AGN vs. host galaxy properties in the COSMOS field
  The coeval AGN and galaxy evolution and the observed local relations between
SMBHs and galaxy properties suggest some connection or feedback between SMBH
growth and galaxy build-up. We looked for correlations between properties of
X-ray detected AGN and their FIR detected host galaxies, to find quantitative
evidences for this connection, highly debated in the latest years. We exploit
the rich multi-wavelength data set available in the COSMOS field for a large
sample (692 sources) of AGN and their hosts, in the redshift range $0.1<z<4$.
We use X-ray data to select AGN and determine their properties (intrinsic
luminosity and nuclear obscuration), and broad-band SED fitting to derive host
galaxy properties (stellar mass $M_*$ and star formation rate SFR). We find
that the AGN 2-10 keV luminosity ($L_{\rm X}$) and the host $8-1000~\mu m$ star
formation luminosity ($L_{\rm IR}^{\rm SF}$) are significantly correlated.
However, the average host $L_{\rm IR}^{\rm SF}$ has a flat distribution in bins
of AGN $L_{\rm X}$, while the average AGN $L_{\rm X}$ increases in bins of host
$L_{\rm IR}^{\rm SF}$, with logarithmic slope of $\sim0.7$, in the redshifts
range $0.4<z<1.2$. We also discuss the comparison between the distribution of
these two quantities and the predictions from hydro-dynamical simulations.
Finally we find that the average column density ($N_H$) shows a positive
correlation with the host $M_*$, at all redshifts, but not with the SFR (or
$L_{\rm IR}^{\rm SF}$). This translates into a negative correlation with
specific SFR. Our results are in agreement with the idea that BH accretion and
SF rates are correlated, but occur with different variability time scales. The
presence of a positive correlation between $N_H$ and host $M_*$ suggests that
the X-ray $N_H$ is not entirely due to the circum-nuclear obscuring torus, but
may also include a contribution from the host galaxy.
