Estimating SI violation in CMB due to non-circular beam and complex scan
  in minutes
  Mild, unavoidable deviations from circular-symmetry of instrumental beams
along with scan strategy can give rise to measurable Statistical Isotropy (SI)
violation in Cosmic Microwave Background (CMB) experiments. If not accounted
properly, this spurious signal can complicate the extraction of other SI
violation signals (if any) in the data. However, estimation of this effect
through exact numerical simulation is computationally intensive and time
consuming. A generalized analytical formalism not only provides a quick way of
estimating this signal, but also gives a detailed understanding connecting the
leading beam anisotropy components to a measurable BipoSH characterisation of
SI violation. In this paper, we provide an approximate generic analytical
method for estimating the SI violation generated due to a non-circular (NC)
beam and arbitrary scan strategy, in terms of the Bipolar Spherical Harmonic
(BipoSH) spectra. Our analytical method can predict almost all the features
introduced by a NC beam in a complex scan and thus reduces the need for
extensive numerical simulation worth tens of thousands of CPU hours into
minutes long calculations. As an illustrative example, we use WMAP beams and
scanning strategy to demonstrate the easability, usability and efficiency of
our method. We test all our analytical results against that from exact
numerical simulations.
