We report on a detailed investigation of the high-energy γ-ray emission from NGC 1275, a well-known radio galaxy hosted by a giant elliptical located at the center of the nearby Perseus cluster. With the increased photon statistics, the center of the γ-ray-emitting region is now measured to be separated by only 0.46 arcmin from the nucleus of NGC 1275, well within the 95% confidence error circle with radius ≃1.5 arcmin. Early Fermi Large Area Telescope (LAT) observations revealed a significant decade-timescale brightening of NGC 1275 at GeV photon energies, with a flux about 7 times higher than the one implied by the upper limit from previous EGRET observations. With the accumulation of one year of Fermi-LAT all-sky-survey exposure, we now detect flux and spectral variations of this source on month timescales, as reported in this paper. The average >100 MeV γ-ray spectrum of NGC 1275 shows a possible deviation from a simple power-law shape, indicating a spectral cutoff around an observed photon energy of εγ = 42.2 19.6 GeV, with an average flux of F γ = (2.31 0.13) × 10 -7 photons cm-2 s-1 and a power-law photon index, Γγ = 2.13 0.02. The largest γ-ray flaring event was observed in 2009 April-May and was accompanied by significant spectral variability above εγ ≳ 1-2 GeV. The γ-ray activity of NGC 1275 during this flare can be described by a hysteresis behavior in the flux versus photon index plane. The highest energy photon associated with the γ-ray source was detected at the very end of the observation, with the observed energy of εγ = 67.4 GeV and an angular separation of about 2.4 arcmin from the nucleus. In this paper we present the details of the Fermi-LAT data analysis, and briefly discuss the implications of the observed γ-ray spectral evolution of NGC 1275 in the context of γ-ray blazar sources in general.
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