Abstract Major solar eruptions (flares, coronal mass ejections (CMEs) and solar energetic particles (SEPs)) strongly influence geospace and space weather. Currently, the mechanism of their influence on space weather is not well understood and requires a detailed study of the energetic relationship among these eruptive phenomena. From this perspective, we investigate 30 flares (observed by RHESSI), followed by weak to strong geomagnetic storms. Spectral analysis of these flares suggests a new power-law relationship (r ~ 0.79) between the hard X-ray (HXR) spectral index (before flare-peak) and linear speed of the associated CME observed by LASCO/SOHO. For 12 flares which were followed by SEP enhancement near Earth, HXR and SEP spectral analysis reveals a new scaling law (r ~ 0.9) between the hardest X-ray flare spectrum and the hardest SEP spectrum. Furthermore, a strong correlation is obtained between the linear speed of the CME and the hardest spectrum of the corresponding SEP event (r ~ 0.96). We propose that the potentially geoeffective flare and associated CME and SEP are well-connected through a possible feedback mechanism, and should be regarded within the framework of a solar eruption. Owing to their space weather effects, these new results will help improve our current understanding of the Sun-Earth relationship, which is a major goal of research programs in heliophysics.

Keywords Sun: coronal mass ejections (CMEs) — Sun: flares — Sun: particle emission — Sun: solar-terrestrial relations — Sun: X-rays

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