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We present deep ROSAT PSPC images of the radio lobes of the nearby galaxy Fornax~A (= NGC~1316). After removal of point sources, particle background and scattered solar X-rays, the X-ray emission closely mimics the radio emission. This result is discussed in terms of inverse Compton radiation, produced when cosmic microwave background photons are upscattered off synchrotron emitting electrons in the radio lobes. We compare the derived magnetic field in the lobes to that expected from equipartition arguments and also discuss the possibility of thermal Bremsstrahlung emission as a source of lobe X-rays. This observation constitutes the clearest detection of inverse Compton X-rays in radio lobes to date.
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