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This white paper, submitted to the Heliophysics 2050 Workshop, discusses the diagnostic power and need for soft X-ray spectroscopy of the Sun to understand heating of plasma in the solar corona. Significant progress into the critical coronal heating question – and other closely related questions – is easily achievable by 2050 if we leverage these advances and prioritize development of new solar SXR observatories, {"references":["Grotrian, W. 1939, Naturwissenschaften, 27, 214","Edlén, B. 1943, Zeitschrift für Astrophysik, 22, 30","Klimchuk, J.A. 2006, Sol. Phys., 234, 41","Welsch, B. T. 2014, PASJ, 67, 18","Klimchuk, J. A., et al. 2020a, Heliophysics 2050 Workshop, white paper #4027","Klimchuk, J. A., et al. 2020b, Heliophysics 2050 Workshop, white paper #4028","Parker, E. N. 1988, ApJ, 330, 474","Cargill, P. J., & Klimchuk, J. A. 2004, ApJ, 605, 911","Cargill, P. J. 2014, ApJ, 784, 49","van Ballegooijen, A. A., et al. 2011, ApJ, 736, 3","Asgari-Targhi, M., et al. 2013, ApJ, 773, 111","Miceli, M., et al. 2012, A&A, 544, A139","Brosius, J. W., et al. 2014, ApJ, 790, 112","Caspi, A., et al. 2015a, ApJL, 802, L2","Sylwester, J., et al. 2012, ApJ, 751, 111","Schrijver, C. J., et al. 1998, Nature, 394, 152","Reale, F., et al. 2009, ApJ, 698, 756","Schmelz, J. T., et al. 2009, ApJL, 693, L131","Warren, H. P., et al. 2012, ApJ, 759, 141","Del Zanna, G., & Mason, H. E. 2014, A&A, 565, A14","Caspi, A., & Lin, R. P. 2010, ApJ, 725, 161","Caspi, A., et al. 2014, ApJ, 781, 43","Fletcher, L., et al. 2011, Space Sci. Rev., 159, 19","Holman, G. D., et al. 2011, Space Sci. Rev., 159, 107","Allred, J. C., et al. 2005, ApJ, 630, 573","Allred, J. C., et al. 2015, ApJ, 809, 104","Liu, W.-J., et al. 2013, ApJ, 770, 111","Aschwanden, M. J., et al. 2015, ApJ, 802, 53","Caspi, A., et al. 2015b, ApJL, 811, L1","Aschwanden, M. J., et al. 2016, ApJ, 832, 27","Warmuth, A., & Mann, G. 2016, A&A, 588, A116","Longcope, D. W., & Guidoni, S. E. 2011, ApJ, 740, 73","Shih, A. Y., et al. 2020, Heliophysics 2050 Workshop, white paper #4023","Laming, J. M. 2015, Liv. Rev. Sol. Phys., 12, 2","Wieman, S., et al. 2015, AGU Fall Meeting, #SH23B-2446","Warren, H. P. 2014, ApJ, 786, L2","Dennis, B. R., et al. 2015, ApJ, 803, 67","Sylwester, J., et al. 1984, Nature, 310, 665","Schmelz, J. T. 1993, ApJ, 408, 373","Doschek, G. A., et al. 2015, ApJ, 808, 7","Doschek, G. A. & Warren, H. P. 2016, ApJ, 825, 36","Widing, K. G., & Feldman, U. 2001, ApJ, 555, 426","Baker, D., et al. 2015, ApJ, 802, 104","Winebarger, A. R., et al. 2012, ApJL, 746, L17","Mason, J. P., et al. 2016, J. Spacecraft Rockets, 53, 328","Moore, C. S., et al. 2018, Sol Phys., 293, 21","Soman, M., et al. 2016, Proc. SPIE, 9915, 991540","Narukage, N. et al. 2017, Proc. SPIE., 10397, 1039709","Tousey, R., et al. 1977, Appl. Optics, 16, 870","Golub, L., et al. 2020, J. Space Weather Space Climate, 10, 37","Caspi, A., et al. 2016, Proc. SPIE, 9905, 9905226"]}

While there have been significant advances in our understanding of impulsive energy release at the Sun through the combination ofRHESSIX-ray observations andSDO/AIA EUV observations, there is a clear science need for significantly improved X-ray and EUV observations. These new observations must capture the full range of emission in flares and CMEs (e.g., faint coronal sources near bright chromospheric sources), connect the intricate evolution of energy release with dynamic changes in the configuration of plasma structures, and identify the signatures of impulsive energy release in even the quiescent Sun. TheFundamentals of Impulsive Energy Release in the Corona Explorer(FIERCE) MIDEX mission concept makes these observations by combining the two instruments previously proposed on theFOXSISMEX mission concept – a focusing hard X-ray spectroscopic imager and a soft X-ray spectrometer – with a high-resolution EUV imager that will not saturate for even intense flares. All instruments observe at high cadence to capture the initiation of solar transient events and the fine time structure within events.FIERCEwould launch in mid-2025, near the peak of the next solar cycle, which is also well timed with perihelions of Parker Solar Probe and Solar Orbiter. The goals ofFIERCEinclude improving our understanding of the genesis of space-weather events, andFIERCEobserations would vitally complement observations by other observatories both near Earth and elsewhere in the heliosphere.

Coronal loops reveal crucial information about the nature of both coronal magnetic fields and coronal heating. The shape of the corresponding flux tube cross section and how it varies with position are especially important properties. They are a direct indication of the expansion of the field and of the cross-field spatial distribution of the heating. We have studied 20 loops using high spatial resolution observations from the first flight of the Hi-C rocket experiment, measuring the intensity and width as a function of position along the loop axis. We find that intensity and width tend to either be uncorrelated or to have a direct dependence, such that they increase or decrease together. This implies that the flux tube cross sections are approximately circular under the assumptions that the tubes have non-negligible twist and that the plasma emissivity is approximately uniform along the magnetic field. The shape need not be a perfect circle and the emissivity need not be uniform within the cross section, but sub-resolution patches of emission must be distributed quasi-uniformly within an envelope that has an aspect ratio of order unity. This raises questions about the suggestion that flux tubes expand with height, but primarily in the line-of-sight direction so that the corresponding (relatively noticeable) loops appear to have roughly uniform width, a long-standing puzzle. It also casts doubt on the idea that most loops correspond to simple warped sheets, although we leave open the possibility of more complex manifold structures., Comment: 27 pages, 9 figures, accepted by Astrophysical Journal

Even in the absence of resolved flares, the corona is heated to several million degrees. However, despite its importance for the structure, dynamics, and evolution of the solar atmosphere, the origin of this heating remains poorly understood. Several observational and theoretical considerations suggest that the heating is driven by small, impulsive energy bursts which could be Parker-style "nanoflares" (Parker 1988) that arise via reconnection within the tangled and twisted coronal magnetic field. The classical "smoking gun" (Klimchuk 2009; Cargill et al. 2013) for impulsive heating is the direct detection of widespread hot plasma (T > 6 MK) with a low emission measure. In recent years there has been great progress in the development of Transition Edge Sensor (TES) X-ray microcalorimeters that make them more ideal for studying the Sun. When combined with grazing-incidence focusing optics, they provide direct spectroscopic imaging over a broad energy band (0.5 to 10 keV) combined with extremely impressive energy resolution in small pixels, as low as 0.7 eV (FWHM) at 1.5 keV (Lee 2015), and 1.56 eV (FWHM) at 6 keV (Smith 2012), two orders of magnitude better than the current best traditional solid state photon-counting spectrometers. Decisive observations of the hot plasma associated with nanoflare models of coronal heating can be provided by new solar microcalorimeters. These measurements will cover the most important part of the coronal spectrum for searching for the nanoflare-related hot plasma and will characterize how much nanoflares can heat the corona both in active regions and the quiet Sun. Finally, microcalorimeters will enable to study all of this as a function of time and space in each pixel simultaneously a capability never before available., Next Generation Solar Physics Mission, 2 figures

Impulsive particle acceleration and plasma heating at the Sun, from the largest solar eruptive events to the smallest flares, are related to fundamental processes throughout the Universe. While there have been significant advances in our understanding of impulsive energy release since the advent of RHESSI observations, there is a clear need for new X-ray observations that can capture the full range of emission in flares (e.g., faint coronal sources near bright chromospheric sources), follow the intricate evolution of energy release and changes in morphology, and search for the signatures of impulsive energy release in even the quiescent Sun. The FOXSI Small Explorer (SMEX) mission concept combines state-of-the-art grazing-incidence focusing optics with pixelated solid-state detectors to provide direct imaging of hard X-rays for the first time on a solar observatory. We present the science objectives of FOXSI and how its capabilities will address and resolve open questions regarding impulsive energy release at the Sun. These questions include: What are the time scales of the processes that accelerate electrons? How do flare-accelerated electrons escape into the heliosphere? What is the energy input of accelerated electrons into the chromosphere, and how is super-heated coronal plasma produced?

In this paper, the ability of the Hinode/EIS instrument to detect radiative signatures of coronal heating is investigated. Recent observational studies of AR cores suggest that both the low and high frequency heating mechanisms are consistent with observations. Distinguishing between these possibilities is important for identifying the physical mechanism(s) of the heating. The Differential Emission Measure (DEM) tool is one diagnostic that allows to make this distinction, through the amplitude of the DEM slope coolward of the coronal peak. It is therefore crucial to understand the uncertainties associated with these measurements. Using proper estimations of the uncertainties involved in the problem of DEM inversion, we derive confidence levels on the observed DEM slope. Results show that the uncertainty in the slope reconstruction strongly depends on the number of lines constraining the slope. Typical uncertainty is estimated to be about $\pm 1.0$, in the more favorable cases., Comment: 29 pages, 8 figures

Studying the Doppler shifts and the temperature dependence of Doppler shifts in moss regions can help us understand the heating processes in the core of the active regions. In this paper we have used an active region observation recorded by the Extreme-ultraviolet Imaging Spectrometer (EIS) onboard Hinode on 12-Dec-2007 to measure the Doppler shifts in the moss regions. We have distinguished the moss regions from the rest of the active region by defining a low density cut-off as derived by Tripathi et al. (2010). We have carried out a very careful analysis of the EIS wavelength calibration based on the method described in Young et al. (2012). For spectral lines having maximum sensitivity between log T = 5.85 and log T = 6.25 K, we find that the velocity distribution peaks at around 0 km/s with an estimated error of 4-5 km/s. The width of the distribution decreases with temperature. The mean of the distribution shows a blue shift which increases with increasing temperature and the distribution also shows asymmetries towards blue-shift. Comparing these results with observables predicted from different coronal heating models, we find that these results are consistent with both steady and impulsive heating scenarios. However, the fact that there are a significant number of pixels showing velocity amplitudes that exceed the uncertainty of 5 km s$^{-1}$ is suggestive of impulsive heating. Clearly, further observational constraints are needed to distinguish between these two heating scenarios., Comment: 21 pages (single column), 7 figures, Accepted for Publication in The Astrophysical Journal

It was once thought that all coronal loops are in static equilibrium, but observational and modeling developments over the past decade have shown that this is clearly not the case. It is now established that warm (~1 MK) loops observed in the EUV are explainable as bundles of unresolved strands that are heated impulsively by storms of nanoflares. A raging debate concerning the multi-thermal versus isothermal nature of the loops can be reconciled in terms of the duration of the storm. We show that short and long storms produce narrow and broad thermal distributions, respectively. We also examine the possibility that warm loops can be explained with thermal nonequilibrium, a process by which steady heating produces dynamic behavior whenever the heating is highly concentrated near the loop footpoints. We conclude that this is not a viable explanation for monolithic loops under the conditions we have considered, but that it may have application to multi-stranded loops. Serious questions remain, however., Comment: 13 pages, 8 figures; to appear in the Proceedings of the Hinode-2 Meeting, based on a keynote talk given at the meeting

Nanoflares, short and intense heat pulses within spatially unresolved magnetic strands, are now considered a leading candidate to solve the coronal heating problem. However, the frequent occurrence of nanoflares requires that flare-hot plasma be present in the corona at all times. Its detection has proved elusive until now, in part because the intensities are predicted to be very faint. Here we report on the analysis of an active region observed with five filters by Hinode/XRT in November 2006. We have used the filter ratio method to derive maps of temperature and emission measure both in soft and hard ratios. These maps are approximate in that the plasma is assumed to be isothermal along each line-of-sight. Nonetheless, the hardest available ratio reveals the clear presence of plasma around 10 MK. To obtain more detailed information about the plasma properties, we have performed Monte Carlo simulations assuming a variety of non-isothermal emission measure distributions along the lines-of-sight. We find that the observed filter ratios imply bi-modal distributions consisting of a strong cool (log T ~ 6.3-6.5) component and a weaker (few percent) and hotter (6.6 < log T < 7.2) component. The data are consistent with bi-modal distributions along all lines of sight, i.e., throughout the active region. We also find that the isothermal temperature inferred from a filter ratio depends sensitively on the precise temperature of the cool component. A slight shift of this component can cause the hot component to be obscured in a hard ratio measurement. Consequently, temperature maps made in hard and soft ratios tend to be anti-correlated. We conclude that this observation supports the presence of widespread nanoflaring activity in the active region., 12 figures, accepted for publication on refereed journal

A well known behavior of EUV light curves of discrete coronal loops is that the peak intensities of cooler channels or spectral lines are reached at progressively later times than hotter channels. This time lag is understood to be the result of hot coronal loop plasma cooling through these lower respective temperatures. However, loops typically comprise only a minority of the total emission in active regions. Is this cooling pattern a common property of active region coronal plasma, or does it only occur in unique circumstances, locations, and times? The new SDO/AIA data provide a wonderful opportunity to answer this question systematically for an entire active region. We measure the time lag between pairs of SDO/AIA EUV channels using 24 hours of images of AR 11082 observed on 19 June 2010. We find that there is a time-lag signal consistent with cooling plasma, just as is usually found for loops, throughout the active region including the diffuse emission between loops for the entire 24 hour duration. The pattern persists consistently for all channel pairs and choice of window length within the 24 hour time period, giving us confidence that the plasma is cooling from temperatures of greater than 3 MK, and sometimes exceeding 7 MK, down to temperatures lower than ~ 0.8 MK. This suggests that the bulk of the emitting coronal plasma in this active region is not steady; rather, it is dynamic and constantly evolving. These measurements provide crucial constraints on any model which seeks to describe coronal heating., 17 pages text, 7 figures in main body, 5 Appendix figures