Constraints on mode couplings and modulation of the CMB with WMAP data

TL;DR

The paper develops an estimator for detecting dipolar modulations that induce $\Delta\ell=1$ correlations in the CMB, explicitly incorporating partial-sky masking via a spherical-harmonic kernel. Applying the method to WMAP V and W bands, the authors find a signal in the V band that disappears under foreground tests and with point-source masking, indicating the observed correlations are dominated by foregrounds rather than cosmological modulation. The work provides a rigorous framework to separate primordial dipolar signals from mask and foreground-induced couplings, clarifying the interpretation of large-scale CMB anomalies and guiding future isotropy analyses. Overall, it demonstrates the necessity of robust foreground treatment when constraining mode couplings in CMB data and offers a concrete statistical tool for such investigations, with implications for both CMB analyses and tests of isotropy.

Abstract

We investigate a possible asymmetry in the statistical properties of the cosmic microwave background temperature field and to do so we construct an estimator aiming at detecting a dipolar modulation. Such a modulation is found to induce correlations between multipoles with $Δ\ell=1$. Applying this estimator, to the V and W bands of the WMAP data, we found a significant detection in the V band. We argue however that foregrounds and in particular point sources are the origin of this signal.

Figures (9)

• Figure 1: (left) The coefficients of the decomposition of the mask function on spherical harmonics for different galactic cuts, $\mu_c=10,20$ and 30 deg. (respectively black, red and blue lines). Only the non-vanishing, that is even, multipoles are plotted. (right) The ratio $w_\ell/w_0$ decreases rapidly and becomes typically smaller than 0.1% for $\ell$ larger than 20 (plain=10 deg., dot=20 deg., dash-dot=30 deg.).
• Figure 2: $D_\ell$ measured on the WMAP data (W band) [green triangles]. Blue triangles are the measurements on a simulated map with ${\varepsilon_{0}}=0.2$ and the red lines are $1\sigma$ error bars.
• Figure 3: Comparison of 1000 simulations with the WMAP data. We use the W band and sum the multipole between $\ell=20$ and $\ell=100$ (top panel) and between $\ell=100$ and $\ell=300$ (bottom panel). The color code is identical to the one of Fig. \ref{['fres1']} that is the green line correspond to the measurement on the WMAP data and the blue line the measurement on a simulation.
• Figure 4: $D_\ell$ measured on the WMAP data (V band) [green traingles]. Blue triangles are the measurements on a simulated map with ${\varepsilon_{0}}=0.2$ and the red lines are $1\sigma$ error bars.
• Figure 5: Comparison of 1000 simulations with the WMAP data. We use the V band and sum the multipole between $\ell=20$ and $\ell=100$ (top panel) and between $\ell=100$ and $\ell=300$ (bottom panel).