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Interface Region Imaging Spectrograph (IRIS) Observations of the Fractal Dimension in the Solar Atmosphere  

Markus J. Aschwanden   Submitted: 2022-07-21 10:31

While previous work explored the fractality and self-organized criticality (SOC) of flares and nanoflares in wavelengths emitted in the solar corona (such as in hard X-rays, soft X-rays, and EUV wavelenghts), we focus here on impulsive phenomena in the photosphere and transition region, as observed with the Interface Region Imaging Spectrograph (IRIS) in the temperature range of Te ≈ 104-106 K. We find the following fractal dimensions (in increasing order): D_A=1.21 ± 0.07 for photospheric granulation, D_A=1.29 ± 0.15 for plages in the transition region, D_A=1.54 ± 0.16 for sunspots in the transition region, D_A=1.59 ± 0.08 for magnetograms in active regions, D_A=1.56 ± 0.08 for EUV nanoflares, D_A=1.76 ± 0.14 for large solar flares, and up to D_A=1.89 ± 0.05 for the largest X-class flares. We interpret low values of the fractal dimension (1.0 ≈ D_A ≈ 1.5) in terms of sparse curvi-linear flow patterns, while high values of the fractal dimension (1.5 ≈ D_A ≈ 2.0) indicate near space-filling transport processes, such as chromospheric evaporation. Phenomena in the solar transition region appear to be consistent with SOC models, based on their size distributions of fractal areas A and (radiative) energies E, which show power law slopes of α _Aobs=2.51 ± 0.21 (with α _Atheo=2.33 predicted), and α _Eobs=2.03 ± 0.18 (with α _Etheo=1.80 predicted).

Authors: Markus J. Aschwanden and Nived Vilangot Nhalil
Projects: None

Publication Status: Frontiers in Astronomy and Space Sciences (subm. 2022 Jul 21)
Last Modified: 2022-07-27 10:13
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Reconciling Power Law Slopes in Solar Flare and Nanoflare Size Distributions  

Markus J. Aschwanden   Submitted: 2022-04-25 11:40

We unify the power laws of size distributions of solar flare and nanoflare energies. We present three models that predict the power law slopes α _E of flare energies defined in terms of the 2-D and 3-D fractal dimensions (D_A, D_V): (i) The spatio-temporal standard SOC model, defined by the power law slope α E1=1+2/(D_V+2)=(13/9)≈ 1.44; (ii) the 2-D thermal energy model, α E2=1+2/D_A=(7/3)≈ 2.33, and (iii) the 3-D thermal energy model, α E3=1+2/D_V=(9/5)≈ 1.80. The theoretical predictions of energies are consistent with the observational values of these three groups, i.e., α E1=1.47 ± 0.07; α E2=2.38 ± 0.09, and α E3=1.80 ± 0.18. These results corroborate that the energy of nanoflares does not diverge at small energies, since ( α E1<2) and ( α E3<2), except for the unphyiscal 2-D model ( α E2>2). This conclusion adds an additional argument against the scenario of coronal heating by nanoflares.

Authors: Markus J. Aschwanden
Projects: SDO-AIA

Publication Status: ApJL (submitted 2022 April 25)
Last Modified: 2022-04-26 16:10
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Global Energetics in Solar Flares. XIII. The Neupert Effect and Acceleration of Coronal Mass Ejections  

Markus J. Aschwanden   Submitted: 2021-12-08 13:28

Our major aim is a height-time model r(t) of the propagation of Coronal Mass Ejections (CMEs), where the lower corona is self-consistently connected to the heliospheric path. We accomplish this task by using the Neupert effect to derive the peak time, duration, and rate of the CME acceleration phase, as obtained from the time derivative of the soft X-ray (SXR) light curve. This novel approach offers the advantage to obtain the kinematics of the CME height-time profile r(t), the CME velocity profile v(t)=dr(t)/dt, and the CME acceleration profile a(t)=dv(t)/dot from Geostationary Orbiting Earth Satellite (GOES) and white-light data, without the need ofl hard X-ray (HXR)} data. We apply this technique to a data set of 576 (GOES X and M-class) flare events observed with GOES and the Large Angle Solar Coronagraph (LASCO). Our analysis yields acceleration rates in the range of a_A = 0.1-13 km s-2, acceleration durations of tau_A = 1.2-45 min, and acceleration distances in the range of d_A = 3-1063 Mm, with a median of d_A=39 Mm, which corresponds to the hydrostatic scale height of a corona with a temperature of Te ~ 0.8 MK. The results are consistent with standard flare/CME models that predict magnetic reconnection and synchronized (primary) acceleration of CMEs in the low corona (at a height of ~0.1 R, while secondary (weaker) acceleration may occur further out at heliospheric distances.

Authors: Markus J. Aschwanden
Projects: SoHO-LASCO

Publication Status: submitted 2021 Dec 8
Last Modified: 2021-12-10 15:08
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The Solar Memory From Hours to Decades  

Markus J. Aschwanden   Submitted: 2021-07-29 11:43

Waiting time distributions allow us to distinguish at least three different types of dynamical systems, such as (i) linear random processes (with no memory); (ii) nonlinear, avalanche-type, nonstationary Poisson processes (with memory during the exponential growth of the avalanche rise time); and (iii) chaotic systems in the state of a nonlinear limit cycle (with memory during the oscillatory phase). We describe the temporal evolution of the flare rate \lambda(t) ∝ t^p with a polynomial function, which allows us to distinguish linear (p ≈ 1) from nonlinear (p ≳ 2) events. The power law slopes α of observed waiting times (with full solar cycle coverage) cover a range of α =2.1-2.4, which agrees well with our prediction of α = 2.0+1/p = 2.3-2.5. The memory time can also be defined with the time evolution of the logistic equation, for which we find a relationship between the nonlinear growth time τ_G = τrise/(4p) and the nonlinearity index p. We find a nonlinear evolution for most events, in particular for the clustering of solar flares (p=2.2±0.1), partially occulted flare events (p=1.8±0.2), and the solar dynamo (p=2.8±0.5). The Sun exhibits memory on time scales of ≈2 hours to 3 days (for solar flare clustering), 6 to 23 days (for partially occulted flare events), and 1.5 month to 1 year (for the rise time of the solar dynamo).

Authors: Aschwanden, M.J. and Johnson, J.R.
Projects: None

Publication Status: submitted
Last Modified: 2021-08-01 20:58
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Correlation of the sunspot number and the waiting time distribution of solar flares, coronal mass ejections, and solar wind switchback events observed with the Parker Solar Probe  

Markus J. Aschwanden   Submitted: 2021-06-11 12:47

Waiting-time distributions of solar flares and coronal mass ejections (CMEs) exhibit power-law-like distribution functions with slopes in the range of ατ ≈ 1.4–3.2, as observed in annual data sets during four solar cycles (1974–2012). We find a close correlation between the waiting-time power-law slope ατ and the sunspot number (SN), i.e., ατ = 1.38 + 0.01 × SN. The waiting-time distribution can be fitted with a Pareto-type function of the -at form N(τ) = N0 (t0 + t) , where the offset τ0 depends on the instrumental sensitivity, the detection threshold of events, and pulse pileup effects. The time-dependent power-law slope ατ(t) of waiting-time distributions depends only on the global solar magnetic flux (quantified by the sunspot number) or flaring rate, which is not predicted by self-organized criticality or magnetohydrodynamic turbulence models. Power-law slopes of ατ ≈ 1.2–1.6 were also found in solar wind switchback events, as observed with the Parker Solar Probe during the solar minimum, while steeper slopes are predicted during the solar maximum. We find that the annual variability of switchback events in the heliospheric solar wind and solar flare and CME rates (originating in the photosphere and lower corona) are highly correlated.

Authors: Aschwanden, M.J. and Dudok de Wit, T.
Projects: PSP-WISPR

Publication Status: Aschwanden,M.J. and Dudok de Wit,T. 2021, ApJ 912:94
Last Modified: 2021-06-12 00:56
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Finite system-size effectrs in self-organizing criticality systems  

Markus J. Aschwanden   Submitted: 2021-06-11 12:37

We explore upper limits for the largest avalanches or catastrophes in nonlinear energy dissipation systems governed by self-organized criticality. We generalize the idealized “straight” power-law size distribution and Pareto distribution functions in order to accommodate incomplete sampling, limited instrumental sensitivity, finite system-size effects, and “Black Swan” and “Dragon King” extreme events. Our findings are as follows. (i) Solar flares show no finite system-size limits up to L~200 Mm, but solar flare durations reveal an upper flare duration limit of hr. (ii) Stellar flares observed with Kepler exhibit inertial ranges of E ≈ 1034–1037 erg, finite system- size ranges of E ≈ 1037–1038 erg, and extreme events at E ≈ (1–5) × 1038 erg. (iii) The maximum flare energies of different spectral type stars (M, K, G, F, A, giants) reveal a positive correlation with the stellar radius, which indicates a finite system-size limit imposed by the stellar surface area. Fitting our finite system-size models to terrestrial data sets (earthquakes, wildfires, city sizes, blackouts, terrorism, words, surnames, web links) yields evidence (in half of the cases) for finite system-size limits and extreme events, which can be modeled with dual power-law size distributions.

Authors: Aschwanden, M.J.
Projects: SDO-AIA

Publication Status: Aschwanden,M.J. 2021, ApJ 909:69
Last Modified: 2021-06-12 00:56
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Global energetics of solar flares. XII. Energy scaling laws  

Markus J. Aschwanden   Submitted: 2021-06-11 12:31

In this study we test 18 versions of 5 fundamental energy scaling laws that operate in large solar flares. We express scaling laws in terms of the magnetic potential field energy Ep, the mean potential field strength Bp, the free energy Efree, the dissipated magnetic flare energy Ediss, the magnetic length scale L, the thermal length scale Lth, the mean helically twisted flux tube radius R, the sunspot radius r, the emission measure-weighted flare temperature Te, the electron density ne, and the total emission measure EM, measured from a data set of 173 GOES M- and X-class flare events. The 5 categories of physical scaling laws include (i) a scaling law of the potential-field energy, (ii) a scaling law for helical twisting, (iii) a scaling law for Petschek-type magnetic reconnection, (iv) the Rosner- Tucker-Vaiana scaling law, and (v) the Shibata-Yokoyama scaling law. We test the self-consistency of these theoretical scaling laws with observed parameters by requiring two criteria: a cross-corrleation coefficient of CCC>0.5 between the theoretically predicted scaling laws and observed values, and a linear regression fit with a slope of α ≈ 1 within one standard deviation σ. These two criteria enable us (i) to corroborate some existing (or modified) scaling laws, (ii) to reject other scaling laws that are not consistent with the observations, (iii) to probe the dimensionality of flare geometries, and (iv) to predict various energy parameters based on tested scaling laws.

Authors: Aschwanden, M.J.
Projects: GOES X-rays

Publication Status: Aschwanden,M.J. 2020, ApJ 903:23
Last Modified: 2021-06-12 00:57
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Global energetics of solar flares. XI. Flare magnitude predictions of the GOES class  

Markus J. Aschwanden   Submitted: 2021-06-11 12:25

In this study we determine scaling relationships of observed solar flares that can be used to predict upper limits of the GOES-class magnitude of solar flares. The flare prediction scheme is based on the scaling of the slowly-varying potential energy Ep(t), which is extrapolated in time over an interval of ∆t ≤ 24 hrs. The observed scaling of the dissipated energy Ediss scales with the potential field energy as E ∝ E1.32. In addition, the observed scaling relationship of the flare volume, V ∝ E1.17, diss p diss the multi-thermal energy, Eth ∝ V 0.76, the flare emission measure EM ∝ E0.79, the EM-weighted th temperature Tw, and the GOES flux, F8(t) ∝ Ep(t)0.92, allows us then to predict an upper limit of the GOES-class flare magnitude in the extrapolated time window. We find a good correlation (CCC≈ 0.7) between the observed and predicted GOES-class flare magnitudes (in 172 X and M-class events). This is the first algorithm that employs observed scaling laws of physical flare parameters to predict GOES flux upper limits, an important capability that complements previous flare prediction methods based on machine-learning algorithms used in space weather forecasting.

Authors: Aschwanden, M.J.
Projects: GOES X-rays

Publication Status: Aschwanden,M.J. 2020, ApJ 897:16
Last Modified: 2021-06-12 00:57
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Global Energetics of Solar Flares, X. Petschek Reconnection Rate and Alfvén Mach Number of Magnetic Reconnection Outflows  

Markus J. Aschwanden   Submitted: 2020-05-07 13:48

We investigate physical scaling laws for magnetic energy dissipation in solar flares, in the framework of the Sweet-Parker model and the Petschek model. We find that the total dissipated magnetic energy Ediss in a flare depends on the mean magnetic field component Bf associated with the free energy Ef, the length scale L of the magnetic area, the hydrostatic density scale height lambda of the solar corona, the Alfvén Mach number M_A=v_1/vA (the ratio of the inflow speed v1 to the Alfvénic outflow speed vA), and the flare duration au_f, i.e., Ediss = (1/4π) B_f^2 L lambda vA M_A au_f, where the Alfvén speed depends on the nonpotential field strength Bnp and the mean electron density ne in the reconnection outflow. Using MDI/SDO and AIA/SDO observations and 3-D magnetic field solutions obtained with the vertical-current approximation nonlinear force-free field code (VCA-NLFFF) we measure all physical parameters necessary to test scaling laws, which represents a new method to measure Alfvén Mach numbers MA, the reconnection rate, and the total free energy dissipated in solar flares.

Authors: Markus J. Aschwanden
Projects: SDO-HMI

Publication Status: ApJ (in press)
Last Modified: 2020-05-11 15:28
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Global Energetics of Solar Flares. IX. Refined Magnetic Modeling  

Markus J. Aschwanden   Submitted: 2019-09-18 13:37

A more accurate analyticalsolution of the vertical-current approximation nonlinear force-freefield (VCA3-NLFFF) model is presented that includes besides theradial (Br) and the azimuthal(Bϕ ) magnetic field components, apoloidal component (Bθ ≠ 0) also. This new analytical solution is of second-order accuracy in the divergence-freeness condition, and of third-order accuracy in the force-freeness condition. We re-analyze the sample of 173 GOES M- and X-class flares observed with the Atmospheric Imaging Assembly (AIA) and Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). The new code reproduces helically twisted loops with a low winding number below the kink instability consistently, avoiding unstable, highly-twisted structures of the Gold-Hoyle flux rope type. The magnetic energies agree within EVCA3 / EW = 0.99±0.21 with the Wiegelmann (W-NLFFF) code. The time evolution of the magnetic field reveals multiple, intermittent energy build-up and releases in most flares, contradicting both the Rosner-Vaiana model (with gradual energy storage in the corona) and the principle of time scale separation (τflare ≪ τstorage) postulated in self-organized criticality models. The mean dissipated flare energy is found to amount to 7%±3% of the potential energy, or 60%±26% of the free energy, a result that can be used for predicting flare magnitudes based on the potential field of active regions.

Authors: Markus J. Aschwanden
Projects:

Publication Status: ApJ (Sept 23, 2019; in press)
Last Modified: 2019-09-23 13:47
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Global Energetics of Solar Flares. IX. Refined Magnetic Modeling  

Markus J. Aschwanden   Submitted: 2019-09-18 13:37

A more accurate analytical solution of the vertical-current approximation nonlinear force-free field (VCA3-NLFFF) model is presented that includes besides the radial (Br) and the azimuthal (Bϕ ) magnetic field components, a poloidal component (Bθ ≠ 0) also. This new analytical solution is of second-order accuracy in the divergence-freeness condition, and of third-order accuracy in the force-freeness condition. We re-analyze the sample of 173 GOES M- and X-class flares observed with the Atmospheric Imaging Assembly (AIA) and Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). The new code reproduces helically twisted loops with a low winding number below the kink instability consistently, avoiding unstable, highly-twisted structures of the Gold-Hoyle flux rope type. The magnetic energies agree within EVCA3 / EW = 0.99±0.21 with the Wiegelmann (W-NLFFF) code. The time evolution of the magnetic field reveals multiple, intermittent energy build-up and releases in most flares, contradicting both the Rosner-Vaiana model (with gradual energy storage in the corona) and the principle of time scale separation (τflare ≪ τstorage) postulated in self-organized criticality models. The mean dissipated flare energy is found to amount to 7%±3% of the potential energy, or 60%±26% of the free energy, a result that can be used for predicting flare magnitudes based on the potential field of active regions.

Authors: Markus J. Aschwanden
Projects: None

Publication Status: Aschwanden, M.J. 2019, ApJ 885:49
Last Modified: 2021-06-12 00:57
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Helical Twisting Number and Braiding Linkage Number of Solar Coronal Loops  

Markus J. Aschwanden   Submitted: 2019-02-27 08:49

Coronal loops in active regions are often characterized by quasi-circular and helically twisted (sigmoidal) geometries, which are consistent with dipolar potential field models in the former case, and with nonlinear force-free field models with vertical currents in the latter case. Alternatively, Parker-type nanoflare models of the solar corona hypothesize that a braiding mechanism operates between unresolved loop strands, which is a more complex topological model. In this study we use the vertical-current approximation of a nonpotential magnetic field solution (that fulfills the divergence-free and force-free conditions) to characterize the number of helical turns Ntwist in twisted coronal loops. We measure the helical twist in 15 active regions observed with AIA and HMI/SDO and find a mean nonpotentiality angle (between the potential and nonpotential field directions) of μNP = 15° ± 3°. The resulting mean rotational twist angle is ϕ = 49° ± 11°, which corresponds to Ntwist=ϕ/360° = 0.14±0.03 turns with respect to the untwisted potential field, with an absolute upper limit of Ntwist ≈ 0.5, which is far below the kink instability limit of |Ntwist| ≳ 1. The number of twist turns Ntwist corresponds to the Gauss linkage number Nlink in braiding topologies. We conclude that any braided topology (with |Nlink| ≥ 1) cannot explain the observed stability of loops in a force-free corona, nor the observed low twist number. Parker-type nanoflaring can thus occur in non-forcefree environments only, such as in the chromosphere and transition region.

Authors: Markus J. Aschwanden
Projects: SDO-HMI

Publication Status: ApJ (in press, February 27, 2019)
Last Modified: 2019-02-27 12:12
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Helical Twisting Number and Braiding Linkage Number of Solar Coronal Loops  

Markus J. Aschwanden   Submitted: 2019-02-27 08:49

Coronal loops in active regions are often characterized by quasi-circular and helically twisted (sigmoidal) geometries, which are consistent with dipolar potential field models in the former case, and with nonlinear force-free field models with vertical currents in the latter case. Alternatively, Parker-type nanoflare models of the solar corona hypothesize that a braiding mechanism operates between unresolved loop strands, which is a more complex topological model. In this study we use the vertical-current approximation of a nonpotential magnetic field solution (that fulfills the divergence-free and force-free conditions) to characterize the number of helical turns Ntwist in twisted coronal loops. We measure the helical twist in 15 active regions observed with AIA and HMI/SDO and find a mean nonpotentiality angle (between the potential and nonpotential field directions) of muNP = 15° pm 3°. The resulting mean rotational twist angle is varphi = 49° pm 11°, which corresponds to Ntwist=varphi/360° = 0.14pm0.03 turns with respect to the untwisted potential field, with an absolute upper limit of Ntwist lapprox 0.5, which is far below the kink instability limit of |Ntwist| gapprox 1. The number of twist turns Ntwist corresponds to the Gauss linkage number Nlink in braiding topologies. We conclude that any braided topology (with |Nlink| ge 1) cannot explain the observed stability of loops in a force-free corona, nor the observed low twist number. Parker-type nanoflaring can thus occur in non-forcefree environments only, such as in the chromosphere and transition region.

Authors: Markus J. Aschwanden
Projects: SDO-HMI

Publication Status: ApJ 874:131 (10 pp)
Last Modified: 2019-04-03 12:30
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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:

Publication Status: 2017, ApJ 847:27 (19pp)
Last Modified: 2017-09-25 09:09
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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:

Publication Status: 2018, New Astronomy 58C, 107-123
Last Modified: 2017-09-25 09:16
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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
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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
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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

Publication Status: ApJ, subm. 2016 May 16
Last Modified: 2016-05-16 20:09
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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

Publication Status: ApJ, subm. 2016 Feb 5
Last Modified: 2016-02-09 14:59
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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
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Abstracts by Author
Interface Region Imaging Spectrograph (IRIS) Observations of the Fractal Dimension in the Solar Atmosphere
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Tracing the Chromospheric and Coronal Magnetic Field with AIA, IRIS, IBIS, and ROSA Data
The Vertical Current Approximation Nonlinear Force-Free Field Code - Description, Performance Tests, and Measurements of Magnetic Energies Dissipated in Solar Flares
Benchmark Test of Differential Emission Measure Codes and Multi-Thermal 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 Self-Organized Criticality: Solar and Astrophysics
The Magnetic Field of Active Region 11158 During the 2011 February 12-17 Flares : Differences between Photospheric Extrapolation and Coronal Forward-Fitting Methods
A Macroscopic Description of Self-Organized Criticality Systems and Astrophysical Applications
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Multi-Wavelength Observations of the Spatio-Temporal Evolution of Solar Flares with AIA/SDO:I. Universal Scaling Laws of Space and Time Parameters
Optimization of Curvi-Linear Tracing Applied to Solar Physics and Biophysics
Nonlinear Force-Free Magnetic Field Fitting to Coronal Loops with and without Stereoscopy
A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops III. The Free Energy
The Spatio-Temporal Evolution of Solar Flare Observed with AIA/SDO: Fractal Diffusion, Sub-Diffusion, or Logistic Growth ?}
Self-Organized Criticality Systems in Astrophysics (Chapter 13)
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First 3D Reconstructions of Coronal Loops with the STEREO A+B Spacecraft: IV. Magnetic Modeling with Twisted Force-Free Fields
A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. II. Numeric Code and Tests
A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. I. Theory
Automated Solar Flare Statistics in Soft X-rays over 37 Years of GOES Observations - The Invariance of Self-Organized 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 Fractal-Diffusive Avalanche Model of a Slowly-Driven Self-Organized 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 : Kink-mode with cross-sectional and density oscillation
Solar Corona Loop Studies with AIA: I. Cross-Sectional Temperature Structure
The State of Self-Organized Criticality of the Sun During the Last Three Solar Cycles. II. Theoretical Model
The State of Self-Organized Criticality of the Sun During the Last Three Solar Cycles. II. Theoretical Model
The State of Self-Organized Criticality of the Sun During the Last Three Solar Cycles. II. Theoretical Model
A Universal Scaling Law for the Fractal Energy Dissipation Domain in Self-Organized Criticality Systems
The State of Self-Organized Criticality of the Sun During the Last 3 Solar Cycles. I. Observations
The State of Self-Organized 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
Self-Organized 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 X-rays
A Code for Automated Tracing of Coronal Loops Approaching Visual Perception
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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
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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
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