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

Abstract

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.

Statistical isotropy violation in WMAP CMB maps resulting from non-circular beams

“…However, EG approximation of the beam profile does not provide adequately accurate model for the problem. Specifically, such an approximation cannot explain subtle zero crossing features seen in the BipoSH spectra caused by non-circular beams (Pant et al 2016). Moreover, the effect of scanning creates varying effective beam profile across the sky (Mitra et al 2011).…”

QuickPol: Fast calculation of effective beam matrices for CMB polarization

“…An example of such joint developments is the study of the impact of optics-and electronics-related imperfections on the measured CMB temperature and polarization angular power spectra and their statistical isotropy. Systematic effects such as beam non-circularity, response mismatch in dual polarization measurements and scanning strategy imperfections, as well as how they can be mitigated, have been extensively studied in the preparation of forthcoming instruments (including, but not limited to Souradeep & Ratra 2001;Fosalba et al 2002;Hu et al 2003;Mitra et al 2004Mitra et al , 2009O'Dea et al 2007;Rosset et al 2007;Shimon et al 2008;Miller et al 2009a,b;Hanson et al 2010;Leahy et al 2010;Rosset et al 2010;Ramamonjisoa et al 2013;Rathaus & Kovetz 2014;Wallis et al 2014;Pant et al 2016), and during the analysis of data collected by WMAP 1 (Smith et al 2007;Hinshaw et al 2007;Page et al 2007) or Planck 2 (Planck 2013-VII 2014Planck 2013-XVII 2014Planck 2015-XI 2016 satellite missions. At the same time, several deconvolution algorithms and codes have been proposed to clean up the CMB maps from such beam-related effects prior to the computation of the power spectra, like PreBeam (Armitage-Caplan & Wandelt 2009), ArtDeco (Keihänen & Reinecke 2012), and in Bennett et al (2013) and Wallis et al (2015).…”

SI Toolbox - Full documentation

“…The Package SIToolBox is coded up by Santanu Das. However, the work is based on multiple research papers [1][2][3][4]. Here, I have listed everyone, who were directly or indirectly involved in developing the package SIToolBox.…”

“…• Nidhi Panth and Aditya Rotti The subroutine CalcBipoSH is based on some of the software package, initially developed in cooperation with Nidhi Panth and Aditya Rotti [3,4]. They also helped the project by participating in multiple interesting discussions during the project.…”