Data-driven Simulations of Magnetic Connectivity in Behind-the-Limb $\gamma$-ray Flares and Associated Coronal Mass Ejections

Recent detections of high-energy $\gamma$-rays by \emph{Fermi} from behind-the-limb (BTL) solar flares pose a puzzle on the particle acceleration/transport mechanisms in such events. Due to the large separation between the flare site and the location of $\gamma$-ray emission, it is suggested that the associated coronal mass ejections (CMEs) play an important role in accelerating and subsequently transporting particles back to the Sun to produce the observed $\gamma$-rays. We explore this scenario by simulating the CME associated with a BTL flare that occurred on 2014 September 1 about 40$\arcdeg$ behind the east solar limb. The flare was well observed by {\it Fermi}, {\it RHESSI}, {\it SDO}, and {\it STEREO}. \emph{Fermi}/LAT detected a substantial flux of $>$100 MeV $\gamma$-rays for more than an hour with an emission centroid located near the east limb but about 300$\arcsec$ north of the centroid of the \emph{RHESSI} HXR source. We utilize a data-driven global magnetohydrodynamics model (AWSoM: Alfv\'{e}n-wave Solar Model) and initiate the CME by the Gibson-Low flux rope to track the dynamic evolution of the global magnetic field during the event and investigate the magnetic connectivity between the CME/CME-driven shock and the \emph{Fermi}/LAT emission region. Moreover, we derive the time-varying shock parameters over the area that becomes magnetically connected to \emph{Fermi} $\gamma$-ray emission region on the visible solar disk. Our simulations show that the CME/CME-driven shock develops connections both to the flare region and the visible solar disk during the eruption, indicating that the CME's interaction with the global solar corona is critical for \emph{Fermi} BTL events and the associated long duration $\gamma$-ray emission.