Supermassive Black Hole Growth in Starburst Galaxies over Cosmic Time: Constraints from the Deepest Chandra Fields

We present an analysis of deep multiwavelength data for z 0.3-3 starburst galaxies selected by their 70 Delta *mm emission in the Extended-Chandra Deep Field-South and Extended Groth Strip. We identify active galactic nuclei (AGNs) in these infrared sources through their X-ray emission and quantify the fraction that host an AGN. We find that the fraction depends strongly on both the mid-infrared color and rest-frame mid-infrared luminosity of the source, rising to ~50%-70% at the warmest colors (F 24 Delta *mm/F 70 Delta *mm 0.2) and highest mid-infrared luminosities (corresponding to ultraluminous infrared galaxies), similar to the trends found locally. Additionally, we find that the AGN fraction depends strongly on the star formation rate (SFR) of the host galaxy (inferred from the observed-frame 70 Delta *mm luminosity after subtracting the estimated AGN contribution), particularly for more luminous AGNs (L 0.5 -- 8.0keV 1043 erg s--1). At the highest SFRs (~1000 M yr--1), the fraction of galaxies with an X-ray detected AGN rises to 30%, roughly consistent with that found in high-redshift submillimeter galaxies. Assuming that the AGN fraction is driven by the SFR (rather than stellar mass or redshift, for which our sample is largely degenerate), this result implies that the duty cycle of luminous AGN activity increases with the SFR of the host galaxy: specifically, we find that luminous X-ray detected AGNs are at least ~5-10 times more common in systems with high SFRs ( 300 M yr--1) than in systems with lower SFRs ( 30 M yr--1). Lastly, we investigate the ratio between the supermassive black hole accretion rate (inferred from the AGN X-ray luminosity) and the bulge growth rate of the host galaxy (approximated as the SFR) and find that, for sources with detected AGNs and star formation (and neglecting systems with low star formation rates to which our data are insensitive), this ratio in distant starbursts agrees well with that expected from the local scaling relation assuming the black holes and bulges grew at the same epoch. These results imply that black holes and bulges grow together during periods of vigorous star formation and AGN activity.