An analysis of data from the Fermi LAT on long time scales shows strong evidence that the flux of GeV gammas from Sgr A* has a significant component that varies with a period gtrsim4 yr. The flux varied about 15% over the 3-years of LAT observations. Orbits of over 100 stars in the innermost arcsecond of our Galaxy have been tracked around the massive black hole that resides there. Of these, the star S2 has the shortest orbital period 15.8 yr. This suggests that the GeV gamma flux is being modulated by accretion flow of matter accompanying the orbiting stars into the black hole.
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