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 Global Energetics of Solar Flares: VI. Refined Energetics of Coronal Mass Ejections Markus J. Aschwanden   Submitted: 2017-04-06 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 X-class flare events observed during the first 7 years (2010-2016) 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 self-similar 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 self-consistent relationship between the CME center-of-mass motion detected during EUV dimming and the leading-edge motion observed in white-light coronagraphs; (5) the equi-partition of the CME kinetic and thermal energy; and (6) the Rosner-Tucker-Vaiana (RTV) scaling law. The refined CME model is entirely based on EUV dimming observations (using AIA/SDO data) and complements the traditional white-light 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 ~ 1014 g are under-estimated 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 measure-weighted flare peak temperature Te, and length scale L are consistent with the following scaling laws (derived from first principles): v ~ Te^1/2, v~ (m_cme)^1/4, and m_cme ~ L2. Authors: Markus J. Aschwanden Projects:

 Self-Organizing Systems in Planetary Physics: Harmonic Resonances of Planet and Moon orbits Markus J. Aschwanden   Submitted: 2017-01-27 12:58 The geometric arrangement of planet and moon orbits into a regularly spaced pattern of distances is the result of a self-organizing system. The positive feedback mechanism that operates a self-organizing system is accomplished by harmonic orbit resonances, leading to long-term stable planet and moon orbits in solar or stellar systems. The distance pattern of planets was originally described by the empirical Titius-Bode law, and by a generalized version with a constant geometric progression factor (corresponding to logarithmic spacing). We find that the orbital periods Ti and planet distances Ri from the Sun are not consistent with logarithmic spacing, but rather follow the quantized scaling (Ri+1/Ri) = (Ti+1/Ti)2/3 = (Hi+1/Hi)2/3, where the harmonic ratios are given by five dominant resonances, namely (Hi+1 : Hi) = (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 exo-planets of 55 Cnc and HD 10180 planetary systems. The model allows us a prediction of missing planets in each planetary system, based on the quasi-regular self-organizing pattern of harmonic orbit resonance zones. We predict 7 (and 4) missing exo-planets 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 long-term stable orbits. Authors: Markus J. Aschwanden Projects:

 The Width Distribution of Loops and Strands in the Solar Corona - Are we Hitting Rock Bottom ? Markus J. Aschwanden   Submitted: 2017-01-04 16:32 In this study we analyze Atmospheric Imaging Assembly (AIA) and Hi-C images in order to investigate absolute limits for the finest loop strands. We develop a model of the occurrence-size distribution function of coronal loop widths, characterized by a lower limit of widths wmin, a peak width wp, a peak occurrence number np, and a power law slope a. Our data analysis includes automated tracing of curvi-linear features with the OCCULT-2 code, automated sampling of the cross-sectional widths of coronal loops, and fitting of the theoretical size distribution to the observed distribution. With Monte-Carlo simulations and variable pixel sizes Δ x we derive a first diagnostic criterion to discriminate whether the loop widths are unresolved (wp/Δ x ≈ 2.5±0.2), or fully resolved (if wp/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, wmin ≈ 3 (Δ xcrit-0.37") Mm) as a function of the critical resolution Δ xcrit. We find that the loop widths are marginally resolved in AIA images, but are fully resolved in Hi-C images, where our model predicts a lower limit of loop widths at wmin ≈ 100 km and a most frequent (peak) value at wp ≈ 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 magneto-convection, rather than nanoflare heating models with unresolved microscopic scales. Authors: Markus J. Aschwanden and Hardi Peter Projects: Hi-C
 Publication Status: The Astrophysical Journal (2017 Jan 4, subm.) Last Modified: 2017-01-11 12:08

 Global Energetics of Solar Flares and CMEs: V. Energy Closure Markus J. Aschwanden   Submitted: 2017-01-04 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 X-class 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 flare-accelerated particles (Ent), the energy of direct heating (Edir), and the energy in coronal mass ejections (ECME), which are the primary energy dissipation processes in a flare, is found to have a ratio of (Ent+Edir+ ECME)/Emag = 0.87 ± 0.18, compared with the dissipated magnetic free energy Emag, 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 thick-target model; (4) The bolometric luminosity in white-light flares is comparable with the thermal energy in soft X-rays (SXR); (5) Solar Energetic Particle (SEP) events carry a fraction ≈ 0.03 of the CME energy, which is consistent with CME-driven shock acceleration; and (6) The warm-target model predicts a lower limit of the low-energy cutoff at ec ≈ 6 keV, based on the mean differential emission measure (DEM) peak temperature of Te=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: SDO-AIA
 Publication Status: The Astrophysical Journal (accepted 2017 Jan 4, in press) Last Modified: 2017-01-11 12:08

 Global Energetics of Solar Flares: IV. Coronal Mass Ejection Energetics Markus J. Aschwanden   Submitted: 2016-05-16 14:50 This study entails the fourth part of a global flare energetics project, in which the mass mcme, kinetic energy Ekin, and the gravitational potential energy Egrav of coronal mass ejections (CMEs) is measured in 399 M and X-class 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: SDO-AIA

 Tracing the Chromospheric and Coronal Magnetic Field with AIA, IRIS, IBIS, and ROSA Data Markus J. Aschwanden   Submitted: 2016-02-05 11:42 The aim of this study is to explore the suitability of chromospheric images for magnetic modeling of active regions. We use high-resolution 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 non-potential 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. Curvi-linear structures are automatically traced in those images with the OCCULT-2 code, to which we forward-fitted magnetic field lines computed with the Vertical-Current Approximation Non-Linear Force Free Field (VCA-NLFFF) code. We find that the chromospheric images: (1) reveal crisp curvi-linear structures (fibrils, loop segments, spicules) that are extremely well-suited for constraining magnetic modeling; (2) that these curvi-linear structures are field-aligned with the best-fit solution by a median misalignment angle of ~4-7 deg; (3) the free energy computed from coronal data may underestimate that obtained from cromospheric data by a factor of ~ 2-4, (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 plasma-beta 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: SDO-AIA

 The Vertical Current Approximation Nonlinear Force-Free Field Code - Description, Performance Tests, and Measurements of Magnetic Energies Dissipated in Solar Flares Markus J. Aschwanden   Submitted: 2016-02-01 11:19 In this work we provide an updated description of the Vertical Current Approximation Nonlinear Force-Free Field (VCA-NLFFF) 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 VCA-NLFFF code over traditional NLFFF codes are the circumvention of the unrealistic assumption of a force-free 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 VCA-NLFFF 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 VCA-NLFFF code is found to detect decreases in flare energies in most X, M, and C-class flares. The successful detection of energy decreases during a variety of flares with the VCA-NLFFF code indicates that current-driven 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 VCA-NLFFF code is also publicly available in the Solar SoftWare (SSW). Authors: Markus J. Aschwanden Projects: SDO-AIA
 Publication Status: ApJ Suppl.Ser., subm. 2016 Feb 1 Last Modified: 2016-02-03 09:17

 Thresholded Power Law Size Distributions of Instabilities in Astrophysics Markus J. Aschwanden   Submitted: 2015-10-07 09:11 Power law-like 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 x0; (3) contamination by an event-unrelated background xb; 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 exponential-growth evolution model, which produces avalanches only when a disturbance exceeds a critical threshold x0. 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 self-organized 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 2015-Oct-7, in press) Last Modified: 2015-10-07 12:57

 Benchmark Test of Differential Emission Measure Codes and Multi-Thermal Energies in Solar Active Regions Markus J. Aschwanden   Submitted: 2015-09-23 10:09 We compare the ability of 11 Differential Emission Measure (DEM) forward-fitting 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 single-Gaussian DEM, a bi-Gaussian DEM, a fixed-Gaussian DEM, a linear spline DEM, the spatial synthesis DEM, the Monte-Carlo 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 EM-weighted temperature T_wfit/T_wsim=0.9pm0.1, the peak emission measure EM_pfit/EM_psim=0.6pm0.2, the total emission measure EM_tfit/EM_tsim=0.8pm0.3, and the multi-thermal energies Ethfit/EMthsim=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 X-rays ,RHESSI,SDO-AIA,SDO-EVE
 Publication Status: Solar Physics, (accepted 2015 Sep 23), in press Last Modified: 2015-09-26 14:55

 Blind Stereoscopy of the Coronal Magnetic Field Markus J. Aschwanden   Submitted: 2015-06-15 13:13 We test the feasibility of 3D coronal-loop 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 spacecraft-separation angle and as a function of the spatial resolution. We also test the sensitivity to magnetic non-potentiality. 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 non-potential 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 spacecraft-separation angle of α _s ≈ 5^\circ. Authors: Aschwanden,J.M., Schrijver, C.J., and Malanushenko, A. Projects: None
 Publication Status: Solar Physics, (accepted 2015 Jun 15), in press Last Modified: 2015-06-17 12:58

 Magnetic Energy Dissipation during the 2014 March 29 Solar Flare Markus J. Aschwanden   Submitted: 2015-04-13 12:52 We calculated the time evolution of the free magnetic energy during the 2014-Mar-29 flare (SOL2014-03-29T17:48), the first X-class flare detected by IRIS. The free energy was calculated from the difference between the nonpotential field, constrained by the geometry of observed loop structures, and the potential field. We use AIA/SDO and IRIS images to delineate the geometry of coronal loops in EUV wavelengths, as well as to trace magnetic field directions in UV wavelengths in the chromosphere and transition region. We find an identical evolution of the free energy for both the coronal and chromospheric tracers, as well as agreement between AIA and IRIS results, with a peak free energy of Efree(tpeak) ≈ (45 ± 2) x 1030 erg, which decreases by an amount of Δ Efree ≈ (29 ± 3) x 1030 erg during the flare decay phase. The consistency of free energies measured from different EUV and UV wavelengths for the first time here, demonstrates that vertical electric currents (manifested in form of helically twisted loops) can be detected and measured from both chromospheric and coronal tracers. Authors: Markus J. Aschwanden Projects: IRIS
 Publication Status: ApJ Letters (accepted 2015-Apr-10, in press) Last Modified: 2015-04-14 07:25

 Global Energetics of Solar Flares: II. Thermal Energies Markus J. Aschwanden   Submitted: 2015-02-19 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 X-class 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 multi-thermal energies,using a spatially-synthesized Gaussian DEM forward-fitting method.The multi-thermal 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 Eth/Ediss ≈ 2%-40%between the multi-thermal energy Eth and themagnetically dissipated energy Ediss,which is an order of magnitude higher than the estimatesof Emslie et al. 2012. For the analyzed set of M and X-class flareswe find the following physical parameter ranges:L=108.2-109.7 cm for the length scale of the flare areas,T_p=105.7-107.4 K for the DEM peak temperature,T_w=106.8-107.6 K for the emission measure-weighted temperature,n_p=1010.3-1011.8 cm-3 for the average electron density,EM_p=1047.3-1050.3 cm-3 for the DEM peak emission measure,and Eth=1026.8-1032.0 erg for the multi-thermal energies.The deduced multi-thermal energies are consistentwith the RTV scaling law Eth,RTV = 7.3 x 10-10 Tp3 Lp2, which predicts extremal values ofEth,max ≈ 1.5 x 1033 erg for the largest flareand Eth,min ≈ 1 x 1024 erg for the smallestcoronal nanoflare.The size distributions of the spatial parameters exhibit powerlaw tails thatare consistent with the predictions of the fractal-diffusiveself-organized 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: SDO-AIA
 Publication Status: The Astrophysical Journal, (accepted 2015-Feb-19, in press) Last Modified: 2015-02-21 19:18

 Global Energetics of Solar Flares: I. Magnetic Energies Markus J. Aschwanden   Submitted: 2014-10-28 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 X-class flares observed with AIA and HMI onboard SDO. We calculate the potential (Ep), the nonpotential (Enp) or free energies (Efree =Enp-E_p), and the flare-dissipated magnetic energies (Ediss). We calculate these magnetic parameters using two different NLFFF codes: The COR-NLFFF code uses the line-of-sight magnetic field component Bz 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 PHOT-NLFFF 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 fractal-diffusive self-organized criticality model. The magnetic parameters exhibit scaling laws for the nonpotential energy, Enp ∝ E_p1.02, for the free energy, Efree ∝ E_p1.7 and Efree ∝ B\varphi1.0 L1.5, for the dissipated energy, Ediss ∝ E_p1.6 and Ediss ∝ Efree0.9, and the energy dissipation volume, V ∝ Ediss1.2. The potential energies vary in the range of E_p = 1 x 1031 - 4 x 1033 erg, while the free energy has a ratio of Efree/E_p ≈ 1%-25%. The Poynting flux amounts to Fflare ≈ 5 x 108 - 1010 erg cm-2 s-1 during flares, which averages to FAR ≈ 6 x 106 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: SDO-HMI

 25 Years of Self-Organized Criticality: Solar and Astrophysics Markus J. Aschwanden   Submitted: 2014-03-25 16:18 Shortly after the seminal paper Self-Organized Criticality: An explanation of 1/f noise'' by Bak, Tang, and Wiesenfeld (1987), the idea has been applied to solar physics, inAvalanches and the Distribution of Solar Flares'' by Lu and Hamilton (1991). In the following years, an inspiring cross-fertilization 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 X-ray repeaters, blazars, black-hole objects, cosmic rays, and boson clouds. The application of SOC concepts has been performed by numerical cellular automaton simulations, by analytical calculations of statistical (powerlaw-like) 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 magneto-hydrodynamics (MHD) processes. The novel applications stimulated also vigorous debates about the discrimination between SOC models, SOC-like, and non-SOC processes, such as phase transitions, turbulence, random-walk diffusion, percolation, branching processes, network theory, chaos theory, fractality, multi-scale, 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: 2014-03-26 12:35

 The Magnetic Field of Active Region 11158 During the 2011 February 12-17 Flares : Differences between Photospheric Extrapolation and Coronal Forward-Fitting Methods Markus J. Aschwanden   Submitted: 2014-02-21 09:14 We developed a {sl coronal non-linear force-free field (COR-NLFFF)} forward-fitting code that fits an approximate {sl non-linear force-free 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 non-forcefreeness in the lower chromosphere. In this study we applied the COR-NLFFF code to active region NOAA 11158, during the time interval of 2011 Feb 12 to 17, which includes an X2.2 GOES-class flare plus 35 M and C-class flares. We calcuated the free magnetic energy with a 6-minute cadence over 5 days. We find good agreement between the two types of codes for the total nonpotential EN and potential energy EP, but find up to a factor of 4 discrepancy in the free energy Efree=E_N-E_P, and up to a factor of 10 discrepancy in the decrease of the free energy Delta Efree 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 pre-processing of photospheric vector data, but more likely due to the non-forcefreeness 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: SDO-AIA

 A Macroscopic Description of Self-Organized Criticality Systems and Astrophysical Applications Markus J. Aschwanden   Submitted: 2013-10-15 14:18 We suggest a generalized definition of self-organized 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 system-wide instability threshold, producing scale-free, fractal-diffusive, and intermittent avalanches with powerlaw-like 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 fractal-diffusive transport (FD-SOC). 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 scale-free 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 gamma-ray repeaters, black-hole objects, blazars, and cosmic rays. The FD-SOC model predicts correctly the size distributions of 7 out of these 12 astrophysical phenomena, and indicates non-standard scaling laws and measurement biases for the others. Authors: Markus J. Aschwanden Projects:

 Multi-Wavelength Observations of the Spatio-Temporal Evolution of Solar Flares with AIA/SDO: II. Hydrodynamic Scaling Laws and Thermal Energies Markus J. Aschwanden   Submitted: 2013-08-23 12:16 In this study we measure physical parameters of the same set of 155 M and X-class 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 Tp, electron density np, and thermal energy Eth, in addition to the spatial scales L, areas A, and volumes V measured in Paper I. The parameter ranges for M and X-class flares are: log(EM_p)=47.0-50.5, T_p=5.0-17.8 MK, n_p=4 imes 109-9 imes 1011 cm-3, and thermal energies of Eth=1.6 imes 1028-1.1 imes 1032 erg. We find that these parameters obey the Rosner-Tucker-Vaiana (RTV) scaling law T_p^2 propto n_p L and H propto T7/2 L-2 during the peak time tp of the flare density np, 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 Monte-Carlo 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 fractal-diffusive self-organized 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:

 Multi-Wavelength Observations of the Spatio-Temporal Evolution of Solar Flares with AIA/SDO:I. Universal Scaling Laws of Space and Time Parameters Markus J. Aschwanden   Submitted: 2013-08-22 11:43 We extend a previous statistical solar flare study of 155 GOES M- and X-class flares observed with AIA/SDO (Aschwanden 2012) to all 7 coronal wavelengths (94, 131, 171, 193, 211, 304, 335 ang ) to test the wavelength-dependence 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 near-identical size distributions of geometric (lengths L, flare areas A, volumes V, fractal dimension D2), temporal (flare durations T), and spatio-temporal parameters (diffusion coefficient kappa, spreading exponent eta, and maximum expansion velocities vmax) in different wavelengths, which are consistent with the universal predictions of the fractal-diffusive avalanche model of a slowly-driven self-organized criticality (FD-SOC) 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 L0.94pm0.01 and the 3-parameter scaling law L propto kappa T0.1, which is more consistent with the logistic-growth model than with classical diffusion. The findings suggest long-range correlation lengths in the FD-SOC 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 X-ray fluxes, and somewhat larger diffusion coefficients kappa than confined flares (without CMEs). Authors: Aschwanden,J.M., Zhang, J., Liu,K. Projects: None

 Multi-Wavelength Observations of the Spatio-Temporal Evolution of Solar Flares with AIA/SDO:I. Universal Scaling Laws of Space and Time Parameters Markus J. Aschwanden   Submitted: 2013-08-22 11:43 We extend a previous statistical solar flare study of 155 GOES M- and X-class flares observed with AIA/SDO (Aschwanden 2012) to all 7 coronal wavelengths (94, 131, 171, 193, 211, 304, 335 ang ) to test the wavelength-dependence 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 near-identical size distributions of geometric (lengths L, flare areas A, volumes V, fractal dimension D2), temporal (flare durations T), and spatio-temporal parameters (diffusion coefficient kappa, spreading exponent eta, and maximum expansion velocities vmax) in different wavelengths, which are consistent with the universal predictions of the fractal-diffusive avalanche model of a slowly-driven self-organized criticality (FD-SOC) 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 L0.94pm0.01 and the 3-parameter scaling law L propto kappa T0.1, which is more consistent with the logistic-growth model than with classical diffusion. The findings suggest long-range correlation lengths in the FD-SOC 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 X-ray fluxes, and somewhat larger diffusion coefficients kappa than confined flares (without CMEs). Authors: Aschwanden,J.M., Zhang, J., Liu,K. Projects: None

 Optimization of Curvi-Linear Tracing Applied to Solar Physics and Biophysics Markus J. Aschwanden   Submitted: 2013-07-18 12:23 We developed an automated pattern recognition code that is particularly well suited to extract one-dimensional curvi-linear features from two-dimensional 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 ultra-violet wavelengths. Here we apply an advanced version of this code ({sl OCCULT-2}) 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: 2013-07-18 18:46

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