Distribution Of Flares Research Articles

Frequency distribution of x-ray flares for low-mass young stellar objects in the Orion nebula

The frequency distribution of x-ray flares is determined for the young, lowest-mass stellar objects in the Orion nebula. The methods used to do this have been developed previously for determining the analogous function for optical flares of flare stars. For this sample it is found that the x-ray flaring frequency distribution can be described by an exponential function.

SIZE DISTRIBUTIONS OF SOLAR FLARES AND SOLAR ENERGETIC PARTICLE EVENTS

We suggest that the flatter size distribution of solar energetic proton (SEP) events relative to that of flare soft X-ray (SXR) events is primarily due to the fact that SEP flares are an energetic subset of all flares. Flares associated with gradual SEP events are characteristically accompanied by fast (much > 1000 km/s) coronal mass ejections (CMEs) that drive coronal/interplanetary shock waves. For the 1996-2005 interval, the slopes (alpha values) of power-law size distributions of the peak 1-8 Angs fluxes of SXR flares associated with (a) >10 MeV SEP events (with peak fluxes much > 1 pr/sq cm/s/sr) and (b) fast CMEs were approx 1.3-1.4 compared to approx 1.2 for the peak proton fluxes of >10 MeV SEP events and approx 2 for the peak 1-8 Angs fluxes of all SXR flares. The difference of approx 0.15 between the slopes of the distributions of SEP events and SEP SXR flares is consistent with the observed variation of SEP event peak flux with SXR peak flux.

Spatial distribution of solar flares in 23rd solar cycle

H-alpha flares accompanied by the X-radiation f ≥ 10−6 wm−2 in power are examined; 2331 flares were registered during the first half of the 23rd solar cycle (1997–2000). The specific power of the X-radiation of the flares monotonically doubles from the minimum to the maximum of the sunspot. An increase in the number of flares in each solar rotation is nonmonotonic and disproportional to the relative number of sunspots. Several longitudinal intervals with increased flare activity can be distinguished in the entire time interval of five to ten rotations. The longitudinal distributions of flares and boundaries of the sector structures of a large-scale magnetic field differ considerably. This confirms the existence of two types of zero lines; the first type is determined by active regions, and the second one is determined by large-scale structures with weak magnetic fields. The flares concentrate near Hale’s zero lines of the first type.

Optimized Multigrid Strategy for Accurate Flare Modeling with Three-Dimensional Mask Effect in Extreme-Ultraviolet Lithography

Extreme-ultraviolet (EUV) lithography has many critical challenges regarding its implementation in the semiconductor industry. One of the main challenges is flare, the unwanted total integrated light scattering at the wafer level, which reduces the critical dimension and imaging performance. Therefore, EUV flare has been intensively studied and has been compensated by a rule-based method for many years. However, there are few results with regard to developing more accurate and feasible flare-modeling techniques to enable us to satisfy the criteria of the sub-22 nm half pitch (HP) technology node and beyond. In this work, we studied an improved flare-modeling technique considering the interaction of scattered EUV light with a three-dimensional EUV mask topography in order to obtain an accurate flare distribution and an optimized multigrid strategy for generating a flare map over the full-field scale. Also, we proposed a flare-modeling technique based on the pedestal model, which we developed using novel effective reflection coefficients in order to achieve sufficient accuracy. Such an approach is thought to be needed instead of the conventional pattern density approach in preparation for upcoming advanced HP technology nodes or for different absorber materials and illumination angles. Lastly, the need for a flare map shift to compensate for the mask defocus error is introduced and some flare evaluations of mask patterns used in the exposure-dose-monitoring technique were performed.

820 FREQUENCY AND DURATION SPECTRUM OF UROLOGIC CHRONIC PELVIC PAIN SYMPTOM FLARES

You have accessJournal of UrologyInfections/Inflammation of the Genitourinary Tract: Interstitial Cystitis1 Apr 2012820 FREQUENCY AND DURATION SPECTRUM OF UROLOGIC CHRONIC PELVIC PAIN SYMPTOM FLARES Siobhan Sutcliffe, Graham Colditz, Ratna Pakpahan, David Song, Rebecca Bristol, Vivien Gardner, Gerald Andriole, and H. Henry Lai Siobhan SutcliffeSiobhan Sutcliffe St. Louis, MO More articles by this author , Graham ColditzGraham Colditz St. Louis, MO More articles by this author , Ratna PakpahanRatna Pakpahan St. Louis, MO More articles by this author , David SongDavid Song St. Louis, MO More articles by this author , Rebecca BristolRebecca Bristol Stanford, CA More articles by this author , Vivien GardnerVivien Gardner St. Louis, MO More articles by this author , Gerald AndrioleGerald Andriole St. Louis, MO More articles by this author , and H. Henry LaiH. Henry Lai St. Louis, MO More articles by this author View All Author Informationhttps://doi.org/10.1016/j.juro.2012.02.910AboutPDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareFacebookTwitterLinked InEmail INTRODUCTION AND OBJECTIVES Based on anecdotal clinical evidence, urologic chronic pelvic pain symptom exacerbations, commonly referred to as flares, are believed to occur approximately once a year and last approximately one week. However, no studies, to our knowledge, have investigated the frequency and duration of flares in interstitial cystitis/bladder pain syndrome (IC/BPS) and chronic prostatitis/chronic pelvic pain syndrome (CP/CPPS) patients. Therefore, we conducted a study to describe the spectrum of frequency and duration of flares among IC/BPS and CP/CPPS participants at the Washington University site of the ongoing Multidisciplinary Approaches to the study of chronic Pelvic Pain (MAPP) study. METHODS At their six month study visit, participants were asked to complete an additional form on their frequency and duration of flares, defined as “symptoms that are much worse than usual”. Specifically, they were asked whether they had ever had flares that lasted: 1) less than one hour; 2) more than an hour but less than one day; and 3) more than one day. For each question to which they responded affirmatively, they were also asked to report the average frequency and duration of each type of flare. RESULTS Date, 24 female and 16 male participants have provided information on frequency and duration of flares. The distribution of flares by sex is provided in the table. Table. Distribution of the duration of urologic chronic pelvic pain symptoms flares, Washington University, 2010-11 Female Male No reported flares (%) 0.0 12.5 Duration of flares (%): Only minutes-long 8.3 18.8 Minutes- to hours-long 0.0 6.2 Only hours-long 0.0 12.5 Minutes- to days-long 20.8 6.2 Hours- to days-long 29.2 25.0 Only days-long 41.7 18.8 The distribution of flares appeared to differ by sex (p=0.07), with female participants being considerably more likely to have days-long flares than male participants (91.7 vs 50.0%, p=0.0068). For either sex, minutes-long flares lasted <1-60 minutes and occurred 6 times/day to once every 2 months; hours-long flares lasted 1-23 hours and occurred 3 times/week to 1-2 times/year; and days-long flares lasted 2 days to several months and occurred twice per week to less than once per year. CONCLUSIONS Our findings suggest that there may be a previously unappreciated wide spectrum of frequency and duration of urologic chronic pelvic pain flares that may vary by sex. Future research should investigate the spectrum of symptoms and bother associated with these flares. © 2012 by American Urological Association Education and Research, Inc.FiguresReferencesRelatedDetails Volume 187Issue 4SApril 2012Page: e335 Advertisement Copyright & Permissions© 2012 by American Urological Association Education and Research, Inc.MetricsAuthor Information Siobhan Sutcliffe St. Louis, MO More articles by this author Graham Colditz St. Louis, MO More articles by this author Ratna Pakpahan St. Louis, MO More articles by this author David Song St. Louis, MO More articles by this author Rebecca Bristol Stanford, CA More articles by this author Vivien Gardner St. Louis, MO More articles by this author Gerald Andriole St. Louis, MO More articles by this author H. Henry Lai St. Louis, MO More articles by this author Expand All Advertisement Advertisement PDF downloadLoading ...

Frequency distribution of x-ray flares for young stellar objects in the region of ρ Oph

Methods for determining the frequency distribution function of optical flares have been developed and successfully applied in statistical studies of flare stars. X-ray observations of flare stars provide a basis for extending the use of these methods to statistical studies of X-ray flares of young stellar objects. This article gives a brief description of methods which can be used for determining the frequency distribution of the X-ray flares of young stellar objects. The corresponding function is determined for a sample of 195 low-mass young stellar objects in the cloud L1688, which forms part of the complex of dark clouds ρ Oph. It is found to have an exponential form.

The near-infrared spectral index of Sagittarius A* derived fromKs- andH-band flare statistics

Context. The near-infrared (NIR) counterpart of Sagittarius A* (SgrA*) at the position of the 4 x 10(6) M(circle dot) supermassive black hole at the center of the Milky Way has strongly varying flux densities. The broad-band near-infrared spectral index is an essential parameter to determine the underlying emission mechanism for the observed flare emission. Aims. We present a method to derive the NIR spectral index of SgrA* between the H- and Ks-band from the statistics of the observed flare emission. Our spectral index derivation is therefore based on an unprecedentedly large timebase of about seven years of monitoring the infrared counterpart of SgrA*. Methods. We examined NIR light curves of SgrA* in the H- and Ks-band and established flare number distributions as a function of peak flare flux. We assume that in both bands the same optically thin dominant emission mechanism is at work and produces similar number distributions of flares. We cross-correlated these histograms and determined a statistical expectation value of the H-Ks-band spectral index during the bright phases of SgrA*. Results. With this new method, we can independently confirm that the expectation value of the spectral index for brighter flares is consistent with alpha = -0.7 (with the flux density (F(nu) proportional to nu(+alpha))) which is expected for pure synchrotron radiation. We find a tendency for weaker flares to exhibit a steeper spectrum. Conclusions. We conclude that the distribution of spectral indices as a function of Ks-band flux density can successfully be described by an exponential cutoff proportional to expleft perpendicular-(nu/nu(0))(0.5)right perpendicular because of synchrotron losses, with nu(0) being a characteristic cutoff frequency. Varying nu(0) between the NIR and sub-mm domain and assuming a sub-mm flux density variation of about one Jansky and optically thin spectral indices of alpha = -0.7 +/- 0.3 explains the observed spectral properties of SgrA* in the NIR.

Longitudinal Distribution of Solar Flares and Their Association with Coronal Mass Ejections and Forbush Decreases

Major Hα solar-flare events of high optical importance have been employed to study their heliographic distribution in longitude around the Sun for the period of 2001 to 2006. A statistical analysis was performed to obtain their relationship with halo/partial-halo CMEs and Forbush decreases (Fds) of cosmic-ray intensity. Our analysis indicates that 63% of the solar flares associated with halo CMEs and Fds occur in the western hemisphere and of 37% of such flares occur in the eastern hemisphere. Similarly, we found that nearly 60% of the solar flares associated with partial- halo CMEs and Fds occur in the western hemisphere and the rest (40%) occur in the eastern hemisphere. Finally, we conclude that the flares in association with CMEs and located in the western hemisphere of the solar disk are more effective in producing Fds. The magnitudes of Fds are observed to be higher when in association of halo CMEs. A slight excess in the eastern hemisphere is found for both the halo and partial-halo CMEs.

RECONCILIATION OF WAITING TIME STATISTICS OF SOLAR FLARES OBSERVED IN HARD X-RAYS

We study the waiting time distributions of solar flares observed in hard X-rays with ISEE-3/ICE, HXRBS/SMM, WATCH/GRANAT, BATSE/CGRO, and RHESSI. Although discordant results and interpretations have been published earlier, based on relatively small ranges ($< 2$ decades) of waiting times, we find that all observed distributions, spanning over 6 decades of waiting times ($\Delta t \approx 10^{-3}- 10^3$ hrs), can be reconciled with a single distribution function, $N(\Delta t) \propto \lambda_0 (1 + \lambda_0 \Delta t)^{-2}$, which has a powerlaw slope of $p \approx 2.0$ at large waiting times ($\Delta t \approx 1-1000$ hrs) and flattens out at short waiting times $\Delta t \lapprox \Delta t_0 = 1/\lambda_0$. We find a consistent breakpoint at $\Delta t_0 = 1/\lambda_0 = 0.80\pm0.14$ hours from the WATCH, HXRBS, BATSE, and RHESSI data. The distribution of waiting times is invariant for sampling with different flux thresholds, while the mean waiting time scales reciprocically with the number of detected events, $\Delta t_0 \propto 1/n_{det}$. This waiting time distribution can be modeled with a nonstationary Poisson process with a flare rate $\lambda=1/\Delta t$ that varies as $f(\lambda) \propto \lambda^{-1} \exp{-(\lambda/\lambda_0)}$. This flare rate distribution represents a highly intermittent flaring productivity in short clusters with high flare rates, separated by quiescent intervals with very low flare rates.

A WHITE LIGHT MEGAFLARE ON THE dM4.5e STAR YZ CMi

On UT 2009 January 16, we observed a white light megaflare on the dM4.5e star YZ CMi as part of a long-term spectroscopic flare-monitoring campaign to constrain the spectral shape of optical flare continuum emission. Simultaneous U-band photometric and 3350A-9260A spectroscopic observations were obtained during 1.3 hours of the flare decay. The event persisted for more than 7 hours and at flare peak, the U-band flux was almost 6 magnitudes brighter than in the quiescent state. The properties of this flare mark it as one of the most energetic and longest-lasting white light flares ever to be observed on an isolated low-mass star. We present the U-band flare energetics and a flare continuum analysis. For the first time, we show convincingly with spectra that the shape of the blue continuum from 3350A to 4800A can be represented as a sum of two components: a Balmer continuum as predicted by the Allred et al radiative hydrodynamic flare models and a T ~ 10,000K blackbody emission component as suggested by many previous studies of the broadband colors and spectral distributions of flares. The areal coverage of the Balmer continuum and blackbody emission regions vary during the flare decay, with the Balmer continuum emitting region always being significantly (~3-16 times) larger. These data will provide critical constraints for understanding the physics underlying the mysterious blue continuum radiation in stellar flares.

10.1007/s11208-008-2008-6

The results of the statistical analysis of the GOES data related to the length of the period, during which the X-ray emission of solar flares increases, provide reliable grounds for the objective distinction of different types, sometimes referred to in the literature as typical and nontypical for bimodal classification. The events may be also partitioned into three (“impulsive”, “typical”, and “long duration”) or more “types”. These “types” should be separated from statistical fluctuations in the case of rare events. When the number of analyzed events increases, these fluctuations are gradually smoothed and become less significant, and the distribution of flares according to the duration of their growth is, on the whole, well described by the single lognormal law.

Kappa distribution and hard X-ray emission of solar flares

<i>Aims. <i/>We investigate whether the so-called kappa distribution, often used to fit electron distributions detected in situ in the solar wind, can describe electrons producing the hard X-ray emission in solar flares.<i>Methods. <i/>Using Ramaty High Energy Solar Spectroscopic imager (RHESSI) flare data we fit spatially- and feature-integrated spectra, assuming a kappa distribution for the mean electron flux spectrum.<i>Results. <i/>We show that a single kappa distribution generally cannot describe spatially integrated X-ray emission composed of both footpoint and coronal sources. In contrast, the kappa distribution is consistent with mean electron spectra producing hard X-ray emission in some coronal sources.

Self‐organized Critical Model of Energy Release in an Idealized Coronal Loop

We present and discuss a new avalanche model for solar flares, based on an idealized representation of a coronal loop as a bundle of magnetic flux strands wrapping around one another. The model is based on a two-dimensional cellular automaton with anisotropic connectivity, where linear ensembles of interconnected nodes define the individual strands collectively making up the coronal loop. The system is driven by random deformation of the strands, and a form of reconnection is assumed to take place when the angle subtended by two strands crossing at the same lattice site exceed some preset threshold. Driven in this manner, the cellular automaton produces avalanches of reconnection events characterized by scale-free size distributions that compare favorably with the corresponding size distribution of solar flares, as inferred observationally. Although lattice-based and highly idealized, the model satisfies the constraints Δ B = 0 by design and is defined in such a way as to be readily mapped back onto coronal loops with set physical dimensions. Carrying this exercise for a generic coronal loop of length 1010 cm and diameter 108 cm yields flare energies ranging from 1023 to 1029 erg, for an instability threshold angle of 11° between contiguous magnetic flux strands. These figures square well with both observational determinations and theoretical estimates.

The flaring and quiescent components of the solar corona

Context. The solar corona is a template to understand stellar activity. The Sun is a moderately active star, and its corona differs from that of active stars: for instance, active stellar coronae have a double-peaked emission measure distribution $EM(T)$ with a hot peak at $8{-}20$ MK, while the non-flaring solar corona has one peak at $1{-}2$ MK and, typically, much cooler plasma. Aims. We study the average contribution of flares to the solar emission measure distribution to investigate indirectly the hypothesis that the hot peak in the $EM(T)$ of active stellar coronae is due to a large number of unresolved solar-like flares, and to infer properties about the flare distribution from nano- to macro-flares. Methods. We measure the disk-integrated time-averaged emission measure, $EM_{\rm F}(T)$, of an unbiased sample of solar flares, analyzing uninterrupted GOES/XRS light curves over time intervals of one month. We obtain the $EM_{\rm Q}(T)$ of quiescent corona for the same time intervals from Yohkoh/SXT data. To investigate how $EM_{\rm F}(T)$ and $EM_{\rm Q}(T)$ vary during the solar cycle, we evaluate them at different phases of the cycle between December 1991 and April 1998. Results. Irrespective of the solar cycle phase, $EM_{\rm F}(T)$ appears as a peak in the distribution, and it is significantly larger than the values of $EM_{\rm Q}(T)$ for $T\sim5{-}10$ MK. As a result, the time-averaged $EM(T)$ of the entire solar corona is double-peaked, with the hot peak, due to time-averaged flares, being located at temperatures similar to those of active stars, but less enhanced. The $EM_{\rm F}(T)$ shape supports the hypothesis that the hot $EM(T)$ peak of active coronae is due to unresolved solar-like flares. If this is the case, quiescent and flare components should follow different scaling laws for increasing stellar activity. In the assumption that the heating of the corona is entirely due to flares, from nano- to macro-flares, then either the flare distribution or the confined plasma response to flares, or both, are bimodal.

On the nature of late X-ray flares in Swift gamma-ray bursts

Previously detected in only a few gamma-ray bursts (GRBs), X-ray flares are now observed in ~50% of Swift GRBs, though their origins remain unclear. Most flares are seen early on in the afterglow decay, while some bursts exhibit flares at late times of 10^4 to 10^5 seconds, which may have implications for flare models.We investigate whether a sample of late time (> 10^4s) flares are different from previous samples of early time flares, or whether they are merely examples on the tail of the early flare distribution. We examine the X-ray light curves of Swift bursts for late flares and compare the flare and underlying temporal power-law properties with those of early flares, and the values of these properties predicted by the blast wave model. The burst sample shows late flare properties consistent with those of early flares, where the majority of the flares can be explained by either internal or external shock, though in a few cases one origin is favoured over the other. The underlying power laws are mainly consistent with the normal decay phases of the afterglow. If confirmed by the ever growing sample of late time flares, this would imply that, in some cases, prolonged activity out to a day or a restarting of the central engine is required.

Solar geoeffective phenomena: Impact on the near-Earth space and the opportunity to forecast

the state of near-Earth space (NES) are extremely large flare events and coronal holes. We attribute to the class of flare phenomena solar flares with a complete spectrum of dynamic manifestations of the mass motion and radiation in all ranges of the electromagnetic spectrum as well as solar filament eruptions with all accompanying phenomena. The possibility to predict geoeective solar phenomena and their eects on NES is based on the analysis of correlations: emergence of new magnetic fluxes in the solar atmosphere, their physical characteristics, and the character of their interaction with the already present magnetic field; time distribution of large flares within active regions; temporal and spatial distribution of solar filament eruptions; formation, distribution, and evolution of solar coronal holes (CH). The agents causing NES disturbances are transient structures: coronal mass ejections, which result from active processes in flares and filament eruptions; high-speed flows of solar plasma following a shock wave from large solar flares and solar filament eruptions or outflowing from regions with an open magnetic configuration. Prediction for the beginning of NES disturbances and of their duration is possible for a period from 1 to 5 days and for coronal holes for a period of one solar revolution (27.3 days). This makes possible planning various technological, biological, and medical experiments together with protective measures for the team and instruments of space laboratories. INDEX TERMS: 7536 Solar Physics, Astrophysics, and Astronomy: Solar activity cycle; 7899 Space Plasma Physics: General or miscellaneous; 7974 Space Weather: Solar eects; 7984 Space Weather: Space radiation environment; KEYWORDS: Solar geoeective phenomena, near-Earth space, forecasting, cyclicity of solar activity.

RHESSIMicroflare Statistics. II. X‐Ray Imaging, Spectroscopy, and Energy Distributions

We present the first statistical analysis of the thermal and nonthermal X-ray emission of all 25,705 microflares (RHESSI) observed between 2002 March and 2007 March. These events were found by searching the 6-12 keV energy range (see Paper I) and are small active region flares, from low (GOES) C class to below A class. Each microflare is automatically analyzed at the peak time of the 6-12 keV emission: the thermal source size is found by forward-fitting the complex visibilities for 4-8 keV, and the spectral parameters (temperature, emission measure, power-law index) are found by forward-fitting a thermal plus nonthermal model. The resulting wealth of information we determine about the events allows a range of the thermal and nonthermal properties to be investigated. In particular, we find that there is no correlation between the thermal loop size and the flare magnitude, indicating that microflares are not necessarily spatially small. We present the first thermal energy distribution of RHESSI flares and compare it to previous thermal energy distributions of transient events. We also present the first nonthermal power distribution of RHESSI flares and find that a few microflares have unexpectedly large nonthermal powers up to 1028 erg s−1. The total microflare nonthermal energy, however, is still small compared to that of large flares as it occurs for shorter durations. These large energies and difficulties in analyzing the steep nonthermal spectra suggest that a sharp broken power law and thick-target bremsstrahlung model may not be appropriate for microflares.

Statistical distributions and classification of X-ray flares according to their duration on the sun

The results of the statistical analysis of the GOES data related to the length of the period, during which the X-ray emission of solar flares increases, provide reliable grounds for the objective distinction of different types, sometimes referred to in the literature as typical and nontypical for bimodal classification. The events may be also partitioned into three (“impulsive”, “typical”, and “long duration”) or more “types”. These “types” should be separated from statistical fluctuations in the case of rare events. When the number of analyzed events increases, these fluctuations are gradually smoothed and become less significant, and the distribution of flares according to the duration of their growth is, on the whole, well described by the single lognormal law.

ASTROPHYSICAL ASPECTS IN THE STUDIES OF SOLAR COSMIC RAYS

This review paper comprises main concepts, available observational data and recent theoretical results related to astrophysical aspects of particle acceleration at/near the Sun and extreme capacities of the solar accelerator(s). We summarize underground and ground-based observations of solar cosmic rays (SCR) accumulated since 1942, direct spacecraft measurements of solar energetic particles (SEP) near the Earth's orbit, indirect information on the SCR variations in the past, and other relevant astrophysical, solar and geophysical data. The list of the problems under discussion includes: upper limit spectrum (ULS) for solar cosmic rays; maximum energy (rigidity), Em(Rm), of particles accelerated at/near the Sun; production of the flare neutrinos; energetics of SCR and solar flares; production of flare neutrons and gamma rays; charge states and elemental abundances of accelerated solar ions; coronal mass ejections (CME's) and extended coronal structures in acceleration models; magnetic reconnection in acceleration scenarios; size (frequency) distributions of solar proton events (SPE) and stellar flares; occurrence probability of giant flares; archaeology of solar cosmic rays. The discussion allows us to outline a series of interesting conceptual and physical associations of SCR generation with the high-energy processes at other stars. The most reliable estimates of various parameters are given in each of research fields mentioned above; a set of promising lines of future studies is highlighted. A great importance of SCR data for resolving some general astrophysical problems is emphasized.

Peak-Size Distributions of Proton Fluxes and Associated Soft X-Ray Flares

A database combining information about solar proton enhancements (SPEs) near the Earth and soft X-ray flares (GOES measurements) has been used for the study of different correlations through the period from 1975 to May 2006. The emphasis of this work is on the treatment of peak-size distributions of SXR flares and SPEs. The frequency of SXR flares and solar proton events (>10 and >100 MeV, respectively) for the past three solar cycles has been found to follow mainly a power-law distribution over three to five orders of magnitude of fluxes, which is physically correct beyond the “sensitivity” problem with the smallest peak values. The absence of significant spectral steepening in the domain of the highest peak values demonstrates that during the period considered, lasting 30 years, the limit of the highest flare’s energy release has not yet been achieved. The power-law exponents were found to be −2.19±0.04, −1.34±0.02, and −1.46±0.04, for the total SXR flare distribution and the total SPE distributions (for both E P>10 MeV and E P>100 MeV), respectively. For SPEs associated with flares located to the West of 20° W, the exponents are −1.22±0.05 (E P>10 MeV) and −1.26±0.03 (E P>100 MeV). The size distribution for corresponding flares follows a power law with a slope of −1.29±0.12. Thus, X-ray and proton fluxes produced in the same solar events have very similar distribution shapes. Moreover, the derived slopes are not incompatible with a linear dependence between X-ray flare power and proton fluxes near the Earth. A similar statistical relation is obtained independently from the direct comparison of the X-ray and proton fluxes. These all argue for a statistically significant relationship between X-ray and proton emissions.