We perform spatial and spectral analyses of the LMC gamma-ray emission collected over 66 months by the Fermi Gamma-ray Space Telescope .
In our spatial analysis , we model the LMC cosmic-ray distribution and gamma-ray production using observed maps of the LMC interstellar medium , star formation history , interstellar radiation field , and synchrotron emission .
We use bootstrapping of the data to quantify the robustness of spatial model performance .
We model the LMC gamma-ray spectrum using fitting functions derived from the physics of \pi ^ { 0 } decay , bremsstrahlung , and inverse Compton scattering .
We find the integrated gamma-ray flux of the LMC from 200 MeV to 20 GeV to be 1.37 \pm 0.02 \times 10 ^ { -7 } ph cm ^ { -2 } s ^ { -1 } , of which we attribute about 6 % to inverse Compton scattering and 44 % to bremsstrahlung .
From our work , we conclude that the spectral index of the LMC cosmic-ray proton population is 2.4 \pm 0.2 , and we find that cosmic-ray energy loss through gamma-ray production is concentrated within a few 100 pc of acceleration sites .
Assuming cosmic-ray energy equipartition with magnetic fields , we estimate LMC cosmic rays encounter an average magnetic field strength \sim 3 \mu G .