Using peak distribution of the cosmic microwave background for WMAP and Planck data analysis:: Formalism and simulations

We implement and further refine the recently proposed method at Kashlinsky et al. (2001) (KHA) for a time efficient extraction of the power spectrum from future cosmic microwave background (CMB) maps. The method is based on the clustering properties of peaks and troughs of the Gaussian CMB sky. The procedure takes only 1/2 [f (nu)]N-2(2) steps where f (nu) is the fraction of pixels with \deltaT\greater than or equal tonu standard deviations in the map of N pixels. We use the new statistic introduced in KHA, xi(nu), which characterizes spatial clustering of the CMB sky peaks of progressively increasing thresholds. The tiny fraction of the remaining pixels (peaks and troughs) contains the required information on the CMB power spectrum of the entire map. The threshold nu is the only parameter that determines the accuracy of the final spectrum. We performed detailed numerical simulations for parameters of the two-year WMAP and Planck CMB sky data including cosmological signal, inhomogeneous noise and foreground residuals. In all cases we find that the method can recover the power spectrum out to the Nyquist scale of the experiment channel. We discuss how the error bars scale with nu allowing to decide between accuracy and speed. The method can determine with significant accuracy the CMB power spectrum from the upcoming CMB maps in only similar to(10(-5)-10(-3))x N-2 operations.