We explore the question of whether low and moderate luminosity active galactic nuclei (AGNs) are preferentially found in galaxies that are undergoing a transition from active star formation (SF) to quiescence. This notion has been suggested by studies of the UV-optical colors of AGN hosts, which find them to be common among galaxies in the so-called Green Valley, a region of galaxy color space believed to be composed mostly of galaxies undergoing SF quenching. Combining the deepest current X-ray and Herschel/PACS far-infrared (FIR) observations of the two Chandra Deep Fields with redshifts, stellar masses, and rest-frame photometry derived from the extensive and uniform multi-wavelength data in these fields, we compare the rest-frame U – V color distributions and star formation rate distributions of AGNs and carefully constructed samples of inactive control galaxies. The UV-to-optical colors of AGNs are consistent with equally massive inactive galaxies at redshifts out to z ~ 2, but we show that such colors are poor tracers of SF. While the FIR distributions of both star-forming AGNs and star-forming inactive galaxies are statistically similar, we show that AGNs are preferentially found in star-forming host galaxies, or, in other words, AGNs are less likely to be found in weakly star-forming or quenched galaxies. We postulate that, among X-ray-selected AGNs of low and moderate accretion luminosities, the supply of cold gas primarily determines the accretion rate distribution of the nuclear black holes.
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