In a Universe where AGN feedback regulates star formation in massive galaxies, a strong correlation between these two quantities is expected. If the gas causing star formation is also responsible for feeding the central black hole, then a positive correlation is expected. If powerful AGNs are responsible for the star formation quenching, then a negative correlation is expected. Observations so far have mainly found a mild correlation or no correlation at all (i.e. a flat relation between star formation rate (SFR) and AGN luminosity), raising questions about the whole paradigm of AGN feedback. In this paper, we report the predictions of the GALFORM semi-analytical model, which has a very strong coupling between AGN activity and quenching of star formation. The predicted SFR-AGN luminosity correlation appears negative in the low AGN luminosity regime, where AGN feedback acts, but becomes strongly positive in the regime of the brightest AGN. Our predictions reproduce reasonably well recent observations by Rosario et al., yet there is some discrepancy in the normalisation of the correlation at low luminosities and high redshifts. Though this regime could be strongly influenced by observational biases, we argue that the disagreement could be ascribed to the fact that GALFORM neglects AGN variability effects. Interestingly, the galaxies that dominate the regime where the observations imply a weak correlation are massive early-type galaxies that are subject to AGN feedback. Nevertheless, these galaxies retain high enough molecular hydrogen contents to maintain relatively high star formation rates and strong infrared emission.
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