Simple halo model formalism for the cosmic infrared background and its correlation with the thermal Sunyaev Zel'dovich effect

Abstract

Modelling the anisotropies in the CIB on all the scales is a challenging task due to the complex nature of the galaxy evolution and thus often requires too many parameters in order to fit the observational data. In this paper, we present a new halo model for the anisotropies of the CIB using only four parameters. Our model connects the mass accretion on the dark matter halos to the star formation rate. Using this model, we find that the halo mass with the maximum efficiency for converting the accreted baryons into stars is $\log_{10}M_\mathrm{max} = {12.94}^{+0.02}_{-0.02} \: M_\odot$, consistent with other studies. Accounting for the mass loss through stellar evolution, we find, for an intermediate age galaxy, that the star formation efficiency defined as $M_\star(z)/M_b(z)$ is equal to 0.19 and 0.21 at redshift 0.1 and 2 respectively, in good agreement with the values obtained by previous studies. It is the first time that a CIB model is used to fit Planck and Herschel CIB power spectra simultaneously. However we find that the large angular scale Planck and Herschel data are not fully compatible with the small scale Herschel data (for $\ell>3000$). The CIB is expected to be correlated with the tSZ signal of the galaxy clusters. Using this halo model for the CIB, and a halo model for the tSZ with a single parameter, we also provide a consistent framework to calculate this cross-correlation, which requires no extra parameter. The CIB$\times$tSZ correlation is found to be higher when inferred with a combination of two widely spaced frequency channels (e.g. 143x857 GHz). The CIB, tSZ, and CIB$\times$tSZ act as foregrounds while measuring the kSZ power spectrum from the CMB power spectrum and need to be removed. Due to its simplistic nature and low number of parameters, the halo model formalism presented here is quite useful for such an analysis to measure the kSZ power spectrum accurately.