Statistical Property of Logrithmic Flare Indices; Distribution and Evolution

For the needs of researches and predictions of flare activities in the middle-term(10¹-10²days), the first thing is that we should establish a suitable form describing flare activities.We have found that the daily flare indices I_f published by NOAA deviate seriously from the normal distribution. Through conversion, we obtained the logarithmic flar indices F_L corresponding to the order of magnitude of integral radiant intensity from flares F_L=log(0.76/T^*ΣA_???²) and found that in this case the normal distribution holds good for F_L·. Consequently, their mean F_L and standard deviation σ_F in any period of time can perfectly statistically describe the level of flare activity in that period.According to the probability theory, using the random number generator, we deduced the approximate values of F_L below the thresholds of reporting, and composed the complete alignment F_L(t), which describes the continual changes of solar flare activities.We have calculated F_L and σ_F of every cycle of the solar rotation cycles from 1642 to 1684 and found them to evolve correlatively with the slowly varying component of the Sun (solar flux S_a at 2800 Me). The compound correlation coefficient R_F=0.93, and R_σ=0.46. On the other hand, the relative regression residuals (Σ(F_F-Λ/F_L)²/ΣF_L²)^½~20%,and (Σ(σ_F-σ_F)/Σσ_F²)^½~30%. Evidently, it is difficult to explain and forecast them quantitatively, and we should further explore the law.In addition, we have also found that the correlation coefficint of F_L with S_a equals 0.93 and the corresponding regression equation is Λ/F_L=-0.70 + 0.0155S_a By relying on the forecasts of the mean S_a of the Solar flux at 2800Mc, we cancomparatively accurately forecast the average Λ/F_L of the logarithmic flare indices.