Full‐sky map of the ISW and Rees–Sciama effect from Gpc simulations

We present a new method for constructing maps of the secondary temperature fluctuations imprinted on the cosmic microwave background (CMB) radiation by photons propagating through the evolving cosmic gravitational potential. Large cosmological N-body simulations are used to calculate the complete non-linear evolution of the peculiar gravitational potential. Tracing light rays back through the past light cone of a chosen observer accurately captures the temperature perturbations generated by linear (the integrated Sachs-Wolfe or ISW effect) and non-linear (the Rees-Sciama or RS effect) evolution. These effects give rise to three kinds of non-linear features in the temperature maps. (i) In overdense regions, converging flows of matter induce cold spots of the order of 100 Mpc in extent which can dominate over the ISW effect at high redshift, and are surrounded by hot rings. (ii) In underdense regions, the RS effect enhances ISW cold spots which can be surrounded by weak hot rings. (iii) Transverse motions of large lumps of matter produce characteristic dipole features, consisting of adjacent hot and cold spots separated by a few tens of megaparsecs. These non-linear features are not easily detectable; they modulate the ISW sky maps at about the 10 per cent level. The RS effect causes the angular power spectrum to deviate from linear theory at l ∼ 50 and generates non-Gaussianity, skewing the one-point distribution function to negative values. Cold spots of similar angular size, but much smaller amplitude than the CMB cold spot reported by Cruz et al. are produced. Joint analysis of our maps and the corresponding galaxy distribution may enable techniques to be developed to detect these non-linear, non-Gaussian features. Our maps are available at http://astro.dur.ac.uk/∼cai/ISW.