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We report the relationship between the luminosities of active galactic nuclei(AGNs) and the rates of star formation (SF) for a sample of 323 far-infrared(FIR)-detected AGNs. This sample has a redshift range of 0.2 $< z <$ 2.5, andspans three orders of magnitude in luminosity, ${\rm L_{X} \sim10^{42-45}}$erg$s^{-1}$. We find that in AGN hosts, the total IR luminosity(8-1000$\mu$m) has a significant AGN contribution (average$\sim$20%), and wesuggest using the FIR luminosity (30-1000 $\mu$m) as a more reliable starformation rate (SFR) estimator. We also conclude that monochromaticluminosities at 60 and 100\,$\mu$\,m are also good SFR indicators withnegligible AGN contributions, and are less sensitive than integrated infraredluminosities to the shape of the AGN SED, which is uncertain at$\lambda>$100\micron. Significant bivariate $L_{\rm X}$-$L_{\rm IR}$correlations are found, which remain significant in the combined sample whenusing residual partial correlation analysis to account for the inherentredshift dependence. No redshift or mass dependence is found for the ratiobetween SFR and black hole accretion rate (BHAR), which has a mean and scatterof log (SFR/BHAR) $=3.1 \pm$ 0.5, agreeing with the local mass ratio betweensupermassive black hole and host galaxies. The large scatter in this ratio andthe strong AGN-SF correlation found in these IR-bright AGNs are consistent withthe scenario of an AGN-SF dependence on a common gas supply, regardless of theevolutionary model.

Is there a relationship between AGN and star formation in IR-bright AGNs?