  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, 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 (Ajello et al. 2021). We found that
'Delayed'-component-associated CMEs have higher initial acceleration and space
speed 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 distance and speed of the
CME-driven shocks at the end time of the 2012 January 23 and March 07 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.
