Fast Clustering Analysis of Inhomogeneous Megapixel CMB maps

TL;DR

This paper introduces a fast algorithm using spherical harmonics transforms to efficiently compute correlation functions in high-resolution CMB maps, enabling quick power spectrum estimation even with inhomogeneous sky coverage.

Contribution

The paper presents a novel, efficient algorithm for calculating pixel space correlation functions in high-resolution CMB maps, significantly reducing computation time.

Findings

The new method computes correlations from a 512-resolution HEALPix map in about 5 minutes.

The approach accurately recovers theoretical $C_$ spectra from simulated MAP data.

The implementation is publicly available as the SpICE software.

Abstract

Szapudi et al (2001) introduced the method of estimating angular power spectrum of the CMB sky via heuristically weighted correlation functions. Part of the new technique is that all (co)variances are evaluated by massive Monte Carlo simulations, therefore a fast way to measure correlation functions in a high resolution map is essential. This letter presents a new algorithm to calculate pixel space correlation functions via fast spherical harmonics transforms. Our present implementation of the idea extracts correlations from a MAP-like CMB map (HEALPix resolution of 512, i.e. $ \simeq 3 \times 10^6$ pixels) in about 5 minutes on a 500MHz computer, including $C_\ell$ inversion; the analysis of one Planck-like map takes less then one hour. We use heuristic window and noise weighting in pixel space, and include the possibility of additional signal weighting as well, either in $\ell$ or pixel space. We apply the new code to an ensemble of MAP simulations, to test the response of our method to the inhomogenous sky coverage/noise of MAP. We show that the resulting $C_\ell$'s are very close to the theoretical expectations. The HEALPix based implementation of the method, SpICE (Spatially Inhomogenous Correlation Estimator) will be available to the public from the authors.