Constraints on AGN feedback from its Sunyaev-Zel'dovich imprint on the
  cosmic background radiation
  We derive constraints on feedback by active galactic nuclei (AGN) by setting
limits on their thermal Sunyaev-Zel'dovich (SZ) imprint on the cosmic microwave
background (CMB). The amplitude of any SZ signature is small and degenerate
with the poorly known sub-mm spectral energy distribution of the AGN host
galaxy and other unresolved dusty sources along the line of sight. Here we
break this degeneracy by combining microwave and sub-mm data from Planck with
all-sky far-infrared maps from the AKARI satellite. We first test our
measurement pipeline using the Sloan Digital Sky Survey (SDSS) redMaPPer
catalogue of galaxy clusters, finding a highly significant detection
($>$$20\sigma$) of the SZ effect together with correlated dust emission. We
then constrain the SZ signal associated with spectroscopically confirmed
quasi-stellar objects (QSOs) from SDSS data release 7 (DR7) and the Baryon
Oscillation Spectroscopic Survey (BOSS) DR12. We obtain a low-significance
($1.6\sigma$) hint of an SZ signal, pointing towards a mean thermal energy of
$\simeq 5 \times 10^{60}$ erg, lower than reported in some previous studies. A
comparison of our results with high-resolution hydrodynamical simulations
including AGN feedback suggests QSO host masses of $M_{200c} \sim 4 \times
10^{12}~h^{-1}M_\odot$, but with a large uncertainty. Our analysis provides no
conclusive evidence for an SZ signal specifically associated with AGN feedback.
