A Simulation-based Method for Correcting Mode Coupling in CMB Angular Power Spectra

Abstract Modern cosmic microwave background (CMB) analysis pipelines regularly employ complex time-domain filters, beam models, masking, and other techniques during the production of sky maps and their corresponding angular power spectra. However, these processes can generate couplings between multipoles from the same spectrum and from different spectra, in addition to the typical power attenuation. Within the context of pseudo- C ℓ based, MASTER -style analyses, the net effect of the time-domain filtering is commonly approximated by a multiplicative transfer function, F ℓ , that can fail to capture mode mixing and is dependent on the spectrum of the signal. To address these shortcomings, we have developed a simulation-based spectral correction approach that constructs a two-dimensional transfer matrix, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>J</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="italic">ℓ</mml:mi> <mml:mi mathvariant="italic">ℓ</mml:mi> <mml:mo accent="false">′</mml:mo> </mml:mrow> </mml:msub> </mml:math> , which contains information about mode mixing in addition to mode attenuation. We demonstrate the application of this approach on data from the first flight of the Spider balloon-borne CMB experiment.