Can we detect Hot or Cold spots in the CMB with Minkowski Functionals?

TL;DR

This paper evaluates the effectiveness of Minkowski Functionals in detecting hot or cold spots in the CMB, resolving systematic issues, and demonstrating that such effects are only detectable with large sample averaging at current resolution.

Contribution

We identify and correct a systematic residual issue in Minkowski Functional analysis of the CMB, and develop a map-independent estimator to improve detection capabilities.

Findings

Residuals are caused by binning, not pixelation or masking.

Small disk effects are only detectable with large sample averaging.

Applying the estimator to WMAP7 data yields null results.

Abstract

In this paper, we investigate the utility of Minkowski Functionals as a probe of cold/hot disk-like structures in the CMB. In order to construct an accurate estimator, we resolve a long-standing issue with the use of Minkowski Functionals as probes of the CMB sky -- namely that of systematic differences ("residuals") when numerical and analytical MF are compared. We show that such residuals are in fact by-products of binning, and not caused by pixelation or masking as originally thought. We then derive a map-independent estimator that encodes the effects of binning, applicable to beyond our present work. Using this residual-free estimator, we show that small disk-like effects (as claimed by Vielva et al.) can be detected only when a large sample of such maps are averaged over. In other words, our estimator is noise-dominated for small disk sizes at WMAP resolution. To confirm our suspicion, we apply our estimator to the WMAP7 data to obtain a null result.