Fast computation of angular power spectra and covariances of high-resolution cosmic microwave background maps using the Toeplitz approximation

Abstract

We present a simple approximation that can speed up the computation of the mode-coupling matrices, which are usually the bottleneck for computing unbiased angular power spectra, as well as their associated covariance matrices, of the cosmic microwave background temperature and polarization anisotropies. The approximation results in the speed up of the MASTER algorithm by more than an order of magnitude with very little loss of precision. We demonstrate the performance on simulations of forthcoming cosmic microwave background surveys such as the Simons Observatory and CMB-S4 for a wide variety of survey window functions.

arXiv comment10 pages, 7 figures. The code used to produce all results of the paper is publicly available on Github

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• The Atacama Cosmology Telescope: Semi-Analytic Covariance Matrices for the DR6 CMB Power Spectra
• The Simons Observatory: impact of bandpass, polarization angle and calibration uncertainties on small-scale power spectrum analysis
• Fast computation of temperature and polarization coupling matrices