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Table 4.

Pearson’s correlation coefficients between the logarithm of the proton peak fluxes (E > 10; >30; >60 and >100 MeV) (upper part of the Table), the logarithm of the fluence (lower part of the table) and the basic characteristics of the parent solar events: flare (CME) parameters – logarithm of the SXR peak flux, (log SXRs); SXR fluence, (ISXR); the maximum flux value of the time derivative of the SXRs (i.e. “Neupert effect”) (Ne); longitude of the associated flare, (Lon); flare rise time, (RT); flare duration, (D); velocity of the CME, (u) and the angular width of the CME, (s). The number of pairs for the calculation of each coefficient are presented in the parenthesis next to the coefficient at each case. The most significant coefficients are emphasized with bold fonts.

Solar flare
CME
Peak flux log10 ([pfu]) log [SXRs] ISXR N Lon RT D u s
E > 10 MeV 0.49 (284) 0.47 (146) 0.23 (149) 0.11 (262) 0.07 (279) 0.13 (280) 0.57 (158) 0.21 (158)
90% CI [0.42, 0.55] [0.37, 0.56] [0.11, 0.34] [0.02, 0.20] [−0.017, 0.16] [0.046, 0.22] [0.49, 0.65] [0.09, 0.32]
p-value <1 × 10–6 1.34 × 10–9 0.005 0.072 0.234 0.024 3.55 × 10–15 0.008
E > 30 MeV 0.47 (207) 0.49 (119) 0.25 (121) 0.22 (194) 0.05 (204) 0.09 (205) 0.51 (127) 0.09 (127)
90 %CI [0.39, 0.55] [0.38, 0.59] [0.12, 0.37] [0.12, 0.32] [−0.05, 0.15] [−0.009, 0.19] [0.40, 0.59] [−0.04, 0.22]
p-value 5.28 × 10–13 1.62 × 10−8 0.006 0.0017 0.46 0.18 1.33 × 10–9 0.30
E > 60 MeV 0.48 (157) 0.44 (88) 0.11 (89) 0.23 (147) 0.07 (155) 0.13 (157) 0.44 (93) −0.01 (93)
90% CI [0.39, 0.57] [0.30, 0.55] [−0.04, 0.27] [0.11, 0.34] [−0.05, 0.19] [0.017, 0.25] [0.30, 0.55] [−0.166, 0.15]
p-value 1.39 × 10–10 2.21 × 10–5 0.285 0.0045 0.39 0.09 1.63 × 10–5 0.90
E > 100 MeV 0.49 (118) 0.42 (64) 0.13 (64) 0.19 (112) 0.18 (116) 0.19 (118) 0.40 (62) −0.01 (62)
90% CI [0.38, 0.59] [0.25, 0.56] [−0.06, 0.30] [0.05, 0.32] [0.047, 0.31] [0.05, 0.31] [0.23, 0.55] [−0.20. 0.18]
p-value 1.77 × 10–8 <5 × 10–4 0.308 0.044 0.048 0.042 0.001 0.911
Fluence log10 ([cm–2 sr–1]) log[SXRs] ISXR N Lon RT D u s
E > 10 MeV 0.48 (284) 0.49 (146) 0.21 (149) 0.058 (262) 0.08 (279) 0.15 (280) 0.60 (158) 0.20 (158)
90% CI [0.41, 0.54] [0.39, 0.58] [0.09, 0.32] [−0.03, 0.15] [−0.007, 0.19] [0.06, 0.23] [0.52, 0.67] [0.089, 0.31]
p-value <1 × 10–6 2.72 × 10–10 0.008 0.347 0.177 0.014 <1 × 10–6 0.0096
E > 30 MeV 0.42 (207) 0.49 (119) 0.20 (121) 0.13 (194) 0.098 (204) 0.13 (205) 0.53 (127) 0.11 (127)
90% CI [0.33, 0.50] [0.37, 0.58] [0.06, 0.32] [0.027, 0.23] [−0.005, 0.20] [0.03, 0.23] [0.43, 0.62] [−0.021, 0.24]
p-value 2.72 × 10–10 2.27 × 10–8 0.03 0.065 0.163 0.059 1.52 × 10–10 0.217
E > 60 MeV 0.41 (157) 0.35 (88) 0.08 (89) 0.11 (147) 0.10 (155) 0.17 (157) 0.45 (93) 0.03 (93)
90% CI [0.31, 0.51] [0.21, 0.48] [−0.08, 0.23] [−0.01, 0.23] [−0.017, 0.22] [0.06, 0.29] [0.32, 0.56] [−0.13, 0.18]
p-value 6.74 × 10–8 <1 × 10–3 0.47 0.184 0.207 0.0288 6.7 × 10–6 0.80
E > 100 MeV 0.42 (118) 0.38 (64) 0.13 (64) 0.07 (112) 0.20 (116) 0.25 (118) 0.46 (62) 0.04 (62)
90% CI [0.30, 0.53] [0.20, 0.57] [−0.064, 0.30] [−0.07, 0.21] [0.06, 0.33] [0.11, 0.37] [0.30, 0.60] [−0.16, 0.22]
p-value 2.4 × 10–6 <1 × 10–3 0.333 0.449 0.03 0.007 <1 × 10–4 0.789

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