We present an analysis of deep multiwavelength data for z \approx 0.3 –3 starburst galaxies selected by their 70 \mu m 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 \sim 50 –70 % at the warmest colors ( F _ { 24 \mu m } / F _ { 70 \mu m } \lesssim 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 of the host galaxy ( inferred from the observed-frame 70 \mu m luminosity after subtracting the estimated AGN contribution ) , particularly for more luminous AGNs ( L _ { 0.5 - 8.0 { ~ { } keV } } \gtrsim 10 ^ { 43 } erg s ^ { -1 } ) .
At the highest star formation rates ( \sim 1000 M _ { \odot } yr ^ { -1 } ) , the fraction of galaxies with an X-ray detected AGN rises to \approx 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 \sim 5 –10 times more common in systems with high star formation rates ( \gtrsim 300 M _ { \odot } yr ^ { -1 } ) than in systems with lower star formation rates ( \lesssim 30 M _ { \odot } 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 star formation rate ) 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 .