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



The SpatioTemporal Evolution of Solar Flare Observed with AIA/SDO: Fractal Diffusion, SubDiffusion, or Logistic Growth ?} 

Markus J. Aschwanden Submitted: 20120807 15:05
We explore the spatiotemporal evolution of solar flares by fitting
a radial expansion model r(t) that consists of an exponentially
growing acceleration phase, followed by a deceleration phase that
is parameterized by the generalized diffusion function
r(t) propto kappa (tt_1)^{eta/2}, which
includes the logistic growth limit (eta=0), subdiffusion
(eta = 01), classical diffusion (eta=1), superdiffusion
(eta = 12), and the linear expansion limit (eta=2).
We analyze all M and Xclass flares observed with GOES and AIA/SDO
during the first two years of the SDO mission, amounting to 155 events.
We find that most flares operate in the subdiffusive regime
(eta=0.53pm0.27), which we interpret in terms of anisotropic
chain reactions of intermittent magnetic reconnection episodes
in a low plasmaeta corona. We find a mean propagation speed of
v=15pm12 km s^{1}, with maximum speeds of v_{max}=80 pm 85
km s^{1} per flare, which is substantially slower than the
sonic speeds expected for thermal diffusion of flare plasmas.
The diffusive characteristics established here (for the first time
for solar flares) is consistent with the fractaldiffusive
selforganized criticality (FDSOC) model, which predicted
diffusive transport merely based on cellular automaton simulations.
Authors: Markus J. Aschwanden
Projects: SDOAIA

Publication Status: ApJ Vol. 757, p.94 (2012)
Last Modified: 20120911 13:42



Solar Stereoscopy with STEREO/EUVI A and B spacecraft from small (6°) to large (170°) spacecraft separation angles 

Markus J. Aschwanden Submitted: 20120711 14:11
We performed for the first time stereoscopic triangulation of coronalloops in active regions over the entire range of spacecraft separationangles ( α _{sep}≈ 6°, 43°, 89°, 127°,and 170°). The accuracy of stereoscopic correlation depends mostlyon the viewing angle with respect to the solar surface for eachspacecraft,which affects the stereoscopic correspondence identification of loops inimage pairs. From a simple theoretical model we predict an optimum rangeof α _{sep} ≈ 22°125°, which is also experimentallyconfirmed. The best accuracy is generally obtained when an active regionpasses the central meridian (viewed from Earth), which yields asymmetricview for both STEREO spacecraft and causes minimum horizontalforeshortening.For the extended angular range of α _{sep}≈6°127° wefind a mean 3D misalignment angle of μ_{PF} ≈ 21°39°of stereoscopically triangulated loops with magnetic potential fieldmodels,and μ_{FFF} ≈ 15°21° for a forcefree field model,which is partly caused by stereoscopic uncertainties mu_{SE} ≈9°. We predict optimum conditions for solar stereoscopy duringthe timeintervals of 20122014, 20162017, and 20212023.
Authors: Markus J. Aschwanden, JeanPierre Wülser, Nariaki Nitta, and James Lemen
Projects: STEREO

Publication Status: Solar Physics (in press)
Last Modified: 20120712 09:38



First 3D Reconstructions of Coronal Loops with the STEREO A+B Spacecraft: IV. Magnetic Modeling with Twisted ForceFree Fields 

Markus J. Aschwanden Submitted: 20120711 14:09
The threedimensional (3D) coordinates of stereoscopically triangulated
loops provide strong constraints for magnetic field models of
active regions in the solar corona. Here we use STEREO/A and B data from
some 500 stereoscopically triangulated loops observed in four active
regions (2007 Apr 30, May 9, May 19, Dec 11), together with SOHO/MDI
lineofsight magnetograms. We measure the average misalignment angle
between the stereoscopic loops and theoretical magnetic field models,
finding a mismatch of mu=19°46° for a potential field model,
which is reduced to mu=14°19° for a nonpotential field model
parameterized by twist parameters.
The residual error is commensurable with stereoscopic measurement
errors (mu_{SE} approx 8°12°). We developed a potential
field code that deconvolves a lineofsight magnetogram into three
magnetic field components (B_x, B_y, B_z), as well as a nonpotential
field forwardfitting code that determines the full
length of twisted loops (L approx 50300 Mm),
the number of twist turns (median N_{twist}=0.06),
the nonlinear forcefree α parameter
(median α approx 4 imes 10^{11} cm^{1}),
and the current density (median j_z approx 1500 Mx cm^{2} s^{1}).
All twisted loops are found to be far below the critical value
for kink instability, and Joule dissipation of their currents
is found be be far below the coronal heating requirement.
The algorithm developed here, based on an analytical solution of
nonlinear forcefree fields that is accurate to second order
(in the forcefree parameter α ),
represents the first code that enables fast forwardfitting
to photospheric magnetograms and stereoscopically triangulated loops
in the solar corona.
Authors: Markus J. Aschwanden, JeanPierre Wuelser, Nariaki V. Nitta, James R. Lemen, Marc L. DeRosa, and Anna Malanushenko
Projects: STEREO

Publication Status: The Astrophysical Journal (in press)
Last Modified: 20120712 09:38



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Abstracts by Author

 Global Energetics of Solar Flares, X. Petschek Reconnection Rate and Alfven Mach Number of Magnetic Reconnection Outflows 
 Global Energetics of Solar Flares. IX. Refined Magnetic Modeling 
 Helical Twisting Number and Braiding Linkage Number of Solar Coronal Loops 
 Helical Twisting Number and Braiding Linkage Number of Solar Coronal Loops 
 Global Energetics of Solar Flares: VI. Refined Energetics of Coronal Mass Ejections 
 SelfOrganizing Systems in Planetary Physics: Harmonic Resonances of Planet and Moon orbits 
 The Width Distribution of Loops and Strands in the Solar Corona  Are we Hitting Rock Bottom ? 
 Global Energetics of Solar Flares and CMEs: V. Energy Closure 
 Global Energetics of Solar Flares: IV. Coronal Mass Ejection Energetics 
 Tracing the Chromospheric and Coronal Magnetic Field with AIA, IRIS, IBIS, and ROSA Data 
 The Vertical Current Approximation Nonlinear ForceFree Field Code  Description, Performance Tests, and Measurements of Magnetic Energies Dissipated in Solar Flares 
 Benchmark Test of Differential Emission Measure Codes and MultiThermal Energies in Solar Active Regions 
 Blind Stereoscopy of the Coronal Magnetic Field 
 Magnetic Energy Dissipation during the 2014 March 29 Solar Flare 
 Global Energetics of Solar Flares: II. Thermal Energies 
 Global Energetics of Solar Flares: I. Magnetic Energies 
 25 Years of SelfOrganized Criticality: Solar and Astrophysics 
 The Magnetic Field of Active Region 11158 During the 2011 February 1217 Flares : Differences between Photospheric Extrapolation and Coronal ForwardFitting Methods 
 A Macroscopic Description of SelfOrganized Criticality Systems and Astrophysical Applications 
 MultiWavelength Observations of the SpatioTemporal Evolution of Solar Flares with AIA/SDO: II. Hydrodynamic Scaling Laws and Thermal Energies 
 MultiWavelength Observations of the SpatioTemporal Evolution of Solar Flares with AIA/SDO:I. Universal Scaling Laws of Space and Time Parameters 
 MultiWavelength Observations of the SpatioTemporal Evolution of Solar Flares with AIA/SDO:I. Universal Scaling Laws of Space and Time Parameters 
 Optimization of CurviLinear Tracing Applied to Solar Physics and Biophysics 
 Nonlinear ForceFree Magnetic Field Fitting to Coronal Loops with and without Stereoscopy 
 A Nonlinear ForceFree Magnetic Field Approximation Suitable for Fast ForwardFitting to Coronal Loops III. The Free Energy 
 The SpatioTemporal Evolution of Solar Flare Observed with AIA/SDO: Fractal Diffusion, SubDiffusion, or Logistic Growth ?} 
 SelfOrganized Criticality Systems in Astrophysics (Chapter 13) 
 Solar Stereoscopy with STEREO/EUVI A and B spacecraft from small (6°) to large (170°) spacecraft separation angles 
 First 3D Reconstructions of Coronal Loops with the STEREO A+B Spacecraft: IV. Magnetic Modeling with Twisted ForceFree Fields 
 A Nonlinear ForceFree Magnetic Field Approximation Suitable for Fast ForwardFitting to Coronal Loops. II. Numeric Code and Tests 
 A Nonlinear ForceFree Magnetic Field Approximation Suitable for Fast ForwardFitting to Coronal Loops. I. Theory 
 Automated Solar Flare Statistics in Soft Xrays over 37 Years of GOES Observations  The Invariance of SelfOrganized Criticality during Three Solar Cycles 
 Flares in the Crab Nebula Driven by Untwisting Magnetic Fields 
 GeV Particle Acceleration in Solar Flares and Ground Level Enhancement (GLE) Events 
 A Statistical FractalDiffusive Avalanche Model of a SlowlyDriven SelfOrganized Criticality System 
 Solar Stereoscopy with STEREO/EUVI A and B spacecraft from small (6 deg) to large (170 deg) spacecraft separation angles 
 First 3D Reconstructions of Coronal Loops with the STEREO A+B Spacecraft: IV. Magnetic Field Modeling with Uniformly Twisted Flux Tubes 
 Coronal loop oscillations observed with AIA : Kinkmode with crosssectional and density oscillation 
 Solar Corona Loop Studies with AIA: I. CrossSectional Temperature Structure 
 The State of SelfOrganized Criticality of the Sun During the Last Three Solar Cycles. II. Theoretical Model 
 The State of SelfOrganized Criticality of the Sun During the Last Three Solar Cycles. II. Theoretical Model 
 The State of SelfOrganized Criticality of the Sun During the Last Three Solar Cycles. II. Theoretical Model 
 A Universal Scaling Law for the Fractal Energy Dissipation Domain in SelfOrganized Criticality Systems 
 The State of SelfOrganized Criticality of the Sun During the Last 3 Solar Cycles. I. Observations 
 The State of SelfOrganized Criticality of the Sun During the Last 3 Solar Cycles. I. Observations 
 GeV Particle Acceleration in Solar Flares and Ground Level Enhancement (GLE) Events 
 Bootstrapping the coronal magnetic field with STEREO: I. Unipolar Potential Field Modeling 
 SelfOrganized Criticality in Solar Physics and Astrophysics 
 3D Reconstruction of Active Regions with STEREO (Invited Review) 
 Reconciliation of waiting time statistics of solar flares observed in hard Xrays 
 A Code for Automated Tracing of Coronal Loops Approaching Visual Perception 
 4DModeling of CME Expansion and EUV Dimming Observed with STEREO/EUVI 
 First Measurements of the Mass of Coronal Mass Ejections from the EUV Dimming Observed with STEREO EUVI A+B Spacecraft 
 The 3D Geometry, 3D Motion, and Hydrodynamics of Oscillating Coronal Loops 
 Hydrodynamic Modeling of Coronal Loops with Hinode and STEREO 
 First 3D Reconstructions of Coronal Loops with the STEREO A+B Spacecraft: III. Instant Stereoscopic Tomography of Active Regions 
 Solar Flare and CME Observations with STEREO/EUVI 
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 The Effect of Radiative Cooling on Coronal Loop Oscillations 
 New Aspects on Particle Acceleration in Solar Flares from RHESSI Observations 
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 An Observational Test That Disproves Coronal Nanoflare Heating Models 
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 Solar Flare Geometries. II. The Volume Fractal Dimension 
 Comparison of Five Numerical Codes for Automated Tracing of Coronal Loops 
 ASTROPHYSICS IN 2006 
 Solar Flare Physics Enlivened by TRACE and RHESSI (Invited) 
 Keynote Address: Outstanding Problems in Solar Physics 
 Scaling Laws for Solar and Stellar Flares 
 From Solar Nanoflares to Stellar Giant Flares  Scaling Laws and NonImplications for Coronal Heating 
 Solar Flare Geometries. I. The Area Fractal Dimension 
 The Coronal Heating Paradox 
 Theoretical Modeling for the STEREO Mission 
 The Localization of Particle Acceleration Sites in Solar Flares and CMEs 
 Three Criteria to Discriminate Between Elementary and Composite Coronal Loops 
 Elementary Loop Structures in the Solar Corona Analyzed from TRACE TripleFilter Images 


