Flare Energy Distribution Research Articles

Измерение энергетического распределения нановспышек малой мощности

We propose a method to measure the energy distribution of low-energy flares (nanoflares) in the energy range below 1023 erg. As an example, we measured the spectrum of nanoflares in the 1021–1026 erg range for two Sun’s frames observed by the SDO/AIA telescope in the 171 Å channel. Nanoflares are shown to have the power law spectrum in the 1022–1026 erg range. The spectral index is approximately constant, i.e. energy-independent. For energies below 1022 erg, the spectrum begins to collapse. For lower energies, below 1021 erg, the method does not give statistically significant results due to major errors. The results of the study indicate that solar nanoflares can be detected up to 1021–1022 erg energies. Results have previously been reported only for 1023 erg and above. The total energy flux of nanoflares in the energy range above 1022 erg, according to our data, is P2104 erg cm–2 s–1, which is about 15 times less than heating losses of the solar corona.

Измерение энергетического распределения нановспышек малой мощности

We propose a method to measure the energy distribution of low-energy flares (nanoflares) in the energy range below 1023 erg. As an example, we measured the spectrum of nanoflares in the 1021–1026 erg range for two Sun’s frames observed by the SDO/AIA telescope in the 171 Å channel. Nanoflares are shown to have the power law spectrum in the 1022–1026 erg range. The spectral index is approximately constant, i.e. energy-independent. For energies below 1022 erg, the spectrum begins to collapse. For lower energies, below 1021 erg, the method does not give statistically significant results due to major errors. The results of the study indicate that solar nanoflares can be detected up to 1021–1022 erg energies. Results have previously been reported only for 1023 erg and above. The total energy flux of nanoflares in the energy range above 1022 erg, according to our data, is P2104 erg cm–2 s–1, which is about 15 times less than heating losses of the solar corona.

Correcting Stellar Flare Frequency Distributions Detected by TESS and Kepler

The habitability of planets is closely connected with stellar activity, mainly the frequency of flares and the distribution of flare energy. Kepler and TESS find many flaring stars via precise time-domain photometric data, and the frequency and energy distribution of stellar flares on different types of stars are studied statistically. However, the completeness and observational bias of detected flare events from different missions (e.g., Kepler and TESS) vary a lot. We use a unified data processing and detection method for flare events based on the light curves from Kepler and TESS. Then we perform injection and recovery tests in the original light curve of each star for each flare event to correct the completeness and energy of flares. Three samples of flaring stars are selected from Kepler and TESS, with rotation periods from 1 to ∼5 days. Adopting a hot-blackbody assumption, our results show that the cumulative flare frequency distributions (FFDs) of the same stars in Kepler and TESS bands tend to be consistent after correction, revealing a more natural flaring frequency and energy distribution. Our results also extend the low-energy limit in cumulative FFD fitting to 1031.5−33 erg on different types of stars. For solar-type stars, the average power-law index of cumulative FFD (α cum) is −0.84, which indicates that low-energy flares contribute less to the total flare energy. With a piecewise correlation between α cum and T eff, α cum first rises from M2 to K1 stars, then slightly decreases for stars hotter than K1.

Nanoflare distributions over solar cycle 24 based on SDO/AIA differential emission measure observations

Aims. 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. Methods. Extreme ultraviolet filters of the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) were used. We analyzed 30 AIA/SDO image series between 2011 and 2018, each covering a 400″ × 400″ quiet-Sun field-of-view of over two hours with a 12-s cadence. Differential emission measure (DEM) analysis was used to derive the emission measure (EM) and temperature evolution for each pixel. We detected nanoflares as EM enhancements using a threshold-based algorithm and derived their thermal energy from the DEM observations. Results. Nanoflare energy distributions follow power laws that show slight variations in steepness (α = 2.02–2.47), but no correlation to the solar activity level. The combined nanoflare distribution of all data sets covers five orders of magnitude in event energies (1024 − 1029 erg) with a power-law index α = 2.28 ± 0.03. The derived mean energy flux of (3.7 ± 1.6)×104 erg cm−2 s−1 is one order of magnitude smaller than the coronal heating requirement. We found no correlation between the derived energy flux and solar activity. Analysis of the spatial distribution reveals clusters of high energy flux (up to 3 × 105 erg cm−2 s−1) surrounded by extended regions with lower activity. Comparisons with magnetograms from the Helioseismic and Magnetic Imager demonstrate that high-activity clusters are preferentially located in the magnetic network and above regions of enhanced magnetic flux density. Conclusions. The steep power-law slope (α > 2) suggests that the total energy in the flare energy distribution is dominated by the smallest events, that is to say nanoflares. We demonstrate that in the quiet-Sun, the nanoflare distributions and their contribution to coronal heating does not vary over the solar cycle.

X-ray variability of HD 189733 across eight years of XMM-Newton observations

The characterization of exoplanets, their formation, evolution, and chemical changes is tightly linked to our knowledge of their host stars. In particular, stellar X-rays and UV emission have a strong impact on the dynamical and chemical evolution of planetary atmospheres. We analyzed 25 XMM-Newton observations encompassing about eight years and totaling about 958 ks in order to study the X-ray emission of HD 189733 A. We find that the corona of HD 189733 A has an average temperature of 0.4 keV and it is only during flares that the mean temperature increases to 0.9 keV. Apart from the flares, there is no significant change in the flux and hardness of the coronal emission on a timescale of several months to years. Thus, we conclude that there is no detectable activity cycle on such timescales. We identified the flares and built their energy distribution. The number of flares observed around the phases of the planetary eclipses is not statistically different from the number of flares during transit phases. However, we do find a hint of a difference in the flare-energy distributions, as the flares observed around the planetary eclipses tend to be more energetic than the flares observed around the primary transits of the planet. We modeled the distribution of the number of flares per day with a power law, showing that it is steeper than the one observed in the Sun and in other Main Sequence stars. The steepness hints at a significant fraction of undetected micro-flares. Altogether, the plasma temperatures below 1 keV observed during the flares, along with the slightly larger fraction of energetic flares seen at the secondary transits highlight the peculiarity of the corona of HD 189733 A and points to star-planet interaction as the plausible origin of part of its X-ray emission. However, more observational and modeling efforts are required to confirm or disprove this scenario.

Theoretical and Observational Evidence for Coriolis Effects in Coronal Magnetic Fields via Direct Current Driven Flaring Events

Abstract All stars produce explosive surface events such as flares and coronal mass ejections. These events are driven by the release of energy stored in coronal magnetic fields, generated by the stellar dynamo. However, it remains unclear if the energy deposition in the magnetic fields is driven by direct or alternating currents. Recently, we presented observational measurements of the flare intensity distributions for a sample of ∼105 stars across the main sequence observed by TESS, all of which exhibited power-law distributions similar to those observed in the Sun, albeit with varying slopes. Here we investigate the mechanisms required to produce such a distribution of flaring events via direct current energy deposition, in which coronal magnetic fields braid, reconnect, and produce flares. We adopt a topological model for this process, which produces a power-law distribution of energetic flaring events. We expand this model to include the Coriolis effect, which we demonstrate produces a shallower distribution of flare energies in stars that rotate more rapidly (corresponding to a weaker decline in occurrence rates toward increasing flare energies). We present tentative evidence for the predicted rotation-power-law index correlation in the observations. We advocate for future observations of stellar flares that would improve our measurements of the power-law exponents, and yield key insights into the underlying dynamo mechanisms that underpin the self-similar flare intensity distributions.

Unified model for orphan and multiwavelength blazar flares

Blazars are a class of active galactic nuclei that host relativistic jets oriented close to the observer's line of sight. Blazars have very complex variability properties. Flares, namely flux variations around the mean value with a well-defined shape and duration, are one of the identifying properties of the blazar phenomenon. Blazars are known to exhibit multiwavelength flares, but also ``orphan'' flares, namely flux changes that appear only in a specific energy range. Various models, sometimes at odds with each other, have been proposed to explain specific flares even for a single source, and cannot be synthesized into a coherent picture. In this paper, we propose a unified model for explaining orphan and multiwavelength flares from blazars in a common framework. We assume that the blazar emission during a flare consists of two components: (i) a quasistable component that arises from the superposition of numerous but comparatively weak dissipation zones along the jet, forming the background (low-state) emission of the blazar, and (ii) a transient component, which is responsible for the sudden enhancement of the blazar flux, forming at a random distance along the jet by a strong energy dissipation event. Whether a multiwavelength or orphan flare is emitted depends on the distance from the base of the jet where the dissipation occurs. Generally speaking, if the dissipation occurs at a small/large distance from the supermassive black hole, the inverse Compton/synchrotron radiation dominates and an orphan $\ensuremath{\gamma}$-ray/optical flare tends to appear. On the other hand, we may expect a multiwavelength flare if the dissipation occurs at an intermediate distance. We show that the model can successfully describe the spectral energy distribution of different flares from the flat spectrum radio quasar 3C 279 and the BL Lacertae object PKS 2155-304.

The flare-activity of 2MASS J16111534–1757214 in the upper Scorpius association

ABSTRACT Flares are known to play an important role for the evolution of the atmospheres of young planets. In order to understand the evolution of planets, it is thus important to study the flare-activity of young stars. This is particularly the case for young M-stars, because they are very active. We study photometrically and spectroscopically the highly active M-star 2MASS J16111534–1757214. We show that it is a member of the Upper Sco OB association, which has an age of 5–10 Myrs. We also re-evaluate the status of other bona-fide M-stars in this region and identify 42 members. Analyzing the K2-light curves, we find that 2MASS J16111534–1757214 has, on average, one super-flare with $\rm E\ge 10^{35}$ erg every 620 h, and one with $\rm E\ge 10^{34}$ erg every 52 h. Although this is the most active M-star in the Upper Sco association, the power-law index of its flare-distribution is similar to that of other M-stars in this region. 2MASS J16111534–1757214 as well as other M-stars in this region show a broken power-law distribution in the flare-frequency diagram. Flares larger than $\rm E \ge 3\, 10^{34}$ erg have a power-law index $\rm \beta =-1.3\pm 0.1$ and flares smaller than that $\rm \beta =-0.8\pm 0.1$. We furthermore conclude that the flare-energy distribution for young M-stars is not that different from solar-like stars.

Toward the true number of flaring giant stars in the Kepler field

Aims. We aim to give a reliable estimate of the number of flaring giant stars in the Kepler field. By analyzing the flaring activity of these stars, we explored their flare statistics and the released flare energies. The role of oscillation in suppressing magnetic activity was also investigated. We searched for flaring specialities that may be associated with the giant nature across a sample of flaring giant stars. Methods. We searched for flares using the ≈4 yr long Kepler data on a sample of 706 stars compiled from two lists of flaring giants (log g ≤ 3.5) found in the literature. To lessen the probability of false positives two different pipelines are used independently for flare detection. Tests are carried out to correct the detection bias at low flare energies for a subsample of 19 further studied, frequently flaring stars. For these 19 stars flare energy distributions and flare frequency diagrams (FFDs) are constructed. For comparison purposes KIC 2852961 is re-analyzed with our present approach. Results. From the 706 Kepler flaring giant candidates, we ruled out those where oscillations or pulsations were misclassified and those that turned out to be dwarf stars. Finally, we confirm only 61 stars as flaring giants. Among these 61 flaring giants, we found only six that also show oscillations; we suggest that a large fraction of the 61 flaring giants are members of spectroscopic binaries, which has already been proven for 11 of them. The number of detected flares on giant stars correlate only weakly with the rotational periods. The FFDs for the 19 most flaring stars were fit by power-law functions. Regarding log–log representation, the slopes of the individual fits lead to an average α = 2.01 ± 0.16 power-law index, but the ranges of flare energies scatter within almost two orders, showing the inherent heterogeneity of the sample of flaring giants. Broken power-law fits are applied for two giant stars that have similar flare energy ranges; however, the energy at the breakpoints of the power laws are different, unveiling possible differences in the magnetic field strengths and atmospheric structures of these stars. The average power-law index of α ≈ 2 is the same for the flaring giants, the (super)flaring G-dwarfs, and dwarf stars between spectral types M6 and L0. Conclusions. The 61 confirmed flaring giant stars make up only ≈0.3% of the entire giant star population in the Kepler database, which is in contrast with previous estimates of about an order higher percentage. We found that most of the false positives are in fact oscillating red giants. No strong correlation was found between the stellar properties and the flaring characteristics. The majority of the flaring specialities are hardly related to the giant nature, if at all. This, together with the finding that the observed flare durations correlate with flare energies, regardless of the flare energy level and stellar luminosity class, suggests common background physics in flaring stars, or in other words, a general scaling effect behind the flares on different stars.

Flares in open clusters with K2

Context. Magnetic fields are a key component in the main sequence evolution of low mass stars. Flares, energetic eruptions on the surfaces of stars, are an unmistakable manifestation of magnetically driven emission. The occurrence rates and energy distributions of flares trace stellar characteristics such as mass and age. However, before flares can be used to constrain stellar properties, the flaring-age-mass relation requires proper calibration. Aims. This work sets out to quantify the flaring activity of independently age-dated main sequence stars for a broad range of spectral types using optical light curves obtained by the Kepler satellite. Methods. Drawing from the complete K2 archive, we searched 3435 ∼80 day long light curves of 2111 open cluster members for flares using the open-source software packages K2SC to remove instrumental and astrophysical variability from K2 light curves, and AltaiPony to search and characterize the flare candidates. Results. We confirmed a total of 3844 flares on high probability open cluster members with ages from zero age main sequence (Pleiades) to 3.6 Gyr (M 67). We extended the mass range probed in the first study of this series to span from Sun-like stars to mid-M dwarfs. We added the Hyades (690 Myr) to the sample as a comparison cluster to Praesepe (750 Myr), the 2.6 Gyr old Ruprecht 147, and several hundred light curves from the late K2 Campaigns in the remaining clusters. We found that the flare energy distribution was similar in the entire parameter space, following a power law relation with exponent α ≈ 1.84−2.39. Conclusions. We confirm that flaring rates decline with age, and decline faster for higher mass stars. Our results are in good agreement with most previous statistical flare studies. We find evidence that a rapid decline in flaring activity occurred in M1–M2 dwarfs around the ages of the Hyades and Praesepe, when these stars spun down to rotation periods of about 10 d, while higher mass stars had already transitioned to lower flaring rates and lower mass stars still resided in the saturated activity regime. We conclude that some discrepancies between our results and flare studies that used rotation periods for their age estimates could be explained by sample selection bias toward more active stars, but others may point to the limitations of using rotation as an age indicator without additional constraints from stellar activity.

Energy Distribution of Small-scale Flares Derived Using a Genetic Algorithm

Abstract To understand the mechanism of coronal heating, it is crucial to derive the contribution of small-scale flares, the so-called nanoflares, to the heating up of the solar corona. To date, several studies have tried to derive the occurrence frequency distribution of flares as a function of energy to reveal the contribution of small-scale flares. However, there are no studies that derive the distribution with considering the following conditions: (1) evolution of the coronal loop plasma heated by small-scale flares, (2) loops smaller than the spatial resolution of the observed image, and (3) multiwavelength observation. To take into account these conditions, we introduce a new method to analyze small-scale flares statistically based on a one-dimensional loop simulation and a machine-learning technique, that is, the genetic algorithm. First, we obtain six channels of Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA) light curves of the active-region coronal loops. Second, we carry out many coronal loop simulations and obtain the SDO/AIA light curves for each simulation in a pseudo-manner. Third, using the genetic algorithm, we estimate the best combination of simulated light curves that reproduce the observation. Consequently, the observed coronal loops are heated by small-scale flares with energy flux larger than that typically required to heat up an active region intermittently. Moreover, we derive the occurrence frequency distribution which has various power-law indices in the range from 1–3, which partially supports the nanoflare heating model. In contrast, we find that 90% of the coronal heating is done by flares that have energy larger than 1025 erg.

X-ray and gamma-ray emission from solar flares

We present a brief review of the contemporary understanding of and topical problems in solar flare physics that can be clarified by methods of X-ray and gamma-ray astronomy. The review focuses on several issues, including the conditions and mechanisms of electron acceleration in solar flares, the flare energy distribution between thermal and nonthermal components, the gamma-ray emission from solar flares and its dynamics, and the spatial structure of X-ray and gamma-ray sources. Discussed in this context are the latest data obtained by the joint Russia–US experiment Konus-Wind, which in 2019 celebrated the 25th anniversary of continuous operation in space.

Superflares on the late-type giant KIC 2852961

Context. The most powerful superflares reaching 1039 erg bolometric energy are from giant stars. The mechanism behind flaring is thought to be the magnetic reconnection, which is closely related to magnetic activity (including starspots). However, it is poorly understood how the underlying magnetic dynamo works and how the flare activity is related to the stellar properties that eventually control the dynamo action. Aims. We analyze the flaring activity of KIC 2852961, a late-type giant star, in order to understand how its flare statistics are related to those of other stars with flares and superflares, and to understand the role of the observed stellar properties in generating flares. Methods. We searched for flares in the full Kepler dataset of KIC 2852961 using an automated technique together with visual inspection. We cross-matched the flare-like events detected by the two different approaches and set a final list of 59 verified flares during the observing term. We calculated flare energies for the sample and performed a statistical analysis. Results. The stellar properties of KIC 2852961 are revised and a more consistent set of parameters are proposed. The cumulative flare energy distribution can be characterized by a broken power law; that is to say, on the log-log representation the distribution function is fitted by two linear functions with different slopes, depending on the energy range fitted. We find that the total flare energy integrated over a few rotation periods correlates with the average amplitude of the rotational modulation due to starspots. Conclusions. Flares and superflares seem to be the result of the same physical mechanism at different energy levels, also implying that late-type stars in the main sequence and flaring giant stars have the same underlying physical process for emitting flares. There might be a scaling effect behind the generation of flares and superflares in the sense that the higher the magnetic activity, the higher the overall magnetic energy released by flares and/or superflares.

KEPLER FLARES. IV. A COMPREHENSIVE ANALYSIS OF THE ACTIVITY OF THE dM4e STAR GJ 1243

ABSTRACT We present a comprehensive study of the active dM4e star GJ 1243. We use previous observations and ground-based echelle spectroscopy to determine that GJ 1243 is a member of the Argus association of field stars, suggesting it is old. We analyze 11 months of 1 minute cadence data from Kepler, presenting Kepler flare frequency distributions, as well as determining correlations between flare energy, amplitude, duration, and decay time. We find that the exponent α of the power-law flare energy distribution varies in time, primarily due to completeness of sample and the low frequency of high-energy flares. We also find a deviation from a single power law at high energy. We use ground-based spectroscopic observations that were simultaneous with the Kepler data to provide simultaneous photometric and spectroscopic analysis of three low-energy flares, the lowest-energy dMe flares with detailed spectral analysis to date on any star. The spectroscopic data from these flares extend constraints for radiative hydrodynamic flare models to a lower energy regime than has previously been studied. We use this simultaneous spectroscopy and Kepler photometry to develop approximate conversions from the Kepler bandpass to the traditional U and B bands. This conversion will be a critical factor in comparing any Kepler flare analyses to the canon of previous ground-based flare studies.

Characterization of X-ray flare properties of AB Dor

AbstractThe strong similarities between the flares observed on the Sun and in low mass stars has raised question regarding dynamo in these stars. Using the Sun as a prototype, one may be able to address this. In this paper, we present an analysis of 30 intense X-ray flares observed from AB Dor. These flares detected in XMM-Newton data show a rapid rise (500-3000 s) and a slow decay (1000-6000 s). Our studies suggest that the scaling law between the flare peak emission measure and the flare peak temperature for all the flares observed on AB Dor is very similar to the relationship followed by solar flares. Furthermore, we obtain the frequency distribution of flare energies which is a crucial diagnostic to calculate the overall energy residing in a flare. Our results of this study indicate that the large flare (1033 ≤ E ≤ 1034 erg) may not contribute to the heating of the corona.

The view from K2: questioning the traditional view of flaring on early dM stars

We use K2 short cadence data obtained over a duration of 50 days during Campaign 0 to observe two M1V dwarf stars, TYC 1330-879-1 and RXJ 0626+2349. We provide an overview of our data analysis, in particular, making a comparison between using a fixed set of pixels and an aperture which follows the position of the source. We find that this moving aperture approach can give fewer non-astrophysical features compared to a fixed aperture. Both sources shows flares as energetic as observed from several M4V stars using both Kepler and ground based telescopes. We find that the flare energy distribution of the sources shown here are very similar to the less active M3-M5 stars but are ~8 times less likely to produce a flare of a comparable energy to the more active M0--M5 stars. We discuss the biases and sources of systematic errors when comparing the activity of stars derived from different instruments. We conclude that K2 observations will provide an excellent opportunity to perform a census of flare activity across the full range of M dwarf spectral class and hence the physical mechanisms which power them.

Modelling the influence of photospheric turbulence on solar flare statistics.

Solar flares stem from the reconnection of twisted magnetic field lines in the solar photosphere. The energy and waiting time distributions of these events follow complex patterns that have been carefully considered in the past and that bear some resemblance with earthquakes and stockmarkets. Here we explore in detail the tangling motion of interacting flux tubes anchored in the plasma and the energy ejections resulting when they recombine. The mechanism for energy accumulation and release in the flow is reminiscent of self-organized criticality. From this model, we suggest the origin for two important and widely studied properties of solar flare statistics, including the time-energy correlations. We first propose that the scale-free energy distribution of solar flares is largely due to the twist exerted by the vorticity of the turbulent photosphere. Second, the long-range temporal and time-energy correlations appear to arise from the tube-tube interactions. The agreement with satellite measurements is encouraging.

Short-duration high-amplitude flares detected on the M dwarf star KIC 5474065

Using data obtained during the RATS-Kepler project, we identified one short-duration flare in a 1 h sequence of ground-based photometry of the dwarf star KIC 5474065. Observations made using Gran Telescopio Canarias show that it is a star with an M4V spectral type. Kepler observations made using 1 min sampling show that KIC 5474065 exhibits large-amplitude (δF/F > 0.4) optical flares which have a duration as short as 10 min. We compare the energy distribution of flares from KIC 5474065 with that of KIC 9726699, which has also been observed using 1-min sampling, and ground-based observations of other M dwarf stars in the literature. We discuss the possible implications these short-duration, relatively low-energy flares would have on the atmosphere of exoplanets orbiting in the habitable zone of these flare stars.

Current Fragmentation and Particle Acceleration in Solar Flares

Particle acceleration in solar flares remains an outstanding problem in plasma physics and space science. While the observed particle energies and timescales can perhaps be understood in terms of acceleration at a simple current sheet or turbulence site, the vast number of accelerated particles, and the fraction of flare energy in them, defies any simple explanation. The nature of energy storage and dissipation in the global coronal magnetic field is essential for understanding flare acceleration. Scenarios where the coronal field is stressed by complex photospheric motions lead to the formation of multiple current sheets, rather than the single monolithic current sheet proposed by some. The currents sheets in turn can fragment into multiple, smaller dissipation sites. MHD, kinetic and cellular automata models are used to demonstrate this feature. Particle acceleration in this environment thus involves interaction with many distributed accelerators. A series of examples demonstrate how acceleration works in such an environment. As required, acceleration is fast, and relativistic energies are readily attained. It is also shown that accelerated particles do indeed interact with multiple acceleration sites. Test particle models also demonstrate that a large number of particles can be accelerated, with a significant fraction of the flare energy associated with them. However, in the absence of feedback, and with limited numerical resolution, these results need to be viewed with caution. Particle in cell models can incorporate feedback and in one scenario suggest that acceleration can be limited by the energetic particles reaching the condition for firehose marginal stability. Contemporary issues such as footpoint particle acceleration are also discussed. It is also noted that the idea of a “standard flare model” is ill-conceived when the entire distribution of flare energies is considered.

STATISTICAL ANALYSES ON THERMAL ASPECTS OF SOLAR FLARES

The frequency distribution of flare energies provides a crucial diagnostic to calculate the overall energy residing in flares and to estimate the role of flares in coronal heating. It often takes a power law as its functional form. We have analyzed various variables, including the thermal energies E-th of 1843 flares at their peak time. They were recorded by both Geostationary Operational Environmental Satellites and Reuven Ramaty High-Energy Solar Spectroscopic Imager during the time period from 2002 to 2009 and are classified as flares greater than C 1.0. The relationship between different flare parameters is investigated. It is found that fitting the frequency distribution of E-th to a power law results in an index of -2.38. We also investigate the corrected thermal energy E-c_th, which represents the flare total thermal energy including the energy loss in the rising phase. Its corresponding power-law slope is -2.35. Compilation of the frequency distributions of the thermal energies from nanoflares, microflares, and flares in the present work and from other authors shows that power-law indices below -2.0 have covered the range from 10(24) to 10(32) erg. Whether this frequency distribution can provide sufficient energy to coronal heatings in active regions and the quiet Sun is discussed.