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.     

Non-thermal processes in large solar flares

We analyze particle acceleration processes in large solar flares, using observations of the August, 1972, series of large events. The energetic particle populations are estimated from the hard X-ray and γ-ray emission, and from direct interplanetary particle observations. The collisional energy losses of these particles are computed as a function of height, assuming that the particles are accelerated high in the solar atmosphere and then precipitate down into denser layers. We compare the computed energy input with the flare energy output in radiation, heating, and mass ejection, and find for large proton event flares that:

1. The ～10–10² keV electrons accelerated during the flash phase constitute the bulk of the total flare energy.
2. The flare can be divided into two regions depending on whether the electron energy input goes into radiation or explosive heating. The computed energy input to the radiative quasi-equilibrium region agrees with the observed flare energy output in optical, UV, and EUV radiation.
3. The electron energy input to the explosive heating region can produce evaporation of the upper chromosphere needed to form the soft X-ray flare plasma.
4. Very intense energetic electron fluxes can provide the energy and mass for interplanetary shock wave by heating the atmospheric gas to energies sufficient to escape the solar gravitational and magnetic fields. The threshold for shock formation appears to be ～10³¹ ergs total energy in >20 keV electrons, and all of the shock energy can be supplied by electrons if their spectrum extends down to 5–10 keV.
5. High energy protons are accelerated later than the 10–10² keV electrons and most of them escape to the interplanetary medium. The energetic protons are not a significant contributor to the energization of flare phenomena. The observations are consistent with shock-wave acceleration of the protons and other nuclei, and also of electrons to relativistic energies.
6. The flare white-light continuum emission is consistent with a model of free-bound transitions in a plasma with strong non-thermal ionization produced in the lower solar chromosphere by energetic electrons. The white-light continuum is inconsistent with models of photospheric heating by the energetic particles. A threshold energy of ～5×10³⁰ ergs in >20 keV electrons is required for detectable white-light emission.

The highly efficient electron energization required in these flares suggests that the flare mechanism consists of rapid dissipation of chromospheric and coronal field-aligned or sheet currents, due to the onset of current-driven Buneman anomalous resistivity. Large proton flares then result when the energy input from accelerated electrons is sufficient to form a shock wave.     

On the power-law distributions of X-ray fluxes from solar flares observed with GOES

The power-law frequency distributions of the peak flux of solar flare X-ray emission have been studied extensively and attributed to a system having self-organized criticality(SOC).In this paper,we first show that,so long as the shape of the normalized light curve is not correlated with the peak flux,the flux histogram of solar flares also follows a power-law distribution with the same spectral index as the powerlaw frequency distribution of the peak flux,which may partially explain why power-law distributions are ubiquitous in the Universe.We then show that the spectral indexes of the histograms of soft X-ray fluxes observed by GOES satellites in two different energy channels are different:the higher energy channel has a harder distribution than the lower energy channel,which challenges the universal power-law distribution predicted by SOC models and implies a very soft distribution of thermal energy content of plasmas probed by the GOES satellites.The temperature(T) distribution,on the other hand,approaches a power-law distribution with an index of 2 for high values of T.Hence the application of SOC models to the statistical properties of solar flares needs to be revisited.     

An electric-current description of solar flares

The presently prevailing theories of solar flares rely on the hypothetical presence of magnetic flux tubes beneath the photosphere and the two subsequent hypotheses, their emergence above the photosphere and explosive magnetic reconnection, converting magnetic energy carried by the flux tubes to solar flare energy. In this paper, we discuss solar flares from an entirely different point of view, namely in terms of power supply by a dynamo process in the photosphere. By this process, electric currents flowing along the magnetic field lines are generated and the familiar ‘force-free’ fields or the ‘sheared’ magnetic fields are produced. Upward field-aligned currents thus generated are carried by downward streaming electrons; these electrons can excite hydrogen atoms in the chromosphere, causing the optical Hα flares or ‘low temperature flares’. It is thus argued that as the ‘force-free’ fields are being built up for the magnetic energy storage, a flare must already be in progress.     

Solar Impulsive Hard X-Ray Emission and Two-Stage Electron Acceleration

Heating and acceleration of electrons in solar impulsive hard X-ray (HXR) flares are studied according to the two-stage acceleration model developed by Zhang for solar 3He-rich events. It is shown that electrostatic H-cyclotron waves can be excited at a parallel phase velocity less than about the electron thermal velocity and thus can significantly heat the electrons (up to 40 MK) through Landau resonance. The preheated electrons with velocities above a threshold are further accelerated to high energies in the flare-acceleration process. The flare-produced electron spectrum is obtained and shown to be thermal at low energies and power law at high energies. In the non-thermal energy range, the spectrum can be double power law if the spectral power index is energy dependent or related. The electron energy spectrum obtained by this study agrees quantitatively with the result derived from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) HXR observations in the flare of 2002 July 23. The total flux and energy flux of electrons accelerated in the solar flare also agree with the measurements.     

On the generation of high-energy particles in solar flares

This paper discusses the relationship between some characteristics of microwave type IV radio bursts and solar cosmic ray protons of MeV energy. It is shown that the peak flux intensity of those bursts is almost linearly correlated with the MeV proton peak flux observed by satellites near the Earth and that protons and electrons would be accelerated simultaneously by a similar mechanism during the explosive phase of solar flares.Brief discussion is given on the propagation of solar cosmic rays in the solar envelope after ejection from the flare regions.     

Measurements of Electron Anisotropy in Solar Flares Using Albedo with RHESSI X-Ray Data

The angular distribution of electrons accelerated in solar flares is a key parameter in the understanding of the acceleration and propagation mechanisms that occur there. However, the anisotropy of energetic electrons is still a poorly known quantity, with observational studies producing evidence for an isotropic distribution and theoretical models mainly considering the strongly beamed case. We use the effect of photospheric albedo to infer the pitch-angle distribution of X-ray emitting electrons using Hard X-ray data from RHESSI. A bi-directional approximation is applied and a regularised inversion is performed for eight large flare events to deduce the electron spectra in both downward (towards the photosphere) and upward (away from the photosphere) directions. The electron spectra and the electron anisotropy ratios are calculated for a broad energy range, from about ten up to ～?300 keV, near the peak of the flares. The variation of electron anisotropy over short periods of time lasting 4, 8 and 16 seconds near the impulsive peak has been examined. The results show little evidence for strong anisotropy and the mean electron flux spectra are consistent with the isotropic electron distribution. The 3σ level uncertainties, although energy and event dependent, are found to suggest that anisotropic distribution with anisotropy larger than ～?three are not consistent with the hard X-ray data. At energies above 150?–?200 keV, the uncertainties are larger and thus the possible electron anisotropies could be larger.     

Energies of Electrons Accelerated in Turbulent Reconnecting Current Sheets in Solar Flares

Yohkoh observations strongly suggest that electron acceleration in solar flares occurs in magnetic reconnection regions in the corona above the soft X-ray flare loops. Unfortunately, models for particle acceleration in reconnecting current sheets predict electron energy gains in terms of the reconnection electric field and the thickness of the sheet, both of which are extremely difficult to measure. It can be shown, however, that application of Ohm's law in a turbulent current sheet, combined with energy and Maxwell's equations, leads to a formula for the electron energy gain in terms of the flare power output, the magnetic field strength, the plasma density and temperature in the sheet, and its area. Typical flare parameters correspond to electron energies between a few tens of keV and a few MeV. The calculation supports the viewpoint that electrons that generate the continuum gamma-ray and hard X-ray emissions in impulsive solar flares are accelerated in a large-scale turbulent current sheet above the soft X-ray flare loops.     

Evolvement of microwave spike bursts in a solar flare on 2006 December 13

Solar radio spikes are one of the most intriguing spectral types of radio bursts. Their very short lifetimes, small source size and super-high brightness temperature indicate that they should be involved in some strong energy release, particle acceleration and coherent emission processes closely related to solar flares. In particular, for the microwave spike bursts, their source regions are much close to the related flaring source region which may provide the fundamental information of the flaring process. In this work,we identify more than 600 millisecond microwave spikes which recorded by the Solar Broadband Radio Spectrometer in Huairou(SBRS/Huairou) during an X3.4 solar flare on 2006 December 13 and present a statistical analysis about their parametric evolution characteristic. We find that the spikes have nearly the same probability of positive and negative frequency drifting rates not only in the flare rising phase, but also in the peak and decay phases. So we suppose that the microwave spike bursts should be generated by shockaccelerated energetic electrons, just like the terminational shock(TS) wave produced by the reconnection outflows near the loop top. The spike bursts occurred around the peak phase have the highest central frequency and obviously weak emission intensity, which imply that their source region should have the lowest position with higher plasma density due to the weakened magnetic reconnection and the relaxation of TS during the peak phase. The right-handed polarization of the most spike bursts may be due to the TS lying on the top region of some very asymmetrical flare loops.     

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.     

Deterministically Driven Avalanche Models of Solar Flares

We develop and discuss the properties of a new class of lattice-based avalanche models of solar flares. These models are readily amenable to a relatively unambiguous physical interpretation in terms of slow twisting of a coronal loop. They share similarities with other avalanche models, such as the classical stick–slip self-organized critical model of earthquakes, in that they are driven globally by a fully deterministic energy-loading process. The model design leads to a systematic deficit of small-scale avalanches. In some portions of model space, mid-size and large avalanching behavior is scale-free, being characterized by event size distributions that have the form of power-laws with index values, which, in some parameter regimes, compare favorably to those inferred from solar EUV and X-ray flare data. For models using conservative or near-conservative redistribution rules, a population of large, quasiperiodic avalanches can also appear. Although without direct counterparts in the observational global statistics of flare energy release, this latter behavior may be relevant to recurrent flaring in individual coronal loops. This class of models could provide a basis for the prediction of large solar flares.     

Electrons > 40 ke V and protons > 500 ke V of solar origin

Following many solar flares, electrons with kinetic energy > 40 keV appear in interplanetary space. There are two classes of such electrons: prompt electrons which arrive within an hour of the flare and delayed electrons which arrive about a day following the flare. The promptly arriving electrons are found to be of two types: Simple (S) events are associated with solar flares which occur in the absence of large area Type I radio noise storm and the complex (C) events resulting from flares beneath these large radio noise regions. The propagation of energetic solar flare electrons to the earth is best described in terms of cones of propagation. In the S-events the cones have about 30° opening angle whereas in the C-type events the cones open to about 90° full angle. Outside the boundaries of these cones the electron flux is much reduced. Within the cones there is a net streaming of the electrons away from the sun. Solar flare electron fluxes do not show filamentary structure even at times when protons from the same flare do. This suggests that the electrons are injected into the interplanetary field from regions distinct from the proton injection region. The delayed solar electron events are accompanied by large fluxes of protons > 500 keV. These events are sometimes closely related to a sudden commencement.     

The State of Self-organized Criticality of the Sun During the Last Three Solar Cycles. I. Observations

We analyze the occurrence-frequency distributions of peak fluxes [P], total fluxes [E], and durations [T] of solar flares over the last three solar cycles (during 1980??C?2010) from SMM/HXRBS, CGRO/BATSE, and RHESSI hard X-ray data. From the synthesized data we find powerlaw slopes with mean values of ?? _P =1.73±0.07 for the peak flux, ?? _E =1.62±0.12 for the total flux, and ?? _T =1.99±0.35 for flare durations. We find a tendency of an anti-correlation of the powerlaw slope of peak fluxes with the flare rate or sunspot number as a function of the solar cycle. The occurrence powerlaw slope is always steeper by ??????0.1 during a solar-cycle minimum compared with the previous solar-cycle maximum, but the relative amplitude varies for each cycle or instrument. Since each solar cycle has been observed with a different instrument, part of the variation could be attributed to instrumental characteristics and different event selection criteria used in generating the event catalogs. The relatively flatter powerlaw slopes during solar maxima could indicate more energetic flares with harder electron-energy spectra, probably due to a higher magnetic complexity of the solar corona. This would imply a non-stationarity (or solar-cycle dependence) of the coronal state of self-organized criticality.     

A study of X-ray flares – I. Active late-type dwarfs

We present temporal and spectral characteristics of X-ray flares observed from six late-type G–K active dwarfs (V368 Cep, XI Boo, IM Vir, V471 Tau, CC Eri and EP Eri) using data from observations with the XMM–Newton observatory. All the stars were found to be flaring frequently and altogether a total of 17 flares were detected above the 'quiescent' state X-ray emission which varied from 0.5 to  8.3 × 10²⁹ erg s⁻¹  . The largest flare was observed in a low-activity dwarf XI Boo with a decay time of 10 ks and ratio of peak flare luminosity to 'quiescent' state luminosity of 2. We have studied the spectral changes during the flares by using colour–colour diagram and by detailed spectral analysis during the temporal evolution of the flares. The exponential decay of the X-ray light curves, and time evolution of the plasma temperature and emission measure are similar to those observed in compact solar flares. We have derived the semiloop lengths of flares based on the hydrodynamic flare model. The size of the flaring loops is found to be less than the stellar radius. The hydrodynamic flare decay analysis indicates the presence of sustained heating during the decay of most flares.     

Flares before and after coronal mass ejections

Flare characteristics such as the flare occurrence number density and the distribution of peak flux as well as duration of flares occurring on either side of a coronal mass ejection(CME) onset time are studied. While the flares are rather evenly distributed statistically on either side of the CME onset time,the flare peak flux and duration tend to decrease depending upon their occurrence either before or after the CME onset. This is consistent with the earlier findings that flares emit higher energy before a CME whereas the energy is less in flares occurring after a CME.     

The solar particle events of May 23 and May 28, 1967

McMath plage region 8818 passed over the visible solar disk on May 17–31, 1967. It was very active from its first appearance on the Eastern limb, several times producing bright optical flares and hard X-ray emission, accompanied by intense type II, type IV and centimeter radio bursts. Nevertheless, no solar particles could be detected near the earth until the evening of May 23, when three bright flares were observed in close succession at 25°–28° E. During the following build-up of the solar particle flux over 36 hours, the galactic cosmic ray flux > 1 GeV decreased gradually by about 5%. The flux of solar particles decreased in two steps on May 25, both accompanied by decreases in the equatorial geomagnetic field. These field depressions are attributed to storm plasma ejected from the parent flare of the May 23 particle event. The propagation of solar particles from May 23 on thus appears to be strongly affected by storm plasma from the parent flare of the May 23 event, without any indications of solar particles being trapped in that plasma.A later particle event early on May 28 was also associated with a bright flare in McMath region 8818, at 33° W. This event displayed a rapid build-up, with electrons arriving first, and an exponential decay. A smooth proton peak, 20 min wide, was detected on May 30 closely associated with an SSC attributed to plasma ejection from the parent flare of the May 28 event.Between the geomagnetic storms beginning on May 25 and May 30 an anomalous daily variation was observed in the cosmic ray flux >1 GeV, the time of maximum falling 7–10 hours earlier than normal. Storm time increases in the flux of galactic cosmic rays were seen on May 26 when the equatorial geomagnetic field was depressed by more than 400 . Low latitude auroras were also observed during that time.On leave from the University of Uppsala, Sweden.     

X-ray Flares Observed from Six Young Stars Located in the Region of Star Clusters NGC 869 and IC 2602

We present, for the first time, an analysis of seven intense X-ray flares observed from six stars (LAV 796, LAV 1174, SHM2002 3734, 2MASS 02191082+5707324, V553 Car, V557 Car). These stars are located in the region of young open star clusters NGC 869 and IC 2602. These flares detected in the XMM-Newton data show a rapid rise (10–40 min) and a slow decay (20–90 min). The X-ray luminosities during the flares in the energy band 0.3–7.5 keV are in the range of 10^29.9 to 10^31.7 erg s^?1. The strongest flare was observed with the ratio ～13 for count rates at peak of the flare to the quiescent intensity. The maximum temperature during the flares has been found to be ～100 MK. The semi-loop lengths for the flaring loops are estimated to be of the order of 10¹⁰ cm. The physical parameters of the flaring structure, the peak density, pressure and minimum magnetic field required to confine the plasma have been derived and found to be consistent with flares from pre-main sequence stars in the Orion and the Taurus-Auriga-Perseus region.     

Spectral Flattening During Solar Radio Bursts At Cm–mm Wavelengths and the Dynamics of Energetic Electrons in a Flare Loop

Until recently, most of the information on particle acceleration processes in solar flares has been obtained from hard X-ray and cm-microwave observations. As a rule they provide information on electrons with energies below 300 keV. During recent years it became possible to measure the gamma-ray and millimeter radio emission with improved sensitivities. These spectral ranges carry information on much higher energy electrons. We studied the temporal and spectral behaviour of the radio burst emission at centimeter-millimeter wavelengths (8–50 GHz) by using the data from the patrol instruments of IAP (Bern University). We have analyzed more than 20 impulsive and long duration radio bursts (of 10 s to several 100 s duration).The main finding of the data analysis is the presence of spectral flattening throughout the bursts, which occurs always during the decay phase of flux peaks, at frequencies well above the spectral peak frequency and independently of burst duration. Furthermore, for some of the bursts, the flux maxima at higher frequencies are delayed. These findings can serve as evidence of the hardening of the electron spectrum at energies above some hundreds of keV during the decay phase of cm–mm flux peaks. As a most likely reason for such a hardening we consider Coulomb collisions of energetic electrons continuously injected and trapped in a flaring loop.     

Long-term variation in the flaring activity of flare stars

The frequency of flares is one of the basic characteristics of the activity of flare stars. Long-term variations in the flaring frequency are determined by comparing the distribution functions of the flaring frequency for systems of flare stars with different ages. __________ Translated from Astrofizika, Vol. 51, No. 1, pp. 63–74 (February 2008).