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The motion of the electron-positron pair causes a Doppler shift on the energy of the annihilation radiation.
A year-long study with a GRO detector has for the first time mapped in detail the distribution of this emission along the plane of the galaxy To the astonishment of astronomers, it also recorded a broad distribution of the same annihilation radiation in a region some 3,000 light-years out from the disk of the Milky Way.
Matter falling onto such a compact object would produce low-energy gamma rays, which in turn would generate the positrons needed to produce the annihilation radiation.