In order to discuss the potential impact of solar ’ superflares ’ on space weather , we investigated statistical relations among energetic proton peak flux with energy higher than 10 MeV ( F _ { p } ) , CME speed near the Sun ( V _ { CME } ) obtained by SOHO /LASCO coronagraph and flare soft X-ray peak flux in 1-8Åband ( F _ { SXR } ) during 110 major solar proton events ( SPEs ) recorded from 1996 to 2014 .
The linear regression fit results in the scaling relations V _ { CME } \propto F _ { SXR } ^ { \alpha } , F _ { p } \propto F _ { SXR } ^ { \beta } and F _ { p } \propto V _ { CME } ^ { \gamma } with \alpha = 0.30 \pm 0.04 , \beta = 1.19 \pm 0.08 and \gamma = 4.35 \pm 0.50 , respectively .
On the basis of simple physical assumptions , on the other hand , we derive scaling relations expressing CME mass ( M _ { CME } ) , CME speed and energetic proton flux in terms of total flare energy ( E _ { flare } ) as , M _ { CME } \propto E _ { flare } ^ { 2 / 3 } , V _ { CME } \propto E _ { flare } ^ { 1 / 6 } and F _ { p } \propto E _ { flare } ^ { 5 / 6 } \propto V _ { CME } ^ { 5 } , respectively .
We then combine the derived scaling relations with observation , and estimated the upper limit of V _ { CME } and F _ { p } to be associated with possible solar superflares .