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* News 04/04/20 * The archive is using a new backend database. This has thrown up a few SQL errors in the last few days. If you have any issues please email adavey@nso.edu with either the number of eprint you are trying to edit or a link to your preprint.

Torsional slow-mode oscillations discovered in the magnetic free energy during solar flares  

Markus J Aschwanden   Submitted: 2020-01-27 15:08

We report the discovery of torsional Alfvénic oscillations in solar flares, which modulate the time evolution of the magnetic free energy E_f(t), while the magnetic potential energy E_p(t) is uncorrelated, and the nonpotential energy varies as Enp(t) = E_p + E_f(t). The mean observed time period of the torsional oscillations is Pobs=15.1 ± 3.9 min, the mean field line length is L=135±35 Mm, and the mean phase speed is vphase =315 ± 120 km s-1, which we interpret as torsional Alfvénic waves in flare loops with enhanced electron densities. Most of the torsional oscillations are found to be decay-less, but exhibit a positive or negative trend in the evolution of the free energy, indicating new emerging flux (if positive), magnetic cancellation, or flare energy dissipation (if negative). The time evolution of the free energy has been calculated in this study with the Vertical-Current Approximation (Version 4) Nonlinear Force-Free Field (VCA4-NLFFF) code, which incorporates automatically detected coronal loops in the solution and bypasses the non-forcefreeness of the photospheric boundary condition, in contrast to traditional NLFFF codes.

Authors: Aschwanden,M.J. and Wang,T.J.
Projects: None

Publication Status: ApJ (2020, Jan 27; in press)
Last Modified: 2020-01-29 13:13
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Non-Stationary Fast-Driven Self-Organized Criticality in Solar Flares  

Markus J Aschwanden   Submitted: 2019-09-18 13:40

The original concept of self-organized criticality (Bak et al. 1987), applied to solar flare statistics (Lu and Hamilton 1991), assumed a slow-driven and stationary flaring rate, which warrants time scale separation (between flare durations and inter-flare waiting times), it reproduces power-law distributions for flare peak fluxes and durations, but predicts an exponential waiting time distribution. In contrast to these classical assumptions we observe: (i) multiple energy dissipation episodes during most flares, (ii) violation of the principle of time scale separation, (iii) a fast-driven and non-stationary flaring rate, (iv) a power law distribution for waiting times Δ t, with a slope of α Δ t ≈ 2.0, as predicted from the universal reciprocality between mean flaring rates and mean waiting times; and (v) pulses with rise times and decay times of the dissipated magnetic free energy on time scales of 12±6 min, up to 13 times in long-duration (≈ 4 hrs) flares. These results are inconsistent with coronal long-term energy storage (Rosner and Vaiana 1978), but require photospheric-chromospheric current injections into the corona.

Authors: Markus J. Aschwanden
Projects: SDO-AIA

Publication Status: ApJ (subm)
Last Modified: 2019-09-18 23:40
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Exoplanet predictions based on harmonic orbit resonances  

Markus J Aschwanden   Submitted: 2019-06-13 09:55

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

Authors: Aschwanden,M.J. and Scholkmann,F. 2017,
Projects: None

Publication Status: Galaxies 5(4), 56
Last Modified: 2019-06-19 13:35
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The width distribution of solar coronal loops and strands - Are we hitting rock bottom ?  

Markus J Aschwanden   Submitted: 2019-06-13 09:55

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 the lower limit of widths wmin, the peak (or most frequent) width wp, the peak occurrence number np, and a power-law slope a. Our data analysis includes automated tracing of curvilinear 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 Δx, we derive a first diagnostic criterion to discriminate whether the loop widths are unresolved (wp / Δx ≈ 2.5 ? 0.2) or fully resolved (if wp / Δx ≳ 2.7). For images with resolved loop widths, we can apply a second diagnostic criterion that predicts the lower limit of loop widths as a function of the spatial resolution. We find that the loop widths are marginally resolved in AIA images but are fully resolved in Hi-C images, where our model predicts a most frequent (peak) value at wp ≈ 550 km, in agreement with recent results of Brooks et al. This result agrees with the statistics of photospheric granulation sizes and thus supports coronal heating mechanisms operating on the macroscopic scale of photospheric magneto-convection, rather than nanoflare braiding models on unresolved microscopic scales.

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

Publication Status: ApJ 840:4 (24pp)
Last Modified: 2019-07-07 03:55
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Order out of randomness: Self-organization processes in astrophysics  

Markus J Aschwanden   Submitted: 2019-06-13 09:49

Self-organization is a property of dissipative nonlinear processes that are gov- erned by a global driving force and a local positive feedback mechanism, which creates regular geometric and/or temporal patterns, and decreases the entropy locally, in contrast to random processes. Here we investigate for the first time a comprehensive number of (17) self-organization processes that operate in planetary physics, solar physics, stellar physics, galactic physics, and cosmology. Self-organizing systems create spontaneous ?order out of randomness?, during the evolution from an initially disordered system to an ordered quasistationary system, mostly by quasi-periodic limit-cycle dynamics, but also by harmonic (me- chanical or gyromagnetic) resonances. The global driving force can be due to gravity, elec- tromagnetic forces, mechanical forces (e.g., rotation or differential rotation), thermal pres- sure, or acceleration of nonthermal particles, while the positive feedback mechanism is of- ten an instability, such as the magneto-rotational (Balbus-Hawley) instability, the convective (Rayleigh-B?nard) instability, turbulence, vortex attraction, magnetic reconnection, plasma condensation, or a loss-cone instability. Physical models of astrophysical self-organization processes require hydrodynamic, magneto-hydrodynamic (MHD), plasma, or N-body simu- lations. Analytical formulations of self-organizing systems generally involve coupled differ- ential equations with limit-cycle solutions of the Lotka-Volterra or Hopf-bifurcation type.

Authors: Aschwanden,M.J., Scholkmann,F., Bethune,W., Schmutz,W., Abramenko,W., Cheung,M.C.M., Mueller,D., Benz,A.O., Chernov,G., Kritsuk,A.G., Scargle,J.D., Melatos,A., Wagoner,R.V., Trimble,V., Green,W.
Projects: None

Publication Status: Space Science Reviews 214:55
Last Modified: 2019-06-15 17:41
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Convection-driven generation of ubiquitous coronal waves  

Markus J Aschwanden   Submitted: 2019-06-13 09:46

We develop a new method to measure the 3-D kinematics of the sub-photospheric motion of magnetic elements, which is used to study the coupling between the convection-driven vortex motion and the generation of ubiquitous coronal waves. We use the method of decomposing a line-of-sight magnetogram from HMI/SDO into unipolar magnetic charges, which yields the (projected) 2-D motion [x(t), y(t)] and the (half) width evolution w(t) of an emerging magnetic el- ement, from an initial depth of d <∼ 1500 km below the photosphere. A simple model of rotational vortex motion with magnetic flux conservation during the emergence process of a magnetic ele- ment predicts the width evolution, i.e., w(t)/w0 = [B(t)/B0]-1/2, and an upper limit of the depth variation d(t) ≤ 1.3 w(t). While previous 2-D tracing of magnetic elements provided information on advection and super-diffusion, our 3-D tracing during the emergence process of a magnetic element is consistent with a ballistic trajectory in upward direction. From the estimated Poynt- ing flux and life times of convective cells we conclude that the CoMP-detected low-amplitude transverse MHD waves are generated by the convection-driven vortex motion. Our observational measurements of magnetic elements appear to contradict the theoretical random-walk braiding scenario of Parker (1983, 1988).

Authors: Aschwanden,M.J., Gosic,M., Hurlburt,N.E., and Scullion,E.
Projects: SDO-HMI

Publication Status: ApJ 866, 72 (13pp)
Last Modified: 2019-06-15 17:41
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The minimum energy principle applied to Parker's coronal braiding and nanoflaring scenario  

Markus J Aschwanden   Submitted: 2019-06-13 09:41

Parker?s coronal braiding and nanoflaring scenario predicts the development of tangential discontinuities and highly misaligned magnetic field lines, as a consequence of random buffeting of their footpoints due to the action of sub-photospheric convection. The increased stressing of magnetic field lines is thought to become unstable above some critical misalignment angle and to result into local magnetic reconnection events, which is generally referred to as Parker?s "nanoflaring scenario". In this study we show that the minimum (magnetic) energy principle leads to a bifurcation of force-free field solutions for helical twist angles at |φ(t)| = π, which prevents the build-up of arbitrary large free energies and misalignment angles. The minimum energy principle predicts that neighbored magnetic field lines are almost parallel (with misalignment angles of ∆μ ≈ 1.6 - 1.8 deg ), and do not reach a critical misalignment angle prone to nanoflaring. Consequently, no nanoflares are expected in the divergence-free and force-free parts of the solar corona, while they are more likely to occur in the chromosphere and transition region.

Authors: Aschwanden,M.J. and vanBallegooijen,A.A.
Projects: None

Publication Status: ArXiv e-print: 1808.05269
Last Modified: 2019-06-15 17:39
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Self-organizing systems in planetary physics: Harmonic resonances of planet and moon orbits  

Markus J Aschwanden   Submitted: 2019-06-13 09:38

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 where the harmonic ratios are given by five dominant resonances, namely . 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  ≈ 10 resonant zones that can be occupied with planets (or moons) in long-term stable orbits.

Authors: Aschwanden M.J.
Projects: None

Publication Status: New Astronomy 58C, 107-123
Last Modified: 2019-06-19 13:35
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Global energetics of solar flares: VIII. The Low-Energy Cutoff  

Markus J Aschwanden   Submitted: 2019-06-13 09:28

One of the key problems in solar flare physics is the determination of the low-energy cut-off; the value that determines the energy of nonthermal electrons and hence flare energetics. We discuss different approaches to determine the low-energy cut-off in the spectrum of accelerated electrons: (i) the total electron number model, (ii) the time-of-flight model (based on the equivalence of the time-of-flight and the collisional deflection time); (iii) the warm target model of Kontar et al. (2015), and (iv) the model of the spectral cross-over between thermal and nonthermal components. We find that the first three models are consistent with a low-energy cutoff with a mean value of ≈ 10 keV, while the cross-over model provides an upper limit for the low-energy cutoff with a mean value of ≈ 21 keV. Combining the first three models we find that the ratio of the nonthermal energy to the dissipated magnetic energy in solar flares has a mean value of qE = 0.57 ? 0.08, which is consistent with an earlier study based on the simplified approximation of the warm target model alone (qE = 0.51 ? 0.17). This study corroborates the self-consistency between three different low-energy cutoff models in the calculation of nonthermal flare energies.

Authors: Aschwanden,M.J., Kontar, E.P., and Jeffrey, N.L.S.
Projects: None

Publication Status: The Astrophysicak Journal (subm.)
Last Modified: 2019-06-15 17:38
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Global energetics of solar flares: VIII. The Low-Energy Cutoff  

Markus J Aschwanden   Submitted: 2019-06-13 09:28

One of the key problems in solar flare physics is the determination of the low-energy cut-off; the value that determines the energy of nonthermal electrons and hence flare energetics. We discuss different approaches to determine the low-energy cut-off in the spectrum of accelerated electrons: (i) the total electron number model, (ii) the time-of-flight model (based on the equivalence of the time-of-flight and the collisional deflection time); (iii) the warm target model of Kontar et al. (2015), and (iv) the model of the spectral cross-over between thermal and nonthermal components. We find that the first three models are consistent with a low-energy cutoff with a mean value of ≈ 10 keV, while the cross-over model provides an upper limit for the low-energy cutoff with a mean value of ≈ 21 keV. Combining the first three models we find that the ratio of the nonthermal energy to the dissipated magnetic energy in solar flares has a mean value of qE = 0.57 ? 0.08, which is consistent with an earlier study based on the simplified approximation of the warm target model alone (qE = 0.51 ? 0.17). This study corroborates the self-consistency between three different low-energy cutoff models in the calculation of nonthermal flare energies.

Authors: Aschwanden,M.J., Kontar, E.P., and Jeffrey, N.L.S.
Projects: RHESSI

Publication Status: The Astrophysicak Journal (in press.)
Last Modified: 2019-06-26 12:43
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Global Energetics of Solar Flares: VII. Aerodynamic Drag in Coronal Mass Ejections  

Markus J Aschwanden   Submitted: 2019-06-13 09:23

The free energy that is dissipated in a magnetic reconnection process of a solar flare, generally accompanied by a coronal mass ejection (CME), has been considered as the ultimate energy source of the global energy budget of solar flares in previous statistical studies. Here we explore the effects of the aerodynamic drag force on CMEs, which supplies additional energy from the slow solar wind to a CME event, besides the magnetic energy supply. For this purpose we fit the analytical aerodynamic drag model of Cargill (2004) and Vrsnak et al. (2013) to the height-time profiles r(t) of LASCO/SOHO data in 14,316 CME events observed during the first 8 years (2010-2017) of the SDO era {\bf (ensuring EUV coverage with AIA)}. Our main findings are: (i) a mean solar wind speed of w=472 ± 414 km s-1, (ii) a maximum drag-accelerated CME energy of Edrag ≈ 2 * 1032 erg, (iii) a maximum flare-accelerated CME energy of Eflare < 1.5 * 1033 erg; (iv) the ratio of the summed kinetic energies of all flare-accelerated CMEs to the drag-accelerated CMEs amounts to a factor of 4; (v) the inclusion of the drag force slightly lowers the overall energy budget of CME kinetic energies in flares from ~ 7% to ~ 4%; and (vi) the arrival times of CMEs at Earth can be predicted with an accuracy of ~23%.

Authors: Aschwanden, M.J. and Gopalswamy, N.
Projects: None

Publication Status: The Astrophysical Journal 877:149 (14pp)
Last Modified: 2019-06-15 17:38
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Self-organized criticality in solar and stellar flares: Are extreme events scale-free ?  

Markus J Aschwanden   Submitted: 2019-06-13 09:15

We search for outliers in extreme events of statistical size distributions of astrophysical data sets, motivated by the Dragon-King hypothesis of Sornette (2009), which suggests that the most extreme events in a statistical distribution may belong to a different population, and thus may be generated by a different phyiscal mechanism, in contrast to the strict power law behavior of self-organized criticality (SOC) models. Identifying such disparate outliers is important for space weather predictions. Possible physical mechanisms to produce such outliers could be generated by sympathetic flaring. However, we find that Dragon-King events are not common in solar and stellar flares, identified in 4 out of 25 solar and stellar flare data sets only. Consequently, small, large, and extreme flares are essentially scale-free and can be modeled with a single physical mechanism. In very large data sets (N > 104) we find significant deviations from ideal poer laws in almost all data sets. Neverthess, the fitted power law slopes constrain physcial scaling laws in terms of flare areas and volumes, which have the highest nonlinearity in their scaling laws.

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

Publication Status: The Astrophysical Journal (June 13, 2019, accepted), in press
Last Modified: 2019-06-15 17:38
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The Minimum Energy Principle Applied to Parker's Coronal Braiding and Nanoflaring Scenario  

Markus J Aschwanden   Submitted: 2018-08-15 13:25

Parker's coronal braiding and nanoflaring scenario predicts the development of tangential discontinuities and highly misaligned magnetic field lines, as a consequence of random buffeting of their footpoints due to the action of sub-photospheric convection. The increased stressing of magnetic field lines is thought to become unstable above some critical misalignment angle and to result into local magnetic reconnection events, which is generally referred to as Parker's ''nanoflaring scenario''. In this study we show that the minimum (magnetic) energy principle leads to a bifurcation of force-free field solutions for helical twist angles at |ϕ(t)| = π, which prevents the build-up of arbitrary large free energies and misalignment angles. The minimum energy principle predicts that neighbored magnetic field lines are almost parallel (with misalignment angles of Δμ approx 1.6°-1.8°), and do not reach a critical misalignment angle prone to nanoflaring. Consequently, no nanoflares are expected in the divergence-free and force-free parts of the solar corona, while they are more likely to occur in the chromosphere and transition region.

Authors: Aschwanden, M.J. and van Ballegooijen,A.A.
Projects:

Publication Status: submit. (2018 Aug 15)
Last Modified: 2018-08-27 11:22
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Exoplanet Predictions Based on Harmonic Orbit Resonances  

Markus J Aschwanden   Submitted: 2017-05-19 12:52

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

Authors: Markus J. Aschwanden and Felix Scholkmann
Projects:

Publication Status: 2017, Galaxies 5(4), 56
Last Modified: 2017-09-25 09:07
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Modeling of Coronal EUV Loops Observed with TRACE : I. Hydrostatic Steady-State Solutions with Nonuniform Heating  

Markus J Aschwanden   Submitted: 2000-08-18 13:05

Recent observations of coronal loops in EUV wavelengths with the {sl Transition Region and Coronal Explorer (TRACE)} and the {sl Extreme-ultraviolet Imaging Telescope (EIT)} on the {sl Solar and Heliospheric Observatory (SoHO)} demonstrated three new results that cannot be explained with most of the existing loop models: (1) EUV loops are near-isothermal along their coronal segments, (2) they show an overpressure or overdensity compared with the requirements of steady-state loops with uniform heating, and (3) the brightest EUV loops exhibit extended scale heights up to four times the hydrostatic scale height. These observations cannot be reconciled with the classical RTV (Rosner, Tucker, & Vaiana) model, they do not support models with uniform heating, and partially even violate the requirements of hydrostatic equilibrium. - In this study we conduct numeric calculations of steady-state solutions of the hydrodyn- hydrodynamic equations of mass conservation, momentum balance, and energy balance. We calculate some 500 solutions that cover a large parameter space of loop lengths (L approx 4-300 Mm), of nonuniform heating functions (with heating scale heights in the range of {lambda}_H approx 1-300 Mm), as well as the limit of uniform heating ({lambda}_H gg L). The parameter space can be subdivided into 3 regimes, which contain (1) solutions for stable loops, (2) solutions for unstable loops, and (3) no solutions. Short heating scale heights ({lambda}H, Mm lapprox sqrt{LMm}) lead to unstable loops. Fitting the hydrostatic solutions to 41 EUV loops observed with {sl TRACE} we find that 60% are dynamically unstable, 30% are near a steady-state equilibrium, and 10% are cooling off. Those loops near steady-state are all found to be heated near the footpoints, with a heating scale height of {lambda}_H=12 pm 5 Mm, covering a fraction {lambda}_H/L=0.2pm0.1 of the loop length. None of the observed loops is consistent with a uniform heating function in steady-state. Because the observed heating scale heights are all found less than a factor of 2 within the instability limit, most of the coronal heating episodes seem to operate with relatively short heating scale heights, producing mostly dynamical- dynamically unstable loops and transient brightenings.

Authors: Markus J. Aschwanden, Carolus J. Schrijver, and David Alexander
Projects:

Publication Status: ApJ, subm. (2000 Aug 7)
Last Modified: 2000-08-18 13:05
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Evidence for Nonuniform Heating of Coronal Loops Inferred from Multi-Thread Modeling of TRACE Data  

Markus J Aschwanden   Submitted: 2000-05-26 13:04

The temperature Te(s) and density structure n_e(s) of active region loops in EUV observed with {sl TRACE} is modeled with a multi-thread model, synthesized from the summed emission of many loop threads that have a distribution of maximum temperatures and that satisfy the steady-state Rosner-T- Rosner-Tucker-Vaiana (RTV) scaling law, modified by Serio et al. for gravitatio- gravitational stratification (called RTVS_p in the following). In a recent Letter, Reale & Peres demonstrated that this method can explain the almost isothermal appearance of TRACE loops (observed by Lenz et al.) as derived from the filter-ratio method. From model-fitting of the 171 and 195 ang fluxes of 41 loops, which have loop half lengths in the range of L=4-320 Mm, we find: (1) The EUV loops consist of near-isothermal loop threads with substantially smaller temperature gradients than predicted by the RTVS_p model, (2) the loop base pressure, p_0 approx 0.3pm 0.1 dyne cm-2, is independent of the loop length L, it agrees with the RTVS_p model for the shortest loops, but exceeds the RTVS_p model up to a factor of 35 for the largest loops, and (3) the pressure scale height is consistent with hydrostatic equilibrium for the shortest loops, but exceeds the temperature scale height up to a factor of approx 3 for the largest loops. The data indicate that cool EUV loops in the temperature range of Teapprox 0.8-1.6 MK cannot be explained with the static steady-state RTVS_p model in terms of uniform heating, but are fully consistent with Serio's model in the case of nonuniform heating (RTVSph), with heating scale heights in the range of s_H=17 pm 6 Mm. This heating function provides almost uniform heating for small loops (L lapprox 20 Mm), but restricts heating to the footpoints of large loops (Lapprox 50-300 Mm). Chromospheric upflows appear to be the most likely heating source of EUV loops.

Authors: Markus J. Aschwanden, Richard W. Nightingale, and David Alexander
Projects:

Publication Status: ApJ 541:1059-1077 (2000 October 1)
Last Modified: 2000-10-06 08:35
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Tomography of the Soft X-Ray Corona: Measurements of Electron Densities, Temperatures, and Differential Emission Measure Distributions above the Limb  

Markus J Aschwanden   Submitted: 2000-05-04 16:02

We analyze long-exposure and off-pointing {sl Yohkoh/SXT} data of the solar corona observed on 1992 Aug 26. We develop a new tomographic method which is based on a forward-fitting method of a 4-parameter model to the observed soft X-ray fluxes F_1(h) and F_2(h) of two {sl SXT} wavelength filters as function of height h. The model is defined in terms of a {sl differential emission measure (DEM)} distribution dEM(h, T)/dT, which includes also a temperature dependence of density scale heights {lambda}_n(T) =qlambda {lambda}_T and allows to quantify deviations (qlambda eq 1) from hydrostatic equilibrium, i.e. {lambda}_n(T)={lambda}_T. This parametrization faciliates a proper line-of-sight integration and relates the widely-used filter-ratio temperature TFR to the peak of the DEM distribution. A direct consequence of the multi-scale-height atmosphere is that the filter ratio temperature TFR(h) is predicted to increase with height, even if all magnetic field lines are isothermal. Our model-fitting reveals that coronal holes and Quiet Sun regions are in perfect hydrostatic equilibrium, but that coronal streamers have a scale height that exceeds the hydrostatic scale height by a factor of up to qlambdalapprox 2.3, which underscores the dynamic nature of coronal streamers. Our density measurements in coronal holes are slightly lower than most of the white-light polarized brightness inversions, and seem to come closer to the requirements of solar wind models. Our DEM model provides also a physical framework for the semi-empirical {sl Baumbach-Allen formula}, and quantifies the temperature ranges and degree of hydrostaticity of the {sl K-, L-, } and {sl F-corona}.

Authors: Markus J. Aschwanden and Loren W. Acton
Projects:

Publication Status: ApJ 550, 475-492
Last Modified: 2001-04-09 07:52
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The Effect of Hydrostatic Weighting on the Vertical Temperature Structure of the Solar Corona  

Markus J Aschwanden   Submitted: 2000-04-07 13:05

We investigate the effect of hydrostatic scale heights {lambda}(T) in coronal loops on the determination of the vertical temperature structure T(h) of the solar corona. Every method that determines an average temperature at a particular line-of-sight from optically thin emission (e.g. in EUV or soft X-ray wavelengths) of a mutli-temperature plasma, is subject to the emission measure- measure-weighted contributions dEM(T)/dT from different temperatures. Because most of the coronal structures (along open or closed field lines) are close to hydrostatic equilibrium, the hydrostatic temperature scale height introduces a height-dependent weighting function that causes a systematic bias in the determination of the temperature structure T(h) as function of altitude h. The net effect is that the averaged temperature seems to increase with altitude, dT(h)/dh > 0, even if every coronal loop is isothermal (at different temperatures). We simulate this effect with differential emission measure distributions observed by {sl SERTS} for an instrument with a broadband temperature filter such as {sl Yohkoh/SXT} and find that the apparent temperature increase due to hydrostatic weighting is of order Delta T approx T (h/rsun). We suggest that this effect largely explains the systematic temperature increase in the upper corona reported in recent studies (e.g. by Sturrock et al., Wheatland et al., or Priest et al.), rather than being an intrinsic signature of a coronal heating mechanism.

Authors: Aschwanden,M.J. and Nitta,N.
Projects:

Publication Status: 2000, ApJ 535, L59-L62
Last Modified: 2000-08-31 08:01
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Quadrupolar Magnetic Reconnection in Solar Flares: I. 3D Geometry inferred from Yohkoh Observations  

Markus J Aschwanden   Submitted: 2000-01-25 14:02

We analyze the 3-dimensional (3D) geometry of solar flares that show so-called {sl interacting flare loops} in soft X-ray, hard X-ray, and radio emission, as previously identified by Hanaoka and Nishio. The two flare loops that appear brightest after the flare are assumed to represent the outcome of a quadrupolar magnetic reconnection process, during which the connectivity of magnetic polarities is exchanged between the four loop footpoints. We parametrize the 3D geometry of the 4 involved magnetic field lines with circular segments, additionally constrained by the geometric condition that the two pre-reconnecti- pre-reconnection field lines have to intersect each other at the onset of the reconnection process, leading to a 10-parameter model. We fit this 10-parameter model to Yohkoh SXT and HXT data of 10 solar flares and determine this way the loop sizes and relative orientation of interacting field lines before and after reconnection. We apply a flare model of Melrose to calculate the magnetic flux transfer and energy released when two current-carrying field lines reconnect to form a new current-carrying system in a quadrupolar geometry. The findings and conclusions are: (1) The pre-reconnection field lines always show a strong asymmetry in size, consistent with the scenario of new-emerging small-scale loops that reconnect with pre-existing large-scale loops. (2) The relative angle between reconnecting field lines is near-collinear in half of the cases, and near-perpendicular in the other half, contrary to the anti-parallel configurati- configuration that is considered to be most efficient for magnetic reconnection. (3) The angle between interacting field lines reduces by approx 10°-50^- 10°-50° after quadrupolar reconnection. (4) The small-scale flare loop experiences a shrinkage by a factor of 1.31pm0.44, which is consistent with the scaling law found from previous electron time-of-flight measurements, suggesting that electron acceleration occurs near the cusp of quadrupolar configurations. (5) The large-scale loop is found to dominate the total induction between current-carrying loops, providing a simple estimate of the maximum magnetic energy available for flare energy release due to current transfer, which scales as Delta E^I approx 1029.63 (r_2/109 { m cm}) (I_2/1011 A)^2, (with r2 the curvature radius and I2 the current of the large-scale loop) and is found to correlate with observed flare energies deduced from soft X-ray and hard X-ray fluxes. Most of the energy is transferred to small-scale loops that have half of the large-scale current (I_1=I_2/2). (6) The quadrupolar reconnection geometry provides also a solution of {sl Canfield's dilemma} of the offset between the maximum of vertical currents and the HXR flare loop footpoints. (7) The quadrupolar geometry provides not only a framework for interacting double-loop flares, but can also be considered as a generalized version of (cusp-shaped) single-loop flares.

Authors: Aschwanden,M.J., Kosugi,T., Hanaoka,Y., Nishio,M., and Melrose,D.B.
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Publication Status: Astrophys.J. 1999, Vol. 526, p. 1026-1045.
Last Modified: 2000-01-25 14:02
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3D-Stereoscopic Analysis of Solar Active Region Loops:  

Markus J Aschwanden   Submitted: 2000-01-25 14:02

In this paper we study the three-dimensional (3D) structure of hot (Teapprox 1.5-2.5 MK) loops in solar active region NOAA 7986, observed on 1996 August 30 with the {sl Extreme-ultraviolet Imaging Telescope (EIT)} onboard the {sl Solar and Heliospheric Observatory (SoHO)}. This complements a first study (Paper I) on cooler (Teapprox 1.0-1.5 MK) loops of the same active region, using the same method of {sl Dynamic Stereoscopy} to reconstruct the 3D geometry. We reconstruct the 3D-coordinates x(s), y(s), z(s), the density n_e(s), and temperature profile Te(s) of 35 individual loop segments (as a function of the loop coordinate s) using EIT 195 ang and 284 ang images. The major findings are: (1) All loops are found to be in hydrostatic equilibrium, in the entire temperature regime of Te=1.0-2.5 MK; (2) The analyzed loops have a height of 2-3 scale heights, and thus only segments extending over about one vertical scale height have sufficient emission measure contrast for detection; (3) The temperature gradient over the lowest scale height is of order dT/dsapprox 1-10 K/km; (4) The radiative loss rate is found to exceed the conductive loss rate by about two orders or magnitude in the coronal loop segments, implying that the loops cannot be in quasistatic equilibrium, since standard steady-state loop models show that radiative and conductive losses are comparable; (5) A steady-state could only be maintained if the heating rate EH matches exactly the radiative loss rate in hydrostatic equilibrium, requiring a heat deposition length {lambda}_H of the half density scale height lambda. (6) We find a correlation of p propto L-1 between loop base pressure and loop length, which is not consistent with the scaling law predicted from steady-state models of large-scale loops. - All observational findings indicate consistently that the energy balance of the observed EUV loops cannot be described by steady-state models.

Authors: Aschwanden,M.J., Alexander,D., Hurlburt,N., Newmark,J.S.,Neupert,W.M., Klimchuk,J.A., and G.A.Gary
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Publication Status: 1999, ApJ 515, 842-867
Last Modified: 2000-08-31 08:27
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