Gravitational lensing of the microwave background by galaxy clusters

Galaxy clusters will distort the pattern of temperature anisotropies in the microwave background via gravitational lensing. We create lensed microwave background maps using clusters drawn from numerical cosmological simulations. A distinctive dipole-like temperature fluctuation pattern is formed aligned with the underlying microwave temperature gradient. For a massive cluster, the characteristic angular size of the temperature distortion is a few arcminutes, and the characteristic amplitude a few microkelvins. We demonstrate a simple technique for estimating the lensing deflection induced by the cluster; microwave background lensing measurements have the potential to determine the mass distribution for some clusters with good accuracy on angular scales up to a few arcminutes. Future high-resolution, high-sensitivity microwave background maps will have the capability of detecting lensing by clusters; we discuss various systematic limitations on probing cluster masses using this technique.