Sunyaev-Zel'dovich fluctuations in the cold dark matter scenario

Abstract

We calculate, in the context of the cold dark matter cosmology, the ΔT/T fluctuations induced in the microwave background radiation by the hot gas confined by the dark matter potential wells via the Sunyaev–Zel'dovich effect. We show that the fluctuations should be dominated by the rare massive clusters at moderate redshifts, and this motivates our simple modelling in which the form of the model clusters are chosen to mimic real clusters, but the evolution of the cluster population derives from the theory. The clusters produce a characteristic non-Gaussian field, with ($$(\Delta T/T)_\text{rms}\sim10^{-5}$$ for an angular scale of around a few arcminutes. The amplitude of $$(\Delta T/T)_\text{rms}$$ depends sensitively on the adopted normalization and of the assumed gas fraction. The variation of $$(\Delta T/T)_\text{rms}$$ with angular scale is slow and is insensitive to this normalization. Clustering of clusters is included in the analysis. Simulated sky maps are shown, and from these the distribution function for the fluctuations is deduced.