Flare Duration Research Articles

Unexpected stratification in the equivalent-duration distributions of flare stars

ABSTRACT In this study, the results obtained from the statistical models of flares observed with ground-based telescopes and TESS observations for the UV Ceti-type stars AD Leo and V1005 Ori are presented. The distribution of flare equivalent duration versus total flare duration for the flares of both stars, observed with different telescopes, has been modelled using the one-phase exponential association (OPEA) model. Although no bifurcation was observed in the models derived with the flare data of V1005 Ori, the OPEA model exhibited bifurcation in almost all observation data of AD Leo. While many similar studies have shown that such models derived for a star do not vary over time and exhibit a single distribution in the same observation season, the stratification in AD Leo’s distributions and consequently in its model is an unexpected result.

Properties of flare events based on light curves from the TESS survey

Aims. Stellar flares are sudden bursts of energy and are the result of magnetic activity. We used light curves from the TESS 20-second cadence survey from 2020 to 2023 to detect flare events and determine their properties. Methods. By means of repeated fitting to distinguish stellar background light curves and flare events, we detected 32 978 flare events associated with 5463 flaring stars. Furthermore, we cross-matched our samples with the Gaia and SDSS surveys, obtaining additional stellar parameters that we used to determine the relationships between stellar and flare properties. Results. We find that the durations of 55% of the studied flares were less than 8 minutes. The flare energies of the TESS 20-second cadence data are typically lower than those obtained from TESS 2-minute cadence data. We identify 28 425 flare events associated with 4784 flaring stars. The relationships between the flare energy and duration for both giant and main sequence stars display a consistent V-shaped distribution, with 1034 erg the midway point. Stars with lower effective temperatures and masses generate more frequent flare events. In summary, it is necessary to detect more flare events with a higher time resolution, and our flare samples with 20-second cadences allowed us to discover additional new properties.

Transient study using LoTSS – framework development and preliminary results

ABSTRACT We present a search for transient radio sources on time-scales of seconds to hours at 144 MHz using the LOFAR Two-metre Sky Survey (LoTSS). This search is conducted by examining short time-scale images derived from the LoTSS data. To allow imaging of LoTSS on short time-scales, a modern imaging procedure and fast filtering strategy are introduced. This includes sky model source subtraction, no cleaning or primary beam correction, a simple source finder, fast filtering schemes, and source catalogue matching. This new strategy is first tested by injecting simulated transients, with a range of flux densities and durations, into the data. We find the limiting sensitivity to be 113 and 6 mJy for 8 s and 1 h transients, respectively. The new imaging and filtering strategies are applied to 58 fields of the LoTSS survey, corresponding to LoTSS-DR1 (2 per cent of the survey). One transient source is identified in the 8 s and 2 min snapshot images. The source shows 1 min duration flare in the 8 h observation. Our method puts the most sensitive constraints on/estimates of the transient surface density at low frequencies at time-scales of seconds to hours; <4.0 × 10−4 deg−2 at 1 h at a sensitivity of 6.3 mJy; 5.7 × 10−7 deg−2 at 2 min at a sensitivity of 30 mJy; and 3.6 × 10−8 deg−2 at 8 s at a sensitivity of 113 mJy. In the future, we plan to apply the strategies presented in this paper to all LoTSS data.

Shock Cooling and Breakout Emission for Optical Flares Associated with Gravitational-wave Events

The astrophysical origin of stellar-mass black hole (BH) mergers discovered through gravitational waves (GWs) is widely debated. Mergers in the disks of active galactic nuclei (AGNs) represent promising environments for at least a fraction of these events, with possible observational clues in the GW data. An additional clue to unveil AGN merger environments is provided by possible electromagnetic emission from postmerger accreting BHs. Associated with BH mergers in AGN disks, emission from shocks emerging around jets launched by accreting merger remnants is expected. Here we compute the properties of the emission produced during breakout and the subsequent adiabatic expansion phase of the shocks, and we then apply this model to optical flares suggested to be possibly associated with GW events. We find that the majority of the reported flares can be explained by breakout and shock cooling emission. If the optical flares are produced by shock cooling emission, they would display moderate color evolution, possibly color variations among different events, and a positive correlation between delay time and flare duration and would be preceded by breakout emission in X-rays. If the breakout emission dominates the observed lightcurve, we predict the color to be distributed in a narrow range in the optical band and the delay time from GW to electromagnetic emission to be longer than ∼2 days. Hence, further explorations of delay time distributions, flare color evolution, and associated X-ray emission will be useful to test the proposed emission model for the observed flares.

Maser flares driven by isothermal shock waves

ABSTRACT We use 3D computer modelling to investigate the time-scales and radiative output from maser flares generated by the impact of shock waves on astronomical unit-scale clouds in interstellar and star-forming regions, and in circumstellar regions in some circumstances. Physical conditions are derived from simple models of isothermal hydrodynamic (single-fluid) and C-type (ionic and neutral fluid) shock waves, and based on the ortho-H2O 22-GHz transition. Maser saturation is comprehensively included, and we find that the most saturated maser inversions are found predominantly in the shocked material. We study the effect on the intensity, flux density, and duration of flares of the following parameters: the pre-shock level of saturation, the observer’s viewpoint, and the shock speed. Our models are able to reproduce observed flare rise times of a few times 10 d, specific intensities of up to 105 times the saturation intensity and flux densities of order 100(R/d)2 Jy from a source of radius R astronomical units at a distance of d kiloparsec. We found that flares from C-type shocks are approximately five times more likely to be seen by a randomly placed observer than flares from hydrodynamically shocked clouds of similar dimensions. We computed intrinsic beaming patterns of the maser emission, finding substantial extension of the pattern parallel to the shock front in the hydrodynamic models. Beaming solid angles for hydrodynamic models can be as small as 1.3 × 10−5 sr, but are an order of magnitude larger for C-type models.

Maintenance of Investigator's Static Global Assessment Response with Once-Daily Crisaborole in Participants with Mild to Moderate Atopic Dermatitis.

Treatments for atopic dermatitis (AD) often fail to achieve lasting disease control. In the CrisADe CONTROL phase III study (ClinicalTrials.gov: NCT04040192), participants aged ≥ 3months with mild to moderate AD treated with once-daily (QD) crisaborole, following initial treatment success with crisaborole twice daily (BID), had longer periods of flare-free maintenance, a higher number of flare-free days, and a lower number of flares compared with those who received vehicle. The study was an exploratory analysis of data on the maintenance of response per Investigator's Static Global Assessment (ISGA; ISGA score of 0 [clear] or 1 [almost clear]) during the CrisADe CONTROL study through week 52. Exploratory endpoints were the time to ISGA response during the open-label run-in period, and the maintenance of ISGA response and the severity and duration of flares during the double-blind maintenance period. Outcomes were stratified by age (participants aged 3months to < 12years and ≥ 12years) and duration of crisaborole BID treatment (< 4weeks or ≥ 4weeks) during the open-label run-in period. During the open-label run-in period, the median time to ISGA response was 41.5days. From week 4 to week 52 of the double-blind maintenance period, the proportion of participants who maintained ISGA response was greater with crisaborole versus vehicle, and this difference was statistically significant up to week 36 (P < 0.05). Duration of flare periods during the maintenance period were 54.1 and 54.0days for the vehicle and crisaborole-treated groups, respectively. Numerically fewer crisaborole-treated participants experienced a flare with an ISGA score of ≥ 2 compared with vehicle-treated participants (64.8% vs. 74.4%, respectively). Findings were comparable across most subgroups. Adult and pediatric participants with mild to moderate AD at baseline who had achieved responder criteria (treatment success) with crisaborole BID during the run-in period maintained response per ISGA with crisaborole QD during the double-blind maintenance period through week 52. ClinicalTrials.gov: NCT04040192.

The complex circumstellar environment of supernova 2023ixf.

The early evolution of a supernova (SN) can reveal information about the environment and the progenitor star. When a star explodes in vacuum, the first photons to escape from its surface appear as a brief, hours-long shock-breakout flare1,2, followed by a cooling phase of emission. However, for stars exploding within a distribution of dense, optically thick circumstellar material (CSM), the first photons escape from the material beyond the stellar edge and the duration of the initial flare can extend to several days, during which the escaping emission indicates photospheric heating3. Early serendipitous observations2,4 that lacked ultraviolet (UV) data were unable to determine whether the early emission is heating or cooling and hence the nature of the early explosion event. Here we report UV spectra of the nearby SN 2023ixf in the galaxy Messier 101 (M101). Using the UV data as well as a comprehensive set of further multiwavelength observations, we temporally resolve the emergence of the explosion shock from a thick medium heated by the SN emission. We derive a reliable bolometric light curve that indicates that the shock breaks out from a dense layer with a radius substantially larger than typical supergiants.

A Statistical Study of Soft X-Ray Flares on Solar-type Stars

The statistical characteristics of stellar flares at optical bands have received extensive study, but they remain to be studied at soft X-ray bands, in particular for solar-type stars. Here, we present a statistical study of soft X-ray flares on solar-type stars, which can help in understanding the multiwavelength behaviors of stellar flares. We mainly use Chandra Source Catalog Release 2.0, which includes a number of flaring stars with denoted variability, and Gaia Data Release 3, which includes the necessary information for classifying stars. We also develop a set of methods for identifying and classifying stellar soft X-ray flares and estimating their properties. A detailed statistical investigation of 129 flare samples on 103 nearby solar-type stars as selected yields the following main results. (1) The flare energy emitted at the soft X-ray band in our sample ranges from ∼1033 to ∼1037 erg, and the majority of them are superflares, with the most energetic one having energy of 6.0−4.7+3.2×1037erg . (2) The flare duration is related to its energy as formulated by Tduration,SXR∝Eflare,SXR0.201±0.024 , which is different from those derived at optical and near-IR bands, indicating distinct radiation mechanisms at different bands. (3) The frequency distribution of stellar flares as a function of energy is formulated as dNflare/dEflare,SXR∝Eflare,SXR−1.77 , which is similar to the results found at other bands and on other types of stars, indicating that the energy emitted at the soft X-ray band could be a constant fraction of the full-band bolometric energy.

The Scaling of Vortical Electron Acceleration in Thin-current Magnetic Reconnection and Its Implications in Solar Flares

To investigate how magnetic reconnection (MR) accelerates electrons to a power-law energy spectrum in solar flares, we explore the scaling of a kinetic model proposed by Che & Zank (CZ) and compare it to observations. Focusing on thin current sheet MR particle-in-cell (PIC) simulations, we analyze the impact of domain size on the evolution of the electron Kelvin–Helmholtz instability (EKHI). We find that the duration of the growth stage of the EKHI ( tG∼Ωe−1 ) is short and remains nearly unchanged because the electron gyrofrequency Ω e is independent of domain size. The quasi-steady stage of the EKHI (t MR) dominates the electron acceleration process and scales linearly with the size of the simulations as L/v A0, where v A0 is the Alfvén speed. We use the analytical results obtained by CZ to calculate the continuous temporal evolution of the electron energy spectra from PIC simulations and linearly scale them to solar flare observational scales. For the first time, an electron acceleration model predicts the sharp two-stage transition observed in typical soft–hard–harder electron energy spectra, implying that the electron acceleration model must be efficient with an acceleration timescale that is a small fraction of the duration of solar flares. Our results suggest that we can use PIC MR simulations to investigate the observational electron energy spectral evolution of solar flares if the ratio t MR/t G is sufficiently small, i.e., ≲10%.

Properties of PSR J1023+0038 Based on Kepler, TESS, and FAST

The pulsar system PSR J1023+0038 is a very interesting binary with radio millisecond pulsar and low-mass X-ray binary transitions, which depend on the stellar accretion process. We have used Kepler light curves with 1 minute cadence and TESS light curves with 2 minute cadence to study the flare properties of PSR J1023+0038. We detected 516 flare events in the K2 data and 84 flare events in the TESS survey data. We determined the flare rise and delay times, the flare durations and amplitudes, and flare energies. We obtained a value of the power-law index of 0.359 ± 0.023 between the flare energies and decay times, which is similar to the theoretically predicted value of 1/3. This in turn indicates that PSR J1023+0038 might be exhibiting physical mechanisms described by magnetic reconnection theory. Using the maximum likelihood estimation method, we also calculated the power-law index of the cumulative flare frequency distribution, finding 1.87 ± 0.27 for the Kepler data and 1.74 ± 0.29 for the TESS data. Meanwhile, we reduced six FAST observations of PSR J1023+0038 from 2019–2021 using a standard pulsar search procedure. We report that we detected a prompt signal with a period compatible with that found in previous observations of PSR J1023+0038. However, there are several reasons (statistical, excess DM, pulse shape, etc.) as to why the association is not likely.

Urologic Chronic Pelvic Pain Syndrome Flares: A Comprehensive, Systematic Review and Meta-Analysis of the Peer-Reviewed Flare Literature.

We sought to systematically review and summarize the peer-reviewed literature on urologic chronic pelvic pain syndrome flares, including their terminology, manifestation, perceived triggers, management and prevention strategies, impact on quality of life, and insights into pathophysiologic mechanisms, as a foundation for future empirical research. We searched 6 medical databases for articles related to any aspect of symptom exacerbations for interstitial cystitis/bladder pain syndrome and chronic prostatitis/chronic pelvic pain syndrome. A total of 1486 abstracts and 398 full-text articles were reviewed, and data were extracted by at least 2 individuals. Overall, we identified 59 articles, including 36 qualitative, cross-sectional, or case-control; 15 cohort-based; and 8 experimental articles. The majority of studies described North American patients with confirmed diagnoses. "Flare" was a commonly used term, but additional terminology (eg, exacerbation) was also used. Most flares involved significant increases in pain intensity, but less data were available on flare frequency and duration. Painful, frequent, long-lasting, and unpredictable flares were highly impactful, even over and above participants' nonflare symptoms. A large number of perceived triggers (eg, diet, stress) and management/prevention strategies (eg, analgesics, thermal therapy, rest) were proposed by participants, but few had empirical support. In addition, few studies explored underlying biologic mechanisms. Overall, we found that flares are painful and impactful, but otherwise poorly understood in terms of manifestation (frequency and duration), triggers, treatment, prevention, and pathophysiology. These summary findings provide a foundation for future flare-related research and highlight gaps that warrant additional empirical studies.

A Comparative Study of Ground-level Enhancement Events of Solar Energetic Particles

Major solar eruptions can accelerate protons up to relativistic energies. Solar relativistic ions arriving at 1 au may cause a solar particle event detectable by the worldwide network of neutron monitors (NMs), a ground-level enhancement (GLE) event. Using the newly computed NM yield function, we have fitted the 15 historic GLEs. Moments of the fitted proton distributions are used for the analysis. Profiles of the proton net flux are very diverse, while some profiles are similar. For this study, we select two events with similar time profiles, GLE 60 (2001 April 15) and GLE 65 (2003 October 28), and ask what makes these GLEs similar. We compare the GLEs with their progenitor solar flares and coronal mass ejections (CMEs). We find a close relationship between the rise and peak of the GLE, on the one hand, and the solar flare and the metric radio emissions from extended coronal sources at the base of the CME, on the other hand. The GLE decay time, the rate of the proton spectrum evolution, and the CME speed are proportional to the duration of the soft X-ray flare. We compare the two GLEs with GLE 59 (2000 July 14) analyzed by Klein et al. and with the deka-MeV nucleon−1 proton and helium data from the ERNE instrument on the Solar and Heliospheric Observatory spacecraft. The comparison indicates that a single solar eruption can produce more than one component of solar energetic particles, differently contributing at different energies and locations.

Flare Frequency and Duration in Patients with Generalized Pustular Psoriasis (GPP)

Introduction: Generalized pustular psoriasis (GPP) is a rare, neutrophilic, chronic skin disease in which an overactivation of inflammatory pathways causes widespread erythema and eruption of sterile pustules that may coalesce into ‘lakes of pus’. GPP flares are heterogeneous, and there is no standard clinical definition. GPP flares are painful; severe cases may require emergency treatment and can lead to life-threatening complications such as sepsis. The objective of this study was to characterize the frequency, number, and duration of flares in patients with GPP.&#x0D; Methods: We conducted a retrospective chart review including patients of all ages with a confirmed diagnosis of GPP after 2011 receiving care at 27 sites in France, Malaysia, and Tunisia.&#x0D; Results: Data from 175 patients were included (France: 58.9%, Malaysia: 31.4%, Tunisia: 9.7%). Mean (SD) follow-up was 5.0 (3.1) years. Flare-related care was the second most common reason for patient visits, accounting for 200 of 1378 follow-up visits after GPP diagnosis, surpassed only by routine follow-up. The mean (SD) annual number of flare episodes was 2.3 (2.0); the total number of flare episodes since the initial flare leading to diagnosis ranged from 0 to 9. Eighty-three (47.4%) patients experienced ≥1 flare episode after diagnosis, though individual country data suggested a higher flare burden in Tunisia (70.6%) and Malaysia (54.5%) versus France (39.8%). Twenty-eight patients (16.0%) had ≥2 flare episodes (60 visits); median (min, max) time between episodes was 11.6 (0.1, 52) months. The mean (SD) duration of flares was 34.3 (41.3) days during follow-up. Of 254 hospitalizations, 128 (50.4%) were flare-related inpatient admissions. Overall, 37.5% of GPP flares required inpatient care. The mean (SD) duration of flare-related admissions was almost twice as long as non-flare admissions at 19.2 (23.1) days versus 10.5 (8.1) days. Mean (SD) time between flare-related hospitalizations among 66 patients (128 hospitalizations) was 14.1 (17.1) months, with a median of 9.5 months indicating a skew distribution.&#x0D; Conclusion: Flare episodes are a heavy burden for patients with GPP, with flares recurring as often as once a year and lasting up to 2 weeks or more. Flares account for &gt;50% of hospitalizations for patients with GPP and are an important cause of follow-up care visits. The frequency of flares varied between patients, with some individuals experiencing up to 10 episodes over the study period. Heterogeneity of flares and rarity of GPP make diagnosis and clinical study challenging, while the severity of acute episodes and the burden of flare reoccurrence demonstrate the need for more effective treatment options.

Understanding the Duration of Solar and Stellar Flares at Various Wavelengths

Recent irradiance measurements from numerous heliophysics and astrophysics missions including Solar Dynamics Observatory (SDO), GOES, Kepler, TESS, Chandra, the X-ray Multi-Mirror Mission, and NICER have provided critical input into understanding the physics of the most powerful transient events on the Sun and magnetically active stars:solar and stellar flares. The light curves of flare events from the Sun and stars show remarkably similar shapes, typically with a sharp rise and protracted decay phase. The duration of solar and stellar flares has been found to be correlated with the intensity of the event in some wavelengths, such as white light, but not in other wavelengths, such as soft X-rays, but it is not evident why this is the case. In this study, we use a radiative hydrodynamics code to examine factors affecting the duration of flare emission at various wavelengths. The duration of a light curve depends on the temperature of the plasma, the height in the atmosphere at which the emission forms, and the relative importance of cooling due to radiation, thermal conduction, and enthalpy flux. We find that there is a clear distinction between emission that forms low in the atmosphere and responds directly to heating, and emission that forms in the corona, indirectly responding to heating-induced chromospheric evaporation, a facet of the Neupert effect. We discuss the implications of our results for a wide range of flare energies.

Atopic dermatitis phenotypes based on cluster analysis ofthe Danish Skin Cohort.

Despite previous attempts to classify atopic dermatitis (AD) into subtypes (e.g. extrinsic vs. intrinsic), there is a need to better understand specific phenotypes in adulthood. To identify, using machine learning (ML), adult AD phenotypes. We used unsupervised cluster analysis to identify AD phenotypes by analysing different responses to predetermined variables (age of disease onset, severity, itch and skin pain intensity, flare frequency, anatomical location, presence and/or severity of current comorbidities) in adults with AD from the Danish Skin Cohort. The unsupervised cluster analysis resulted in five clusters where AD severity most clearly differed. We classified them as 'mild', 'mild-to-moderate', 'moderate', 'severe' and 'very severe'. The severity of multiple predetermined patient-reported outcomes was positively associated with AD, including an increased number of flare-ups and increased flare-up duration and disease severity. However, an increased severity of rhinitis and mental health burden was also found for the mild-to-moderate phenotype. ML confirmed the use of disease severity for the categorization of phenotypes, and our cluster analysis provided novel detailed information about how flare patterns and duration are associated with AD disease severity.

Statistical Analysis of Long GRBs’ Prompt Emission and X-Ray Flares: Multivariate Clustering and Correlations

The extensive observations done by the X-ray Telescope on board Neil Gehrels Swift Observatory have revealed the presence of late-time flares concurrent with the decaying afterglow emission. However, the origins of these flares are elusive. In this work, we make use of the large database of Swift observations (2005–2020) of long gamma-ray bursts (GRBs) to conduct a systematic statistical study between the prompt gamma-ray emission and X-ray flares by characterizing their temporal and spectral properties of duration, quiescent period, peak flux, fluence, minimum variability timescale, and spectral power-law index. The multidimensional database of parameters thereby generated was investigated by principal component analysis, which revealed there is no evident correlation between the different parameters of the prompt emission and X-ray flares. Furthermore, the correlation studies revealed that while there is a trend of positive correlation between the minimum variability timescale of the flare and its duration, and of strong negative correlation with its peak flux, there are no such correlations observed in the prompt emission. Similarly, we find a positive correlation between the quiescent period and the flare duration, and a negative correlation with the flare peak flux, while no such correlations are observed for the prompt emission of the GRBs. Finally, among the X-ray flares, we find two dominant classes, whose variations are driven by the minimum variability timescale, peak flux, and fluence of the flares. A catalog of these different parameters characterizing the prompt and flare emissions is presented.

Duration and extent of solar X-ray flares and shortwave fadeouts likely to impact high frequency radio wave propagation based on an evaluation of absorption at 30 MHz

High frequency (HF; 3–30 MHz) radio wave propagation can be impacted by absorption that results from enhanced photoionization in the dayside D-region following a solar X-ray flare. A database of >25,000 solar X-ray flares was evaluated to characterize the relationship between flare duration and the peak of the 0.1–0.8 nm solar X-ray flux. Expressions describing the mean and 90th percentile duration were developed. Based on these models, mean durations of 13, 18, 27, and 39 min and 90th percentile durations of 30, 48, 77, and 123 min are expected for C1, M1, X1 and X10 solar X-ray flares, respectively. A probability distribution of flare durations was developed to describe the probability of flare duration lasting 0–15, 15–30, 30–45, 45–60, 60–90, >90 min. In addition to flare duration, the duration of the expected impact to HF radio waves was evaluated. By considering examples where HF radio wave propagation in the 5–15 MHz range was impacted by space weather, a 0.5 dB threshold at 30 MHz was observed in samples of riometer data. Absorption modelled at 1-min increments from 1986 to 2017 was evaluated to create a probability distribution of impact duration, defined as the length of time the modelled 30 MHz absorption exceeded 0.5 dB during a single event. Modelled absorption was further evaluated to demonstrate the geographic extent of enhanced absorption, and to determine the minimum solar X-ray flux required to exceed the 0.5 dB impact threshold at a given latitude as a function of solar zenith angle and time of year. The results of this paper provide a better understanding of the impact of solar X-ray flares on high frequency radio wave propagation and aid in the development of tools and services for mitigating space weather impacts to systems that rely on HF radio wave propagation.

Statistical Study of Confined Filament/Prominence Eruptions during Solar Cycle 23

Filament/prominence eruptions can have a significant impact on Earth's upper atmosphere and space environment, and are the primary drivers of what is now called space weather. To distinguish the different types of filament eruptions we statistically examine them during the 23rd Solar cycle. In this study we use 159 filament eruptions using the List of interplanetary (IP) Shocks Observed during Solar Cycle 23 (May 1996 – January 2008) and their Source Information Environmental Satellites (GOES) X-ray plots (see Gopalswamy et al. [Gopalswamy N., H. Xie, P. Mäkelä, S. Akiyama, S. Yashiro et al. (2010) Interplanetary shocks lacking type II radio bursts, Astrophys. J., 710, 1111–1126]). It is found that 69% of the filament eruptions are confined eruptions, while 31% are ejective eruptions. Confined eruptions are 110 and 34 events (21%). They are due to active filaments and 76 events (48%) are due to disappearing filaments. The occurrences of active and disappearing filaments during the increasing phase of solar cycle 23 is found to be 80% while in the decreasing phase they are 13%. We have found that the dominant X-ray flare energy of confined eruptions is that of C class. The most common filaments field extent is located between 5 and 15 degrees. The most common flare duration is between 16 and 40 minutes.

A Small-scale Structure Model of a Jet Based on Observations of Microvariability

We developed a multiregion radiation model for the evolution of flux and spectral index with time. In this model, each perturbation component in the jet produces an independent flare. The model can be used to study the decomposition of microvariability, the structural scale of the perturbed components, and the physical parameters of the acceleration processes. Based on the shock acceleration model for a relativistic jet, the influence of the acceleration parameters on multiband flare parameters is calculated. We present the results of multiband optical microvariability of the blazar BL Lacertae observed during 89 nights in the period from 2009 to 2021, and use them as a sample for model fitting. The results show that both the amplitude and duration of flares decomposed from the microvariability light curves conform to a log-normal distribution. The time delays between the optical bands follow a normal distribution and amount to several minutes, which corroborate with both predictions from the theoretical model and the calculation of the discrete correlation function. Using the spectral index evolution and the simultaneous fitting of the multiband variability curves, we obtain the acceleration and radiation parameters to constrain and distinguish the origins of different flares. Based on the flare decomposition, we can effectively reproduce the time-domain evolution trends of the optical variations and energy spectrum, and explain the various redder-when-brighter and bluer-when-brighter behaviors.

The statistical OPEA models indicate an anomaly in the solar X-ray flare energy levels

We have recognized an anomaly on the solar activity cycle, while we researching on the question that there can be two different flare mechanisms working on the stellar surface. We discuss an anomaly in the solar flare activity levels in the cycle minima and maxima from the 20th to 22nd Solar Activity Cycles, depending on the models and analyses of the X-ray data. In this study, we used the GOES satellite data accumulated from 1976 to 1989 and detected 670 solar flares. We have separately carried out two independent statistical analyses for the examination of the solar flare activity. Firstly, we derived the equivalent durations distribution via the total durations of flares. Contrary to our expectations based on flare stars, it seems that this distribution is modelled by four different fits, instead of just one model fit. We found that the model parameters, such as plateau, half−time, and span, vary via time in the different trends from the Solar Activity Cycle. Secondly, we have derived the cumulative frequency models for solar flares. Contrary to the studies in the literature, we found that these frequency models do not take shape depending on the minimum or maximum of a solar activity cycle. If these results are not an unexpected anomaly, this study indicates that the existence of a different trend can be revealed apart from the solar activity cycle for the flare energy level variation, when the solar flare behaviour is separately determined for each cycle and they are compared with each other.