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Nanoflares are thought to be one of the prime candidates that can heat the solar corona to its multi-million kelvin temperature. Individual nanoflares are difficult to detect with the present generation instruments, however their presence can be inferred by comparing simulated nanoflare-heated plasma emissions with the observed emission. Using HYDRAD coronal loop simulations, we model the emission from an X-ray bright point (XBP) observed by the Marshall Grazing Incidence X-ray Spectrometer (MaGIXS), along with nearest-available observations from the Atmospheric Imaging Assembly (AIA) onboard Solar Dynamics Observatory (SDO) and X-Ray Telescope (XRT) onboard Hinode observatory. The length and magnetic field strength of the coronal loops are derived from the linear-force-free extrapolation of the observed photospheric magnetogram by Helioseismic and Magnetic Imager (HMI) onboard SDO. Each loop is assumed to be heated by random nanoflares, whose magnitude and frequency are determined by the loop length and magnetic field strength. The simulation results are then compared and matched against the measured intensity from AIA, XRT, and MaGIXS. Our model results indicate the observed emissions from the XBP under study could be well matched by a distribution of nanoflares with average delay times 1500 s to 3000 s, which suggest that the heating is dominated by high-frequency events. Further, we demonstrate the high sensitivity of MaGIXS and XRT to diagnose the heating frequency using this method, while AIA passbands are found to be the least sensitive., Comment: Accepted for publication in the Astrophysical Journal (ApJ)

The Marshall Grazing Incidence X-ray Spectrometer (MaGIXS) sounding rocket experiment launched on July 30, 2021 from the White Sands Missile Range in New Mexico. MaGIXS is a unique solar observing telescope developed to capture X-ray spectral images, in the 6 - 24 Angstrom wavelength range, of coronal active regions. Its novel design takes advantage of recent technological advances related to fabricating and optimizing X-ray optical systems as well as breakthroughs in inversion methodologies necessary to create spectrally pure maps from overlapping spectral images. MaGIXS is the first instrument of its kind to provide spatially resolved soft X-ray spectra across a wide field of view. The plasma diagnostics available in this spectral regime make this instrument a powerful tool for probing solar coronal heating. This paper presents details from the first MaGIXS flight, the captured observations, the data processing and inversion techniques, and the first science results., Comment: 20 pages, 18 figures

The outer atmosphere of the Sun is composed of plasma heated to temperatures well in excess of the visible surface. We investigate short cool and warm (<1 MK) loops seen in the core of an active region to address the role of field-line braiding in energising these structures. We report observations from the High-resolution Coronal imager (Hi-C) that have been acquired in a coordinated campaign with the Interface Region Imaging Spectrograph (IRIS). In the core of the active region, the 172 A band of Hi-C and the 1400 A channel of IRIS show plasma loops at different temperatures that run in parallel. There is a small but detectable spatial offset of less than 1 arcsec between the loops seen in the two bands. Most importantly, we do not see observational signatures that these loops might be twisted around each other. Considering the scenario of magnetic braiding, our observations of parallel loops imply that the stresses put into the magnetic field have to relax while the braiding is applied: the magnetic field never reaches a highly braided state on these length-scales comparable to the separation of the loops. This supports recent numerical 3D models of loop braiding in which the effective dissipation is sufficiently large that it keeps the magnetic field from getting highly twisted within a loop., Comment: Accepted for publication in the Astrophysical Journal, 24 pages, 18 figures

Coronal loop observations have existed for many decades yet the precise shape of these fundamental coronal structures is still widely debated since the discovery that they appear to undergo negligible expansion between their footpoints and apex. In this work a selection of eight EUV loops and their twenty-two sub-element strands are studied from the second successful flight of NASA's High resolution Coronal Imager (Hi-C 2.1). Four of the loops correspond to open fan structures with the other four considered to be magnetically closed loops. Width analysis is performed on the loops and their sub-resolution strands using our method of fitting multiple Gaussian profiles to cross-sectional intensity slices. It is found that whilst the magnetically closed loops and their sub-element strands do not expand along their observable length, open fan structures may expand an additional 150% of their initial width. Following recent work, the Pearson correlation coefficient between peak intensity and loop/strand width are found to be predominantly positively correlated for the loops (~88%) and their sub-element strands (~80%). These results align with the hypothesis of Klimchuk & DeForest that loops and - for the first time - their sub-element strands have approximately circular cross-sectional profiles.

Coronal loops form the basic building blocks of the magnetically closed solar corona yet much is still to be determined concerning their possible fine-scale structuring and the rate of heat deposition within them. Using an improved multi-stranded loop model to better approximate the numerically challenging transition region, this paper examines synthetic NASA Solar Dynamics Observatory's (SDO) Atmospheric Imaging Assembly (AIA) emission simulated in response to a series of prescribed spatially and temporally random, impulsive and localised heating events across numerous sub-loop elements with a strong weighting towards the base of the structure; the nanoflare heating scenario. The total number of strands and nanoflare repetition times are varied systematically in such a way that the total energy content remains approximately constant across all the cases analysed. Repeated time lag detection during an emission time series provides a good approximation for the nanoflare repetition time for low-frequency heating. Furthermore, using a combination of AIA 171/193 and 193/211 channel ratios in combination with spectroscopic determination of the standard deviation of the loop apex temperature over several hours alongside simulations from the outlined multi-stranded loop model, it is demonstrated that both the imposed heating rate and number of strands can be realised.

Previous work utilising NASA's High-resolution Coronal Imager (Hi-C 2.1) 17.2 nm observations revealed that, even at the increased spatial scales available in the data-set, there may be evidence for coronal structures that are still not fully resolved. In this follow-up study, cross-section slices of coronal strands are taken across the Hi-C 2.1 field-of-view. Following previous loop width studies, the background emission is removed to isolate the coronal strands. The resulting intensity variations are reproduced by simultaneously fitting multiple Gaussian profiles using a non-linear least-squares curve fitting method. In total, 183 Gaussian profiles are examined for possible structures that are hinted at in the data. The full width at half maximum (FWHM) is determined for each Gaussian, which are then collated and analysed. The most frequent structural widths are $\approx$450-575 km with 47% of the strand widths beneath NASA's Solar Dynamics Observatory Atmospheric Imaging Assembly (AIA) resolving scale (600-1000 km). Only 17% reside beneath an AIA pixel width (435 km) with just 6% of the strands at the Hi-C 2.1 resolving scale ($\approx$220-340 km). These results suggest that non-Gaussian shaped cross-sectional emission profiles observed by Hi-C 2.1 are the result of multiple strands along the integrated line-of-sight that can be resolved, rather than being the result of even finer sub-resolution elements.

Following the success of the first mission, the High-Resolution Coronal Imager (Hi-C) was launched for a third time (Hi-C 2.1) on 29th May 2018 from the White Sands Missile Range, NM, USA. On this occasion, 329 seconds of 17.2 nm data of target active region AR 12712 was captured with a cadence of ~4s, and a plate scale of 0.129''/pixel. Using data captured by Hi-C 2.1 and co-aligned observations from SDO/AIA 17.1 nm we investigate the widths of 49 coronal strands. We search for evidence of substructure within the strands that is not detected by AIA, and further consider whether these strands are fully resolved by Hi-C 2.1. With the aid of Multi-Scale Gaussian Normalization (MGN), strands from a region of low-emission that can only be visualized against the contrast of the darker, underlying moss are studied. A comparison is made between these low-emission strands with those from regions of higher emission within the target active region. It is found that Hi-C 2.1 can resolve individual strands as small as ~202km, though more typical strands widths seen are ~513km. For coronal strands within the region of low-emission, the most likely width is significantly narrower than the high-emission strands at ~388km. This places the low-emission coronal strands beneath the resolving capabilities of SDO/AIA, highlighting the need of a permanent solar observatory with the resolving power of Hi-C., Comment: 19 pages, 10 images, 3 tables

We present high-resolution, high-cadence observations of six, fine-scale, on-disk jet-like events observed by the High-resolution Coronal Imager 2.1 (Hi-C 2.1) during its sounding-rocket flight. We combine the Hi-C 2.1 images with images from SDO/AIA, and IRIS, and investigate each event's magnetic setting with co-aligned line-of-sight magnetograms from SDO/HMI. We find that: (i) all six events are jetlet-like (having apparent properties of jetlets), (ii) all six are rooted at edges of magnetic network lanes, (iii) four of the jetlet-like events stem from sites of flux cancelation between majority-polarity network flux and merging minority-polarity flux, and (iv) four of the jetlet-like events show brightenings at their bases reminiscent of the base brightenings in coronal jets. The average spire length of the six jetlet-like events (9,000$\pm$3000km) is three times shorter than that for IRIS jetlets (27,000$\pm$8000km). While not ruling out other generation mechanisms, the observations suggest that at least four of these events may be miniature versions of both larger-scale coronal jets that are driven by minifilament eruptions and still-larger-scale solar eruptions that are driven by filament eruptions. Therefore, we propose that our Hi-C events are driven by the eruption of a tiny sheared-field flux rope, and that the flux-rope field is built and triggered to erupt by flux cancelation., Comment: 10 pages, 5 figures, 1 Table, accepted for publication in ApJ Letters

The second Hi-C flight (Hi-C2.1) provided unprecedentedly-high spatial and temporal resolution ($\sim$250km, 4.4s) coronal EUV images of Fe IX/X emission at 172 \AA, of AR 12712 on 29-May-2018, during 18:56:21-19:01:56 UT. Three morphologically-different types (I: dot-like, II: loop-like, III: surge/jet-like) of fine-scale sudden-brightening events (tiny microflares) are seen within and at the ends of an arch filament system in the core of the AR. Although type Is (not reported before) resemble IRIS-bombs (in size, and brightness wrt surroundings), our dot-like events are apparently much hotter, and shorter in span (70s). We complement the 5-minute-duration Hi-C2.1 data with SDO/HMI magnetograms, SDO/AIA EUV images, and IRIS UV spectra and slit-jaw images to examine, at the sites of these events, brightenings and flows in the transition-region and corona and evolution of magnetic flux in the photosphere. Most, if not all, of the events are seated at sites of opposite-polarity magnetic flux convergence (sometimes driven by adjacent flux emergence), implying likely flux cancellation at the microflare's polarity inversion line. In the IRIS spectra and images, we find confirming evidence of field-aligned outflow from brightenings at the ends of loops of the arch filament system. In types I and II the explosion is confined, while in type III the explosion is ejective and drives jet-like outflow. The light-curves from Hi-C, AIA and IRIS peak nearly simultaneously for many of these events and none of the events display a systematic cooling sequence as seen in typical coronal flares, suggesting that these tiny brightening-events have chromospheric/transition-region origin., Comment: 35 pages, 25 figures, 1 table, accepted for publication in ApJ

The third flight of the High-Resolution Coronal Imager (Hi-C 2.1) occurred on May 29, 2018, the Sounding Rocket was launched from White Sands Missile Range in New Mexico. The instrument has been modified from its original configuration (Hi-C 1) to observe the solar corona in a passband that peaks near 172 Angstrom and uses a new, custom-built low-noise camera. The instrument targeted Active Region 12712, and captured 78 images at a cadence of 4.4 sec (18:56:22 - 19:01:57 UT; 5 min and 35 sec observing time). The image spatial resolution varies due to quasi-periodic motion blur from the rocket; sharp images contain resolved features of at least 0.47 arcsec. There are coordinated observations from multiple ground- and space-based telescopes providing an unprecedented opportunity to observe the mass and energy coupling between the chromosphere and the corona. Details of the instrument and the data set are presented in this paper., Comment: 26 pages, 15 figures, submitted to Solar Physics

A sunspot acts as a waveguide in response to the dynamics of the solar interior; the trapped waves and oscillations could reveal its thermal and magnetic structures. We study the oscillations in a sunspot intruded by a light bridge, the details of the oscillations could reveal the fine structure of the magnetic topology. We use the Solar Dynamics Observatory/Atmospheric Imaging Assembly data to analyse the oscillations in the emission intensity of light bridge plasma at different temperatures and investigate their spatial distributions. The extreme ultraviolet emission intensity exhibits two persistent oscillations at five-minute and sub-minute ranges. The spatial distribution of the five-minute oscillation follows the spine of the bridge; whereas the sub-minute oscillations overlap with two flanks of the bridge. Moreover, the sub-minute oscillations are highly correlated in spatial domain, however, the oscillations at the eastern and western flanks are asymmetric with regard to the lag time. In the meanwhile, jet-like activities are only found at the eastern flank. Asymmetries in forms of oscillatory pattern and jet-like activities \textbf{are} found between two flanks of a granular light bridge. Based on our study and recent findings, we propose a new model of twisted magnetic field for a light bridge and its dynamic interactions with the magnetic field of a sunspot., Comment: 5 figures, Accepted version in A&A

Fast magnetoacoustic wave is an important tool for inferring solar atmospheric parameters. We numerically simulate the propagation of fast wave pulses in randomly structured plasmas mimicking the highly inhomogeneous solar corona. A network of secondary waves is formed by a series of partial reflections and transmissions. These secondary waves exhibit quasi-periodicities in both time and space. Since the temporal and spatial periods are related simply through the fast wave speed, we quantify the properties of secondary waves by examining the dependence of the average temporal period ($\bar{p}$) on the initial pulse width ($w_0$) as well as the density contrast ($\delta_\rho$) and correlation length ($L_c$) that characterize the randomness of the equilibrium density profiles. For small-amplitude pulses, $\delta_\rho$ does not alter $\bar{p}$ significantly. Large-amplitude pulses, on the other hand, enhance the density contrast when $\delta_\rho$ is small but have a smoothing effect when $\delta_\rho$ is sufficiently large. We found that $\bar{p}$ scales linearly with $L_c$ and that the scaling factor is larger for a narrower pulse. However, in terms of the absolute values of $\bar{p}$, broader pulses generate secondary waves with longer periods, and this effect is stronger in random plasmas with shorter correlation lengths. Secondary waves carry the signatures of both the leading wave pulse and background plasma, our study may find applications in MHD seismology by exploiting the secondary waves detected in the dimming regions after CMEs or EUV waves., Comment: 10 pages, 5 figures, accepted by ApJ

Solar dynamics and turbulence occur at all heights of the solar atmosphere and could be described as stochastic processes. We propose that finite lifetime transients recurring at a certain place could trigger quasi-periodic processes in the associated structures. In this study, we developed a mathematical model for finite lifetime and randomly occurring transients, and found that quasi-periodic processes, with period longer than the time scale of the transients, are detectable intrinsically in form of trains. We simulate their propagation in an empirical solar atmospheric model with chromosphere, transition region and corona. We found that, due to the filtering effect of the chromospheric cavity, only the resonance period of the acoustic resonator is able to propagate to the upper atmosphere, such a scenario is applicable to slow magnetoacoustic waves in sunspots and active regions. If the thermal structure of the atmosphere is less wild and acoustic resonance does not take effect, the long period oscillations could propagate to the upper atmosphere. Such case would be more likely to occur at polar plumes., Comment: 20 pages, 12 figures

Plasma flows within prominences/filaments have been observed for many years and hold valuable clues concerning the mass and energy balance within these structures. Previous observations of these flows primarily come from H-alpha and cool EUV lines (e.g., 304A) where estimates of the size of the prominence threads has been limited by the resolution of the available instrumentation. Evidence of `counter-steaming' flows has previously been inferred from these cool plasma observations but now, for the first time, these flows have been directly imaged along fundamental filament threads within the million degree corona (at 193A). In this work we present observations of an active region filament observed with Hi-C that exhibits anti-parallel flows along adjacent filament threads. Complementary data from SDO/AIA and HMI are presented. The ultra-high spatial and temporal resolution of Hi-C allow the anti-parallel flow velocities to be measured (70-80 km/s) and gives an indication of the resolvable thickness of the individual strands (0.8'' +/- 0.1''). The temperature distribution of the plasma flows was estimated to be log T(K) = 5.45 +/- 0.10 using EM loci analysis. We find that SDO/AIA cannot clearly observe these anti-parallel flows nor measure their velocity or thread width due to its larger pixel size. We suggest that anti-parallel/counter-streaming flows are likely commonplace within all filaments and are currently not observed in EUV due to current instrument spatial resolution., Comment: 6 pages, 5 figures

Determining the preferred spatial location of the energy input to solar coronal loops would be an important step forward towards a more complete understanding of the coronal heating problem. Following on from Sarkar & Walsh (2008) this paper presents a short 10e9 cm "global loop" as 125 individual strands, where each strand is modelled independently by a one-dimensional hydrodynamic simulation. The strands undergo small-scale episodic heating and are coupled together through the frequency distribution of the total energy input to the loop which follows a power law distribution with index ~ 2.29. The spatial preference of the swarm of heating events from apex to footpoint is investigated. From a theoretical perspective, the resulting emission measure weighted temperature profiles along these two extreme cases does demonstrate a possible observable difference. Subsequently, the simulated output is folded through the TRACE instrument response functions and a re-derivation of the temperature using different filter-ratio techniques is performed. Given the multi-thermal scenario created by this many strand loop model, a broad differential emission measure results; the subsequent double and triple filter ratios are very similar to those obtained from observations. However, any potential observational signature to differentiate between apex and footpoint dominant heating is possibly below instrumental thresholds. The consequences of using a broadband instrument like TRACE and Hinode-XRT in this way are discussed., Comment: Astrophysical Journal (Accepted)

Active region 10961 was observed over a five day period (2007 July 2-6) by instrumentation on-board STEREO, Hinode, TRACE and SOHO. As it progressed from Sun centre to the solar limb a comprehensive analysis of the EUV, X-ray and magnetic field data reveals clearly observable changes in the global nature of the region. Temperature analyses undertaken using STEREO EUVI double filter ratios and XRT single and combined filter ratios demonstrate an overall cooling of the region from between 1.6 - 3.0 MK to 1.0 - 2.0 MK over the five days. Similarly, Hinode EIS density measurements show a corresponding increase in density of 27%. Moss, cool (1 MK) outer loop areas and hotter core loop regions were examined and compared with potential magnetic field extrapolations from SOHO MDI magnetogram data. In particular it was found that the potential field model was able to predict the structure of the hotter X-ray loops and that the larger cool loops seen in 171 Angstrom images appeared to follow the separatrix surfaces. The reasons behind the high density moss regions only observed on one side of the active region are examined further., Comment: Submitted ApJ

One way of revealing the nature of the coronal heating mechanism is by comparing simple theoretical one dimensional hydrostatic loop models with observations at the temperature and/or density structure along these features. The most well-known method for dealing with comparisons like that is the $\chi^2$ approach. In this paper we consider the restrictions imposed by this approach and present an alternative way for making model comparisons using Bayesian statistics. In order to quantify our beliefs we use Bayes factors and information criteria such as AIC and BIC. Three simulated datasets are analyzed in order to validate the procedure and assess the effects of varying error bar size. Another two datasets (Ugarte-Urra et al., 2005; Priest et al., 2000) are re-analyzed using the method described above. In one of these two datasets (Ugarte-Urra et al., 2005), due to the error estimates in the observed temperature values, it is not posible to distinguish between the different heating mechanisms. For this we suggest that both Classical and Bayesian statistics should be applied in order to make safe assumptions about the nature of the coronal heating mechanisms., Comment: 22 pages, 5 figures, Solar Physics submitted

There is a growing body of evidence that the plasma loops seen with current instrumentation (SOHO, TRACE and Hinode) may consist of many sub-resolution elements or strands. Thus, the overall plasma evolution we observe in these features could be the cumulative result of numerous individual strands undergoing sporadic heating. This paper presents a short (10^9 cm ~ 10 Mm) ``global loop'' as 125 individual strands where each strand is modelled independently by a one-dimensional hydrodynamic simulation. The energy release mechanism across the strands consists of localised, discrete heating events (nano-flares). The strands are ``coupled'' together through the frequency distribution of the total energy input to the loop which follows a power law distribution with index alpha. The location and lifetime of each energy event occurring is random. Although a typical strand can go through a series of well-defined heating/cooling cycles, when the strands are combined, the overall quasi-static emission measure weighted thermal profile for the global loop reproduces a hot apex/cool base structure. Localised cool plasma blobs are seen to travel along individual strands which could cause the loop to `disappear' from coronal emission and appear in transition or chromospheric ones. As alpha increases (from 0 to 2.29 to 3.29), more weight is given to the smallest heating episodes. Consequently, the overall global loop apex temperature increases while the variation of the temperature around that value decreases. Any further increase in alpha saturates the loop apex temperature variations at the current simulation resolution. The effect of increasing the number of strands and the loop length as well as the implications of these results upon possible future observing campaigns for TRACE and Hinode are discussed., Comment: 23 pages, 10 Figures. ApJ (accepted)