Peculiar velocity effects in high-resolution microwave background experiments

We investigate the impact of peculiar velocity effects due to the motion of the solar system relative to the cosmic microwave background (CMB) on high resolution CMB experiments. It is well known that on the largest angular scales the combined effects of Doppler shifts and aberration are important; the lowest Legendre multipoles of total intensity receive power from the large CMB monopole in transforming from the CMB frame. On small angular scales aberration dominates and is shown here to lead to significant distortions of the total intensity and polarization multipoles in transforming from the rest frame of the CMB to the frame of the solar system. We provide convenient analytic results for the distortions as series expansions in the relative velocity of the two frames, but at the highest resolutions a numerical quadrature is required. Although many of the high resolution multipoles themselves are severely distorted by the frame transformations, we show that their statistical properties distort by only an insignificant amount. Therefore, the cosmological parameter estimation is insensitive to the transformation from the CMB frame (where theoretical predictions are calculated) to the rest frame of the experiment.