2001/03/31 by A. Kashlinsky, C. Hernández-Monteagudo, C. Hernández--Monteagudo +2 · 12 citations
Physics and Astronomy · #Amplitude #Cosmic background radiation #Cosmic microwave background #Cosmic variance #Cosmology and Gravitation Theories #Electrical and Electromagnetic Research #Formalism (music) #Galaxies: Formation, Evolution, Phenomena #Gaussian #Microwave #Polarization (electrochemistry) #Spectral density #astro-ph
paper · pdf · doi:10.1086/323172
published in The Astrophysical Journal 557(1), L1-L5 (IOP Publishing) · To be published in Ap.J. Letters. Minor changes to match the journal version
arxiv created 2001/07/10 · openalex publication_date 2001/08/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present a new method for time-efficient and accurate extraction of the power spectrum from future cosmic microwave background (CMB) maps based on properties of peaks and troughs of the Gaussian CMB sky. We construct a statistic describing their angular clustering analogously to galaxies, the two-point angular correlation function, ξ ν (θ). We show that for increasing peak threshold ν, ξ ν (θ) is strongly amplified and becomes measurable for ν ≳ 1 on angular scales ≤10°. Its amplitude at every scale depends uniquely on the CMB temperature correlation function, C (θ), and thus the measured ξ ν can be uniquely inverted to obtain C (θ) and its Legendre transform, the power spectrum of the CMB field. Because in this method the CMB power spectrum is deduced from high peaks/troughs of the CMB field, the procedure takes only [ f (ν)] 2 N 2 operations, where f (ν) is the fraction of pixels with |δ T | ≥ ν standard deviations in the map of N pixels and is, e.g., 0.045 and 0.01 for ν = 2 and 2.5, respectively. We develop theoretical formalism for the method and show with detailed simulations, using the Microwave Anisotropy Probe mission parameters, that this method allows us to determine very accurately the CMB power spectrum from the upcoming CMB maps in only ~(10 -4 to 10 -3 ) N 2 operations.