Planck 2015 results. XXIII. The thermal Sunyaev-Zeldovich effect--cosmic
  infrared background correlation
  We use Planck data to detect the cross-correlation between the thermal
Sunyaev-Zeldovich (tSZ) effect and the infrared emission from the galaxies that
make up the the cosmic infrared background (CIB). We first perform a stacking
analysis towards Planck-confirmed galaxy clusters. We detect infrared emission
produced by dusty galaxies inside these clusters and demonstrate that the
infrared emission is about 50% more extended than the tSZ effect. Modelling the
emission with a Navarro--Frenk--White profile, we find that the radial profile
concentration parameter is $c_{500} = 1.00^{+0.18}_{-0.15}$. This indicates
that infrared galaxies in the outskirts of clusters have higher infrared flux
than cluster-core galaxies. We also study the cross-correlation between tSZ and
CIB anisotropies, following three alternative approaches based on power
spectrum analyses: (i) using a catalogue of confirmed clusters detected in
Planck data; (ii) using an all-sky tSZ map built from Planck frequency maps;
and (iii) using cross-spectra between Planck frequency maps. With the three
different methods, we detect the tSZ-CIB cross-power spectrum at significance
levels of (i) 6 $\sigma$, (ii) 3 $\sigma$, and (iii) 4 $\sigma$. We model the
tSZ-CIB cross-correlation signature and compare predictions with the
measurements. The amplitude of the cross-correlation relative to the fiducial
model is $A_{\rm tSZ-CIB}= 1.2\pm0.3$. This result is consistent with
predictions for the tSZ-CIB cross-correlation assuming the best-fit
cosmological model from Planck 2015 results along with the tSZ and CIB scaling
relations.
