(16 votes from 14 institutions)
We study the relationship between the X-ray luminosity and star formation rate (SFR) in an unbiased sample of dusty active galactic nuclei (AGNs), detected in both the hard X-ray and far-infrared (IR) bands in the XMM-LSS field. The sample consists of 451 AGNs with spectroscopic redshifts of 0.04 < z <3.3, and spans an X-ray luminosity range of L(2-10keV)=10^41-45 erg/s. We find a positive correlation between the X-ray luminosity and SFR derived from AGN-removed IR luminosity. We find that binning the sample by SFR instead of LX results in a more positive correlation. This is consistent with the scenario in which the shorter variability time scale of AGN than star formation flattens the observed correlation between AGN and star formation. We do not find significant diversity in the observed correlation when considering subsets selected based on supermassive black hole mass or Eddington ratio, indicating that AGN accretion has at most a limited effect on the SFR-Lx relation. Comparing to results in the literature, we propose a picture in which the correlation depends on sample composition. Additionally, we find a constant ratio between the SFR and the black hole accretion rate (BHAR) of log(SFR/BHAR)=(3.03+/-0.55). This value coincides with the ratio between galaxy bulge/total stellar mass and SMBH mass found in the local universe. Our results are consistent with the secular evolution scenario, in which dusty AGNs are coevolving with the host from the same gas supply at a constant rate regardless of accretion activity.