Scaling Relations in Coronal Mass Ejections and Energetic Proton Events associated with Solar Superflares

Takuya Takahashi, Yoshiyuki Mizuno, Kazunari Shibata

Published 2016-11-18Version 1

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 \rm MeV$ ($F_p$), CME speed near the Sun ($V_{CME}$) obtained by {\it SOHO}/LASCO coronagraph and flare soft X-ray peak flux in 1-8\AA band ($F_{SXR}$) 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.