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

Modelling the anisotropies in the cosmic infrared background (CIB) on all the scales is a challenging task because the nature of the galaxy evolution is complex and too many parameters are therefore often required to fit the observational data. 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 haloes to the star formation rate. Despite its relative simplicity, it is able to fit both the Planck and Herschel CIB power spectra and is consistent with the external constraints for the obscured star formation history derived from infrared deep surveys used as priors for the fit. Using this model, we find that the halo mass with the maximum efficiency for converting the accreted baryons into stars is log10Mmax = 12.94-0.02+0.02 M⊙, 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⋆(z)/Mb(z) is equal to 0.19 and 0.21 at redshift 0.1 and 2, respectively, which agrees well with the values obtained by previous studies. A CIB model is used for the first time to simultaneously fit Planck and Herschel CIB power spectra. The high angular resolution of Herschel allows us to reach very small scales, making it possible to constrain the shot noise and the one-halo term separately, which is difficult to do using the Planck data alone. However, we find that large angular scale Planck and Herschel data are not fully compatible with the small-scale Herschel data (for ℓ > 3000). The CIB is expected to be correlated with the thermal Sunyaev-Zel’dovich (tSZ) signal of 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 for calculating the CIB × tSZ cross correlation, which requires no additional parameter. To a certain extent, the CIB at high frequencies traces galaxies at low redshifts that reside in the clusters contributing to the tSZ, giving rise to the one-halo term of this correlation, while the two-halo term comes from the overlap in the redshift distribution of the tSZ clusters and CIB galaxies. The CIB × tSZ correlation is thus found to be higher when inferred with a combination of two widely spaced frequency channels (e.g. 143 × 857 GHz). We also find that even at ℓ ∼ 2000, the two-halo term of this correlation is still comparable to the one-halo term and has to be accounted for in the total cross-correlation. The CIB, tSZ, and CIB × tSZ act as foregrounds when the kinematic SZ (kSZ) power spectrum is measured from the cosmic microwave background power spectrum and need to be removed. Because of its simplistic nature and the low number of parameters, the halo model formalism presented here for these foregrounds is quite useful for such an analysis to measure the kSZ power spectrum accurately.

The information content of Cosmic Infrared Background anisotropies

We use analytic computations to predict the power spectrum as well as the bispectrum of Cosmic Infrared Background (CIB) anisotropies. Our approach is based on the halo model and takes into account the mean luminosity-mass relation. The model is used to forecast the possibility to simultaneously constrain cosmological, CIB and halo occupation distribution (HOD) parameters in the presence of foregrounds. For the analysis we use wavelengths in eight frequency channels between 200 and 900 GHz with survey specifications given by Planck and LiteBird. We explore the sensitivity to the model parameters up to multipoles of ℓ = 1000 using auto- and cross-correlations between the different frequency bands. With this setting, cosmological, HOD and CIB parameters can be constrained to a few percent. Galactic dust is modeled by a power law and the shot noise contribution as a frequency dependent amplitude which are marginalized over. We find that dust residuals in the CIB maps only marginally influence constraints on standard cosmological parameters. Furthermore, the bispectrum yields tighter constraints (by a factor four in 1σ errors) on almost all model parameters while the degeneracy directions are very similar to the ones of the power spectrum. The increase in sensitivity is most pronounced for the sum of the neutrino masses. Due to the similarity of degeneracies a combination of both analysis is not needed for most parameters. This, however, might be due to the simplified bias description generally adopted in such halo model approaches.

Have we seen all the galaxies that comprise the cosmic infrared background at 250 μm ≤λ ≤ 500 μm?

The cosmic infrared background (CIB) provides a fundamental observational constraint on the star-formation history of galaxies over cosmic history. We estimate the contribution to the CIB from catalogued galaxies in the COSMOS field by using a novel map fitting technique on the Herschel SPIRE maps. Prior galaxy positions are obtained using detections over a large range in wavelengths in the Ks–3 GHz range. Our method simultaneously fits the galaxies, the system foreground, and the leakage of flux from galaxies located in masked areas and corrects for an “over-fitting” effect not previously accounted for in stacking methods. We explore the contribution to the CIB as a function of galaxy survey wavelength and depth. We find high contributions to the CIB with the deep r (mAB ≤ 26.5), Ks (mAB ≤ 24.0) and 3.6 μm (mAB ≤ 25.5) catalogues. We combine these three deep catalogues and find a total CIB contributions of 10.5 ± 1.6, 6.7 ± 1.5 and 3.1 ± 0.7 nWm−2sr−1 at 250, 350 and 500 μm, respectively. Our CIB estimates are consistent with recent phenomenological models, prior based SPIRE number counts and with (though more precise than) the diffuse total measured by FIRAS. Our results raise the interesting prospect that the CIB contribution at λ ≤ 500 μm from known galaxies has converged. Future large-area surveys like those with the Large Synoptic Survey Telescope are therefore likely to resolve a substantial fraction of the population responsible for the CIB at 250 μm ≤λ ≤ 500 μm.