Fast Pixel Space Convolution for CMB Surveys with Asymmetric Beams and
  Complex Scan Strategies: FEBeCoP
  Precise measurement of the angular power spectrum of the Cosmic Microwave
Background (CMB) temperature and polarization anisotropy can tightly constrain
many cosmological models and parameters. However, accurate measurements can
only be realized in practice provided all major systematic effects have been
taken into account. Beam asymmetry, coupled with the scan strategy, is a major
source of systematic error in scanning CMB experiments such as Planck, the
focus of our current interest. We envision Monte Carlo methods to rigorously
study and account for the systematic effect of beams in CMB analysis. Toward
that goal, we have developed a fast pixel space convolution method that can
simulate sky maps observed by a scanning instrument, taking into account real
beam shapes and scan strategy. The essence is to pre-compute the "effective
beams" using a computer code, "Fast Effective Beam Convolution in Pixel space"
(FEBeCoP), that we have developed for the Planck mission. The code computes
effective beams given the focal plane beam characteristics of the Planck
instrument and the full history of actual satellite pointing, and performs very
fast convolution of sky signals using the effective beams. In this paper, we
describe the algorithm and the computational scheme that has been implemented.
We also outline a few applications of the effective beams in the precision
analysis of Planck data, for characterizing the CMB anisotropy and for
detecting and measuring properties of point sources.
