The Sunyaev-Zel'dovich effect contribution to WMAP:: a cross-correlation between WMAP and ROSAT

We cross-correlate WMAP and ROSAT diffuse X-ray background maps and look for common features in both data sets. We use the power spectrum of the product maps and the cross-power spectrum to highlight a possible correlation. The power spectrum of the product maps does not detect any correlation and the cross-power spectrum does not show any significant deviation from zero. We explore different explanations for this lack of correlation. A universe with a low value of sigma(8) could naturally explain the lack of correlation. We also discuss the systematic effects that can affect this result, in particular the subtraction of some cluster signal from the ROSAT diffuse maps, which could significantly suppress the correlation signal. These systematic effects considerably reduce the significance of our constraints on the cosmological model. When we include the systematic effects, we find a weaker constraint on sigma(8), allowing models with values as large as sigma(8) = 1 (for Omega(m) = 0.3) to be consistent with the lack of correlation. To illustrate the capabilities of the method with future high-quality data, we show how from the correlation signal it should be possible to predict the level of contamination of the Sunyaev-Zel'dovich effect on the power spectrum of the cosmic microwave background. Within the systematic errors, we find evidence that this contribution is negligible for WMAP and is expected to be small in experiments like ACBAR or CBI, but can be important for future high-resolution experiments.