Efficient power spectrum estimation for high resolution CMB maps

Estimation of the angular power spectrum of the cosmic microwave background on a small patch of sky is usually plagued by serious spectral leakage, especially 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 $8\mathrm{degree}\times 8\mathrm{degree}$ patch of the sky with 2% area masked due to point sources, our estimator halves the error bars at $\ell =2000$ and achieves a more than fourfold reduction in error bars at $\ell =3500$. Thus, a properly analyzed experiment will have error bars at $\ell =3500$ equivalent to those of an experiment analyzed with the now standard technique with $\sim 16–25$ times the integration time.