Efficient Power Spectrum Estimation for High Resolution CMB Maps

TL;DR

This paper introduces a new local method for estimating the CMB power spectrum on small sky patches that significantly reduces spectral leakage and variance, improving accuracy over standard techniques.

Contribution

A novel fast and simple local estimator for CMB power spectrum that minimizes spectral leakage and reduces variance, outperforming standard uniform sampling methods.

Findings

Halves error bars at l=2000

Reduces error bars by over four times at l=3500

Achieves similar precision as much longer experiments

Abstract

Estimation of the angular power spectrum of the Cosmic Microwave Background (CMB) on a small patch of sky is usually plagued by serious spectral leakage, specially when the map has a hard edge. Even on a full sky map, point source masks can alias power from large scales to small scales producing excess variance at high multipoles. We describe a new fast, simple and local method for estimation of power spectra on small patches of the sky that minimizes spectral leakage and reduces the variance of the spectral estimate. For example, when compared with the standard uniform sampling approach on a 8 degree X 8 degree patch of the sky with 2% area masked due to point sources, our estimator halves the errorbars at l=2000 and achieves a more than fourfold reduction in errorbars at l=3500. Thus, a properly analyzed experiment will have errorbars at l=3500 equivalent to those of an experiment analyzed with the now standard technique with ~ 16-25 times the integration time.