On the large-angle anomalies of the microwave sky

[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.