The properties expected of "hot" non-flaring plasmas due to nanoflare heating in active regions are investigated using hydrodynamic modeling tools, including a two-fluid development of the EBTEL code. Here we study a single nanoflare and show that while simple models predict an emission measure distribution extending well above 10 MK that is consistent with cooling by thermal conduction, many other effects are likely to limit the existence and detectability of such plasmas. These include: differential heating between electrons and ions, ionization non-equilibrium and, for short nanoflares, the time taken for the coronal density to increase. The most useful temperature range to look for this plasma, often called the "smoking gun" of nanoflare heating, lies between $10^{6.6}$ and $10^7$ K. Signatures of the actual heating may be detectable in some instances.
Despite its prediction over two decades ago, the detection of faint, high-temperature ("hot") emission due to nanoflare heating in non-flaring active region cores has proved challenging. Using an efficient two-fluid hydrodynamic model, this paper investigates the properties of the emission expected from repeating nanoflares (a nanoflare train) of varying frequency as well as the separate heating of electrons and ions. If the emission measure distribution ($\mathrm{EM}(T)$) peaks at $T = T_m$, we find that $\mathrm{EM}(T_m)$ is independent of details of the nanoflare train, and $\mathrm{EM}(T)$…
The nanoflare-heating theory predicts steady hot plasma emission in the non-flaring active regions. It is hard to find this emission with conventional non-monochromatic imagers (such as Atmospheric Imaging Assembly or X-Ray Telescope), because their images contain a cool temperature background. In this work, we search for hot plasma in non-flaring active regions using the Mg XII spectroheliograph onboard Complex Orbital Observations Near-Earth of Activity on the Sun (CORONAS)-F/SPectroheliographIc X-ray Imaging Telescope (SPIRIT). This instrument acquired monochromatic images of the solar coro…
Nanoflare models for heating the solar corona usually assume magnetic braiding and reconnection as the source of the energy. However, recent observations at record spatial resolution from the {\sc Sunrise} balloon mission suggest that photospheric magnetic flux cancellation is much more common than previously realised. We therefore examine the possibility of three-dimensional reconnection driven by flux cancellation as a cause of chromospheric and coronal heating. In particular, we estimate how the heights and amount of energy release produced by flux cancellation depend on flux size, flux can…
Observational measurements of active region emission measures contain clues to the time-dependence of the underlying heating mechanism. A strongly non-linear scaling of the emission measure with temperature indicates a large amount of hot plasma relative to warm plasma. A weakly non-linear (or linear) scaling of the emission measure indicates a relatively large amount of warm plasma, suggesting that the hot active region plasma is allowed to cool and so the heating is impulsive with a long repeat time. This case is called {\it low-frequency} nanoflare heating and we investigate its feasibility…
It is largely agreed that many coronal loops---those observed at a temperature of about 1 MK--- are bundles of unresolved strands that are heated by storms of impulsive nanoflares. The nature of coronal heating in hotter loops and in the very important but largely ignored diffuse component of active regions is much less clear. Are these regions also heated impulsively, or is the heating quasi steady? The spectacular new data from the Atmospheric Imaging Assembly (AIA) telescopes on the Solar Dynamics Observatory (SDO) offer an excellent opportunity to address this question. We analyze the ligh…
Nanoflares, the basic unit of impulsive energy release may produce much of the solar background emission. Extrapolation of the energy frequency distribution of observed microflares, which follows a power law to lower energies can give an estimation of the importance of nanoflares for heating the solar corona. If the power law index is greater than 2, then the nanoflare contribution is dominant. We model time series of extreme ultraviolet emission radiance, as random flares with a power law exponent of the flare event distribution. The model is based on three key parameters, the flare rate, the…
We analyzed the occurrence rates of flares on stars of spectral types K, G, F, and A, observed by Kepler. We found that the histogram of occurrence frequencies of stellar flares is systematically shifted towards a high-energy tail for A-type stars compared to stars of cooler spectral types. We extrapolated the fitted power laws towards flares with smaller energies (nanoflares) and made estimates for total energy flux to stellar atmospheres by flares. We found that for A-type stars the total energy flux density was at least 4-times smaller than for G-stars. We speculate that this deficit in ene…
We model nanoflare heating of extrapolated active-region coronal loops via the acceleration of electrons and protons in Harris-type current sheets. The kinetic energy of the accelerated particles is estimated using semi-analytical and test-particle-tracing approaches. Vector magnetograms and photospheric Doppler velocity maps of NOAA active region 09114, recorded by the Imaging Vector Magnetograph (IVM), were used for this analysis. A current-free field extrapolation of the active-region corona was first constructed. The corresponding Poynting fluxes at the footpoints of 5000 extrapolated coro…
All theories that attempt to explain the heating of the high temperature plasma observed in the solar corona are based on short bursts of energy. The intensities and velocities measured in the cores of quiescent active regions, however, can be steady over many hours of observation. One heating scenario that has been proposed to reconcile such observations with impulsive heating models is the "long nanoflare storm," where short duration heating events occur infrequently on many sub-resolutions strands; the emission of the strands is then averaged together to explain the observed steady structur…
Heating signatures from small-scale magnetic reconnection events in the solar atmosphere have proven to be difficult to detect through observations. Numerical models that reproduce flaring conditions are essential in the understanding of how nanoflares may act as a heating mechanism of the corona. We study the effects of non-thermal electrons in synthetic spectra from 1D hydrodynamic RADYN simulations of nanoflare heated loops to investigate the diagnostic potential of chromospheric emission from small-scale events. The Mg II h and k, Ca II H and K, Ca II 854.2 nm, H-alpha and H-beta chromosph…
Parker (1983) suggested a mechanism for the formation of current sheets (CSs) in the solar atmosphere. His main idea was that the tangling of coronal magnetic field lines by photospheric random flows facilitates the continuous formation of CSs in the solar atmosphere. This part of his idea represents one of the many ways by which the turbulent convection zone drives the formation of coherent structures and CSs in the solar atmosphere. Other mechanisms include emerging magnetic flux, interaction of current filaments, and explosive magnetic structures. However, there are two unproven assumptions…
The time-dependence of heating in solar active regions can be studied by analyzing the slope of the emission measure distribution cool-ward of the peak. In a previous study we showed that low-frequency heating can account for 0% to 77% of active region core emission measures. We now turn our attention to heating by a finite succession of impulsive events for which the timescale between events on a single magnetic strand is shorter than the cooling timescale. We refer to this scenario as a "nanoflare train" and explore a parameter space of heating and coronal loop properties with a hydrodynamic…
We present the results of 1D hydrodynamic simulations of coronal loops which are subject to nanoflares, caused by either in-situ thermal heating, or non-thermal electrons (NTE) beams. The synthesized intensity and Doppler shifts can be directly compared with IRIS and AIA observations of rapid variability in the transition region (TR) of coronal loops, associated with transient coronal heating. We find that NTE with high enough low-energy cutoff (E$_\textrm{C}$) deposit energy in the lower TR and chromosphere causing blueshifts (up to~$\sim$~20 km/s) in the \emph{IRIS} \siiv~lines, which therma…
Self-Consistent Heating of the Magnetically Closed Solar Corona: Generation of Nanoflares, Thermodynamic Response of the Plasma and Observational Signatures
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 emi…
Much evidence suggests that the solar corona is heated impulsively, meaning that nanoflares may be ubiquitous in quiet and active regions (ARs). Hard X-ray (HXR) observations with unprecedented sensitivity $>$3~keV are now enabled by focusing instruments. We analyzed data from the \textit{Focusing Optics X-ray Solar Imager (FOXSI)} rocket and the \textit{Nuclear Spectroscopic Telescope Array (NuSTAR)} spacecraft to constrain properties of AR nanoflares simulated by the EBTEL field-line-averaged hydrodynamics code. We generated model X-ray spectra by computing differential emission measures for…
Small-scale impulsive events, known as nanoflares, are thought to be one of the prime candidates that can keep the solar corona hot at its multi-million Kelvin temperature. Individual nanoflares are difficult to detect with the current generation instruments; however, their presence can be inferred through indirect techniques such as a Differential Emission Measure (DEM) analysis. Here we employ this technique to investigate the possibility of nanoflare heating of the quiet corona during the minimum of solar cycle 24. During this minimum, active regions (ARs) were absent on the solar-disk for …
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.
The million degree plasma of the solar corona must be supplied by the underlying layers of the atmosphere. The mechanism and location of energy release, and the precise source of coronal plasma, remain unresolved. In earlier work we pursued the idea that warm plasma is supplied to the corona via direct heating of the chromosphere by nanoflares, contrary to the prevailing belief that the corona is heated in-situ and the chromosphere is subsequently energized and ablated by thermal conduction. We found that single (low-frequency) chromospheric nanoflares could not explain the observed intensitie…
Recent observations at high spatial resolution have shown that magnetic flux cancellation occurs on the solar surface much more frequently than previously thought, and so this led Priest et al 2018 to propose magnetic reconnection driven by photospheric flux cancellation as a mechanism for chromospheric and coronal heating. In particular, they estimated analytically the amount of energy released as heat and the height of the energy release during flux cancellation. In the present work, we take the next step in the theory by setting up a two-dimensional resistive MHD simulation of two canceling…
Small-scale magnetic reconnection processes, in the form of nanoflares, have become increasingly hypothesized as important mechanisms for the heating of the solar atmosphere, for driving propagating disturbances along magnetic field lines in the Sun's corona, and for instigating rapid jet-like bursts in the chromosphere. Unfortunately, the relatively weak signatures associated with nanoflares places them below the sensitivities of current observational instrumentation. Here, we employ Monte Carlo techniques to synthesize realistic nanoflare intensity time series from a dense grid of power-law …
The existence of the million-degree corona above the cooler photosphere is an unsolved problem in astrophysics. Detailed study of quiescent corona that exists regardless of the phase of the solar cycle may provide fruitful hints towards resolving this conundrum. However, the properties of heating mechanisms can be obtained only statistically in these regions due to their unresolved nature. Here, we develop a two-step inversion scheme based on the machine learning scheme of Upendran & Tripathi (2021a) for the empirical impulsive heating model of Pauluhn & Solanki (2007), and apply it to disk in…
Using data from the Extreme-ultraviolet Imaging Spectrometer aboard Hinode, we have studied the coronal plasma in the core of two active regions. Concentrating on the area between opposite polarity moss, we found emission measure distributions having an approximate power-law form EM$\propto T^{2.4}$ from $\log\,T = 5.5$ up to a peak at $\log\,T = 6.55$. We show that the observations compare very favorably with a simple model of nanoflare-heated loop strands. They also appear to be consistent with more sophisticated nanoflare models. However, in the absence of additional constraints, steady hea…
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 …
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 dir…
Nanoflares are regarded as one of the major mechanisms of magnetic energy release and coronal heating in the solar outer atmosphere. We conduct a statistical study on the response of the chromosphere and transition region to nanoflares, as observed by the Interface Region Imaging Spectrograph (IRIS), by using an algorithm for the automatic detection of these events. The initial atmospheric response to these small heating events is observed, with IRIS, as transient brightening at the footpoints of coronal loops heated to high temperatures (>4 MK). For four active regions, observed over 143 hour…
Inspired by recent observations suggesting that photospheric magnetic flux cancellation occurs much more frequently than previously thought, we analytically estimated the energy released from reconnection driven by photospheric flux cancellation, and proposed that it can act as a mechanism for chromospheric and coronal heating (Priest et al., 2018). Using two-dimensional simulations we validated the analytical estimates and studied the resulting atmospheric response (Syntelis et al. 2019). In the present work, we set up three-dimensional resistive MHD simulations of two cancelling polarities i…
Context. We investigate the statistics of the spatial and temporal distribution of the coronal heating in a three-dimensional magneto- hydrodynamical (3D MHD) model. The model describes the temporal evolution of the corona above an observed active region. The model is driven by photospheric granular motions which braid the magnetic field lines. This induces currents and their dissipation heats the plasma. We evaluate the transient heating as subsequent heating events and analyze their statistics. The results are then interpreted in the context of observed flare statistics and coronal heating m…
In a recent computational campaign [Ng et al., Astrophys. J. 747, 109, 2012] to investigate a three-dimensional model of coronal heating using reduced magnetohydrodynamics (RMHD), we have obtained scaling results of heating rate versus Lundquist number based on a series of runs in which random photospheric motions are imposed for hundreds to thousands of Alfvén time in order to obtain converged statistical values. Using this collection of numerical data, we have performed additional statistical analysis related to the formation of current sheets and heating events, or nanoflares [Parker, Astro…
Nanoflares in quiet-Sun regions during solar cycle 24 are studied with the best available plasma diagnostics to derive their energy distribution and contribution to coronal heating during different levels of solar activity. Extreme ultraviolet (EUV) filters of the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) are used. We analyze 30 AIA/SDO image series between 2011 and 2018, each covering a $400 \times 400$ arcsec quiet-Sun field-of-view over two hours with a 12-second cadence. Differential emission measure (DEM) analysis is used to derive the emission measur…
The nanoflare paradigm of coronal heating has proven extremely promising for explaining the presence of hot, multi-million degree loops in the solar corona. In this paradigm, localized heating events supply enough energy to heat the solar atmosphere to its observed temperatures. Rigorously modeling this process, however, has proven difficult, since it requires an accurate treatment of both the magnetic field dynamics and reconnection as well as the plasma's response to magnetic perturbations. In this paper, we combine fully 3D magnetohydrodynamic (MHD) simulations of coronal active region plas…
The High-resolution Coronal Imager (Hi-C) has provided Fe XII 193A images of the upper transition region moss at an unprecedented spatial (~0.3-0.4 arcsec) and temporal (5.5s) resolution. The Hi-C observations show in some moss regions variability on timescales down to ~15s, significantly shorter than the minute scale variability typically found in previous observations of moss, therefore challenging the conclusion of moss being heated in a mostly steady manner. These rapid variability moss regions are located at the footpoints of bright hot coronal loops observed by SDO/AIA in the 94A channel…
It is generally agreed that small impulsive energy bursts called nanoflares are responsible for at least some of the Sun's hot corona, but whether they are the explanation for most of the multi-million degree plasma has been a matter of ongoing debate. We here present evidence that nanoflares are widespread in an active region observed by the X-Ray Telescope on-board the Hinode mission. The distributions of intensity fluctuations have small but important asymmetries, whether taken from individual pixels, multi-pixel subregions, or the entire active region. Negative fluctuations (corresponding …
We highlight ten key aspects of coronal heating that must be understood before we can consider the problem to be solved. (1) All coronal heating is impulsive. (2) The details of coronal heating matter. (3) The corona is filled with elemental magnetic stands. (4) The corona is densely populated with current sheets. (5) The strands must reconnect to prevent an infinite buildup of stress. (6) Nanoflares repeat with different frequencies. (7) What is the characteristic magnitude of energy release? (8) What causes the collective behavior responsible for loops? (9) What are the onset conditions for …
Context: One of the most prominent processes suggested to heat the corona to well above 10^6 K builds on nanoflares, short bursts of energy dissipation. Aims: We compare observations to model predictions to test the validity of the nanoflare process. Methods: Using extreme UV data from AIA/SDO and HMI/SDO line-of-sight magnetograms we study the spatial and temporal evolution of a set of loops in active region AR 11850. Results: We find a transient brightening of loops in emission from Fe xviii forming at about 7.2 MK while at the same time these loops dim in emission from lower temperatures. T…
We present a detailed analysis of a reflecting intensity perturbation in a large coronal loop that appeared as sloshing oscillation and lasted for at least one and a half periods. The perturbation is initiated by a microflare at one footpoint of the loop, propagates along the loop and is eventually reflected at the remote footpoint where significant brightenings are observed in all the AIA extreme-ultraviolet (EUV) channels. This unique observation provides us with the opportunity to better understand not only the thermal properties and damping mechanisms of the sloshing oscillation, but also …
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 ~ 2.2…
In the work described here we investigate atomic processes leading to the formation of emission lines within the IRIS wavelength range at temperatures near $10^5$~K. We focus on (1) non-equilibrium and (2) density-dependent effects influencing the formation and radiative properties of S IV and O IV. These two effects have significant impacts on spectroscopic diagnostic measurements of quantities associated with the plasma that emission lines from S IV and O IV provide. We demonstrate this by examining nanoflare-based coronal heating to determine what the detectable signatures are in transition…
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 acco…
We study a 2D cellular automaton (CA) model for the evolution of coronal loop plasmas. The model is based on the idea that coronal loops are made of elementary magnetic strands that are tangled and stressed by the displacement of their footpoints by photospheric motions. The magnetic stress accumulated between neighbor strands is released in sudden reconnection events or nanoflares that heat the plasma. We combine the CA model with the Enthalpy Based Thermal Evolution of Loops (EBTEL) model to compute the response of the plasma to the heating events. Using the known response of the XRT telesco…
3D MHD simulations of coronal loops heated via magnetic braiding II. Automatic detection of reconnection outflows and statistical analysis of their properties
We analyze and model a C5.7 two-ribbon solar flare observed by SDO, Hinode and GOES on 2011 December 26. The flare is made of many loops formed and heated successively over one and half hours, and their footpoints are brightened in the UV 1600 A before enhanced soft X-ray and EUV missions are observed in flare loops. Assuming that anchored at each brightened UV pixel is a half flaring loop, we identify more than 6,700 half flaring loops, and infer the heating rate of each loop from the UV light curve at the foot-point. In each half loop, the heating rate consists of two phases, an intense impu…
The physical processes causing energy exchange between the Sun's hot corona and its cool lower atmosphere remain poorly understood. The chromosphere and transition region (TR) form an interface region between the surface and the corona that is highly sensitive to the coronal heating mechanism. High resolution observations with the Interface Region Imaging Spectrograph (IRIS) reveal rapid variability (about 20 to 60 seconds) of intensity and velocity on small spatial scales at the footpoints of hot dynamic coronal loops. The observations are consistent with numerical simulations of heating by b…
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…
The nanoflare model of coronal heating is one of the most successful scenarios to explain, within a single framework, the diverse set of coronal observations available with the present instrument resolutions. The model is based on the idea that the coronal structure is formed by elementary magnetic strands which are tangled and twisted by the displacement of their photospheric footpoints by convective motions. These displacements inject magnetic stress between neighbor strands that promotes current sheet formation, reconnection, plasma heating, and possibly also particle acceleration. Among ot…
The formation of the observed core-halo feature in the solar wind electron velocity distribution function is a long-time puzzle. In this letter based on the current knowledge of nanoflares we show that the nanoflare-accelerated electron beams are likely to trigger a strong electron two-stream instability that generates kinetic Alfvén wave and whistler wave turbulence, as we demonstrated in a previous paper. We further show that the core-halo feature produced during the origin of kinetic turbulence is likely to originate in the inner corona and can be preserved as the solar wind escapes to spac…
Magnetic energy is required to heat the corona, the outer atmosphere of the Sun, to millions of degrees. We study the nature of the magnetic energy source that is probably responsible for the brightening of coronal loops driven by nanoflares in the cores of solar active regions. We consider observations of two active regions (ARs), 11890 and 12234, in which nanoflares have been detected. To this end, we use ultraviolet (UV) and extreme ultraviolet (EUV) images from the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) for coronal loop diagnostics. These images are…
The infrared Mg I lines near 12 microns are a pair of emission lines which are magnetically sensitive and have been used to measure solar magnetic fields. Here we calculate the response of the Mg I 12.32 $μ$m line during a flare and find that in our modeling this line has a complicated behavior. At the beginning of the flare heating, this line shows an intensity dimming at the line center. The intensity then increases when heating continues, with increasing contributions from the heated layers in the chromosphere. The line formation height and the line width also increase as a result. As for t…
Spectral line widths are often observed to be larger than can be accounted for by thermal and instrumental broadening alone. This excess broadening is a key observational constraint for both nanoflare and wave dissipation models of coronal heating. Here we present a survey of non-thermal velocities measured in the high temperature loops (1--5MK) often found in the cores of solar active regions. This survey of $\textit{Hinode}$ Extreme Ultraviolet Imaging Spectrometer (EIS) observations covers 15 non-flaring active regions that span a wide range of solar conditions. We find relatively small non…
The quiet solar corona consists of myriads of loop-like features, with magnetic fields originating from network and internetwork regions on the solar surface. The continuous interaction between these different magnetic patches leads to transient brightenings or bursts that might contribute to the heating of the solar atmosphere. However, it remains unclear whether such transients, which are mostly observed in the EUV, play a significant role in atmospheric heating. We revisit the open question of these bursts as a prelude to the new high-resolution EUV imagery expected from the recently launch…
We present new constraints on the high-temperature emission measure of a non-flaring solar active region using observations from the recently flown Focusing Optics X-ray Solar Imager sounding rocket payload. FOXSI has performed the first focused hard X-ray (HXR) observation of the Sun in its first successful flight on 2012 November 2. Focusing optics, combined with small strip detectors, enable high-sensitivity observations with respect to previous indirect imagers. This capability, along with the sensitivity of the HXR regime to high-temperature emission, offers the potential to better charac…
We investigate intensity variations and energy deposition in five coronal loops in active region cores. These were selected for their strong variability in the AIA/SDO 94 Å intensity channel. We isolate the hot Fe XVIII and Fe XXI components of the 94 Å and 131 Å by modeling and subtracting the "warm" contributions to the emission. HMI/SDO data allow us to concentrate on "inter-moss" regions in the loops. The detailed evolution of the inter-moss intensity time series reveals loops that are impulsively heated in a mode compatible with a nanoflare storm, with a spike in the hot 131 Å signals lea…
