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Understanding the relationship between the magnetic field and coronal heating is one of the central problems of solar physics. However, studies of the magnetic properties of impulsively heated loops have been rare. We present results from a study of 34 evolving coronal loops observed in the Fe XVIII line component of AIA/SDO 94 A filter images from three active regions with different magnetic conditions. We show that the peak intensity per unit cross-section of the loops depends on their individual magnetic and geometric properties. The intensity scales proportionally to the average field strength along the loop ($B_{avg}$) and inversely with the loop length ($L$) for a combined dependence of $(B_{avg}/L)^{0.52\pm0.13}$. These loop properties are inferred from magnetic extrapolations of the photospheric HMI/SDO line-of-sight and vector magnetic field in three approximations: potential and two Non Linear Force-Free (NLFF) methods. Through hydrodynamic modeling (EBTEL model) we show that this behavior is compatible with impulsively heated loops with a volumetric heating rate that scales as $\epsilon_H\sim B_{avg}^{0.3\pm0.2}/L^{0.2\pm^{0.2}_{0.1}}$., Comment: Astrophysical Journal, in press

Understanding the dynamics of the solar chromosphere is crucial to understanding energy transport across the solar atmosphere. The chromosphere is optically thick at many wavelengths and described by non-local thermodynamic equilibrium (NLTE), making it difficult to interpret observations. Furthermore, there is considerable evidence that the atmosphere is filamented, and that current instruments do not sufficiently resolve small scale features. In flares, it is likely that multithreaded models are required to describe the heating. The combination of NLTE effects and multithreaded modeling requires computationally demanding calculations, which has motivated the development of a model that can efficiently treat both. We describe the implementation of a solver in a hydrodynamic code for the hydrogen level populations that approximates the NLTE solutions. We derive an accurate electron density across the atmosphere, that includes the effects of non-equilibrium ionization for helium and metals. We show the effects on hydrodynamic simulations, which are used to synthesize light curves using a post-processing radiative transfer code. We demonstrate the utility of this model on IRIS observations of a small flare. We show that the Doppler shifts in Mg II, C II, and O I can be explained with a multithreaded model of loops subjected to electron beam heating, so long as NLTE effects are treated. The intensities, however, do not match observed values very well, which is due to assumptions about the initial atmosphere. We briefly show how altering the initial atmosphere can drastically alter line profiles, and therefore derived quantities, and suggest that it should be tuned to pre-flare observations., Comment: Now accepted to ApJ. Comments and criticisms encouraged!

It is widely believed that loops observed in the solar atmosphere trace out magnetic field lines. However, the degree to which magnetic field extrapolations yield field lines that actually do follow loops has yet to be studied systematically. In this paper we apply three different extrapolation techniques - a simple potential model, a NLFF model based on photospheric vector data, and a NLFF model based on forward fitting magnetic sources with vertical currents - to 15 active regions that span a wide range of magnetic conditions. We use a distance metric to assess how well each of these models is able to match field lines to the 12,202 loops traced in coronal images. These distances are typically 1-2". We also compute the misalignment angle between each traced loop and the local magnetic field vector, and find values of 5-12$^\circ$. We find that the NLFF models generally outperform the potential extrapolation on these metrics, although the differences between the different extrapolations are relatively small. The methodology that we employ for this study suggests a number of ways that both the extrapolations and loop identification can be improved., Comment: Accepted for publication in ApJ

Solar flares form and release energy across a large number of magnetic loops. The global parameters of flares, such as the total energy released, duration, physical size, etc., are routinely measured, and the hydrodynamics of a coronal loop subjected to intense heating have been extensively studied. It is not clear, however, how many loops comprise a flare, nor how the total energy is partitioned between them. In this work, we employ a hydrodynamic model to better understand the energy partition by synthesizing Si IV and Fe XXI line emission and comparing to observations of these lines with IRIS. We find that the observed temporal evolution of the Doppler shifts holds important information on the heating duration. To demonstrate this we first examine a single loop model, and find that the properties of chromospheric evaporation seen in Fe XXI can be reproduced by loops heated for long durations, while persistent red-shifts seen in Si IV cannot be reproduced by any single loop model. We then examine a multi-threaded model, assuming both a fixed heating duration on all loops, and a distribution of heating durations. For a fixed heating duration, we find that durations of 100 -- 200 s do a fair job of reproducing both the red- and blue-shifts, while a distribution of durations, with a median of about 50 -- 100 s, does a better job. Finally, we compare our simulations directly to observations of an M-class flare seen by IRIS, and find good agreement between the modeled and observed values given these constraints., Comment: Accepted to ApJ

We report on the structure and evolution of a current sheet that formed in the wake of an eruptive X8.3 flare observed at the west limb of the Sun on September 10, 2017. Using observations from the EUV Imaging Spectrometer (EIS) on Hinode and the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO), we find that plasma in the current sheet reaches temperatures of about 20 MK and that the range of temperatures is relatively narrow. The highest temperatures occur at the base of the current sheet, in the region near the top of the post-flare loop arcade. The broadest high temperature line profiles, in contrast, occur at the largest observed heights. Further, line broadening is strong very early in the flare and diminishes over time. The current sheet can be observed in the AIA 211 and 171 channels, which have a considerable contribution from thermal bremsstrahlung at flare temperatures. Comparisons of the emission measure in these channels with other EIS wavelengths and AIA channels dominated by Fe line emission indicate a coronal composition and suggest that the current sheet is formed by the heating of plasma already in the corona. Taken together, these observations suggest that some flare heating occurs in the current sheet while additional energy is released as newly reconnected field lines relax and become more dipolar., Comment: Submitted to ApJ, but comments are welcome!

Measuring the temperature structure of the solar atmosphere is critical to understanding how it is heated to high temperatures. Unfortunately, the temperature of the upper atmosphere cannot be observed directly, but must be inferred from spectrally resolved observations of individual emission lines that span a wide range of temperatures. Such observations are "inverted" to determine the distribution of plasma temperatures along the line of sight. This inversion is ill-posed and, in the absence of regularization, tends to produce wildly oscillatory solutions. We introduce the application of sparse Bayesian inference to the problem of inferring the temperature structure of the solar corona. Within a Bayesian framework a preference for solutions that utilize a minimum number of basis functions can be encoded into the prior and many ad hoc assumptions can be avoided. We demonstrate the efficacy of the Bayesian approach by considering a test library of 40 assumed temperature distributions., Comment: Not submitted yet. Comments are welcome!

Results from the Solar Maximum Mission showed a close connection between the hard X-ray and transition region emission in solar flares. Analogously, the modern combination of RHESSI and IRIS data can inform the details of heating processes in ways never before possible. We study a small event that was observed with RHESSI, IRIS, SDO, and Hinode, allowing us to strongly constrain the heating and hydrodynamical properties of the flare, with detailed observations presented in a previous paper. Long duration red-shifts of transition region lines observed in this event, as well as many other events, are fundamentally incompatible with chromospheric condensation on a single loop. We combine RHESSI and IRIS data to measure the energy partition among the many magnetic strands that comprise the flare. Using that observationally determined energy partition, we show that a proper multi-threaded model can reproduce these red-shifts in magnitude, duration, and line intensity, while simultaneously being well constrained by the observed density, temperature, and emission measure. We comment on the implications for both RHESSI and IRIS observations of flares in general, namely that: (1) a single loop model is inconsistent with long duration red-shifts, among other observables; (2) the average time between energization of strands is less than 10 seconds, which implies that for a hard X-ray burst lasting ten minutes, there were at least 60 strands within a single IRIS pixel located on the flare ribbon; (3) the majority of these strands were explosively heated with energy distribution well described by a power law of slope $\approx -1.6$; (4) the multi-stranded model reproduces the observed line profiles, peak temperatures, differential emission measure distributions, and densities., Comment: 10 pages, 8 figures. Accepted to ApJ

We exploit the high spatial resolution and high cadence of the Interface Region Imaging Spectrograph (IRIS) to investigate the response of the transition region and chromosphere to energy deposition during a small flare. Simultaneous observations from RHESSI provide constraints on the energetic electrons precipitating into the flare footpoints while observations of XRT, AIA, and EIS allow us to measure the temperatures and emission measures from the resulting flare loops. We find clear evidence for heating over an extended period on the spatial scale of a single IRIS pixel. During the impulsive phase of this event the intensities in each pixel for the Si IV 1402.770, C II 1334.535, Mg II 2796.354 and O I 1355.598 emission lines are characterized by numerous, small-scale bursts typically lasting 60s or less. Red shifts are observed in Si IV, C II, and Mg II during the impulsive phase. Mg II shows red-shifts during the bursts and stationary emission at other times. The Si IV and C II profiles, in contrast, are observed to be red-shifted at all times during the impulsive phase. These persistent red-shifts are a challenge for one-dimensional hydrodynamic models, which predict only short-duration downflows in response to impulsive heating. We conjecture that energy is being released on many small-scale filaments with a power-law distribution of heating rates., Comment: Comments are welcome!