Modelling the correlation between the thermal Sunyaev Zel'dovich effect and the cosmic infrared background

We show how the correlation between the thermal Sunyaev Zel'dovich effect (tSZ) from galaxy clusters and dust emission from cosmic infrared background (CIB) sources can be calculated in a halo model framework. Using recent tSZ and CIB models, we find that the size of the tSZ x CIB cross-correlation is approximately 20 per cent at 150 GHz. The contribution to the total angular power spectrum is of order -2 \mu K^2 at ell=3000, however, this value is uncertain by a factor of two to three, primarily because of CIB source modelling uncertainties. We expect the large uncertainty in this component to degrade upper limits on the kinematic Sunyaev Zel'dovich effect (kSZ), due to similarity in the frequency dependence of the tSZ x CIB and kSZ across the frequency range probed by current Cosmic Microwave Background missions. We also find that the degree of tSZ x CIB correlation is higher for mm x sub-mm spectra than mm x mm, because more of the sub-mm CIB originates at lower redshifts (z<2), where most tSZ clusters are found.