Estimating SI violation in CMB due to non-circular beam and complex scan in minutes

TL;DR

This paper introduces a fast analytical method to estimate the statistical isotropy violation in CMB data caused by non-circular beams and complex scan strategies, significantly reducing computational effort.

Contribution

The paper presents a generalized analytical formalism to estimate SI violation from non-circular beams and scan strategies, connecting beam anisotropy to BipoSH spectra, and demonstrating its effectiveness with WMAP data.

Findings

Analytical method predicts features of SI violation with high accuracy.

Reduces simulation time from tens of thousands of CPU hours to minutes.

Validated against exact numerical simulations.

Abstract

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.