Revisiting empirical solar energetic particle scaling relations - II. Coronal mass ejections

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Table B.1.

Upper limit peak proton fluxes (I_P, [pfu]) and fluences (F_P, [cm⁻²]) for the SEP event on AD774/775 and GLE05 derived in this work, for each integral proton energy.

	V_CME, upper \| Eq.(1)		V_CME, upper \| Eq.(6)		V_CME \| Eq.(5)

	AD774/775	GLE05	AD774/775	GLE05	AD774/775	GLE05
Integral
Energy	Peak Proton Flux - I_P	Peak Proton Flux - I_P	Peak Proton Flux - I_P
(MeV)	(pfu)	(pfu)	(pfu)	(pfu)	(pfu)	(pfu)

E>10	2.26E+07 $_{1.27 E + 07}^{3.17 E + 07}$ $_{1.27\rm E+07}^{3.17\rm E+07}$	2.47E+06 $_{1.39 E + 06}^{3.46 E + 06}$ $_{1.39\rm E+06}^{3.46\rm E+06}$	6.16E+06 $_{4.01 E + 06}^{7.92 E + 06}$ $_{4.01\rm E+06}^{7.92\rm E+06}$	1.18E+06 $_{7.71 E + 05}^{1.52 E + 06}$ $_{7.71\rm E+05}^{1.52\rm E+06}$	6.23E+05 $_{3.60 E + 05}^{8.58 E + 05}$ $_{3.60\rm E+05}^{8.58\rm E+05}$	7.63E+04 $_{4.41 E + 04}^{1.05 E + 05}$ $_{4.41\rm E+04}^{1.05\rm E+05}$
E>30	7.16E+06 $_{4.02 E + 06}^{1.00 E + 07}$ $_{4.02\rm E+06}^{1.00\rm E+07}$	7.80E+05 $_{4.38 E + 05}^{1.09 E + 06}$ $_{4.38\rm E+05}^{1.09\rm E+06}$	1.95E+06 $_{1.27 E + 06}^{2.50 E + 06}$ $_{1.27\rm E+06}^{2.50\rm E+06}$	3.75E+05 $_{2.44 E + 05}^{4.82 E + 05}$ $_{2.44\rm E+05}^{4.82\rm E+05}$	1.97E+05 $_{1.14 E + 05}^{2.71 E + 05}$ $_{1.14\rm E+05}^{2.71\rm E+05}$	2.41E+04 $_{1.40 E + 04}^{3.32 E + 04}$ $_{1.40\rm E+04}^{3.32\rm E+04}$
E>60	1.84E+06 $_{1.03 E + 06}^{2.58 E + 06}$ $_{1.03\rm E+06}^{2.58\rm E+06}$	2.01E+05 $_{1.13 E + 05}^{2.81 E + 05}$ $_{1.13\rm E+05}^{2.81\rm E+05}$	5.01E+05 $_{3.26 E + 05}^{6.44 E + 05}$ $_{3.26\rm E+05}^{6.44\rm E+05}$	9.63E+04 $_{6.27 E + 04}^{1.24 E + 05}$ $_{6.27\rm E+04}^{1.24\rm E+05}$	5.06E+04 $_{2.93 E + 04}^{6.98 E + 04}$ $_{2.93\rm E+04}^{6.98\rm E+04}$	6.20E+03 $_{3.59 E + 03}^{8.54 E + 03}$ $_{3.59\rm E+03}^{8.54\rm E+03}$
E>100	5.69E+05 $_{3.19 E + 05}^{7.97 E + 05}$ $_{3.19\rm E+05}^{7.97\rm E+05}$	6.20E+04 $_{3.48 E + 04}^{8.69 E + 04}$ $_{3.48\rm E+04}^{8.69\rm E+04}$	1.55E+05 $_{1.01 E + 05}^{1.99 E + 05}$ $_{1.01\rm E+05}^{1.99\rm E+05}$	2.98E+04 $_{1.94 E + 04}^{3.83 E + 04}$ $_{1.94\rm E+04}^{3.83\rm E+04}$	1.57E+04 $_{9.05 E + 03}^{2.16 E + 04}$ $_{9.05\rm E+03}^{2.16\rm E+04}$	1.92E+03 $_{1.11 E + 03}^{2.64 E + 03}$ $_{1.11\rm E+03}^{2.64\rm E+03}$

Integral
Energy	Fluence - F_P	Fluence - F_P	Fluence - F_P
(MeV)	(cm⁻²)	(cm⁻²)	(cm⁻²)	(cm⁻²)	(cm⁻²)	(cm⁻²)

E>10	6.18E+13 $_{3.22 E + 13}^{9.05 E + 13}$ $_{3.22\rm E+13}^{9.05\rm E+13}$	5.05E+12 $_{2.63 E + 12}^{7.40 E + 12}$ $_{2.63\rm E+12}^{7.40\rm E+12}$	1.42E+13 $_{8.73 E + 12}^{1.89 E + 13}$ $_{8.73\rm E+12}^{1.89\rm E+13}$	2.20E+12 $_{1.36 E + 12}^{2.93 E + 12}$ $_{1.36\rm E+12}^{2.93\rm E+12}$	1.07E+12 $_{5.74 E + 11}^{1.53 E + 12}$ $_{5.74\rm E+11}^{1.53\rm E+12}$	9.93E+10 $_{5.35 E + 10}^{1.43 E + 11}$ $_{5.35\rm E+10}^{1.43\rm E+11}$
E>30	1.37E+13 $_{7.18 E + 12}^{2.00 E + 13}$ $_{7.18\rm E+12}^{2.00\rm E+13}$	1.15E+12 $_{6.00 E + 11}^{1.67 E + 12}$ $_{6.00\rm E+11}^{1.67\rm E+12}$	3.19E+12 $_{1.97 E + 12}^{4.23 E + 12}$ $_{1.97\rm E+12}^{4.23\rm E+12}$	5.04E+11 $_{3.11 E + 11}^{6.68 E + 11}$ $_{3.11\rm E+11}^{6.68\rm E+11}$	2.45E+11 $_{1.33 E + 11}^{3.51 E + 11}$ $_{1.33\rm E+11}^{3.51\rm E+11}$	2.34E+10 $_{1.26 E + 10}^{3.34 E + 10}$ $_{1.26\rm E+10}^{3.34\rm E+10}$
E>60	1.89E+12 $_{1.01 E + 12}^{2.72 E + 12}$ $_{1.01\rm E+12}^{2.72\rm E+12}$	1.72E+11 $_{9.24 E + 10}^{2.48 E + 11}$ $_{9.24\rm E+10}^{2.48\rm E+11}$	4.63E+11 $_{2.91 E + 11}^{6.07 E + 11}$ $_{2.91\rm E+11}^{6.07\rm E+11}$	7.80E+10 $_{4.91 E + 10}^{1.02 E + 11}$ $_{4.91\rm E+10}^{1.02\rm E+11}$	3.90E+10 $_{2.16 E + 10}^{5.51 E + 10}$ $_{2.16\rm E+10}^{5.51\rm E+10}$	4.03E+09 $_{2.23 E + 09}^{5.70 E + 09}$ $_{2.23\rm E+09}^{5.70\rm E+09}$
E>100	2.93E+11 $_{1.62 E + 11}^{4.15 E + 11}$ $_{1.62\rm E+11}^{4.15\rm E+11}$	2.99E+10 $_{1.65 E + 10}^{4.24 E + 10}$ $_{1.65\rm E+10}^{4.24\rm E+10}$	7.68E+10 $_{4.93 E + 10}^{9.95 E + 10}$ $_{4.93\rm E+10}^{9.95\rm E+10}$	1.41E+10 $_{9.03 E + 09}^{1.82 E + 10}$ $_{9.03\rm E+09}^{1.82\rm E+10}$	7.25E+09 $_{4.13 E + 09}^{1.01 E + 10}$ $_{4.13\rm E+09}^{1.01\rm E+10}$	8.83E+08 $_{4.74 E + 08}^{1.16 E + 09}$ $_{4.74\rm E+08}^{1.16\rm E+09}$

Notes. Peak proton fluxes were calculated via the $I_{P} \propto V_{CME}^{5}$ $I_{P} \propto V_{CME}^{5}$ relations (provided in Figs. 1 & A.1) and Fluence via Eq. 7 for a given V_CME, upper. The upper and lower limits included in the Table are driven by the V_CME range of the associated solar flare per event. The second and third columns provide outputs based on V_CME, upper from Eq. (1). The fourth and fifth columns provide the same results based on V_CME, upper from Eq. (6) and the sixth and seventh columns provide the same results based on V_CME from Eq. (5).

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