Power-law distribution for solar energetic proton events

Analyses of the time-integrated fluxes of solar energetic particle events during the period 1965–1990 show that the differential distribution of events with flux F is given by a power law, with indices between 1.2 and 1.4 depending on energy. The power law represents a good fit over three to four orders of magnitude in fluence. Similar power-law distributions have been found for peak proton and electron fluxes, X-ray flares and radio and type III bursts. At fluences greater than 10⁹ cm^–2, the slope of the distribution steepens and beyond 10¹⁰ cm^–2 the power-law index is estimated to be 3.5. At energies greater than 10 MeV, the slope of the distribution was found to be essentially independent of solar cycle, when the active years of solar cycles 20, 21, and 22 were analysed. The results presented are the first for a complete period of 27 years, covering nearly 3 complete solar cycles. Other new aspects of the results include the invariance of the exponent with solar cycle and also with integral energy.     

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.     

Flare event statistics on UV Ceti-type stars

A statistical study of 228 flares on the three UV Ceti-type stars, i.e., YZ CMi, AD Leo, and EV Lac, is presented. Observations were gathered by Ichimura and Shimizu over a total monitoring time of 907 hours distributed over 18 years (1971 to 1988). Period analysis of flare activity was performed, and no periodicity was detected on the three stars for either the flare number rate or the energy rate in time-scales ranging from a year up to 14 years. Average colour of flares at peak was (U-B)=–0.98±0.17 and (B-V)=0.05±0.13. Cumulative number distributions of flare event time-integrated energies were solved by a least-squares method on a log-log plot for a power-law function to get both the constant of and the gradient , which were found to be similar among the three stars. The gradient showed that rare large flare events radiate most of the energy released by all the flare events in the monitoring time. The flare number rate and energy rate are similar if the power-law distributions are extended up to a specific maximum energy. In reality, the Kolmogorov-Smirnov test showed that the observed cumulative number distributions of flare event energy were not necessarily a power-law function. The monte-Carlo simulation, however, indicates that the monitoring time and/or the patrol observation time interval may not be long enough to get the average flare number rate and energy rate, especially at the upper energy limits which are statistically unreliable.     

Estimation of an upper limit for the solar neutron emission during large flares

Solar neutron emission during large flares is investigated by using neutron monitor data from the mountain stations Chacaltaya (Bolivia), Mina Aguilar (Argentine), Pic-du-Midi (France) and Jungfraujoch (Switzerland). Registrations from such days on which large flares appeared around the local noon time of the monitor station are superimposed with the time of the optical flare as reference point.No positive evidence for a solar neutron emission was found with this method, However, by using an extrapolation of the neutron transport functions given by Alsmiller and Boughner a rough estimation of mean upper limits for the solar neutron flux is possible. The flux limits are compared with Lingenfelter's model calculations.From the Chacaltaya measurements it follows: N ₀2.8 × 10^{–3 N} cm^–2 s^–1 per proton flare, E > 50 MeV, if P0 = 125 MV N ₀1.4 × 10^{–2 N} cm^–2 s^–1 per proton flare, E > 50 MeV, if P ₀ = 60 MV and from Pic-du-Midi measurements: N ₀6.7 × 10^{–3 N} cm^–2 s^–1 per proton flare, E > 50 MeV, if P ₀ = 125 MV N ₀4 × 10^{–2 N} cm^–2 s^–1 per proton flare, E > 50 MeV, if P ₀ = 60 MV P ₀ = characteristic rigidity of the producing proton spectrum on the Sun.The flux limits estimated for some special proton flares are consistent with Lingenfelter's predictions for the acceleration phase but are too small for the slowing down phase. Therefore it is believed that Lingenfelter's assumption of isotropic proton emission from the flare region is not fulfilled.     

Solar flare neutrons and their capture gamma ray emission

We briefly describe our recent Monte Carlo calculations of the energy and angular distributions of neutrons escaping from the solar atmosphere. Comparing the calculation results with measurements of the neutron flux from the flares, we determined the angular distribution and energy spectrum of the accelerated ions. We also describe our calculations of the time dependence of the 2.223 MeV line emission, which provide a sensitive measure of the photospheric ³He abundance. We find that the SMM measurements of the time dependence of the 2.2 MeV line emission from the flare of 1982 June 3 imply a ³He/H ratio of (2.3±1.2)×10^–5 at the 90% confidence level.     

Relativistic electrons from the Sun observed by IMP-4

Data are presented from the IMP-4 satellite of 0.3–12 MeV electrons from the Sun between May 24, 1967 and May 2, 1969. Correlations with contemporary proton intensity increases at energies above 1 MeV are studied. Classical solar flare events such as those frequently observed from 30°W–60°W in solar longitude are not discussed. Categories of unusual events are defined and examples of each type are given. Discussion of these events centers around the emission and propagation of energetic particles from the point of origin on the Sun to the Earth. The results of this study are the following: (1) The differential electron energy spectrum (0.3–12 keV) from solar flares appears to be a constant of the flare process, with the spectral index = (-)3.0 ± 0.2. (2) Particle emission from solar flares contains a prompt component, which is injected into the interplanetary medium beyond the Sun and which is responsible for the diffusion characteristics of solar particle events, and a delayed component which is effectively contained in the lower solar atmosphere where it diffuses typically ± 100° in longitude and gradually escapes into interplanetary space. The delayed component gives rise to the corotating features commonly observed after the impulsive and diffusive onset from the prompt component. This is not the same as the two component model discussed by Lin (1970a) in which 40 keV electrons are often observed as a separate phenomenon and frequently precede higher energy particles observed at 1 AU. (3) Storage of electrons > 300 keV and protons > 1 MeV is essential to explain emission and propagation characteristics of solar particle events. In some rare cases the storage mechanism appears to be very efficient, culminating in a catastrophic decay of the trapping region. (4) The events with low proton/electron ratios all occur at least three weeks after the previous relativistic electron producing flare.     

The study of multi-band radio observations on ultraviolet flares of chromospheric active binary V711 Tauri

The chromospherically-active binary, V711 Tau, had been observed by using the American Very Large Array (VLA) at five bands from 1.4 to 15 GHz. During the observation, the source was undergoing an intense flare, its radio luminosity up to 1.8 × 10¹⁸ erg s^–1 Hz^–1. The degree of circular polarization in the phase of the most intense flare was very small. With the decaying of the flare the flux density decreased, spectral index became smaller, spectra steeper and reversal frequency lower; the degree of circular polarization increased and its direction was dependent on frequency. These observational facts support the conclusion that the emission during intense flare is synchrotron (or synchro-cyclotron) mechanism. The magnetic intensity is about 10 G near = 1, the average electron energy, 4 MeV, the electron density with larger than 10 keV, 3 × 10⁴–9 × 10⁴ cm^–3 and the electronic energy spectrum index in power-law distribution 1.3.     

2.2 MeV gamma-ray line observed during two SN solar flares

On December 15, 1978, an omnidirectional gamma-ray detector for the energy range 0.3 to 10 MeV was flown from São José dos Campos, Brazil at a latitude of about -23°. Around noon time, when the Sun was in the field of view of the detector, various solar flares of importance SN and SF occurred. The 2.2 MeV line flux was monitored during this time. A statistically significant line flux of (1.55 ± 0.50) × 10^–2 photons cm^–2 s^–1 and (9.97 ± 4.85) × 10^–3 photons cm^–2 s^–1 was observed within a few minutes of t maxima of the two long-duration SN flares respectively, whereas during SF flares only upper limits were obtained.     

A search for solar neutrons during solar flares

The upper limit on the solar neutron flux from 1–20 MeV has been measured, by a neutron detector on the OGO-6 satellite, to be less than 5 × 10^–2 n cm^–2 s^–1 at the 95% confidence level for several flares including two flares of importance 3B and a solar proton event of importance 3B. The measurements are consistent with the models proposed by Lingenfelter (1969) and by Lingenfelter and Ramaty (1967) for solar neutron production during solar flares. The implied upper limit on the flux of 2.2 MeV solar gamma rays is about the same as the 2.2 MeV flux observed by Chupp et al. (1973).     

Solar particle events with helium-over-hydrogen enhancement in the energy range up to 100 MeV nucl−1

Flux measurements of solar energetic particles (SEPs) in the ERNE instrument onboard SOHO indicate that the abundance of ⁴He-nuclei compared to protons in the energy range up to 100 MeV nucl^–1 was exceptionally high during the particle events on 27 May 1998 and 28 December 1999. The ⁴He/p ratio stayed between 0.15–0.50 for more than ten hours. There was also a prolonged enhancement in helium-3, ³He/⁴H 1%. Observations of EIT and LASCO on board SOHO confirm that the originators of both SEP events were western eruptions, flares and coronal mass ejections (CMEs). The onset of the SEP release took place close to the maximum of flares which were probably triggered by the rising CMEs. The observations suggest that the SEP events were started with the flare-(pre)accelerated particles, but impact of the CME-associated shocks might explain the continuation and modification of the helium and proton fluxes well after the flare production. These observations support the idea that the helium enhancements in the CME-associated events reflect the availability of seed particles that originate previously in flares.     

Proton Enhancements and Their Relation to the X-Ray Flares During the Three Last Solar Cycles

Energetic proton measurements obtained from the GOES and IMP-8 satellites as well as from ground-based neutron monitors are compared with the GOES soft X-ray measurements of the associated solar flares for the period 1975–2003. The present study investigates a broad range of phenomenology relating proton events to flares (with some references to related interplanetary disturbances), including correlations of occurrence, intensities, durations and timing of both the particle event and the flare as well as the role of the heliographic location of the designated active region. 1144 proton events of > 10 MeV energy were selected from this 28-year period. Owing primarily to the low particle flux threshold employed more than half of this number was found to be reliably connected with an X-ray flare. The statistical analysis indicates that the probability and magnitude of the near-Earth proton enhancement depends critically on the flare's importance and its heliolongitude. In this study all flares of X-ray importance > X5 and located in the most propitious heliolongitude range, 15^∘W to 75^∘W, were succeeded by a detectable proton enhancement. It was also found that the heliolongitude frequently determines the character of the proton event time profile. In addition to intensity, duration and timing, proton events were found to be related to the other flare properties such as lower temperatures and longer loop lengths.     

The Hard X-Ray Burst Spectrometer on the Solar Maximum Mission

The primary scientific objectives of the Hard X-Ray Burst Spectrometer (HXRBS) to be flown on the Solar Maximum Mission are as follows: (1) To determine the nature of the mechanisms which accelerate electrons to 20–100 keV in the first stage of a solar flare and to > 1 MeV in the second stage of many flares; and (2) to characterize the spatial and temporal relation between electron acceleration, storage and energy loss throughout a solar flare.Measurements of the spectrum of solar X-rays will be made in the energy range from 20 to 260 keV using an actively-shielded CsI(Na) scintillator with a thickness of 0.635 cm and a sensitive area of 71 cm². Continuous measurements with a time resolution of 0.128 s will be made of the 15-channel energy-loss spectrum of events in this scintillator in anticoincidence with events in the CsI(Na) shield. Counting-rate data with a time resolution as short as 1 ms will also be available from a limited period each orbit using a 32K-word circulating memory triggered by a high event rate.In the first year after launch, it is expected that approximately 1000 flares will be observed above the instrument sensitivity threshold, which corresponds to a 20–200 keV X-ray flux of 2 × 10^–1 photons (cm² s)^–1 lasting for at least one second.     

Relativistic electrons in solar particle events

We present here the results of the first systematic study of electrons of energies greater than 10 MeV associated with solar flares. We have made direct measurements of the frequency with which these particles are found in solar flare related events, the spectra of the particles, and the evolution of the spectra during these events. In addition the nature of the propagation of these electrons is studied and the degree of anisotropy in their diffusion is measured for the first time.The observations were made aboard the spacecraft OGO-5 from 1968, March through 1969, August. It is found that electrons in the energy range 12–45 MeV are normally present in major solar particle events. The time-intensity profiles of the fluxes indicate diffusive propagation; and the time-to-maximum intensity is found to vary with solar longitude in a way which can only be the result of anisotropic propagation with the perpendicular diffusion coefficient comparable in magnitude to, but smaller than, the parallel diffusion coefficient. Spectra during the observed events fit the power law AE ^– with 2.5 3.8. The time evolution of the spectrum throughout the course of the 4 most intense events shows that the spectrum steepens rapidly during the initial phase but retains a constant slope through the decay phase.Events which behave in a manner which is not described by the normal diffusion picture are also discussed. These examples show phenomena other than direct flare injection followed by anisotropic diffusion.This work was supported in part by the National Aeronautics and Space Administration under Contract NAS 5-9096 and Grant NGL 14-001-005.Submitted to the Department of Physics, University of Chicago, Chicago, Illinois in partial fulfillment of the requirements for the Ph. D. degree.NASA Trainee 1967–1969.     

A search for neutrons of solar origin using balloon borne detectors 1967–69

A series of telescopes having approximately a 30° half opening angle and responding to neutrons in the energy range 50 MeV to 350 MeV has been flown to the top of the atmosphere on balloons released from an equatorial launching site at Kampala, Uganda, between 1967 and 1969. The aim of the experiment was to attempt to detect solar neutrons during periods of enhanced solar activity. No neutrons of solar origin were detected, but an upper limit of the order of 30 neutrons m^–2 s^–1 at the Earth has been placed on the continuous solar neutron flux in the above energy range, and a limit of four photons m^–2 s^–1 has also been placed on the corresponding -ray flux above 80 MeV. Limits have likewise been placed on the total emission from various flares. For a 1B flare the values were 23 × 10⁴ neutrons m^–2 and 6 × 10⁴ photons m^–2.     

A search for energetic neutrons emitted during solar flares

On the basis of solar flare forecasts, balloon flights were made from Hyderabad, India (vertical geomagnetic threshold rigidity of 16.9 GV), to detect the possible emission of high energy neutrons during solar flares. The detector comprised of a central plastic scintillator, completely surrounded by an anticoincidence plastic scintillator shield. The instrument responds to neutrons of about 15–150 MeV and gamma rays of about 5–30 MeV with about the same efficiency. The detector was flown to an atmospheric depth of 25 g cm^-2 on February 26, 1969; while the balloon was at ceiling a flare of importance 2B and one of 1N occurred. No perceptible flare associated increase in the counting rate was observed. Using the observed counting rates, an upper limit of 1.2 × 10^-2 neutrons cm^-2 sec^-1 is obtained for the first time for a flare of importance 2B for neutrons of energy 15–150 MeV. The corresponding upper limit for gamma rays of energy 5–30 MeV is found to be 10^-2 photons cm^-2 sec^-1. The neutron flux limits are compared with the recent calculations of Lingenfelter.     

Understanding Solar Flare Waiting-Time Distributions

The observed distribution of waiting times t between X-ray solar flares of greater than C1 class listed in the Geostationary Operational Environmental Satellite (GOES) catalog exhibits a power-law tail (t) for large waiting times (t>10hours). It is shown that the power-law index varies with the solar cycle. For the minimum phase of the cycle the index is =–1.4±0.1, and for the maximum phase of the cycle the index is –3.2±0.2. For all years 1975–2001, the index is –2.2±0.1. We present a simple theory to account for the observed waiting-time distributions in terms of a Poisson process with a time-varying rate (t). A common approximation of slow variation of the rate with respect to a waiting time is examined, and found to be valid for the GOES catalog events. Subject to this approximation the observed waiting-time distribution is determined by f(), the time distribution of the rate . If f() has a power-law form for low rates, the waiting time-distribution is predicted to have a power-law tail (t)^–(3+) (>–3). Distributions f() are constructed from the GOES data. For the entire catalog a power-law index =–0.9±0.1 is found in the time distribution of rates for low rates (<0.1hours ^–1). For the maximum and minimum phases power-law indices =–0.1±0.5 and =–1.7±0.2, respectively, are observed. Hence, the Poisson theory together with the observed time distributions of the rate predict power-law tails in the waiting-time distributions with indices –2.2±0.1 (1975–2001), –2.9±0.5 (maximum phase) and –1.3±0.2 (minimum phase), consistent with the observations. These results suggest that the flaring rate varies in an intrinsically different way at solar maximum by comparison with solar minimum. The implications of these results for a recent model for flare statistics (Craig, 2001) and more generally for our understanding of the flare process are discussed.     

The November 22, 1977 solar flare: Evidence for 2.23 and 4.43 MeV line emission from the signe 2MP experiment

The November 22, 1977 solar flare was observed at energies up to 4.9 MeV by French-built gamma ray detectors aboard the Soviet Prognoz-6 satellite. The data show evidence for 2.23 and 4.43 MeV line emission, with the 2.23 MeV emission occurring about 3 min after the flare onset in hard X-rays. The line intensities, 0.11 cm^–2s^–1 and 0.06 cm^–2s^–1 for the 2.23 and 4.43 lines, respectively, are roughly comparable to intensities observed in other events. Particle detectors aboard the Prognoz-6 satellite, however, recorded a proton flux much lower than that observed for the 4 August 1972 event. It is shown that this may be taken as evidence for a thick target interpretation of the proton interactions in the solar atmosphere.     

Multiple acceleration of protons on the Sun and their free propagation to the Earth on January 20, 2005

We analyze the observations of solar protons with energies >80 MeV near the Earth and the January 20, 2005, solar flare in various ranges of the electromagnetic spectrum. Within approximately the first 30 min after their escape into interplanetary space, the solar protons with energies above 80 MeV propagated without scattering to the Earth and their time profiles were determined only by the time profile of the source on the Sun and its energy spectrum. The 80–165 MeV proton injection function was nonzero beginning at 06:43:80 UT and can be represented as the product of the temporal part, the ACS (Anticoincidence System) SPI (Spectrometer on INTEGRAL) count rate, and the energy part, a power-law proton spectrum ～E ^?4.7±0.1. Protons with energies above 165 MeV and relativistic electrons were injected, respectively, 4 and 9 min later than this time. The close correlation between high-energy solar electromagnetic emission and solar proton fluxes near the Earth is evidence for prolonged and multiple proton acceleration in solar flares. The formation of a posteruptive loop system was most likely accompanied by successive energy releases and acceleration of charged particles with various energies. Our results are in conflict with the ideas of cosmic-ray acceleration in gradual solar particle events at the shock wave driven by a coronal mass ejection.     

Rates of Flaring in Individual Active Regions

Rates of flaring in individual active regions on the Sun during the period 1981–1999 are examined using United States Air Force/Mount Wilson (USAF/MWL) active-region observations together with the Geostationary Operational Environmental Satellite (GOES) soft X-ray flare catalog. Of the flares in the catalog above C1 class, 61.5% are identified with an active region. Evidence is presented for obscuration, i.e. that the increase in soft X-ray flux during a large flare decreases the likelihood of detection of soft X-ray events immediately following the large flare. This effect means that many events are missing from the GOES catalog. It is estimated that in the absence of obscuration the number of flares above C1 class would be higher by (75±23)%. A second observational selection effect – an increased tendency for larger flares to be identified with an active region – is also identified. The distributions of numbers of flares produced by individual active regions and of mean flaring rate among active regions are shown to be approximately exponential, although there are excess numbers of active regions with low flare numbers and low flaring rates. A Bayesian procedure is used to analyze the time history of the flaring rate in the individual active regions. A substantial number of active regions appear to exhibit variation in flaring rate during their transit of the solar disk. Examples are shown of regions with and without rate variation, illustrating the different distributions of times between events (waiting-time distributions) that are observed. A piecewise constant Poisson process is found to provide a good model for the observed waiting-time distributions. Finally, applications of analysis of the rate of flaring to understanding the flare mechanism and to flare prediction are discussed.     

A model of solar flares and faculae

Theories of solar flares based on the storage of energy (usually as magnetic energy) in the solar atmosphere are shown to be incompatible with observational data.The sunspot energy deficit and the photospheric faculae both involve energy fluxes comparable with the flare requirement ( 3 × 10²⁹ erg s^–1). Both also require a subsurface system of waves or oscillations, perhaps those discussed by Danielson and Savage and by Wilson. The flare model proposed is based on a temporary diversion of this energy carried by Alfvén waves through spots and magnetic elements or micro-pores; the calculated plasma perturbation velocity in the umbra is about 6 km s^–1 for a major flare.In the atmosphere the wave energy divides into two parts to produce the cool, stationary optical flare and the particle flare. The first part is dissipated around flux tubes which are mainly horizontal in the chromosphere and which tend to concentrate along the magnetic neutral line (B = 0). Each tube vibrates individually as a taut wire in a viscous fluid, to excite the fluid just outside the tube. The second part of the energy emerges along tubes mainly vertical in the chromosphere and is converted to shock waves in the corona and then to particle energy for the radio and X-ray flare and the blast wave.The model includes white-light faculae, quasi-permanent X-ray and fast-particle emissions, sympathetic flares and surges. An unambiguous test would be provided by observations of plasma motions of a few kilometres per second in spots and micro-pores.