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Modeling of Coronal EUV Loops Observed with TRACE : I. Hydrostatic Steady-State Solutions with Nonuniform Heating
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Markus J Aschwanden Submitted: 2000-08-18 13:05
Recent observations of coronal loops in EUV wavelengths with the {sl Transition
Region and Coronal Explorer (TRACE)} and the {sl Extreme-ultraviolet Imaging
Telescope (EIT)} on the {sl Solar and Heliospheric Observatory (SoHO)}
demonstrated three new results that cannot be explained with most of the
existing loop models: (1) EUV loops are near-isothermal along their coronal
segments, (2) they show an overpressure or overdensity compared with the
requirements of steady-state loops with uniform heating, and (3) the brightest
EUV loops exhibit extended scale heights up to four times the hydrostatic scale
height. These observations cannot be reconciled with the classical RTV (Rosner,
Tucker, & Vaiana) model, they do not support models with uniform heating, and
partially even violate the requirements of hydrostatic equilibrium. - In this
study we conduct numeric calculations of steady-state solutions of the hydrodyn-
hydrodynamic equations of mass conservation, momentum balance, and energy
balance. We calculate some 500 solutions that cover a large parameter space of
loop lengths (L approx 4-300 Mm), of nonuniform heating functions (with
heating scale heights in the range of {lambda}_H approx 1-300 Mm), as well
as the limit of uniform heating ({lambda}_H gg L). The parameter space can
be subdivided into 3 regimes, which contain (1) solutions for stable loops, (2)
solutions for unstable loops, and (3) no solutions. Short heating scale heights
({lambda}H, Mm lapprox sqrt{LMm}) lead to unstable loops. Fitting the
hydrostatic solutions to 41 EUV loops observed with {sl TRACE} we find that
60\% are dynamically unstable, 30\% are near a steady-state equilibrium, and
10\% are cooling off. Those loops near steady-state are all found to be heated
near the footpoints, with a heating scale height of {lambda}_H=12 pm 5 Mm,
covering a fraction {lambda}_H/L=0.2pm0.1 of the loop length. None of the
observed loops is consistent with a uniform heating function in steady-state.
Because the observed heating scale heights are all found less than a factor of 2
within the instability limit, most of the coronal heating episodes seem to
operate with relatively short heating scale heights, producing mostly dynamical-
dynamically unstable loops and transient brightenings.
Authors: Markus J. Aschwanden, Carolus J. Schrijver, and David Alexander
Projects:
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Publication Status: ApJ, subm. (2000 Aug 7)
Last Modified: 2000-08-18 13:05
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Evidence for Nonuniform Heating of Coronal Loops Inferred from Multi-Thread Modeling of TRACE Data
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Markus J Aschwanden Submitted: 2000-05-26 13:04
The temperature T_e(s) and density structure n_e(s) of active region loops
in EUV observed with {sl TRACE} is modeled with a multi-thread model,
synthesized from the summed emission of many loop threads that have a
distribution of maximum temperatures and that satisfy the steady-state Rosner-T-
Rosner-Tucker-Vaiana (RTV) scaling law, modified by Serio et al. for gravitatio-
gravitational stratification (called RTVS_p in the following). In a recent
Letter, Reale & Peres demonstrated that this method can explain the almost
isothermal appearance of TRACE loops (observed by Lenz et al.) as derived from
the filter-ratio method. From model-fitting of the 171 and 195 ang fluxes of
41 loops, which have loop half lengths in the range of L=4-320 Mm, we find:
(1) The EUV loops consist of near-isothermal loop threads with substantially
smaller temperature gradients than predicted by the RTVS_p model, (2) the loop
base pressure, p_0 approx 0.3pm 0.1 dyne cm-2, is independent of the
loop length L, it agrees with the RTVS_p model for the shortest loops, but
exceeds the RTVS_p model up to a factor of 35 for the largest loops, and (3)
the pressure scale height is consistent with hydrostatic equilibrium for the
shortest loops, but exceeds the temperature scale height up to a factor of
approx 3 for the largest loops. The data indicate that cool EUV loops in the
temperature range of T_eapprox 0.8-1.6 MK cannot be explained with the static
steady-state RTVS_p model in terms of uniform heating, but are fully
consistent with Serio's model in the case of nonuniform heating (RTVSph),
with heating scale heights in the range of s_H=17 pm 6 Mm. This heating
function provides almost uniform heating for small loops (L lapprox 20 Mm),
but restricts heating to the footpoints of large loops (Lapprox 50-300 Mm).
Chromospheric upflows appear to be the most likely heating source of EUV loops.
Authors: Markus J. Aschwanden, Richard W. Nightingale, and David Alexander
Projects:
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Publication Status: ApJ 541:1059-1077 (2000 October 1)
Last Modified: 2000-10-06 08:35
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Tomography of the Soft X-Ray Corona: Measurements of Electron Densities, Temperatures, and Differential Emission Measure Distributions above the Limb
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Markus J Aschwanden Submitted: 2000-05-04 16:02
We analyze long-exposure and off-pointing {sl Yohkoh/SXT} data of the solar
corona observed on 1992 Aug 26. We develop a new tomographic method which is
based on a forward-fitting method of a 4-parameter model to the observed soft
X-ray fluxes F_1(h) and F_2(h) of two {sl SXT} wavelength filters as
function of height h. The model is defined in terms of a {sl differential
emission measure (DEM)} distribution dEM(h, T)/dT, which includes also a
temperature dependence of density scale heights ${lambda}_n(T) =qlambda
{lambda}_T and allows to quantify deviations (qlambda
eq 1$) from
hydrostatic equilibrium, i.e. {lambda}_n(T)={lambda}_T. This parametrization
faciliates a proper line-of-sight integration and relates the widely-used
filter-ratio temperature TFR to the peak of the DEM distribution. A direct
consequence of the multi-scale-height atmosphere is that the filter ratio
temperature TFR(h) is predicted to increase with height, even if all
magnetic field lines are isothermal. Our model-fitting reveals that coronal
holes and Quiet Sun regions are in perfect hydrostatic equilibrium, but that
coronal streamers have a scale height that exceeds the hydrostatic scale height
by a factor of up to qlambdalapprox 2.3, which underscores the dynamic
nature of coronal streamers. Our density measurements in coronal holes are
slightly lower than most of the white-light polarized brightness inversions, and
seem to come closer to the requirements of solar wind models. Our DEM model
provides also a physical framework for the semi-empirical {sl Baumbach-Allen
formula}, and quantifies the temperature ranges and degree of hydrostaticity of
the {sl K-, L-, } and {sl F-corona}.
Authors: Markus J. Aschwanden and Loren W. Acton
Projects:
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Publication Status: ApJ 550, 475-492
Last Modified: 2001-04-09 07:52
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The Effect of Hydrostatic Weighting on the Vertical Temperature Structure of the Solar Corona
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Markus J Aschwanden Submitted: 2000-04-07 13:05
We investigate the effect of hydrostatic scale heights {lambda}(T) in coronal
loops on the determination of the vertical temperature structure T(h) of the
solar corona. Every method that determines an average temperature at a
particular line-of-sight from optically thin emission (e.g. in EUV or soft X-ray
wavelengths) of a mutli-temperature plasma, is subject to the emission measure--
measure-weighted contributions dEM(T)/dT from different temperatures. Because
most of the coronal structures (along open or closed field lines) are close to
hydrostatic equilibrium, the hydrostatic temperature scale height introduces a
height-dependent weighting function that causes a systematic bias in the
determination of the temperature structure T(h) as function of altitude h.
The net effect is that the averaged temperature seems to increase with altitude,
dT(h)/dh > 0, even if every coronal loop is isothermal (at different
temperatures). We simulate this effect with differential emission measure
distributions observed by {sl SERTS} for an instrument with a broadband
temperature filter such as {sl Yohkoh/SXT} and find that the apparent
temperature increase due to hydrostatic weighting is of order $Delta T approx
T (h/rsun)$. We suggest that this effect largely explains the systematic
temperature increase in the upper corona reported in recent studies (e.g. by
Sturrock et al., Wheatland et al., or Priest et al.), rather than being an
intrinsic signature of a coronal heating mechanism.
Authors: Aschwanden,M.J. and Nitta,N.
Projects:
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Publication Status: 2000, ApJ 535, L59-L62
Last Modified: 2000-08-31 08:01
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Quadrupolar Magnetic Reconnection in Solar Flares: I. 3D Geometry inferred from Yohkoh Observations
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Markus J Aschwanden Submitted: 2000-01-25 14:02
We analyze the 3-dimensional (3D) geometry of solar flares that show so-called
{sl interacting flare loops} in soft X-ray, hard X-ray, and radio emission, as
previously identified by Hanaoka and Nishio. The two flare loops that appear
brightest after the flare are assumed to represent the outcome of a quadrupolar
magnetic reconnection process, during which the connectivity of magnetic
polarities is exchanged between the four loop footpoints. We parametrize the 3D
geometry of the 4 involved magnetic field lines with circular segments,
additionally constrained by the geometric condition that the two pre-reconnecti-
pre-reconnection field lines have to intersect each other at the onset of the
reconnection process, leading to a 10-parameter model. We fit this 10-parameter
model to Yohkoh SXT and HXT data of 10 solar flares and determine this way the
loop sizes and relative orientation of interacting field lines before and after
reconnection. We apply a flare model of Melrose to calculate the magnetic flux
transfer and energy released when two current-carrying field lines reconnect to
form a new current-carrying system in a quadrupolar geometry. The findings and
conclusions are: (1) The pre-reconnection field lines always show a strong
asymmetry in size, consistent with the scenario of new-emerging small-scale
loops that reconnect with pre-existing large-scale loops. (2) The relative angle
between reconnecting field lines is near-collinear in half of the cases, and
near-perpendicular in the other half, contrary to the anti-parallel configurati-
configuration that is considered to be most efficient for magnetic reconnection.
(3) The angle between interacting field lines reduces by $approx 10°-50^-
10°-50°$ after quadrupolar reconnection. (4) The small-scale flare
loop experiences a shrinkage by a factor of 1.31pm0.44, which is consistent
with the scaling law found from previous electron time-of-flight measurements,
suggesting that electron acceleration occurs near the cusp of quadrupolar
configurations. (5) The large-scale loop is found to dominate the total
induction between current-carrying loops, providing a simple estimate of the
maximum magnetic energy available for flare energy release due to current
transfer, which scales as $Delta E^I approx 1029.63 (r_2/10^9 {
m cm})
(I_2/1011 A)^2, (with r_2 the curvature radius and I_2$ the current of
the large-scale loop) and is found to correlate with observed flare energies
deduced from soft X-ray and hard X-ray fluxes. Most of the energy is transferred
to small-scale loops that have half of the large-scale current (I_1=I_2/2).
(6) The quadrupolar reconnection geometry provides also a solution of {sl
Canfield's dilemma} of the offset between the maximum of vertical currents and
the HXR flare loop footpoints. (7) The quadrupolar geometry provides not only a
framework for interacting double-loop flares, but can also be considered as a
generalized version of (cusp-shaped) single-loop flares.
Authors: Aschwanden,M.J., Kosugi,T., Hanaoka,Y., Nishio,M., and Melrose,D.B.
Projects:
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Publication Status: Astrophys.J. 1999, Vol. 526, p. 1026-1045.
Last Modified: 2000-01-25 14:02
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3D-Stereoscopic Analysis of Solar Active Region Loops:
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Markus J Aschwanden Submitted: 2000-01-25 14:02
In this paper we study the three-dimensional (3D) structure of hot ($T_eapprox
1.5-2.5$ MK) loops in solar active region NOAA 7986, observed on 1996 August 30
with the {sl Extreme-ultraviolet Imaging Telescope (EIT)} onboard the {sl
Solar and Heliospheric Observatory (SoHO)}. This complements a first study
(Paper I) on cooler (T_eapprox 1.0-1.5 MK) loops of the same active region,
using the same method of {sl Dynamic Stereoscopy} to reconstruct the 3D
geometry. We reconstruct the 3D-coordinates x(s), y(s), z(s), the density
n_e(s), and temperature profile T_e(s) of 35 individual loop segments (as a
function of the loop coordinate s) using EIT 195 ang and 284 ang images.
The major findings are: (1) All loops are found to be in hydrostatic
equilibrium, in the entire temperature regime of T_e=1.0-2.5 MK; (2) The
analyzed loops have a height of 2-3 scale heights, and thus only segments
extending over about one vertical scale height have sufficient emission measure
contrast for detection; (3) The temperature gradient over the lowest scale
height is of order dT/dsapprox 1-10 K/km; (4) The radiative loss rate is
found to exceed the conductive loss rate by about two orders or magnitude in the
coronal loop segments, implying that the loops cannot be in quasistatic
equilibrium, since standard steady-state loop models show that radiative and
conductive losses are comparable; (5) A steady-state could only be maintained if
the heating rate E_H matches exactly the radiative loss rate in hydrostatic
equilibrium, requiring a heat deposition length {lambda}_H of the half
density scale height lambda. (6) We find a correlation of p propto L-1
between loop base pressure and loop length, which is not consistent with the
scaling law predicted from steady-state models of large-scale loops. - All
observational findings indicate consistently that the energy balance of the
observed EUV loops cannot be described by steady-state models.
Authors: Aschwanden,M.J., Alexander,D., Hurlburt,N., Newmark,J.S.,Neupert,W.M., Klimchuk,J.A., and G.A.Gary
Projects:
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Publication Status: 1999, ApJ 515, 842-867
Last Modified: 2000-08-31 08:27
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Particle Acceleration and Kinematics in Solar Flares and the Solar Corona'' (Invited Review)
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Markus J Aschwanden Submitted: 1999-10-06 21:04
and the Solar Corona'' (Invited Review)
We review theoretical models of particle acceleration applied to solar flares
(DC electric fields, wave-turbulence stochastic acceleration, shock acceleration
acceleration) and confront these models with new observational findings from the
{sl Compton Gamma Ray Observatory (CGRO), Solar Maximum Mission (SMM), Yohkoh},
and radio observations. Remote sensing of energetic particles via hard X-ray
bremsstrahlung, gyrosynchrotron emission, and beam-driven plasma emission requi-
requires a self-consistent modeling of the particle kinematics in the solar
flare plasma, including acceleration, injection, propagation, trapping, and
energy loss of the particles. New insights in these kinematic processes have
been obtained, besides modeling of energetic particle spectra, increasingly from
sub-second timing studies, e.g. in the context of Masuda's discovery of
above-the-loop-top hard X-ray sources, from electron time-of-flight delay
measurements, from the relative timing of propagation to magnetically conjugate
footpoints, from the relative timing of particle signatures in interacting flare
loops with quadrupolar geometry, and from the relative timing of gyrosynchrotron
emission and hard X-ray signatures in magnetic traps. We anticipate significant
progress to be made with the {sl High Energy Solar Spectroscopic Imager
(HESSI)}, to be launched in 2000.
``Magnetic Fields and Solar Processes'', Florence, Italy,
12-18 Sept 1999, ESA SP-448, Dec 1999, in press.
Authors: Aschwanden,M.J.
Projects:
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Publication Status: in Proc. of the Ninth European Meeting on Solar Physics,
Last Modified: 1999-10-06 21:04
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Radio and Hard X-Ray Observations of Flares and their Physical Interpretation'', (Invited Review)
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Markus J Aschwanden Submitted: 1999-10-06 21:04
Interpretation'', (Invited Review)
We review a selection of observations in radio, hard X-rays (HXR) and soft
X-rays (SXR) that constrain geometrical and physical requirements for solar
flare models. Guided by observations of interacting flare loops we discuss a
flare model based on shear-driven quadrupolar reconnection, which explains
single-loop and double-loop flares in a unified picture. We interpret various
observational findings in the light of this unified flare model: {- topology
and geometry of interacting flare loops, } {- localization of particle
acceleration region, } {- scale invariance of electron time-of-flight path and
flare loop geometry, } {- density and magnetic field diagnostic in accelerati-
acceleration region, } {- bi-directionality of injected electron beams, } {-
electron beam trajectories and correlated HXR pulses, } {- bifurcation of
directly-precipitating and trap-precipitating electrons, } {- density and
magnetic field diagnostic of trap region, } {- elementary time scales and
dynamics in acceleration region. }
on
Authors: Aschwanden,M.J.
Projects:
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Publication Status: in Proc. Nobeyama Symposium
Last Modified: 1999-10-06 21:04
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Do EUV Nanoflares Account for Coronal Heating?
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Markus J Aschwanden Submitted: 1999-10-06 21:04
Recent observations with EUV imaging instruments such as SoHO/EIT and TRACE have
shown evidence for flare-like processes at the bottom end of the energy scale,
in the range of Ethapprox 1024-1027 erg. Here we compare these EUV
nanoflares with soft X-ray microflares and hard X-ray flares across the entire
energy range. From the observations we establish empirical scaling laws for the
flare loop length, L(T) propto T, the electron density, n_e(T) propto T^2,
from which we derive scaling laws for the loop pressure, p(T) propto T^3, and
the thermal energy, Eth propto T^6. Extrapolating these scaling laws into
the {sl picoflare regime} we find that the pressure conditions in the
chromosphere constrain a height level for flare loop footpoints, which scales
with heq(T) propto T-0.5. Based on this chromospheric pressure limit we
predict a lower cutoff of flare loop sizes at Lminlapprox 5 Mm and flare
energies Eminlapprox 1024 erg. We show evidence for such a rollover in
the flare energy size distribution from recent TRACE EUV data. Based on this
energy cutoff imposed by the chromospheric boundary condition we find that the
energy content of the heated plasma observed in EUV, SXR, and HXR flares is
insufficient (by 2-3 orders of magnitude) to account for coronal heating.
and Transition Region'', Monterey, California, 24-27 August 1999),
Solar Physics, Dec issue, in press.
Authors: Aschwanden,M.J.
Projects:
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Publication Status: (Contribution to the TRACE workshop ``Physics of the Solar Corona
Last Modified: 1999-10-06 21:04
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Time Variability of the Quiet Sun Observed with TRACE. I. Instrumental Effects, Event Detection, and Discrimination of EUV Nanoflares
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Markus J Aschwanden Submitted: 1999-10-06 21:02
The {sl Transition and Coronal Explorer (TRACE)} observed a ``Quiet Sun''
region on 1999 Feb 17 from 01: 30 UT to 10: 00 UT with full resolution (0.5''
pixel size), high cadence (125 s), and deep exposures (65 s and 46 s) in the 171
ang and 195 ang wavelengths. We start our investigation of the time
variability of ``Quiet Sun'' images with a detailed analysis of instrumental and
nonsolar effects, such as orbital temperature variations, filtering of particle
radiation spikes, spacecraft pointing jitter, and solar rotation tracking. We
quantify the magnitude of various noise components (photon Poisson statistics,
data digitization, data compression, readout noise) and establish an upper limit
for the data noise level, above which temporal variability can safely be
attributed to solar origin. We develop a pattern recognition code which extracts
spatio-temporal events with significant variability, yielding a total of 3131
events in 171 ang and 904 events in 195 ang . We classify all 904 events
detected in 195 ang according to flare-like characteristics and establish a
numerical flare criterion based on temporal, spatial, and dynamic cross-correla-
cross-correlation coefficients between the two observed temperatures (0.9 MK and
1.4 MK). This numerical criterion matches the visual flare classification in
83\% and can be used for automated flare search. Using this flare discrimination
criterion we find that only 35\% (and 25\%) of the events detected in 171 (and
195) ang represent flare-like events. The discrimination of flare events leads
to a frequency distribution of peak fluxes, $N(Delta F) propto Delta
F-1.83pm0.07$ at 195 ang, that is significantly flatter than the distribut-
distribution of all events. A sensitive discrimination criterion of flare events
is therefore important for microflare statistics and for conclusions on their
occurrence rate and efficiency for coronal heating.
Authors: Aschwanden,M.J., Nightingale,R., Tarbell,T. S., and Wolfson,C.J.
Projects:
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Publication Status: ApJ 535, 1027-1046, (2000)
Last Modified: 2000-08-31 07:47
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Time Variability of the Quiet Sun Observed with TRACE. II. Physical Parameters, Temperature Evolution, and Energetics of EUV Nanoflares
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Markus J Aschwanden Submitted: 1999-10-06 21:02
We present a detailed analysis of the geometric and physical parameters of 281
EUV nanoflares, simultaneously detected with the {sl TRACE} telescope in the
171 and 195 ang wavelengths. The detection and discrimination of these
flare-like events is detailed in Paper I. We determine the loop length l, loop
width w, emission measure EM, the evolution of the electron density n_e(t)
and temperature T_e(t), the flare decay time { au}decay, and calculate
the radiative loss time { au}loss, the conductive loss time ${ au}cond
{ au}cond, and the thermal energy Eth. The findings are: (1) EUV
nanoflares in the energy range of 1024-1026 erg represent miniature
versions of larger flares observed in soft X-rays and hard X-rays, scaled to
lower temperatures (T_e lapprox 2 MK), lower densities (n_e lapprox 10^9
cm-3), and somewhat smaller spatial scales (lapprox 2-20 Mm); (2) The
cooling time { au}decay is compatible with the radiative cooling time
{ au}rad, but the conductive cooling time scale { au}cond is about
an order of magnitude shorter, suggesting repetitive heating cycles in time
intervals of a few minutes; (3) The frequency distribution of thermal energies
of EUV nanoflares, N(E)approx 10-46(E/1024)-1.8 [s-1 cm-2
erg-1] matches that of SXR microflares in the energy range of $1026-10^-
1026-1029, and exceeds that of nonthermal energies of larger flares
observed in HXR by a factor of 3-10 (in the energy range of 1029-1032
erg. Discrepancies of the power-law slope with other studies, which report
higher values in the range of aschwanden@lmsal.com: =2.3-2.6$ (Krucker & Benz, or Parnell & Jupp),
are attributed to methodical differences in the detection and discrimination of
EUV microflares, as well as to different model assumptions in the calculation of
the electron density. Besides the insufficient power of nanoflares to heat the
corona, we find also other physical limits for nanoflares at energies $lapprox
1024$ erg, such as the area coverage limit, the heating temperature limit,
the lower coronal density limit, and the chromospheric loop height limit. Based
on these quantitative physical limitations, it appears that coronal heating
requires other energy carriers that are not luminous in EUV, SXR, and HXR.
Authors: Aschwanden,M.J., Tarbell,T.D., Nightingale,R.W., Schrijver,C.J., Title,A.,
Projects:
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Publication Status: 2000, ApJ 535, 1047-1065
Last Modified: 2000-08-31 07:59
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