On the Coherence of WMAP and Planck Temperature Maps (1307.1111v2)

Abstract: The recent data release of ESA's Planck mission together with earlier WMAP releases provide the first opportunity to compare high resolution full sky Cosmic Microwave Background temperature anisotropy maps. To quantify the coherence of these maps beyond the power spectrum we introduce Generalized Phases, unit vectors in the (2l+1) dimensional representation spaces. For a Gaussian distribution, Generalized Phases are random and if there is non-Gaussianity, they represent most of the non-Gaussian information. The alignment of these unit vectors from two maps can be characterized by their angle, 0 deg expected for full coherence, and 90 deg for random vectors. We analyze maps from both missions with the same mask and Nside=512 resolution, and compare both power spectra and Generalized Phases. We find excellent agreement of the Generalize Phases of Planck Smica map with that of the WMAP Q,V,W maps, rejecting the null hypothesis of no correlations at 5 sigma for l's l<700, l<900 and l<1100, respectively, except perhaps for l<10. Using foreground reduced maps for WMAP increases the phase coherence. The observed coherence angles can be explained with a simple assumption of Gaussianity and a WMAP noise model neglecting Planck noise, except for low-intermediate l's there is a slight, but significant off-set, depending on WMAP band. On the same scales WMAP power spectrum is about 2.6% higher at a very high significance, while at higher l's there appears to be no significant bias. Using our theoretical tools, we predict the phase alignment of Planck with a hypothetical perfect noiseless CMB experiment, finding decoherence at l > 2900; below this value Planck can be used most efficiently to constrain non-Gaussianity.

• The paper introduces generalized phases as a novel metric to assess the alignment of CMB temperature maps from WMAP and Planck.
• It employs SO(3)-based unit vectors to measure coherence, demonstrating high agreement up to multipoles ℓ ≈ 700–1100 and within 5σ for low ℓ values.
• The study identifies a 2.6% higher amplitude in WMAP power spectra compared to Planck, highlighting subtle systematic differences for further investigation.

Coherence of WMAP and Planck Temperature Maps

This paper investigates the coherence between the temperature anisotropy maps of the Cosmic Microwave Background (CMB) from the WMAP and Planck missions. By leveraging newly defined Generalized Phases (GPs) within the context of the orthogonal group SO(3), the authors go beyond power spectrum analysis to explore the alignment of these phases as a metric of map correlation. The aim is to provide a refined comparison method that can potentially reveal coherent structures, or lack thereof, resulting from observational or systematic discrepancies between the two datasets.

Generalized Phases and Their Role

GPs are introduced as unit vectors in a $(2\ell+1)$-dimensional space, built from the real and imaginary components of the CMB's spherical harmonic coefficients. Aligned GPs between two datasets would indicate coherence, with the angle formed between them being a primary statistic of interest. A $0^\circ$ angle suggests full coherence, whereas a $90^\circ$ angle indicates randomness.

Key Findings

The comparison between the Planck Smica map and the WMAP maps (specifically the Q, V, and W channels) revealed a high level of coherence up to certain multipole moments ($\ell$ values). The authors find decoherence levels at $\ell \approx 700$, $\ell \approx 900$, and $\ell \approx 1100$ across the Q, V, and W bands, respectively. The coherence angles remain within $5\sigma$ of expectation given Gaussian assumptions for $\ell < 10$. These findings emphasize the significant agreement between the two maps for most scales relevant to cosmological analysis.

Statistical Analysis and Noise Considerations

Using rigorous statistical analysis, the authors incorporate a noise model from WMAP into their coherence predictions. While the overall correlation falls within expected noise levels, a significant deviation is observed around low-intermediate multipoles where a small yet significant offset exists. Notably, a stark difference of 2.6% higher amplitude is observed in the WMAP power spectra compared to Planck for certain scales, highlighting an area which might require further investigation.

Implications

The results have substantial implications for our understanding of primordial non-Gaussianity and the integrity of CMB measurements. The established coherence across the majority of scales suggests systematic errors between these datasets are below the important cosmological thresholds. This work sets a precedent for future CMB datasets to be analyzed using phase information, especially when corroborating results between newer datasets such as future CMB-probing missions and simulated forecasts of a 'perfect' noiseless experiment.

Future Directions

The analysis techniques introduced herein, such as the use of GPs, can be extended to future studies assessing the fidelity of CMB data. The potential of decoherence at $\ell \approx 2900$ for Planck relative to a perfect CMB experiment also provides a foundation for exploring higher multipole datasets. These insights can refine cosmological parameter estimation, particularly in the context of searching for clues about the non-linear or non-Gaussian aspects of primordial fluctuations.

This analysis between WMAP and Planck exemplifies a transformation in CMB data analysis methodologies, promoting a high benchmark for future observational cosmology. By emphasizing phase coherence, the authors provide tools that can further demystify the early universe's subtleties through the CMB lens.