Non Gaussianity and Minkowski Functionals: forecasts for Planck

TL;DR

This paper evaluates Minkowski Functionals as tools to measure primordial non-Gaussianity in the CMB, demonstrating that with optimal filtering and masking, the Planck experiment can achieve precise estimates of the f_NL parameter despite noise and foreground contamination.

Contribution

It introduces a comprehensive analysis of Minkowski Functionals for f_NL estimation in Planck data, including noise, point sources, and galactic foreground effects, with optimized filtering and masking strategies.

Findings

Expected error on f_NL measurement is about 10 with Wiener filtering.

Bias from point sources can be minimized with masking, especially in lower frequency channels.

Galactic foreground biases are significant and depend on component separation quality.

Abstract

We study Minkowski Functionals as probes of primordial non-Gaussianity in the Cosmic Microwave Background, specifically for the estimate of the primordial `local' bi-spectrum parameter f_NL, with instrumental parameters which should be appropriate for the Planck experiment. We use a maximum likelihood approach, which we couple with various filtering methods and test thoroughly for convergence. We included the effect of inhomogeneous noise as well as astrophysical biases induced by point sources and by the contamination from the Galaxy. We find that, when Wiener filtered maps are used (rather than simply smoothed with Gaussian), the expected error on the measurement of f_NL should be as small as \Delta f_NL \simeq 10 when combining the 3 channels at 100, 143 and 217 GHz in the Planck extended mission setup. This result is fairly insensitive to the non homogeneous nature of the noise, at least for realistic hit-maps expected from Planck. We then estimate the bias induced on the measurement of f_NL by point sources in those 3 channels. With the appropriate masking of the bright sources, this bias can be reduced to a negligible level in the 100 and 143 GHz channels. It remains significant in the 217 GHz channel, but can be corrected for. The galactic foreground biases are quite important and present a complex dependence on sky coverage: making them negligible will depend strongly on the quality of the component separation methods.