On the large-angle anomalies of the microwave sky

TL;DR

The paper presents a comprehensive analysis of large-angle CMB anomalies using the multipole-vector formalism, focusing on the quadrupole and octopole and their surprising alignments with the ecliptic and solar-system directions. It develops the Maxwell-based multipole-vector framework, connects it to angular-momentum dispersion, and introduces robust S and T statistics to quantify alignments, applying them to WMAP full-sky maps (ILC, LILC, TOH) and COBE comparisons. The results show highly significant quadrupole–octopole correlations, with the planes defined by these multipoles perpendicular to the ecliptic and aligned with the solar-dipole directions at >99% CL, while Galactic foregrounds are unlikely culprits. The work also analyzes foreground effects and cut-sky consequences, concluding that the observed signals are unlikely to be cosmological Gaussian isotropy violations, but may indicate new foregrounds or unrecognized systematics, with polarization and Planck data highlighted as key tests for the future.

Abstract

[Abridged] We apply the multipole vector framework to full-sky maps derived from the first year WMAP data. We significantly extend our earlier work showing that the two lowest cosmologically interesting multipoles, l=2 and 3, are not statistically isotropic. These results are compared to the findings obtained using related methods. In particular, the planes of the quadrupole and the octopole are unexpectedly aligned. Moreover, the combined quadrupole plus octopole is surprisingly aligned with the geometry and direction of motion of the solar system: the plane they define is perpendicular to the ecliptic plane and to the plane defined by the dipole direction, and the ecliptic plane carefully separates stronger from weaker extrema, running within a couple of degrees of the null-contour between a maximum and a minimum over more than 120deg of the sky. Even given the alignment of the quadrupole and octopole with each other, we find that their alignment with the ecliptic is unlikely at >98% C.L., and argue that it is in fact unlikely at >99.9% C.L. We explore the role of foregrounds showing that the known Galactic foregrounds are unlikely to lead to these correlations. Multipole vectors, like individual a_lm, are very sensitive to sky cuts, and we demonstrate that analyses using cut skies induce relatively large errors, thus weakening the observed correlations but preserving their consistency with the full-sky results. Finally we apply our tests to COBE cut-sky maps and briefly extend the analysis to higher multipoles. If the correlations we observe are indeed a signal of non-cosmic origin, then the lack of low-l power will very likely be exacerbated, with important consequences for our understanding of cosmology on large scales.

Figures (8)

• Figure 1: The $\ell=2$ multipole from the TOH cleaned map, presented in Galactic coordinates, after correcting for the kinetic quadrupole. The solid line is the ecliptic plane and the dashed line is the supergalactic plane. The directions of the equinoxes (EQX), dipole due to our motion through the Universe, north and south ecliptic poles (NEP and SEP) and north and south supergalactic poles (NSGP and SSGP) are shown. The multipole vectors are plotted as the solid red (dark gray in gray scale version) symbols for each map, ILC (circles), TOH (diamonds), and LILC (squares). The open symbols of the same shapes are for the normal vector for each map. The dotted line is the great circle connecting the two multipole vectors for this map. The minimum and maximum temperature locations in this multipole are shown as the white stars. The direction that maximizes the angular momentum dispersion of any of the maps coincides with the respective normal vector as discussed in the text.
• Figure 2: The $\ell=3$ multipole from the TOH cleaned map, presented in Galactic coordinates. The solid line is the ecliptic plane and the dashed line is the supergalactic plane. The directions of the equinoxes (EQX), dipole due to our motion through the Universe, north and south ecliptic poles (NEP and SEP) and north and south supergalactic poles (NSGP and SSGP) are shown. The multipole vectors are the solid magenta (medium gray in gray scale version) symbols for each map, ILC (circles), TOH (diamonds), and LILC (squares). The open symbols of the same shapes are for the normal vectors for each map. The dotted lines are the great circles connecting each pair of multipole vectors for this map. The light gray stars are particular sums of the multipole vectors which are very close to the temperature minima and maxima of the multipole. The solid black star shows the direction of the vector that appears in the trace of the octopole, $\mathcal{T}_3$ (\ref{['eqn:octopole:trace']}), of the TOH map. The solid magenta (again medium gray in the gray scale version) star is the direction to the maximum angular momentum dispersion for the octopole, again for the TOH map.
• Figure 3: The $\ell=2+3$ multipoles from the TOH cleaned map, presented in Galactic coordinates. This is a combination of Figs. \ref{['fig:map:tegmark:2']} and \ref{['fig:map:tegmark:3']} with only the multipole vectors for the TOH map shown for clarity. The solid line is the ecliptic plane and the dashed line is the supergalactic plane. The directions of the equinoxes (EQX), dipole due to our motion through the Universe, north and south ecliptic poles (NEP and SEP) and north and south supergalactic poles (NSGP and SSGP) are shown. The $\ell=2$ multipole vectors are plotted as the solid red (dark gray in gray scale version) diamond and their normal is the open red (dark gray in the gray scale version) diamond. The $\ell=3$ multipole vectors are the solid magenta (medium gray in gray scale version) diamonds and their three normals are the open magenta (medium gray in the gray scale version) diamonds. The dotted lines are the great circles connecting the multipole vectors for this map (one for the quadrupole vectors and three for the octopole vectors). The minimum and maximum temperature locations of the $\ell=2$ multipole are shown as the white stars. The light gray stars are particular sums of the $\ell=3$ multipole vectors which are very close to the temperature minima and maxima of the octopole. The solid black star shows the direction of the vector that appears in the trace of the octopole, $\mathcal{T}_3$ (\ref{['eqn:octopole:trace']}). The solid magenta (again medium gray in the gray scale version) star is the direction to the maximum angular momentum dispersion for the octopole, again for the TOH map.
• Figure 4: Histograms of $S^{(n, m)}$ statistics (left column) and $T^{(n, m)}$ statistics (right column) for Gaussian random, statistically isotropic Monte Carlo maps with $m=1\ldots n$ of the most aligned area vectors considered separately in each panel. First row panels show the $n=3$ mutual dot-products of quadrupole and octopole area vectors $A_i$, second row shows dot-products of the $n=4$ normals with the ecliptic plane, third row shows dot-products of the $n=4$ normals with the north Galactic pole while the fourth row shows dot-products of the $n=4$ normals with the supergalactic plane. Specific values for the WMAP (TOH DQ-corrected map), for each $m$, are shown with vertical lines. The numbers show the percentage of MC maps that have a more extreme value (i.e. larger mutual dot-products $A_i$, larger products with the NGP, or smaller dot-products with the NEP and NSGP). In other words, the numbers show the extremeness of each vertical line's value in the corresponding histogram. Note that the statistical significance is strongest when all vectors are considered (that is, when $m=n$), except for the supergalactic plane where a single octopole normal is only $0\fdg07$ away from this plane while the other three are not particularly unusual.
• Figure 5: Histogram of the $S^{(4, 4)}$ statistics applied to the TOH map quadrupole and octopole area vectors and a fixed direction or plane on the sky, where the area vectors have been rotated together in a random direction $10^5$ times. Vertical lines show the $S$ statistics of the actual area vectors applied to the ecliptic plane, NGP, supergalactic plane, dipole and equinox directions (Table \ref{['tab:given23']} shows the actual product percentile ranks among the random rotations for all three full-sky maps). This Figure and Table \ref{['tab:given23']} show that, even given the relative location of the quadrupole-octopole area vectors (i.e. their mutual alignment), the ecliptic plane, dipole and equinox alignments are unlikely at the $\ga 95\%$ C.L. while the NGP and supergalactic plane alignments are not.