Identifying the subtle signatures of feedback from distant AGN using
  ALMA observations and the EAGLE hydrodynamical simulations
  We present sensitive 870$\mu$m continuum measurements from our ALMA
programmes of 114 X-ray selected AGN in the CDF-S and COSMOS fields. We use
these observations in combination with data from Spitzer and Herschel to
construct a sample of 86 X-ray selected AGN, 63 with ALMA constraints at
$z=1.5-3.2$ with stellar mass $>2\times10^{10}M_{\odot}$. We constructed
broad-band spectral energy distributions in the infrared band (8 - 1000$\mu$m)
and constrain star-formation rates (SFRs) uncontaminated by the AGN. Using a
hierarchical Bayesian method that takes into account the information from upper
limits, we fit SFR and specific SFR (sSFR) distributions. We explore these
distributions as a function of both X-ray luminosity and stellar mass. We
compare our measurements to two versions of the EAGLE hydrodynamical
simulations: the reference model with AGN feedback and the model without AGN.
We find good agreement between the observations and that predicted by the EAGLE
reference model for the modes and widths of the sSFR distributions as a
function of both X-ray luminosity and stellar mass; however, we found that the
EAGLE model without AGN feedback predicts a significantly narrower width when
compared to the data. Overall, from the combination of the observations with
the model predictions, we conclude that (1) even with AGN feedback, we expect
no strong relationship between the sSFR distribution parameters and
instantaneous AGN luminosity and (2) a signature of AGN feedback is a broad
distribution of sSFRs for all galaxies (not just those hosting an AGN) with
stellar masses above $\approx 10^{10}$M$_{\odot}$.
