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Astron. Astrophys. 334, 299-313 (1998)

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1. Introduction

It is well known that the solar corona is a very dynamic region which is the seat of many phenomena related to magnetic energy releases in a large range of sizes and occurring on time scales going from a few seconds or less to hours. Physical processes leading to magnetic energy releases have been analyzed in individual solar flares using multi-wavelength observations. Such single-case studies constrain the number and energy spectrum of accelerated electrons and ions and the characteristics of magnetic structures at different scales in which energetic particles are produced, propagate and radiate.

The statistical behaviour of solar flares has been characterized with frequency distributions of hard X-ray parameters (Datlowe et al. 1974; Lin et al. 1984; Dennis 1985; Schwartz et al. 1992; Crosby et al. 1993; Lee et al. 1993; Pearce et al. 1993; Bai 1993; Biesecker 1994; Biesecker et al. 1994; Bromund et al. 1995; Lee et al. 1995; Kucera et al. 1997). It is found that most of the distributions can be represented by power-laws having a slope ranging from -2.4 and -1.4 above a threshold (usually attributed to the sensitivity of the experiment used), (see Crosby (1996) for a review).

The most recent statistical studies were based on hard X-ray data originating from long-term solar flare observations obtained with the Hard X-Ray Burst Spectrometer (HXRBS) on the Solar Maximum Mission (SMM) spacecraft (Crosby et al. 1993) and by the X-ray spectrometer aboard the International Cometary Explorer (ICE, formerly known as ISEE 3) spacecraft (Bromund et al. 1995). The measured parameters are the peak count rate (C), the total duration (D) and the peak photon flux (F). The peak energy flux (E) and the total energy (W) in accelerated electrons were also computed using a single power-law photon spectrum and a thick-target interaction model. The slopes of the power-law distributions computed above a threshold are summarized for both studies in Table 1.


Table 1. Characteristics of the occurrence distributions of HXR flare parameters

Power-law distributions are found to extend for several decades. The slopes deduced by Bromund et al. (1995) are found to be slightly steeper than the ones deduced by Crosby et al (1993). This may be due to differences in instrument sensitivity for the measured parameters or to different methods of estimating electron energy for computed parameters. It was pointed out by Crosby et al. (1993) that the distribution in photon flux obtained for the microflares observed by Lin et al. (1984) closely agrees with the extrapolated distribution of all flares observed near solar maximum. This strengthens the assumption that the deviation from the power-law observed below the threshold of 1.5 ph cm-2 s-1 with HXRBS/SMM reflects only the effect of the instrumental sensitivity threshold. On the other hand it has been noticed that there seems to be a deficiency of stronger/longer events seen in the frequency distributions of durations and fluxes. It is possible that this may be due to an observational effect (data gaps, saturation) but as suggested by Lu et al. (1993), it cannot be excluded that this effect may be real.

Another statistical study was performed on the HXRBS/SMM data by Pearce et al. (1993) leading to similar results for the distribution in peak count rates as in Crosby et al. (1993). They furthermore studied the distribution of the time intervals between consecutive HXRBS events (limited to the 60 minute spacecraft day) and found that the flares did not seem to be randomly distributed in time, but that the occurrence distribution of time intervals was best fitted by a power-law distribution. Similar results were also found using observations from BATSE (Biesecker 1994). More recently (Kucera et al. 1997) studied if the frequency distribution of HXRBS/SMM flares varies as a function of the size of the active region. Basically they find that fewer large flares are produced by active regions with small total sunspot area and that large complex regions appear to produce a lower percentage of low energy flares than smaller, simpler regions.

In the soft X-ray domain, frequency distributions of global soft X-ray parameters are also found (Hudson et al. 1969; Drake, 1971; Lee et al. 1995; Shimizu 1994, 1995) to be all well-represented by power-laws with slopes ranging from -1.4 to -2.5. Shimizu (1994, 1995) performed frequency distributions on the estimated energy content of transient brightenings measured by the soft X-ray telescope aboard YOHKOH in the 0.4-4.0 keV range. He found that the distributions can be represented by a single power-law with a slope [FORMULA] -1.5, -1.6, which is similar to what has been found for energy distributions in the hard X-ray range. This may suggest that independently of the form under which the released energy is converted (plasma heating or production of non-thermal particles), frequency distributions of total energy contained in either non-thermal particles or hot plasmas give good indications on the energy release distribution itself. Lee et al. (1995) have compared the soft X-ray peak flux and the hard X-ray fluence distribution. Different slopes are found, leading the authors to conclude that other heating mechanisms than energy deposited by accelerated electrons must act in flares.

The interpretation of the shape of the frequency distributions has been investigated in the literature and basically two classes of models ('stochastic relaxation' and 'avalanche model') have been developed (see Sect. 5.2). Assuming that the total energy contained in non-thermal electrons or hot plasmas is correlated to the total energy released during a flare, the observed distributions can be confronted to the predictions of these models. This has been done for hard X-ray flares with an energy range between 1028 to 1033 ergs. However, very little information is known on the distributions of X-ray flare parameters for weaker events.

In this paper we present a new solar X-ray flare statistical study based on observations at photon X-ray energies above 10 keV recorded by the Danish Wide Angle Telescope for Cosmic Hard X-Rays (WATCH) experiment aboard the Russian spacecraft GRANAT. The energy release in these flares is estimated to lie below the range observed by ISEE-3/ICE or HXRBS/SMM. Frequency distributions are performed on the different measured X-ray parameters.

WATCH measures the X-ray flux in the deka-keV range for which few observations have been performed with scintillators. This experiment allows to make systematic observations in this intermediate zone between hard X-ray observations above 20 keV and observations in the soft X-ray thermal range (e.g. with GOES). In Sect. 2 the WATCH unit that observes the Sun (referred to as WATCH-0) is presented including a description of how the energy calibration of the detector was performed. Thereafter (Sect. 3) the creation of the WATCH solar flare catalogue is explained and some examples of solar observations are given. For some of the solar events we discuss the possible interpretations of the radiation observed and an estimation of the energy content of the largest flares observed is given. Sect. 4 presents the different statistical studies that were performed on the WATCH solar database. In Sect. 5 the results of the statistical study are discussed in relation with previous studies and in the context of avalanche models. Sect. 5 furthermore summarizes the conclusions of the paper and discusses some prospective studies.

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© European Southern Observatory (ESO) 1998

Online publication: May 12, 1998