Microwave background fluctuations due to the Sunyaev-Zel'dovich effects in pancakes

We calculate distortions in the microwave background radiation from the Sunyaev-Zel'dovich effect, produced by hot gas in large (approximately 100 Mpc) pancakes. The large-scale distribution of the pancakes is taken to be that of a Voronoi foam. Fluctuations for this scenario are estimated to be on the order of delta T/T is approximately 10(exp -5). Using computer simulations, we produce several 32 deg x 32 deg images with 0.25 deg resolution. These images show characteristic linear features produced when a pancake is viewed nearly edge-on. By calculating the two-point and the degenerate three-point correlation functions, we are able to statistically detect such non-Gaussian features even in the presence of a relatively large amount of Gaussian noise. The degenerate three-point correlation function is found to be particularly useful since it is insensitive to correlated Gaussian noise. We also smooth our data over a 7 deg Full Width at Half Maximum (FWHM) Gaussian window to simulate the Cosmic Background Explorer Satellite (COBE) observations. We find that under such low-resolution conditions, the features are highly suppressed.