We use a suite of hydrodynamical simulations of galaxy mergers to compare star formation rate (SFR) and black hole accretion rate (BHAR) for galaxies before the interaction (stochastic phase), during the `merger proper, lasting ~0.2-0.3 Gyr, and in the `remnant phase. We calculate the bi-variate distribution of SFR and BHAR and define the regions in the SFR-BHAR plane that the three phases occupy. No strong correlation between BHAR and galaxy-wide SFR is found. A possible exception are galaxies with the highest SFR and the highest BHAR. We also bin the data in the same way used in several observational studies, by either measuring the mean SFR for AGN in different luminosity bins, or the mean BHAR for galaxies in bins of SFR. We find that the apparent contradiction or SFR versus BHAR for observed samples of AGN and star forming galaxies is actually caused by binning effects. The two types of samples use different projections of the full bi-variate distribution, and the full information would lead to unambiguous interpretation. We also find that a galaxy can be classified as AGN-dominated up to 1.5 Gyr after the merger-driven starburst took place. Our study is consistent with the suggestion that most low-luminosity AGN hosts do not show morphological disturbances.
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