Examination of frequency and scale dependence of CMB hemispherical power asymmetry

TL;DR

This work reexamines the hemispherical power asymmetry (HPA) in CMB temperature maps from Planck PR4 and WMAP using the Local Variance Estimator (LVE) to test for frequency and scale dependence. By constructing local variance maps over circular discs of varying radius and fitting dipoles, it extracts amplitude and direction information while applying bias corrections from isotropic simulations. A power-law model $A(\ell) = A_0 (\ell_0/\ell)^n$ with pivot $\ell_0 = 10$ is fitted to the bias-corrected dipole amplitudes, yielding a consistent $A_0 \approx 0.086$ and $n \approx 0.31$ across seven frequency maps, indicating a genuine scale dependence. The analysis finds a coherent dipole signal across instruments and frequencies, arguing against instrumental origins and pointing toward a persistent cosmological feature of the CMB sky, with polarization studies proposed for future clarification.

Abstract

In this study, we revisit the well-known cosmic microwave background (CMB) anomaly referred to as Hemispherical Power Asymmetry (HPA), using CMB temperature maps from the Planck mission public release 4 (PR4) and the WMAP nine-year data release. Employing the Local Variance Estimator (LVE) method, we systematically reexamine the properties of HPA to investigate possible frequency dependence as well as scale dependence in its amplitude and direction. We model the HPA as a scale-dependent dipole modulation following a power-law form, rather than assuming a scale-invariant case. Our analysis incorporates seven cleaned frequency-specific CMB temperature maps from both the Planck and WMAP missions to test the robustness of the observed asymmetry across instruments and frequency channels. We find that the dipolar modulation characteristic of HPA is present in all cases examined, with consistent estimates of the preferred direction and scale-dependent variation in dipole amplitudes. These results support the conclusion that the observed asymmetry is unlikely to arise from instrumental artifacts or data-processing effects, and instead points toward a persistent large-scale feature of the CMB sky with a possible cosmological origin.

Figures (6)

• Figure 1: Frequency-specific cleaned CMB maps from observations, all of which are synthesized at HEALPix$N_{\rm side}$=512 with a Gaussian beam of FWHM$=30'$. Sequentially (top to bottom & left to right), the WMAP 9yr Q (41 GHz), V (61 GHz) and W (94 GHz) band maps are shown first, followed by the Planck PR4 SEVEM cleaned 70, 100, 143 and 217 GHz maps are displayed.
• Figure 2: The KQ85 mask from WMAP 9yr data release (top left), the Planck PR3 common mask downgraded to $N_{\rm side}$ = 512 (top right), and their union (bottom) which is used commonly on all foreground-reduced CMB maps considered in this work are shown here.
• Figure 3: Top : Dipole amplitudes estimated from the LVE map of different frequency-specific CMB temperature data maps are shown in different colours: red, blue, green are used for WMAP 9yr Q, V, and W band foreground-reduced CMB maps, whereas magenta, cyan, black, and yellow are used for Planck PR4 SEVEM cleaned 70, 100, 143, and 217 GHz frequency maps, respectively, as a function of disc size '$r$' used in generating LVMs. The error bars are estimated from respective isotropic simulation ensembles. The dashed lines denote expected random dipole amplitude levels in them, that are also estimated from the same set of simulations. Bottom : The dipole directions recovered from WMAP 9yr Q, V, and W band maps, and the Planck PR4 SEVEM cleaned 70, 100, 143, and 217 GHz frequency-specific CMB maps are represented using the same colour scheme as used in the top panel. The LVM dipole directions from different disc radii ($r=1^{\circ}$ to $40^{\circ}$) are shown in open circle point type with increasing point size. The diamond shape in brown colour is the variance asymmetry direction reported by Planck team using PR3 SMICA cleaned CMB temperature map. The hexagonal shape in gray colour is the average $\approx(215^\circ, -30^\circ)$ of all dipole directions from various frequency-specific temperature maps for all choices of disc sizes.
• Figure 4: $p$-values obtained from various frequency-specific cleaned CMB maps as indicated in the legend are plotted against disc radii. The yellow and green open circle highlight those disc sizes for which $p$-values are $<1/N_{\rm sim}$ as no simulations are found to have an LVM dipole amplitude that exceeds the data value. Here, the number of simulations $N_{\rm sim}=$1000 and 600, respectively, complementing the WMAP's (Q, V, and W band) and Planck's SEVEM cleaned PR4 (70, 100, 143, and 217 GHz channel) maps.
• Figure 5: Likelihood 2D contour plots along with posteriors of the parameters '$A_{0}$' and '$n$' to fit the scale dependence of HPA (per Eq. \ref{['eq:pl']}) are shown with contours signifying $1\sigma$ and $2\sigma$ confidence intervals. The distributions agree well across all cleaned frequency channel maps. See text for more details.