  It has recently been shown that the spatially and temporally extended
gamma-ray emission in solar eruptions are caused by greater than 300 MeV
protons precipitating on the Sun from shocks driven by coronal mass ejections
(CMEs). The gamma-rays result from the decay of neutral pions produced in the
proton-proton interaction when the greater than 300 MeV protons collide with
those in the chromosphere. The evidence comes from the close correlation
between the durations of the sustained gamma-ray emission (SGRE) and the
associated interplanetary (IP) type II radio bursts. In this paper, we provide
further evidence that support the idea that protons accelerated in IP shocks
driven by CMEs propagate toward the Sun, precipitate in the chromosphere to
produce the observed SGRE. We present the statistical properties of the SGRE
events and the associated CMEs, flares, and type II radio bursts. It is found
that the SGRE CMEs are similar to those associated with ground level
enhancement events. The CME speed is well correlated with the SGRE fluence.
High CME speed is an important requirement for the occurrence of SGRE, while
the flare size is not. Based on these results, we present a schematic model
illustrating the spatially and temporally extended nature of SGRE related to
the CME flux rope-shock structure.

Solar and Stellar Astrophysics;High Energy Astrophysical Phenomena