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The Enthalpy Based Thermal Evolution of Loops (EBTEL) approximate model for static and dynamic coronal loops is developed to include the effect of a loop cross-sectional area which increases from the base of the transition region (TR) to the corona. The TR is defined as the part of a loop between the top of the chromosphere and the location where thermal conduction changes from an energy loss to an energy gain. There are significant differences from constant area loops due to the manner in which the reduced volume of the TR responds to conductive and enthalpy fluxes from the corona. For static loops with modest area variation the standard picture of loop energy balance is retained, with the corona and TR being primarily a balance between heating and conductive losses in the corona, and downward conduction and radiation to space in the TR. As the area at the loop apex increases, the TR becomes thicker and the density in TR and corona larger. For large apex areas, the coronal energy balance changes to one primarily between heating and radiation, with conduction playing an increasingly unimportant role, and the TR thickness becoming a significant fraction of the loop length. Approximate scaling laws are derived that give agreement with full numerical solutions for the density, but not the temperature. For non-uniform areas, dynamic loops have a higher peak temperature and are denser in the radiative cooling phase by of order 50% than the constant area case for the examples considered. They also show a final rapid cooling and draining once the temperature approaches 1 MK. Although the magnitude of the emission measure will be enhanced in the radiative phase, there is little change in the important observational diagnostic of its temperature dependence., Comment: 10 pages, 9 figures, published in MNRAS

Coronal loops, seen in solar coronal images, are believed to represent emission from magnetic flux tubes with compact cross-sections. We examine the 3D structure of plasma above an active region in a radiative magnetohydrodynamic simulation to locate volume counterparts for coronal loops. In many cases, a loop cannot be linked to an individual thin strand in the volume. While many thin loops are present in the synthetic images, the bright structures in the volume are fewer, and of complex shape. We demonstrate that this complexity can form impressions of thin bright loops, even in the absence of thin bright plasma strands. We demonstrate the difficulty of discerning from observations whether a particular loop corresponds to a strand in the volume, or a projection artifact. We demonstrate how apparently isolated loops could deceive observers, even when observations from multiple viewing angles are available. While we base our analysis on a simulation, the main findings are independent from a particular simulation setup and illustrate the intrinsic complexity involved in interpreting observations resulting from line-of-sight integration in an optically thin plasma. We propose alternative interpretation for strands seen in EUV images of the corona. The "coronal veil" hypothesis is mathematically more generic, and naturally explains properties of loops that are difficult to address otherwise -- such as their constant cross section and anomalously high density scale height. We challenge the paradigm of coronal loops as thin magnetic flux tubes, offering new understanding of solar corona and, by extension, of other magnetically confined bright, hot plasmas., Comment: ApJ (in press)

We discuss the diagnostics available to study the 5-10 MK plasma in the solar corona, which is key to understanding the heating in the cores of solar active regions. We present several simulated spectra, and show that excellent diagnostics are available in the soft X-rays, around 100 Angstroms, as six ionisation stages of Fe can simultaneously be observed, and electron densities derived, within a narrow spectral region. As this spectral range is almost unexplored, we present an analysis of available and simulated spectra, to compare the hot emission with the cooler component. We adopt recently designed multilayers to present estimates of count rates in the hot lines, with a baseline spectrometer design. Excellent count rates are found, opening up the exciting opportunity to obtain high-resolution spectroscopy of hot plasma., Comment: Accepted for publication in Frontiers in Astronomy and Space Sciences, section Stellar and Solar Physics

Magnetic reconnection underlies many explosive phenomena in the heliosphere and in laboratory plasmas. The new research capabilities in theory/simulations, observations, and laboratory experiments provide the opportunity to solve the grand scientific challenges summarized in this whitepaper. Success will require enhanced and sustained investments from relevant funding agencies, increased interagency/international partnerships, and close collaborations of the solar, heliospheric, and laboratory plasma communities. These investments will deliver transformative progress in understanding magnetic reconnection and related explosive phenomena including space weather events., Comment: 4 pages (including a title page), white paper submitted to Helio2050 workshop at https://www.hou.usra.edu/meetings/helio2050/. arXiv admin note: substantial text overlap with arXiv:2004.00079

This white paper summarizes major scientific challenges and opportunities in understanding magnetic reconnection and related explosive phenomena as a fundamental plasma process., Comment: 6 pages, 1 figure, white paper submitted to both Plasma 2020 and Astro 2020 Decadal Surveys

Coronal loops, constituting the basic building blocks of the active Sun, serve as primary targets to help understand the mechanisms responsible for maintaining multi-million Kelvin temperatures in the solar and stellar coronae. Despite significant advances in observations and theory, our knowledge on the fundamental properties of these structures is limited. Here, we present unprecedented observations of accelerating slow magnetoacoustic waves along a coronal loop that show differential propagation speeds in two distinct temperature channels, revealing the multi-stranded and multi-thermal nature of the loop. Utilizing the observed speeds and employing nonlinear force-free magnetic field extrapolations, we derive the actual temperature variation along the loop in both channels, and thus are able to resolve two individual components of the multi-thermal loop for the first time. The obtained positive temperature gradients indicate uniform heating along the loop, rather than isolated footpoint heating., Comment: accepted for publication in ApJ

Observations reveal a correspondence between chromospheric type II spicules and bright upwardly moving fronts in the corona observed in the EUV band. However, theoretical considerations suggest that these flows are unlikely to be the main source of heating in coronal magnetic loops. We investigate the propagation of high-speed chromospheric flows into coronal magnetic flux tubes, and the possible production of emission in the EUV band. We simulate the propagation of a dense $10^4$ K chromospheric jet upwards along a coronal loop, by means of a 2-D cylindrical MHD model, including gravity, radiative losses, thermal conduction and magnetic induction. The jet propagates in a complete atmosphere including the chromosphere and a tenuous cool ($\sim 0.8$ MK) corona, linked through a steep transition region. In our reference model, the jet's initial speed is 70 km/s, its initial density is $10^{11}$ cm$^{-3}$, and the ambient uniform magnetic field is 10 G. We explore also other values of jet speed and density in 1-D, and of magnetic field in 2-D, and the jet propagation in a hotter ($\sim 1.5$ MK) background loop. While the initial speed of the jet does not allow it to reach the loop apex, a hot shock front develops ahead of it and travels to the other extreme of the loop. The shock front compresses the coronal plasma and heats it to about $10^6$ K. As a result, a bright moving front becomes visible in the 171 \AA\ channel of the SDO/AIA mission. This result generally applies to all the other explored cases, except for the propagation in the hotter loop. For a cool, low-density initial coronal loop, the post-shock plasma ahead of upward chromospheric flows might explain at least part of the observed correspondence between type II spicules and EUV emission excess., Comment: 10 pages; 8 figures, accepted for publication on A&A

It has been suggested that the hot plasma of the solar corona comes primarily from impulsive heating events, or nanoflares, that occur in the lower atmosphere, either in the upper part of the ordinary chromosphere or at the tips of type II spicules. We test this idea with a series of hydrodynamic simulations. We find that synthetic Fe XII (195) and Fe XIV (274) line profiles generated from the simulations disagree dramatically with actual observations. The integrated line intensities are much too faint; the blue shifts are much too fast; the blue-red asymmetries are much too large; and the emission is confined to low altitudes. We conclude that chromospheric nanoflares are not a primary source of hot coronal plasma. Such events may play an important role in producing the chromosphere and powering its intense radiation, but they do not, in general, raise the temperature of the plasma to coronal values. Those cases where coronal temperatures are reached must be relatively uncommon. The observed profiles of Fe XII and Fe XIV come primarily from plasma that is heated in the corona itself, either by coronal nanoflares or a quasi-steady coronal heating process. Chromospheric nanoflares might play a role in generating waves that provide this coronal heating., Comment: 14 pages, 6 figures, accepted by Astrophysical Journal

The expansion of coronal loops in the transition region may considerably influence the diagnostics of the plasma emission measure. The cross sectional area of the loops is expected to depend on the temperature and pressure, and might be sensitive to the heating rate. The approach here is to study the area response to slow changes in the coronal heating rate, and check the current interpretation in terms of steady heating models. We study the area response with a time-dependent 2D MHD loop model, including the description of the expanding magnetic field, coronal heating and losses by thermal conduction and radiation from optically thin plasma. We run a simulation for a loop 50 Mm long and quasi-statically heated to about 4 MK. We find that the area can change substantially with the quasi-steady heating rate, e.g. by ~40% at 0.5 MK as the loop temperature varies between 1 and 4 MK, and, therefore, affects the interpretation of DEM(T) curves., Comment: 9 pages, 5 figures, accepted for publication

We will use new data from the High-resolution Coronal Imager (Hi-C) with unprecedented spatial resolution of the solar corona to investigate the structure of coronal loops down to 0.2 arcsec. During a rocket flight Hi-C provided images of the solar corona in a wavelength band around 193 A that is dominated by emission from Fe XII showing plasma at temperatures around 1.5 MK. We analyze part of the Hi-C field-of-view to study the smallest coronal loops observed so far and search for the a possible sub-structuring of larger loops. We find tiny 1.5 MK loop-like structures that we interpret as miniature coronal loops. These have length of the coronal segment above the chromosphere of only about 1 Mm and a thickness of less than 200 km. They could be interpreted as the coronal signature of small flux tubes breaking through the photosphere with a footpoint distance corresponding to the diameter of a cell of granulation. We find loops that are longer than 50 Mm to have a diameter of about 2 arcsec or 1.5 Mm, consistent with previous observations. However, Hi-C really resolves these loops with some 20 pixels across the loop. Even at this greatly improved spatial resolution the large loops seem to have no visible sub-structure. Instead they show a smooth variation in cross-section. The fact that the large coronal loops do not show a sub-structure at the spatial scale of 0.1 arcsec per pixel implies that either the densities and temperatures are smoothly varying across these loops or poses an upper limit on the diameter of strands the loops might be composed of. We estimate that strands that compose the 2 arcsec thick loop would have to be thinner than 15 km. The miniature loops we find for the first time pose a challenge to be properly understood in terms of modeling., Comment: Accepted for publication in A&A (Jun 19, 2013), 11 pages, 10 figures

We examine the suggestion that most of the hot plasma in the Sun's corona comes from type II spicule material that is heated as it is ejected from the chromosphere. This contrasts with the traditional view that the corona is filled via chromospheric evaporation that results from coronal heating. We explore the observational consequences of a hypothetical spicule dominated corona and conclude from the large discrepancy between predicted and actual observations that only a small fraction of the hot plasma can be supplied by spicules (<2% in active regions, <5% in the quiet Sun, and <8% in coronal holes). The red-blue asymmetries of EUV spectral lines and the ratio of lower transition region (LTR; T<0.1 MK) to coronal emission measures are both predicted to be 2 orders of magnitude larger than observed. Furthermore, hot spicule material would cool dramatically by adiabatic expansion as it rises into the corona, so substantial coronal heating would be needed to maintain the high temperatures that are seen at all altitudes. We suggest that the corona contains a mixture of thin strands, some of which are populated by spicule injections, but most of which are not. A majority of the observed hot emission originates in non-spicule strands and is explained by traditional coronal heating models. However, since these models predict far too little emission from the LTR, most of this emission comes from the bulk of the spicule material that is only weakly heated and visible in He II (304 A) as it falls back to the surface., Comment: 11 pages, 5 figures, published

Since the launch of NASA's Solar Dynamics Observatory on 2010 February 11, the Extreme ultraviolet Variability Experiment (EVE) has observed numerous flares. One interesting feature observed by EVE is that a subset of flares exhibit an additional enhancement of the 2-3 million K emission several hours after the flare's soft X-ray emission. From the Atmospheric Imaging Assembly (AIA) images, we observe that this secondary emission, dubbed the EUV late phase, occurs in the same active region as the flare but not in the same coronal loops. Here, we examine the C8.8 flare that occurred on 2010 May 5 as a case study of EUV late phase flares. In addition to presenting detailed observations from both AIA and EVE, we develop a physical model of this flare and test it using the Enthalpy Based Thermal Evolution of Loops (EBTEL) model., Comment: submitted to ApJ

The heating of the solar corona is one of the big questions in astrophysics. Rapid pulses called nanoflares are among the best candidate mechanisms. The analysis of the time variability of coronal X-ray emission is potentially a very useful tool to detect impulsive events. We analyze the small-scale variability of a solar active region in a high cadence Hinode/XRT observation. The dataset allows us to detect very small deviations of emission fluctuations from the distribution expected for a constant rate. We discuss the deviations in the light of the pulsed-heating scenario., Comment: 6 pages, 4 figures

We present the science case for a broadband X-ray imager with high-resolution spectroscopy, including simulations of X-ray spectral diagnostics of both active regions and solar flares. This is part of a trilogy of white papers discussing science, instrument (Bandler et al. 2010), and missions (Bookbinder et al. 2010) to exploit major advances recently made in transition-edge sensor (TES) detector technology that enable resolution better than 2 eV in an array that can handle high count rates. Combined with a modest X-ray mirror, this instrument would combine arcsecondscale imaging with high-resolution spectra over a field of view sufficiently large for the study of active regions and flares, enabling a wide range of studies such as the detection of microheating in active regions, ion-resolved velocity flows, and the presence of non-thermal electrons in hot plasmas. It would also enable more direct comparisons between solar and stellar soft X-ray spectra, a waveband in which (unusually) we currently have much better stellar data than we do of the Sun., Comment: 7 pages, white paper submitted the Solar and Heliophsyics Decadal Survey

We develop and analyze a simple cellular automaton (CA) model that reproduces the main properties of the evolution of soft X-ray coronal loops. We are motivated by the observation that these loops evolve in three distinguishable phases that suggest the development, maintainance, and decay of a self-organized system. The model is based on the idea that loops are made of elemental strands that are heated by the relaxation of magnetic stress in the form of nanoflares. In this vision, usually called "the Parker conjecture" (Parker 1988), the origin of stress is the displacement of the strand footpoints due to photospheric convective motions. Modeling the response and evolution of the plasma we obtain synthetic light curves that have the same characteristic properties (intensity, fluctuations, and timescales) as the observed cases. We study the dependence of these properties on the model parameters and find scaling laws that can be used as observational predictions of the model. We discuss the implications of our results for the interpretation of recent loop observations in different wavelengths., Comment: 2010, accepted for publication in ApJ

Any successful model of coronal loops must explain a number of observed properties. For warm (~ 1 MK) loops, these include: 1. excess density, 2. flat temperature profile, 3. super-hydrostatic scale height, 4. unstructured intensity profile, and 5. 1000--5000 s lifetime. We examine whether thermal nonequilibrium can reproduce the observations by performing hydrodynamic simulations based on steady coronal heating that decreases exponentially with height. We consider both monolithic and multi-stranded loops. The simulations successfully reproduce certain aspects of the observations, including the excess density, but each of them fails in at least one critical way. Monolithic models have far too much intensity structure, while multi-strand models are either too structured or too long-lived. Our results appear to rule out the widespread existence of heating that is both highly concentrated low in the corona and steady or quasi-steady (slowly varying or impulsive with a rapid cadence). Active regions would have a very different appearance if the dominant heating mechanism had these properties. Thermal nonequilibrium may nonetheless play an important role in prominences and catastrophic cooling events (e.g., coronal rain) that occupy a small fraction of the coronal volume. However, apparent inconsistencies between the models and observations of cooling events have yet to be understood., Comment: 40 pages, 10 figures, accepted by the Astrophysical Journal (vol. 714)

EUV observations of warm coronal loops suggest that they are bundles of unresolved strands that are heated impulsively to high temperatures by nanoflares. The plasma would then have the observed properties (e.g., excess density compared to static equilibrium) when it cools into the 1-2 MK range. If this interpretation is correct, then very hot emission should be present outside of proper flares. It is predicted to be vey faint, however. A critical element for proving or refuting this hypothesis is the existence of hot, very faint plasmas which should be at amounts predicted by impulsive heating. We report on the first comprehensive spectroscopic study of hot plasmas in active regions. Data from the EIS spectrometer on Hinode were used to construct emission measure distributions in quiescent active regions in the 1-5 MK temperature range. The distributions are flat or slowly increasing up to approximately 3 MK and then fall off rapidly at higher temperatures. We show that active region models based on impulsive heating can reproduce the observed EM distributions relatively well. Our results provide strong new evidence that coronal heating is impulsive in nature., Comment: ApJ, 2009, in press

The X-Ray Telescope (XRT) on the Japanese/USA/UK {\it Hinode (Solar-B)} spacecraft has detected emission from a quiescent active region core that is consistent with nanoflare heating. The fluxes from 10 broadband X-ray filters and filter combinations were used to constructed Differential Emission Measure (DEM) curves. In addition to the expected active region peak at Log T = 6.3-6.5, we find a high-temperature component with significant emission measure at Log T $>$ 7.0. This emission measure is weak compared to the main peak -- the DEM is down by almost three orders of magnitude -- which accounts of the fact that it has not been observed with earlier instruments. It is also consistent with spectra of quiescent active regions: no Fe XIX lines are observed in a CHIANTI synthetic spectrum generated using the XRT DEM distribution. The DEM result is successfully reproduced with a simple two-component nanoflare model., Comment: Submitted to ApJ Letters

Commission 10 deals with solar activity in all of its forms, ranging from the smallest nanoflares to the largest coronal mass ejections. This report reviews scientific progress over the roughly two-year period ending in the middle of 2008. This has been an exciting time in solar physics, highlighted by the launches of the Hinode and STEREO missions late in 2006. The report is reasonably comprehensive, though it is far from exhaustive. Limited space prevents the inclusion of many significant results. The report is divided into the following sections: Photosphere and Chromosphere; Transition Region; Corona and Coronal Heating; Coronal Jets; Flares; Coronal Mass Ejection Initiation; Global Coronal Waves and Shocks; Coronal Dimming; The Link Between Low Coronal CME Signatures and Magnetic Clouds; Coronal Mass Ejections in the Heliosphere; and Coronal Mass Ejections and Space Weather. Primary authorship is indicated at the beginning of each section., Comment: 26 pages, to be published in Transactions IAU, Vol. XXVIIA, Reports on Astronomy 2006-2009, ed. K. A. van der Hucht

The physical modeling of active regions (ARs) and of the global coronal is receiving increasing interest lately. Recent attempts to model ARs using static equilibrium models were quite successful in reproducing AR images of hot soft X-ray (SXR) loops. They however failed to predict the bright EUV warm loops permeating ARs: the synthetic images were dominated by intense footpoint emission. We demonstrate that this failure is due to the very weak dependence of loop temperature on loop length which cannot simultaneously account for both hot and warm loops in the same AR. We then consider time-dependent AR models based on nanoflare heating. We demonstrate that such models can simultaneously reproduce EUV and SXR loops in ARs. Moreover, they predict radial intensity variations consistent with the localized core and extended emissions in SXR and EUV AR observations respectively. We finally show how the AR morphology can be used as a gauge of the properties (duration, energy, spatial dependence, repetition time) of the impulsive heating., Comment: ApJ, in press

Observational and theoretical evidence suggests that coronal heating is impulsive and occurs on very small cross-field spatial scales. A single coronal loop could contain a hundred or more individual strands that are heated quasi-independently by nanoflares. It is therefore an enormous undertaking to model an entire active region or the global corona. Three-dimensional MHD codes have inadequate spatial resolution, and 1D hydro codes are too slow to simulate the many thousands of elemental strands that must be treated in a reasonable representation. Fortunately, thermal conduction and flows tend to smooth out plasma gradients along the magnetic field, so "0D models" are an acceptable alternative. We have developed a highly efficient model called Enthalpy-Based Thermal Evolution of Loops (EBTEL) that accurately describes the evolution of the average temperature, pressure, and density along a coronal strand. It improves significantly upon earlier models of this type--in accuracy, flexibility, and capability. It treats both slowly varying and highly impulsive coronal heating; it provides the differential emission measure distribution, DEM(T), at the transition region footpoints; and there are options for heat flux saturation and nonthermal electron beam heating. EBTEL gives excellent agreement with far more sophisticated 1D hydro simulations despite using four orders of magnitude less computing time. It promises to be a powerful new tool for solar and stellar studies., Comment: 34 pages, 8 figures, accepted by Astrophysical Journal (minor revisions of original submitted version)

We study the effect of the coronal background in the determination of the diameter of EUV loops, and we analyze the suitability of the procedure followed in a previous paper (L\'opez Fuentes, Klimchuk & D\'emoulin 2006) for characterizing their expansion properties. For the analysis we create different synthetic loops and we place them on real backgrounds from data obtained with the Transition Region and Coronal Explorer (\textit{TRACE}). We apply to these loops the same procedure followed in our previous works, and we compare the results with real loop observations. We demonstrate that the procedure allows us to distinguish constant width loops from loops that expand appreciably with height, as predicted by simple force-free field models. This holds even for loops near the resolution limit. The procedure can easily determine when loops are below resolution limit and therefore not reliably measured. We find that small-scale variations in the measured loop width are likely due to imperfections in the background subtraction. The greatest errors occur in especially narrow loops and in places where the background is especially bright relative to the loop. We stress, however, that these effects do not impact the ability to measure large-scale variations. The result that observed loops do not expand systematically with height is robust., Comment: Accepted for publication in ApJ

We study the temporal evolution of coronal loops using data from the Solar X-ray Imager (SXI) on board of GOES-12. This instrument allows us to follow in detail the full lifetime of coronal loops. The observed light curves suggest three somewhat distinct evolutionary phases: rise, main, and decay. The durations and characteristic timescales of these phases are much longer than a cooling time and indicate that the loop-averaged heating rate increases slowly, reaches a maintenance level, and then decreases slowly. This suggests that a single heating mechanism operates for the entire lifetime of the loop. For monolithic loops, the loop-averaged heating rate is the intrinsic energy release rate of the heating mechanism. For loops that are bundles of impulsively heated strands, it is an indication of the frequency of occurrence of individual heating events, or nanoflares. We show that the timescale of the loop-averaged heating rate is proportional to the timescale of the observed intensity variation. The ratios of the radiative to conductive cooling times in the loops are somewhat less than 1, putting them intermediate between the values measured previously for hotter and cooler loops. Our results provide further support for the existence of a trend suggesting that all loops are heated by the same mechanism, or that different mechanisms have fundamental similarities (e.g., are all impulsive or are all steady with similar rates of heating)., Comment: Accepted for publication in ApJ

Previous studies have found that coronal loops have a nearly uniform thickness, which seems to disagree with the characteristic expansion of active region magnetic fields. This is one of the most intriguing enigmas in solar physics. We here report on the first comprehensive one-to-one comparison of observed loops with corresponding magnetic flux tubes obtained from cotemporal magnetic field extrapolation models. We use EUV images from TRACE, magnetograms from the MDI instrument on SOHO, and linear force-free field extrapolations. For each loop, we find the particular value of the force-free parameter (alpha) that best matches the observed loop axis and then construct flux tubes using different assumed cross sections at one footpoint (circle and ellipses with different orientations). We find that the flux tubes expand with height by typically twice as much as the corresponding loops. We also find that many flux tubes are much wider at one footpoint than the other, whereas the corresponding loops are far more symmetric. It is clear that the actual coronal magnetic field is more complex than the models we have considered. We suggest that the observed symmetry of loops is related to the tangling of elemental magnetic flux strands produced by photospheric convection., Comment: Accepted for publication in ApJ

We use a combination of analytical theory, numerical simulation, and data analysis to study the propagation of acoustic waves along coronal loops. We show that the intensity perturbation of a wave depends on a number of factors, including dissipation of the wave energy, pressure and temperature gradients in the loop atmosphere, work action between the wave and a flow, and the sensitivity properties of the observing instrument. In particular, the scale length of the intensity perturbation varies directly with the dissipation scale length (i.e., damping length) and the scale lengths of pressure, temperature, and velocity. We simulate wave propagation in three different equilibrium loop models and find that dissipation and pressure and temperature stratification are the most important effects in the low corona where the waves are most easily detected. Velocity effects are small, and cross-sectional area variations play no direct role for lines-of-sight that are normal to the loop axis. The intensity perturbation scale lengths in our simulations agree very well with the scale lengths we measure in a sample of loops observed by TRACE. The median observed value is 4.35x10^9 cm. In some cases the intensity perturbation increases with height, which is likely an indication of a temperature inversion in the loop (i.e., temperature that decreases with height). Our most important conclusion is that thermal conduction, the primary damping mechanism, is accurately described by classical transport theory. There is no need to invoke anomalous processes to explain the observations., Comment: To appear in the Dec. 1, 2004 issue of the Astrophysical Journal

We propose a new model for the initiation of a solar coronal mass ejection (CME). The model agrees with two properties of CMEs and eruptive flares that have proved to be very difficult to explain with previous models. a) Very low-lying magnetic field lines, down to the photospheric neutral line, can open toward infinity during an eruption. b) The eruption is driven solely by magnetic free energy stored in a closed, sheared arcade; consequently, the magnetic energy of the closed state is well above that of the post-eruption open state. The key new feature of our model is that CMEs occur in multi-polar topologies, in which reconnection between a sheared arcade and neighboring flux systems triggers the eruption. In this ``magnetic breakout'' model, reconnection removes the unsheared field above the low-lying, sheared core flux near the neutral line, thereby allowing this core flux to burst open. We present numerical simulations which demonstrate that our model can account for the energy requirements for CMEs. We discuss the implication of the model for CME/flare prediction., Comment: Astrophysical Journal latex file, 28 pages, 8 color and 2 b-w figures (gif files)

One of the greatest challenges in solar physics is understanding the heating of the Sun's corona. Most theories for coronal heating postulate that free energy in the form of magnetic twist/stress is injected by the photosphere into the corona where the free energy is converted into heat either through reconnection or wave dissipation. The magnetic helicity associated with the twist/stress, however, is expected to be conserved and appear in the corona. In previous works, we showed that the helicity associated with the small-scale twists undergoes an inverse cascade via stochastic reconnection in the corona and ends up as the observed large-scale shear of filament channels. Our "helicity condensation" model accounts for both the formation of filament channels and the observed smooth, laminar structure of coronal loops. In this paper, we demonstrate, using helicity- and energy-conserving numerical simulations of a coronal system driven by photospheric motions, that the model also provides a natural mechanism for heating the corona. We show that the heat generated by the reconnection responsible for the helicity condensation process is sufficient to account for the observed coronal heating. We study the role that helicity injection plays in determining coronal heating and find that, crucially, the heating rate is only weakly dependent on the net helicity preference of the photospheric driving. Our calculations demonstrate that motions with 100% helicity preference are least efficient at heating the corona; those with 0% preference are most efficient. We discuss the physical origins of this result and its implications for the observed corona.

Numerous observations have revealed that power-law distributions are ubiquitous in energetic solar processes. Hard X-rays, soft X-rays, extreme ultraviolet radiation, and radio waves all display power-law frequency distributions. Since magnetic reconnection is the driving mechanism for many energetic solar phenomena, it is likely that reconnection events themselves display such power-law distributions. In this work, we perform numerical simulations of the solar corona driven by simple convective motions at the photospheric level. Using temperature changes, current distributions, and Poynting fluxes as proxies for heating, we demonstrate that energetic events occurring in our simulation display power-law frequency distributions, with slopes in good agreement with observations. We suggest that the braiding-associated reconnection in the corona can be understood in terms of a self-organized criticality model driven by convective rotational motions similar to those observed at the photosphere.

The detailed shapes of spectral line profiles provide valuable information about the emitting plasma, especially when the plasma contains an unresolved mixture of velocities, temperatures, and densities. As a result of finite spectral resolution, the intensity measured by a spectrometer is the average intensity across a wavelength bin of non-zero size. It is assigned to the wavelength position at the center of the bin. However, the actual intensity at that discrete position will be different if the profile is curved, as it invariably is. Standard fitting routines (spline, Gaussian, etc.) do not account for this difference, and this can result in significant errors when making sensitive measurements. Detection of asymmetries in solar coronal emission lines is one example. Removal of line blends is another. We have developed an iterative procedure that corrects for this effect. It can be used with any fitting function, but we employ a cubic spline in a new analysis routine called Intensity Conserving Spline Interpolation (ICSI). As the name implies, it conserves the observed intensity within each wavelength bin, which ordinary fits do not. Given the rapid convergence, speed of computation, and ease of use, we suggest that ICSI be made a standard component of the processing pipeline for spectroscopic data.

Recent solar spectroscopic observations have shown that coronal spectral lines can exhibit asymmetric profiles, with enhanced emissions at their blue wings. These asymmetries correspond to rapidly upflowing plasmas at speeds exceeding approximately equal to 50 km per sec. Here, we perform a study of the density of the rapidly upflowing material and compare it with that of the line core that corresponds to the bulk of the plasma. For this task, we use spectroscopic observations of several active regions taken by the Extreme Ultraviolet Imaging Spectrometer of the Hinode mission. The density sensitive ratio of the Fe(sub XIV) lines at 264.78 and 274.20 Angstroms is used to determine wing and core densities.We compute the ratio of the blue wing density to the core density and find that most values are of order unity. This is consistent with the predictions for coronal nanoflares if most of the observed coronal mass is supplied by chromospheric evaporation driven by the nanoflares. However, much larger blue wing-to-core density ratios are predicted if most of the coronal mass is supplied by heated material ejected with type II spicules. Our measurements do not rule out a spicule origin for the blue wing emission, but they argue against spicules being a primary source of the hot plasma in the corona. We note that only about 40% of the pixels where line blends could be safely ignored have blue wing asymmetries in both Fe(sub XIV) lines. Anticipated sub-arcsecond spatial resolution spectroscopic observations in future missions could shed more light on the origin of blue, red, and mixed asymmetries.

Since the launch of NASA's Solar Dynamics Observatory on 2010 February 11, the Extreme ultraviolet Variability Experiment (EVE) has observed numerous flares. One interesting feature observed by EVE is that a subset of flares exhibit an additional enhancement of the 2-3 million K emission several hours after the flares soft X-ray emission. From the Atmospheric Imaging Assembly (AIA) images, we observe that this secondary emission, dubbed the EUV late phase, occurs in the same active region as the flare but not in the same coronal loops. Here, we examine the C8.8 flare that occurred on 2010 May 5 as a case study of EUV late phase flares. In addition to presenting detailed observations from both AIA and EVE, we develop a physical model of this flare and test it using the Enthalpy Based Thermal Evolution of Loops (EBTEL) model.

This paper further develops the zero-dimensional (0D) hydrodynamic coronal loop model "Enthalpy-based Thermal Evolution of Loops" (EBTEL) originally proposed by Klimchuk et al (2008), which studies the plasma response to evolving coronal heating. It has typically been applied to impulsive heating events. The basis of EBTEL is the modelling of mass exchange between the corona and transition region and chromosphere in response to heating variations, with the key parameter being the ratio of transition region to coronal radiation. We develop new models for this parameter that now include gravitational stratification and a physically motivated approach to radiative cooling. A number of examples are presented, including nanoflares in short and long loops, and a small flare. It is found that while the evolution of the loop temperature is rather insensitive to the details of the model, accurate tracking of the density requires the inclusion of our new features. In particular, we are able to now obtain highly over-dense loops in the late cooling phase and decreases to the coronal density arising due to stratification. The 0D results are compared to a 1D hydro code (Hydrad). The agreement is acceptable, with the exception of the flare case where some versions of Hydrad can give significantly lower densities. This is attributed to the method used to model the chromosphere in a flare. EBTEL is suitable for general use as a tool for (a) quick-look results of loop evolution in response to a given heating function and (b) situations where the modelling of hundreds or thousands of elemental loops is needed. A single run takes a few seconds on a contemporary laptop.

The investigation of the heating mechanisms of the confined coronal plasma is still under intense debate. It is widely believed that the energy source for coronal heating is the magnetic energy stored in the solar corona. An unsolved problem is how this magnetic energy is converted into thermal energy of the confined coronal plasma. As Parker proposed in 1988 rapid pulses called nanoflares are among the best candidate mechanisms of magnetic energy release. Nowadays a challenging problem is to obtain evidence that such nanoflares are really at work. If small energy discharges (nanoflares) contribute in some way to coronal heating, they could be too small and frequent to be resolved as independent events. In this case, we would need to search for indirect evidence. The idea of this work is that, if the solar corona emission is sustained by repeated nanoflares, locally the X-ray emission may not be entirely constant but may show variations around the mean intensity. So the nanoflares may leave their signature on the light curves. Many authors (Shimizu & Tsuneta 1997; Vekstein & Katsukawa 2000; Katsukawa & Tsuneta 2001; Katsukawa 2003; Sakamoto et al. 2008) pointed out that a detailed analysis of intensity fluctuations of the coronal X-ray emission could give us information on these smallest flares. Following this hint we use this approach for the first time on Hinode data, searching, with statistical analysis, for small but systematic variability in noisy background light curves and their link to coronal heating models.

Recent measurements have shown that the quiet unstructured solar corona observed at the solar limb is close to isothermal, at a temperature that does not appear to change over wide areas or with time. Some in dividual active loop structures have also been found to be nearly iso thermal both along their axis and across their cross-section. Even a complex active region observed at the solar limb has been found to be composed of three distinct isothermal plasmas. If confirmed, these r esults would pose formidable challenges to the current theoretical understanding of the thermal structure and heating of the solar corona. For example, no current theoretical model can explain the excess dens ities and lifetimes of many observed loops if the loops are in fact i sothermal. All of these measurements are based on the so-called emiss ion measure (EM) diagnostic technique that is applied to a set of opt ically thin lines under the assumption of isothermal plasma. It provi des simultaneous measurement of both the temperature and EM. However, no study has ever been carried out to quantify the uncertainties in the technique and to rigorously assess its ability to discriminate bet ween isothermal and multithermal plasmas. Such a study is the topic o f the present work. We define a formal measure of the uncertainty in the EM diagnostic technique that can easily be applied to real data. We here apply it to synthetic data based on a variety of assumed plas ma thermal distributions, and develop a method to quantitatively asse ss the degree of multithermality of a plasma.

We develop and analyze a simple cellular automaton (CA) model that reproduces the main properties of the evolution of soft X-ray coronal loops. We are motivated by the observation that these loops evolve in three distinguishable phases that suggest the development, maintainance, and decay of a self-organized system. The model is based on the idea that loops are made of elemental strands that are heated by the relaxation of magnetic stress in the form of nanoflares. In this vision, usually called "the Parker conjecture" (Parker 1988), the origin of stress is the displacement of the strand footpoints due to photospheric convective motions. Modeling the response and evolution of the plasma we obtain synthetic light curves that have the same characteristic properties (intensity, fluctuations, and timescales) as the observed cases. We study the dependence of these properties on the model parameters and find scaling laws that can be used as observational predictions of the model. We discuss the implications of our results for the interpretation of recent loop observations in different wavelengths. Subject headings: Sun: corona - Sun: flares - Sun: magnetic topology - Sun: X-rays, gamma rays