The Fractality and Size Distributions of Astrophysical SelfOrganized Criticality Systems 

Markus J Aschwanden Submitted: 20220322 14:57
The statistics of nonlinear processes in avalanching systems,
based on the selforganized criticality (SOC) concept
of Bak et al. (1987), predicts power lawlike size (or
occurrence frequency) distribution functions. Following up
on previous work we define a standard SOC model in terms
of six assumptions: (i) multifractality; (ii) the
lengthareavolume relationship of Mandelbrot (1977);
(iii) the fluxvolume relationship, (iv) classical
diffusion, (v) the Euclidean volume limit at the event peak time,
and (vi) the spatiotemporal fluence or energy of an
avalanche event. We gather data of the fractal dimension
and power law slopes from 162 publications and assemble
them in 28 groups (e.g., solar and stellar flare energies),
from which we find that 75% of the groups
are consistent with the standard SOC model.
Alternative SOC models (Levyflight, flatworld, nonfractal)
are slightly less correlated with the data. The remaining
discrepancies are attributed to outliers caused by
smallnumber statistics, background subtraction problems,
inadequate fitting ranges, and deviations from ideal power laws.
Authors: Markus J. Aschwanden
Projects: SDOAIA

Publication Status: submitted. 20220322
Last Modified: 20220323 13:12



Torsional slowmode oscillations discovered in the magnetic free energy during solar flares 

Markus J Aschwanden Submitted: 20200127 15:08
We report the discovery of torsional Alfvénic oscillations in
solar flares, which modulate the time evolution of the magnetic free
energy E_f(t), while the magnetic potential energy E_p(t) is
uncorrelated, and the nonpotential energy varies as
E_{np}(t) = E_p + E_f(t). The mean observed time period of the
torsional oscillations is P_{obs}=15.1 ± 3.9 min, the mean field
line length is L=135±35 Mm, and the mean phase speed is v_{phase}
=315 ± 120 km s^{1}, which we interpret as torsional
Alfvénic waves in flare loops with enhanced electron densities.
Most of the torsional oscillations are found to be decayless,
but exhibit a positive or negative trend in the evolution of the
free energy, indicating new emerging flux (if positive),
magnetic cancellation, or flare energy dissipation (if negative).
The time evolution of the free energy has been calculated
in this study with the VerticalCurrent Approximation
(Version 4) Nonlinear ForceFree Field (VCA4NLFFF) code,
which incorporates automatically detected coronal loops in
the solution and bypasses the nonforcefreeness of the
photospheric boundary condition, in contrast to traditional
NLFFF codes.
Authors: Aschwanden,M.J. and Wang,T.J.
Projects: None

Publication Status: ApJ (2020, Jan 27; in press)
Last Modified: 20200129 13:13



NonStationary FastDriven SelfOrganized Criticality in Solar Flares 

Markus J Aschwanden Submitted: 20190918 13:40
The original concept of selforganized criticality
(Bak et al. 1987), applied to solar flare statistics
(Lu and Hamilton 1991), assumed a slowdriven and
stationary flaring rate, which warrants time scale
separation (between flare durations and interflare
waiting times), it reproduces powerlaw distributions for
flare peak fluxes and durations, but predicts an
exponential waiting
time distribution. In contrast to these classical
assumptions we observe: (i) multiple energy dissipation
episodes during most flares, (ii) violation of the
principle of time scale separation, (iii) a fastdriven
and nonstationary flaring rate, (iv) a power law
distribution for waiting times Δ t, with a slope
of α _{Δ t} ≈ 2.0, as predicted from
the universal reciprocality between mean flaring rates
and mean waiting times; and (v) pulses with rise times
and decay times of the dissipated magnetic free energy on time
scales of 12±6 min, up to 13 times in longduration
(≈ 4 hrs) flares. These results are inconsistent
with coronal longterm energy storage (Rosner and Vaiana 1978),
but require photosphericchromospheric current injections
into the corona.
Authors: Markus J. Aschwanden
Projects: SDOAIA

Publication Status: ApJ (subm)
Last Modified: 20190918 23:40



Exoplanet predictions based on harmonic orbit resonances 

Markus J Aschwanden Submitted: 20190613 09:55
The current exoplanet database includes 5454 confirmed and candidate planets observed with the Kepler mission. We find 932 planet pairs from which we extract distance and orbital period ratios. While earlier studies used a logarithmic spacing, which lacks a physical model, we employ here the theory of harmonic orbit resonances, which contains quantized ratios instead, to explain the observed planet distance ratios and to predict undetected exoplanets. We find that the most prevailing harmonic ratios are (2:1), (3:2), and (5:3) in 73% of the cases, while alternative harmonic ratios of (5:4), (4:3), (5:2), and (3:1) occur in the other 27% of the cases. Our orbital predictions include 171 exoplanets, 2 Jupiter moons, 1 Saturn moon, 3 Uranus moons, and 4 Neptune moons. The accuracy of the predicted planet distances amounts to a few percent, which fits the data significantly better than the logarithmic spacing. This information may be useful for targeted exoplanet searches with Kepler data and to estimate the number of livecarrying planets in habitable zones.
Authors: Aschwanden,M.J. and Scholkmann,F. 2017,
Projects: None

Publication Status: Galaxies 5(4), 56
Last Modified: 20190619 13:35



The width distribution of solar coronal loops and strands  Are we hitting rock bottom ? 

Markus J Aschwanden Submitted: 20190613 09:55
In this study, we analyze Atmospheric Imaging Assembly (AIA) and HiC images in order to investigate absolute limits for the finest loop strands. We develop a model of the occurrencesize distribution function of coronal loop widths, characterized by the lower limit of widths wmin, the peak (or most frequent) width w_{p}, the peak occurrence number n_{p}, and a powerlaw slope a. Our data analysis includes automated tracing of curvilinear features with the OCCULT2 code, automated sampling of the crosssectional widths of coronal loops, and fitting of the theoretical size distribution to the observed distribution. With Monte Carlo simulations and variable pixel sizes Δx, we derive a first diagnostic criterion to discriminate whether the loop widths are unresolved (w_{p} / Δx ≈ 2.5 ? 0.2) or fully resolved (if w_{p} / Δx ≳ 2.7). For images with resolved loop widths, we can apply a second diagnostic criterion that predicts the lower limit of loop widths as a function of the spatial resolution. We find that the loop widths are marginally resolved in AIA images but are fully resolved in HiC images, where our model predicts a most frequent (peak) value at w_{p} ≈ 550 km, in agreement with recent results of Brooks et al. This result agrees with the statistics of photospheric granulation sizes and thus supports coronal heating mechanisms operating on the macroscopic scale of photospheric magnetoconvection, rather than nanoflare braiding models on unresolved microscopic scales.
Authors: Aschwanden, M.J., Peter, H.
Projects: SDOAIA

Publication Status: ApJ 840:4 (24pp)
Last Modified: 20190707 03:55



Order out of randomness: Selforganization processes in astrophysics 

Markus J Aschwanden Submitted: 20190613 09:49
Selforganization is a property of dissipative nonlinear processes that are gov erned by a global driving force and a local positive feedback mechanism, which creates regular geometric and/or temporal patterns, and decreases the entropy locally, in contrast to random processes. Here we investigate for the first time a comprehensive number of (17) selforganization processes that operate in planetary physics, solar physics, stellar physics, galactic physics, and cosmology. Selforganizing systems create spontaneous ?order out of randomness?, during the evolution from an initially disordered system to an ordered quasistationary system, mostly by quasiperiodic limitcycle dynamics, but also by harmonic (me chanical or gyromagnetic) resonances. The global driving force can be due to gravity, elec tromagnetic forces, mechanical forces (e.g., rotation or differential rotation), thermal pres sure, or acceleration of nonthermal particles, while the positive feedback mechanism is of ten an instability, such as the magnetorotational (BalbusHawley) instability, the convective (RayleighB?nard) instability, turbulence, vortex attraction, magnetic reconnection, plasma condensation, or a losscone instability. Physical models of astrophysical selforganization processes require hydrodynamic, magnetohydrodynamic (MHD), plasma, or Nbody simu lations. Analytical formulations of selforganizing systems generally involve coupled differ ential equations with limitcycle solutions of the LotkaVolterra or Hopfbifurcation type.
Authors: Aschwanden,M.J., Scholkmann,F., Bethune,W., Schmutz,W., Abramenko,W., Cheung,M.C.M., Mueller,D., Benz,A.O., Chernov,G., Kritsuk,A.G., Scargle,J.D., Melatos,A., Wagoner,R.V., Trimble,V., Green,W.
Projects: None

Publication Status: Space Science Reviews 214:55
Last Modified: 20190615 17:41



Convectiondriven generation of ubiquitous coronal waves 

Markus J Aschwanden Submitted: 20190613 09:46
We develop a new method to measure the 3D kinematics of the subphotospheric motion of magnetic elements, which is used to study the coupling between the convectiondriven vortex motion and the generation of ubiquitous coronal waves. We use the method of decomposing a lineofsight magnetogram from HMI/SDO into unipolar magnetic charges, which yields the (projected) 2D motion [x(t), y(t)] and the (half) width evolution w(t) of an emerging magnetic el ement, from an initial depth of d <∼ 1500 km below the photosphere. A simple model of rotational vortex motion with magnetic flux conservation during the emergence process of a magnetic ele ment predicts the width evolution, i.e., w(t)/w0 = [B(t)/B0]1/2, and an upper limit of the depth variation d(t) ≤ 1.3 w(t). While previous 2D tracing of magnetic elements provided information on advection and superdiffusion, our 3D tracing during the emergence process of a magnetic element is consistent with a ballistic trajectory in upward direction. From the estimated Poynt ing flux and life times of convective cells we conclude that the CoMPdetected lowamplitude transverse MHD waves are generated by the convectiondriven vortex motion. Our observational measurements of magnetic elements appear to contradict the theoretical randomwalk braiding scenario of Parker (1983, 1988).
Authors: Aschwanden,M.J., Gosic,M., Hurlburt,N.E., and Scullion,E.
Projects: SDOHMI

Publication Status: ApJ 866, 72 (13pp)
Last Modified: 20190615 17:41



Selforganized criticality in solar and stellar flares: Are extreme events scalefree ? 

Markus J Aschwanden Submitted: 20190613 09:15
We search for outliers in extreme events of statistical
size distributions of astrophysical data sets, motivated
by the DragonKing hypothesis of Sornette (2009),
which suggests that the most extreme events in a statistical
distribution may belong to a different population, and thus
may be generated by a different phyiscal mechanism, in contrast
to the strict power law behavior of selforganized
criticality (SOC) models. Identifying such disparate outliers
is important for space weather predictions. Possible physical
mechanisms to produce such outliers could be generated by
sympathetic flaring. However, we find that DragonKing events
are not common in solar and stellar flares, identified in
4 out of 25 solar and stellar flare data sets only.
Consequently, small, large, and extreme flares are essentially
scalefree and can be modeled with a single physical mechanism.
In very large data sets (N > 10^{4}) we find significant
deviations from ideal poer laws in almost all data sets.
Neverthess, the fitted power law slopes constrain
physcial scaling laws in terms of flare areas and volumes,
which have the highest nonlinearity in their scaling laws.
Authors: Markus, J. Aschwanden
Projects: SDOAIA

Publication Status: The Astrophysical Journal (June 13, 2019, accepted), in press
Last Modified: 20190615 17:38



Exoplanet Predictions Based on Harmonic Orbit Resonances 

Markus J Aschwanden Submitted: 20170519 12:52
The current exoplanet database includes 5454 confirmed planets
and candidate planets observed with the KEPLER mission. We find
932 planet pairs from which we extract distance and orbital period
ratios. While earlier studies used the TitiusBode law or a
generalized version with logarithmic spacing, which both lack
a physical model, we employ here the theory of harmonic orbit
resonances, which contains quantized ratios instead, to explain the
observed planet distance ratios and to predict undetected exoplanets.
We find that the most prevailing
harmonic ratios are (2:1), (3:2), and (5:3), in 73% of the cases,
while alternative harmonic ratios of (5:4), (4:3), (5:2), (3:1)
occur in 27% of the other cases. Our orbital predictions includes
171 exoplanets, 2 Jupiter moons, one Saturn moon, 3 Uranus moons,
and 4 Neptune moons. The accuracy of the predicted planet distances
amounts to a few percent, which fits the data significantly better
than the TitiusBode law or a logarithmic spacing. This information
may be useful for targeted exoplanet searches with Kepler data
and to estimate the number of livecarrying planets in habitable zones.
Authors: Markus J. Aschwanden and Felix Scholkmann
Projects:

Publication Status: 2017, Galaxies 5(4), 56
Last Modified: 20170925 09:07



Modeling of Coronal EUV Loops Observed with TRACE : I. Hydrostatic SteadyState Solutions with Nonuniform Heating 

Markus J Aschwanden Submitted: 20000818 13:05
Recent observations of coronal loops in EUV wavelengths with the {sl Transition Region and Coronal Explorer (TRACE)} and the {sl Extremeultraviolet 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 nearisothermal along their coronal segments, (2) they show an overpressure or overdensity compared with the requirements of steadystate 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 steadystate 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 4300 Mm), of nonuniform heating functions (with heating scale heights in the range of {lambda}_H approx 1300 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{L_{Mm}}) 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 steadystate equilibrium, and 10% are cooling off. Those loops near steadystate 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 steadystate. 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:

Publication Status: ApJ, subm. (2000 Aug 7)
Last Modified: 20000818 13:05



Evidence for Nonuniform Heating of Coronal Loops Inferred from MultiThread Modeling of TRACE Data 

Markus J Aschwanden Submitted: 20000526 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 multithread model,
synthesized from the summed emission of many loop threads that have a
distribution of maximum temperatures and that satisfy the steadystate RosnerT
RosnerTuckerVaiana (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 filterratio method. From modelfitting of the 171 and 195 ang fluxes of
41 loops, which have loop half lengths in the range of L=4320 Mm, we find:
(1) The EUV loops consist of nearisothermal 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_{e}approx 0.81.6 MK cannot be explained with the static
steadystate RTVS_p model in terms of uniform heating, but are fully
consistent with Serio's model in the case of nonuniform heating (RTVS_{ph}),
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 50300 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:

Publication Status: ApJ 541:10591077 (2000 October 1)
Last Modified: 20001006 08:35



Tomography of the Soft XRay Corona: Measurements of Electron Densities, Temperatures, and Differential Emission Measure Distributions above the Limb 

Markus J Aschwanden Submitted: 20000504 16:02
We analyze longexposure and offpointing {sl Yohkoh/SXT} data of the solar
corona observed on 1992 Aug 26. We develop a new tomographic method which is
based on a forwardfitting method of a 4parameter model to the observed soft
Xray 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) =q_{lambda}
{lambda}_T and allows to quantify deviations (q_{lambda}
eq 1) from
hydrostatic equilibrium, i.e. {lambda}_n(T)={lambda}_T. This parametrization
faciliates a proper lineofsight integration and relates the widelyused
filterratio temperature T_{FR} to the peak of the DEM distribution. A direct
consequence of the multiscaleheight atmosphere is that the filter ratio
temperature T_{FR}(h) is predicted to increase with height, even if all
magnetic field lines are isothermal. Our modelfitting 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 q_{lambda}lapprox 2.3, which underscores the dynamic
nature of coronal streamers. Our density measurements in coronal holes are
slightly lower than most of the whitelight 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 semiempirical {sl BaumbachAllen
formula}, and quantifies the temperature ranges and degree of hydrostaticity of
the {sl K, L, } and {sl Fcorona}.
Authors: Markus J. Aschwanden and Loren W. Acton
Projects:

Publication Status: ApJ 550, 475492
Last Modified: 20010409 07:52



The Effect of Hydrostatic Weighting on the Vertical Temperature Structure of the Solar Corona 

Markus J Aschwanden Submitted: 20000407 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 lineofsight from optically thin emission (e.g. in EUV or soft Xray
wavelengths) of a mutlitemperature plasma, is subject to the emission measure
measureweighted 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
heightdependent 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/r_{sun}). 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:

Publication Status: 2000, ApJ 535, L59L62
Last Modified: 20000831 08:01



Quadrupolar Magnetic Reconnection in Solar Flares: I. 3D Geometry inferred from Yohkoh Observations 

Markus J Aschwanden Submitted: 20000125 14:02
We analyze the 3dimensional (3D) geometry of solar flares that show socalled {sl interacting flare loops} in soft Xray, hard Xray, 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 prereconnecti prereconnection field lines have to intersect each other at the onset of the reconnection process, leading to a 10parameter model. We fit this 10parameter 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 currentcarrying field lines reconnect to form a new currentcarrying system in a quadrupolar geometry. The findings and conclusions are: (1) The prereconnection field lines always show a strong asymmetry in size, consistent with the scenario of newemerging smallscale loops that reconnect with preexisting largescale loops. (2) The relative angle between reconnecting field lines is nearcollinear in half of the cases, and nearperpendicular in the other half, contrary to the antiparallel 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 smallscale flare loop experiences a shrinkage by a factor of 1.31pm0.44, which is consistent with the scaling law found from previous electron timeofflight measurements, suggesting that electron acceleration occurs near the cusp of quadrupolar configurations. (5) The largescale loop is found to dominate the total induction between currentcarrying 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 10^{29.63} (r_2/10^{9} {
m cm}) (I_2/10^{11} A)^2, (with r_{2} the curvature radius and I_{2} the current of the largescale loop) and is found to correlate with observed flare energies deduced from soft Xray and hard Xray fluxes. Most of the energy is transferred to smallscale loops that have half of the largescale 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 doubleloop flares, but can also be considered as a generalized version of (cuspshaped) singleloop flares.
Authors: Aschwanden,M.J., Kosugi,T., Hanaoka,Y., Nishio,M., and Melrose,D.B.
Projects:

Publication Status: Astrophys.J. 1999, Vol. 526, p. 10261045.
Last Modified: 20000125 14:02



3DStereoscopic Analysis of Solar Active Region Loops: 

Markus J Aschwanden Submitted: 20000125 14:02
In this paper we study the threedimensional (3D) structure of hot (T_{e}approx
1.52.5 MK) loops in solar active region NOAA 7986, observed on 1996 August 30
with the {sl Extremeultraviolet Imaging Telescope (EIT)} onboard the {sl
Solar and Heliospheric Observatory (SoHO)}. This complements a first study
(Paper I) on cooler (T_{e}approx 1.01.5 MK) loops of the same active region,
using the same method of {sl Dynamic Stereoscopy} to reconstruct the 3D
geometry. We reconstruct the 3Dcoordinates 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}=1.02.5 MK; (2) The
analyzed loops have a height of 23 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 110 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 steadystate loop models show that radiative and
conductive losses are comparable; (5) A steadystate 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 steadystate models of largescale loops.  All
observational findings indicate consistently that the energy balance of the
observed EUV loops cannot be described by steadystate models.
Authors: Aschwanden,M.J., Alexander,D., Hurlburt,N., Newmark,J.S.,Neupert,W.M., Klimchuk,J.A., and G.A.Gary
Projects:

Publication Status: 1999, ApJ 515, 842867
Last Modified: 20000831 08:27



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