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The sustained gamma-ray emission (SGRE) from the Sun is a prolongedenhancement of >100 MeV gamma-ray emission that extends beyond the flareimpulsive phase.The origin of the >300 MeV protons resulting in SGRE isdebated, both flares and shocks driven by coronal mass ejections (CMEs) beingthe suggested sites of proton acceleration. We compared the near-Sunacceleration 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 spacespeed than 'Prompt-only'-component-associated CMEs. We selected halo CMEs(HCMEs) associated with type II radio bursts (shock-driving HCMEs) and comparedthe average acceleration and space speed between HCME populations with orwithout SGRE events, major solar energetic particle (SEP) events, metric, ordecameter-hectometric (DH) type II radio bursts. We found that theSGRE-producing HCMEs associated with a DH type II radio burst and/or a majorSEP event have higher space speeds and especially initial accelerations thanthose without an SGRE event. We estimated the radial distance and speed of theCME-driven shocks at the end time of the 2012 January 23 and March 07 SGREevents using white-light images of STEREO Heliospheric Imagers and radiodynamic spectra of Wind WAVES. The shocks were at the radial distances of0.6-0.8 au and their speeds were high enough (~975 km s$^{-1}$ and ~750 kms$^{-1}$, respectively) for high-energy particle acceleration. Therefore, weconclude that our findings support the CME-driven shock as the source of >300MeV protons.

Speed and Acceleration of CMEs Associated with Sustained Gamma-Ray Emission Events Observed by Fermi/LAT