We present evidence that the incidence of active galactic nuclei (AGNs) and the distribution of their accretion rates do not depend on the stellar masses of their host galaxies, contrary to previous studies. We use hard (2-10 keV) X-ray data from three extragalactic fields (XMM-LSS, COSMOS and ELAIS-S1) with redshifts from the Prism Multi-object Survey to identify 242 AGNs with L_{2-10 keV}=10^{42-44} erg /s within a parent sample of ~25,000 galaxies at 0.2<z<1.0 over ~3.4 deg^2 and to i~23. We find that although the fraction of galaxies hosting an AGN at fixed X-ray luminosity rises strongly with stellar mass, the distribution of X-ray luminosities is independent of mass. Furthermore, we show that the probability that a galaxy will host an AGN can be defined by a universal Eddington ratio distribution that is independent of the host galaxy stellar mass and has a power-law shape with slope -0.65. These results demonstrate that AGNs are prevalent at all stellar masses in the range 9.5<log M_*/M_sun<12 and that the same physical processes regulate AGN activity in all galaxies in this stellar mass range. While a higher AGN fraction may be observed in massive galaxies, this is a selection effect related to the underlying Eddington ratio distribution. We also find that the AGN fraction drops rapidly between z~1 and the present day and is moderately enhanced (factor~2) in galaxies with blue or green optical colors. Consequently, while AGN activity and star formation appear to be globally correlated, we do not find evidence that the presence of an AGN is related to the quenching of star formation or the color transformation of galaxies.
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