The Fermi Large Area Telescope (LAT) detected gamma-rays up to 4 GeV from two bright X-class solar flares on 2012 March 7, showing both an impulsive and temporally extended emission phases. The gamma-rays appear to originate from the same active region as the X-rays associated with these flares. The >100 MeV gamma-ray flux decreases monotonically during the first hour (impulsive phase) followed by a slower decrease for the next 20 hr. A power law with a high-energy exponential cutoff can adequately describe the photon spectrum. Assuming that the gamma rays result from the decay of pions produced by accelerated protons and ions with a power-law spectrum, we find that the index of that spectrum is ~3, with minor variations during the impulsive phase. During the extended phase the photon spectrum softens monotonically, requiring the proton index varying from ~4 to >5. The >30 MeV proton flux observed by the GOES satellites also shows a flux decrease and spectral softening, but with a harder spectrum (index ~2-3). Based on these observations, we explore the relative merits of prompt or continuous acceleration scenarios, hadronic or leptonic emission processes, and acceleration at the solar corona or by the fast coronal mass ejections. We conclude that the most likely scenario is continuous acceleration of protons in the solar corona that penetrate the lower solar atmosphere and produce pions that decay into gamma rays. However, acceleration in the downstream of the shock cannot be definitely ruled out.
