The statistical properties of the solar soft X-ray fluence during 1997–2008

The statistical properties of the solar soft X-ray (SXR) flare fluence, i.e. the time integral of SXR flux of a flare, \(F_{\mathit{SXR}}\), and sum of the \(F_{\mathit{SXR}}\) of all flares produced by a solar active region (AR), \(F_{\mathit{AR}}\), during 1997–2008 have been investigated. The results show that \(F_{\mathit{SXR}}\) has moderate correlation with the area of the associated AR, while the correlation between \(F_{\mathit{AR}}\) and the largest area of the associated AR is also moderate. The total number of ARs that can produce at least one SXR flare during 1997–2008, \(N_{t}\), is 1408. The sum of \(F_{\mathit{AR}}\) produced by 1408 ARs, \(\sum F_{\mathit{AR}}\), is 89 585.81 (erg s cm−2) and the average value of \(F_{\mathit{AR}}\) is 63.6 (erg s cm−2). 34 ARs (\(F_{\mathit{AR}}\ge 500\ \mbox{erg}\,\mbox{s}\,\mbox{cm}^{-2}\)) contributed 55.72 % of \(\sum F_{\mathit{AR}}\). 111 ARs \((100\ (\mbox{erg}\,\mbox{s}\,\mbox{cm}^{-2})\le F_{\mathit{AR}}<500\ (\mbox{erg}\,\mbox{s}\,\mbox{cm}^{-2}))\) contributed 24.33 % of \(\sum F_{\mathit{AR}}\). 437 ARs \((10\ (\mbox{erg}\,\mbox{s}\,\mbox{cm}^{-2} )\le F_{\mathit{AR}}< 100\ (\mbox{erg}\,\mbox{s}\,\mbox{cm}^{-2}))\) contributed 17.48 % of \(\sum F_{\mathit{AR}}\). The rest 826 ARs only contributed 2.52 % of \(\sum F_{\mathit{AR}}\). The number of ARs decreases dramatically with \(F_{\mathit{AR}}\) and the distribution function of \(F_{\mathit{AR}}\) is \(N(F_{\mathit{AR}})=2840e^{-0.1286F_{\mathit{AR}}}\).