Role of magnetic arcades in explaining the puzzle of the gamma-ray emission from the solar disk

The interpretation of gamma-ray emission originating from the solar disk ($0.5^\circ$ in angular size) as due to the interaction of Galactic Cosmic Rays (GCRs) with the solar atmosphere has remained a central challenge in solar physics. After the seminal work by Seckel, Stanev, and Gaisser (SSG91) based on GCRs magnetic mirroring, discrepancies between models and observations persist, indicating the need for a novel approach. The present work focuses on exploring the impact of a closed magnetic field geometry in the low photosphere on the observed gamma-ray flux. We track numerically with the PLUTO code the trajectories of test-particle protons within a static $\sim 20$ Mm scale height magnetic arcade adjacent to jets. By making use of numerical vertical density profiles we inject particles at distinct chromospheric/photospheric altitudes, mimicking the migration of GCRs from neighboring flux tubes into closed arcades. Remarkably, our model reproduces a flat gamma-ray spectrum below $\sim 33$ GeV, a nearly-isotropic emission at $\sim 10$ GeV, both consistent with Fermi-LAT observations, and a near-limb emission at $\sim 1$ TeV. Our model can also reproduce the flux-drop detected by HAWC ($\sim 1$ TeV). Finally, we argue that the spectral dip observed at $\sim$ 40 GeV may result from the flux suppression at low energy due to the cross-field diffusion, which would produce a cutoff. These findings underscore the pivotal role of closed magnetic field structures in shaping the solar disk gamma-ray emission.