SECONDARY MICROWAVE BACKGROUND ANISOTROPIES INDUCED BY PANCAKES

A non-linear, flattened cosmic structure is modelled as an extremely oblate, homogeneous, 'compensated' ellipsoid. An analytical formula is derived for the amplitude of the fractional secondary anisotropy (DELTAT/T) induced in the cosmic microwave background by the gravitational evolution of such a structure. This formula turns out to be a simple generalization of the corresponding result calculated previously in the model of a thin collapsing 'compensated disc'. Earlier results for DELTAT/T induced by pancakes are confirmed here. The compensation scheme fails for perturbations such as the Great Wall in the CfA survey. Nevertheless, it can be used to put a reliable upper limit on the anisotropy induced by the Great Wall, (DELTAT/T)GW. The calculated value is (DELTAT/T)GW less than or similar to 2 x 10(-6), which is below the accuracy of present-day observations.