| Summary: | The sustained gamma-ray emission (SGRE) from the Sun is a prolonged enhancement of >100 MeV gamma-ray emission that extends beyond the flare impulsive phase. The origin of the >300 MeV protons resulting in SGRE is debated, with both flares and shocks driven by coronal mass ejections (CMEs) being the suggested sites of proton acceleration. We compared the near-Sun acceleration and space speed of CMEs with “Prompt” and “Delayed” (SGRE) gamma-ray components. We found that “Delayed”-component-associated CMEs have higher initial accelerations and space speeds than “Prompt Only”-component-associated CMEs. We selected halo CMEs (HCMEs) associated with type II radio bursts (shock-driving HCMEs) and compared the average acceleration and space speed between HCME populations with or without SGRE events, major solar energetic particle (SEP) events, metric, or decameter-hectometric (DH) type II radio bursts. We found that the SGRE-producing HCMEs associated with a DH type II radio burst and/or a major SEP event have higher space speeds and especially initial accelerations than those without an SGRE event. We estimated the radial distances and speeds of the CME-driven shocks at the end time of the 2012 January 23 and March 7 SGRE events using white-light images of STEREO Heliospheric Imagers and radio dynamic spectra of Wind WAVES. The shocks were at the radial distances of 0.6–0.8 au and their speeds were high enough (≈975 km s ^−1 and ≈750 km s ^−1 , respectively) for high-energy particle acceleration. Therefore, we conclude that our findings support the CME-driven shock as the source of >300 MeV protons.
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