Global Energetics of Solar Flares: VI. Refined Energetics of Coronal Mass Ejections 

Markus J. Aschwanden Submitted: 20170406 13:14
In this study we refine a CME model presented in an earlier study
on the global energetics of solar flares and associated CMEs, and
apply it to all (860) GOES M and Xclass flare events observed
during the first 7 years (20102016) of the Solar Dynamics Observatory
(SDO) mission, which doubles the statistics of the earlier study.
The model refinements include: (1) the CME geometry in terms of a
3D sphere undergoing selfsimilar adiabatic expansion; (2) the
inclusion of solar gravitational deceleration during the acceleration
and propagation of the CME, which discriminates eruptive and confined
CMEs; (4) a selfconsistent relationship between the CME centerofmass
motion detected during EUV dimming and the leadingedge motion observed
in whitelight coronagraphs; (5) the equipartition of the CME kinetic and
thermal energy; and (6) the RosnerTuckerVaiana (RTV) scaling law. The
refined CME model is entirely based on EUV dimming observations (using
AIA/SDO data) and complements the traditional whitelight scattering model
(using LASCO/SOHO data), and both models are independently capable to
determine fundamental CME parameters such as the CME mass, speed,
and energy. Comparing the two methods we find that: (1) LASCO is
less sensitive than AIA in detecting CMEs (in 24% of the cases);
(2) CME masses below m_cme ~ 10^{14} g are underestimated
by LASCO; (3) AIA and LASCO masses, speeds, and energy agree closely in the
statistical mean after elimination of outliers; (4) the CMEs parameters
of the speed v, emission measureweighted flare peak temperature T_{e},
and length scale L are consistent with the following scaling laws
(derived from first principles): v ~ T_{e}^1/2, v~ (m_cme)^1/4, and m_cme ~ L^{2}.
Authors: Markus J. Aschwanden
Projects:

Publication Status: 2017, ApJ 847:27 (19pp)
Last Modified: 20170925 09:09



SelfOrganizing Systems in Planetary Physics: Harmonic Resonances of Planet and Moon orbits 

Markus J. Aschwanden Submitted: 20170127 12:58
The geometric arrangement of planet and moon orbits into a
regularly spaced pattern of distances is the result of a
selforganizing system. The positive feedback mechanism
that operates a selforganizing system is accomplished by
harmonic orbit resonances, leading to longterm stable
planet and moon orbits in solar or stellar systems.
The distance pattern of planets was originally
described by the empirical TitiusBode law, and by a generalized
version with a constant geometric progression factor (corresponding
to logarithmic spacing).
We find that the orbital periods T_{i} and planet distances R_{i} from
the Sun are not consistent with
logarithmic spacing, but rather follow the quantized scaling
(R_{i+1}/R_{i}) = (T_{i+1}/T_{i})^{2/3} = (H_{i+1}/H_{i})^{2/3}, where
the harmonic ratios are given by five dominant resonances, namely
(H_{i+1} : H_{i}) = (3:2), (5:3), (2:1), (5:2), (3:1).
We find that the orbital period ratios tend to follow the quantized harmonic
ratios in increasing order. We apply this harmonic orbit resonance model
to the planets and moons in our solar system, and to the exoplanets
of 55 Cnc and HD 10180 planetary systems.
The model allows us a prediction of missing planets
in each planetary system, based on the quasiregular selforganizing
pattern of harmonic orbit resonance zones. We predict 7 (and 4) missing
exoplanets around the star 55 Cnc (and HD 10180).
The accuracy of the predicted planet and moon distances amounts
to a few percents. All analyzed systems are found to have
approx 10 resonant zones that can be occupied with planets
(or moons) in longterm stable orbits.
Authors: Markus J. Aschwanden
Projects:

Publication Status: 2018, New Astronomy 58C, 107123
Last Modified: 20170925 09:16



The Width Distribution of Loops and Strands in the Solar Corona  Are we Hitting Rock Bottom ? 

Markus J. Aschwanden Submitted: 20170104 16:32
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 a lower limit of widths w_{min}, a peak
width w_{p}, a peak occurrence number n_{p}, and a power law 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 MonteCarlo simulations and variable pixel
sizes Δ x we derive a first diagnostic criterion to discriminate
whether the loop widths are unresolved (w_{p}/Δ x ≈ 2.5±0.2),
or fully resolved (if w_{p}/Δ x ≳ 2.7). For images with
resolved loop widths we can apply a second diagnostic criterion that
predicts the lower limit of loop widths, w_{min} ≈ 3
(Δ x_{crit}0.37") Mm) as a function of the critical resolution
Δ x_{crit}. We find that the loop widths are marginally resolved
in AIA images, but are fully resolved in HiC images, where our model
predicts a lower limit of loop widths at w_{min} ≈ 100 km and
a most frequent (peak) value at w_{p} ≈ 300 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 heating models with unresolved
microscopic scales.
Authors: Markus J. Aschwanden and Hardi Peter
Projects: HiC

Publication Status: The Astrophysical Journal (2017 Jan 4, subm.)
Last Modified: 20170111 12:08



Global Energetics of Solar Flares and CMEs: V. Energy Closure 

Markus J. Aschwanden Submitted: 20170104 16:28
In this study we synthesize the results of four previous studies
on the global energetics of solar flares and associated coronal
mass ejections (CMEs), which include magnetic, thermal, nonthermal,
and CME energies in 399 solar M and Xclass flare events observed
during the first 3.5 years of the Solar Dynamics Observatory (SDO)
mission. Our findings are: (1) The sum of the mean nonthermal energy
of flareaccelerated particles (E_{nt}), the energy of direct heating
(E_{dir}), and the energy in coronal mass ejections (E_{CME}),
which are the primary energy dissipation processes in a flare, is found
to have a ratio of (E_{nt}+E_{dir}+
E_{CME})/E_{mag} = 0.87 ± 0.18,
compared with the dissipated magnetic free energy E_{mag}, which confirms
energy closure within the measurement uncertainties and corroborates the
magnetic origin of flares and CMEs;
(2) The energy partition of the dissipated magnetic free energy is:
0.51±0.17 in nonthermal energy of ≥ 6 keV electrons,
0.17±0.17 in nonthermal ≥ 1 MeV ions, 0.07±0.14 in
CMEs, and 0.07±0.17 in direct heating;
(3) The thermal energy is almost always less
than the nonthermal energy, which is consistent with the thicktarget model;
(4) The bolometric luminosity in whitelight flares is comparable with
the thermal energy in soft Xrays (SXR); (5) Solar Energetic Particle (SEP)
events carry a fraction ≈ 0.03 of the CME energy, which is consistent
with CMEdriven shock acceleration;
and (6) The warmtarget model predicts a lower limit of the
lowenergy cutoff at e_{c} ≈ 6 keV, based on the mean differential
emission measure (DEM) peak temperature of T_{e}=8.6 MK during flares.
This work represents the first statistical study that establishes energy
closure in solar flare/CME events.
Authors: Markus J. Aschwanden, Amir Caspi, Christina M.S. Cohen, Gordon Holman, Ju Jing, Matthieu, Kretzschmar, Eduard P. Kontar, James M. McTiernan, Richard A. Mewaldt, Aidan O'Flannagain, Ian G. Richardson, Daniel Ryan, Harry P. Warren, Yan Xu
Projects: SDOAIA

Publication Status: The Astrophysical Journal (accepted 2017 Jan 4, in press)
Last Modified: 20170111 12:08



Global Energetics of Solar Flares: IV. Coronal Mass Ejection Energetics 

Markus J. Aschwanden Submitted: 20160516 14:50
This study entails the fourth part of a global flare energetics project, in which the mass m_{cme}, kinetic energy E_{kin}, and the gravitational potential energy E_{grav} of coronal mass ejections (CMEs) is measured in 399 M and Xclass flare events observed during the first 3.5 yrs of the Solar Dynamics Observatory (SDO) mission, using a new method based on the EUV dimming effect. The EUV dimming is modeled in terms of a radial adiabatic expansion process, which is fitted to the observed evolution of the total emission measure of the CME source region. The model derives the evolution of the mean electron density, the emission measure, the bulk plasma expansion velocity, the mass, and the energy in the CME source region. The EUV dimming method is truly complementary to the Thomson scattering method in white light, which probes the CME evolution in the heliosphere at ≳2 R_{⊙}, while the EUV dimming method tracks the CME launch in the corona. We compare the CME parameters obtained in white light with the LASCO/C2 coronagraph with those obtained from EUV dimming with the Atmospheric Imaging Assembly (AIA) onboard SDO for all identical events in both data sets. We investigate correlations between CME parameters, the relative timing with flare parameters, frequency occurrence distributions, and the energy partition between magnetic, thermal, nonthermal, and CME energies. CME energies are found to be systematically lower than the dissipated magnetic energies, which is consistent with a magnetic origin of CMEs.
Authors: Aschwanden, M.J.
Projects: SDOAIA

Publication Status: ApJ, subm. 2016 May 16
Last Modified: 20160516 20:09



Tracing the Chromospheric and Coronal Magnetic Field with AIA, IRIS, IBIS, and ROSA Data 

Markus J. Aschwanden Submitted: 20160205 11:42
The aim of this study is to explore the suitability of chromospheric images for magnetic modeling of active regions. We use highresolution images (0.1") from the Interferometric Bidimensional Spectrometer (IBIS) in the Ca II 8542 Å line, the Rapid Oscillations in the Solar Atmosphere (ROSA) instrument in the Hα 6563 Å line, the Interface Region Imaging Spectrograph (IRIS) in the 2796 Å line, and compare nonpotential magnetic field models obtained from those chromospheric images with those obtained from images of the Atmospheric Imaging Assembly (AIA) in coronal (171 Å, etc.) and in chromospheric (304 Å) wavelengths. Curvilinear structures are automatically traced in those images with the OCCULT2 code, to which we forwardfitted magnetic field lines computed with the VerticalCurrent Approximation NonLinear Force Free Field (VCANLFFF) code. We find that the chromospheric images: (1) reveal crisp curvilinear structures (fibrils, loop segments, spicules) that are extremely wellsuited for constraining magnetic modeling; (2) that these curvilinear structures are fieldaligned with the bestfit solution by a median misalignment angle of ~47 deg; (3) the free energy computed from coronal data may underestimate that obtained from cromospheric data by a factor of ~ 24, (4) the height range of chromospheric features is confined to h ~ 4000 km, while coronal features are detected up to h ~ 35,000 km; and (5) the plasmabeta parameter is beta ~ 10^{5}10^{1} for all traced features. We conclude that chromospheric images reveal important magnetic structures that are complementary to coronal images and need to be included in comprehensive magnetic field models, a quest that is not accomodated in standard NLFFF codes.
Authors: Aschwanden, M.J., Reardon, K., and Jess, D.
Projects: SDOAIA

Publication Status: ApJ, subm. 2016 Feb 5
Last Modified: 20160209 14:59



The Vertical Current Approximation Nonlinear ForceFree Field Code  Description, Performance Tests, and Measurements of Magnetic Energies Dissipated in Solar Flares 

Markus J. Aschwanden Submitted: 20160201 11:19
In this work we provide an updated description of the Vertical
Current Approximation Nonlinear ForceFree Field (VCANLFFF)
code, which is designed to measure the evolution of the potential,
nonpotential, free energies, and the dissipated magnetic energies
during solar flares. This code provides a complementary and
alternative method to existing traditional NLFFF codes.
The chief advantages of the VCANLFFF code over traditional NLFFF
codes are the circumvention of the unrealistic assumption of a
forcefree photosphere in the magnetic field extrapolation method,
the capability to minimize the misalignment angles between observed
coronal loops (or chromospheric fibril structures) and theoretical
model field lines, as well as computational speed.
In performance tests of the VCANLFFF code, by comparing with the
NLFFF code of Wiegelmann (2004), we find agreement in the potential,
nonpotential, and free energy within a factor of about 1.3,
but the Wiegelmann code yields in the average a factor of 2 lower
flare energies. The VCANLFFF code is found to detect decreases
in flare energies in most X, M, and Cclass flares.
The successful detection of energy decreases during a variety
of flares with the VCANLFFF code indicates that currentdriven
twisting and untwisting of the magnetic field is an adequate
model to quantify the storage of magnetic energies in active
regions and their dissipation during flares.  The VCANLFFF
code is also publicly available in the Solar SoftWare (SSW).
Authors: Markus J. Aschwanden
Projects: SDOAIA

Publication Status: ApJ Suppl.Ser., subm. 2016 Feb 1
Last Modified: 20160203 09:17



Thresholded Power Law Size Distributions of Instabilities in Astrophysics 

Markus J. Aschwanden Submitted: 20151007 09:11
Power lawlike size distributions are ubiquitous in astrophysical
instabilities. There are at least four natural effects that cause
deviations from ideal power law size distributions, which we model here
in a generalized way: (1) a physical threshold of an instability; (2)
incomplete sampling of the smallest events below a threshold x_{0};
(3) contamination by an eventunrelated background x_{b}; and
(4) truncation effects at the largest events due to a finite system size.
These effects can be modeled in simplest terms with a
``thresholded power law'' distribution function (also called generalized
Pareto [type II] or Lomax distribution), N(x) dx ∝ (x+x_0)^{a} dx,
where x_0 > 0 is positive for a threshold effect, while x_0 < 0 is
negative for background contamination.
We analytically derive the functional shape of this thresholded power law
distribution function from an exponentialgrowth evolution model, which
produces avalanches only when a disturbance exceeds a critical
threshold x_{0}. We apply the thresholded power law distribution function
to terrestrial, solar (HXRBS, BATSE, RHESSI), and stellar flare (Kepler)
data sets. We find that the thresholded power law model provides
an adequate fit to most of the observed data. Major advantages of
this model are the automated choice of the power law fitting range,
diagnostics of background contamination, physical inastability thresholds,
instrumental detection thresholds, and finite system size limits. When
testing selforganized criticality models, which predict ideal power laws, we
suggest to include these natural truncation effects.
Authors: Markus J. Aschwanden
Projects: None

Publication Status: The Astrophysical Journal (accepted 2015Oct7, in press)
Last Modified: 20151007 12:57



Benchmark Test of Differential Emission Measure Codes and MultiThermal Energies in Solar Active Regions 

Markus J. Aschwanden Submitted: 20150923 10:09
We compare the ability of 11 Differential Emission Measure (DEM) forwardfitting and inversion methods to constrain the properties of active regions and solar flares by simulating synthetic data using the instrumental response functions of SDO/AIA, SDO/EVE, RHESSI, and GOES/XRS. The codes include the singleGaussian DEM, a biGaussian DEM, a fixedGaussian DEM, a linear spline DEM, the spatial synthesis DEM, the MonteCarlo Markov chain DEM, the regularized DEM inversion, the Hinode/XRT method, a polynomial spline DEM, an EVE+GOES, and an EVE+RHESSI method. Averaging the results from all 11 DEM methods, we find the following accuracies in the inversion of physical parameters: the EMweighted temperature T_w^{fit}/T_w^{sim}=0.9pm0.1, the peak emission measure EM_p^{fit}/EM_p^{sim}=0.6pm0.2, the total emission measure EM_t^{fit}/EM_t^{sim}=0.8pm0.3, and the multithermal energies E_{th}^{fit}/EM_{th}^{sim}=1.2pm0.4. We find that the AIA spatial synthesis, the EVE+GOES, and the EVE+RHESSI method yield the most accurate results.
Authors: Aschwanden, M. J., Boerner, P., Caspi, A., McTiernan, J. M., Ryan, D., and Warren, H. P.
Projects: GOES Xrays ,RHESSI,SDOAIA,SDOEVE

Publication Status: Solar Physics, (accepted 2015 Sep 23), in press
Last Modified: 20150926 14:55



Blind Stereoscopy of the Coronal Magnetic Field 

Markus J. Aschwanden Submitted: 20150615 13:13
We test the feasibility of 3D coronalloop tracing in stereoscopic
EUV image pairs, with the ultimate goal of enabling efficient 3D
reconstruction of the coronal magnetic field that drives flares and
coronal mass ejections (CMEs). We developed an automated code
designed to perform triangulation of coronal loops in pairs (or
triplets) of EUV images recorded from different perspectives. The
automated (or blind) stereoscopy code includes three major tasks:
(i) automated pattern recognition of coronal loops in EUV images,
(ii) automated pairing of corresponding loop patterns from two
different aspect angles, and (iii) stereoscopic triangulation of 3D
loop coordinates. We perform tests with simulated stereoscopic EUV
images and quantify the accuracy of all three procedures. In
addition we test the performance of the blind stereoscopy code as a
function of the spacecraftseparation angle and as a function of the
spatial resolution. We also test the sensitivity to magnetic
nonpotentiality. The automated code developed here can be used for
analysis of existing Solar TErrestrial RElationship Observatory
(STEREO) data, but primarily serves for a design
study of a future mission with dedicated diagnostics of
nonpotential magnetic fields. For a pixel size of 0.6"
(corresponding to the Solar Dynamics Observatory (SDO)
Atmospheric Imaging Assembly (AIA) spatial resolution of 1.4"),
we find an optimum spacecraftseparation angle of α _s
≈ 5°.
Authors: Aschwanden,J.M., Schrijver, C.J., and Malanushenko, A.
Projects: None

Publication Status: Solar Physics, (accepted 2015 Jun 15), in press
Last Modified: 20150617 12:58



Global Energetics of Solar Flares: II. Thermal Energies 

Markus J. Aschwanden Submitted: 20150219 14:23
We present the second part of a project on the global energeticsof solar flares and coronal mass ejections (CMEs) that includes about400 M and Xclass flares observed with the Atmospheric Imaging Assembly AIA) onboard the Solar Dynamics Observatory (SDO) during the first 3.5 yearsof its mission. In this Paper II we compute the differential emissionmeasure (DEM) distribution functions and associated multithermal energies,using a spatiallysynthesized Gaussian DEM forwardfitting method.The multithermal DEM function yields a significantly higher (by anaverage factor of ≈ 14), but more comprehensive(multi)thermal energy than an isothermal energy estimate fromthe same AIA data.We find a statistical energy ratio of E_{th}/E_{diss} ≈ 2%40%between the multithermal energy E_{th} and themagnetically dissipated energy E_{diss},which is an order of magnitude higher than the estimatesof Emslie et al. 2012. For the analyzed set of M and Xclass flareswe find the following physical parameter ranges:L=10^{8.2}10^{9.7} cm for the length scale of the flare areas,T_p=10^{5.7}10^{7.4} K for the DEM peak temperature,T_w=10^{6.8}10^{7.6} K for the emission measureweighted temperature,n_p=10^{10.3}10^{11.8} cm^{3} for the average electron density,EM_p=10^{47.3}10^{50.3} cm^{3} for the DEM peak emission measure,and E_{th}=10^{26.8}10^{32.0} erg for the multithermal energies.The deduced multithermal energies are consistentwith the RTV scaling law E_{th,RTV} = 7.3 x 10^{10} T_{p}^{3} L_{p}^{2}, which predicts extremal values ofE_{th,max} ≈ 1.5 x 10^{33} erg for the largest flareand E_{th,min} ≈ 1 x 10^{24} erg for the smallestcoronal nanoflare.The size distributions of the spatial parameters exhibit powerlaw tails thatare consistent with the predictions of the fractaldiffusiveselforganized criticality model combined with the RTV scaling law.
Authors: Aschwanden,J.M., Boerner, P., Ryan, D., Caspi, A., McTiernan, J.M., and Warren, H.P.
Projects: SDOAIA

Publication Status: The Astrophysical Journal, (accepted 2015Feb19, in press)
Last Modified: 20150221 19:18



Global Energetics of Solar Flares: I. Magnetic Energies 

Markus J. Aschwanden Submitted: 20141028 08:46
We present the first part of a project on the global energetics of
solar flares and coronal mass ejections (CMEs) that includes about
400 M and Xclass flares observed with AIA and HMI onboard SDO.
We calculate the potential (E_{p}), the nonpotential (E_{np})
or free energies (E_{free} =E_{np}E_p), and the flaredissipated
magnetic energies (E_{diss}). We calculate these magnetic parameters
using two different NLFFF codes: The CORNLFFF code uses the lineofsight
magnetic field component B_{z} from HMI to define the potential field,
and the 2D coordinates of automatically detected coronal loops in 6
coronal wavelengths from AIA to measure the helical twist of coronal
loops caused by vertical currents, while the PHOTNLFFF code
extrapolates the photospheric 3D vector fields. We find agreement between
the two codes in the measurement of free energies and dissipated
energies within a factor of \lapprox 3. The size distributions of
magnetic parameters exhibit powerlaw slopes that are approximately
consistent with the fractaldiffusive selforganized criticality
model. The magnetic parameters exhibit scaling laws for the
nonpotential energy, E_{np} ∝ E_p^{1.02}, for the
free energy, E_{free} ∝ E_p^{1.7} and E_{free} ∝
B_{ϕ}^{1.0} L^{1.5}, for the dissipated
energy, E_{diss} ∝ E_p^{1.6} and E_{diss} ∝ E_{free}^{0.9},
and the energy dissipation volume, V ∝ E_{diss}^{1.2}.
The potential energies vary in the range of
E_p = 1 x 10^{31}  4 x 10^{33} erg, while the free energy
has a ratio of E_{free}/E_p ≈ 1%25%. The Poynting flux amounts to
F_{flare} ≈ 5 x 10^{8}  10^{10} erg cm^{2} s^{1}
during flares,
which averages to F_{AR} ≈ 6 x 10^{6} erg cm^{2} s^{1}
during the entire observation period and is comparable with the
coronal heating rate requirement in active regions.
Authors: Markus J. Aschwanden, Yan Xu, and Ju Jing
Projects: SDOHMI

Publication Status: ApJ (accepted 2014oct28, in press)
Last Modified: 20141028 13:37



25 Years of SelfOrganized Criticality: Solar and Astrophysics 

Markus J. Aschwanden Submitted: 20140325 16:18
Shortly after the seminal paper ``SelfOrganized
Criticality: An explanation of 1/f noise'' by Bak, Tang, and Wiesenfeld
(1987), the idea has been applied to solar physics, in``Avalanches
and the Distribution of Solar Flares'' by Lu and Hamilton (1991).
In the following years, an inspiring crossfertilization from complexity
theory to solar and astrophysics took place, where the SOC concept was
initially applied to solar flares, stellar flares, and magnetospheric
substorms, and later extended to the radiation belt, the heliosphere,
lunar craters, the asteroid belt, the Saturn ring,
pulsar glitches, soft Xray repeaters, blazars, blackhole
objects, cosmic rays, and boson clouds. The application of SOC concepts
has been performed by numerical cellular automaton simulations, by
analytical calculations of statistical (powerlawlike) distributions
based on physical scaling laws, and by observational tests of theoretically
predicted size distributions and waiting time distributions. Attempts have been
undertaken to import physical models into the numerical SOC toy models,
such as the discretization of magnetohydrodynamics (MHD) processes.
The novel applications stimulated also vigorous debates about the
discrimination between SOC models, SOClike, and nonSOC processes,
such as phase transitions, turbulence, randomwalk diffusion,
percolation, branching processes, network theory, chaos theory,
fractality, multiscale, and other complexity phenomena.
We review SOC studies from the last 25 years and highlight new trends,
open questions, and future challenges, as discussed during two recent
ISSI workshops on this theme.
Authors: Aschwanden, M.J., Crosby, N., Dimitropoulou, M., Geogoulis, M.K., Hergarten, S., McAteer, J., Milovanov, A.V., Mineshige, S., Morales, L., Nishizuka, N., Pruessner, G., Sanchez, R., Sharma, S., Strugarek, A., and Uritsky, V.
Projects: None

Publication Status: Space Science Reviews (subm. March 24, 2014)
Last Modified: 20140326 12:35



The Magnetic Field of Active Region 11158 During the 2011 February 1217 Flares : Differences between Photospheric Extrapolation and Coronal ForwardFitting Methods 

Markus J. Aschwanden Submitted: 20140221 09:14
We developed a {sl coronal nonlinear forcefree field (CORNLFFF)}
forwardfitting code that fits an approximate {sl nonlinear forcefree
field (NLFFF)} solution to the observed geometry of automatically traced
coronal loops. In contrast to photospheric NLFFF codes, which calculate
a magnetic field solution from the constraints of the transverse
photospheric field, this new code uses coronal constraints instead, and
this way provides important information on systematic errors of
each magnetic field calculation method, as well as on the nonforcefreeness
in the lower chromosphere. In this study we applied the CORNLFFF code
to active region NOAA 11158, during the time interval of 2011 Feb 12 to 17,
which includes an X2.2 GOESclass flare plus 35 M and Cclass flares.
We calcuated the free magnetic energy with a 6minute cadence over
5 days. We find good agreement between the two types of codes for
the total nonpotential E_{N} and potential energy E_{P}, but find
up to a factor of 4 discrepancy in the free energy E_{free}=E_NE_P,
and up to a factor of 10 discrepancy in the decrease of the free energy
Delta E_{free} during flares. The coronal NLFFF code exhibits
a larger time variability, and yields
a decrease of free energy during the flare that is sufficient to satisfy
the flare energy budget, while the photospheric NLFFF code shows much
less time variability and an order of magnitude less free energy
decrease during flares. The discrepancy may partly be due to the
preprocessing of photospheric vector data, but more likely due to
the nonforcefreeness in the lower chromosphere. We conclude that
the coronal field cannot be correctly calculated based on photospheric
data alone, but requires additional information on coronal loop
geometries.
Authors: Aschwanden, M.J., Sun, X.D., and Liu, Y.
Projects: SDOAIA

Publication Status: The Astrophysical Journal 785, 34
Last Modified: 20140325 16:21



A Macroscopic Description of SelfOrganized Criticality Systems and Astrophysical Applications 

Markus J. Aschwanden Submitted: 20131015 14:18
We suggest a generalized definition of selforganized criticality (SOC)
systems: SOC is a critical state of a nonlinear energy dissipation
system that is slowly and continuously driven towards a critical value
of a systemwide instability threshold, producing scalefree,
fractaldiffusive, and intermittent avalanches with powerlawlike size
distributions. We develop here a macroscopic description of SOC systems
that provides an equivalent description of the complex microscopic fine
structure, in terms of fractaldiffusive transport (FDSOC). Quantitative
values for the size distributions of SOC parameters (length scales L,
time scales T, fluxes F, and energies E) are derived from first
principles, using the scalefree probability theorem, N(L) dL propto
L^{d}, for Euclidean space dimension d. We apply this model to
astrophysical SOC systems, such as lunar craters, the asteroid belt,
Saturn ring particles, magnetospheric substorms, radiation belt electrons,
solar flares, stellar flares, pulsar glitches, soft gammaray repeaters,
blackhole objects, blazars, and cosmic rays. The FDSOC model predicts
correctly the size distributions of 7 out of these 12 astrophysical
phenomena, and indicates nonstandard scaling laws and measurement biases
for the others.
Authors: Markus J. Aschwanden
Projects:

Publication Status: The Astrophysical Journal 782, 54
Last Modified: 20140325 16:23



MultiWavelength Observations of the SpatioTemporal Evolution of Solar Flares with AIA/SDO: II. Hydrodynamic Scaling Laws and Thermal Energies 

Markus J. Aschwanden Submitted: 20130823 12:16
In this study we measure physical parameters of the same set of 155 M and Xclass
solar flares observed with AIA/SDO as analyzed in Paper I, by performing a
{sl differential emission measure (DEM)} analysis to determine the flare
peak emission measure EM_p, peak temperature T_{p}, electron density n_{p},
and thermal energy E_{th}, in addition to the spatial scales L, areas A,
and volumes V measured in Paper I. The parameter ranges for M and Xclass
flares are: log(EM_p)=47.050.5, T_p=5.017.8 MK,
n_p=4 imes 10^{9}9 imes 10^{11} cm^{3}, and thermal energies of
E_{th}=1.6 imes 10^{28}1.1 imes 10^{32} erg.
We find that these parameters obey the RosnerTuckerVaiana (RTV) scaling law
T_p^2 propto n_p L and H propto T^{7/2} L^{2} during the peak time t_{p}
of the flare density n_{p}, when energy balance between the heating rate H
and the conductive and radiative loss rates is achieved for a short instant,
and thus enables the applicability of the RTV scaling law.
The application of the RTV scaling law predicts powerlaw
distributions for all physical parameters, which we demonstrate with numerical
MonteCarlo simulations as well as with analytical calculations. A consequence
of the RTV law is also that we can retrieve the size distribution of heating
rates, for which we find N(H) propto H^{1.8}, which is consistent with
the magnetic flux distribution N(Phi) propto Phi^{1.85} observed by
Parnell et al. (2009) and the heating flux scaling law
F_H propto H L propto B/L of Schrijver et al. (2004).
The fractaldiffusive selforganized criticality model in conjunction with
the RTV scaling law reproduces the observed powerlaw distributions and their
slopes for all geometrical and physical parameters and can be used to predict
the size distributions for other flare datasets, instruments, and detection
algorithms.
Authors: Markus J. Aschwanden and Toshifumi Shimizu
Projects:

Publication Status: The Astrophysical Journal 776, 132
Last Modified: 20140325 16:25



MultiWavelength Observations of the SpatioTemporal Evolution of Solar Flares with AIA/SDO:I. Universal Scaling Laws of Space and Time Parameters 

Markus J. Aschwanden Submitted: 20130822 11:43
We extend a previous statistical solar flare study of 155 GOES
M and Xclass flares observed with AIA/SDO (Aschwanden 2012)
to all 7 coronal wavelengths (94, 131, 171, 193, 211, 304, 335 ang )
to test the wavelengthdependence of scaling laws and statistical
distributions. Except for the 171 and 193 ang wavelengths, which
are affected by EUV dimming caused by coronal mass ejections (CMEs),
we find nearidentical
size distributions of geometric (lengths L, flare areas A, volumes
V, fractal dimension D_{2}), temporal (flare durations T), and
spatiotemporal parameters (diffusion coefficient kappa, spreading
exponent eta, and maximum expansion velocities v_{max}) in
different wavelengths, which are consistent with the universal
predictions of the fractaldiffusive avalanche model of a
slowlydriven selforganized criticality (FDSOC) system,
i.e., N(L) propto L^{3}, N(A) propto A^{2},
N(V) propto V^{5/3}, N(T) propto T^{2},
D_2=3/2, for a Euclidean dimension d=3.
Empirically we find also a new strong correlation kappa propto
L^{0.94pm0.01} and the 3parameter scaling law L propto kappa T^{0.1},
which is more consistent with the logisticgrowth model than with
classical diffusion. The findings suggest longrange correlation
lengths in the FDSOC system that operate in the vicinity of a critical state,
which could be used for predictions of individual extreme events.
We find also that eruptive flares (with accompanying CMEs),
have larger volumes V, longer flare durations T, higher EUV and
soft Xray fluxes, and somewhat larger diffusion coefficients kappa
than confined flares (without CMEs).
Authors: Aschwanden,J.M., Zhang, J., Liu,K.
Projects: None

Publication Status: (2013), ApJ 775, 23
Last Modified: 20131007 18:23



MultiWavelength Observations of the SpatioTemporal Evolution of Solar Flares with AIA/SDO:I. Universal Scaling Laws of Space and Time Parameters 

Markus J. Aschwanden Submitted: 20130822 11:43
We extend a previous statistical solar flare study of 155 GOES
M and Xclass flares observed with AIA/SDO (Aschwanden 2012)
to all 7 coronal wavelengths (94, 131, 171, 193, 211, 304, 335 ang )
to test the wavelengthdependence of scaling laws and statistical
distributions. Except for the 171 and 193 ang wavelengths, which
are affected by EUV dimming caused by coronal mass ejections (CMEs),
we find nearidentical
size distributions of geometric (lengths L, flare areas A, volumes
V, fractal dimension D_{2}), temporal (flare durations T), and
spatiotemporal parameters (diffusion coefficient kappa, spreading
exponent eta, and maximum expansion velocities v_{max}) in
different wavelengths, which are consistent with the universal
predictions of the fractaldiffusive avalanche model of a
slowlydriven selforganized criticality (FDSOC) system,
i.e., N(L) propto L^{3}, N(A) propto A^{2},
N(V) propto V^{5/3}, N(T) propto T^{2},
D_2=3/2, for a Euclidean dimension d=3.
Empirically we find also a new strong correlation kappa propto
L^{0.94pm0.01} and the 3parameter scaling law L propto kappa T^{0.1},
which is more consistent with the logisticgrowth model than with
classical diffusion. The findings suggest longrange correlation
lengths in the FDSOC system that operate in the vicinity of a critical state,
which could be used for predictions of individual extreme events.
We find also that eruptive flares (with accompanying CMEs),
have larger volumes V, longer flare durations T, higher EUV and
soft Xray fluxes, and somewhat larger diffusion coefficients kappa
than confined flares (without CMEs).
Authors: Aschwanden,J.M., Zhang, J., Liu,K.
Projects: None

Publication Status: (2013), ApJ 775, 23
Last Modified: 20140325 16:26



Optimization of CurviLinear Tracing Applied to Solar Physics and Biophysics 

Markus J. Aschwanden Submitted: 20130718 12:23
We developed an automated pattern recognition code that is
particularly well suited to extract onedimensional curvilinear features
from twodimensional digital images. A former version of this
{sl Oriented Coronal CUrved Loop Tracing (OCCULT)} code was applied
to spacecraft images of magnetic loops in the solar corona, recorded
with the NASA spacecraft {sl Transition Region And Coronal Explorer (TRACE)}
in extreme ultraviolet wavelengths. Here we apply an advanced version of this
code ({sl OCCULT2}) also to similar images from the {sl Solar Dynamics
Observatory (SDO)}, to chromospheric H α images obtained with the
{sl Swedish Solar Telescope (SST)}, and to microscopy images of
microtubule filaments in live cells in biophysics. We provide a full
analytical description of the code, optimize the control parameters,
and compare the automated tracing with visual/manual methods.
The traced structures differ by up to 16 orders of magnitude in size,
which demonstrates the universality of the tracing algorithm.
Authors: Markus J. Aschwanden, Bart De Pontieu, and Eugene A. Katrukha
Projects: None

Publication Status: Entropy, Special Issue on Advanced Signal Processing in Heliopspheric Physics, (in press)
Last Modified: 20130718 18:46



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