Dissecting the $\gamma$-ray emissions of the nearby galaxies NGC 1068 and NGC 253

Intrigued by recent high-energy study results for nearby galaxies with gamma-ray emission and in particular NGC~1068 that has been detected as a neutrino-emitting source by the IceCube Neutrino Observatory, we conduct detailed analysis of the $\gamma$-ray data for the galaxies NGC~1068 and NGC~253, obtained with the Large Area Telescope onboard {\it the Fermi Gamma-ray Space Telescope}. By checking for their possible spectral features and then constructing light curves in corresponding energy ranges, we identify flare-like activity from NGC ~1068 in $\geq$2\,GeV energy range and significant long-term variations of NGC~253 in $\geq$5\,GeV energy range. In the former, the emission appears harder in the two half-year flare-like events than that in the otherwise `quiescent' state. In the latter, there is a 2-times decrease in the flux before and after MJD~57023, which is clearly revealed by the test-statistic maps we obtain. Considering studies carried out and models proposed for the $\gamma$-ray emissions of the two sources, we discuss the implications of our findings. The jet in NGC~1068 may contribute to the \gr\ emission. The nature of the long-term variations in NGC~253 is not clear, but the variation part of the emission may be connected to the very-high-energy (VHE) emission of the galaxy and could be verified by VHE observations.