions with roughly the same total magnetic flux. We first determine several coronal properties, such as X-ray luminosity (calculated using Hinode XRT), peak temperature (calculated using Hinode EIS), and total Fe XVIII emission (calculated using SDO AIA). We present the dependence of these properties on a proxy of the free magnetic energy of the active region

Winebarger, Amy↗
NASA NTRS1983

Coronal heating by waves

Alfven waves or Alfvenic surface waves carry enough energy into the corona to provide the coronal energy requirements. Coronal loop resonances are an appealing means by which large energy fluxes enter active region loops. The wave dissipation mechanism still needs to be elucidated, but a Kolmogoroff turbulent cascade is fully consistent with the heating requirements in coronal holes and active region loops.

Hollweg, J. V.↗
NASA NTRS1992

Heating coronal holes and accelerating the solar wind

The special energy requirements of a coronal hole combined with current knowledge of the limited dissipation of Alfven and fast mode MHD waves in the solar corona suggest a unique source of heat for the coronal hole. The near coronal hole requires approximately 3 - 4 x 10 exp 5 ergs/sq cm s, which can come only from the fluid jets, fast particles, and short period MHD waves from the network activity. The high speed streams of solar wind from coronal holes show that there is substantial heating, of 1 - 2 x 10 exp 5 ergs/sq cm s, beyond the sonic point in the wind, which can come only from the dissipation by thermal conduction of long period (approximately equal or greater than 100 sec) MHD waves from subphotospheric convection. Although the Alfven wave flux from the photosphere is generally taken for granted in the literature, we point out that it is a crucial phenomenon that has yet to be established on either a theoretical or observational scientific basis.

Parker, E. N.↗
NASA NTRS1999

TRACE Observation of Damped Coronal Loop Oscillations: Implicating for Coronal Heating

The imaging telescope on board the Transition Region and Coronal Explorer (TRACE) spacecraft observed the decaying transversal oscillations of a long [(130 +/- 6) x 10(exp 6) meters], thin [diameter (2.0 +/- 0.36) x 10(exp 6) meters], bright coronal loop in the 171 angstrom Fe-IX emission line. The oscillations were excited by a solar flare in the adjacent active region. The decay time of the oscillations is 12.1 +/- 6.7 minutes for an oscillation with a frequency 3.90 +/- 0.13 millihertz The coronal dissipation coefficient is estimated to be eight to nine orders of magnitude larger than the theoretically predicted classical value. The larger dissipation coefficient may solve existing difficulties with wave heating and reconnection theories.

Nakariakov, V. M.↗
NASA NTRS1999

Large-Scale Coronal Heating from "Cool" Activity in the Solar Magnetic Network

In Fe XII images from SOHO/EIT, the quiet solar corona shows structure on scales ranging from sub-supergranular (i.e., bright points and coronal network) to multi-supergranular (large-scale corona). In Falconer et al 1998 (Ap.J., 501, 386) we suppressed the large-scale background and found that the network-scale features are predominantly rooted in the magnetic network lanes at the boundaries of the supergranules. Taken together, the coronal network emission and bright point emission are only about 5% of the entire quiet solar coronal Fe XII emission. Here we investigate the relationship between the large-scale corona and the network as seen in three different EIT filters (He II, Fe IX-X, and Fe XII). Using the median-brightness contour, we divide the large-scale Fe XII corona into dim and bright halves, and find that the bright-half/dim half brightness ratio is about 1.5. We also find that the bright half relative to the dim half has 10 times greater total bright point Fe XII emission, 3 times greater Fe XII network emission, 2 times greater Fe IX-X network emission, 1.3 times greater He II network emission, and has 1.5 times more magnetic flux. Also, the cooler network (He II) radiates an order of magnitude more energy than the hotter coronal network (Fe IX-X, and Fe XII). From these results we infer that: 1) The heating of the network and the heating of the large-scale corona each increase roughly linearly with the underlying magnetic flux. 2) The production of network coronal bright points and heating of the coronal network each increase nonlinearly with the magnetic flux. 3) The heating of the large-scale corona is driven by widespread cooler network activity rather than by the exceptional network activity that produces the network coronal bright points and the coronal network. 4) The large-scale corona is heated by a nonthermal process since the driver of its heating is cooler than it is. 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.

Falconer, D. A.↗
NASA NTRS2012

Extreme-Ultraviolet Spectroscopic Observation of Direct Coronal Heating During a C-Class Solar Flare

With the Coronal Diagnostic Spectrometer operating in rapid cadence (9.8 s) stare mode during a C6.6 flare on the solar disk, we observed a sudden brightening of Fe xix line emission (formed at temperature T ≈ 8 MK) above the pre-flare noise without a corresponding brightening of emission from ions formed at lower temperatures, including He i (0.01 MK), Ov (0.25 MK), and Si xii (2 MK). The sudden brightening persisted as a plateau of Fe xix intensity that endured more than 11 minutes. The Fe xix emission at the rise and during the life of the plateau showed no evidence of significant bulk velocity flows, and hence cannot be attributed to chromospheric evaporation. However, the line width showed a significant broadening at the rise of the plateau, corresponding to nonthermal velocities of at least 89 km s−1 due to reconnection outflows or turbulence. During the plateau He i, Ov, and Si xii brightened at successively later times starting about 3.5 minutes after Fe xix, which suggests that these brightenings were produced by thermal conduction from the plasma that produced the Fe xix line emission; however, we cannot rule out the possibility that they were produced by a weak beam of nonthermal particles. We interpret an observed shortening of the Ov wavelength for about 1.5 minutes toward the middle of the plateau to indicate new upward motions driven by the flare, as occurs during gentle chromospheric evaporation; relative to a quiescent interval shortly before the flare, the Ov upward velocity was around −10 km s−1.

Activity↗
NASA NTRS1975

Time variations in extreme-ultraviolet emission lines and the problem of coronal heating

We have analyzed the time structure of the intensity of solar chromospheric and coronal extreme-ultraviolet lines, obtained by the Harvard College Observatory spectrometer aboard Skylab. We find changes in the intensity of up to 50 percent in times as short as 1 minute, but not periodic oscillations. Some evidence is found for the presence of shock waves in the chromosphere and the transition region. It is suggested that the solar chromosphere and corona are heated by nonperiodic waves.

Vernazza, J. E.↗
NASA NTRS2003

Solar Coronal Heating and the Magnetic Flux Content of the Network

We investigate the heating of the quiet corona by measuring the increase of coronal luminosity with the amount of magnetic flux in the underlying network at solar minimum when there were no active regions on the face of the Sun. The coronal luminosity is measured from Fe IX/X-Fe XII pairs of coronal images from SOHO/EIT. The network magnetic flux content is measured from SOHO/MDI magnetograms. We find that the luminosity of the corona in our quiet regions increases roughly in proportion to the square root of the magnetic flux content of the network and roughly in proportion to the length of the perimeter of the network magnetic flux clumps. From (1) this result, (2) other observations of many fine-scale explosive events at the edges of network flux clumps, and (3) a demonstration that it is energetically feasible for the heating of the corona in quiet regions to be driven by explosions of granule-sized sheared-core magnetic bipoles embedded in the edges of network flux clumps, we infer that in quiet regions that are not influenced by active regions the corona is mainly heated by such magnetic activity in the edges of the network flux clumps. Our observational results together with our feasibility analysis allow us to predict that (1) at the edges of the network flux clumps there are many transient sheared-core bipoles of the size and lifetime of granules and having transverse field strengths greater than approximately - 100 G, (2) approximately 30 of these bipoles are present per supergranule, and (3) most spicules are produced by explosions of these bipoles.

Moore, R. L.↗
NASA NTRS2003

Solar Coronal Heating and the Magnetic Flux Content of the Network

We investigate the heating of the quiet corona by measuring the increase of coronal luminosity with the amount of magnetic flux in the underlying network at solar minimum when there were no active regions on the face of the Sun. The coronal luminosity is measured from Fe IX/X-Fe XII pairs of coronal images from SOHO/EIT. The network magnetic flux content is measured from SOHO/MDI magnetograms. We find that the luminosity of the corona in our quiet regions increases roughly in proportion to the square root of the magnetic flux content of the network and roughly in proportion to the length of the perimeter of the network magnetic flux clumps. From (1) this result, (2) other observations of many fine-scale explosive events at the edges of network flux clumps, and (3) a demonstration that it is energetically feasible for the heating of the corona in quiet regions to be driven by explosions of granule-sized sheared-core magnetic bipoles embedded in the edges of network flux clumps, we infer that in quiet regions that are not influenced by active regions the corona is mainly heated by such magnetic activity in the edges of the network flux clumps. Our observational results together with our feasibility analysis allow us to predict that (1) at the edges of the network flux clumps there are many transient sheared-core bipoles of the size and lifetime of granules and having transverse field strengths > approx. 100 G, (2) approx. 30 of these bipoles are present per supergranule, and (3) most spicules are produced by explosions of these bipoles.

Falconer, D. A.↗
NASA NTRS1994

Electric currents and coronal heating in NOAA active region 6952

We examine the spatial and temporal relationship between coronal structures observed with the soft X-ray telescope (SXT) on board the Yohkoh spacecraft and the vertical electric current density derived from photospheric vector magnetograms obtained using the Stokes Polarimeter at the Mees Solar Observatory. We focus on a single active region: AR 6952 which we observed on 7 days during 1991 December. For 11 independent maps of the vertical electric current density co-aligned with non-flaring X-ray images, we search for a morphological relationship between sites of high vertical current density in the photosphere and enhanced X-ray emission in the overlying corona. We find no compelling spatial or temporal correlation between the sites of vertical current and the bright X-ray structures in this active region.

Metcalf, T. R.↗
NASA NTRS2003

Coronal Heating, Spicules, and Solar-B

Falconer et al. investigated the heating of the quiet corona by measuring the increase of coronal luminosity with the amount of the magnetic flux in the underlying network at solar minimum when there were no active regions on the face of the Sun. The coronal luminosity was measured from Fe IX/X - Fe XII pairs of coronal images from SOHO/EIT, under the assumption that practically all of the coronal luminosity in these very quiet regions came from plasma in the temperature range 0.9 x 10(exp 6) K is less than or equal to T is less than or equal to 1.3 x 10(exp 6) K. The network magnetic flux content was measured from SOHO/MDI magnetograms. It was found that luminosity of the corona in these quiet regions increased roughly in proportion to the square root of the magnetic flux content of the network and roughly in proportion to the length of the perimeter of the network flux clumps. From 1) this result; 2) the observed occurrence of many fine-scale explosive events (e.g., spicules) at the edges of network flux clumps; and 3) a demonstration that it is energetically feasible for the heating of the corona in quiet regions to be driven by explosions of granule-sized sheared-core magnetic bipoles embedded in the edges of the network flux clumps, Falconer et al. infer that in quiet regions that are not influenced by active regions the corona is mainly heated by such magnetic activity in the edges of the network flux clumps. From their observational results together with their feasibility analysis, Falconer et al. predict that 1) At the edges of the network flux clumps there are many transient sheared core bipoles of the size and lifetime of granules and having transverse field strengths greater than approx. 100 G; 2) Approx. 30 of these bipoles are present per supergranule; and 3) Most spicules are produced by explosions of these bipoles. The photospheric vector magnetograms, chromospheric filtergrams, and EUV spectra from Solar-B are expected to have sufficient sensitivity, spatial resolution, and cadence to test these predictions. The Falconer et al. (2003) inferred mixed-polarity magnetic flux at the base of spicules is compatible with the observed magnetic structure of Ha macrospicules recently found by Yamuchi et al. (2003).

Moore, Ron↗
NASA NTRS1980

Coronal heating by stochastic magnetic pumping

Recent observational data cast serious doubt on the widely held view that the Sun's corona is heated by traveling waves (acoustic or magnetohydrodynamic). It is proposed that the energy responsible for heating the corona is derived from the free energy of the coronal magnetic field derived from motion of the 'feet' of magnetic field lines in the photosphere. Stochastic motion of the feet of magnetic field lines leads, on the average, to a linear increase of magnetic free energy with time. This rate of energy input is calculated for a simple model of a single thin flux tube. The model appears to agree well with observational data if the magnetic flux originates in small regions of high magnetic field strength. On combining this energy input with estimates of energy loss by radiation and of energy redistribution by thermal conduction, we obtain scaling laws for density and temperature in terms of length and coronal magnetic field strength.

Sturrock, P. A.↗
NASA NTRS1981

Coronal heating by stochastic magnetic pumping

Recent observational data cast serious doubt on the widely held view that the sun's corona is heated by traveling waves (acoustic or magnetohydrodynamic). It is here proposed that the energy responsible for heating the corona is derived from the free energy of the coronal magnetic field derived from motion of the 'feet' of magnetic field lines in the photosphere. Stochastic motion of the feet of magnetic field lines leads, on the average, to a linear increase of magnetic free energy with time. This rate of energy input is calculated for a simple model of a single thin flux tube. The model appears to agree well with observational data if the magnetic flux originates in small regions of high magnetic field strength as proposed by Tarbell et al. (1979). On combining this energy input with estimates of energy loss by radiation and of energy redistribution by thermal conduction, scaling laws are obtained for density and temperature in terms of length and coronal magnetic field strength.

Sturrock, P. A.↗
NASA NTRS1993

Flux-tube divergence, coronal heating, and the solar wind

Using model calculations based on a self-consistent treatment of the coronal energy balance, we show how the magnetic flux-tube divergence rate controls the coronal temperature and the properties of the solar wind. For a fixed input of mechanical and Alfven-wave energy at the coronal base, we find that as the divergence rate increases, the maximum coronal temperature decreases but the mass flux leaving the sun gradually increases. As a result, the asymptotic wind speed decreases with increasing expansion factor near the sun, in agreement with empirical studies. As noted earlier by Withbroe, the calculated mass flux at the sun is remarkably insensitive to parameter variations; when combined with magnetohydrodynamic considerations, this self-regulatory property of the model explains the observed constancy of the mass flux at earth.

Wang, Y.-M.↗
NASA NTRS1983

Empirical scaling laws for coronal heating

The origins and uses of scaling laws in studies of stellar outer atmospheres are reviewed with particular emphasis on the properties of coronal loops. Some evidence is presented for a fundamental structuring of the solar corona and the thermodynamics of scaling laws are discussed. It is found that magnetic field-related scaling laws can be obtained by relating coronal pressure, temperature, and magnetic field strength. Available data validate this method. Some parameters of the theory, however, must be treated as adjustable, and it is considered necessary to examine data from other stars in order to determine the validity of the parameters. Using detailed observational data, the applicability of single loop models is examined.

Golub, L.↗
NASA NTRS1999

Large-Scale Coronal Heating from the Solar Magnetic Network

In Fe 12 images from SOHO/EIT, the quiet solar corona shows structure on scales ranging from sub-supergranular (i.e., bright points and coronal network) to multi- supergranular. In Falconer et al 1998 (Ap.J., 501, 386) we suppressed the large-scale background and found that the network-scale features are predominantly rooted in the magnetic network lanes at the boundaries of the supergranules. The emission of the coronal network and bright points contribute only about 5% of the entire quiet solar coronal Fe MI emission. Here we investigate the large-scale corona, the supergranular and larger-scale structure that we had previously treated as a background, and that emits 95% of the total Fe XII emission. We compare the dim and bright halves of the large- scale corona and find that the bright half is 1.5 times brighter than the dim half, has an order of magnitude greater area of bright point coverage, has three times brighter coronal network, and has about 1.5 times more magnetic flux than the dim half These results suggest that the brightness of the large-scale corona is more closely related to the large- scale total magnetic flux than to bright point activity. We conclude that in the quiet sun: (1) Magnetic flux is modulated (concentrated/diluted) on size scales larger than supergranules. (2) The large-scale enhanced magnetic flux gives an enhanced, more active, magnetic network and an increased incidence of network bright point formation. (3) The heating of the large-scale corona is dominated by more widespread, but weaker, network activity than that which heats the bright points. 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.

Falconer, David A.↗