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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 um 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 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 of the host galaxy (inferred from the observed 70 um luminosity after subtracting the estimated AGN contribution), particularly for more luminous AGNs (L_X > 10^43 erg/s). At the highest star formation rates (~ 1000 M_sun/yr), 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 star formation rate (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 star formation rate 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 star formation rates (> 300 M_sun/yr) than in systems with lower star formation rates (< 30 M_sun/yr). Lastly, we investigate the ratio between the supermassive black hole accretion rate and the growth rate of the host galaxy and find that, for sources with detected AGNs and star formation, 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.